Finite Group Databasebeta

← #11909923

Subgroups — #11909923

Order 1152.

2095 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596199C211yesmaximal, characteristic, complemented
2C3×#5732C211yesmaximal, characteristic, complemented
3C3×#5721C211yesmaximal, characteristic, complemented
4#10595422C212yesmaximal, complemented
5#10595384C212yesmaximal, complemented
6#10595382C212yesmaximal
7#10595374C212yesmaximal, complemented
8#10594584C212yesmaximal, complemented
9#10594462C214yesmaximal, complemented
10#10594459C214yesmaximal, complemented
11#10594383C212yesmaximal, complemented
12#10594357C212yesmaximal, complemented
13#10594346C212yesmaximal, complemented
14Dic6×D12C211yesmaximal, characteristic, complemented
15C4×#3797C211yesmaximal, characteristic, complemented
16#10593875C211yesmaximal, characteristic
17#10593860C211yesmaximal, characteristic, complemented
18#87024—31nomaximal
19#86993—31nomaximal
20C2×#3797C2211yescharacteristic
21C2×D3×Dic6C2212yes—
22C32×C4⋊Q8C2211yescharacteristic
23#64155C2212yes—
24Q8×C3⋊Dic3C2212yes—
25#64106C2212yes—
26#64101C2212yes—
27#64099C2212yes—
28#64096C2212yes—
29C42×C3⋊D3C2211yescharacteristic
30#64078C2211yescharacteristic
31C3×#947C2212yes—
32C3×Q8×Dic3C2212yes—
33C3×Q8×Dic3C2212yes—
34C3×#944C2212yes—
35C3×#898C2214yes—
36C3×#897C2212yes—
37C3×#892C2212yes—
38C3×#890C2212yes—
39C3×#889C2214yes—
40C3×#887C2212yes—
41C3×C4×D12C2211yescharacteristic
42C3×C4×Dic6C2211yescharacteristic
43C3×C4×Dic6C2211yescharacteristic
44C3×C4×Dic6C2211yescharacteristic
45#63918C2212yes—
46#63918C2214yes—
47C4×#627C2214yes—
48C4×#627C2212yes—
49#63916C2211yescharacteristic
50C4×#626C2212yes—
51#63900C2211yescharacteristic
52#63895C2214yes—
53#63893C2214yes—
54#63893C2214yes—
55Dic3×D12C2212yes—
56#63883C2212yes—
57C4×#624C2212yes—
58#63880C2214yes—
59#63878C2214yes—
60#63877C2214yes—
61#63872C2214yes—
62#63872C2211yescharacteristic
63#63871C2211yescharacteristic
64#63869C2214yes—
65#63869C2212yes—
66#63866C2212yes—
67#63863C2211yescharacteristic
68#63862C2214yes—
69#63862C2212yes—
70#63861C2214yes—
71#63858C2214yes—
72#63857C2212yes—
73#63855C2212yes—
74#63854C2214yes—
75#63853C2212yes—
76#63846C2214yes—
77#63845C2214yes—
78#63844C2212yes—
79#63843C2211yescharacteristic
80#63843C2211yescharacteristic
81Dic3×Dic6C2212yes—
82#63838C2212yes—
83#63837C2214yes—
84#63836C2214yes—
85C3×#557—31no—
86C3×#556—31no—
87#5732—32no—
88#5732D311yescharacteristic, complemented
89#5728—31no—
90#5728—31no—
91#5728—32no—
92#5728—61no—
93#5721D311yescharacteristic, complemented
94#5708—34no—
95#5701—34no—
96#5698—34no—
