Finite Group Databasebeta

← #11872763

Subgroups — #11872763

Order 1152.

887 conjugacy classes of subgroups.

The subgroup lattice has 799 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5697C211yesmaximal, characteristic, complemented
2#10593994C211yesmaximal, characteristic, complemented
3#10592765C211yesmaximal, characteristic, complemented
4C3×#5066C211yesmaximal, characteristic, complemented
5#10590595C211yesmaximal, characteristic, complemented
6#10590595C211yesmaximal, characteristic, complemented
7#10590589C211yesmaximal, characteristic, complemented
8#10590456C211yesmaximal, characteristic, complemented
9#10590455C211yesmaximal, characteristic, complemented
10#10590452C211yesmaximal, characteristic, complemented
11#10590449C211yesmaximal, characteristic, complemented
12#10590446C211yesmaximal, characteristic, complemented
13#10590355C211yesmaximal, characteristic, complemented
14#10590347C211yesmaximal, characteristic, complemented
15#10590253C211yesmaximal, characteristic, complemented
16#83435—31nomaximal
17#81146—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C32×#125C2211yescharacteristic, complemented
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C3×#895—21no—
22C3×#895—21no—
23C3×#895C2211yescharacteristic
24C3×#895C2211yescharacteristic
25C3×#894—21no—
26C3×#894—21no—
27C3×#893C2211yescharacteristic, complemented
28C3×#893C2211yescharacteristic, complemented
29C3×#874C2211yescharacteristic, complemented
30C3×C4×D12C2211yescharacteristic
31C3×#872C2211yescharacteristic
32#63921—21no—
33D3×(C2×D3)⋊C4—21no—
34#63904—21no—
35#63894C2211yescharacteristic
36Dic3×D12C2211yescharacteristic
37#63881—21no—
38#63841C2211yescharacteristic
39C2×#3714C2211yescharacteristic
40C2×#3714C2211yescharacteristic
41C2×#3713C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43#63636C2211yescharacteristic
44#63636C2211yescharacteristic
45#63635C2211yescharacteristic, complemented
46#63634C2211yescharacteristic, complemented
47C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#808C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63563C2211yescharacteristic, complemented
54#63563C2211yescharacteristic, complemented
55#63562C2211yescharacteristic, complemented
56#63562C2211yescharacteristic, complemented
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59#63554C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#540—31no—
62#5697D311yescharacteristic, complemented
63#5545—31no—
64#5521—31no—
65C3×#478—31no—
66#5072—31no—
67#5072—31no—
68#5066—31no—
69#5066—31no—
70#5066—61no—
71#5066D311yescharacteristic, complemented
72#5036—31no—
73#5036—31no—
74#5035—31no—
75#5035—31no—
76#5015—31no—
77#5014—31no—
78#5014—31no—
79C4×#213—31no—
80C4×#213—31no—
81#5000—31no—
82#4885—31no—
83#4872—31no—
84#4869—31no—
85#4866—31no—
86#4843—31no—
87#4840—31no—
88#4785—31no—
89#4773—31no—
90#4773—31no—
91#4756—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×C3×D12—21no—
96C2×C3×D12—21no—
97C2×C3×D12—21no—
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×#626—21no—
107C2×#624—21no—
108C2×D3×Dic3—21no—
109D3×D12—22no—
110D3×D12—22no—
111C32×C4⋊C4—21no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C42C2311yescharacteristic
116#3752—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4D411yescharacteristic
129C3×Dic3⋊C4D411yescharacteristic
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133#3722—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136Dic32—21no—
137#3714—22no—
138#3714—22no—
139#3713—22no—
140#3713—22no—
141#3122—91noSylow
142C2×D3×D4—31no—
143C22×D12—31no—
144C3×#127—31no—
145C3×#125—21no—
146C3×#125C2×D311yescharacteristic, complemented
147C3×#125C2×D311yescharacteristic, complemented
148C3×#123—61no—
149C3×#123—61no—
150C3×#121—31no—
151C3×#121—31no—
152C3×#121—61no—
153C3×#121—61no—
154C3×C4×D4—31no—
155C3×C4×D4—31no—
