Finite Group Databasebeta

← #11904328

Subgroups — #11904328

Order 1152.

3973 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64330C211yesmaximal, characteristic, complemented
2C22×D3×#67C211yesmaximal, characteristic, complemented
3#10595964C211yesmaximal, characteristic, complemented
4C2×C3×#882C211yesmaximal, characteristic, complemented
5C3×#5486C211yesmaximal, characteristic, complemented
6#10595519C211yesmaximal, characteristic, complemented
7C2×#63977C211yesmaximal, characteristic, complemented
8#10595073C214yesmaximal, complemented
9D12×#67C214yesmaximal, complemented
10#10594292C214yesmaximal, complemented
11#10594290C212yesmaximal, complemented
12#10594277C214yesmaximal, complemented
13D3×#882C212yesmaximal, complemented
14#10594080C212yesmaximal, complemented
15#10594078C212yesmaximal, complemented
16#85919—31nomaximal
17#85867—31nomaximal
18C24×C3×D3C2211yescharacteristic, complemented
19C23×D32C2211yescharacteristic, complemented
20C22×#638C2211yescharacteristic, complemented
21C22×#638C2211yescharacteristic, complemented
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic, complemented
24C22×C3×D12C2212yescomplemented
25#64330—28no—
26C2×#3811C2212yescomplemented
27C2×D3×#67—28no—
28C2×D3×#67C2214yescomplemented
29C2×D3×#67C2214yescomplemented
30C2×D3×#67C2212yescomplemented
31C2×D3×#67C2212yescomplemented
32C22×#626C2211yescharacteristic, complemented
33C22×#626C2212yescomplemented
34C22×#625C2211yescharacteristic, complemented
35C2×#3805C2212yescomplemented
36C2×#3804C2212yescomplemented
37C2×#3804C2212yescomplemented
38C22×D3×Dic3C2211yescharacteristic, complemented
39C2×D3×D12C2214yescomplemented
40C2×C32×C22⋊C4C2211yescharacteristic, complemented
41#64139C2214yescomplemented
42#64095C2212yescomplemented
43#64095C2212yescomplemented
44#64091C2212yescomplemented
45#64091C2212yescomplemented
46C2×C3×#217C2211yescharacteristic, complemented
47C3×C4×#67C2214yescomplemented
48C2×C3×(C2×D3)⋊C4C2212yescomplemented
49C3×#882C2212yescomplemented
50C3×#882C2214yescomplemented
51C3×#882C2212yescomplemented
52C3×#67⋊C4C2214yescomplemented
53C3×D3×C22⋊C4C2212yescomplemented
54C3×#877C2212yescomplemented
55#63981C2212yescomplemented
56#63978C2214yescomplemented
57#63977C2212yescomplemented
58#63977C2214yescomplemented
59#63977C2212yescomplemented
60#63977C2212yescomplemented
61#63966C2212yescomplemented
62#63962C2212yescomplemented
63C2×(C2×D3)⋊Dic3C2212yescomplemented
64#63923C2214yescomplemented
65#63922C2214yescomplemented
66#63922C2214yescomplemented
67D3×(C2×D3)⋊C4C2214yescomplemented
68#63911C2214yescomplemented
69#63910C2214yescomplemented
70#63908C2214yescomplemented
71#63906C2214yescomplemented
72#63893C2214yescomplemented
73Dic3×D12C2214yescomplemented
74#63891C2214yescomplemented
75#63886C2214yescomplemented
76#63886C2214yescomplemented
77#63880C2214yescomplemented
78#63852C2214yescomplemented
79C23×#67—31no—
80C2×#1004—31no—
81C2×#1004—31no—
82C22×D3×D4—31no—
83C2×C3×#120—31no—
84C3×#518—31no—
85C2×#953—31no—
86#5804—31no—
87D4×#67—34no—
88#5592—32no—
89#5591—34no—
90#5590—34no—
91#5589—32no—
92D3×#120—32no—
93#5586—32no—
94#5554—34no—
95#5554—34no—
96D4×D12—34no—
97D4×D12—34no—
98#5525—32no—
99#5524—32no—
100#5493—31no—
101#5493—31no—
102#5493—31no—
103#5493—32no—
104#5493—61no—
105#5490—34no—
106C2×#882—31no—
107C2×#882—32no—
108C2×#882D311yescharacteristic, complemented
109#5486D311yescharacteristic, complemented
110C24×C32C2311yescharacteristic
111C23×C3⋊D3C2311yescharacteristic
112C23×C3⋊D3C2311yescharacteristic, complemented
