Finite Group Databasebeta

← #11906375

Subgroups — #11906375

Order 1152.

2223 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595990C211yesmaximal, characteristic, complemented
2C3×#5522C211yesmaximal, characteristic
3C3×#5519C211yesmaximal, characteristic, complemented
4#10595049C211yesmaximal, characteristic, complemented
5C2×#63918C211yesmaximal, characteristic, complemented
6#10594992C211yesmaximal, characteristic
7#10594986C211yesmaximal, characteristic
8#10594452C212yesmaximal, complemented
9#10594376C212yesmaximal, complemented
10#10594321C212yesmaximal, complemented
11#10594312C212yesmaximal, complemented
12#10594146C214yesmaximal, complemented
13#10594071C214yesmaximal, complemented
14#10593959C212yesmaximal, complemented
15#10593954C212yesmaximal, complemented
16D3×#869C212yesmaximal, complemented
17#10593874C212yesmaximal, complemented
18#86586—31nomaximal
19#85828—31nomaximal
20C2×C3×#235C2211yescharacteristic
21C22×#627C2212yes—
22C2×D3×Dic6C2214yes—
23C32×#117C2211yescharacteristic
24#64135C2211yescharacteristic
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
26#64099C2212yes—
27#64097C2212yes—
28#64087C2214yes—
29#64079C2212yes—
30#64078C2212yes—
31C3×#926C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C3×#893C2211yescharacteristic
35C3×#893C2211yescharacteristic
36C3×#890C2212yes—
37C3×#888C2212yes—
38C3×#887C2211yescharacteristic
39C3×#887C2211yescharacteristic
40C3×#67⋊C4C2212yes—
41C3×#67⋊C4C2212yes—
42C3×#878C2214yes—
43C3×#872C2212yes—
44C3×C42×D3C2212yes—
45C3×#870C2212yes—
46C3×#869C2212yes—
47#67⋊Dic3C2214yes—
48Dic3×#67C2214yes—
49C2×Dic3⋊Dic3C2212yes—
50#63964C2212yes—
51#63964C2212yes—
52#63918C2212yes—
53#63918C2214yes—
54#63918C2212yes—
55#63918C2211yescharacteristic
56#63918C2212yes—
57#63918C2211yescharacteristic
58#63918C2212yes—
59C4×#627C2212yes—
60C4×#627C2212yes—
61#63899C2214yes—
62#63898C2212yes—
63#63896C2214yes—
64#63893C2214yes—
65Dic3×D12C2212yes—
66D3×C4⋊Dic3C2214yes—
67D3×C4⋊Dic3C2212yes—
68D3×C4⋊Dic3C2212yes—
69#63887C2214yes—
70#63869C2211yescharacteristic
71#63869C2211yescharacteristic
72#63866C2214yes—
73#63851C2214yes—
74#63851C2214yes—
75#63846C2214yes—
76#63845C2214yes—
77#63843C2212yes—
78Dic3×Dic6C2212yes—
79#63841C2212yes—
80#63841C2212yes—
81#63840C2214yes—
82#63839C2214yes—
83#63837C2214yes—
84#63837C2214yes—
85C3×#544—31no—
86C3×C4×#41—31no—
87#5827—31no—
88#5827—31no—
89#5729—32no—
90#5727—32no—
91D3×C4⋊Q8—32no—
