Finite Group Databasebeta

← #11906362

Subgroups — #11906362

Order 1152.

2267 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595994C211yesmaximal, characteristic
2C3×#5519C211yesmaximal, characteristic, complemented
3C3×#5517C211yesmaximal, characteristic, complemented
4#10595052C211yesmaximal, characteristic, complemented
5C2×#63918C211yesmaximal, characteristic, complemented
6#10594990C211yesmaximal, characteristic
7#10594954C211yesmaximal, characteristic
8#10594508C212yesmaximal, complemented
9#10594448C212yesmaximal, complemented
10#10594374C212yesmaximal, complemented
11#10594325C212yesmaximal, complemented
12#10594141C214yesmaximal, complemented
13#10594072C214yesmaximal, complemented
14#10593938C212yesmaximal, complemented
15#10593903C212yesmaximal, complemented
16#10593856C212yesmaximal, complemented
17#10593852C212yesmaximal, complemented
18#86586—31nomaximal
19#86281—31nomaximal
20C2×#3828C2211yescharacteristic
21C22×#627C2212yes—
22C2×#3797C2214yes—
23C32×#117C2211yescharacteristic
24C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
25#64101C2212yes—
26C4⋊C4×C3⋊D3C2212yes—
27#64090C2214yes—
28C4×C4⋊(C3⋊D3)C2212yes—
29C4×#634C2212yes—
30C3×#926C2211yescharacteristic
31C3×#926C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C3×#890C2211yescharacteristic
35C3×#890C2211yescharacteristic
36C3×#890C2212yes—
37C3×#888C2212yes—
38C3×#888C2211yescharacteristic
39C3×#888C2211yescharacteristic
40C3×#878C2212yes—
41C3×#878C2214yes—
42C3×#878C2212yes—
43C3×#870C2212yes—
44C3×#869C2212yes—
45C3×C4×Dic6C2212yes—
46C3×C4×Dic6C2212yes—
47#63982C2214yes—
48C2×Dic3⋊Dic3C2212yes—
49#63952C2212yes—
50#63952C2214yes—
51#63952C2212yes—
52#63919C2214yes—
53#63918C2212yes—
54#63918C2212yes—
55#63918C2212yes—
56#63918C2212yes—
57#63918C2212yes—
58#63918C2212yes—
59#63900C2212yes—
60#63895C2214yes—
61#63895C2214yes—
62#63895C2214yes—
63#63894C2211yescharacteristic
64#63894C2212yes—
65#63894C2211yescharacteristic
66#63888C2214yes—
67#63883C2214yes—
68C4×#624C2212yes—
69#63874C2212yes—
70#63871C2214yes—
71#63870C2214yes—
72#63869C2212yes—
73#63869C2212yes—
74#63865C2214yes—
75#63849C2212yes—
76#63847C2214yes—
77#63844C2211yescharacteristic
78#63844C2212yes—
79#63844C2211yescharacteristic
80#63843C2214yes—
81#63839C2214yes—
82#63839C2214yes—
83#63839C2214yes—
84#63838C2214yes—
85C3×#544—31no—
86C3×#533—31no—
87#5729—32no—
88#5728—32no—
89#5727—32no—
