Finite Group Databasebeta

← #11868969

Subgroups — #11868969

Order 1152.

847 conjugacy classes of subgroups.

The subgroup lattice has 739 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5545C211yesmaximal, characteristic
2#10593954C211yesmaximal, characteristic, complemented
3#10592708C211yesmaximal, characteristic, complemented
4C3×#5008C211yesmaximal, characteristic, complemented
5#10591421C211yesmaximal, characteristic
6D3×#832C211yesmaximal, characteristic
7#10591410C211yesmaximal, characteristic, complemented
8#10591409C211yesmaximal, characteristic, complemented
9#10590572C211yesmaximal, characteristic, complemented
10#10590558C211yesmaximal, characteristic, complemented
11#10590545C211yesmaximal, characteristic, complemented
12#10590437C211yesmaximal, characteristic, complemented
13#10590324C211yesmaximal, characteristic, complemented
14#10590271C211yesmaximal, characteristic, complemented
15#10590269C211yesmaximal, characteristic, complemented
16#82539—31nomaximal
17#81062—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20#64079C2211yescharacteristic, complemented
21C3×D4×Dic3C2211yescharacteristic
22C3×C4×#67—21no—
23C2×C3×(C2×D3)⋊C4—21no—
24C3×#893C2211yescharacteristic
25C3×#892C2211yescharacteristic
26C3×#67⋊C4—21no—
27C3×D3×C22⋊C4—21no—
28C3×C4×D12C2211yescharacteristic
29C3×#872C2211yescharacteristic
30C3×#869C2211yescharacteristic, complemented
31#63918C2211yescharacteristic, complemented
32#63899—21no—
33D3×C4⋊Dic3C2211yescharacteristic
34#63887—21no—
35#63869C2211yescharacteristic, complemented
36#63846—21no—
37#63841C2211yescharacteristic
38#63839—21no—
39C2×#3711C2211yescharacteristic
40C2×D3×C3⋊C8C2211yescharacteristic
41#63659C2211yescharacteristic
42#63659C2211yescharacteristic
43#63635C2211yescharacteristic, complemented
44#63634C2211yescharacteristic, complemented
45C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#808C2211yescharacteristic, complemented
49C3×#808C2211yescharacteristic, complemented
50C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52#63576C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61C3×#518—31no—
62#5729—31no—
63#5545D311yescharacteristic
64#5519—31no—
65C3×#476—31no—
66#5215—31no—
67C2×#832—31no—
68#5087—31no—
69#5009—31no—
70#5009—31no—
71#5009—31no—
72#5009—31no—
73#5009—31no—
74#5009—61no—
75#5008—31no—
76#5008D311yescharacteristic, complemented
77#5007—31no—
78#5007—31no—
79#4999—31no—
80#4998—31no—
81#4995—31no—
82#4871—31no—
83#4870—31no—
84#4861—31no—
85#4860—31no—
86#4847—31no—
87#4839—31no—
88#4770—31no—
89D3×#102—31no—
90#4763—31no—
91#4759—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C3×#67—21no—
96C22×C3×Dic3—21no—
97C3×D3×D4—22no—
98C3×D3×D4Q814yescomplemented
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6—21no—
104C2×#627—21no—
105C2×D3×Dic3—21no—
106C32×C4⋊C4C2311yescharacteristic
107C32×C22⋊C4—21no—
108C32×C42C2311yescharacteristic
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111#3750—21no—
112#3750—21no—
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C3×#217—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4D411yescharacteristic
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4D411yescharacteristic
126C3×Dic3⋊C4D411yescharacteristic
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136Dic32—21no—
137#3711—22no—
138D3×C3⋊C8—22no—
139#3081—91noSylow
140C22×C3×D4—31no—
141C2×D3×D4C2×D311yescharacteristic