97#5698—32no—
98#5694—34no—
99#5694—32no—
100#5680—32no—
101#5671—32no—
102#5632—32no—
103#5625—32no—
104#5580—32no—
105#5580—31no—
106#5578—32no—
107Q8×D12—32no—
108Q8×D12—31no—
109#5572—32no—
110C4×D3×Q8—31no—
111C4×D3×Q8—31no—
112#5570—32no—
113#5570—31no—
114#5569—32no—
115#5567—31no—
116#5557—31no—
117D4×Dic6—31no—
118#5529—32no—
119#5516—32no—
120C2×C32×Q8C2312yes—
121C2×C4×C3⋊D3C2311yescharacteristic
122C2×C4×C3⋊D3C2311yescharacteristic
123C2×C4×C3⋊D3C2311yescharacteristic
124C2×#634C2312yes—
125C2×C3×D12C2311yescharacteristic
126C2×C3×C4×D3C2312yes—
127C2×C3×Dic6C2311yescharacteristic
128C2×C3×Dic6C2311yescharacteristic
129C2×C3×Dic6C2311yescharacteristic
130C2×#627C2314yes—
131C2×#627C2312yes—
132C2×#626C2312yes—
133C2×#624C2312yes—
134C2×#624C2312yes—
135C2×D3×Dic3C2314yes—
136#3797—24no—
137D3×Dic6—28no—
138C32×C4⋊C4C2312yes—
139C32×C4⋊C4C2312yes—
140C32×C42C2311yescharacteristic
141#3752C2314yes—
142C4⋊(C3⋊Dic3)C2312yes—
143C4⋊(C3⋊Dic3)C2312yes—
144C4⋊(C3⋊Dic3)C2314yes—
145#3750C2314yes—
146C4×C3⋊Dic3C2311yescharacteristic
147C4×C3⋊Dic3C2311yescharacteristic
148C4×C3⋊Dic3C2311yescharacteristic
149C4×C3⋊Dic3C2314yes—
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2312yes—
153C3×C4⋊Dic3C2314yes—
154C3×C4⋊Dic3C2311yescharacteristic
155C3×C4⋊Dic3C2311yescharacteristic
156C3×C4⋊Dic3C2314yes—
157C3×C4⋊Dic3C2311yescharacteristic
158C3×C4⋊Dic3C2311yescharacteristic
159C3×Dic3⋊C4C2314yes—
160C3×Dic3⋊C4C2312yes—
161C3×Dic3⋊C4C2312yes—
162C3×Dic3⋊C4C2314yes—
163C3×Dic3⋊C4C2312yes—
164C3×C4×Dic3C2314yes—
165C3×C4×Dic3C2312yes—
166C3×C4×Dic3C2314yes—
167C3×C4×Dic3C2312yes—
168C3×C4×Dic3C2312yes—
169#3724C2312yes—
170#3724C2314yes—
171Dic3⋊Dic3C2314yes—
172Dic3⋊Dic3C2312yes—
173Dic3⋊Dic3C2314yes—
174Dic3⋊Dic3C2312yes—
175Dic3⋊Dic3C2312yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2312yes—
178Dic3⋊Dic3C2312yes—
179#3722C2312yes—
180(C2×D3)⋊Dic3C2312yes—
181(C2×D3)⋊Dic3C2314yes—
182(C2×D3)⋊Dic3C2312yes—
183(C2×D3)⋊Dic3C2312yes—
184Dic32C2314yes—
185Dic32C2312yes—
186Dic32C2312yes—
187#3523—91noSylow
188C2×D3×Q8—32no—
189C2×D3×Q8—31no—
190C2×D3×Q8—31no—
191C22×Dic6—32no—
192C3×C4⋊Q8—21no—
193C3×C4⋊Q8—32no—
194C3×C4⋊Q8C2×D311yescharacteristic
195C3×C4⋊Q8C2×D311yescharacteristic
196C3×#126—34no—
197C3×#125—34no—
198C3×#125—32no—
199C3×#124—32no—
200C3×C22⋊Q8—32no—
201C3×C4×Q8—32no—
202C3×C4×Q8—32no—
203C3×C4×Q8—32no—
204C3×C4×Q8—31no—
205C3×C4×Q8—31no—
206C3×C4×Q8—31no—
207C3×C4×D4—31no—
208C3×#117—32no—
209#947—31no—
210#947C2×D312yes—
211#946—32no—
212#946—32no—
213#946—31no—
214#946—62no—
215Q8×Dic3—32no—
216Q8×Dic3—32no—
