Finite Group Databasebeta

← #11901951

Subgroups — #11901951

Order 1152.

2095 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#10595990C211yesmaximal, characteristic, complemented
2C3×D3×#117C211yesmaximal, characteristic
3C3×#5519C211yesmaximal, characteristic, complemented
4#10595052C211yesmaximal, characteristic, complemented
5#10595051C211yesmaximal, characteristic, complemented
6D3×#926C211yesmaximal, characteristic
7C2×#63841C211yesmaximal, characteristic
8#10594477C212yesmaximal, complemented
9#10594445C212yesmaximal, complemented
10#10594344C212yesmaximal, complemented
11#10594342C212yesmaximal, complemented
12#10594170C214yesmaximal
13#10594029C214yesmaximal, complemented
14#10593959C212yesmaximal, complemented
15#10593954C212yesmaximal, complemented
16#10593874C212yesmaximal, complemented
17#10593859C212yesmaximal, complemented
18#86581—31nomaximal
19#85725—31nomaximal
20C22×C3×C4×D3C2211yescharacteristic
21C32×#117C2211yescharacteristic
22#64135C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24#64099C2212yescomplemented
25#64097C2212yescomplemented
26#64087C2214yes—
27#64079C2212yescomplemented
28#64078C2212yescomplemented
29C3×#926C2211yescharacteristic
30C3×#926C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C3×#892C2211yescharacteristic
33C3×#892C2211yescharacteristic
34C3×D3×C4⋊C4C2211yescharacteristic
35C3×D3×C4⋊C4C2211yescharacteristic
36C3×#890C2212yescomplemented
37C3×#888C2212yescomplemented
38C3×D3×C22⋊C4C2212yes—
39C3×#878C2214yes—
40C3×#877C2212yes—
41C3×#872C2212yes—
42C3×C42×D3C2212yes—
43C3×#870C2212yescomplemented
44C3×#869C2212yescomplemented
45#63982C2214yes—
46D3×#217C2212yes—
47#63964C2214yes—
48C2×(C2×D3)⋊Dic3C2212yes—
49#63955C2212yes—
50C2×Dic32C2212yes—
51#63919C2212yescomplemented
52#63918C2212yescomplemented
53#63918C2212yescomplemented
54#63918C2212yescomplemented
55#63899C2214yes—
56#63896C2214yes—
57#63893C2214yes—
58D3×C4⋊Dic3C2211yescharacteristic
59D3×C4⋊Dic3C2211yescharacteristic
60#63887C2214yes—
61C4×D3×Dic3C2212yes—
62#63872C2212yescomplemented
63#63869C2212yescomplemented
64#63869C2212yescomplemented
65#63869C2212yescomplemented
66#63857C2214yes—
67#63856C2214yes—
68#63855C2212yes—
69#63851C2214yes—
70#63851C2214yes—
71#63846C2214yescomplemented
72#63845C2214yescomplemented
73#63844C2214yescomplemented
74Dic3×Dic6C2214yescomplemented
75#63841C2212yes—
76#63841C2211yescharacteristic
77#63841C2212yes—
78#63841C2211yescharacteristic
79#63841C2212yes—
80#63841C2212yes—