142C3×C4⋊Q8—31no—
143C3×C4×D4—21no—
144C3×C4×D4—31no—
145C3×C4×D4—31no—
146C3×C4×D4—31no—
147C3×C4×D4—61no—
148C3×C4×D4—61no—
149C3×C4×D4C2×D311yescharacteristic
150C3×C4×D4C2×D311yescharacteristic
151C3×#117—31no—
152C3×#117—31no—
153C2×C3×C22⋊C4—61no—
154C2×C3×C22⋊C4—61no—
155#946—61no—
156#944—61no—
157D4×Dic3C2×D311yescharacteristic
158C4×#67—21no—
159C2×(C2×D3)⋊C4—21no—
160#926—31no—
161C2×C4⋊Dic3—31no—
162C2×#208—31no—
163C22×C3⋊C8—31no—
164C2×ΓL(1,𝔽25)—31no—
165C2×D3×C8—31no—
166#896—61no—
167#893C2×D311yescharacteristic
168#892—31no—
169#892C2×D311yescharacteristic
170D3×C4⋊C4—31no—
171#890—31no—
172#890—61no—
173#889—61no—
174#888—31no—
175#888—61no—
176#67⋊C4—21no—
177D3×C22⋊C4—21no—
178#878—61no—
179#878—61no—
180C4×D12C2×D311yescharacteristic
181#872C2×D311yescharacteristic
182#870—31no—
183#870—31no—
184#870—31no—
185#870—61no—
186#869—31no—
187#869C2×D311yescharacteristic, complemented
188C3×#106—31no—
189C3×#106—31no—
190C3×C4⋊C8—31no—
191C3×#102—31no—
192C3×#102—31no—
193#832—31no—
194#832—31no—
195#832—31no—
196#832—31no—
197#832—31no—
198#832—31no—
199#832—31no—
200#832—31no—
201#832—61no—
202#832—61no—
203#832C2×D311yescharacteristic
204#832C2×D311yescharacteristic
205#821—31no—
206#821—31no—
207#818—31no—
208#817—31no—
209Dic3⋊C8—31no—
210Dic3⋊C8—31no—
211#809—31no—
212#809—31no—
213#808—31no—
214#808—31no—
215#808—31no—
216#808—61no—
217#808C2×D311yescharacteristic, complemented
218#808C2×D311yescharacteristic, complemented
219#807—31no—
220#807—31no—
221#807—31no—
222#807—31no—
223#807—31no—
224#807—31no—
225#807—31no—
226#807—61no—
227C4⋊(C3⋊C8)—31no—
228C4⋊(C3⋊C8)—31no—
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—61no—
232C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
233C23×C32—21no—
234C22×C3×D3—21no—
235C22×C3×D3—24no—
236C22×C3×D3—81no—
237C22×C3×D3—81no—
238C22×C3×D3C2×D411yescharacteristic
239C32×D4—21no—
240C32×D4C2×Q812yes—
241C2×C32×C4—21no—
242C2×C32×C4—81no—
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C3×#67—24no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—81no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×D12—21no—
257C3×D12C2×Q812yes—
258C3×C4×D3—81no—
259C3×C4×D3—81no—
260C3×C4×D3C2×Q812yes—
261C3×C4×D3#4112yes—
262C3×Dic6—81no—
263#627—81no—
264D3×Dic3—81no—
265C3⋊(C3⋊C8)—21no—
266C3⋊(C3⋊C8)—21no—
267C3×C3⋊C8—21no—
268C3×C3⋊C8—21no—
269#544—91no—
270#518—31no—
271#478—91no—
272#478—91no—
273#478—91no—
274#478—91no—
275#476—31no—
276#476—91no—
277#474—91no—
278#474—91no—
279#428—91no—
280#427—91no—
281#424—91no—
282#418—91no—
283C2×#102—91no—
284C24×C3—61no—
285C23×D3—21no—
286C2×C3×Q8—61no—
287C2×C3×D4—21no—
288C2×C3×D4—34no—
289C2×C3×D4—31no—
290C2×C3×D4—62no—
291C2×C3×D4—61no—
292C2×C3×D4C22×D311yescharacteristic
293C2×C3×D4C22×D311yescharacteristic
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—31no—
297C22×C3×C4—41no—
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300C22×C3×C4—61no—
301C2×#67—21no—
302C22×Dic3—21no—
303C22×Dic3—61no—
304D3×D4—22no—
305D3×D4Dic614yescomplemented
306C2×D12C22×D311yescharacteristic
307C2×C4×D3—21no—
308C2×C4×D3—21no—
309C2×C4×D3—61no—
310C2×C4×D3C22×D311yescharacteristic
311C2×Dic6—21no—
312C2×Dic6—61no—
313C2×Dic6—61no—
314C2×C3×C8—31no—
315C2×C3×C8—31no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—31no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—31no—
322C3×C4⋊C4—61no—
323C3×C4⋊C4C22×D311yescharacteristic
