Finite Group Databasebeta

← #11904326

Subgroups — #11904326

Order 1152.

4131 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64330C211yesmaximal, characteristic, complemented
2C22×#3811C211yesmaximal, characteristic, complemented
3C2×#64091C211yesmaximal, characteristic, complemented
4C3×#5493C211yesmaximal, characteristic, complemented
5C3×#5486C211yesmaximal, characteristic, complemented
6#10595519C211yesmaximal, characteristic, complemented
7C2×#63981C211yesmaximal, characteristic, complemented
8#10595075C214yesmaximal, complemented
9#10595074C214yesmaximal, complemented
10#10594293C214yesmaximal, complemented
11#10594291C212yesmaximal, complemented
12#10594277C214yesmaximal, complemented
13D3×#882C212yesmaximal, complemented
14#10594080C212yesmaximal, complemented
15#10594079C212yesmaximal, complemented
16#86308—31nomaximal
17#85867—31nomaximal
18C24×C3⋊D3C2211yescharacteristic, complemented
19C23×D32C2211yescharacteristic, complemented
20C22×#638C2211yescharacteristic, complemented
21C22×C4⋊(C3⋊D3)C2212yescomplemented
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic, complemented
24C22×C3×#67C2211yescharacteristic, complemented
25#64330—28no—
26C2×#3811—28no—
27C2×#3811C2214yescomplemented
28C2×#3811C2214yescomplemented
29C2×#3811C2212yescomplemented
30C2×D3×#67C2212yescomplemented
31C2×D3×#67C2212yescomplemented
32C22×#626C2211yescharacteristic, complemented
33C22×#626C2211yescharacteristic, complemented
34C22×#626C2212yescomplemented
35C22×#624C2211yescharacteristic, complemented
36C2×#3805C2212yescomplemented
37C2×#3804C2212yescomplemented
38C2×#3804C2212yescomplemented
39C2×D3×D12C2214yescomplemented
40C2×C32×C22⋊C4C2211yescharacteristic, complemented
41C2×#3752C2212yescomplemented
42#64091C2212yescomplemented
43#64091C2214yescomplemented
44#64091C2212yescomplemented
45C2×C3×#217C2211yescharacteristic, complemented
46C3×#930C2214yescomplemented
47C3×C4×#67C2214yescomplemented
48C3×#886C2212yescomplemented
49C3×#886C2212yescomplemented
50C3×#882C2212yescomplemented
51C3×#882C2212yescomplemented
52C3×#67⋊C4C2214yescomplemented
53C3×D3×C22⋊C4C2212yescomplemented
54C3×#877C2212yescomplemented
55#63981C2212yescomplemented
56#63981C2214yescomplemented
57#63981C2212yescomplemented
58#63981C2212yescomplemented
59#63978C2214yescomplemented
60#63977C2212yescomplemented
61#63966C2212yescomplemented
62C2×#3722C2212yescomplemented
63#63962C2212yescomplemented
64#63923C2214yescomplemented
65#63923C2214yescomplemented
66#63922C2214yescomplemented
67D3×(C2×D3)⋊C4C2214yescomplemented
68#63911C2214yescomplemented
69#63910C2214yescomplemented
70#63910C2214yescomplemented
71#63909C2214yescomplemented
72#63906C2214yescomplemented
73#63895C2214yescomplemented
74#63894C2214yescomplemented
75#63890C2214yescomplemented
76#63886C2214yescomplemented
77#63880C2214yescomplemented
78#63852C2214yescomplemented
79C2×#1004—31no—
80C2×#1004—31no—
81C22×D3×D4—31no—
82C22×D3×D4—31no—
83C3×#534—31no—
84C3×#518—31no—
85#5804—31no—
86C2×#937—31no—
87#5656—32no—
88#5654—34no—
89#5653—32no—
90#5610—34no—
91#5609—34no—
92#5592—32no—
93#5590—34no—
94D3×#120—32no—
95#5554—34no—
96#5554—34no—
97D4×D12—34no—
98D4×D12—34no—
99#5525—32no—
100#5524—32no—
101#5493—31no—
102#5493—32no—
103#5493D311yescharacteristic, complemented
104C2×#882—31no—
105C2×#882—31no—
106C2×#882—31no—
107C2×#882—32no—
108C2×#882—61no—
109#5486D311yescharacteristic, complemented
110C24×C32C2311yescharacteristic
111C23×C3⋊D3—24no—