90D3×C4⋊Q8—32no—
91D3×C4⋊Q8—32no—
92#5722—32no—
93#5690—32no—
94#5689—32no—
95#5689—32no—
96#5689—32no—
97#5688—32no—
98#5685—32no—
99#5636—34no—
100#5635—34no—
101#5632—34no—
102#5632—34no—
103#5579—32no—
104Q8×D12—32no—
105#5567—32no—
106Q8×Dic6—32no—
107#5523—31no—
108#5523—31no—
109#5523—31no—
110#5523—61no—
111#5522—31no—
112#5519—31no—
113#5519—31no—
114#5519D311yescharacteristic, complemented
115#5517D311yescharacteristic, complemented
116#5504—31no—
117C2×#888—31no—
118C4×#235—31no—
119C2×#869—31no—
120C22×C32×C4C2311yescharacteristic
121C2×#638C2312yes—
122C22×C3⋊Dic3C2312yes—
123#3828Q818yescomplemented
124C2×C4⋊(C3⋊D3)C2311yescharacteristic
125C2×C4×C3⋊D3C2314yes—
126C2×C4×C3⋊D3C2312yes—
127C2×#634C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2312yes—
131C2×C3×Dic6C2312yes—
132C2×C3×Dic6C2312yes—
133C2×C3×Dic6C2314yes—
134C2×#627—44no—
135C2×#627C2314yes—
136C2×#627C2314yes—
137C2×#627C2314yes—
138C2×#624C2312yes—
139C2×#624C2312yes—
140C2×#624C2314yes—
141#3797—48no—
142C32×C4⋊C4C2311yescharacteristic
143C32×C4⋊C4C2311yescharacteristic
144C32×C22⋊C4C2312yes—
145C32×C42C2312yes—
146#3752C2314yes—
147C4⋊(C3⋊Dic3)C2312yes—
148C4⋊(C3⋊Dic3)C2312yes—
149#3750C2314yes—
150C4×C3⋊Dic3C2314yes—
151C3×#217C2312yes—
152C3×#217C2312yes—
153C3×C4⋊Dic3C2314yes—
154C3×C4⋊Dic3C2312yes—
155C3×C4⋊Dic3C2312yes—
156C3×C4⋊Dic3C2312yes—
157C3×C4⋊Dic3C2311yescharacteristic
158C3×C4⋊Dic3C2311yescharacteristic
159C3×C4⋊Dic3C2312yes—
160C3×C4⋊Dic3C2311yescharacteristic
161C3×C4⋊Dic3C2311yescharacteristic
162C3×Dic3⋊C4C2312yes—
163C3×Dic3⋊C4C2312yes—
164C3×Dic3⋊C4C2314yes—
165C3×Dic3⋊C4C2314yes—
166C3×Dic3⋊C4C2312yes—
167C3×Dic3⋊C4C2312yes—
168C3×C4×Dic3C2311yescharacteristic
169C3×C4×Dic3C2312yes—
170C3×C4×Dic3C2311yescharacteristic
171C3×C4×Dic3C2311yescharacteristic
172C3×C4×Dic3C2311yescharacteristic
173C3×C4×Dic3C2312yes—
174#3724C2314yes—
175#3724C2314yes—
176#3724C2312yes—
177#3724C2312yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2314yes—
182#3722C2314yes—
183#3722C2312yes—
184#3722C2312yes—
185Dic32C2312yes—
186Dic32C2314yes—
187Dic32C2312yes—
188#3503—91noSylow
189C2×D3×Q8—34no—
190C2×D3×Q8—34no—
191C2×#235—31no—
192C2×#235—31no—
193C2×#235—61no—
194C22×Dic6—32no—
195C22×Dic6—32no—
196C3×C4⋊Q8—31no—
197C3×C4⋊Q8—32no—
198C3×C4⋊Q8—31no—
199C3×C4⋊Q8—32no—
200C3×#125—32no—
201C3×#125—31no—
202C3×#125—31no—
203C3×#125—32no—
204C3×C22⋊Q8—32no—