92#5722—32no—
93#5690—32no—
94#5689—32no—
95#5688—32no—
96#5685—32no—
97#5636—34no—
98#5632—34no—
99#5570—32no—
100Q8×Dic6—32no—
101#5543—32no—
102#5543—34no—
103D4×Dic6—32no—
104D4×Dic6—34no—
105#5523—31no—
106#5522D311yescharacteristic
107#5519—31no—
108#5519—31no—
109#5519—32no—
110#5519—32no—
111#5519—61no—
112#5519D311yescharacteristic, complemented
113#5517—31no—
114#5504—31no—
115C2×#888—31no—
116#5470—31no—
117#5470—32no—
118C2×#869—31no—
119C2×#869—32no—
120C22×C32×C4C2311yescharacteristic
121C22×C3⋊Dic3C2312yes—
122C2×#634C2314yes—
123C2×C3×#67C2312yes—
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2312yes—
127C3×#235Q818yescomplemented
128C2×C3×D12C2311yescharacteristic
129C2×C3×C4×D3C2312yes—
130C2×C3×C4×D3C2312yes—
131C2×C3×C4×D3C2312yes—
132C2×C3×Dic6C2314yes—
133C2×C3×Dic6C2311yescharacteristic
134C2×#627—44no—
135C2×#627C2312yes—
136C2×#627C2314yes—
137C2×#627C2312yes—
138C2×#627C2314yes—
139C2×D3×Dic3C2314yes—
140C2×D3×Dic3C2314yes—
141D3×Dic6—48no—
142C32×C4⋊C4C2311yescharacteristic
143C32×C4⋊C4C2311yescharacteristic
144C32×C22⋊C4C2312yes—
145C32×C42C2312yes—
146#3757C2312yes—
147C4⋊(C3⋊Dic3)C2311yescharacteristic
148C4⋊(C3⋊Dic3)C2312yes—
149C4⋊(C3⋊Dic3)C2314yes—
150C4⋊(C3⋊Dic3)C2311yescharacteristic
151C4⋊(C3⋊Dic3)C2312yes—
152#3750C2314yes—
153#3750C2314yes—
154C4×C3⋊Dic3C2312yes—
155C3×#217C2312yes—
156C3×(C2×D3)⋊C4C2312yes—
157C3×(C2×D3)⋊C4C2312yes—
158C3×C4⋊Dic3C2314yes—
159C3×C4⋊Dic3C2312yes—
160C3×C4⋊Dic3C2312yes—
161C3×C4⋊Dic3C2311yescharacteristic
162C3×C4⋊Dic3C2311yescharacteristic
163C3×Dic3⋊C4C2314yes—
164C3×Dic3⋊C4C2314yes—
165C3×Dic3⋊C4C2312yes—
166C3×Dic3⋊C4C2312yes—
167C3×C4×Dic3C2312yes—
168C3×C4×Dic3C2312yes—
169C3×C4×Dic3C2311yescharacteristic
170C3×C4×Dic3C2311yescharacteristic
171C3×C4×Dic3C2312yes—
172C3×C4×Dic3C2311yescharacteristic
173C3×C4×Dic3C2311yescharacteristic
174#3724C2312yes—
175#3724C2312yes—
176Dic3⋊Dic3C2312yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2312yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2314yes—
182Dic3⋊Dic3C2312yes—
183Dic3⋊Dic3C2312yes—
184(C2×D3)⋊Dic3C2314yes—
185(C2×D3)⋊Dic3C2314yes—
186Dic32C2314yes—
187Dic32C2314yes—
188#3503—91noSylow
189C2×C3×#41—31no—
190C2×D3×Q8—34no—
191C2×#235C2×D311yescharacteristic
192C22×Dic6—32no—
193C22×Dic6—32no—
194C22×Dic6—34no—
195C3×C4⋊Q8—32no—
196C3×C4⋊Q8—32no—
197C3×#125—32no—
198C3×#125—32no—
199C3×C22⋊Q8—34no—
200C3×C4×Q8—31no—
201C3×C4×Q8—31no—