113C23×C3×D3—24no—
114C23×C3×D3—44no—
115C23×C3×D3C2311yescharacteristic
116C23×C3×D3C2312yes—
117C23×C3×D3C2312yes—
118C23×C3×D3C2311yescharacteristic
119C23×C3×D3C2311yescharacteristic
120C23×C3×D3C2311yescharacteristic, complemented
121C22×D32—24no—
122C22×D32—44no—
123C22×D32C2314yes—
124C22×D32C2312yescomplemented
125C22×C32×C4C2312yescomplemented
126C2×#638—24no—
127C2×#638—24no—
128C2×#638C2312yes—
129C2×#638C2312yes—
130C2×#638C2312yes—
131C2×#638C2312yescomplemented
132C22×C3⋊Dic3C2311yescharacteristic
133C22×C3⋊Dic3C2311yescharacteristic, complemented
134C2×C4⋊(C3⋊D3)C2314yescomplemented
135C2×C3×#67—24no—
136C2×C3×#67D418yescomplemented
137C2×C3×#67C2312yes—
138C2×C3×#67C2312yes—
139C2×C3×#67C2312yes—
140C2×C3×#67C2312yescomplemented
141C22×C3×Dic3C2311yescharacteristic
142C22×C3×Dic3C2311yescharacteristic, complemented
143C22×C3×Dic3C2312yescomplemented
144C2×C3×D12—44no—
145C2×C3×D12C2314yes—
146C2×C3×D12C2314yescomplemented
147C2×C3×C4×D3C2314yescomplemented
148#3811—28no—
149D3×#67—28no—
150D3×#67—216no—
151D3×#67—216no—
152D3×#67—28no—
153C2×#627C2312yescomplemented
154C2×#626—24no—
155C2×#626—44no—
156C2×#626C2314yes—
157C2×#626C2314yes—
158C2×#626C2312yescomplemented
159C2×#626C2312yescomplemented
160C2×#626C2314yescomplemented
161C2×#626C2314yescomplemented
162C2×#625—24no—
163C2×#625C2314yes—
164C2×#625C2312yescomplemented
165C2×#624C2312yescomplemented
166#3805—28no—
167#3804—28no—
168#3804—28no—
169C2×D3×Dic3—24no—
170C2×D3×Dic3C2314yes—
171C2×D3×Dic3C2312yescomplemented
172C2×D3×Dic3C2312yescomplemented
173D3×D12—48no—
174C32×C22⋊C4C2312yes—
175C32×C22⋊C4C2312yescomplemented
176#3752C2314yescomplemented
177#3752C2314yescomplemented
178C4⋊(C3⋊Dic3)C2314yescomplemented
179C3×#217C2312yes—
180C3×#217C2312yescomplemented
181C3×(C2×D3)⋊C4C2314yes—
182C3×(C2×D3)⋊C4C2314yescomplemented
183C3×(C2×D3)⋊C4C2314yescomplemented
184C3×Dic3⋊C4C2314yescomplemented
185C3×C4×Dic3C2314yescomplemented
186Dic3⋊Dic3C2314yescomplemented
187#3722C2314yescomplemented
188(C2×D3)⋊Dic3C2314yes—
189(C2×D3)⋊Dic3C2314yescomplemented
190(C2×D3)⋊Dic3C2314yescomplemented
191#3484—91noSylow
192C25×C3—31no—
193C24×D3—31no—
194C24×D3—31no—
195C24×D3C2×D311yescharacteristic, complemented
196C22×C3×D4—31no—
197C22×C3×D4—31no—
198C22×C3×D4—32no—
199C22×#67—31no—
200C22×#67—31no—
201C22×#67—31no—
202C22×#67—31no—
203C22×#67—31no—
204C22×#67—31no—
205C22×#67—32no—
206C22×#67—32no—
207C22×#67—34no—
208C22×#67—34no—
209C22×#67—31no—
210C22×#67—32no—
211C22×#67—61no—
212C22×#67—61no—
213C22×#67—68no—
214C22×#67C2×D311yescharacteristic
215C22×#67C2×D311yescharacteristic, complemented
216C23×Dic3—31no—
217#1004—68no—
218#1004—68no—
219C2×#237—32no—
220C2×#237—32no—
221C2×#237—32no—
222C2×#237—32no—
223C2×D3×D4—34no—
224C2×D3×D4—34no—
225C2×D3×D4—32no—
226C2×D3×D4—32no—
227C2×D3×D4—32no—
228C2×D3×D4—32no—
229C2×D3×D4—34no—
230C2×D3×D4—68no—
231C2×#235—32no—
232C2×#235—32no—
233C22×D12—31no—
234C22×D12—32no—
235C22×D12—34no—
236C22×D12C2×D312yescomplemented
237C22×C4×D3—31no—
238C3×#120—32no—
239C3×#120—32no—
240C3×#120—34no—
241C3×C4×D4—34no—
242C3×C4×D4—34no—
243C3×#117—32no—
244C2×C3×C22⋊C4—21no—
245C2×C3×C22⋊C4—31no—
246C2×C3×C22⋊C4—32no—
247C2×C3×C22⋊C4—32no—
248C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
249C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
250#953—32no—
251#953—32no—
252#953—34no—
253#953—32no—
254C2×#217—32no—
255C2×#217C2×D311yescharacteristic, complemented
256#940—34no—
257#939—34no—
258#939—34no—
259#939—34no—
260#938—34no—
261#937—32no—
262#937—34no—