217Q8×Dic3—31no—
218Q8×Dic3—31no—
219Q8×Dic3—32no—
220Q8×Dic3—62no—
221Q8×Dic3C2×D312yes—
222Q8×Dic3C2×D312yes—
223#944—32no—
224#944C2×D312yes—
225#938—31no—
226#936—31no—
227D4×Dic3—32no—
228C4×#67—32no—
229#926—32no—
230#924—32no—
231#898—34no—
232#898—34no—
233#898—34no—
234#898—32no—
235#898C2×D314yes—
236#897—32no—
237#897—31no—
238#897—32no—
239#897—32no—
240#897—34no—
241#897—34no—
242#897—34no—
243#897—62no—
244#897C2×D312yes—
245#896—34no—
246#895—31no—
247#894—32no—
248#894—34no—
249#892—32no—
250#892—32no—
251#892—34no—
252#892—34no—
253#892—62no—
254#892C2×D312yes—
255D3×C4⋊C4—31no—
256D3×C4⋊C4—31no—
257D3×C4⋊C4—32no—
258D3×C4⋊C4—32no—
259#890—32no—
260#890—32no—
261#890—34no—
262#890—34no—
263#890—34no—
264#890—31no—
265#890—31no—
266#890—34no—
267#890—34no—
268#890—32no—
269#890—62no—
270#890C2×D312yes—
271#889—34no—
272#889—34no—
273#889C2×D314yes—
274#888—34no—
275#888—32no—
276#887—31no—
277#887—31no—
278#887—32no—
279#887—32no—
280#887—32no—
281#887—32no—
282#887—34no—
283#887—32no—
284#887—62no—
285#887C2×D312yes—
286#883—34no—
287#883—32no—
288#67⋊C4—34no—
289#879—34no—
290#879—34no—
291#879—34no—
292#879—32no—
293#878—34no—
294#878—34no—
295#877—34no—
296#877—34no—
297C4×D12—32no—
298C4×D12—32no—
299C4×D12—34no—
300C4×D12C2×D311yescharacteristic
301#872—32no—
302#872—34no—
303#872—34no—
304C42×D3—31no—
305C42×D3—31no—
306C42×D3—32no—
307C42×D3—32no—
308C42×D3—61no—
309#870—32no—
310#870—34no—
311#869—32no—
312#869—31no—
313#869—31no—
314#869—34no—
315#869—32no—
316#869—61no—
317C4×Dic6—32no—
318C4×Dic6—32no—
319C4×Dic6—34no—
320C4×Dic6—32no—
321C4×Dic6—34no—
322C4×Dic6—34no—
323C4×Dic6—32no—
324C4×Dic6C2×D311yescharacteristic
325C4×Dic6C2×D311yescharacteristic
326C4×Dic6C2×D311yescharacteristic
327C22×C3⋊D3C2411yescharacteristic
328C22×C3×D3C2412yes—
329C32×Q8—24no—
330C2×C32×C4C2414yes—
331C2×C32×C4C2411yescharacteristic
332C2×C32×C4C2411yescharacteristic
333C2×C32×C4C2411yescharacteristic
334C2×C3⋊Dic3C2411yescharacteristic
335C2×C3⋊Dic3C2414yes—
336C2×C3⋊Dic3C2411yescharacteristic
337C2×C3⋊Dic3C2411yescharacteristic
338C4×C3⋊D3—22no—
339C4×C3⋊D3—22no—
340C4×C3⋊D3—22no—
341#634—24no—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C3×D12—22no—
350C3×C4×D3—24no—
351C3×Dic6—22no—
352C3×Dic6—22no—
353C3×Dic6#4114yes—
354#627—28no—
355#627—24no—
356#626—24no—
357#624—24no—
358#624—24no—
359D3×Dic3—28no—
360#557—31no—
361#557—91no—
362#557—92no—
363#556—31no—
364#556—92no—
365#552—92no—
366#552—94no—
367D4×Q8—91no—
368D4×Q8—92no—
369#541—92no—
370#541—94no—
371#533—92no—
372#533—91no—
373#529—91no—
374#529—92no—