81#63840C2214yescomplemented
82#63839C2214yescomplemented
83#63837C2214yescomplemented
84#63837C2214yescomplemented
85C3×#544—31no—
86C2×C3×#117—31no—
87C2×#926—31no—
88C2×#926—31no—
89#5729—32no—
90#5729—32no—
91#5728—32no—
92#5728—32no—
93#5689—32no—
94#5689—32no—
95#5688—32no—
96#5688—32no—
97#5634—34no—
98#5622—34no—
99D3×#117—31no—
100D3×#117D311yescharacteristic
101#5519—31no—
102#5519—31no—
103#5519—31no—
104#5519—31no—
105#5519—31no—
106#5519—32no—
107#5519—32no—
108#5519—61no—
109#5519D311yescharacteristic, complemented
110#5517—32no—
111#5517—32no—
112#5517—34no—
113C2×#892—31no—
114#5500—31no—
115#5500—32no—
116#5500—32no—
117#5483—34no—
118#5470—32no—
119#5470—32no—
120C23×C3×D3C2311yescharacteristic
121C22×C32×C4C2311yescharacteristic
122C22×C3⋊Dic3C2312yes—
123C2×#634C2314yes—
124C22×C3×Dic3C2312yes—
125C22×C3×Dic3C2311yescharacteristic
126C2×C3×C4×D3Q818yescomplemented
127C2×C3×C4×D3C2312yes—
128C2×C3×C4×D3C2312yes—
129C2×C3×C4×D3C2311yescharacteristic
130C2×C3×C4×D3C2311yescharacteristic
131C2×C3×C4×D3C2311yescharacteristic
132C2×C3×C4×D3C2311yescharacteristic
133C2×C3×Dic6C2314yes—
134C2×#627C2314yes—
135C2×#627C2314yes—
136C2×D3×Dic3C2312yes—
137C2×D3×Dic3C2312yes—
138C32×C4⋊C4C2311yescharacteristic
139C32×C4⋊C4C2311yescharacteristic
140C32×C22⋊C4C2312yes—
141C32×C42C2312yes—
142#3757C2312yes—
143C4⋊(C3⋊Dic3)C2311yescharacteristic
144C4⋊(C3⋊Dic3)C2312yes—
145C4⋊(C3⋊Dic3)C2314yes—
146C4⋊(C3⋊Dic3)C2311yescharacteristic
147C4⋊(C3⋊Dic3)C2312yes—
148#3750C2314yes—
149#3750C2314yes—
150C4×C3⋊Dic3C2312yes—
151C3×#217C2312yes—
152C3×#217C2312yes—
153C3×(C2×D3)⋊C4C2312yes—
154C3×(C2×D3)⋊C4C2312yes—
155C3×C4⋊Dic3C2314yes—
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×C4×Dic3C2312yes—
167C3×C4×Dic3C2312yes—
168C3×C4×Dic3C2312yes—
169C3×C4×Dic3C2312yes—
170#3724C2314yes—
171#3724C2314yes—
172Dic3⋊Dic3C2314yes—
173Dic3⋊Dic3C2314yes—
174Dic3⋊Dic3C2312yes—
175Dic3⋊Dic3C2312yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2314yes—
178(C2×D3)⋊Dic3C2314yes—
179(C2×D3)⋊Dic3C2314yes—
180(C2×D3)⋊Dic3C2312yes—
181(C2×D3)⋊Dic3C2312yes—
182Dic32C2312yes—
183Dic32C2314yes—
184Dic32C2314yes—
185Dic32C2312yes—
186#3458—91noSylow
187C23×C3×C4—31no—
188C22×C4×D3C2×D311yescharacteristic
189C3×C4⋊Q8—32no—
190C3×C4⋊Q8—32no—
191C3×#125—32no—
192C3×#125—32no—
193C3×C22⋊Q8—34no—
194C3×#117—21no—
195C3×#117—31no—
196C3×#117—31no—
197C3×#117—31no—
198C3×#117—31no—
199C3×#117—32no—
200C3×#117—32no—
201C3×#117C2×D311yescharacteristic