205C3×C22⋊Q8—34no—
206C3×C22⋊Q8—32no—
207C3×C4×Q8—32no—
208C3×C4×Q8—32no—
209C3×#117—21no—
210C3×#117—31no—
211C3×#117—31no—
212C3×#117C2×D311yescharacteristic
213C3×#117C2×D311yescharacteristic
214C2×C3×C4⋊C4—31no—
215C2×C3×C42—31no—
216#946—34no—
217#946—34no—
218Q8×Dic3—34no—
219#944—34no—
220#944—34no—
221#944—34no—
222C4×#67—32no—
223C4×#67—34no—
224C4×#67—32no—
225#926C2×D311yescharacteristic
226#926C2×D311yescharacteristic
227C2×C4⋊Dic3—31no—
228C2×C4⋊Dic3—31no—
229C2×C4⋊Dic3—32no—
230C2×C4⋊Dic3—61no—
231C2×C4⋊Dic3C2×D311yescharacteristic
232C2×Dic3⋊C4—32no—
233C2×C4×Dic3C2×D311yescharacteristic
234#897—34no—
235#897—34no—
236#897—34no—
237#897—34no—
238#896—34no—
239#896—34no—
240#896—34no—
241#896—34no—
242#896—34no—
243#896—34no—
244#893—31no—
245#893—32no—
246#893—31no—
247#892—32no—
248#892—32no—
249#892—32no—
250#892—32no—
251#892—62no—
252D3×C4⋊C4—32no—
253D3×C4⋊C4—32no—
254D3×C4⋊C4—32no—
255D3×C4⋊C4—32no—
256D3×C4⋊C4—34no—
257D3×C4⋊C4—34no—
258D3×C4⋊C4—62no—
259#890—32no—
260#890—32no—
261#890C2×D311yescharacteristic
262#890C2×D312yes—
263#890C2×D311yescharacteristic
264#889—34no—
265#889—34no—
266#889—34no—
267#889—34no—
268#888—34no—
269#888—34no—
270#888—34no—
271#888—34no—
272#888—34no—
273#888—32no—
274#888—32no—
275#888—32no—
276#888—32no—
277#888—32no—
278#888—32no—
279#888C2×D311yescharacteristic
280#888C2×D312yes—
281#888C2×D311yescharacteristic
282#887—34no—
283#887—34no—
284#887—34no—
285#887—31no—
286#887—32no—
287#887—31no—
288#67⋊C4—32no—
289#67⋊C4—34no—
290#67⋊C4—32no—
291#67⋊C4—34no—
292#67⋊C4—34no—
293#67⋊C4—64no—
294#878—34no—
295#878—34no—
296#878C2×D312yes—
297#878C2×D314yes—
298#878C2×D312yes—
299C4×D12—32no—
300C4×D12—32no—
301C4×D12—31no—
302C4×D12—31no—
303C4×D12—32no—
304C4×D12—62no—
305#872—32no—
306#872—32no—
307C42×D3—32no—
308C42×D3—32no—
309#870—32no—
310#870—32no—
311#870C2×D312yes—
312#869—32no—
313#869—32no—
314#869—32no—
315#869—32no—
316#869—32no—
317#869—32no—
318#869C2×D312yes—
319C4×Dic6—32no—
320C4×Dic6—32no—
321C4×Dic6—31no—
322C4×Dic6—31no—
323C4×Dic6—32no—
324C4×Dic6—62no—
325C4×Dic6C2×D312yes—
326C4×Dic6C2×D312yes—
327C23×C32C2411yescharacteristic
328C22×C3⋊D3C2412yes—
329C2×C32×C4C2×Q814yescomplemented
330C2×C32×C4C2412yes—
331C2×C32×C4C2412yes—
332C2×C32×C4C2411yescharacteristic
333C2×C32×C4C2411yescharacteristic
334#638C2×Q818yescomplemented
335C2×C3⋊Dic3—42no—
336C2×C3⋊Dic3C2414yes—