375#519—92no—
376C2×C4×Q8—91no—
377C2×C3×Q8—22no—
378C2×C3×Q8—31no—
379C2×C3×Q8—31no—
380C2×C3×Q8—31no—
381C2×C3×Q8C22×D312yes—
382C2×C3×Q8C22×D312yes—
383C2×C3×D4—31no—
384C22×C3×C4—32no—
385C2×#67—32no—
386C22×Dic3—34no—
387D3×Q8—64no—
388D3×Q8—68no—
389D3×Q8—64no—
390C2×D12—32no—
391C2×D12C22×D311yescharacteristic
392C2×C4×D3—34no—
393C2×C4×D3—31no—
394C2×C4×D3—31no—
395C2×C4×D3—31no—
396C2×C4×D3—31no—
397C2×C4×D3—31no—
398C2×C4×D3—31no—
399C2×C4×D3—32no—
400C2×C4×D3—32no—
401C2×C4×D3—32no—
402C2×C4×D3—32no—
403C2×C4×D3—61no—
404C2×C4×D3—61no—
405C2×C4×D3—61no—
406C2×C4×D3C22×D312yes—
407C2×Dic6—32no—
408C2×Dic6—32no—
409C2×Dic6—34no—
410C2×Dic6—32no—
411C2×Dic6—34no—
412C2×Dic6—32no—
413C2×Dic6—62no—
414C2×Dic6—68no—
415C2×Dic6C22×D311yescharacteristic
416C2×Dic6C22×D311yescharacteristic
417C2×Dic6C22×D311yescharacteristic
418C3×C4⋊C4—22no—
419C3×C4⋊C4—22no—
420C3×C4⋊C4—31no—
421C3×C4⋊C4—32no—
422C3×C4⋊C4—32no—
423C3×C4⋊C4—31no—
424C3×C4⋊C4—34no—
425C3×C4⋊C4—31no—
426C3×C4⋊C4—34no—
427C3×C4⋊C4—31no—
428C3×C4⋊C4—32no—
429C3×C4⋊C4—34no—
430C3×C4⋊C4—34no—
431C3×C4⋊C4C22×D312yes—
432C3×C4⋊C4C22×D312yes—
433C3×C4⋊C4C22×D312yes—
434C3×C4⋊C4C22×D312yes—
435C3×C22⋊C4—34no—
436C3×C22⋊C4—32no—
437C3×C22⋊C4—34no—
438C3×C42—21no—
439C3×C42—32no—
440C3×C42—34no—
441C3×C42—32no—
442C3×C42—34no—
443C3×C42—32no—
444C3×C42C22×D311yescharacteristic
445C3×C42C22×D311yescharacteristic
446#217—32no—
447#217—32no—
448#217—32no—
449#217—34no—
450(C2×D3)⋊C4—32no—
451(C2×D3)⋊C4—32no—
452(C2×D3)⋊C4—34no—
453(C2×D3)⋊C4—32no—
454(C2×D3)⋊C4—34no—
455(C2×D3)⋊C4—34no—
456(C2×D3)⋊C4—32no—
457(C2×D3)⋊C4—32no—
458(C2×D3)⋊C4—64no—
459(C2×D3)⋊C4C22×D314yes—
460(C2×D3)⋊C4C22×D314yes—
461(C2×D3)⋊C4C22×D312yes—
462C4⋊Dic3—32no—
463C4⋊Dic3—32no—
464C4⋊Dic3—32no—
465C4⋊Dic3—32no—
466C4⋊Dic3—34no—
467C4⋊Dic3—34no—
468C4⋊Dic3—32no—
469C4⋊Dic3—32no—
470C4⋊Dic3—32no—
471C4⋊Dic3—32no—
472C4⋊Dic3—34no—
473C4⋊Dic3—32no—
474C4⋊Dic3—34no—
475C4⋊Dic3—34no—
476C4⋊Dic3—62no—
477C4⋊Dic3—62no—
478C4⋊Dic3—64no—
479C4⋊Dic3C22×D311yescharacteristic
480C4⋊Dic3C22×D311yescharacteristic
481C4⋊Dic3C22×D311yescharacteristic
482C4⋊Dic3C22×D311yescharacteristic
483C4⋊Dic3C22×D314yes—
484C4⋊Dic3C22×D314yes—
485Dic3⋊C4—34no—
486Dic3⋊C4—34no—
487Dic3⋊C4—32no—
488Dic3⋊C4—32no—
489Dic3⋊C4—34no—
490Dic3⋊C4—34no—
491Dic3⋊C4—32no—
492Dic3⋊C4—34no—
493Dic3⋊C4—32no—
494Dic3⋊C4—32no—
495Dic3⋊C4—32no—
496Dic3⋊C4—34no—
497Dic3⋊C4—34no—
498Dic3⋊C4—32no—
499Dic3⋊C4—64no—
500Dic3⋊C4C22×D314yes—
501Dic3⋊C4C22×D312yes—
502Dic3⋊C4C22×D312yes—
503Dic3⋊C4C22×D312yes—
504Dic3⋊C4C22×D314yes—
505C4×Dic3—31no—