202C3×C4×D4—31no—
203C3×C4×D4—31no—
204C3×C4×D4—32no—
205C3×C4×D4—32no—
206C3×#117—21no—
207C3×#117—31no—
208C3×#117—32no—
209C3×#117C2×D311yescharacteristic
210C3×#117C2×D311yescharacteristic
211C2×C3×C4⋊C4—31no—
212C2×C3×C42—31no—
213C2×C3×C42—32no—
214#946—34no—
215Q8×Dic3—32no—
216Q8×Dic3—32no—
217#944—34no—
218#944—34no—
219D4×Dic3—34no—
220D4×Dic3—34no—
221D4×Dic3—32no—
222D4×Dic3—32no—
223C4×#67—34no—
224#926—31no—
225#926—31no—
226#926—32no—
227#926—32no—
228#926—61no—
229#926C2×D311yescharacteristic
230C2×C4⋊Dic3—31no—
231C2×C4⋊Dic3—31no—
232C2×C4⋊Dic3—32no—
233C2×C4⋊Dic3—32no—
234C2×C4⋊Dic3—32no—
235C2×C4⋊Dic3—34no—
236C2×C4⋊Dic3—61no—
237C2×C4⋊Dic3C2×D311yescharacteristic
238#924—32no—
239#924—32no—
240#924—34no—
241#924—34no—
242C2×Dic3⋊C4—32no—
243C2×C4×Dic3C2×D311yescharacteristic
244#897—34no—
245#896—34no—
246#896—34no—
247#896—34no—
248#896—34no—
249#893—32no—
250#893C2×D311yescharacteristic
251#893C2×D311yescharacteristic
252#892—32no—
253#892—32no—
254D3×C4⋊C4—34no—
255D3×C4⋊C4—32no—
256D3×C4⋊C4—32no—
257#890—32no—
258#890—32no—
259#890—34no—
260#890—34no—
261#890—31no—
262#890—31no—
263#890—62no—
264#890C2×D312yes—
265#889—34no—
266#889—34no—
267#888—34no—
268#888—32no—
269#888—32no—
270#888—34no—
271#888—34no—
272#888—34no—
273#888—32no—
274#888—31no—
275#888—32no—
276#888—32no—
277#888—32no—
278#888—31no—
279#888—62no—
280#888C2×D312yes—
281#887—32no—
282#887—34no—
283#887—34no—
284#887C2×D311yescharacteristic
285#887C2×D311yescharacteristic
286#67⋊C4—34no—
287#67⋊C4C2×D312yes—
288#67⋊C4C2×D312yes—
289#878—32no—
290#878—32no—
291#878—34no—
292#878—34no—
293#878—34no—
294#878—34no—
295#878—34no—
296#878—34no—
297#878—64no—
298#878C2×D314yes—
299C4×D12—32no—
300#872C2×D312yes—
301C42×D3C2×D312yes—
302#870—32no—
303#870—32no—
304#870—31no—
305#870—31no—
306#870—62no—
307#870C2×D312yes—
308#869—34no—
309#869—32no—
310#869—32no—
311#869—32no—
312#869—31no—
313#869—32no—
314#869—34no—
315#869—32no—
316#869—32no—
317#869—31no—
318#869—62no—
319#869C2×D312yes—
320C4×Dic6—32no—
321C4×Dic6—34no—
322C4×Dic6—34no—
323C4×Dic6—32no—
324C4×Dic6—32no—
325C4×Dic6—32no—
326C4×Dic6—32no—
327C23×C32C2411yescharacteristic
328C22×C3×D3C2412yes—
329C2×C32×C4C2×Q814yescomplemented
330C2×C32×C4C2412yes—
331C2×C32×C4C2412yes—
332C2×C32×C4C2411yescharacteristic
333C2×C32×C4C2411yescharacteristic
334C2×C3⋊Dic3—42no—
335C2×C3⋊Dic3C2412yes—
336C2×C3⋊Dic3C2414yes—
337C2×C3⋊Dic3C2412yes—