337C2×C3⋊Dic3C2412yes—
338C4⋊(C3⋊D3)C2×Q814yescomplemented
339C4×C3⋊D3—44no—
340C4×C3⋊D3C2×Q818yescomplemented
341#634C2×Q814yescomplemented
342C2×C3×Dic3—22no—
343C2×C3×Dic3—22no—
344C2×C3×Dic3—42no—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2414yes—
349C2×C3×Dic3C2411yescharacteristic
350C2×C3×Dic3C2411yescharacteristic
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2411yescharacteristic
353C2×C3×Dic3C2411yescharacteristic
354C3×Dic6—24no—
355C3×Dic6—24no—
356C3×Dic6—44no—
357#627—28no—
358#627—44no—
359#627—44no—
360#624—24no—
361#624—24no—
362#624—44no—
363Q82—92no—
364#557—92no—
365#554—92no—
366#554—94no—
367D4×Q8—92no—
368D4×Q8—94no—
369#544—31no—
370#544—91no—
371#544—92no—
372#544—92no—
373#533—31no—
374#533—92no—
375C2×C4⋊Q8—91no—
376C2×C4⋊Q8—92no—
377#520—91no—
378#520—91no—
379C4×#41—91no—
380C2×C3×Q8—32no—
381C2×C3×Q8—32no—
382C2×C3×Q8—34no—
383C22×C3×C4—21no—
384C22×C3×C4—31no—
385C22×C3×C4—31no—
386C22×C3×C4—32no—
387C22×C3×C4C22×D311yescharacteristic
388C22×C3×C4C22×D311yescharacteristic
389C2×#67—32no—
390C2×#67—32no—
391C2×#67—62no—
392C22×Dic3—32no—
393C22×Dic3—32no—
394C22×Dic3—62no—
395C22×Dic3C22×D311yescharacteristic
396C22×Dic3C22×D311yescharacteristic
397C22×Dic3C22×D312yes—
398D3×Q8—128no—
399D3×Q8—128no—
400#235—38no—
401#235—38no—
402#235—68no—
403C2×D12—31no—
404C2×D12—31no—
405C2×D12—61no—
406C2×C4×D3—32no—
407C2×C4×D3—32no—
408C2×C4×D3—32no—
409C2×C4×D3—32no—
410C2×C4×D3—32no—
411C2×C4×D3—32no—
412C2×C4×D3—34no—
413C2×C4×D3—34no—
414C2×C4×D3—34no—
415C2×C4×D3—34no—
416C2×C4×D3—62no—
417C2×C4×D3—64no—
418C2×Dic6—31no—
419C2×Dic6—31no—
420C2×Dic6—34no—
421C2×Dic6—34no—
422C2×Dic6—34no—
423C2×Dic6—34no—
424C2×Dic6—34no—
425C2×Dic6—34no—
426C2×Dic6—61no—
427C2×Dic6—124no—
428C2×Dic6—124no—
429C2×Dic6C22×D312yes—
430C2×Dic6C22×D312yes—
431C2×Dic6C22×D314yes—
432C3×C4⋊C4—21no—
433C3×C4⋊C4—21no—
434C3×C4⋊C4—32no—
435C3×C4⋊C4—32no—
436C3×C4⋊C4—31no—
437C3×C4⋊C4—34no—
438C3×C4⋊C4—34no—
439C3×C4⋊C4—31no—
440C3×C4⋊C4—32no—
441C3×C4⋊C4—31no—
442C3×C4⋊C4—32no—
443C3×C4⋊C4—32no—
444C3×C4⋊C4—32no—
445C3×C4⋊C4—34no—
446C3×C4⋊C4—32no—
447C3×C4⋊C4—32no—
448C3×C4⋊C4—31no—
449C3×C4⋊C4C22×D311yescharacteristic
450C3×C4⋊C4C22×D311yescharacteristic
451C3×C4⋊C4C22×D311yescharacteristic
452C3×C4⋊C4C22×D311yescharacteristic
453C3×C22⋊C4—22no—
454C3×C22⋊C4—32no—
455C3×C22⋊C4—32no—
456C3×C22⋊C4C22×D312yes—
457C3×C22⋊C4C22×D312yes—