263#937—34no—
264#935—32no—
265D4×Dic3—34no—
266#930—34no—
267#930—34no—
268#930—34no—
269#930—34no—
270#930—34no—
271#930—64no—
272#929—32no—
273C4×#67C2×D314yescomplemented
274C2×(C2×D3)⋊C4—32no—
275C2×(C2×D3)⋊C4—34no—
276C2×(C2×D3)⋊C4C2×D312yescomplemented
277#897—34no—
278#895—34no—
279#895—34no—
280#895—34no—
281#886—32no—
282#886—32no—
283#886—32no—
284#886—32no—
285#886—32no—
286#886—32no—
287#886—34no—
288#886—62no—
289#886—62no—
290#885—34no—
291#884—34no—
292#884—34no—
293#883—34no—
294#882—32no—
295#882—32no—
296#882—34no—
297#882—32no—
298#882—32no—
299#882—34no—
300#882—34no—
301#882—32no—
302#882—32no—
303#882—32no—
304#882—32no—
305#882—34no—
306#882—34no—
307#882—62no—
308#882—62no—
309#882C2×D312yescomplemented
310#882C2×D314yescomplemented
311#882C2×D312yescomplemented
312#67⋊C4—34no—
313#67⋊C4C2×D314yescomplemented
314D3×C22⋊C4—34no—
315D3×C22⋊C4C2×D312yescomplemented
316#878—34no—
317#877C2×D312yescomplemented
318#875—34no—
319#874—34no—
320C4×D12—34no—
321C4×D12—34no—
322C23×C32—42no—
323C23×C32C2×D414yescomplemented
324C23×C32C2411yescharacteristic
325C23×C32C2411yescharacteristic
326C23×C32C2411yescharacteristic
327C22×C3⋊D3—22no—
328C22×C3⋊D3—22no—
329C22×C3⋊D3—42no—
330C22×C3⋊D3—42no—
331C22×C3⋊D3C2412yes—
332C22×C3⋊D3C2412yes—
333C22×C3×D3—22no—
334C22×C3×D3—24no—
335C22×C3×D3—22no—
336C22×C3×D3—24no—
337C22×C3×D3—24no—
338C22×C3×D3—22no—
339C22×C3×D3—24no—
340C22×C3×D3—24no—
341C22×C3×D3—42no—
342C22×C3×D3—42no—
343C22×C3×D3—42no—
344C22×C3×D3—42no—
345C22×C3×D3—42no—
346C22×C3×D3—416no—
347C22×C3×D3C2×D414yescomplemented
348C22×C3×D3C2412yes—
349C22×C3×D3C2412yes—
350C22×C3×D3C2412yes—
351C22×C3×D3C2412yes—
352C2×D32—28no—
353C2×D32—28no—
354C2×D32—24no—
355C2×D32—44no—
356C2×D32—416no—
357C2×D32—44no—
358C2×C32×C4—42no—
359C2×C32×C4C2414yes—
360#638—24no—
361#638—24no—
362#638—24no—
363#638—24no—
364C2×C3⋊Dic3—22no—
365C2×C3⋊Dic3—22no—
366C2×C3⋊Dic3C2412yes—
367C2×C3⋊Dic3C2412yes—
368C4⋊(C3⋊D3)—44no—
369C3×#67—24no—
370C3×#67—24no—
371C3×#67C2×D418yescomplemented
372C3×#67C2×D418yescomplemented
373C2×C3×Dic3—22no—
374C2×C3×Dic3—42no—
375C2×C3×Dic3C2×D414yescomplemented
376C2×C3×Dic3C2414yes—
377C2×C3×Dic3C2412yes—
378C2×C3×Dic3C2412yes—
379C3×D12—28no—
380C3×D12—44no—
381C3×C4×D3—44no—
382#627—24no—
383#626—24no—
384#626—28no—
385#626—24no—
386#626—28no—
387#626—44no—
388#626—44no—
389#625—24no—
390#625—28no—
391#624—24no—
392D3×Dic3—24no—
393D3×Dic3—28no—
394D3×Dic3—24no—
395C2×H(5,𝔽2)—91no—
396C23×D4—91no—
397#546—94no—
398#546—94no—
399D42—94no—
400D42—94no—
401#535—92no—
402#534—92no—
403#534—91no—
404#534—91no—
405#525—92no—
406C2×#120—31no—
407C2×#120—92no—
408C2×#120—91no—
409#518—31no—
410C24×C3—21no—
411C24×C3—31no—
412C24×C3—31no—
413C24×C3—32no—
414C24×C3—32no—
415C24×C3—31no—
416C24×C3—31no—
417C24×C3—64no—
418C24×C3—124no—
419C24×C3C22×D311yescharacteristic
420C24×C3C22×D311yescharacteristic
421C23×D3—24no—
422C23×D3—31no—
423C23×D3—31no—
424C23×D3—31no—
425C23×D3—31no—
426C23×D3—34no—
427C23×D3—34no—
428C23×D3—32no—
429C23×D3—32no—
430C23×D3—44no—
431C23×D3—61no—
432C23×D3—61no—
433C23×D3—64no—
434C23×D3—64no—
435C23×D3—124no—
436C23×D3—124no—
437C23×D3C22×D311yescharacteristic
438C23×D3C22×D312yes—
439C23×D3C22×D312yes—
440C23×D3C22×D311yescharacteristic
441C23×D3C22×D311yescharacteristic
442C23×D3C22×D311yescharacteristic, complemented
443C2×C3×D4—38no—
444C2×C3×D4—32no—
445C2×C3×D4—32no—
446C2×C3×D4—32no—
447C2×C3×D4—32no—
448C2×C3×D4—34no—
449C2×C3×D4—34no—
450C2×C3×D4—64no—
451C2×C3×D4—124no—
452C22×C3×C4—22no—