338#634—44no—
339C3×#67C2×Q818yescomplemented
340C2×C3×Dic3—22no—
341C2×C3×Dic3—22no—
342C2×C3×Dic3—42no—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2414yes—
345C2×C3×Dic3C2411yescharacteristic
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2411yescharacteristic
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2411yescharacteristic
350C2×C3×Dic3C2411yescharacteristic
351C3×D12C2×Q814yescomplemented
352C3×C4×D3—24no—
353C3×C4×D3—24no—
354C3×C4×D3C2×Q818yescomplemented
355C3×Dic6—44no—
356C3×Dic6C2×Q814yescomplemented
357#627—24no—
358#627—28no—
359#627—24no—
360#627—44no—
361D3×Dic3—44no—
362D3×Dic3—44no—
363Q82—92no—
364#557—92no—
365#554—94no—
366#554—92no—
367D4×Q8—94no—
368D4×Q8—92no—
369#544—31no—
370#544—92no—
371#544—92no—
372#544—91no—
373#533—91no—
374#533—92no—
375C2×C4⋊Q8—91no—
376C2×C4⋊Q8—92no—
377#520—91no—
378#520—91no—
379C4×#41—31no—
380C3×#41—38no—
381C2×C3×Q8—31no—
382C2×C3×Q8—34no—
383C2×C3×D4—32no—
384C2×C3×D4—31no—
385C22×C3×C4—21no—
386C22×C3×C4—32no—
387C22×C3×C4—31no—
388C22×C3×C4—31no—
389C22×C3×C4—32no—
390C22×C3×C4—32no—
391C22×C3×C4—32no—
392C22×C3×C4C22×D311yescharacteristic
393C22×C3×C4C22×D311yescharacteristic
394C2×#67C22×D312yes—
395C22×Dic3—32no—
396C22×Dic3—32no—
397C22×Dic3—34no—
398C22×Dic3—34no—
399C22×Dic3—62no—
400C22×Dic3C22×D311yescharacteristic
401C22×Dic3C22×D311yescharacteristic
402C22×Dic3C22×D312yes—
403D3×Q8—128no—
404#235Dic618yescomplemented
405C2×D12C22×D311yescharacteristic
406C2×C4×D3—34no—
407C2×C4×D3—34no—
408C2×C4×D3C22×D312yes—
409C2×C4×D3C22×D312yes—
410C2×C4×D3C22×D312yes—
411C2×Dic6—32no—
412C2×Dic6—34no—
413C2×Dic6—32no—
414C2×Dic6—32no—
415C2×Dic6—32no—
416C2×Dic6—34no—
417C2×Dic6—34no—
418C2×Dic6—34no—
419C2×Dic6—34no—
420C2×Dic6—34no—
421C2×Dic6—64no—
422C2×Dic6—128no—
423C2×Dic6—124no—
424C2×Dic6—124no—
425C2×Dic6C22×D314yes—
426C2×Dic6C22×D311yescharacteristic
427C3×C4⋊C4—21no—
428C3×C4⋊C4—21no—
429C3×C4⋊C4—32no—
430C3×C4⋊C4—34no—
431C3×C4⋊C4—34no—
432C3×C4⋊C4—32no—
433C3×C4⋊C4—32no—
434C3×C4⋊C4—34no—
435C3×C4⋊C4—31no—
436C3×C4⋊C4—31no—
437C3×C4⋊C4—32no—
438C3×C4⋊C4C22×D311yescharacteristic
439C3×C4⋊C4C22×D311yescharacteristic
440C3×C4⋊C4C22×D311yescharacteristic
441C3×C4⋊C4C22×D311yescharacteristic
442C3×C22⋊C4—22no—
443C3×C22⋊C4—32no—
444C3×C22⋊C4—32no—
445C3×C22⋊C4—32no—
446C3×C22⋊C4C22×D312yes—
447C3×C22⋊C4C22×D312yes—
448C3×C42—22no—
449C3×C42—32no—
450C3×C42—32no—
451C3×C42—32no—
452C3×C42—31no—