506C4×Dic3—31no—
507C4×Dic3—34no—
508C4×Dic3—34no—
509C4×Dic3—31no—
510C4×Dic3—31no—
511C4×Dic3—31no—
512C4×Dic3—31no—
513C4×Dic3—32no—
514C4×Dic3—34no—
515C4×Dic3—34no—
516C4×Dic3—32no—
517C4×Dic3—32no—
518C4×Dic3—32no—
519C4×Dic3—61no—
520C4×Dic3—61no—
521C4×Dic3—61no—
522C4×Dic3—64no—
523C4×Dic3C22×D312yes—
524C4×Dic3C22×D312yes—
525C4×Dic3C22×D314yes—
526C4×Dic3C22×D314yes—
527C4×Dic3C22×D312yes—
528C22×C32C2511yescharacteristic
529C2×C3⋊D3—21no—
530C2×C3⋊D3—21no—
531C2×C3⋊D32−1+412yes—
532C2×C3×D3—22no—
533C2×C3×D3—22no—
534C2×C3×D3—22no—
535C32×C4—21no—
536C32×C4—24no—
537C32×C4C2×#4112yes—
538C32×C42−1+412yes—
539C3⋊Dic3—21no—
540C3⋊Dic3—24no—
541C3⋊Dic3—21no—
542C3⋊Dic3—21no—
543C3×Dic3—22no—
544C3×Dic3—22no—
545C3×Dic3—22no—
546C3×Dic3—22no—
547C3×Dic3—22no—
548C3×Dic3—22no—
549C3×Dic3C2×#4114yes—
550C22×Q8—92no—
551C22×Q8—91no—
552C4⋊Q8—32no—
553C4⋊Q8—92no—
554C4⋊Q8—94no—
555C4⋊Q8—92no—
556C4⋊Q8—91no—
557C4⋊Q8D3211yescharacteristic
558#126—34no—
559#126—94no—
560#126—92no—
561#126—94no—
562#126—94no—
563#125—34no—
564#125—32no—
565#125—92no—
566#125—94no—
567#125—91no—
568#125—94no—
569#125—94no—
570#125—94no—
571#125—92no—
572#124—32no—
573#124—91no—
574#123—94no—
575#123—92no—
576C22⋊Q8—32no—
577C22⋊Q8—94no—
578C22⋊Q8—94no—
579C22⋊Q8—94no—
580C22⋊Q8—92no—
581C22⋊Q8—91no—
582C22⋊Q8—92no—
583C22⋊Q8—92no—
584#121—91no—
585C4×Q8—32no—
586C4×Q8—32no—
587C4×Q8—32no—
588C4×Q8—31no—
589C4×Q8—31no—
590C4×Q8—31no—
591C4×Q8—92no—
592C4×Q8—94no—
593C4×Q8—94no—
594C4×Q8—92no—
595C4×Q8—92no—
596C4×Q8—92no—
597C4×Q8—91no—
598C4×Q8—91no—
599C4×Q8—92no—
600C4×Q8—92no—
601C4×D4—31no—
602C4×D4—94no—
603C4×D4—92no—
604C4×D4—92no—
605#117—32no—
606#117—94no—
607#117—94no—
608#117—92no—
609#117—94no—
610#117—92no—
611C2×C4⋊C4—91no—
612C2×C4⋊C4—92no—
613C2×C42—92no—
614C2×C42—91no—
615C23×C3—32no—
616C22×D3—31no—
617C22×D3—31no—
618C22×D3—61no—
619C22×D3C23×D312yes—
620C3×Q8—24no—
621C3×Q8—24no—
622C3×Q8—34no—
623C3×Q8—44no—
624C3×Q8—62no—
625C3×Q8—62no—
626C3×D4—62no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—24no—
631C2×C3×C4—32no—
632C2×C3×C4—32no—
633C2×C3×C4—32no—
634C2×C3×C4—32no—
635C2×C3×C4—32no—
636C2×C3×C4—32no—
637C2×C3×C4—32no—
638C2×C3×C4—64no—
639C2×C3×C4C23×D314yes—
640C2×C3×C4C23×D314yes—
641C2×C3×C4C23×D311yescharacteristic
642C2×C3×C4C23×D311yescharacteristic
643C2×C3×C4C23×D311yescharacteristic
644C2×C3×C4C23×D311yescharacteristic
645C2×C3×C4C23×D311yescharacteristic
646C2×C3×C4C23×D311yescharacteristic
647#67—64no—
648C2×Dic3—31no—
649C2×Dic3—31no—
650C2×Dic3—31no—
651C2×Dic3—31no—
652C2×Dic3—34no—
653C2×Dic3—31no—