453C22×C3×C4—31no—
454C22×C3×C4—31no—
455C22×C3×C4—32no—
456C22×C3×C4—34no—
457C22×C3×C4C22×D312yescomplemented
458C22×C3×C4C22×D312yescomplemented
459C2×#67—24no—
460C2×#67—32no—
461C2×#67—32no—
462C2×#67—32no—
463C2×#67—32no—
464C2×#67—32no—
465C2×#67—32no—
466C2×#67—32no—
467C2×#67—32no—
468C2×#67—32no—
469C2×#67—34no—
470C2×#67—34no—
471C2×#67—32no—
472C2×#67—34no—
473C2×#67—32no—
474C2×#67—34no—
475C2×#67—32no—
476C2×#67—34no—
477C2×#67—34no—
478C2×#67—62no—
479C2×#67—62no—
480C2×#67—62no—
481C2×#67—62no—
482C2×#67—68no—
483C2×#67—64no—
484C2×#67—64no—
485C2×#67—64no—
486C2×#67—64no—
487C2×#67—64no—
488C2×#67—64no—
489C2×#67—68no—
490C2×#67—616no—
491C2×#67—616no—
492C2×#67—64no—
493C2×#67—124no—
494C2×#67—124no—
495C2×#67—124no—
496C2×#67D1218yescomplemented
497C2×#67C22×D312yes—
498C2×#67C22×D312yes—
499C2×#67C22×D312yes—
500C2×#67C22×D312yescomplemented
501C22×Dic3—31no—
502C22×Dic3—31no—
503C22×Dic3—31no—
504C22×Dic3—31no—
505C22×Dic3—34no—
506C22×Dic3—32no—
507C22×Dic3—32no—
508C22×Dic3—61no—
509C22×Dic3—61no—
510C22×Dic3—64no—
511C22×Dic3C22×D311yescharacteristic
512C22×Dic3C22×D311yescharacteristic, complemented
513C22×Dic3C22×D312yescomplemented
514#237—68no—
515#237—68no—
516#237—68no—
517#237—68no—
518D3×D4—68no—
519D3×D4—616no—
520D3×D4—616no—
521D3×D4—68no—
522D3×D4—68no—
523D3×D4—68no—
524D3×D4—128no—
525#235—68no—
526#235—68no—
527C2×D12—34no—
528C2×D12—32no—
529C2×D12—34no—
530C2×D12—32no—
531C2×D12—34no—
532C2×D12—34no—
533C2×D12—34no—
534C2×D12—34no—
535C2×D12—44no—
536C2×D12—64no—
537C2×D12—64no—
538C2×D12—128no—
539C2×D12—124no—
540C2×D12C22×D314yes—
541C2×D12C22×D314yescomplemented
542C2×C4×D3—32no—
543C2×C4×D3—34no—
544C2×C4×D3—32no—
545C2×C4×D3—32no—
546C2×C4×D3—32no—
547C2×C4×D3—64no—
548C2×C4×D3C22×D314yescomplemented
549C2×Dic6—32no—
550C2×Dic6—32no—
551C3×C4⋊C4—34no—
552C3×C22⋊C4—22no—
553C3×C22⋊C4—22no—
554C3×C22⋊C4—32no—
555C3×C22⋊C4—32no—
556C3×C22⋊C4—34no—
557C3×C22⋊C4—34no—
558C3×C22⋊C4—34no—
559C3×C22⋊C4C22×D312yes—
560C3×C22⋊C4C22×D312yes—
561C3×C22⋊C4C22×D312yescomplemented
562C3×C22⋊C4C22×D312yescomplemented
563C3×C42—34no—
564#217—34no—
565#217—34no—
566#217—34no—
567#217C22×D312yes—
568#217C22×D312yescomplemented
569(C2×D3)⋊C4—34no—
570(C2×D3)⋊C4—34no—
571(C2×D3)⋊C4—34no—
572(C2×D3)⋊C4—34no—
573(C2×D3)⋊C4—34no—
574(C2×D3)⋊C4—34no—
575(C2×D3)⋊C4—34no—
576(C2×D3)⋊C4—34no—
577(C2×D3)⋊C4—34no—
578(C2×D3)⋊C4—64no—
579(C2×D3)⋊C4—64no—
580(C2×D3)⋊C4C22×D314yes—
581(C2×D3)⋊C4C22×D314yescomplemented
582(C2×D3)⋊C4C22×D314yescomplemented
583C4⋊Dic3—34no—
584C4⋊Dic3—34no—
585C4⋊Dic3—34no—
586C4⋊Dic3—64no—
587Dic3⋊C4—34no—
588Dic3⋊C4C22×D314yescomplemented
589C4×Dic3C22×D314yescomplemented
590C22×C32—22no—
591C22×C32—22no—
592C22×C32—22no—
593C22×C32—44no—
594C22×C32C22×D412yes—
595C22×C32C22×D412yes—
596C22×C32C22×D412yes—
597C22×C32C2511yescharacteristic
598C2×C3⋊D3—22no—
599C2×C3⋊D3—22no—
600C2×C3⋊D3—24no—
601C2×C3⋊D3—24no—
602C2×C3⋊D3—44no—
603C2×C3⋊D3—82no—
604C2×C3×D3—28no—
605C2×C3×D3—22no—
606C2×C3×D3—24no—
607C2×C3×D3—22no—
608C2×C3×D3—22no—
609C2×C3×D3—22no—
610C2×C3×D3—22no—
611C2×C3×D3—24no—
612C2×C3×D3—22no—
613C2×C3×D3—44no—
614C2×C3×D3—48no—
615C2×C3×D3—48no—
616C2×C3×D3—44no—
617C2×C3×D3—82no—
618C2×C3×D3C22×D414yes—
619C2×C3×D3H(5,𝔽2)14yescomplemented
620D32—416no—
621D32—84no—
622C32×C4—24no—
623C3⋊Dic3—22no—
624C3⋊Dic3—22no—
625C3×Dic3—22no—
626C3×Dic3—24no—
627C3×Dic3C22×D414yes—
628C25—31no—
629C25—91no—
630H(5,𝔽2)—188no—
631C2×#41—92no—
632C2×#41—92no—
633C2×#41—92no—
634C22×D4—31no—
635C22×D4—31no—
636C22×D4—32no—