453C3×C42—31no—
454C3×C42—31no—
455C3×C42—31no—
456C3×C42C22×D312yes—
457C3×C42C22×D312yes—
458#217—32no—
459#217—32no—
460#217—34no—
461#217—34no—
462#217—62no—
463#217C22×D312yes—
464(C2×D3)⋊C4—34no—
465(C2×D3)⋊C4—34no—
466(C2×D3)⋊C4C22×D312yes—
467(C2×D3)⋊C4C22×D312yes—
468C4⋊Dic3—32no—
469C4⋊Dic3—31no—
470C4⋊Dic3—32no—
471C4⋊Dic3—34no—
472C4⋊Dic3—31no—
473C4⋊Dic3—32no—
474C4⋊Dic3—31no—
475C4⋊Dic3—32no—
476C4⋊Dic3—34no—
477C4⋊Dic3—31no—
478C4⋊Dic3—32no—
479C4⋊Dic3—34no—
480C4⋊Dic3—32no—
481C4⋊Dic3—32no—
482C4⋊Dic3—32no—
483C4⋊Dic3—34no—
484C4⋊Dic3—34no—
485C4⋊Dic3—34no—
486C4⋊Dic3—61no—
487C4⋊Dic3—62no—
488C4⋊Dic3—64no—
489C4⋊Dic3—61no—
490C4⋊Dic3—62no—
491C4⋊Dic3C22×D312yes—
492C4⋊Dic3C22×D312yes—
493C4⋊Dic3C22×D311yescharacteristic
494C4⋊Dic3C22×D314yes—
495C4⋊Dic3C22×D311yescharacteristic
496Dic3⋊C4—34no—
497Dic3⋊C4—34no—
498Dic3⋊C4—34no—
499Dic3⋊C4—34no—
500Dic3⋊C4—32no—
501Dic3⋊C4—32no—
502Dic3⋊C4—32no—
503Dic3⋊C4—32no—
504Dic3⋊C4—32no—
505Dic3⋊C4—32no—
506Dic3⋊C4—32no—
507Dic3⋊C4—32no—
508Dic3⋊C4—34no—
509Dic3⋊C4—34no—
510Dic3⋊C4—34no—
511Dic3⋊C4—34no—
512Dic3⋊C4—64no—
513Dic3⋊C4—64no—
514Dic3⋊C4C22×D314yes—
515Dic3⋊C4C22×D314yes—
516Dic3⋊C4C22×D312yes—
517Dic3⋊C4C22×D312yes—
518C4×Dic3—32no—
519C4×Dic3—32no—
520C4×Dic3—34no—
521C4×Dic3—34no—
522C4×Dic3—34no—
523C4×Dic3—34no—
524C4×Dic3—62no—
525C4×Dic3C22×D311yescharacteristic
526C4×Dic3C22×D311yescharacteristic
527C4×Dic3C22×D312yes—
528C4×Dic3C22×D311yescharacteristic
529C4×Dic3C22×D312yes—
530C4×Dic3C22×D312yes—
531C4×Dic3C22×D311yescharacteristic
532C22×C32—21no—
533C22×C32—21no—
534C22×C32C22×Q812yes—
535C22×C32C2511yescharacteristic
536C2×C3×D3—22no—
537C2×C3×D3—22no—
538C2×C3×D3C22×Q814yes—
539C32×C4—22no—
540C32×C4—22no—
541C32×C4C22×Q812yes—
542C32×C4C22×Q812yes—
543C3⋊Dic3—22no—
544C3⋊Dic3—24no—
545C3⋊Dic3—22no—
546C3×Dic3—22no—
547C3×Dic3—24no—
548C3×Dic3—21no—
549C3×Dic3—22no—
550C3×Dic3—21no—
551C3×Dic3C22×Q814yes—
552C3×Dic3H(5,𝔽2)12yes—
553C3×Dic32−1+412yes—
554C2×#41—31no—
555C22×Q8—92no—
556C22×Q8—94no—
557C4⋊Q8—32no—
558C4⋊Q8—32no—
559C4⋊Q8—92no—
560C4⋊Q8—91no—
561C4⋊Q8—92no—
562C4⋊Q8—92no—
563C4⋊Q8—94no—
564C4⋊Q8—92no—
565C4⋊Q8—91no—
566C4⋊Q8—94no—
567C4⋊Q8—94no—
568C4⋊Q8—94no—
569C4⋊Q8—92no—
570C4⋊Q8—92no—
571#125—32no—
572#125—32no—
573#125—91no—
574#125—91no—
575#125—94no—
576#125—94no—
577#125—92no—
578#125—92no—
579C22⋊Q8—34no—
580C22⋊Q8—94no—
581C22⋊Q8—94no—
582C22⋊Q8—94no—
583C22⋊Q8—92no—
