Finite Group Databasebeta

← #11904273

Subgroups — #11904273

Order 1152.

2850 conjugacy classes of subgroups.

The subgroup lattice has 1257 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63715C211yesmaximal, characteristic, complemented
2C22×D4×D9C211yesmaximal, characteristic, complemented
3C9×#546C211yesmaximal, characteristic, complemented
4#10589931C211yesmaximal, characteristic, complemented
5D4×#611C211yesmaximal, characteristic, complemented
6#10589778C211yesmaximal, characteristic, complemented
7#10589776C211yesmaximal, characteristic, complemented
8#10589756C212yesmaximal, complemented
9#10589755C212yesmaximal, complemented
10#10589732C211yesmaximal, characteristic, complemented
11#10589729C211yesmaximal, characteristic, complemented
12#10589711C211yesmaximal, characteristic, complemented
13#10589711C212yesmaximal, complemented
14#10589709C211yesmaximal, characteristic, complemented
15#10589707C212yesmaximal, complemented
16#10589692C212yesmaximal, complemented
17D9×#120C212yesmaximal, complemented
18D4×D36C211yesmaximal, characteristic, complemented
19D4×D36C211yesmaximal, characteristic, complemented
20#10589649C211yesmaximal, characteristic, complemented
21#10589647C211yesmaximal, characteristic, complemented
22#10589592C212yesmaximal, complemented
23C2×#63444C212yesmaximal, complemented
24#86662—31nomaximal
25C24×D9C2212yescomplemented
26C2×C9×#41C2211yescharacteristic, complemented
27C22×D4×C9C2211yescharacteristic, complemented
28C22×#611C2212yescomplemented
29C22×#611C2212yescomplemented
30#63715—28no—
31C2×#3701C2211yescharacteristic, complemented
32C2×#3701C2211yescharacteristic, complemented
33C2×D4×D9—28no—
34C2×D4×D9C2211yescharacteristic
35C2×D4×D9C2212yescomplemented
36C2×D4×D9C2211yescharacteristic, complemented
37C2×D4×D9C2212yescomplemented
38C2×D4×D9C2211yescharacteristic, complemented
39C2×D4×D9C2211yescharacteristic, complemented
40C2×D4×D9C2212yescomplemented
41C2×D4×D9C2212yescomplemented
42C2×D4×D9C2212yescomplemented
43C2×D4×D9C2211yescharacteristic, complemented
44C2×D4×D9C2212yescomplemented
45C2×#3697C2211yescharacteristic, complemented
46C2×#3697C2212yescomplemented
47C22×D36C2211yescharacteristic, complemented
48C22×D36C2212yescomplemented
49C22×D36C2211yescharacteristic, complemented
50C22×D36C2212yescomplemented
51C22×C4×D9C2211yescharacteristic, complemented
52C9×#124C2211yescharacteristic, complemented
53C9×#123C2212yescomplemented
54C9×C22⋊Q8C2211yescharacteristic, complemented
55C9×#121C2212yescomplemented
56C9×#121C2211yescharacteristic, complemented
57C9×#120C2212yescomplemented
58C4×D4×C9C2211yescharacteristic, complemented
59C4×D4×C9C2211yescharacteristic, complemented
60C2×C9×C22⋊C4C2212yescomplemented
61#63515C2212yescomplemented
62#63509C2211yescharacteristic, complemented
63#63508C2211yescharacteristic, complemented
64#63502C2212yescomplemented
65#63502C2211yescharacteristic, complemented
66#63501C2211yescharacteristic, complemented
67#63501C2212yescomplemented
68#63501C2212yescomplemented
69#63500C2211yescharacteristic, complemented
70#63499C2211yescharacteristic, complemented
71#63499C2212yescomplemented
72#63499C2212yescomplemented
73#63499C2212yescomplemented
74#63499C2212yescomplemented
75D4×Dic9C2211yescharacteristic, complemented
76#63492C2211yescharacteristic, complemented
77#63492C2211yescharacteristic, complemented
78#63492C2212yescomplemented
79#63491C2212yescomplemented
80C4×#611C2211yescharacteristic, complemented
81C4×#611C2211yescharacteristic, complemented
82C4×#611C2212yescomplemented
83C2×(C2×D9)⋊C4C2212yescomplemented
84C2×(C2×D9)⋊C4C2212yescomplemented
85#63458C2211yescharacteristic, complemented
86#63457C2211yescharacteristic, complemented
87#63457C2211yescharacteristic, complemented
88#63457C2212yescomplemented
89#63457C2212yescomplemented
90#63456C2212yescomplemented
91#63456C2211yescharacteristic, complemented
92#63456C2212yescomplemented
93#63455C2212yescomplemented
94#63455C2211yescharacteristic, complemented
95#63454C2211yescharacteristic, complemented
96#63447C2212yescomplemented
97#63446C2211yescharacteristic, complemented