637C22×D4—94no—
638C22×D4—91no—
639C22×D4—92no—
640C22×D4—92no—
641C22×D4—92no—
642C22×D4—92no—
643C22×D4—94no—
644C22×D4—94no—
645C22×D4—91no—
646C22×D4—91no—
647C22×D4—91no—
648C22×D4—188no—
649C23×C4—91no—
650#127—94no—
651#124—94no—
652#123—94no—
653#123—92no—
654#123—92no—
655#123—92no—
656#123—92no—
657C22⋊Q8—94no—
658#121—94no—
659#121—94no—
660#121—94no—
661#121—94no—
662#121—94no—
663#121—94no—
664#121—94no—
665#120—32no—
666#120—32no—
667#120—34no—
668#120—94no—
669#120—92no—
670#120—94no—
671#120—94no—
672#120—92no—
673#120—92no—
674#120—94no—
675#120—92no—
676#120—92no—
677#120—92no—
678C4×D4—34no—
679C4×D4—34no—
680C4×D4—94no—
681C4×D4—94no—
682#117—32no—
683C2×C22⋊C4—31no—
684C2×C22⋊C4—32no—
685C2×C22⋊C4—32no—
686C2×C22⋊C4—94no—
687C2×C22⋊C4—92no—
688C2×C22⋊C4D3211yescharacteristic, complemented
689C23×C3—21no—
690C23×C3—21no—
691C23×C3—21no—
692C23×C3—24no—
693C23×C3—32no—
694C23×C3—32no—
695C23×C3—34no—
696C23×C3—32no—
697C23×C3—32no—
698C23×C3—42no—
699C23×C3—42no—
700C23×C3—64no—
701C23×C3—64no—
702C23×C3—64no—
703C23×C3—62no—
704C23×C3—64no—
705C23×C3—64no—
706C23×C3—62no—
707C23×C3—62no—
708C23×C3—82no—
709C23×C3—122no—
710C23×C3—122no—
711C23×C3—122no—
712C23×C3—122no—
713C23×C3—122no—
714C23×C3—1216no—
715C23×C3C2×D1214yescomplemented
716C23×C3D3×D414yescomplemented
717C23×C3C23×D311yescharacteristic
718C23×C3C23×D311yescharacteristic
719C23×C3C23×D311yescharacteristic
720C23×C3C23×D311yescharacteristic
721C23×C3C23×D311yescharacteristic
722C23×C3C23×D311yescharacteristic
723C22×D3—22no—
724C22×D3—24no—
725C22×D3—22no—
726C22×D3—24no—
727C22×D3—24no—
728C22×D3—22no—
729C22×D3—24no—
730C22×D3—24no—
731C22×D3—32no—
732C22×D3—32no—
733C22×D3—32no—
734C22×D3—32no—
735C22×D3—42no—
736C22×D3—42no—
737C22×D3—42no—
738C22×D3—42no—
739C22×D3—42no—
740C22×D3—416no—
741C22×D3—62no—
742C22×D3—62no—
743C22×D3—68no—
744C22×D3—68no—
745C22×D3—64no—
746C22×D3—62no—
747C22×D3—62no—
748C22×D3—62no—
749C22×D3—62no—
750C22×D3—68no—
751C22×D3—68no—
752C22×D3—64no—
753C22×D3—122no—
754C22×D3—122no—
755C22×D3—124no—
756C22×D3—124no—
757C22×D3—124no—
758C22×D3—124no—
759C22×D3—1216no—
760C22×D3—1216no—
761C22×D3—122no—
762C22×D3—122no—
763C22×D3—122no—
764C22×D3—122no—
765C22×D3—242no—
766C22×D3—242no—
767C22×D3C2×D1214yescomplemented
768C22×D3C23×D312yes—
769C22×D3C23×D312yes—
770C22×D3C23×D312yes—
771C22×D3C23×D312yes—
772C3×D4—38no—
773C3×D4—38no—
774C3×D4—68no—
775C3×D4—64no—
776C3×D4—64no—
777C3×D4—124no—
778C2×C3×C4—24no—
779C2×C3×C4—34no—
780C2×C3×C4—32no—
781C2×C3×C4—32no—
782C2×C3×C4—34no—
783C2×C3×C4—42no—
784C2×C3×C4—42no—
785C2×C3×C4—62no—
786C2×C3×C4—82no—
787C2×C3×C4—124no—
788C2×C3×C4—122no—
789C2×C3×C4C23×D314yes—
790C2×C3×C4C23×D314yes—
791#67—24no—
792#67—24no—
793#67—64no—
794#67—68no—
795#67—68no—
796#67—64no—
797#67—64no—
798#67—64no—
799#67—64no—
800#67—64no—
801#67—64no—
802#67—64no—
803#67—64no—
804#67—64no—
805#67—64no—
806#67—68no—
807#67—64no—
808#67—68no—
809#67—124no—
810#67—124no—
811#67—124no—
812#67—124no—
813#67—124no—
814#67—124no—
815#67C2×D1218yescomplemented
816#67C2×D1218yescomplemented
817C2×Dic3—22no—
818C2×Dic3—32no—
819C2×Dic3—32no—
820C2×Dic3—32no—
821C2×Dic3—32no—
822C2×Dic3—42no—
823C2×Dic3—62no—
824C2×Dic3—62no—
825C2×Dic3—64no—
826C2×Dic3—62no—
827C2×Dic3—62no—
828C2×Dic3—62no—
829C2×Dic3—62no—
830C2×Dic3—64no—
831C2×Dic3—68no—
832C2×Dic3—122no—
833C2×Dic3—122no—
834C2×Dic3C2×D1214yescomplemented
835C2×Dic3C23×D314yes—
836C2×Dic3C23×D312yes—
837C2×Dic3C23×D312yes—
838D12—28no—
839D12—44no—
840D12—68no—
841D12—64no—