202C3×#117C2×D311yescharacteristic
203C2×C3×C4⋊C4—31no—
204C2×C3×C4⋊C4—31no—
205C2×C3×C4⋊C4—31no—
206C2×C3×C22⋊C4—32no—
207C2×C3×C42—32no—
208C2×#217—32no—
209C2×#217—32no—
210#946—34no—
211#946—34no—
212Q8×Dic3—34no—
213#944—34no—
214C2×(C2×D3)⋊C4—32no—
215#926—31no—
216#926—31no—
217#926—32no—
218#926—31no—
219#926—32no—
220#926—31no—
221#926—32no—
222#926—32no—
223#926—32no—
224#926—32no—
225#926—61no—
226#926C2×D311yescharacteristic
227#926C2×D311yescharacteristic
228C2×C4⋊Dic3—31no—
229C2×C4⋊Dic3—31no—
230C2×C4⋊Dic3—31no—
231C2×C4⋊Dic3—31no—
232C2×C4⋊Dic3—61no—
233C2×C4⋊Dic3C2×D311yescharacteristic
234#924—34no—
235#924—34no—
236#924—34no—
237#924—34no—
238#924—34no—
239C2×C4×Dic3—32no—
240C2×C4×Dic3—32no—
241C2×C4×Dic3—32no—
242#897—34no—
243#897—34no—
244#896—34no—
245#896—34no—
246#896—34no—
247#896—34no—
248#892—31no—
249#892—32no—
250#892—32no—
251#892—32no—
252#892—32no—
253#892—31no—
254#892C2×D311yescharacteristic
255#892C2×D311yescharacteristic
256D3×C4⋊C4—31no—
257D3×C4⋊C4—31no—
258D3×C4⋊C4C2×D311yescharacteristic
259D3×C4⋊C4C2×D311yescharacteristic
260#890—32no—
261#890—32no—
262#890—32no—
263#890—34no—
264#890—32no—
265#890—34no—
266#890—32no—
267#890—32no—
268#890—32no—
269#890—62no—
270#890C2×D312yescomplemented
271#889—34no—
272#889—34no—
273#888—34no—
274#888—32no—
275#888—32no—
276#888—32no—
277#888—32no—
278#888—34no—
279#888—34no—
280#888—32no—
281#888—32no—
282#888—32no—
283#888—62no—
284#888C2×D312yescomplemented
285#887—34no—
286#887—34no—
287#887—34no—
288D3×C22⋊C4—32no—
289D3×C22⋊C4C2×D312yes—
290#878—34no—
291#878—34no—
292#878—34no—
293#878—34no—
294#878—34no—
295#878—34no—
296#878—34no—
297#878—34no—
298#878—34no—
299#878—64no—
300#878C2×D314yes—
301#877—32no—
302#877C2×D312yes—
303#872—32no—
304#872C2×D312yes—
305C42×D3—32no—
306C42×D3C2×D312yes—
307#870—32no—
308#870—32no—
309#870—32no—
310#870—32no—
311#870—32no—
312#870—62no—
313#870C2×D312yescomplemented
314#869—32no—
315#869—32no—
316#869—32no—
317#869—32no—
318#869—32no—
319#869—62no—
320#869C2×D312yescomplemented
321C4×Dic6—34no—
322C4×Dic6—34no—
323C4×Dic6—34no—
324C4×Dic6—34no—
325C23×C32C2411yescharacteristic
326C22×C3×D3—41no—
327C22×C3×D3—41no—
328C22×C3×D3C2×Q814yes—
329C22×C3×D3C2411yescharacteristic
330C22×C3×D3C2411yescharacteristic
331C2×C32×C4C2×Q814yes—
332C2×C32×C4C2412yes—
333C2×C32×C4C2412yes—
334C2×C32×C4C2411yescharacteristic
335C2×C32×C4C2411yescharacteristic
336C2×C3⋊Dic3—42no—
337C2×C3⋊Dic3C2414yes—
338C2×C3⋊Dic3C2412yes—