654C2×Dic3—34no—
655C2×Dic3—31no—
656C2×Dic3—61no—
657C2×Dic3—61no—
658C2×Dic3—61no—
659C2×Dic3—64no—
660C2×Dic3—68no—
661C2×Dic3C23×D312yes—
662C2×Dic3C23×D312yes—
663C2×Dic3C23×D312yes—
664C2×Dic3C23×D312yes—
665C2×Dic3C23×D312yes—
666C2×Dic3C23×D312yes—
667C2×Dic3C23×D312yes—
668D12—22no—
669D12—64no—
670C4×D3—24no—
671C4×D3—64no—
672C4×D3—64no—
673C4×D3—64no—
674C4×D3—62no—
675C4×D3—62no—
676C4×D3—64no—
677C4×D3—68no—
678C4×D3—62no—
679C4×D3—62no—
680C4×D3—62no—
681C4×D3—62no—
682C4×D3—64no—
683C4×D3—122no—
684C4×D3—122no—
685Dic6—22no—
686Dic6—22no—
687Dic6—64no—
688Dic6—68no—
689Dic6—64no—
690Dic6—64no—
691Dic6—68no—
692Dic6—64no—
693Dic6—124no—
694Dic6#23914yes—
695C2×C32C22×#4111yescharacteristic
696C2×C32C2×2−1+411yescharacteristic
697C2×C32C2×2−1+411yescharacteristic
698C3⋊D3—22no—
699C3×D3—42no—
700C2×Q8—31no—
701C2×Q8—31no—
702C2×Q8—31no—
703C2×Q8—94no—
704C2×Q8—92no—
705C2×Q8—92no—
706C2×Q8—188no—
707C2×Q8—184no—
708C2×Q8C2×D3212yes—
709C2×D4—31no—
710C2×D4—92no—
711C22×C4—32no—
712C22×C4—92no—
713C22×C4—92no—
714C22×C4—94no—
715C22×C4—91no—
716C22×C4—91no—
717C22×C4—91no—
718C4⋊C4—31no—
719C4⋊C4—32no—
720C4⋊C4—31no—
721C4⋊C4—32no—
722C4⋊C4—34no—
723C4⋊C4—34no—
724C4⋊C4—31no—
725C4⋊C4—31no—
726C4⋊C4—34no—
727C4⋊C4—32no—
728C4⋊C4—34no—
729C4⋊C4—92no—
730C4⋊C4—92no—
731C4⋊C4—92no—
732C4⋊C4—92no—
733C4⋊C4—94no—
734C4⋊C4—92no—
735C4⋊C4—94no—
736C4⋊C4—92no—
737C4⋊C4—94no—
738C4⋊C4—94no—
739C4⋊C4—94no—
740C4⋊C4—92no—
741C4⋊C4—92no—
742C4⋊C4—94no—
743C4⋊C4C2×D3212yes—
744C4⋊C4C2×D3212yes—
745C22⋊C4—34no—
746C22⋊C4—32no—
747C22⋊C4—34no—
748C22⋊C4—92no—
749C22⋊C4—92no—
750C22⋊C4—92no—
751C22⋊C4—94no—
752C22⋊C4—92no—
753C22⋊C4—94no—
754C42—32no—
755C42—32no—
756C42—34no—
757C42—34no—
758C42—32no—
759C42—92no—
760C42—92no—
761C42—94no—
762C42—91no—
763C42—91no—
764C42—91no—
765C42—94no—
766C42C2×D3211yescharacteristic
767C22×C3—21no—
768C22×C3—62no—
769C22×C3—62no—
770C22×C3—62no—
771C22×C3C24×D311yescharacteristic
772C22×C3C24×D311yescharacteristic
773C2×D3—22no—
774C2×D3—22no—
775C2×D3—22no—
776C2×D3—32no—
777C2×D3—32no—
778C2×D3—62no—
779C2×D3—61no—
780C2×D3—61no—
781C2×D3—61no—
782C2×D3—61no—
783C2×D3—121no—
784C2×D3—121no—
785C3×C4—22no—
786C3×C4—24no—
787C3×C4—24no—
788C3×C4—21no—
789C3×C4—21no—
790C3×C4—22no—
791C3×C4—22no—
792C3×C4—34no—
793C3×C4—44no—
794C3×C4—62no—
795C3×C4—62no—
796C3×C4—62no—
797C3×C4—62no—
798C3×C4—62no—
799C3×C4—62no—
800C3×C4C2×#23912yes—
801C3×C4D3×#4112yes—
802C3×C4#101012yes—
803C3×C4#101012yes—
804Dic3—22no—
805Dic3—22no—
806Dic3—22no—
807Dic3—22no—
808Dic3—22no—
809Dic3—22no—
810Dic3—62no—