842D12—64no—
843D12—68no—
844D12—124no—
845D12—124no—
846D12—124no—
847D12—124no—
848D12—244no—
849C4×D3—44no—
850C4×D3—64no—
851C4×D3—68no—
852C4×D3—64no—
853C4×D3—64no—
854C4×D3—64no—
855Dic6—64no—
856Dic6—64no—
857C2×C32—22no—
858C2×C32—22no—
859C2×C32—22no—
860C2×C32C23×D411yescharacteristic
861C2×C32C2×H(5,𝔽2)12yes—
862C3⋊D3—42no—
863C3⋊D3—42no—
864C3×D3—24no—
865C3×D3—24no—
866C3×D3—42no—
867C3×D3—42no—
868C24—31no—
869C24—31no—
870C24—32no—
871C24—32no—
872C24—31no—
873C24—31no—
874C24—64no—
875C24—94no—
876C24—92no—
877C24—91no—
878C24—91no—
879C24—124no—
880C24—184no—
881C24—364no—
882C24C2×D3211yescharacteristic
883#41—188no—
884#41—188no—
885#41—188no—
886C2×Q8—92no—
887C2×D4—32no—
888C2×D4—32no—
889C2×D4—38no—
890C2×D4—32no—
891C2×D4—32no—
892C2×D4—34no—
893C2×D4—34no—
894C2×D4—64no—
895C2×D4—94no—
896C2×D4—92no—
897C2×D4—94no—
898C2×D4—92no—
899C2×D4—94no—
900C2×D4—94no—
901C2×D4—92no—
902C2×D4—94no—
903C2×D4—92no—
904C2×D4—92no—
905C2×D4—92no—
906C2×D4—92no—
907C2×D4—94no—
908C2×D4—124no—
909C2×D4—184no—
910C2×D4—188no—
911C2×D4—1816no—
912C2×D4—1816no—
913C2×D4—188no—
914C2×D4—188no—
915C2×D4—184no—
916C2×D4—184no—
917C2×D4—184no—
918C2×D4—368no—
919C2×D4—364no—
920C22×C4—31no—
921C22×C4—31no—
922C22×C4—32no—
923C22×C4—34no—
924C22×C4—92no—
925C22×C4—92no—
926C22×C4—92no—
927C22×C4—94no—
928C22×C4—91no—
929C22×C4—91no—
930C22×C4—184no—
931C22×C4C2×D3212yescomplemented
932C4⋊C4—34no—
933C4⋊C4—94no—
934C4⋊C4—94no—
935C22⋊C4—32no—
936C22⋊C4—32no—
937C22⋊C4—34no—
938C22⋊C4—34no—
939C22⋊C4—34no—
940C22⋊C4—94no—
941C22⋊C4—94no—
942C22⋊C4—94no—
943C22⋊C4—94no—
944C22⋊C4—94no—
945C22⋊C4—94no—
946C22⋊C4C2×D3212yes—
947C22⋊C4C2×D3212yescomplemented
948C42—34no—
949C22×C3—22no—
950C22×C3—22no—
951C22×C3—22no—
952C22×C3—22no—
953C22×C3—22no—
954C22×C3—22no—
955C22×C3—22no—
956C22×C3—22no—
957C22×C3—22no—
958C22×C3—21no—
959C22×C3—34no—
960C22×C3—34no—
961C22×C3—42no—
962C22×C3—42no—
963C22×C3—42no—
964C22×C3—44no—
965C22×C3—44no—
966C22×C3—68no—
967C22×C3—62no—
968C22×C3—64no—
969C22×C3—62no—
970C22×C3—62no—
971C22×C3—62no—
972C22×C3—62no—
973C22×C3—64no—
974C22×C3—62no—
975C22×C3—84no—
976C22×C3—124no—
977C22×C3—128no—
978C22×C3—128no—
979C22×C3—124no—
980C22×C3—242no—
981C22×C3C22×D1212yes—
982C22×C3C22×D1212yes—
983C22×C3C22×D1212yes—
984C22×C3C2×D3×D412yes—
985C22×C3C2×D3×D412yes—
986C22×C3C2×D3×D412yes—
987C22×C3C24×D311yescharacteristic
988C22×C3C24×D311yescharacteristic
989C2×D3—28no—
990C2×D3—22no—
991C2×D3—22no—
992C2×D3—24no—
993C2×D3—22no—
994C2×D3—22no—
995C2×D3—24no—
996C2×D3—22no—
997C2×D3—22no—
998C2×D3—44no—
999C2×D3—48no—
1000C2×D3—48no—
1001C2×D3—44no—
1002C2×D3—62no—
1003C2×D3—62no—
1004C2×D3—62no—
1005C2×D3—62no—
1006C2×D3—64no—
1007C2×D3—64no—
1008C2×D3—64no—
1009C2×D3—64no—
1010C2×D3—82no—
1011C2×D3—124no—
1012C2×D3—124no—
1013C2×D3—122no—
1014C2×D3—122no—
1015C2×D3—1216no—
1016C2×D3—1216no—
1017C2×D3—124no—
1018C2×D3—124no—
1019C2×D3—244no—
1020C2×D3—244no—
1021C2×D3—244no—
1022C2×D3—242no—
1023C2×D3—242no—
1024C2×D3—244no—
1025C2×D3C22×D1214yes—
1026C2×D3#100414yescomplemented
1027C3×C4—24no—
1028C3×C4—24no—
1029C3×C4—34no—
1030C3×C4—44no—
1031C3×C4—62no—
1032C3×C4—64no—
1033Dic3—22no—
1034Dic3—24no—
1035Dic3—62no—
1036Dic3—62no—
1037Dic3—62no—
1038Dic3—62no—
1039Dic3—122no—
1040Dic3—122no—
1041Dic3C22×D1214yes—
1042C32#348411yescharacteristic, complemented, Sylow
1043C23—32no—
1044C23—32no—
1045C23—34no—
1046C23—32no—
1047C23—32no—
1048C23—42no—
1049C23—64no—
1050C23—64no—
1051C23—64no—
1052C23—62no—
1053C23—64no—
1054C23—64no—