112C23×C3⋊D3—44no—
113C23×C3⋊D3C2311yescharacteristic
114C23×C3⋊D3C2312yes—
115C23×C3⋊D3C2312yes—
116C23×C3⋊D3C2311yescharacteristic
117C23×C3⋊D3C2311yescharacteristic, complemented
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×#638C2312yes—
128C2×#638C2312yescomplemented
129C22×C3⋊Dic3C2311yescharacteristic, complemented
130C2×C4⋊(C3⋊D3)—44no—
131C2×C4⋊(C3⋊D3)C2314yes—
132C2×C4⋊(C3⋊D3)C2314yescomplemented
133C2×C3×#67—24no—
134C2×C3×#67—24no—
135C2×C3×#67D418yescomplemented
136C2×C3×#67C2312yes—
137C2×C3×#67C2312yes—
138C2×C3×#67C2312yes—
139C2×C3×#67C2312yes—
140C2×C3×#67C2312yes—
141C2×C3×#67C2312yescomplemented
142C22×C3×Dic3C2311yescharacteristic
143C22×C3×Dic3C2311yescharacteristic
144C22×C3×Dic3C2311yescharacteristic, complemented
145C22×C3×Dic3C2312yescomplemented
146C2×C3×D12C2314yescomplemented
147C2×C3×C4×D3C2314yescomplemented
148#3811—216no—
149#3811—216no—
150#3811—28no—
151D3×#67—28no—
152D3×#67—28no—
153C2×#627C2312yescomplemented
154C2×#626—24no—
155C2×#626—24no—
156C2×#626—44no—
157C2×#626C2314yes—
158C2×#626C2314yes—
159C2×#626C2314yes—
160C2×#626C2312yescomplemented
161C2×#626C2312yescomplemented
162C2×#626C2314yescomplemented
163C2×#626C2314yescomplemented
164C2×#625C2312yescomplemented
165C2×#624—24no—
166C2×#624C2314yes—
167C2×#624C2312yescomplemented
168#3805—28no—
169#3804—28no—
170#3804—28no—
171C2×D3×Dic3C2312yescomplemented
172C2×D3×Dic3C2312yescomplemented
173D3×D12—48no—
174C32×C22⋊C4C2312yes—
175C32×C22⋊C4C2312yescomplemented
176#3752C2314yes—
177#3752C2314yescomplemented
178C3×#217C2312yes—
179C3×#217C2312yescomplemented
180C3×(C2×D3)⋊C4C2314yescomplemented
181C3×(C2×D3)⋊C4C2314yescomplemented
182C3×(C2×D3)⋊C4C2314yescomplemented
183C3×C4⋊Dic3C2314yescomplemented
184C3×Dic3⋊C4C2314yescomplemented
185C3×C4×Dic3C2314yescomplemented
186Dic3⋊Dic3C2314yescomplemented
187#3722C2314yes—
188#3722C2314yescomplemented
189#3722C2314yescomplemented
190(C2×D3)⋊Dic3C2314yescomplemented
191#3484—91noSylow
192C24×D3—31no—
193C24×D3—31no—
194C24×D3—31no—
195C24×D3—31no—
196C24×D3—61no—
197C22×C3×D4—31no—
198C22×C3×D4—31no—
199C22×C3×D4—31no—
200C22×#67—31no—
201C22×#67—31no—
202C22×#67—32no—
203C22×#67—32no—
204C22×#67—31no—
205C22×#67—31no—
206C22×#67—32no—
207C22×#67—61no—
208C22×#67C2×D311yescharacteristic
209C22×#67C2×D311yescharacteristic, complemented
210C22×#67C2×D311yescharacteristic, complemented
211#1004—68no—
212#1004—68no—
213C2×#237—32no—
214C2×#237—32no—
215C2×#237—32no—
216C2×#237—32no—
217C2×D3×D4—32no—
218C2×D3×D4—32no—
219C2×D3×D4—34no—
220C2×D3×D4—34no—
221C2×D3×D4—34no—
222C2×D3×D4—34no—
223C2×D3×D4—32no—
224C2×D3×D4—32no—
225C2×D3×D4—34no—
226C2×D3×D4—68no—
227C2×D3×D4—68no—
228C2×#235—32no—
229C2×#235—32no—
230C22×D12—31no—
231C22×D12—31no—
232C22×D12—32no—
233C22×D12—32no—
234C22×D12—32no—
235C22×D12—34no—
236C22×D12—62no—
237C22×C4×D3—31no—
238C22×C4×D3—31no—
239C3×#123—32no—
240C3×#123—32no—
241C3×#121—34no—
242C3×#120—32no—
243C3×#120—32no—
244C3×C4×D4—34no—
245C3×C4×D4—34no—
246C3×#117—32no—
247C2×C3×C22⋊C4—21no—
248C2×C3×C22⋊C4—31no—
249C2×C3×C22⋊C4—32no—
250C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
251C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
252#953—32no—
253C2×#217C2×D311yescharacteristic, complemented
254#940—34no—
255#939—34no—
256#939—34no—
257#937—32no—
258#937—32no—
259#937—34no—
260#937—32no—
261#937—34no—
262#935—32no—
263#930—34no—
264#930—34no—
265#930—34no—
266#930C2×D314yescomplemented
267#929—32no—