339C2×C3⋊Dic3C2412yes—
340#634—44no—
341C2×C3×Dic3—42no—
342C2×C3×Dic3C2×Q814yes—
343C2×C3×Dic3C2414yes—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2411yescharacteristic
349C2×C3×Dic3C2411yescharacteristic
350C3×C4×D3—42no—
351C3×C4×D3—42no—
352C3×C4×D3C2×Q814yes—
353C3×C4×D3C2×Q814yes—
354C3×C4×D3C2×Q814yes—
355C3×C4×D3C2×Q814yes—
356C3×Dic6—44no—
357#627—44no—
358#627—44no—
359D3×Dic3—42no—
360D3×Dic3—42no—
361#544—31no—
362#544—91no—
363#544—92no—
364#544—92no—
365#544—91no—
366#544—92no—
367#544—92no—
368#544—91no—
369#543—94no—
370#533—92no—
371#533—92no—
372#533—94no—
373#533—92no—
374#533—92no—
375C2×#117—31no—
376C2×#117—91no—
377C2×#117—91no—
378C24×C3—31no—
379C23×D3C22×D311yescharacteristic
380C2×C3×Q8—34no—
381C22×C3×C4—21no—
382C22×C3×C4—31no—
383C22×C3×C4—38no—
384C22×C3×C4—31no—
385C22×C3×C4—31no—
386C22×C3×C4—31no—
387C22×C3×C4—31no—
388C22×C3×C4—32no—
389C22×C3×C4—32no—
390C22×C3×C4—32no—
391C22×C3×C4C22×D311yescharacteristic
392C22×C3×C4C22×D311yescharacteristic
393C22×Dic3—32no—
394C22×Dic3—32no—
395C22×Dic3—32no—
396C22×Dic3—32no—
397C22×Dic3—62no—
398C22×Dic3C22×D312yes—
399C22×Dic3C22×D311yescharacteristic
400C2×C4×D3—32no—
401C2×C4×D3—32no—
402C2×C4×D3Dic618yescomplemented
403C2×C4×D3C22×D312yes—
404C2×C4×D3C22×D312yes—
405C2×C4×D3C22×D311yescharacteristic
406C2×C4×D3C22×D311yescharacteristic
407C2×C4×D3C22×D311yescharacteristic
408C2×C4×D3C22×D311yescharacteristic
409C2×Dic6—34no—
410C2×Dic6—34no—
411C2×Dic6—34no—
412C2×Dic6—34no—
413C2×Dic6—34no—
414C2×Dic6—34no—
415C2×Dic6—64no—
416C2×Dic6C22×D314yes—
417C3×C4⋊C4—21no—
418C3×C4⋊C4—21no—
419C3×C4⋊C4—34no—
420C3×C4⋊C4—34no—
421C3×C4⋊C4—34no—
422C3×C4⋊C4—32no—
423C3×C4⋊C4—32no—
424C3×C4⋊C4—31no—
425C3×C4⋊C4—31no—
426C3×C4⋊C4—31no—
427C3×C4⋊C4—32no—
428C3×C4⋊C4—32no—
429C3×C4⋊C4—31no—
430C3×C4⋊C4C22×D311yescharacteristic
431C3×C4⋊C4C22×D311yescharacteristic
432C3×C4⋊C4C22×D311yescharacteristic
433C3×C4⋊C4C22×D311yescharacteristic
434C3×C22⋊C4—22no—
435C3×C22⋊C4—32no—
436C3×C22⋊C4—32no—
437C3×C22⋊C4—32no—
438C3×C22⋊C4—32no—
439C3×C22⋊C4C22×D312yes—
440C3×C22⋊C4C22×D312yes—
441C3×C42—22no—
442C3×C42—32no—
443C3×C42—32no—
444C3×C42—32no—
445C3×C42—32no—
446C3×C42C22×D312yes—
447C3×C42C22×D312yes—
448#217—32no—
449#217—32no—
450#217—34no—
451#217—34no—
452#217—32no—
453#217—32no—
454#217—62no—
455#217C22×D312yes—
456#217C22×D312yes—
457(C2×D3)⋊C4—32no—
458(C2×D3)⋊C4—32no—
459(C2×D3)⋊C4—34no—
460(C2×D3)⋊C4—34no—
461(C2×D3)⋊C4C22×D312yes—