1055C23—62no—
1056C23—62no—
1057C23—92no—
1058C23—92no—
1059C23—122no—
1060C23—122no—
1061C23—122no—
1062C23—122no—
1063C23—122no—
1064C23—1216no—
1065C23—188no—
1066C23—188no—
1067C23—184no—
1068C23—182no—
1069C23—182no—
1070C23—362no—
1071C23—362no—
1072C23—364no—
1073C23—364no—
1074C23—3616no—
1075C23D3×D1214yescomplemented
1076C23C22×D3211yescharacteristic
1077C23C22×D3211yescharacteristic
1078C23C22×D3211yescharacteristic
1079Q8—184no—
1080D4—38no—
1081D4—38no—
1082D4—68no—
1083D4—64no—
1084D4—64no—
1085D4—124no—
1086D4—188no—
1087D4—184no—
1088D4—184no—
1089D4—188no—
1090D4—188no—
1091D4—184no—
1092D4—184no—
1093D4—184no—
1094D4—184no—
1095D4—184no—
1096D4—364no—
1097D4—364no—
1098D4—364no—
1099C2×C4—34no—
1100C2×C4—32no—
1101C2×C4—34no—
1102C2×C4—32no—
1103C2×C4—42no—
1104C2×C4—62no—
1105C2×C4—92no—
1106C2×C4—92no—
1107C2×C4—124no—
1108C2×C4—122no—
1109C2×C4—184no—
1110C2×C4—188no—
1111C2×C4—184no—
1112C2×C4—184no—
1113C2×C4—182no—
1114C2×C4—182no—
1115C2×C4C22×D3214yes—
1116C2×C3—22no—
1117C2×C3—22no—
1118C2×C3—22no—
1119C2×C3—22no—
1120C2×C3—22no—
1121C2×C3—22no—
1122C2×C3—21no—
1123C2×C3—22no—
1124C2×C3—42no—
1125C2×C3—42no—
1126C2×C3—42no—
1127C2×C3—64no—
1128C2×C3—64no—
1129C2×C3—122no—
1130C2×C3—122no—
1131C2×C3C23×D1211yescharacteristic
1132C2×C3C22×D3×D411yescharacteristic
1133C2×C3C2×#100412yes—
1134C2×C3D3×H(5,𝔽2)12yes—
1135D3—24no—
1136D3—24no—
1137D3—42no—
1138D3—42no—
1139D3—122no—
1140D3—122no—
1141D3—122no—
1142D3—122no—
1143D3—242no—
1144D3—242no—
1145C22—22no—
1146C22—22no—
1147C22—22no—
1148C22—34no—
1149C22—34no—
1150C22—44no—
1151C22—68no—
1152C22—62no—
1153C22—64no—
1154C22—62no—
1155C22—62no—
1156C22—62no—
1157C22—64no—
1158C22—62no—
1159C22—62no—
1160C22—124no—
1161C22—128no—
1162C22—128no—
1163C22—124no—
1164C22—182no—
1165C22—182no—
1166C22—184no—
1167C22—184no—
1168C22—242no—
1169C22—364no—
1170C22—3616no—
1171C22—722no—
1172C22—724no—
1173C22C2×D3×D1212yes—
1174C22C2×D3×D1212yes—
1175C22C2×D3×D1212yes—
1176C22C23×D3211yescharacteristic
1177C4—24no—
1178C4—34no—
1179C4—62no—
1180C4—64no—
1181C4—182no—
1182C4—182no—
1183C3—21no—
1184C3#8586711yescharacteristic, complemented
1185C3#8591911yescharacteristic, complemented
1186C2—22no—
1187C2—22no—
1188C2—22no—
1189C2—64no—
1190C2—64no—
1191C2—122no—
1192C2—122no—
1193C2—362no—
1194C2—362no—
1195C2C22×D3×D1211yescharacteristic
1196C2D3×#100412yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#3484
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64330C2semidirect
2. C22×D3×#67C2semidirect
3. #10595964C2semidirect
4. C2×C3×#882C2semidirect
5. C3×#5486C2semidirect
6. #10595519C2semidirect
7. C2×#63977C2semidirect
8. #10595073C2semidirect
9. D12×#67C2semidirect
10. #10594292C2semidirect
11. #10594290C2semidirect
12. #10594277C2semidirect
13. D3×#882C2semidirect
14. #10594080C2semidirect
15. #10594078C2semidirect
18. C24×C3×D3C22semidirect
19. C23×D32C22semidirect
20. C22×#638C22semidirect
21. C22×#638C22semidirect
23. C22×C3×#67C22semidirect
24. C22×C3×D12C22semidirect
26. C2×#3811C22semidirect
28. C2×D3×#67C22semidirect
29. C2×D3×#67C22semidirect
30. C2×D3×#67C22semidirect
31. C2×D3×#67C22semidirect
32. C22×#626C22semidirect
33. C22×#626C22semidirect
34. C22×#625C22semidirect
35. C2×#3805C22semidirect
36. C2×#3804C22semidirect
37. C2×#3804C22semidirect
38. C22×D3×Dic3C22semidirect
39. C2×D3×D12C22semidirect
40. C2×C32×C22⋊C4C22semidirect
41. #64139C22semidirect
42. #64095C22semidirect
43. #64095C22semidirect
44. #64091C22semidirect
45. #64091C22semidirect
46. C2×C3×#217C22semidirect