584C22⋊Q8—92no—
585C22⋊Q8—94no—
586C22⋊Q8—94no—
587C22⋊Q8—94no—
588C22⋊Q8—94no—
589C4×Q8—31no—
590C4×Q8—31no—
591C4×Q8—92no—
592C4×Q8—92no—
593C4×Q8—94no—
594C4×Q8—94no—
595C4×Q8—92no—
596C4×Q8—92no—
597C4×D4—31no—
598C4×D4—31no—
599C4×D4—32no—
600C4×D4—32no—
601C4×D4—92no—
602C4×D4—94no—
603C4×D4—92no—
604C4×D4—94no—
605#117—31no—
606#117—32no—
607#117—92no—
608#117—92no—
609#117—91no—
610#117D3211yescharacteristic
611C2×C4⋊C4—31no—
612C2×C4⋊C4—92no—
613C2×C4⋊C4—92no—
614C2×C4⋊C4—94no—
615C2×C4⋊C4—92no—
616C2×C4⋊C4—91no—
617C2×C42—31no—
618C2×C42—32no—
619C23×C3—21no—
620C23×C3—32no—
621C23×C3C23×D311yescharacteristic
622C23×C3C23×D311yescharacteristic
623C22×D3C23×D312yes—
624C3×Q8—34no—
625C3×Q8—124no—
626C3×D4—38no—
627C3×D4—34no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—22no—
631C2×C3×C4—22no—
632C2×C3×C4—24no—
633C2×C3×C4—32no—
634C2×C3×C4—31no—
635C2×C3×C4—31no—
636C2×C3×C4—38no—
637C2×C3×C4—32no—
638C2×C3×C4—34no—
639C2×C3×C4—31no—
640C2×C3×C4—32no—
641C2×C3×C4—31no—
642C2×C3×C4—64no—
643C2×C3×C4—64no—
644C2×C3×C4—62no—
645C2×C3×C4—62no—
646C2×C3×C4—122no—
647C2×C3×C4C2×Dic614yescomplemented
648C2×C3×C4D3×Q814yescomplemented
649C2×C3×C4C23×D312yes—
650C2×C3×C4C23×D312yes—
651C2×C3×C4C23×D312yes—
652C2×C3×C4C23×D312yes—
653C2×C3×C4C23×D311yescharacteristic
654C2×C3×C4C23×D311yescharacteristic
655C2×C3×C4C23×D311yescharacteristic
656C2×C3×C4C23×D311yescharacteristic
657#67C2×Dic618yescomplemented
658C2×Dic3—22no—
659C2×Dic3—22no—
660C2×Dic3—32no—
661C2×Dic3—32no—
662C2×Dic3—34no—
663C2×Dic3—32no—
664C2×Dic3—34no—
665C2×Dic3—32no—
666C2×Dic3—42no—
667C2×Dic3—62no—
668C2×Dic3—62no—
669C2×Dic3—64no—
670C2×Dic3—124no—
671C2×Dic3—124no—
672C2×Dic3—122no—
673C2×Dic3—122no—
674C2×Dic3—242no—
675C2×Dic3C23×D312yes—
676C2×Dic3C23×D314yes—
677C2×Dic3C23×D311yescharacteristic
678C2×Dic3C23×D311yescharacteristic
679C2×Dic3C23×D312yes—
680C2×Dic3C23×D312yes—
681C2×Dic3C23×D311yescharacteristic
682C2×Dic3C23×D311yescharacteristic
683D12C2×Dic614yescomplemented
684C4×D3—24no—
685C4×D3—24no—
686C4×D3—124no—
687C4×D3—124no—
688C4×D3C2×Dic618yescomplemented
689Dic6—44no—
690Dic6—64no—
691Dic6—64no—
692Dic6—68no—
693Dic6—68no—
694Dic6—64no—
695Dic6—64no—
696Dic6—124no—
697Dic6—124no—
698Dic6—124no—
699Dic6—124no—
700Dic6—244no—
701Dic6C2×Dic614yescomplemented
702C2×C32—22no—
703C2×C32C23×Q811yescharacteristic
704C2×C32C2×H(5,𝔽2)11yescharacteristic
705C2×C32C2×2−1+411yescharacteristic