268C4×#67C2×D314yescomplemented
269C2×(C2×D3)⋊C4—32no—
270C2×(C2×D3)⋊C4—32no—
271C2×(C2×D3)⋊C4—32no—
272C2×(C2×D3)⋊C4—32no—
273C2×(C2×D3)⋊C4—34no—
274C2×(C2×D3)⋊C4—62no—
275#897—34no—
276#896—34no—
277#895—34no—
278#895—34no—
279#895—34no—
280#895—34no—
281#894—34no—
282#893—34no—
283#886—32no—
284#886—32no—
285#886—34no—
286#886C2×D312yescomplemented
287#886C2×D312yescomplemented
288#885—34no—
289#884—34no—
290#884—34no—
291#884—34no—
292#882—32no—
293#882—32no—
294#882—32no—
295#882—32no—
296#882—34no—
297#882—34no—
298#882—32no—
299#882—32no—
300#882—32no—
301#882—32no—
302#882—34no—
303#882—34no—
304#882—34no—
305#882—34no—
306#882—34no—
307#882—34no—
308#882—62no—
309#882—62no—
310#882—64no—
311#882C2×D312yescomplemented
312#882C2×D312yescomplemented
313#67⋊C4—34no—
314#67⋊C4C2×D314yescomplemented
315D3×C22⋊C4—34no—
316D3×C22⋊C4C2×D312yescomplemented
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—24no—
328C22×C3⋊D3—22no—
329C22×C3⋊D3—24no—
330C22×C3⋊D3—22no—
331C22×C3⋊D3—24no—
332C22×C3⋊D3—24no—
333C22×C3⋊D3—22no—
334C22×C3⋊D3—24no—
335C22×C3⋊D3—42no—
336C22×C3⋊D3—42no—
337C22×C3⋊D3—42no—
338C22×C3⋊D3—42no—
339C22×C3⋊D3—416no—
340C22×C3⋊D3C2412yes—
341C22×C3⋊D3C2412yes—
342C22×C3⋊D3C2412yes—
343C22×C3×D3—22no—
344C22×C3×D3—22no—
345C22×C3×D3—42no—
346C22×C3×D3—42no—
347C22×C3×D3—42no—
348C22×C3×D3C2×D414yescomplemented
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—
362C2×C3⋊Dic3—22no—
363C2×C3⋊Dic3C2412yes—
364C4⋊(C3⋊D3)—28no—
365C4⋊(C3⋊D3)—44no—
366C3×#67—24no—
367C3×#67—24no—
368C3×#67—24no—
369C3×#67—24no—
370C3×#67C2×D418yescomplemented
371C3×#67C2×D418yescomplemented
372C2×C3×Dic3—22no—
373C2×C3×Dic3—22no—
374C2×C3×Dic3—42no—
375C2×C3×Dic3C2×D414yescomplemented
376C2×C3×Dic3C2414yes—
377C2×C3×Dic3C2412yes—
378C2×C3×Dic3C2412yes—
379C2×C3×Dic3C2412yes—
380C3×D12—44no—
381C3×C4×D3—44no—
382#627—24no—
383#626—28no—
384#626—24no—
385#626—28no—
386#626—24no—
387#626—28no—
388#626—44no—
389#626—44no—
390#625—24no—
391#624—24no—
392#624—28no—
393D3×Dic3—24no—
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—31no—
403#534—92no—
404#534—91no—
405#525—92no—
406C2×#120—92no—
407C2×#120—91no—
408C2×#120—91no—
409#518—31no—
410C24×C3—21no—
411C24×C3—31no—
412C24×C3—31no—
413C24×C3—31no—
414C24×C3C22×D311yescharacteristic
415C24×C3C22×D311yescharacteristic
416C23×D3—31no—
417C23×D3—31no—
418C23×D3—32no—
419C23×D3—32no—
420C23×D3—32no—
421C23×D3—32no—
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—62no—
431C23×D3—61no—
432C23×D3—62no—
433C23×D3—61no—
434C23×D3—61no—
435C23×D3—64no—
436C23×D3—64no—
437C23×D3—64no—
438C23×D3—64no—
439C23×D3—124no—
440C23×D3—124no—
441C23×D3—124no—
442C23×D3—124no—
443C23×D3—124no—
444C23×D3—128no—
445C23×D3C22×D311yescharacteristic
446C23×D3C22×D311yescharacteristic
447C23×D3C22×D311yescharacteristic, complemented
448C2×C3×D4—38no—
449C2×C3×D4—32no—
450C2×C3×D4—32no—
451C2×C3×D4—32no—
452C2×C3×D4—32no—
453C2×C3×D4—32no—
454C2×C3×D4—32no—
455C2×C3×D4—34no—
456C2×C3×D4—64no—
457C2×C3×D4—64no—
458C22×C3×C4—22no—
459C22×C3×C4—31no—
460C22×C3×C4—31no—
461C22×C3×C4—31no—
462C22×C3×C4—32no—
463C22×C3×C4—34no—
464C22×C3×C4C22×D312yescomplemented
465C22×C3×C4C22×D312yescomplemented
466C2×#67—24no—
467C2×#67—24no—
468C2×#67—32no—
469C2×#67—32no—
470C2×#67—32no—
471C2×#67—32no—
472C2×#67—32no—
473C2×#67—32no—
474C2×#67—34no—
475C2×#67—32no—
476C2×#67—34no—
477C2×#67—32no—
478C2×#67—34no—
479C2×#67—34no—
480C2×#67—34no—
481C2×#67—62no—
482C2×#67—62no—