47. C3×C4×#67C22semidirect
48. C2×C3×(C2×D3)⋊C4C22semidirect
49. C3×#882C22semidirect
50. C3×#882C22semidirect
51. C3×#882C22semidirect
52. C3×#67⋊C4C22semidirect
53. C3×D3×C22⋊C4C22semidirect
54. C3×#877C22semidirect
55. #63981C22semidirect
56. #63978C22semidirect
57. #63977C22semidirect
58. #63977C22semidirect
59. #63977C22semidirect
60. #63977C22semidirect
61. #63966C22semidirect
62. #63962C22semidirect
63. C2×(C2×D3)⋊Dic3C22semidirect
64. #63923C22semidirect
65. #63922C22semidirect
66. #63922C22semidirect
67. D3×(C2×D3)⋊C4C22semidirect
68. #63911C22semidirect
69. #63910C22semidirect
70. #63908C22semidirect
71. #63906C22semidirect
72. #63893C22semidirect
73. Dic3×D12C22semidirect
74. #63891C22semidirect
75. #63886C22semidirect
76. #63886C22semidirect
77. #63880C22semidirect
78. #63852C22semidirect
108. C2×#882D3semidirect
109. #5486D3semidirect
112. C23×C3⋊D3C23semidirect
120. C23×C3×D3C23semidirect
124. C22×D32C23semidirect
125. C22×C32×C4C23semidirect
131. C2×#638C23semidirect
133. C22×C3⋊Dic3C23semidirect
134. C2×C4⋊(C3⋊D3)C23semidirect
136. C2×C3×#67D4semidirect
140. C2×C3×#67C23semidirect
142. C22×C3×Dic3C23semidirect
143. C22×C3×Dic3C23semidirect
146. C2×C3×D12C23semidirect
147. C2×C3×C4×D3C23semidirect
153. C2×#627C23semidirect
158. C2×#626C23semidirect
159. C2×#626C23semidirect
160. C2×#626C23semidirect
161. C2×#626C23semidirect
164. C2×#625C23semidirect
165. C2×#624C23semidirect
171. C2×D3×Dic3C23semidirect
172. C2×D3×Dic3C23semidirect
175. C32×C22⋊C4C23semidirect
176. #3752C23semidirect
177. #3752C23semidirect
178. C4⋊(C3⋊Dic3)C23semidirect
180. C3×#217C23semidirect
182. C3×(C2×D3)⋊C4C23semidirect
183. C3×(C2×D3)⋊C4C23semidirect
184. C3×Dic3⋊C4C23semidirect
185. C3×C4×Dic3C23semidirect
186. Dic3⋊Dic3C23semidirect
187. #3722C23semidirect
189. (C2×D3)⋊Dic3C23semidirect
190. (C2×D3)⋊Dic3C23semidirect
195. C24×D3C2×D3semidirect
215. C22×#67C2×D3semidirect
236. C22×D12C2×D3semidirect
248. C2×C3×C22⋊C4C2×D3semidirect
249. C2×C3×C22⋊C4C2×D3semidirect
255. C2×#217C2×D3semidirect
273. C4×#67C2×D3semidirect
276. C2×(C2×D3)⋊C4C2×D3semidirect
309. #882C2×D3semidirect
310. #882C2×D3semidirect
311. #882C2×D3semidirect
313. #67⋊C4C2×D3semidirect
315. D3×C22⋊C4C2×D3semidirect
317. #877C2×D3semidirect
323. C23×C32C2×D4semidirect
347. C22×C3×D3C2×D4semidirect
371. C3×#67C2×D4semidirect
372. C3×#67C2×D4semidirect
375. C2×C3×Dic3C2×D4semidirect
442. C23×D3C22×D3semidirect
457. C22×C3×C4C22×D3semidirect
458. C22×C3×C4C22×D3semidirect
496. C2×#67D12semidirect
500. C2×#67C22×D3semidirect
512. C22×Dic3C22×D3semidirect
513. C22×Dic3C22×D3semidirect
541. C2×D12C22×D3semidirect
548. C2×C4×D3C22×D3semidirect
561. C3×C22⋊C4C22×D3semidirect
562. C3×C22⋊C4C22×D3semidirect
568. #217C22×D3semidirect
581. (C2×D3)⋊C4C22×D3semidirect
582. (C2×D3)⋊C4C22×D3semidirect
588. Dic3⋊C4C22×D3semidirect
589. C4×Dic3C22×D3semidirect
619. C2×C3×D3H(5,𝔽2)semidirect
688. C2×C22⋊C4D32semidirect
715. C23×C3C2×D12semidirect
716. C23×C3D3×D4semidirect
767. C22×D3C2×D12semidirect
815. #67C2×D12semidirect
816. #67C2×D12semidirect
834. C2×Dic3C2×D12semidirect
931. C22×C4C2×D32semidirect
947. C22⋊C4C2×D32semidirect
1026. C2×D3#1004semidirect
1042. C32#3484semidirect
1075. C23D3×D12semidirect
1184. C3#85867semidirect
1185. C3#85919semidirect

Maximal subgroups

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

subgroupindex
C2×#643302
C22×D3×#672
#105959642
C2×C3×#8822
C3×#54862
#105955192
C2×#639772
#105950732
D12×#672
#105942922
#105942902
#105942772
D3×#8822
#105940802
#105940782
#859193
#858673