458C3×C42—22no—
459C3×C42—31no—
460C3×C42—31no—
461C3×C42—32no—
462C3×C42—31no—
463C3×C42—31no—
464C3×C42—32no—
465C3×C42C22×D312yes—
466C3×C42C22×D312yes—
467#217C22×D312yes—
468#217C22×D312yes—
469(C2×D3)⋊C4—34no—
470(C2×D3)⋊C4—34no—
471(C2×D3)⋊C4—32no—
472(C2×D3)⋊C4—32no—
473(C2×D3)⋊C4—32no—
474(C2×D3)⋊C4—32no—
475(C2×D3)⋊C4—34no—
476(C2×D3)⋊C4—34no—
477(C2×D3)⋊C4—64no—
478C4⋊Dic3—32no—
479C4⋊Dic3—32no—
480C4⋊Dic3—32no—
481C4⋊Dic3—32no—
482C4⋊Dic3—34no—
483C4⋊Dic3—34no—
484C4⋊Dic3—34no—
485C4⋊Dic3—34no—
486C4⋊Dic3—62no—
487C4⋊Dic3—62no—
488C4⋊Dic3C22×D311yescharacteristic
489C4⋊Dic3C22×D312yes—
490C4⋊Dic3C22×D311yescharacteristic
491C4⋊Dic3C22×D312yes—
492C4⋊Dic3C22×D312yes—
493C4⋊Dic3C22×D311yescharacteristic
494C4⋊Dic3C22×D312yes—
495C4⋊Dic3C22×D314yes—
496C4⋊Dic3C22×D311yescharacteristic
497Dic3⋊C4—34no—
498Dic3⋊C4—34no—
499Dic3⋊C4—32no—
500Dic3⋊C4—32no—
501Dic3⋊C4—34no—
502Dic3⋊C4—34no—
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—32no—
507Dic3⋊C4—32no—
508Dic3⋊C4—34no—
509Dic3⋊C4—34no—
510Dic3⋊C4—34no—
511Dic3⋊C4—64no—
512Dic3⋊C4C22×D312yes—
513Dic3⋊C4C22×D312yes—
514Dic3⋊C4C22×D312yes—
515Dic3⋊C4C22×D312yes—
516Dic3⋊C4C22×D314yes—
517Dic3⋊C4C22×D314yes—
518C4×Dic3—34no—
519C4×Dic3—34no—
520C4×Dic3—32no—
521C4×Dic3—32no—
522C4×Dic3—34no—
523C4×Dic3—32no—
524C4×Dic3—32no—
525C4×Dic3—34no—
526C4×Dic3—64no—
527C4×Dic3C22×D311yescharacteristic
528C4×Dic3C22×D311yescharacteristic
529C4×Dic3C22×D312yes—
530C4×Dic3C22×D311yescharacteristic
531C4×Dic3C22×D312yes—
532C4×Dic3C22×D311yescharacteristic
533C22×C32—21no—
534C22×C32—21no—
535C22×C32C22×Q812yes—
536C22×C32C2511yescharacteristic
537C2×C3⋊D3—22no—
538C2×C3⋊D3—22no—
539C2×C3⋊D3C22×Q814yes—
540C32×C4—22no—
541C32×C4—22no—
542C32×C4C22×Q812yes—
543C32×C4C22×Q812yes—
544C3⋊Dic3—24no—
545C3⋊Dic3C22×Q814yes—
546C3×Dic3—22no—
547C3×Dic3—22no—
548C3×Dic3—24no—
549C3×Dic3—21no—
550C3×Dic3—22no—
551C3×Dic3—22no—
552C3×Dic3—21no—
553C3×Dic3H(5,𝔽2)12yes—
554C3×Dic32−1+412yes—
555C2×#41—91no—
556C22×Q8—92no—
557C22×Q8—94no—
558C4⋊Q8—31no—
559C4⋊Q8—32no—
560C4⋊Q8—31no—
561C4⋊Q8—32no—
562C4⋊Q8—92no—
563C4⋊Q8—92no—
564C4⋊Q8—92no—
565C4⋊Q8—92no—
566C4⋊Q8—92no—
567C4⋊Q8—92no—
568C4⋊Q8—94no—
569C4⋊Q8—94no—
570C4⋊Q8—94no—
571C4⋊Q8—94no—
572#125—31no—
573#125—31no—
574#125—32no—
575#125—32no—
576#125—92no—
577#125—92no—
578#125—94no—
579#125—94no—
580C22⋊Q8—32no—
581C22⋊Q8—32no—
582C22⋊Q8—34no—
583C22⋊Q8—94no—