156C3×C4×D4—31no—
157C3×#117—31no—
158D4×Dic3—31no—
159C2×#213—31no—
160C2×#213—31no—
161C2×#213—31no—
162C2×#213—31no—
163C2×#213—31no—
164C2×#213—31no—
165C4×#67—61no—
166C2×(C2×D3)⋊C4—61no—
167#926—31no—
168C2×D24—31no—
169C2×D24—31no—
170#895—21no—
171#895—21no—
172#895C2×D311yescharacteristic
173#895C2×D311yescharacteristic
174#894—21no—
175#894—21no—
176#893—31no—
177#893—61no—
178#893—61no—
179#893C2×D311yescharacteristic, complemented
180#893C2×D311yescharacteristic, complemented
181#892—31no—
182#67⋊C4—61no—
183D3×C22⋊C4—61no—
184D3×C22⋊C4—61no—
185D3×C22⋊C4—61no—
186#874C2×D311yescharacteristic, complemented
187C4×D12—31no—
188C4×D12—31no—
189C4×D12—31no—
190C4×D12—31no—
191C4×D12—61no—
192C4×D12C2×D311yescharacteristic
193#872C2×D311yescharacteristic
194C3×#107—31no—
195C3×#106—31no—
196C3×C4⋊C8—31no—
197C3×#102—31no—
198C3×#102—31no—
199#832—31no—
200#832—31no—
201#832—31no—
202#832—31no—
203#830—31no—
204#830—31no—
205#821—31no—
206#821—31no—
207(C2×D3)⋊C8—31no—
208(C2×D3)⋊C8—31no—
209#815—31no—
210C8×Dic3—31no—
211#809—31no—
212#809—31no—
213#809—31no—
214#809—31no—
215#809—31no—
216#809—31no—
217#809—61no—
218#809—61no—
219#809C2×D311yescharacteristic
220#809C2×D311yescharacteristic
221#808—31no—
222#808—31no—
223#808—61no—
224#808C2×D311yescharacteristic, complemented
225#807—31no—
226#807—31no—
227#807—61no—
228#807C2×D311yescharacteristic, complemented
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—61no—
232C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
233#803—31no—
234C4×C3⋊C8—31no—
235C22×C3⋊D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3C2×D411yescharacteristic
240C2×D32—24no—
241C2×D32—81no—
242C2×D32—81no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C4⋊(C3⋊D3)—21no—
250C4⋊(C3⋊D3)#4112yes—
251C4×C3⋊D3—81no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×D12—21no—
257C3×D12—21no—
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—81no—
262C3×D12—81no—
263C3×D12—81no—
264C3×D12—81no—
265C3×D12#4112yes—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—81no—
269C3×C4×D3—81no—
270C3×C4×D3—81no—
271#626—24no—
272#624—81no—
273D3×Dic3—81no—
274C3⋊(C3⋊C8)—21no—
275C3⋊(C3⋊C8)—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278#540—31no—
279#518—91no—
280#482—91no—
281#482—91no—
282#478—31no—
283#478—91no—
284#459—91no—
285#459—91no—
286#447—91no—
287#447—91no—
288#442—91no—
289#442—91no—
290C4×D8—91no—
291C4×D8—91no—
292#433—91no—
293C23×D3—61no—
294C23×D3—61no—
295C2×C3×D4—31no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C2×C3×D4—61no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C2×C3×D4—61no—
302C22×C3×C4—31no—
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C2×#67—61no—
307C22×Dic3—61no—
308D3×D4—62no—
309D3×D4—62no—
310C2×D12—21no—
311C2×D12—21no—
312C2×D12—21no—
313C2×D12—21no—
314C2×D12—31no—
315C2×D12—31no—
316C2×D12—61no—
317C2×D12—62no—
318C2×D12—61no—
319C2×D12—62no—
320C2×D12C22×D311yescharacteristic
321C2×D12C22×D311yescharacteristic
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—121no—
332C2×C4×D3C22×D311yescharacteristic
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—41no—
345C3×C4⋊C4—41no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C22⋊C4—31no—
351C3×C22⋊C4—31no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C42—21no—
358C3×C42—31no—
359C3×C42C22×D311yescharacteristic
360C3×C42C22×D311yescharacteristic
361#217—61no—
362#217—61no—
363#213—62no—
364#213—62no—
365#213—62no—
366#213—62no—
367#213—62no—
368#213—62no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—121no—
381(C2×D3)⋊C4#6711yescharacteristic
382(C2×D3)⋊C4#6711yescharacteristic
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—61no—
386C4⋊Dic3C22×D311yescharacteristic
387Dic3⋊C4#6711yescharacteristic
388Dic3⋊C4#6711yescharacteristic
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3C22×D311yescharacteristic