462(C2×D3)⋊C4C22×D312yes—
463C4⋊Dic3—34no—
464C4⋊Dic3—31no—
465C4⋊Dic3—32no—
466C4⋊Dic3—31no—
467C4⋊Dic3—31no—
468C4⋊Dic3—32no—
469C4⋊Dic3—32no—
470C4⋊Dic3—34no—
471C4⋊Dic3—31no—
472C4⋊Dic3—32no—
473C4⋊Dic3—34no—
474C4⋊Dic3—34no—
475C4⋊Dic3—34no—
476C4⋊Dic3—32no—
477C4⋊Dic3—32no—
478C4⋊Dic3—34no—
479C4⋊Dic3—61no—
480C4⋊Dic3—62no—
481C4⋊Dic3—64no—
482C4⋊Dic3—61no—
483C4⋊Dic3—62no—
484C4⋊Dic3C22×D314yes—
485C4⋊Dic3C22×D311yescharacteristic
486C4⋊Dic3C22×D311yescharacteristic
487C4⋊Dic3C22×D312yes—
488C4⋊Dic3C22×D311yescharacteristic
489C4⋊Dic3C22×D311yescharacteristic
490C4⋊Dic3C22×D312yes—
491Dic3⋊C4—34no—
492Dic3⋊C4—34no—
493Dic3⋊C4—34no—
494Dic3⋊C4—34no—
495Dic3⋊C4—34no—
496Dic3⋊C4—34no—
497Dic3⋊C4—34no—
498Dic3⋊C4—34no—
499Dic3⋊C4—34no—
500Dic3⋊C4—34no—
501Dic3⋊C4—32no—
502Dic3⋊C4—32no—
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—64no—
506Dic3⋊C4—64no—
507Dic3⋊C4C22×D314yes—
508Dic3⋊C4C22×D314yes—
509Dic3⋊C4C22×D312yes—
510Dic3⋊C4C22×D312yes—
511C4×Dic3—32no—
512C4×Dic3—32no—
513C4×Dic3—34no—
514C4×Dic3—32no—
515C4×Dic3—32no—
516C4×Dic3—32no—
517C4×Dic3—32no—
518C4×Dic3—34no—
519C4×Dic3—34no—
520C4×Dic3—34no—
521C4×Dic3—62no—
522C4×Dic3C22×D312yes—
523C4×Dic3C22×D312yes—
524C4×Dic3C22×D312yes—
525C4×Dic3C22×D312yes—
526C22×C32—21no—
527C22×C32—21no—
528C22×C32C22×Q812yes—
529C22×C32C2511yescharacteristic
530C2×C3×D3—21no—
531C2×C3×D3—21no—
532C2×C3×D3—21no—
533C2×C3×D3—21no—
534C2×C3×D3—44no—
535C2×C3×D3C22×Q812yes—
536C2×C3×D3C22×Q812yes—
537C32×C4—22no—
538C32×C4—22no—
539C32×C4C22×Q812yes—
540C32×C4C22×Q812yes—
541C3⋊Dic3—22no—
542C3⋊Dic3—22no—
543C3⋊Dic3—24no—
544C3×Dic3—22no—
545C3×Dic3—22no—
546C3×Dic3—22no—
547C3×Dic3—22no—
548C3×Dic3—24no—
549C3×Dic3C22×Q812yes—
550C3×Dic3C22×Q812yes—
551C23×C4—31no—
552C4⋊Q8—32no—
553C4⋊Q8—32no—
554C4⋊Q8—92no—
555C4⋊Q8—92no—
556C4⋊Q8—92no—
557C4⋊Q8—94no—
558C4⋊Q8—92no—
559C4⋊Q8—94no—
560C4⋊Q8—92no—
561C4⋊Q8—92no—
562#125—32no—
563#125—32no—
564#125—92no—
565#125—92no—
566#125—92no—
567#125—94no—
568#125—94no—
569#125—92no—
570#125—92no—
571#125—92no—
572C22⋊Q8—34no—
573C22⋊Q8—94no—
574C22⋊Q8—94no—
575C22⋊Q8—94no—
576C22⋊Q8—94no—
577C22⋊Q8—94no—
578C22⋊Q8—94no—
579C22⋊Q8—94no—
580C22⋊Q8—94no—
581C22⋊Q8—94no—
582C22⋊Q8—94no—
583C22⋊Q8—94no—
584C4×Q8—94no—
585C4×Q8—94no—
586C4×Q8—94no—
587C4×Q8—94no—
588#117—31no—
589#117—31no—
590#117—31no—
591#117—31no—
592#117—32no—
593#117—32no—
594#117—92no—
595#117—92no—
596#117—92no—
597#117—92no—
598#117—91no—
599#117—91no—
600#117—92no—
601#117—92no—