584C22⋊Q8—94no—
585C22⋊Q8—94no—
586C22⋊Q8—94no—
587C22⋊Q8—94no—
588C22⋊Q8—94no—
589C22⋊Q8—94no—
590C4×Q8—32no—
591C4×Q8—32no—
592C4×Q8—91no—
593C4×Q8—91no—
594C4×Q8—92no—
595C4×Q8—94no—
596C4×Q8—94no—
597C4×Q8—92no—
598C4×D4—91no—
599C4×D4—91no—
600C4×D4—92no—
601C4×D4—92no—
602C4×D4—92no—
603C4×D4—94no—
604C4×D4—94no—
605C4×D4—92no—
606#117—31no—
607#117—31no—
608#117—92no—
609#117—92no—
610#117—92no—
611#117D3211yescharacteristic
612C2×C4⋊C4—31no—
613C2×C4⋊C4—92no—
614C2×C4⋊C4—94no—
615C2×C4⋊C4—92no—
616C2×C4⋊C4—91no—
617C2×C4⋊C4—92no—
618C2×C42—31no—
619C2×C42—92no—
620C23×C3—21no—
621C23×C3C23×D311yescharacteristic
622C23×C3C23×D311yescharacteristic
623C22×D3—32no—
624C22×D3—32no—
625C22×D3—62no—
626C3×Q8—64no—
627C3×Q8—64no—
628C3×Q8—124no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—22no—
632C2×C3×C4—22no—
633C2×C3×C4—24no—
634C2×C3×C4—31no—
635C2×C3×C4—31no—
636C2×C3×C4—32no—
637C2×C3×C4—32no—
638C2×C3×C4—32no—
639C2×C3×C4—34no—
640C2×C3×C4—32no—
641C2×C3×C4—31no—
642C2×C3×C4—31no—
643C2×C3×C4—62no—
644C2×C3×C4—62no—
645C2×C3×C4—122no—
646C2×C3×C4D3×Q814yescomplemented
647C2×C3×C4D3×Q814yescomplemented
648C2×C3×C4C23×D312yes—
649C2×C3×C4C23×D312yes—
650C2×C3×C4C23×D312yes—
651C2×C3×C4C23×D312yes—
652C2×C3×C4C23×D311yescharacteristic
653C2×C3×C4C23×D311yescharacteristic
654C2×C3×C4C23×D311yescharacteristic
655C2×C3×C4C23×D311yescharacteristic
656#67—38no—
657#67—38no—
658#67—68no—
659C2×Dic3—22no—
660C2×Dic3—22no—
661C2×Dic3—32no—
662C2×Dic3—32no—
663C2×Dic3—34no—
664C2×Dic3—34no—
665C2×Dic3—42no—
666C2×Dic3—62no—
667C2×Dic3—64no—
668C2×Dic3—122no—
669C2×Dic3—122no—
670C2×Dic3—242no—
671C2×Dic3C23×D312yes—
672C2×Dic3C23×D312yes—
673C2×Dic3C23×D312yes—
674C2×Dic3C23×D314yes—
675C2×Dic3C23×D311yescharacteristic
676C2×Dic3C23×D311yescharacteristic
677C2×Dic3C23×D312yes—
678C2×Dic3C23×D311yescharacteristic
679C2×Dic3C23×D311yescharacteristic
680D12—34no—
681D12—34no—
682D12—64no—
683C4×D3—38no—
684C4×D3—38no—
685C4×D3—68no—
686C4×D3—64no—
687C4×D3—64no—
688C4×D3—64no—
689C4×D3—64no—
690C4×D3—124no—
691C4×D3—124no—
692C4×D3—124no—
693C4×D3—124no—
694C4×D3—244no—
695Dic6—24no—
696Dic6—24no—
697Dic6—34no—
698Dic6—34no—
699Dic6—44no—
700Dic6—64no—
701Dic6—68no—
702Dic6—68no—
703Dic6—124no—
704Dic6—124no—
705Dic6—124no—
706Dic6—124no—
707C2×C32—22no—
708C2×C32C23×Q811yescharacteristic
709C2×C32C2×H(5,𝔽2)11yescharacteristic