706C3×D3—24no—
707#41—38no—
708C2×Q8—31no—
709C2×Q8—34no—
710C2×Q8—92no—
711C2×Q8—92no—
712C2×Q8—94no—
713C2×Q8—94no—
714C2×Q8—94no—
715C2×Q8—364no—
716C2×Q8—368no—
717C2×D4—32no—
718C2×D4—31no—
719C22×C4—32no—
720C22×C4—31no—
721C22×C4—31no—
722C22×C4—32no—
723C22×C4—32no—
724C22×C4—32no—
725C22×C4—94no—
726C22×C4—94no—
727C22×C4—92no—
728C22×C4C2×D3211yescharacteristic
729C4⋊C4—32no—
730C4⋊C4—32no—
731C4⋊C4—31no—
732C4⋊C4—34no—
733C4⋊C4—31no—
734C4⋊C4—32no—
735C4⋊C4—32no—
736C4⋊C4—34no—
737C4⋊C4—34no—
738C4⋊C4—92no—
739C4⋊C4—94no—
740C4⋊C4—94no—
741C4⋊C4—94no—
742C4⋊C4—94no—
743C4⋊C4—92no—
744C4⋊C4—92no—
745C4⋊C4—92no—
746C4⋊C4—92no—
747C4⋊C4—92no—
748C4⋊C4—91no—
749C4⋊C4—92no—
750C4⋊C4—92no—
751C4⋊C4—94no—
752C4⋊C4—91no—
753C4⋊C4—94no—
754C4⋊C4—94no—
755C4⋊C4C2×D3211yescharacteristic
756C4⋊C4C2×D3211yescharacteristic
757C22⋊C4—32no—
758C22⋊C4—32no—
759C22⋊C4—32no—
760C22⋊C4—94no—
761C22⋊C4—94no—
762C22⋊C4—92no—
763C22⋊C4C2×D3212yes—
764C42—31no—
765C42—31no—
766C42—32no—
767C42—31no—
768C42—32no—
769C42—31no—
770C42—32no—
771C42—94no—
772C42—94no—
773C42—92no—
774C42C2×D3212yes—
775C22×C3—21no—
776C22×C3—21no—
777C22×C3—21no—
778C22×C3—21no—
779C22×C3—22no—
780C22×C3—21no—
781C22×C3—34no—
782C22×C3—41no—
783C22×C3—41no—
784C22×C3—62no—
785C22×C3—62no—
786C22×C3C22×Dic612yes—
787C22×C3C2×D3×Q812yes—
788C22×C3C24×D311yescharacteristic
789C22×C3C24×D311yescharacteristic
790C2×D3—22no—
791C2×D3—22no—
792C2×D3C22×Dic614yes—
793C3×C4—22no—
794C3×C4—22no—
795C3×C4—22no—
796C3×C4—22no—
797C3×C4—22no—
798C3×C4—22no—
799C3×C4—34no—
800C3×C4—32no—
801C3×C4—32no—
802C3×C4—42no—
803C3×C4—42no—
804C3×C4—64no—
805C3×C4—62no—
806C3×C4—62no—
807C3×C4—61no—
808C3×C4—61no—
809C3×C4C22×Dic612yes—
810C3×C4C22×Dic612yes—
811C3×C4C2×D3×Q812yes—
812C3×C4C2×D3×Q812yes—
813Dic3—21no—
814Dic3—21no—
815Dic3—22no—
816Dic3—24no—
817Dic3—22no—
818Dic3—62no—
819Dic3—64no—
820Dic3—62no—
821Dic3—64no—
822Dic3—62no—
823Dic3—62no—
824Dic3—122no—
825Dic3—124no—
826Dic3—122no—
827Dic3C22×Dic614yes—
828Dic3#100912yes—
829Dic3#101012yes—
830C32#350311yescharacteristic, complemented, Sylow
831C23—32no—
832C23C22×D3211yescharacteristic
833Q8—34no—
834Q8—124no—
835Q8—188no—
836Q8—184no—
837Q8—184no—
838Q8—364no—
839Q8—364no—
840D4—38no—
841D4—34no—
842C2×C4—31no—
843C2×C4—31no—
844C2×C4—32no—
845C2×C4—38no—
846C2×C4—31no—
847C2×C4—31no—
848C2×C4—32no—
849C2×C4—32no—
850C2×C4—34no—
851C2×C4—64no—
852C2×C4—64no—
853C2×C4—62no—