98#63446C2212yescomplemented
99#63446C2212yescomplemented
100#63446C2212yescomplemented
101#63446C2212yescomplemented
102#63445C2211yescharacteristic, complemented
103#63445C2212yescomplemented
104#63444C2212yescomplemented
105#63444C2211yescharacteristic, complemented
106#63444C2212yescomplemented
107#63444C2212yescomplemented
108#63444C2212yescomplemented
109#63444C2212yescomplemented
110#63444C2212yescomplemented
111#63444C2212yescomplemented
112#63444C2212yescomplemented
113#63444C2212yescomplemented
114#63444C2212yescomplemented
115#63444C2212yescomplemented
116#611⋊C4C2212yescomplemented
117#611⋊C4C2212yescomplemented
118C22⋊C4×D9C2212yescomplemented
119C22⋊C4×D9C2212yescomplemented
120C22⋊C4×D9C2212yescomplemented
121#63440C2211yescharacteristic, complemented
122#63436C2211yescharacteristic, complemented
123C4×D36C2211yescharacteristic, complemented
124C4×D36C2211yescharacteristic, complemented
125#63434C2211yescharacteristic, complemented
126C2×#1009—31no—
127C22×D3×D4—31no—
128C3×#546D311yescharacteristic
129#5829—31no—
130D4×#67—31no—
131#5676—31no—
132#5674—31no—
133#5654—32no—
134#5653—32no—
135#5630—31no—
136#5627—31no—
137#5609—31no—
138#5609—32no—
139#5607—31no—
140#5605—32no—
141#5590—32no—
142D3×#120—32no—
143D4×D12—31no—
144D4×D12—31no—
145#5547—31no—
146#5545—31no—
147#5490—32no—
148C2×#882—32no—
149C24×C9C2312yes—
150C23×D9—28no—
151C23×D9—44no—
152C23×D9—44no—
153C23×D9C2311yescharacteristic
154C23×D9C2312yes—
155C23×D9C2312yes—
156C23×D9C2312yes—
157C23×D9C2312yes—
158C23×D9C2312yes—
159C23×D9C2312yescomplemented
160C23×D9C2312yescomplemented
161C9×#41—24no—
162C2×Q8×C9C2311yescharacteristic, complemented
163C2×D4×C9—24no—
164C2×D4×C9C2311yescharacteristic
165C2×D4×C9C2312yes—
166C2×D4×C9C2311yescharacteristic
167C2×D4×C9C2311yescharacteristic
168C2×D4×C9C2312yescomplemented
169C2×D4×C9C2312yescomplemented
170C22×C4×C9C2311yescharacteristic
171C22×C4×C9C2312yescomplemented
172C22×C4×C9C2311yescharacteristic, complemented
173C22×C4×C9C2312yescomplemented
174C2×#611—28no—
175C2×#611—44no—
176C2×#611C2311yescharacteristic
177C2×#611C2311yescharacteristic
178C2×#611C2312yes—
179C2×#611C2312yes—
180C2×#611C2311yescharacteristic
181C2×#611C2312yes—
182C2×#611C2312yes—
183C2×#611C2312yes—
184C2×#611C2312yescomplemented
185C2×#611C2311yescharacteristic, complemented
186C2×#611C2312yescomplemented
187C2×#611C2312yescomplemented
188C2×#611C2312yescomplemented
189C2×#611C2312yescomplemented
190C22×Dic9C2311yescharacteristic
191C22×Dic9C2312yescomplemented
192#3701—24no—
193#3701—24no—
194D4×D9—28no—
195D4×D9—28no—
196D4×D9—24no—
197D4×D9—24no—
198D4×D9—28no—
199D4×D9—28no—
200D4×D9—24no—
201D4×D9—24no—
202D4×D9—44no—
203D4×D9—44no—
204D4×D9D418yescomplemented
205#3697—28no—
206#3697—24no—
207C2×D36—28no—
208C2×D36—24no—
209C2×D36—24no—
210C2×D36—44no—
211C2×D36C2311yescharacteristic
212C2×D36C2311yescharacteristic
213C2×D36C2311yescharacteristic
214C2×D36C2312yes—
215C2×D36C2312yes—
216C2×D36C2312yes—
217C2×D36C2311yescharacteristic
218C2×D36C2311yescharacteristic, complemented
219C2×D36C2312yescomplemented
220C2×D36C2312yescomplemented
221C2×D36C2312yescomplemented
222C2×D36C2312yescomplemented
223C2×D36C2312yescomplemented
224C2×C4×D9—24no—
225C2×C4×D9C2311yescharacteristic
226C2×C4×D9C2311yescharacteristic
227C2×C4×D9C2311yescharacteristic
228C2×C4×D9C2311yescharacteristic
229C2×C4×D9C2311yescharacteristic, complemented
230C2×C4×D9C2312yescomplemented
231C2×C4×D9C2312yescomplemented
232C2×C4×D9C2312yescomplemented
233C2×C4×D9C2312yescomplemented
234C2×Dic18C2311yescharacteristic, complemented
235C9×C4⋊C4C2311yescharacteristic, complemented
236C9×C4⋊C4C2311yescharacteristic, complemented
237C9×C4⋊C4C2312yescomplemented
238C9×C22⋊C4C2311yescharacteristic
239C9×C22⋊C4C2312yes—
240C9×C22⋊C4C2312yescomplemented
241C9×C22⋊C4C2312yescomplemented
242C9×C22⋊C4C2312yescomplemented
243C9×C22⋊C4C2311yescharacteristic, complemented
244C9×C22⋊C4C2312yescomplemented
245C42×C9C2311yescharacteristic, complemented
246#3676C2311yescharacteristic
247#3676C2312yescomplemented
248#3676C2311yescharacteristic, complemented