602#117—91no—
603#117D3211yescharacteristic
604C2×C4⋊C4—31no—
605C2×C4⋊C4—31no—
606C2×C4⋊C4—31no—
607C2×C4⋊C4—91no—
608C2×C4⋊C4—91no—
609C2×C4⋊C4—91no—
610C2×C22⋊C4—32no—
611C2×C22⋊C4—92no—
612C2×C22⋊C4—92no—
613C2×C42—32no—
614C2×C42—92no—
615C2×C42—92no—
616C23×C3—21no—
617C23×C3—31no—
618C23×C3—31no—
619C23×C3—34no—
620C23×C3—121no—
621C23×C3—121no—
622C23×C3C23×D311yescharacteristic
623C23×C3C23×D311yescharacteristic
624C22×D3—41no—
625C22×D3—41no—
626C22×D3C2×Dic614yes—
627C22×D3C23×D311yescharacteristic
628C22×D3C23×D311yescharacteristic
629C3×Q8—124no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—22no—
633C2×C3×C4—22no—
634C2×C3×C4—24no—
635C2×C3×C4—34no—
636C2×C3×C4—31no—
637C2×C3×C4—31no—
638C2×C3×C4—34no—
639C2×C3×C4—34no—
640C2×C3×C4—34no—
641C2×C3×C4—34no—
642C2×C3×C4—34no—
643C2×C3×C4—32no—
644C2×C3×C4—32no—
645C2×C3×C4—32no—
646C2×C3×C4—32no—
647C2×C3×C4—122no—
648C2×C3×C4—122no—
649C2×C3×C4—122no—
650C2×C3×C4C2×Dic614yes—
651C2×C3×C4D3×Q814yes—
652C2×C3×C4C23×D312yes—
653C2×C3×C4C23×D312yes—
654C2×C3×C4C23×D312yes—
655C2×C3×C4C23×D312yes—
656C2×C3×C4C23×D311yescharacteristic
657C2×C3×C4C23×D311yescharacteristic
658C2×C3×C4C23×D311yescharacteristic
659C2×C3×C4C23×D311yescharacteristic
660C2×Dic3—32no—
661C2×Dic3—34no—
662C2×Dic3—32no—
663C2×Dic3—34no—
664C2×Dic3—32no—
665C2×Dic3—32no—
666C2×Dic3—42no—
667C2×Dic3—62no—
668C2×Dic3—62no—
669C2×Dic3—64no—
670C2×Dic3—122no—
671C2×Dic3—122no—
672C2×Dic3—122no—
673C2×Dic3—122no—
674C2×Dic3—242no—
675C2×Dic3C2×Dic614yes—
676C2×Dic3C23×D314yes—
677C2×Dic3C23×D312yes—
678C2×Dic3C23×D312yes—
679C2×Dic3C23×D312yes—
680C2×Dic3C23×D312yes—
681C2×Dic3C23×D311yescharacteristic
682C2×Dic3C23×D311yescharacteristic
683C4×D3—42no—
684C4×D3—42no—
685C4×D3—122no—
686C4×D3—122no—
687C4×D3C2×Dic614yes—
688C4×D3C2×Dic614yes—
689C4×D3C2×Dic614yes—
690C4×D3C2×Dic614yes—
691Dic6—44no—
692Dic6—124no—
693Dic6—124no—
694Dic6—124no—
695Dic6—124no—
696Dic6—124no—
697Dic6—124no—
698Dic6—244no—
699C2×C32—22no—
700C2×C32C23×Q811yescharacteristic
701C2×C32#58511yescharacteristic
702C2×C32#58511yescharacteristic
703C3×D3—22no—
704C3×D3—22no—
705C24—31no—
706C2×Q8—34no—
707C2×Q8—94no—
708C2×Q8—94no—
709C2×Q8—94no—
710C22×C4—31no—
711C22×C4—31no—
712C22×C4—31no—
713C22×C4—31no—
714C22×C4—31no—
715C22×C4—38no—
716C22×C4—32no—
717C22×C4—32no—
718C22×C4—32no—
719C22×C4—92no—
720C22×C4—92no—
721C22×C4—92no—
722C22×C4C2×D3211yescharacteristic
723C4⋊C4—32no—
724C4⋊C4—32no—
725C4⋊C4—31no—
726C4⋊C4—31no—