854C2×C4—62no—
855C2×C4—92no—
856C2×C4—94no—
857C2×C4—92no—
858C2×C4—122no—
859C2×C4—364no—
860C2×C4—364no—
861C2×C4—362no—
862C2×C4D3×Dic614yescomplemented
863C2×C4C22×D3212yes—
864C2×C4C22×D3212yes—
865C2×C4C22×D3211yescharacteristic
866C2×C4C22×D3211yescharacteristic
867C2×C3—22no—
868C2×C3—22no—
869C2×C3—21no—
870C2×C3—21no—
871C2×C3—21no—
872C2×C3—42no—
873C2×C3—64no—
874C2×C3C23×Dic611yescharacteristic
875C2×C3C22×D3×Q811yescharacteristic
876C2×C3C2×#100911yescharacteristic
877C2×C3C2×#101011yescharacteristic
878C2×C3D3×H(5,𝔽2)11yescharacteristic
879C2×C3D3×2−1+411yescharacteristic
880D3—24no—
881C22—21no—
882C22—21no—
883C22—34no—
884C22—62no—
885C22—62no—
886C22C2×D3×Dic612yes—
887C22C23×D3211yescharacteristic
888C4—22no—
889C4—22no—
890C4—34no—
891C4—32no—
892C4—32no—
893C4—61no—
894C4—64no—
895C4—62no—
896C4—61no—
897C4—62no—
898C4—182no—
899C4—184no—
900C4—182no—
901C4C2×D3×Dic612yes—
902C4C2×D3×Dic612yes—
903C3—21no—
904C3#8582811yescharacteristic, complemented
905C3#8658611yescharacteristic, complemented
906C2—22no—
907C2—64no—
908C2C22×D3×Dic611yescharacteristic
909C2D3×#100911yescharacteristic
910C2D3×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
prime radicalC2×C3×#235C22
hypercenter#117D32
hypocenterC32#3503
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595990C2semidirect
3. C3×#5519C2semidirect
4. #10595049C2semidirect
5. C2×#63918C2semidirect
8. #10594452C2semidirect
9. #10594376C2semidirect
10. #10594321C2semidirect
11. #10594312C2semidirect
12. #10594146C2semidirect
13. #10594071C2semidirect
14. #10593959C2semidirect
15. #10593954C2semidirect
16. D3×#869C2semidirect
17. #10593874C2semidirect
112. #5519D3semidirect
127. C3×#235Q8semidirect
329. C2×C32×C4C2×Q8semidirect
339. C3×#67C2×Q8semidirect
351. C3×D12C2×Q8semidirect
354. C3×C4×D3C2×Q8semidirect
356. C3×Dic6C2×Q8semidirect
404. #235Dic6semidirect
647. C2×C3×C4C2×Dic6semidirect
648. C2×C3×C4D3×Q8semidirect
657. #67C2×Dic6semidirect
683. D12C2×Dic6semidirect
688. C4×D3C2×Dic6semidirect
701. Dic6C2×Dic6semidirect
830. C32#3503semidirect
862. C2×C4D3×Dic6semidirect
904. C3#85828semidirect
905. C3#86586semidirect

Maximal subgroups

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

subgroupindex
#105959902
C3×#55222
C3×#55192
#105950492
C2×#639182
#105949922
#105949862
#105944522
#105943762
#105943212
#105943122
#105941462
#105940712
#105939592
#105939542
D3×#8692
#105938742
#865863
#858283