249#3676C2312yescomplemented
250(C2×D9)⋊C4C2311yescharacteristic
251(C2×D9)⋊C4C2311yescharacteristic
252(C2×D9)⋊C4C2312yes—
253(C2×D9)⋊C4C2312yes—
254(C2×D9)⋊C4C2311yescharacteristic
255(C2×D9)⋊C4C2311yescharacteristic
256(C2×D9)⋊C4C2312yescomplemented
257(C2×D9)⋊C4C2312yescomplemented
258(C2×D9)⋊C4C2312yescomplemented
259(C2×D9)⋊C4C2312yescomplemented
260(C2×D9)⋊C4C2311yescharacteristic, complemented
261(C2×D9)⋊C4C2312yescomplemented
262(C2×D9)⋊C4C2312yescomplemented
263(C2×D9)⋊C4C2312yescomplemented
264(C2×D9)⋊C4C2312yescomplemented
265(C2×D9)⋊C4C2311yescharacteristic, complemented
266C4⋊Dic9C2311yescharacteristic, complemented
267C4⋊Dic9C2311yescharacteristic, complemented
268Dic9⋊C4C2311yescharacteristic, complemented
269Dic9⋊C4C2311yescharacteristic, complemented
270Dic9⋊C4C2311yescharacteristic, complemented
271Dic9⋊C4C2312yescomplemented
272Dic9⋊C4C2311yescharacteristic, complemented
273C4×Dic9C2311yescharacteristic, complemented
274C4×Dic9C2312yescomplemented
275#3484—91noSylow
276C24×D3—32no—
277C2×C3×#41C2×D311yescharacteristic
278C22×C3×D4C2×D311yescharacteristic
279C22×#67—32no—
280C22×#67—32no—
281#1009—68no—
282C2×#239—31no—
283C2×#239—31no—
284C2×D3×D4—31no—
285C2×D3×D4—32no—
286C2×D3×D4—32no—
287C2×D3×D4—31no—
288C2×D3×D4—31no—
289C2×D3×D4—31no—
290C2×D3×D4—31no—
291C2×D3×D4—32no—
292C2×D3×D4—32no—
293C2×D3×D4—32no—
294C2×D3×D4—32no—
295C2×D3×D4—68no—
296C2×#235—32no—
297C2×#235—31no—
298C22×D12—32no—
299C22×D12—31no—
300C22×D12—31no—
301C22×D12—32no—
302C22×C4×D3—31no—
303C3×#124C2×D311yescharacteristic
304C3×#123C2×D312yes—
305C3×C22⋊Q8C2×D311yescharacteristic
306C3×#121C2×D312yes—
307C3×#121C2×D311yescharacteristic
308C3×#120C2×D312yes—
309C3×C4×D4C2×D311yescharacteristic
310C3×C4×D4C2×D311yescharacteristic
311C2×C3×C22⋊C4C2×D312yes—
312#953—32no—
313#947—31no—
314#946—31no—
315#940—31no—
316#940—32no—
317#939—32no—
318#939—31no—
319#939—32no—
320#938—31no—
321#937—32no—
322#937—31no—
323#937—32no—
324#937—32no—
325#937—32no—
326D4×Dic3—31no—
327#930—32no—
328#930—31no—
329#930—31no—
330#929—32no—
331C4×#67—32no—
332C4×#67—31no—
333C4×#67—31no—
334C2×(C2×D3)⋊C4—32no—
335C2×(C2×D3)⋊C4—32no—
336#896—31no—
337#895—32no—
338#895—32no—
339#895—31no—
340#895—31no—
341#894—31no—
342#894—32no—
343#894—32no—
344#893—32no—
345#893—31no—
346#892—31no—
347#885—32no—
348#884—32no—
349#884—32no—
350#884—32no—
351#884—32no—
352#884—31no—
353#883—32no—
354#883—31no—
355#882—32no—
356#882—32no—
357#882—32no—
358#882—32no—
359#882—32no—
360#882—32no—
361#882—32no—
362#882—31no—
363#882—32no—
364#882—32no—
365#882—32no—
366#882—32no—
367#67⋊C4—32no—
368#67⋊C4—32no—
369D3×C22⋊C4—32no—
370D3×C22⋊C4—32no—
371D3×C22⋊C4—32no—
372#878—31no—
373#874—31no—
374C4×D12—31no—
375C4×D12—31no—
376#872—31no—
377C23×C9—24no—
378C23×C9—24no—
379C23×C9—42no—
380C23×C9C2412yes—
381C23×C9C2411yescharacteristic
382C23×C9C2412yes—
383C23×C9C2411yescharacteristic
384C22×D9—22no—
385C22×D9—22no—
386C22×D9—22no—
387C22×D9—24no—
388C22×D9—24no—
389C22×D9—24no—
390C22×D9—24no—
391C22×D9—24no—
392C22×D9—24no—
393C22×D9—24no—
394C22×D9—24no—
395C22×D9—24no—
396C22×D9—42no—
397C22×D9—42no—
398C22×D9—42no—
399C22×D9—42no—
400C22×D9—42no—
401C22×D9—42no—
402C22×D9—42no—
403C22×D9—42no—
404C22×D9—42no—
405C22×D9—42no—
406C22×D9—42no—
407C22×D9—432no—
408C22×D9C2×D418yescomplemented
409C22×D9C2412yes—
410C22×D9C2411yescharacteristic
411C22×D9C2412yes—
412C22×D9C2411yescharacteristic
413C22×D9C2412yes—
414C22×D9C2411yescharacteristic
415Q8×C9—22no—
416D4×C9—24no—
417D4×C9—24no—
418D4×C9—22no—
419D4×C9—22no—
420D4×C9—42no—
421D4×C9C2×D414yescomplemented
422C2×C4×C9—24no—
423C2×C4×C9—22no—
424C2×C4×C9—22no—
425C2×C4×C9—42no—
426C2×C4×C9C2412yes—
427C2×C4×C9C2411yescharacteristic
428C2×C4×C9C2411yescharacteristic
429C2×C4×C9C2411yescharacteristic
430C2×C4×C9C2412yes—
431C2×C4×C9C2411yescharacteristic
432C2×C4×C9C2411yescharacteristic
433#611—24no—
434#611—24no—
435#611—24no—
436#611—22no—
437#611—22no—
438#611—24no—
439#611—22no—
440#611—22no—
441#611—24no—
442#611—42no—
443#611—42no—
444#611—42no—
445#611—42no—
446#611C2×D418yescomplemented
447C2×Dic9—22no—