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—61no—
397C2×C3⋊C8—61no—
398C2×C3⋊C8C22×D311yescharacteristic
399C2×C3⋊C8C22×D311yescharacteristic
400D24—62no—
401D24—62no—
402C22×C32C22×D411yescharacteristic
403C2×C3⋊D3—22no—
404C2×C3⋊D3—41no—
405C2×C3⋊D3—41no—
406C2×C3×D3—22no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418D32—84no—
419C32×C4—21no—
420C32×C4—21no—
421C32×C4—41no—
422C32×C4—41no—
423C32×C4C2×#4111yescharacteristic
424C32×C4C2×#4111yescharacteristic
425C3⋊Dic3—41no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C22×D4—91no—
431C2×D8—91no—
432C2×D8—91no—
433C2×D8—91no—
434C2×D8—91no—
435#127—31no—
436#125D3211yescharacteristic, complemented
437#123—61no—
438#123—61no—
439#121—31no—
440#121—31no—
441#121—61no—
442#121—61no—
443C4×D4—31no—
444C4×D4—31no—
445C4×D4—31no—
446C4×D4—91no—
447C4×D4—91no—
448C4×D4—91no—
449C4×D4—181no—
450C4×D4—181no—
451#117—31no—
452#117—91no—
453C2×C22⋊C4—181no—
454C2×C22⋊C4—181no—
455#107—31no—
456#107—91no—
457#106—31no—
458#106—91no—
459C4⋊C8—31no—
460C4⋊C8—91no—
461#102—31no—
462#102—31no—
463#102—91no—
464#102—91no—
465#102—91no—
466#102—91no—
467#102—91no—
468#102—91no—
469C22⋊C8—91no—
470C22⋊C8—91no—
471#97—91no—
472C4×C8—91no—
473C23×C3—31no—
474C23×C3—61no—
475C23×C3—61no—
476C23×C3—61no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—64no—
481C22×D3—64no—
482C22×D3—61no—
483C22×D3—61no—
484C22×D3—121no—
485C22×D3—241no—
486C22×D3—241no—
487C22×D3—241no—
488C22×D3—241no—
489C22×D3C2×#6711yescharacteristic
490C3×D4—32no—
491C3×D4—61no—
492C3×D4—61no—
493C3×D4—61no—
494C3×D4—61no—
495C3×D4—61no—
496C3×D4—241no—
497C3×D4—241no—
498C3×D4—241no—
499C3×D4—241no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—241no—
516C2×C3×C4—241no—
517C2×C3×C4—241no—
518C2×C3×C4D3×D411yescharacteristic
519C2×C3×C4D3×D411yescharacteristic
520C2×C3×C4C2×#6711yescharacteristic
521C2×C3×C4C2×#6711yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524#67—64no—
525C2×Dic3—21no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—121no—
529C2×Dic3—241no—
530C2×Dic3C2×#6711yescharacteristic
531C2×Dic3C2×#6711yescharacteristic
532C2×Dic3C2×#6711yescharacteristic
533D12—21no—
534D12—21no—
535D12—21no—
536D12—21no—
537D12—21no—
538D12—32no—
539D12—32no—
540D12—62no—
541D12—64no—
542D12—61no—
543D12—61no—
544D12—81no—
545D12—81no—
546D12—81no—
547D12—81no—
548D12—121no—
549D12#23912yes—
550C4×D3—21no—
551C4×D3—21no—
552C4×D3—81no—
553C4×D3—81no—
554C4×D3—81no—
555C4×D3—241no—
556C4×D3—241no—
557C4×D3—241no—
558C4×D3—241no—
559C4×D3—241no—
560C4×D3—242no—
561C3×C8—61no—
562C3×C8—61no—
563C3⋊C8—21no—
564C3⋊C8—21no—
565C3⋊C8—61no—
566C3⋊C8—61no—
567C3⋊C8—61no—
568C3⋊C8—61no—
569C3⋊C8—121no—
570C3⋊C8—121no—
571C2×C32#52511yescharacteristic
572C2×C32#57611yescharacteristic
573C2×C32#57611yescharacteristic
574C3⋊D3—42no—
575C3×D3—41no—
576C3×D3—42no—
577C3×D3—81no—
578C3×D3—81no—
579C24—181no—
580C2×D4—31no—
581C2×D4—31no—
582C2×D4—31no—
583C2×D4—61no—
584C2×D4—61no—
585C2×D4—61no—
586C2×D4—61no—
587C2×D4—91no—
588C2×D4—181no—
589C2×D4—182no—
590C2×D4—182no—
591C22×C4—31no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—181no—
596C22×C4—181no—
597C22×C4—181no—
598D8—182no—
599D8—182no—
600D8—182no—
601D8—182no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—91no—
605C2×C8—91no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—91no—
612C4⋊C4C2×D3211yescharacteristic
613C4⋊C4C2×D3211yescharacteristic
614C22⋊C4—31no—
615C22⋊C4—31no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C42—31no—
626C42—181no—
627C42C2×D3211yescharacteristic
628C22×C3—21no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—62no—
632C22×C3—61no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3C2×D3×D411yescharacteristic
642C22×C3C22×#6711yescharacteristic
643C2×D3—21no—