483C2×#67—64no—
484C2×#67—68no—
485C2×#67—64no—
486C2×#67—64no—
487C2×#67—68no—
488C2×#67—64no—
489C2×#67—124no—
490C2×#67—124no—
491C2×#67D1218yescomplemented
492C2×#67C22×D312yes—
493C2×#67C22×D312yes—
494C2×#67C22×D312yes—
495C2×#67C22×D312yes—
496C2×#67C22×D312yes—
497C2×#67C22×D312yescomplemented
498C22×Dic3—31no—
499C22×Dic3—31no—
500C22×Dic3—32no—
501C22×Dic3—32no—
502C22×Dic3—61no—
503C22×Dic3C22×D311yescharacteristic
504C22×Dic3C22×D311yescharacteristic
505C22×Dic3C22×D311yescharacteristic, complemented
506C22×Dic3C22×D312yescomplemented
507#237—68no—
508#237—68no—
509#237—68no—
510#237—68no—
511D3×D4—616no—
512D3×D4—616no—
513D3×D4—68no—
514D3×D4—68no—
515D3×D4—68no—
516D3×D4—616no—
517D3×D4—616no—
518D3×D4—68no—
519D3×D4—128no—
520#235—68no—
521#235—68no—
522C2×D12—34no—
523C2×D12—32no—
524C2×D12—34no—
525C2×D12—32no—
526C2×D12—34no—
527C2×D12—34no—
528C2×D12—34no—
529C2×D12—34no—
530C2×D12—34no—
531C2×D12—34no—
532C2×D12—34no—
533C2×D12—64no—
534C2×D12—64no—
535C2×D12—64no—
536C2×D12—64no—
537C2×D12—128no—
538C2×D12—124no—
539C2×D12—124no—
540C2×D12—124no—
541C2×D12—128no—
542C2×D12C22×D314yescomplemented
543C2×C4×D3—32no—
544C2×C4×D3—32no—
545C2×C4×D3—32no—
546C2×C4×D3—34no—
547C2×C4×D3—34no—
548C2×C4×D3—32no—
549C2×C4×D3—64no—
550C2×C4×D3—64no—
551C2×C4×D3C22×D314yescomplemented
552C2×Dic6—32no—
553C2×Dic6—32no—
554C3×C4⋊C4—34no—
555C3×C4⋊C4—34no—
556C3×C22⋊C4—22no—
557C3×C22⋊C4—22no—
558C3×C22⋊C4—32no—
559C3×C22⋊C4—32no—
560C3×C22⋊C4—34no—
561C3×C22⋊C4—34no—
562C3×C22⋊C4—34no—
563C3×C22⋊C4C22×D312yes—
564C3×C22⋊C4C22×D312yes—
565C3×C22⋊C4C22×D312yescomplemented
566C3×C22⋊C4C22×D312yescomplemented
567C3×C42—34no—
568#217—34no—
569#217C22×D312yes—
570#217C22×D312yescomplemented
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—34no—
579(C2×D3)⋊C4—34no—
580(C2×D3)⋊C4—34no—
581(C2×D3)⋊C4—34no—
582(C2×D3)⋊C4—64no—
583(C2×D3)⋊C4—64no—
584(C2×D3)⋊C4C22×D314yescomplemented
585(C2×D3)⋊C4C22×D314yescomplemented
586(C2×D3)⋊C4C22×D314yescomplemented
587C4⋊Dic3—34no—
588C4⋊Dic3C22×D314yescomplemented
589Dic3⋊C4—34no—
590Dic3⋊C4C22×D314yescomplemented
591C4×Dic3C22×D314yescomplemented
592C22×C32—22no—
593C22×C32—22no—
594C22×C32—22no—
595C22×C32—44no—
596C22×C32C22×D412yes—
597C22×C32C22×D412yes—
598C22×C32C22×D412yes—
599C22×C32C2511yescharacteristic
600C2×C3⋊D3—22no—
601C2×C3⋊D3—28no—
602C2×C3⋊D3—22no—
603C2×C3⋊D3—22no—
604C2×C3⋊D3—22no—
605C2×C3⋊D3—22no—
606C2×C3⋊D3—22no—
607C2×C3⋊D3—24no—
608C2×C3⋊D3—48no—
609C2×C3⋊D3—48no—
610C2×C3⋊D3—44no—
611C2×C3⋊D3—82no—
612C2×C3⋊D3H(5,𝔽2)14yescomplemented
613C2×C3×D3—24no—
614C2×C3×D3—22no—
615C2×C3×D3—22no—
616C2×C3×D3—24no—
617C2×C3×D3—24no—
618C2×C3×D3—44no—
619C2×C3×D3—44no—
620C2×C3×D3—82no—
621C2×C3×D3C22×D414yes—
622D32—416no—
623D32—84no—
624C32×C4—24no—
625C3⋊Dic3—22no—
626C3×Dic3—22no—
627C3×Dic3—22no—
628C3×Dic3—24no—
629C3×Dic3C22×D414yes—
630C25—91no—
631C25—91no—
632H(5,𝔽2)—188no—
633C2×#41—92no—
634C2×#41—92no—
635C2×#41—92no—
636C22×D4—31no—
637C22×D4—31no—
638C22×D4—31no—
639C22×D4—94no—
640C22×D4—91no—
641C22×D4—91no—
642C22×D4—92no—
643C22×D4—92no—
644C22×D4—94no—
645C22×D4—94no—
646C22×D4—92no—
647C22×D4—92no—
648C22×D4—91no—
649C22×D4—92no—
650C22×D4—188no—
651C23×C4—91no—
652#127—94no—
653#124—94no—
654#123—32no—
655#123—32no—
656#123—94no—
657#123—92no—
658#123—92no—
659C22⋊Q8—94no—
660#121—34no—
661#121—94no—
662#121—94no—
663#121—94no—
664#121—94no—
665#121—94no—
666#121—94no—
667#120—32no—
668#120—32no—
669#120—94no—