448C2×Dic9—42no—
449C2×Dic9C2411yescharacteristic
450C2×Dic9C2411yescharacteristic
451C2×Dic9C2412yes—
452C2×Dic9C2411yescharacteristic
453C2×Dic9C2411yescharacteristic
454C2×Dic9C2411yescharacteristic
455D36—22no—
456D36—24no—
457D36—24no—
458D36—24no—
459D36—24no—
460D36—22no—
461D36—24no—
462D36—22no—
463D36—22no—
464D36—42no—
465D36—42no—
466D36—42no—
467D36C2×D414yescomplemented
468C4×D9—22no—
469C4×D9—24no—
470C4×D9—22no—
471C4×D9—22no—
472C4×D9—22no—
473C4×D9—24no—
474C4×D9—42no—
475C4×D9—42no—
476C4×D9C2×D414yescomplemented
477Dic18—22no—
478C2×H(5,𝔽2)—91no—
479C23×D4—91no—
480#546—91no—
481#546—91no—
482#546—92no—
483#546—91no—
484#546—92no—
485#546D911yescharacteristic, complemented
486D42—91no—
487D42—92no—
488D42—91no—
489D42—92no—
490D42—91no—
491D42—91no—
492#535—91no—
493#535—91no—
494#534—92no—
495#534—92no—
496#525—91no—
497#525—91no—
498C2×#120—92no—
499C2×#120—92no—
500#518—91no—
501C24×C3C22×D312yes—
502C23×D3—32no—
503C23×D3—31no—
504C23×D3—32no—
505C23×D3—32no—
506C23×D3—32no—
507C23×D3—32no—
508C23×D3—32no—
509C23×D3—32no—
510C23×D3—68no—
511C23×D3—124no—
512C23×D3—124no—
513C3×#41—24no—
514C2×C3×Q8C22×D311yescharacteristic
515C2×C3×D4—24no—
516C2×C3×D4C22×D311yescharacteristic
517C2×C3×D4C22×D312yes—
518C2×C3×D4C22×D311yescharacteristic
519C2×C3×D4C22×D311yescharacteristic
520C2×C3×D4C22×D312yes—
521C2×C3×D4C22×D312yes—
522C22×C3×C4C22×D311yescharacteristic
523C22×C3×C4C22×D312yes—
524C22×C3×C4C22×D311yescharacteristic
525C22×C3×C4C22×D312yes—
526C2×#67—32no—
527C2×#67—32no—
528C2×#67—31no—
529C2×#67—32no—
530C2×#67—32no—
531C2×#67—32no—
532C2×#67—31no—
533C2×#67—32no—
534C2×#67—31no—
535C2×#67—31no—
536C2×#67—32no—
537C2×#67—32no—
538C2×#67—32no—
539C2×#67—32no—
540C2×#67—68no—
541C2×#67—124no—
542C22×Dic3—31no—
543C22×Dic3—32no—
544#239—64no—
545#239—64no—
546D3×D4—38no—
547D3×D4—64no—
548D3×D4—64no—
549D3×D4—68no—
550D3×D4—68no—
551D3×D4—68no—
552D3×D4—68no—
553D3×D4—64no—
554D3×D4—64no—
555D3×D4—124no—
556D3×D4—124no—
557#235—64no—
558#235—68no—
559C2×D12—31no—
560C2×D12—31no—
561C2×D12—31no—
562C2×D12—31no—
563C2×D12—32no—
564C2×D12—31no—
565C2×D12—32no—
566C2×D12—32no—
567C2×D12—32no—
568C2×D12—32no—
569C2×D12—32no—
570C2×D12—32no—
571C2×D12—32no—
572C2×D12—64no—
573C2×D12—64no—
574C2×D12—68no—
575C2×D12—124no—
576C2×C4×D3—31no—
577C2×C4×D3—31no—
578C2×C4×D3—31no—
579C2×C4×D3—31no—
580C2×C4×D3—31no—
581C2×C4×D3—32no—
582C2×C4×D3—32no—
583C2×C4×D3—32no—
584C2×C4×D3—32no—
585C2×C4×D3—64no—
586C2×Dic6—31no—
587C3×C4⋊C4C22×D311yescharacteristic
588C3×C4⋊C4C22×D312yes—
589C3×C4⋊C4C22×D311yescharacteristic
590C3×C22⋊C4C22×D311yescharacteristic
591C3×C22⋊C4C22×D312yes—
592C3×C22⋊C4C22×D312yes—
593C3×C22⋊C4C22×D312yes—
594C3×C22⋊C4C22×D312yes—
595C3×C22⋊C4C22×D311yescharacteristic
596C3×C22⋊C4C22×D312yes—
597C3×C42C22×D311yescharacteristic
598#217—31no—
599#217—32no—
600#217—32no—
601#217—31no—
602(C2×D3)⋊C4—31no—
603(C2×D3)⋊C4—31no—
604(C2×D3)⋊C4—31no—
605(C2×D3)⋊C4—32no—
606(C2×D3)⋊C4—32no—
607(C2×D3)⋊C4—31no—
608(C2×D3)⋊C4—32no—
609(C2×D3)⋊C4—31no—
610(C2×D3)⋊C4—32no—
611(C2×D3)⋊C4—32no—
612(C2×D3)⋊C4—32no—
613(C2×D3)⋊C4—32no—
614(C2×D3)⋊C4—32no—
615(C2×D3)⋊C4—32no—
616(C2×D3)⋊C4—32no—
617(C2×D3)⋊C4—31no—
618C4⋊Dic3—31no—
619C4⋊Dic3—31no—
620Dic3⋊C4—31no—
621Dic3⋊C4—31no—
622Dic3⋊C4—31no—
623Dic3⋊C4—32no—
624Dic3⋊C4—31no—
625C4×Dic3—31no—
626C4×Dic3—32no—
627C22×C9—21no—
628C22×C9—22no—
629C22×C9—22no—
630C22×C9—21no—
631C22×C9—21no—
632C22×C9—22no—
633C22×C9—21no—
634C22×C9—21no—
635C22×C9—22no—
636C22×C9—22no—
637C22×C9—48no—
638C22×C9C22×D414yes—
639C22×C9H(5,𝔽2)12yescomplemented
640C22×C9C2511yescharacteristic
641C2×D9—28no—
642C2×D9—21no—
643C2×D9—22no—
644C2×D9—22no—
645C2×D9—21no—
646C2×D9—21no—
647C2×D9—21no—
648C2×D9—21no—
649C2×D9—22no—
650C2×D9—22no—
651C2×D9—21no—
652C2×D9—22no—
653C2×D9—22no—
654C2×D9—22no—
655C2×D9—22no—
656C2×D9—21no—
657C2×D9—48no—
658C2×D9—48no—
659C2×D9—48no—
660C2×D9—48no—
661C2×D9—48no—
662C2×D9—84no—
663C2×D9—84no—
664C2×D9C22×D412yes—
665C2×D9C22×D414yes—
666C2×D9H(5,𝔽2)12yescomplemented
667C4×C9—21no—
668C4×C9—21no—
669C4×C9—22no—
670C4×C9—21no—