811Dic3—61no—
812Dic3—64no—
813Dic3—61no—
814Dic3—64no—
815Dic3—61no—
816Dic3—61no—
817Dic3—61no—
818Dic3—61no—
819Dic3—124no—
820Dic3—121no—
821Dic3—121no—
822Dic3C2×#23914yes—
823C32#352311yescharacteristic, complemented, Sylow
824C23—32no—
825C23—91no—
826Q8—24no—
827Q8—34no—
828Q8—62no—
829Q8—62no—
830Q8—188no—
831Q8—184no—
832Q8—184no—
833D4—62no—
834D4—184no—
835C2×C4—32no—
836C2×C4—32no—
837C2×C4—32no—
838C2×C4—32no—
839C2×C4—32no—
840C2×C4—32no—
841C2×C4—32no—
842C2×C4—64no—
843C2×C4—91no—
844C2×C4—91no—
845C2×C4—94no—
846C2×C4—91no—
847C2×C4—182no—
848C2×C4—184no—
849C2×C4—188no—
850C2×C4—184no—
851C2×C4—182no—
852C2×C4—182no—
853C2×C4C22×D3214yes—
854C2×C4C22×D3211yescharacteristic
855C2×C4C22×D3211yescharacteristic
856C2×C4C22×D3211yescharacteristic
857C2×C3—21no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—122no—
861C2×C3C22×#23911yescharacteristic
862C2×C3C2×D3×#4111yescharacteristic
863C2×C3C2×#101011yescharacteristic
864C2×C3C2×#101011yescharacteristic
865C2×C3D3×2−1+411yescharacteristic
866C2×C3D3×2−1+411yescharacteristic
867D3—42no—
868D3—62no—
869D3—62no—
870D3—122no—
871C22—62no—
872C22—62no—
873C22—62no—
874C22—92no—
875C22—181no—
876C22—181no—
877C22C23×D3211yescharacteristic
878C4—24no—
879C4—21no—
880C4—34no—
881C4—62no—
882C4—62no—
883C4—62no—
884C4—62no—
885C4—62no—
886C4—62no—
887C4—181no—
888C4—184no—
889C4—181no—
890C4—181no—
891C4#6430912yes—
892C4D3×#23912yes—
893C3—21no—
894C3#8699311yescharacteristic, complemented
895C3#8702411yescharacteristic, complemented
896C2—122no—
897C2—182no—
898C2C2×#6430911yescharacteristic
899C2C2×D3×#23911yescharacteristic
900C2#1059668711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
prime radical#63916C22
hypercenterC4⋊Q8D32
hypocenterC32#3523
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596199C2semidirect
2. C3×#5732C2semidirect
3. C3×#5721C2semidirect
4. #10595422C2semidirect
5. #10595384C2semidirect
7. #10595374C2semidirect
8. #10594584C2semidirect
9. #10594462C2semidirect
10. #10594459C2semidirect
11. #10594383C2semidirect
12. #10594357C2semidirect
13. #10594346C2semidirect
14. Dic6×D12C2semidirect
15. C4×#3797C2semidirect
17. #10593860C2semidirect
88. #5732D3semidirect
93. #5721D3semidirect
823. C32#3523semidirect
894. C3#86993semidirect
895. C3#87024semidirect

Maximal subgroups

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

subgroupindex
#105961992
C3×#57322
C3×#57212
#105954222
#105953842
#105953822
#105953742
#105945842
#105944622
#105944592
#105943832
#105943572
#105943462
Dic6×D122
C4×#37972
#105938752
#105938602
#870243
#869933