670#120—94no—
671#120—92no—
672#120—92no—
673#120—94no—
674#120—94no—
675#120—92no—
676#120—92no—
677#120—92no—
678#120—92no—
679#120—94no—
680C4×D4—34no—
681C4×D4—34no—
682C4×D4—94no—
683C4×D4—94no—
684#117—32no—
685C2×C22⋊C4—31no—
686C2×C22⋊C4—32no—
687C2×C22⋊C4—94no—
688C2×C22⋊C4—92no—
689C2×C22⋊C4—92no—
690C2×C22⋊C4D3211yescharacteristic, complemented
691C23×C3—21no—
692C23×C3—21no—
693C23×C3—21no—
694C23×C3—24no—
695C23×C3—32no—
696C23×C3—34no—
697C23×C3—32no—
698C23×C3—32no—
699C23×C3—42no—
700C23×C3—42no—
701C23×C3—44no—
702C23×C3—62no—
703C23×C3—62no—
704C23×C3—122no—
705C23×C3—122no—
706C23×C3—122no—
707C23×C3C2×D1214yescomplemented
708C23×C3D3×D414yescomplemented
709C23×C3C23×D311yescharacteristic
710C23×C3C23×D311yescharacteristic
711C23×C3C23×D311yescharacteristic
712C23×C3C23×D311yescharacteristic
713C23×C3C23×D311yescharacteristic
714C23×C3C23×D311yescharacteristic
715C22×D3—22no—
716C22×D3—22no—
717C22×D3—32no—
718C22×D3—32no—
719C22×D3—32no—
720C22×D3—32no—
721C22×D3—32no—
722C22×D3—32no—
723C22×D3—42no—
724C22×D3—42no—
725C22×D3—42no—
726C22×D3—62no—
727C22×D3—62no—
728C22×D3—62no—
729C22×D3—68no—
730C22×D3—68no—
731C22×D3—68no—
732C22×D3—64no—
733C22×D3—64no—
734C22×D3—64no—
735C22×D3—64no—
736C22×D3—64no—
737C22×D3—64no—
738C22×D3—64no—
739C22×D3—62no—
740C22×D3—62no—
741C22×D3—68no—
742C22×D3—62no—
743C22×D3—64no—
744C22×D3—64no—
745C22×D3—62no—
746C22×D3—64no—
747C22×D3—64no—
748C22×D3—62no—
749C22×D3—62no—
750C22×D3—68no—
751C22×D3—64no—
752C22×D3—124no—
753C22×D3—124no—
754C22×D3—122no—
755C22×D3—124no—
756C22×D3—122no—
757C22×D3—124no—
758C22×D3—122no—
759C22×D3—124no—
760C22×D3—124no—
761C22×D3—124no—
762C22×D3—124no—
763C22×D3—1216no—
764C22×D3—1216no—
765C22×D3—122no—
766C22×D3—122no—
767C22×D3—122no—
768C22×D3—122no—
769C22×D3—122no—
770C22×D3—122no—
771C22×D3—122no—
772C22×D3—122no—
773C22×D3—124no—
774C22×D3—124no—
775C22×D3—1216no—
776C22×D3—1216no—
777C22×D3—124no—
778C22×D3—1232no—
779C22×D3—124no—
780C22×D3C2×D1214yescomplemented
781C22×D3C23×D312yes—
782C22×D3C23×D312yes—
783C22×D3C23×D312yes—
784C3×D4—38no—
785C3×D4—38no—
786C3×D4—64no—
787C3×D4—64no—
788C3×D4—64no—
789C3×D4—64no—
790C3×D4—124no—
791C2×C3×C4—24no—
792C2×C3×C4—34no—
793C2×C3×C4—32no—
794C2×C3×C4—32no—
795C2×C3×C4—34no—
796C2×C3×C4—32no—
797C2×C3×C4—42no—
798C2×C3×C4—42no—
799C2×C3×C4—44no—
800C2×C3×C4—62no—
801C2×C3×C4—62no—
802C2×C3×C4—124no—
803C2×C3×C4—122no—
804C2×C3×C4C23×D314yes—
805C2×C3×C4C23×D314yes—
806#67—24no—
807#67—24no—
808#67—24no—
809#67—24no—
810#67—68no—
811#67—68no—
812#67—64no—
813#67—64no—
814#67—64no—
815#67—64no—
816#67—64no—
817#67—64no—
818#67—64no—
819#67—68no—
820#67—64no—
821#67—124no—
822#67—124no—
823#67—124no—
824#67—124no—
825#67C2×D1218yescomplemented
826#67C2×D1218yescomplemented
827C2×Dic3—22no—
828C2×Dic3—22no—
829C2×Dic3—32no—
830C2×Dic3—32no—
831C2×Dic3—42no—
832C2×Dic3—62no—
833C2×Dic3—64no—
834C2×Dic3—62no—
835C2×Dic3—62no—
836C2×Dic3—64no—
837C2×Dic3—122no—
838C2×Dic3C2×D1214yescomplemented
839C2×Dic3C23×D314yes—
840C2×Dic3C23×D312yes—
841C2×Dic3C23×D312yes—
842C2×Dic3C23×D312yes—
843D12—44no—
844D12—68no—
845D12—68no—
846D12—68no—
847D12—64no—
848D12—68no—
849D12—68no—
850D12—64no—
851D12—128no—
852D12—124no—
853D12—124no—
854D12—128no—
855D12—124no—
856D12—124no—
857C4×D3—44no—
858C4×D3—68no—
859C4×D3—64no—
860C4×D3—64no—
861C4×D3—64no—
862C4×D3—68no—
863C4×D3—64no—
864Dic6—64no—
865Dic6—64no—
866C2×C32—22no—
867C2×C32—22no—
868C2×C32—22no—