671C4×C9—22no—
672C4×C9—21no—
673C4×C9C22×D412yes—
674Dic9—21no—
675Dic9—21no—
676Dic9—21no—
677Dic9—22no—
678Dic9—21no—
679Dic9C22×D412yes—
680C25—92no—
681H(5,𝔽2)—188no—
682C2×#41—91no—
683C2×#41—91no—
684C2×#41—91no—
685C2×#41—92no—
686C2×#41C2×D911yescharacteristic, complemented
687C22×D4—91no—
688C22×D4—92no—
689C22×D4—92no—
690C22×D4—92no—
691C22×D4—91no—
692C22×D4—91no—
693C22×D4—92no—
694C22×D4—91no—
695C22×D4—91no—
696C22×D4—92no—
697C22×D4—92no—
698C22×D4—92no—
699C22×D4—92no—
700C22×D4—91no—
701C22×D4—92no—
702C22×D4—91no—
703C22×D4—92no—
704C22×D4—188no—
705C22×D4C2×D911yescharacteristic, complemented
706C23×C4—91no—
707#127—91no—
708#127—92no—
709#127—91no—
710#124—91no—
711#124—92no—
712#124C2×D911yescharacteristic, complemented
713#123—92no—
714#123—92no—
715#123—91no—
716#123—92no—
717#123—91no—
718#123—92no—
719#123C2×D912yescomplemented
720C22⋊Q8—91no—
721C22⋊Q8—91no—
722C22⋊Q8—91no—
723C22⋊Q8C2×D911yescharacteristic, complemented
724#121—91no—
725#121—92no—
726#121—91no—
727#121—92no—
728#121—91no—
729#121—92no—
730#121—91no—
731#121—91no—
732#121—92no—
733#121—92no—
734#121—91no—
735#121—91no—
736#121—92no—
737#121—92no—
738#121—92no—
739#121—92no—
740#121C2×D912yescomplemented
741#121C2×D911yescharacteristic, complemented
742#120—92no—
743#120—91no—
744#120—92no—
745#120—92no—
746#120—92no—
747#120—92no—
748#120—92no—
749#120—91no—
750#120—92no—
751#120—92no—
752#120—92no—
753#120—92no—
754#120—92no—
755#120—92no—
756#120—92no—
757#120—92no—
758#120—92no—
759#120—92no—
760#120C2×D912yescomplemented
761C4×D4—91no—
762C4×D4—91no—
763C4×D4—92no—
764C4×D4—91no—
765C4×D4—91no—
766C4×D4—92no—
767C4×D4—92no—
768C4×D4—92no—
769C4×D4—91no—
770C4×D4—91no—
771C4×D4C2×D911yescharacteristic, complemented
772C4×D4C2×D911yescharacteristic, complemented
773#117—91no—
774#117—91no—
775C2×C22⋊C4—92no—
776C2×C22⋊C4—92no—
777C2×C22⋊C4—92no—
778C2×C22⋊C4—92no—
779C2×C22⋊C4—92no—
780C2×C22⋊C4C2×D912yescomplemented
781C23×C3—24no—
782C23×C3—24no—
783C23×C3—42no—
784C23×C3C23×D312yes—
785C23×C3C23×D311yescharacteristic
786C23×C3C23×D312yes—
787C23×C3C23×D311yescharacteristic
788C22×D3—31no—
789C22×D3—31no—
790C22×D3—32no—
791C22×D3—38no—
792C22×D3—32no—
793C22×D3—32no—
794C22×D3—31no—
795C22×D3—62no—
796C22×D3—62no—
797C22×D3—64no—
798C22×D3—64no—
799C22×D3—64no—
800C22×D3—64no—
801C22×D3—64no—
802C22×D3—64no—
803C22×D3—62no—
804C22×D3—64no—
805C22×D3—64no—
806C22×D3—64no—
807C22×D3—122no—
808C22×D3—122no—
809C22×D3—122no—
810C22×D3—122no—
811C22×D3—122no—
812C22×D3—122no—
813C22×D3—122no—
814C22×D3—122no—
815C22×D3—122no—
816C22×D3—122no—
817C22×D3—122no—
818C22×D3—1232no—
819C3×Q8—22no—
820C3×D4—24no—
821C3×D4—24no—
822C3×D4—22no—
823C3×D4—22no—
824C3×D4—42no—
825C3×D4D3×D414yes—
826C2×C3×C4—24no—
827C2×C3×C4—22no—
828C2×C3×C4—22no—
829C2×C3×C4—42no—
830C2×C3×C4C23×D312yes—
831C2×C3×C4C23×D311yescharacteristic
832C2×C3×C4C23×D311yescharacteristic
833C2×C3×C4C23×D311yescharacteristic
834C2×C3×C4C23×D312yes—
835C2×C3×C4C23×D311yescharacteristic
836C2×C3×C4C23×D311yescharacteristic
837#67—38no—
838#67—62no—
839#67—64no—
840#67—62no—
841#67—64no—
842#67—62no—
843#67—64no—
844#67—64no—
845#67—64no—
846#67—62no—
847#67—122no—
848#67—122no—
849#67—122no—
850#67—122no—
851C2×Dic3—31no—
852C2×Dic3—31no—
853C2×Dic3—31no—
854C2×Dic3—32no—
855C2×Dic3—31no—
856C2×Dic3—31no—
857C2×Dic3—62no—
858C2×Dic3—122no—
859D12—34no—
860D12—62no—
861D12—64no—
862D12—64no—
863D12—64no—
864D12—64no—
865D12—62no—
866D12—64no—
867D12—62no—
868D12—62no—
869D12—122no—
870D12—122no—
871D12—122no—
872C4×D3—34no—
873C4×D3—62no—
874C4×D3—64no—
875C4×D3—62no—
876C4×D3—64no—
877C4×D3—62no—
878C4×D3—62no—
879C4×D3—122no—
880C4×D3—122no—
881Dic6—62no—
882C2×C9—22no—
883C2×C9—24no—
884C2×C9—42no—
885C2×C9—41no—
886C2×C9C23×D411yescharacteristic
887C2×C9C2×H(5,𝔽2)11yescharacteristic
888C2×C9C2×H(5,𝔽2)11yescharacteristic
889D9—22no—
890D9—22no—
891D9—24no—
892D9—42no—
893D9—41no—
894D9—42no—
895C24—92no—
896C24—91no—
897C24—92no—
898C24—92no—
899C24—92no—
900C24—92no—
901C24—92no—
902C24—92no—
903C24—188no—
904C24—364no—
905C24—364no—
906C24C22×D912yes—