727C4⋊C4—32no—
728C4⋊C4—32no—
729C4⋊C4—31no—
730C4⋊C4—31no—
731C4⋊C4—34no—
732C4⋊C4—34no—
733C4⋊C4—34no—
734C4⋊C4—92no—
735C4⋊C4—92no—
736C4⋊C4—94no—
737C4⋊C4—94no—
738C4⋊C4—94no—
739C4⋊C4—94no—
740C4⋊C4—94no—
741C4⋊C4—94no—
742C4⋊C4—92no—
743C4⋊C4—91no—
744C4⋊C4—91no—
745C4⋊C4—92no—
746C4⋊C4—94no—
747C4⋊C4—94no—
748C4⋊C4—94no—
749C4⋊C4C2×D3211yescharacteristic
750C4⋊C4C2×D3211yescharacteristic
751C22⋊C4—32no—
752C22⋊C4—32no—
753C22⋊C4—32no—
754C22⋊C4—32no—
755C22⋊C4—92no—
756C22⋊C4—92no—
757C22⋊C4—94no—
758C22⋊C4—94no—
759C22⋊C4—92no—
760C22⋊C4C2×D3212yes—
761C42—32no—
762C42—32no—
763C42—32no—
764C42—32no—
765C42—92no—
766C42—92no—
767C42—94no—
768C42—94no—
769C42—92no—
770C42C2×D3212yes—
771C22×C3—21no—
772C22×C3—21no—
773C22×C3—21no—
774C22×C3—21no—
775C22×C3—22no—
776C22×C3—21no—
777C22×C3—32no—
778C22×C3—32no—
779C22×C3—41no—
780C22×C3—41no—
781C22×C3—61no—
782C22×C3—61no—
783C22×C3—61no—
784C22×C3—61no—
785C22×C3—124no—
786C22×C3C22×Dic612yes—
787C22×C3C2×D3×Q812yes—
788C22×C3C24×D311yescharacteristic
789C22×C3C24×D311yescharacteristic
790C2×D3—21no—
791C2×D3—21no—
792C2×D3—21no—
793C2×D3—21no—
794C2×D3—44no—
795C2×D3C22×Dic612yes—
796C2×D3C22×Dic612yes—
797C3×C4—22no—
798C3×C4—22no—
799C3×C4—22no—
800C3×C4—22no—
801C3×C4—22no—
802C3×C4—22no—
803C3×C4—32no—
804C3×C4—32no—
805C3×C4—42no—
806C3×C4—42no—
807C3×C4—62no—
808C3×C4—64no—
809C3×C4—62no—
810C3×C4—62no—
811C3×C4—62no—
812C3×C4C22×Dic612yes—
813C3×C4C22×Dic612yes—
814C3×C4C2×D3×Q812yes—
815C3×C4C2×D3×Q812yes—
816Dic3—22no—
817Dic3—22no—
818Dic3—22no—
819Dic3—24no—
820Dic3—22no—
821Dic3—62no—
822Dic3—62no—
823Dic3—64no—
824Dic3—62no—
825Dic3—64no—
826Dic3—62no—
827Dic3—122no—
828Dic3—124no—
829Dic3—122no—
830Dic3C22×Dic612yes—
831Dic3C22×Dic612yes—
832C32#345811yescharacteristic, complemented, Sylow
833C23—31no—
834C23—31no—
835C23—34no—
836C23—121no—
837C23—121no—
838C23C22×D3211yescharacteristic
839Q8—124no—
840Q8—364no—
841Q8—364no—
842Q8—364no—
843C2×C4—34no—
844C2×C4—31no—
845C2×C4—31no—
846C2×C4—34no—
847C2×C4—34no—
848C2×C4—34no—
849C2×C4—34no—
850C2×C4—32no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—32no—
854C2×C4—34no—
855C2×C4—92no—
856C2×C4—94no—
857C2×C4—92no—
858C2×C4—122no—
859C2×C4—122no—
860C2×C4—122no—
861C2×C4—362no—
862C2×C4—362no—
863C2×C4—362no—
864C2×C4D3×Dic614yes—
865C2×C4C22×D3212yes—
866C2×C4C22×D3212yes—
867C2×C4C22×D3211yescharacteristic
868C2×C4C22×D3211yescharacteristic
869C2×C3—22no—
870C2×C3—22no—
871C2×C3—21no—