869C2×C32C23×D411yescharacteristic
870C2×C32C2×H(5,𝔽2)12yes—
871C3⋊D3—24no—
872C3⋊D3—42no—
873C3⋊D3—42no—
874C3×D3—24no—
875C3×D3—42no—
876C3×D3—42no—
877C24—31no—
878C24—31no—
879C24—31no—
880C24—94no—
881C24—92no—
882C24—91no—
883C24—92no—
884C24—92no—
885C24—91no—
886C24—91no—
887C24—184no—
888C24—184no—
889C24—364no—
890C24—364no—
891C24C2×D3211yescharacteristic
892#41—188no—
893#41—188no—
894#41—188no—
895C2×Q8—92no—
896C2×D4—32no—
897C2×D4—32no—
898C2×D4—38no—
899C2×D4—32no—
900C2×D4—32no—
901C2×D4—32no—
902C2×D4—32no—
903C2×D4—34no—
904C2×D4—64no—
905C2×D4—64no—
906C2×D4—94no—
907C2×D4—92no—
908C2×D4—94no—
909C2×D4—94no—
910C2×D4—92no—
911C2×D4—94no—
912C2×D4—94no—
913C2×D4—92no—
914C2×D4—92no—
915C2×D4—92no—
916C2×D4—94no—
917C2×D4—94no—
918C2×D4—184no—
919C2×D4—184no—
920C2×D4—1816no—
921C2×D4—1816no—
922C2×D4—188no—
923C2×D4—188no—
924C2×D4—188no—
925C2×D4—184no—
926C2×D4—364no—
927C2×D4—368no—
928C2×D4—364no—
929C22×C4—31no—
930C22×C4—31no—
931C22×C4—31no—
932C22×C4—32no—
933C22×C4—34no—
934C22×C4—92no—
935C22×C4—94no—
936C22×C4—92no—
937C22×C4—92no—
938C22×C4—91no—
939C22×C4—184no—
940C22×C4C2×D3212yescomplemented
941C4⋊C4—34no—
942C4⋊C4—34no—
943C4⋊C4—94no—
944C22⋊C4—32no—
945C22⋊C4—32no—
946C22⋊C4—34no—
947C22⋊C4—34no—
948C22⋊C4—34no—
949C22⋊C4—94no—
950C22⋊C4—94no—
951C22⋊C4—94no—
952C22⋊C4—94no—
953C22⋊C4—94no—
954C22⋊C4—94no—
955C22⋊C4C2×D3212yes—
956C22⋊C4C2×D3212yescomplemented
957C42—34no—
958C22×C3—24no—
959C22×C3—22no—
960C22×C3—22no—
961C22×C3—22no—
962C22×C3—22no—
963C22×C3—22no—
964C22×C3—22no—
965C22×C3—22no—
966C22×C3—22no—
967C22×C3—22no—
968C22×C3—21no—
969C22×C3—34no—
970C22×C3—42no—
971C22×C3—42no—
972C22×C3—44no—
973C22×C3—44no—
974C22×C3—48no—
975C22×C3—64no—
976C22×C3—62no—
977C22×C3—62no—
978C22×C3—64no—
979C22×C3—64no—
980C22×C3—124no—
981C22×C3—124no—
982C22×C3—242no—
983C22×C3C22×D1212yes—
984C22×C3C22×D1212yes—
985C22×C3C22×D1212yes—
986C22×C3C2×D3×D412yes—
987C22×C3C2×D3×D412yes—
988C22×C3C2×D3×D412yes—
989C22×C3C24×D311yescharacteristic
990C22×C3C24×D311yescharacteristic
991C2×D3—24no—
992C2×D3—22no—
993C2×D3—22no—
994C2×D3—24no—
995C2×D3—24no—
996C2×D3—34no—
997C2×D3—34no—
998C2×D3—44no—
999C2×D3—44no—
1000C2×D3—64no—
1001C2×D3—68no—
1002C2×D3—68no—
1003C2×D3—62no—
1004C2×D3—62no—
1005C2×D3—62no—
1006C2×D3—62no—
1007C2×D3—64no—
1008C2×D3—62no—
1009C2×D3—62no—
1010C2×D3—62no—
1011C2×D3—62no—
1012C2×D3—64no—
1013C2×D3—64no—
1014C2×D3—62no—
1015C2×D3—62no—
1016C2×D3—62no—
1017C2×D3—62no—
1018C2×D3—82no—
1019C2×D3—122no—
1020C2×D3—122no—
1021C2×D3—122no—
1022C2×D3—122no—
1023C2×D3—128no—
1024C2×D3—124no—
1025C2×D3—122no—
1026C2×D3—1216no—
1027C2×D3—1216no—
1028C2×D3—128no—
1029C2×D3—128no—
1030C2×D3—128no—
1031C2×D3—128no—
1032C2×D3—1216no—
1033C2×D3—124no—
1034C2×D3—124no—
1035C2×D3—1216no—
1036C2×D3—128no—
1037C2×D3—244no—
1038C2×D3—244no—
1039C2×D3—242no—
1040C2×D3—242no—
1041C2×D3—244no—
1042C2×D3C22×D1214yes—
1043C3×C4—24no—
1044C3×C4—24no—
1045C3×C4—34no—
1046C3×C4—44no—
1047C3×C4—62no—
1048C3×C4—62no—
1049C3×C4—64no—
1050Dic3—22no—
1051Dic3—22no—
1052Dic3—24no—
1053Dic3—62no—
1054Dic3—62no—
1055Dic3—122no—
1056Dic3C22×D1214yes—
1057C32#348411yescharacteristic, complemented, Sylow
1058C23—32no—
1059C23—34no—
1060C23—32no—
1061C23—32no—
1062C23—42no—
1063C23—62no—
1064C23—62no—
1065C23—92no—
1066C23—92no—
1067C23—92no—
1068C23—122no—
1069C23—122no—
1070C23—122no—
1071C23—184no—
1072C23—184no—
1073C23—184no—
1074C23—188no—
1075C23—184no—