907#41—24no—
908#41—184no—
909#41—188no—
910#41—184no—
911#41—184no—
912C2×Q8—91no—
913C2×Q8C22×D911yescharacteristic, complemented
914C2×D4—24no—
915C2×D4—92no—
916C2×D4—98no—
917C2×D4—91no—
918C2×D4—91no—
919C2×D4—92no—
920C2×D4—91no—
921C2×D4—92no—
922C2×D4—92no—
923C2×D4—92no—
924C2×D4—92no—
925C2×D4—91no—
926C2×D4—92no—
927C2×D4—92no—
928C2×D4—92no—
929C2×D4—92no—
930C2×D4—91no—
931C2×D4—92no—
932C2×D4—91no—
933C2×D4—92no—
934C2×D4—91no—
935C2×D4—92no—
936C2×D4—92no—
937C2×D4—92no—
938C2×D4—91no—
939C2×D4—91no—
940C2×D4—92no—
941C2×D4—92no—
942C2×D4—92no—
943C2×D4—184no—
944C2×D4—184no—
945C2×D4—188no—
946C2×D4—184no—
947C2×D4—188no—
948C2×D4—184no—
949C2×D4—188no—
950C2×D4—188no—
951C2×D4—188no—
952C2×D4—188no—
953C2×D4—184no—
954C2×D4—184no—
955C2×D4—364no—
956C2×D4—364no—
957C2×D4—364no—
958C2×D4—364no—
959C2×D4C22×D911yescharacteristic
960C2×D4C22×D912yes—
961C2×D4C22×D911yescharacteristic
962C2×D4C22×D911yescharacteristic
963C2×D4C22×D912yescomplemented
964C2×D4C22×D912yescomplemented
965C22×C4—91no—
966C22×C4—91no—
967C22×C4—92no—
968C22×C4—92no—
969C22×C4—92no—
970C22×C4—91no—
971C22×C4—91no—
972C22×C4—91no—
973C22×C4—91no—
974C22×C4—92no—
975C22×C4—92no—
976C22×C4—184no—
977C22×C4C22×D911yescharacteristic
978C22×C4C22×D912yescomplemented
979C22×C4C22×D911yescharacteristic, complemented
980C22×C4C22×D912yescomplemented
981C4⋊C4—91no—
982C4⋊C4—91no—
983C4⋊C4—91no—
984C4⋊C4—91no—
985C4⋊C4—92no—
986C4⋊C4—91no—
987C4⋊C4—91no—
988C4⋊C4C22×D911yescharacteristic, complemented
989C4⋊C4C22×D912yescomplemented
990C4⋊C4C22×D911yescharacteristic, complemented
991C22⋊C4—91no—
992C22⋊C4—92no—
993C22⋊C4—92no—
994C22⋊C4—91no—
995C22⋊C4—92no—
996C22⋊C4—91no—
997C22⋊C4—91no—
998C22⋊C4—92no—
999C22⋊C4—91no—
1000C22⋊C4—91no—
1001C22⋊C4—92no—
1002C22⋊C4—92no—
1003C22⋊C4—92no—
1004C22⋊C4—92no—
1005C22⋊C4—92no—
1006C22⋊C4—92no—
1007C22⋊C4—91no—
1008C22⋊C4—92no—
1009C22⋊C4—92no—
1010C22⋊C4—91no—
1011C22⋊C4C22×D912yes—
1012C22⋊C4C22×D911yescharacteristic
1013C22⋊C4C22×D912yescomplemented
1014C22⋊C4C22×D912yescomplemented
1015C22⋊C4C22×D912yescomplemented
1016C22⋊C4C22×D912yescomplemented
1017C22⋊C4C22×D911yescharacteristic, complemented
1018C42—92no—
1019C42—91no—
1020C42C22×D911yescharacteristic, complemented
1021C22×C3—21no—
1022C22×C3—22no—
1023C22×C3—22no—
1024C22×C3—21no—
1025C22×C3—21no—
1026C22×C3—22no—
1027C22×C3—21no—
1028C22×C3—22no—
1029C22×C3—21no—
1030C22×C3—22no—
1031C22×C3—48no—
1032C22×C3C2×D3×D414yes—
1033C22×C3#100912yes—
1034C22×C3C24×D311yescharacteristic
1035C2×D3—32no—
1036C2×D3—34no—
1037C2×D3—32no—
1038C2×D3—68no—
1039C2×D3—61no—
1040C2×D3—62no—
1041C2×D3—61no—
1042C2×D3—61no—
1043C2×D3—62no—
1044C2×D3—61no—
1045C2×D3—62no—
1046C2×D3—61no—
1047C2×D3—62no—
1048C2×D3—62no—
1049C2×D3—62no—
1050C2×D3—61no—
1051C2×D3—61no—
1052C2×D3—62no—
1053C2×D3—62no—
1054C2×D3—128no—
1055C2×D3—128no—
1056C2×D3—128no—
1057C2×D3—128no—
1058C2×D3—128no—
1059C2×D3—244no—
1060C2×D3—244no—
1061C3×C4—21no—
1062C3×C4—21no—
1063C3×C4—22no—
1064C3×C4—21no—
1065C3×C4—22no—
1066C3×C4—21no—
1067C3×C4C2×D3×D412yes—
1068Dic3—32no—
1069Dic3—61no—
1070Dic3—61no—
1071Dic3—62no—
1072Dic3—61no—
1073Dic3—61no—
1074C9#348411yescharacteristic, complemented, Sylow
1075C23—24no—
1076C23—24no—
1077C23—42no—
1078C23—91no—
1079C23—91no—
1080C23—92no—
1081C23—98no—
1082C23—92no—
1083C23—92no—
1084C23—91no—
1085C23—182no—
1086C23—182no—
1087C23—184no—
1088C23—184no—
1089C23—184no—
1090C23—184no—
1091C23—184no—
1092C23—184no—
1093C23—182no—
1094C23—184no—
1095C23—184no—
1096C23—184no—
1097C23—362no—
1098C23—362no—
1099C23—362no—
1100C23—362no—
1101C23—362no—
1102C23—362no—
1103C23—362no—
1104C23—362no—
1105C23—362no—
1106C23—362no—
1107C23—362no—
1108C23—3632no—
1109C23C23×D912yes—
1110C23C23×D911yescharacteristic
1111C23C23×D912yes—
1112C23C23×D911yescharacteristic
1113Q8—22no—
1114Q8—182no—
1115D4—24no—
1116D4—24no—
1117D4—22no—
1118D4—22no—
1119D4—42no—
1120D4—98no—
1121D4—94no—
1122D4—184no—
1123D4—182no—
1124D4—184no—
1125D4—184no—
1126D4—184no—
1127D4—182no—
1128D4—184no—
1129D4—184no—
1130D4—182no—
1131D4—184no—
1132D4—182no—
1133D4—182no—
1134D4—184no—