710C2×C32C2×2−1+411yescharacteristic
711C3⋊D3—24no—
712#41—98no—
713C2×Q8—32no—
714C2×Q8—32no—
715C2×Q8—34no—
716C2×Q8—94no—
717C2×Q8—94no—
718C2×Q8—94no—
719C2×Q8—91no—
720C2×Q8—364no—
721C2×Q8—368no—
722C2×D4—92no—
723C2×D4—91no—
724C22×C4—31no—
725C22×C4—31no—
726C22×C4—32no—
727C22×C4—92no—
728C22×C4—92no—
729C22×C4—94no—
730C22×C4—92no—
731C22×C4—92no—
732C22×C4—94no—
733C22×C4C2×D3211yescharacteristic
734C4⋊C4—32no—
735C4⋊C4—32no—
736C4⋊C4—31no—
737C4⋊C4—32no—
738C4⋊C4—34no—
739C4⋊C4—31no—
740C4⋊C4—31no—
741C4⋊C4—31no—
742C4⋊C4—32no—
743C4⋊C4—32no—
744C4⋊C4—32no—
745C4⋊C4—32no—
746C4⋊C4—32no—
747C4⋊C4—34no—
748C4⋊C4—34no—
749C4⋊C4—94no—
750C4⋊C4—94no—
751C4⋊C4—94no—
752C4⋊C4—94no—
753C4⋊C4—92no—
754C4⋊C4—92no—
755C4⋊C4—94no—
756C4⋊C4—94no—
757C4⋊C4—92no—
758C4⋊C4—94no—
759C4⋊C4—92no—
760C4⋊C4C2×D3211yescharacteristic
761C4⋊C4C2×D3211yescharacteristic
762C22⋊C4—32no—
763C22⋊C4—32no—
764C22⋊C4—92no—
765C22⋊C4—92no—
766C22⋊C4—94no—
767C22⋊C4—94no—
768C22⋊C4C2×D3212yes—
769C42—31no—
770C42—31no—
771C42—31no—
772C42—31no—
773C42—32no—
774C42—32no—
775C42—92no—
776C42—92no—
777C42—94no—
778C42—94no—
779C42C2×D3212yes—
780C22×C3—21no—
781C22×C3—21no—
782C22×C3—21no—
783C22×C3—21no—
784C22×C3—22no—
785C22×C3—21no—
786C22×C3—41no—
787C22×C3—41no—
788C22×C3C2×D3×Q812yes—
789C22×C3C2×D3×Q812yes—
790C22×C3C24×D311yescharacteristic
791C22×C3C24×D311yescharacteristic
792C2×D3—34no—
793C2×D3—34no—
794C2×D3—64no—
795C2×D3—62no—
796C2×D3—62no—
797C2×D3—62no—
798C2×D3—62no—
799C2×D3—122no—
800C2×D3—122no—
801C3×C4—22no—
802C3×C4—22no—
803C3×C4—22no—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—22no—
807C3×C4—32no—
808C3×C4—32no—
809C3×C4—42no—
810C3×C4—42no—
811C3×C4—64no—
812C3×C4—62no—
813C3×C4—62no—
814C3×C4—61no—
815C3×C4—62no—
816C3×C4—61no—
817C3×C4—62no—
818C3×C4C2×D3×Q812yes—
819C3×C4C2×D3×Q812yes—
820C3×C4C2×D3×Q812yes—
821C3×C4C2×D3×Q812yes—
822Dic3—22no—
823Dic3—21no—
824Dic3—22no—
825Dic3—21no—
826Dic3—22no—
827Dic3—24no—
828Dic3—22no—
829Dic3—34no—
830Dic3—34no—
831Dic3—64no—
832Dic3—64no—
833Dic3—64no—
834Dic3—124no—
835Dic3#100912yes—
836Dic3#101012yes—
837C32#350311yescharacteristic, complemented, Sylow
838C23—92no—
839C23C22×D3211yescharacteristic
840Q8—64no—
841Q8—64no—
842Q8—94no—
843Q8—124no—
844Q8—188no—
845Q8—364no—
846Q8—364no—
847D4—98no—
848D4—94no—
849C2×C4—31no—
850C2×C4—31no—
851C2×C4—31no—
852C2×C4—31no—
853C2×C4—32no—
854C2×C4—32no—