1076C23—188no—
1077C23—182no—
1078C23—184no—
1079C23—184no—
1080C23—182no—
1081C23—182no—
1082C23—362no—
1083C23—362no—
1084C23—362no—
1085C23—362no—
1086C23—3616no—
1087C23—364no—
1088C23—364no—
1089C23—3616no—
1090C23D3×D1214yescomplemented
1091C23C22×D3211yescharacteristic
1092C23C22×D3211yescharacteristic
1093C23C22×D3211yescharacteristic
1094Q8—184no—
1095D4—38no—
1096D4—38no—
1097D4—64no—
1098D4—64no—
1099D4—64no—
1100D4—64no—
1101D4—124no—
1102D4—188no—
1103D4—188no—
1104D4—184no—
1105D4—188no—
1106D4—184no—
1107D4—188no—
1108D4—184no—
1109D4—184no—
1110D4—184no—
1111D4—364no—
1112D4—364no—
1113D4—364no—
1114C2×C4—34no—
1115C2×C4—32no—
1116C2×C4—34no—
1117C2×C4—32no—
1118C2×C4—32no—
1119C2×C4—42no—
1120C2×C4—62no—
1121C2×C4—62no—
1122C2×C4—92no—
1123C2×C4—124no—
1124C2×C4—122no—
1125C2×C4—188no—
1126C2×C4—184no—
1127C2×C4—184no—
1128C2×C4—184no—
1129C2×C4—182no—
1130C2×C4C22×D3214yes—
1131C2×C3—24no—
1132C2×C3—22no—
1133C2×C3—22no—
1134C2×C3—22no—
1135C2×C3—22no—
1136C2×C3—22no—
1137C2×C3—22no—
1138C2×C3—21no—
1139C2×C3—22no—
1140C2×C3—42no—
1141C2×C3—42no—
1142C2×C3—64no—
1143C2×C3—122no—
1144C2×C3—122no—
1145C2×C3C23×D1211yescharacteristic
1146C2×C3C22×D3×D411yescharacteristic
1147C2×C3D3×H(5,𝔽2)12yes—
1148C2×C3D3×H(5,𝔽2)12yes—
1149D3—24no—
1150D3—42no—
1151D3—42no—
1152D3—64no—
1153D3—64no—
1154D3—124no—
1155D3—124no—
1156D3—122no—
1157D3—122no—
1158D3—122no—
1159D3—122no—
1160D3—242no—
1161C22—22no—
1162C22—22no—
1163C22—22no—
1164C22—34no—
1165C22—44no—
1166C22—64no—
1167C22—62no—
1168C22—62no—
1169C22—64no—
1170C22—64no—
1171C22—94no—
1172C22—124no—
1173C22—124no—
1174C22—188no—
1175C22—182no—
1176C22—182no—
1177C22—182no—
1178C22—182no—
1179C22—184no—
1180C22—182no—
1181C22—182no—
1182C22—242no—
1183C22—368no—
1184C22—368no—
1185C22—364no—
1186C22—3616no—
1187C22—722no—
1188C22—724no—
1189C22C2×D3×D1212yes—
1190C22C2×D3×D1212yes—
1191C22C2×D3×D1212yes—
1192C22C23×D3211yescharacteristic
1193C4—24no—
1194C4—34no—
1195C4—62no—
1196C4—62no—
1197C4—64no—
1198C4—182no—
1199C3—21no—
1200C3#8586711yescharacteristic, complemented
1201C3#8630811yescharacteristic, complemented
1202C2—22no—
1203C2—22no—
1204C2—22no—
1205C2—64no—
1206C2—122no—
1207C2—122no—
1208C2—184no—
1209C2—362no—
1210C2—362no—
1211C2C22×D3×D1211yescharacteristic
1212C2#1059667512yes—
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×#3811C2semidirect
3. C2×#64091C2semidirect
4. C3×#5493C2semidirect
5. C3×#5486C2semidirect
6. #10595519C2semidirect
7. C2×#63981C2semidirect
8. #10595075C2semidirect
9. #10595074C2semidirect
10. #10594293C2semidirect
11. #10594291C2semidirect
12. #10594277C2semidirect
13. D3×#882C2semidirect
14. #10594080C2semidirect
15. #10594079C2semidirect
18. C24×C3⋊D3C22semidirect
19. C23×D32C22semidirect
20. C22×#638C22semidirect
21. C22×C4⋊(C3⋊D3)C22semidirect
23. C22×C3×#67C22semidirect
24. C22×C3×#67C22semidirect
27. C2×#3811C22semidirect
28. C2×#3811C22semidirect
29. C2×#3811C22semidirect
30. C2×D3×#67C22semidirect
31. C2×D3×#67C22semidirect
32. C22×#626C22semidirect
33. C22×#626C22semidirect
34. C22×#626C22semidirect
35. C22×#624C22semidirect
36. C2×#3805C22semidirect
37. C2×#3804C22semidirect
38. C2×#3804C22semidirect
39. C2×D3×D12C22semidirect
40. C2×C32×C22⋊C4C22semidirect
41. C2×#3752C22semidirect
42. #64091C22semidirect
43. #64091C22semidirect
44. #64091C22semidirect
45. C2×C3×#217C22semidirect
46. C3×#930C22semidirect
47. C3×C4×#67C22semidirect
48. C3×#886C22semidirect
49. C3×#886C22semidirect