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—22no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—62no—
656C2×D3—62no—
657C2×D3—122no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—241no—
663C2×D3—241no—
664C2×D3—244no—
665C2×D3—244no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—61no—
681C3×C4—81no—
682C3×C4—81no—
683C3×C4—121no—
684C3×C4C2×#23911yescharacteristic
685C3×C4D3×#4111yescharacteristic
686C3×C4D3×#4111yescharacteristic
687C3×C4D3×#4111yescharacteristic
688Dic3—21no—
689Dic3—21no—
690Dic3—21no—
691Dic3—41no—
692Dic3—121no—
693Dic3—121no—
694Dic3—241no—
695C32#312211yescharacteristic, complemented, Sylow
696C23—31no—
697C23—61no—
698C23—61no—
699C23—61no—
700C23—184no—
701C23—181no—
702C23—721no—
703C23—721no—
704D4—32no—
705D4—61no—
706D4—61no—
707D4—61no—
708D4—61no—
709D4—61no—
710D4—92no—
711D4—184no—
712D4—181no—
713D4—241no—
714D4—241no—
715D4—241no—
716D4—241no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—181no—
726C2×C4—241no—
727C2×C4—241no—
728C2×C4—241no—
729C2×C4—721no—
730C2×C4—721no—
731C2×C4—721no—
732C2×C4D3×#6711yescharacteristic
733C2×C4D3×#6711yescharacteristic
734C2×C4C22×D3211yescharacteristic
735C8—61no—
736C8—61no—
737C8—181no—
738C8—181no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—122no—
743C2×C3—121no—
744C2×C3—241no—
745C2×C3—241no—
746C2×C3#562711yescharacteristic
747C2×C3#576911yescharacteristic
748C2×C3#577411yescharacteristic
749C2×C3#582811yescharacteristic
750C2×C3#583511yescharacteristic
751C2×C3#583511yescharacteristic
752D3—41no—
753D3—42no—
754D3—81no—
755D3—81no—
756D3—122no—
757D3—122no—
758D3—242no—
759C22—61no—
760C22—62no—
761C22—61no—
762C22—61no—
763C22—121no—
764C22—121no—
765C22—121no—
766C22—121no—
767C22—121no—
768C22—121no—
769C22—121no—
770C22—121no—
771C22—182no—
772C22—361no—
773C22—361no—
774C22—724no—
775C22C2×D3×#6711yescharacteristic
776C4—21no—
777C4—21no—
778C4—41no—
779C4—41no—
780C4—61no—
781C4—61no—
782C4—61no—
783C4—121no—
784C4—361no—
785C4D3×#23911yescharacteristic
786C4#6431911yescharacteristic
787C3—21no—
788C3#8114611yescharacteristic, complemented
789C3#8343511yescharacteristic, complemented
790C2—121no—
791C2—122no—
792C2—241no—
793C2—241no—
794C2—362no—
795C2#1059542411yescharacteristic
796C2#1059545411yescharacteristic
797C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#125C22
socleC22×C32C22×D4
hypercenter#125D32
hypocenterC32#3122
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. C3×#5697C2semidirect
2. #10593994C2semidirect
3. #10592765C2semidirect
4. C3×#5066C2semidirect
5. #10590595C2semidirect
6. #10590595C2semidirect
7. #10590589C2semidirect
8. #10590456C2semidirect
9. #10590455C2semidirect
10. #10590452C2semidirect
11. #10590449C2semidirect
12. #10590446C2semidirect
13. #10590355C2semidirect
14. #10590347C2semidirect
15. #10590253C2semidirect
19. C32×#125C22semidirect
27. C3×#893C22semidirect
28. C3×#893C22semidirect
29. C3×#874C22semidirect
45. #63635C22semidirect
46. #63634C22semidirect
47. C4⋊(C3⋊(C3⋊C8))C22semidirect
50. C3×#808C22semidirect
51. C3×#807C22semidirect
52. C3×C4⋊(C3⋊C8)C22semidirect
53. #63563C22semidirect
54. #63563C22semidirect
55. #63562C22semidirect
56. #63562C22semidirect
59. #63554C22semidirect
60. Dic3×C3⋊C8C22semidirect
62. #5697D3semidirect
71. #5066D3semidirect
146. C3×#125C2×D3semidirect
147. C3×#125C2×D3semidirect
179. #893C2×D3semidirect
180. #893C2×D3semidirect
186. #874C2×D3semidirect
224. #808C2×D3semidirect
228. #807C2×D3semidirect
232. C4⋊(C3⋊C8)C2×D3semidirect
436. #125D32semidirect
695. C32#3122semidirect
788. C3#81146semidirect
789. C3#83435semidirect

Maximal subgroups

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

subgroupindex
C3×#56972
#105939942
#105927652
C3×#50662
#105905952
#105905892
#105904562
#105904552
#105904522
#105904492
#105904462
#105903552
#105903472
#105902532
#834353
#811463