1135D4—184no—
1136D4—184no—
1137D4—182no—
1138D4—182no—
1139D4—182no—
1140D4—362no—
1141D4—362no—
1142D4—362no—
1143D4—362no—
1144D4—362no—
1145D4—362no—
1146D4—362no—
1147D4D4×D914yescomplemented
1148C2×C4—24no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—42no—
1152C2×C4—91no—
1153C2×C4—94no—
1154C2×C4—92no—
1155C2×C4—91no—
1156C2×C4—91no—
1157C2×C4—91no—
1158C2×C4—91no—
1159C2×C4—182no—
1160C2×C4—184no—
1161C2×C4—182no—
1162C2×C4—184no—
1163C2×C4—182no—
1164C2×C4—182no—
1165C2×C4—182no—
1166C2×C4—362no—
1167C2×C4—362no—
1168C2×C4—362no—
1169C2×C4C23×D912yes—
1170C2×C4C23×D911yescharacteristic
1171C2×C4C23×D911yescharacteristic
1172C2×C4C23×D912yes—
1173C2×C4C23×D911yescharacteristic
1174C2×C4C23×D911yescharacteristic
1175C2×C4C23×D911yescharacteristic
1176C2×C3—22no—
1177C2×C3—24no—
1178C2×C3—42no—
1179C2×C3—41no—
1180C2×C3C22×D3×D411yescharacteristic
1181C2×C3C2×#100911yescharacteristic
1182C2×C3D3×H(5,𝔽2)11yescharacteristic
1183D3—62no—
1184D3—62no—
1185D3—64no—
1186D3—122no—
1187D3—122no—
1188D3—121no—
1189C22—21no—
1190C22—22no—
1191C22—22no—
1192C22—21no—
1193C22—21no—
1194C22—22no—
1195C22—21no—
1196C22—22no—
1197C22—21no—
1198C22—22no—
1199C22—48no—
1200C22—92no—
1201C22—94no—
1202C22—92no—
1203C22—188no—
1204C22—181no—
1205C22—182no—
1206C22—181no—
1207C22—181no—
1208C22—182no—
1209C22—181no—
1210C22—182no—
1211C22—181no—
1212C22—182no—
1213C22—182no—
1214C22—181no—
1215C22—182no—
1216C22—181no—
1217C22—182no—
1218C22—182no—
1219C22—368no—
1220C22—368no—
1221C22—368no—
1222C22—368no—
1223C22—368no—
1224C22—724no—
1225C22—724no—
1226C22C2×D4×D914yes—
1227C22#6371512yescomplemented
1228C22C24×D911yescharacteristic
1229C4—21no—
1230C4—21no—
1231C4—22no—
1232C4—21no—
1233C4—21no—
1234C4—22no—
1235C4—92no—
1236C4—181no—
1237C4—181no—
1238C4—182no—
1239C4—181no—
1240C4—181no—
1241C4C2×D4×D912yes—
1242C3#8666211yescharacteristic
1243C2—22no—
1244C2—24no—
1245C2—42no—
1246C2—41no—
1247C2—182no—
1248C2—182no—
1249C2—184no—
1250C2—362no—
1251C2—361no—
1252C2—362no—
1253C2C22×D4×D911yescharacteristic
1254C2C2×#6371511yescharacteristic
1255C2D9×H(5,𝔽2)11yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#546C2
hypercenter#546D9
hypocenterC9#3484
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #546

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#63715C2semidirect
2. C22×D4×D9C2semidirect
3. C9×#546C2semidirect
4. #10589931C2semidirect
5. D4×#611C2semidirect
6. #10589778C2semidirect
7. #10589776C2semidirect
8. #10589756C2semidirect
9. #10589755C2semidirect
10. #10589732C2semidirect
11. #10589729C2semidirect
12. #10589711C2semidirect
13. #10589711C2semidirect
14. #10589709C2semidirect
15. #10589707C2semidirect
16. #10589692C2semidirect
17. D9×#120C2semidirect
18. D4×D36C2semidirect
19. D4×D36C2semidirect
20. #10589649C2semidirect
21. #10589647C2semidirect
22. #10589592C2semidirect
23. C2×#63444C2semidirect
25. C24×D9C22semidirect
26. C2×C9×#41C22semidirect
27. C22×D4×C9C22semidirect
28. C22×#611C22semidirect
29. C22×#611C22semidirect
31. C2×#3701C22semidirect
32. C2×#3701C22semidirect
35. C2×D4×D9C22semidirect
36. C2×D4×D9C22semidirect
37. C2×D4×D9C22semidirect
38. C2×D4×D9C22semidirect
39. C2×D4×D9C22semidirect
40. C2×D4×D9C22semidirect
41. C2×D4×D9C22semidirect
42. C2×D4×D9C22semidirect
43. C2×D4×D9C22semidirect
44. C2×D4×D9C22semidirect
45. C2×#3697C22semidirect
46. C2×#3697C22semidirect
47. C22×D36C22semidirect
48. C22×D36C22semidirect
49. C22×D36C22semidirect
50. C22×D36C22semidirect
51. C22×C4×D9C22semidirect
52. C9×#124C22semidirect
53. C9×#123C22semidirect
54. C9×C22⋊Q8C22semidirect
55. C9×#121C22semidirect
56. C9×#121C22semidirect
57. C9×#120C22semidirect
58. C4×D4×C9C22semidirect
59. C4×D4×C9C22semidirect
60. C2×C9×C22⋊C4C22semidirect
61. #63515C22semidirect
62. #63509C22semidirect
63. #63508C22semidirect
64. #63502C22semidirect
65. #63502C22semidirect
66. #63501C22semidirect
67. #63501C22semidirect
68. #63501C22semidirect
69. #63500C22semidirect
70. #63499C22semidirect
71. #63499C22semidirect
72. #63499C22semidirect
73. #63499C22semidirect
74. #63499C22semidirect
75. D4×Dic9C22semidirect