50. C3×#882C22semidirect
51. C3×#882C22semidirect
52. C3×#67⋊C4C22semidirect
53. C3×D3×C22⋊C4C22semidirect
54. C3×#877C22semidirect
55. #63981C22semidirect
56. #63981C22semidirect
57. #63981C22semidirect
58. #63981C22semidirect
59. #63978C22semidirect
60. #63977C22semidirect
61. #63966C22semidirect
62. C2×#3722C22semidirect
63. #63962C22semidirect
64. #63923C22semidirect
65. #63923C22semidirect
66. #63922C22semidirect
67. D3×(C2×D3)⋊C4C22semidirect
68. #63911C22semidirect
69. #63910C22semidirect
70. #63910C22semidirect
71. #63909C22semidirect
72. #63906C22semidirect
73. #63895C22semidirect
74. #63894C22semidirect
75. #63890C22semidirect
76. #63886C22semidirect
77. #63880C22semidirect
78. #63852C22semidirect
103. #5493D3semidirect
109. #5486D3semidirect
117. C23×C3⋊D3C23semidirect
120. C23×C3×D3C23semidirect
124. C22×D32C23semidirect
125. C22×C32×C4C23semidirect
128. C2×#638C23semidirect
129. C22×C3⋊Dic3C23semidirect
132. C2×C4⋊(C3⋊D3)C23semidirect
135. C2×C3×#67D4semidirect
141. C2×C3×#67C23semidirect
144. C22×C3×Dic3C23semidirect
145. C22×C3×Dic3C23semidirect
146. C2×C3×D12C23semidirect
147. C2×C3×C4×D3C23semidirect
153. C2×#627C23semidirect
160. C2×#626C23semidirect
161. C2×#626C23semidirect
162. C2×#626C23semidirect
163. C2×#626C23semidirect
164. C2×#625C23semidirect
167. C2×#624C23semidirect
171. C2×D3×Dic3C23semidirect
172. C2×D3×Dic3C23semidirect
175. C32×C22⋊C4C23semidirect
177. #3752C23semidirect
179. C3×#217C23semidirect
180. C3×(C2×D3)⋊C4C23semidirect
181. C3×(C2×D3)⋊C4C23semidirect
182. C3×(C2×D3)⋊C4C23semidirect
183. C3×C4⋊Dic3C23semidirect
184. C3×Dic3⋊C4C23semidirect
185. C3×C4×Dic3C23semidirect
186. Dic3⋊Dic3C23semidirect
188. #3722C23semidirect
189. #3722C23semidirect
190. (C2×D3)⋊Dic3C23semidirect
209. C22×#67C2×D3semidirect
210. C22×#67C2×D3semidirect
250. C2×C3×C22⋊C4C2×D3semidirect
251. C2×C3×C22⋊C4C2×D3semidirect
253. C2×#217C2×D3semidirect
266. #930C2×D3semidirect
268. C4×#67C2×D3semidirect
286. #886C2×D3semidirect
287. #886C2×D3semidirect
311. #882C2×D3semidirect
312. #882C2×D3semidirect
314. #67⋊C4C2×D3semidirect
316. D3×C22⋊C4C2×D3semidirect
317. #877C2×D3semidirect
323. C23×C32C2×D4semidirect
348. C22×C3×D3C2×D4semidirect
370. C3×#67C2×D4semidirect
371. C3×#67C2×D4semidirect
375. C2×C3×Dic3C2×D4semidirect
447. C23×D3C22×D3semidirect
464. C22×C3×C4C22×D3semidirect
465. C22×C3×C4C22×D3semidirect
491. C2×#67D12semidirect
497. C2×#67C22×D3semidirect
505. C22×Dic3C22×D3semidirect
506. C22×Dic3C22×D3semidirect
542. C2×D12C22×D3semidirect
551. C2×C4×D3C22×D3semidirect
565. C3×C22⋊C4C22×D3semidirect
566. C3×C22⋊C4C22×D3semidirect
570. #217C22×D3semidirect
584. (C2×D3)⋊C4C22×D3semidirect
585. (C2×D3)⋊C4C22×D3semidirect
586. (C2×D3)⋊C4C22×D3semidirect
588. C4⋊Dic3C22×D3semidirect
590. Dic3⋊C4C22×D3semidirect
591. C4×Dic3C22×D3semidirect
612. C2×C3⋊D3H(5,𝔽2)semidirect
690. C2×C22⋊C4D32semidirect
707. C23×C3C2×D12semidirect
708. C23×C3D3×D4semidirect
780. C22×D3C2×D12semidirect
825. #67C2×D12semidirect
826. #67C2×D12semidirect
838. C2×Dic3C2×D12semidirect
940. C22×C4C2×D32semidirect
956. C22⋊C4C2×D32semidirect
1057. C32#3484semidirect
1090. C23D3×D12semidirect
1200. C3#85867semidirect
1201. C3#86308semidirect

Maximal subgroups

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

subgroupindex
C2×#643302
C22×#38112
C2×#640912
C3×#54932
C3×#54862
#105955192
C2×#639812
#105950752
#105950742
#105942932
#105942912
#105942772
D3×#8822
#105940802
#105940792
#863083
#858673