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—42no—
875C2×C3—62no—
876C2×C3—62no—
877C2×C3C23×Dic611yescharacteristic
878C2×C3C22×D3×Q811yescharacteristic
879C2×C3#596411yescharacteristic
880C2×C3#596411yescharacteristic
881C2×C3#596611yescharacteristic
882C2×C3#596811yescharacteristic
883D3—22no—
884D3—22no—
885C22—21no—
886C22—21no—
887C22—32no—
888C22—32no—
889C22—61no—
890C22—61no—
891C22—61no—
892C22—61no—
893C22—124no—
894C22C2×D3×Dic612yes—
895C22C23×D3211yescharacteristic
896C4—22no—
897C4—22no—
898C4—32no—
899C4—32no—
900C4—64no—
901C4—62no—
902C4—62no—
903C4—62no—
904C4—62no—
905C4—182no—
906C4—182no—
907C4—184no—
908C4C2×D3×Dic612yes—
909C4C2×D3×Dic612yes—
910C3—21no—
911C3#8572511yescharacteristic, complemented
912C3#8658111yescharacteristic, complemented
913C2—22no—
914C2—62no—
915C2—62no—
916C2C22×D3×Dic611yescharacteristic
917C2#1059669611yescharacteristic
918C2#1059669711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
prime radicalC23×C3×D3C23
hypercenter#117D32
hypocenterC32#3458
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. #10595052C2semidirect
5. #10595051C2semidirect
8. #10594477C2semidirect
9. #10594445C2semidirect
10. #10594344C2semidirect
11. #10594342C2semidirect
13. #10594029C2semidirect
14. #10593959C2semidirect
15. #10593954C2semidirect
16. #10593874C2semidirect
17. #10593859C2semidirect
24. #64099C22semidirect
25. #64097C22semidirect
27. #64079C22semidirect
28. #64078C22semidirect
36. C3×#890C22semidirect
37. C3×#888C22semidirect
43. C3×#870C22semidirect
44. C3×#869C22semidirect
51. #63919C22semidirect
52. #63918C22semidirect
53. #63918C22semidirect
54. #63918C22semidirect
62. #63872C22semidirect
63. #63869C22semidirect
64. #63869C22semidirect
65. #63869C22semidirect
71. #63846C22semidirect
72. #63845C22semidirect
73. #63844C22semidirect
74. Dic3×Dic6C22semidirect
81. #63840C22semidirect
82. #63839C22semidirect
83. #63837C22semidirect
84. #63837C22semidirect
109. #5519D3semidirect
126. C2×C3×C4×D3Q8semidirect
270. #890C2×D3semidirect
284. #888C2×D3semidirect
313. #870C2×D3semidirect
320. #869C2×D3semidirect
402. C2×C4×D3Dic6semidirect
832. C32#3458semidirect
911. C3#85725semidirect
912. C3#86581semidirect

Maximal subgroups

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

subgroupindex
#105959902
C3×D3×#1172
C3×#55192
#105950522
#105950512
D3×#9262
C2×#638412
#105944772
#105944452
#105943442
#105943422
#105941702
#105940292
#105939592
#105939542
#105938742
#105938592
#865813
#857253