76. #63492C22semidirect
77. #63492C22semidirect
78. #63492C22semidirect
79. #63491C22semidirect
80. C4×#611C22semidirect
81. C4×#611C22semidirect
82. C4×#611C22semidirect
83. C2×(C2×D9)⋊C4C22semidirect
84. C2×(C2×D9)⋊C4C22semidirect
85. #63458C22semidirect
86. #63457C22semidirect
87. #63457C22semidirect
88. #63457C22semidirect
89. #63457C22semidirect
90. #63456C22semidirect
91. #63456C22semidirect
92. #63456C22semidirect
93. #63455C22semidirect
94. #63455C22semidirect
95. #63454C22semidirect
96. #63447C22semidirect
97. #63446C22semidirect
98. #63446C22semidirect
99. #63446C22semidirect
100. #63446C22semidirect
101. #63446C22semidirect
102. #63445C22semidirect
103. #63445C22semidirect
104. #63444C22semidirect
105. #63444C22semidirect
106. #63444C22semidirect
107. #63444C22semidirect
108. #63444C22semidirect
109. #63444C22semidirect
110. #63444C22semidirect
111. #63444C22semidirect
112. #63444C22semidirect
113. #63444C22semidirect
114. #63444C22semidirect
115. #63444C22semidirect
116. #611⋊C4C22semidirect
117. #611⋊C4C22semidirect
118. C22⋊C4×D9C22semidirect
119. C22⋊C4×D9C22semidirect
120. C22⋊C4×D9C22semidirect
121. #63440C22semidirect
122. #63436C22semidirect
123. C4×D36C22semidirect
124. C4×D36C22semidirect
125. #63434C22semidirect
159. C23×D9C23semidirect
160. C23×D9C23semidirect
162. C2×Q8×C9C23semidirect
168. C2×D4×C9C23semidirect
169. C2×D4×C9C23semidirect
171. C22×C4×C9C23semidirect
172. C22×C4×C9C23semidirect
173. C22×C4×C9C23semidirect
184. C2×#611C23semidirect
185. C2×#611C23semidirect
186. C2×#611C23semidirect
187. C2×#611C23semidirect
188. C2×#611C23semidirect
189. C2×#611C23semidirect
191. C22×Dic9C23semidirect
204. D4×D9D4semidirect
218. C2×D36C23semidirect
219. C2×D36C23semidirect
220. C2×D36C23semidirect
221. C2×D36C23semidirect
222. C2×D36C23semidirect
223. C2×D36C23semidirect
229. C2×C4×D9C23semidirect
230. C2×C4×D9C23semidirect
231. C2×C4×D9C23semidirect
232. C2×C4×D9C23semidirect
233. C2×C4×D9C23semidirect
234. C2×Dic18C23semidirect
235. C9×C4⋊C4C23semidirect
236. C9×C4⋊C4C23semidirect
237. C9×C4⋊C4C23semidirect
240. C9×C22⋊C4C23semidirect
241. C9×C22⋊C4C23semidirect
242. C9×C22⋊C4C23semidirect
243. C9×C22⋊C4C23semidirect
244. C9×C22⋊C4C23semidirect
245. C42×C9C23semidirect
247. #3676C23semidirect
248. #3676C23semidirect
249. #3676C23semidirect
256. (C2×D9)⋊C4C23semidirect
257. (C2×D9)⋊C4C23semidirect
258. (C2×D9)⋊C4C23semidirect
259. (C2×D9)⋊C4C23semidirect
260. (C2×D9)⋊C4C23semidirect
261. (C2×D9)⋊C4C23semidirect
262. (C2×D9)⋊C4C23semidirect
263. (C2×D9)⋊C4C23semidirect
264. (C2×D9)⋊C4C23semidirect
265. (C2×D9)⋊C4C23semidirect
266. C4⋊Dic9C23semidirect
267. C4⋊Dic9C23semidirect
268. Dic9⋊C4C23semidirect
269. Dic9⋊C4C23semidirect
270. Dic9⋊C4C23semidirect
271. Dic9⋊C4C23semidirect
272. Dic9⋊C4C23semidirect
273. C4×Dic9C23semidirect
274. C4×Dic9C23semidirect
408. C22×D9C2×D4semidirect
421. D4×C9C2×D4semidirect
446. #611C2×D4semidirect
467. D36C2×D4semidirect
476. C4×D9C2×D4semidirect
485. #546D9semidirect
639. C22×C9H(5,𝔽2)semidirect
666. C2×D9H(5,𝔽2)semidirect
686. C2×#41C2×D9semidirect
705. C22×D4C2×D9semidirect
712. #124C2×D9semidirect
719. #123C2×D9semidirect
723. C22⋊Q8C2×D9semidirect
740. #121C2×D9semidirect
741. #121C2×D9semidirect
760. #120C2×D9semidirect
771. C4×D4C2×D9semidirect
772. C4×D4C2×D9semidirect
780. C2×C22⋊C4C2×D9semidirect
913. C2×Q8C22×D9semidirect
963. C2×D4C22×D9semidirect
964. C2×D4C22×D9semidirect
978. C22×C4C22×D9semidirect
979. C22×C4C22×D9semidirect
980. C22×C4C22×D9semidirect
988. C4⋊C4C22×D9semidirect
989. C4⋊C4C22×D9semidirect
990. C4⋊C4C22×D9semidirect
1013. C22⋊C4C22×D9semidirect
1014. C22⋊C4C22×D9semidirect
1015. C22⋊C4C22×D9semidirect
1016. C22⋊C4C22×D9semidirect
1017. C22⋊C4C22×D9semidirect
1020. C42C22×D9semidirect
1074. C9#3484semidirect
1147. D4D4×D9semidirect
1227. C22#63715semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#637152
C22×D4×D92
C9×#5462
#105899312
D4×#6112
#105897782
#105897762
#105897562
#105897552
#105897322
#105897292
#105897112
#105897092
#105897072
#105896922
D9×#1202
D4×D362
#105896492
#105896472
#105895922
C2×#634442
#866623