855C2×C4—32no—
856C2×C4—32no—
857C2×C4—34no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—92no—
861C2×C4—98no—
862C2×C4—94no—
863C2×C4—122no—
864C2×C4—184no—
865C2×C4—184no—
866C2×C4—364no—
867C2×C4—364no—
868C2×C4—362no—
869C2×C4#379714yescomplemented
870C2×C4C22×D3212yes—
871C2×C4C22×D3212yes—
872C2×C4C22×D3211yescharacteristic
873C2×C4C22×D3211yescharacteristic
874C2×C3—22no—
875C2×C3—22no—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—21no—
879C2×C3—42no—
880C2×C3C22×D3×Q811yescharacteristic
881C2×C3C22×D3×Q811yescharacteristic
882C2×C3C2×#100911yescharacteristic
883C2×C3C2×#101011yescharacteristic
884C2×C3D3×H(5,𝔽2)11yescharacteristic
885C2×C3D3×2−1+411yescharacteristic
886D3—64no—
887D3—64no—
888D3—124no—
889C22—21no—
890C22—21no—
891C22—94no—
892C22—182no—
893C22—182no—
894C22C2×#379712yes—
895C22C23×D3211yescharacteristic
896C4—22no—
897C4—22no—
898C4—32no—
899C4—32no—
900C4—61no—
901C4—64no—
902C4—62no—
903C4—62no—
904C4—61no—
905C4—62no—
906C4—62no—
907C4—94no—
908C4—184no—
909C4C2×#379712yes—
910C4C2×#379712yes—
911C3—21no—
912C3#8628111yescharacteristic, complemented
913C3#8658611yescharacteristic, complemented
914C2—22no—
915C2—184no—
916C2C22×#379711yescharacteristic
917C2D3×#100911yescharacteristic
918C2D3×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
prime radicalC2×#3828C22
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
2. C3×#5519C2semidirect
3. C3×#5517C2semidirect
4. #10595052C2semidirect
5. C2×#63918C2semidirect
8. #10594508C2semidirect
9. #10594448C2semidirect
10. #10594374C2semidirect
11. #10594325C2semidirect
12. #10594141C2semidirect
13. #10594072C2semidirect
14. #10593938C2semidirect
15. #10593903C2semidirect
16. #10593856C2semidirect
17. #10593852C2semidirect
114. #5519D3semidirect
115. #5517D3semidirect
123. #3828Q8semidirect
329. C2×C32×C4C2×Q8semidirect
334. #638C2×Q8semidirect
338. C4⋊(C3⋊D3)C2×Q8semidirect
340. C4×C3⋊D3C2×Q8semidirect
341. #634C2×Q8semidirect
646. C2×C3×C4D3×Q8semidirect
647. C2×C3×C4D3×Q8semidirect
837. C32#3503semidirect
869. C2×C4#3797semidirect
912. C3#86281semidirect
913. C3#86586semidirect

Maximal subgroups

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

subgroupindex
#105959942
C3×#55192
C3×#55172
#105950522
C2×#639182
#105949902
#105949542
#105945082
#105944482
#105943742
#105943252
#105941412
#105940722
#105939382
#105939032
#105938562
#105938522
#865863
#862813