324C3×C4⋊C4C22×D311yescharacteristic
325C3×C22⋊C4—21no—
326C3×C22⋊C4—21no—
327C3×C22⋊C4—31no—
328C3×C22⋊C4—31no—
329C3×C22⋊C4—41no—
330C3×C22⋊C4—61no—
331C3×C22⋊C4—61no—
332C3×C22⋊C4—61no—
333C3×C22⋊C4—61no—
334C3×C42—21no—
335C3×C42—31no—
336C3×C42—61no—
337C3×C42C22×D311yescharacteristic
338C3×C42C22×D311yescharacteristic
339#217—21no—
340#217—61no—
341(C2×D3)⋊C4—21no—
342(C2×D3)⋊C4—21no—
343(C2×D3)⋊C4—21no—
344(C2×D3)⋊C4—61no—
345(C2×D3)⋊C4#6711yescharacteristic
346(C2×D3)⋊C4#6711yescharacteristic
347C4⋊Dic3—21no—
348C4⋊Dic3—31no—
349C4⋊Dic3—31no—
350C4⋊Dic3—31no—
351C4⋊Dic3—31no—
352C4⋊Dic3—61no—
353C4⋊Dic3—61no—
354C4⋊Dic3—61no—
355C4⋊Dic3—61no—
356C4⋊Dic3—61no—
357C4⋊Dic3C22×D311yescharacteristic
358C4⋊Dic3C22×D311yescharacteristic
359C4⋊Dic3C22×D311yescharacteristic
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—121no—
370Dic3⋊C4—121no—
371Dic3⋊C4#6711yescharacteristic
372Dic3⋊C4#6711yescharacteristic
373C4×Dic3—21no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3C22×D311yescharacteristic
377#208—62no—
378C2×C3⋊C8—31no—
379C2×C3⋊C8—31no—
380C2×C3⋊C8—31no—
381C2×C3⋊C8—31no—
382C2×C3⋊C8—61no—
383C2×C3⋊C8—61no—
384C2×C3⋊C8—62no—
385C2×C3⋊C8C22×D311yescharacteristic
386C2×C3⋊C8C22×D311yescharacteristic
387ΓL(1,𝔽25)—62no—
388D3×C8—62no—
389C22×C32—22no—
390C22×C32—41no—
391C22×C32—41no—
392C22×C32C22×D411yescharacteristic
393C2×C3×D3—21no—
394C2×C3×D3—21no—
395C2×C3×D3—22no—
396C2×C3×D3—41no—
397C2×C3×D3—41no—
398C2×C3×D3—84no—
399C2×C3×D3C22⋊Q812yes—
400C32×C4—21no—
401C32×C4—21no—
402C32×C4—41no—
403C32×C4C22×Q811yescharacteristic
404C32×C4C2×#4111yescharacteristic
405C3⋊Dic3—41no—
406C3⋊Dic3—41no—
407C3×Dic3—21no—
408C3×Dic3—21no—
409C3×Dic3—41no—
410C3×Dic3—41no—
411C3×Dic3—41no—
412C3×Dic3C22⋊Q812yes—
413C22×D4—31no—
414C2×M16—91no—
415C22×C8—91no—
416C4⋊Q8—31no—
417C4⋊Q8—91no—
418C4⋊Q8—181no—
419#125—91no—
420#125—91no—
421#125—181no—
422C22⋊Q8—181no—
423C22⋊Q8—181no—
424C4×D4—31no—
425C4×D4—31no—
426C4×D4—31no—
427C4×D4—61no—
428C4×D4—61no—
429C4×D4D3211yescharacteristic
430#117—31no—
431#117—31no—
432#117—91no—
433C2×C4⋊C4—91no—
434C2×C22⋊C4—61no—
435C2×C22⋊C4—61no—
436#107—91no—
437#107—91no—
438#107—91no—
439#107—91no—
440#106—31no—
441#106—31no—
442#106—91no—
443#106—91no—
444C4⋊C8—31no—
445C4⋊C8—91no—
446C4⋊C8—91no—
447C4⋊C8—91no—
448#102—31no—
449#102—31no—
450#102—91no—
451#102—91no—
452#102—91no—
453#102—91no—
454#102—91no—
455#102—91no—
456C23×C3—21no—
457C23×C3—21no—
458C23×C3—31no—
459C23×C3—41no—
460C23×C3—64no—
461C23×C3—61no—
462C23×C3—241no—
463C23×C3—241no—
464C22×D3—21no—
465C22×D3—24no—
466C22×D3—81no—
467C22×D3—81no—
468C22×D3C2×#6711yescharacteristic
469C3×Q8—241no—
470C3×D4—21no—
471C3×D4—21no—
472C3×D4—22no—
473C3×D4—32no—
474C3×D4—41no—
475C3×D4—64no—
476C3×D4—61no—
477C3×D4C2×Dic612yes—
478C3×D4D3×Q812yes—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—31no—
485C2×C3×C4—32no—
486C2×C3×C4—32no—
487C2×C3×C4—31no—
488C2×C3×C4—31no—
489C2×C3×C4—41no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—81no—
494C2×C3×C4—81no—
495C2×C3×C4—82no—
496C2×C3×C4—241no—
497C2×C3×C4—241no—
498C2×C3×C4—241no—
499C2×C3×C4D3×D411yescharacteristic
500C2×C3×C4D3×D411yescharacteristic
501C2×C3×C4C2×#6711yescharacteristic
502C2×C3×C4C2×#6711yescharacteristic
503C2×C3×C4C23×D311yescharacteristic
504C2×C3×C4C23×D311yescharacteristic
505#67—24no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—81no—
514C2×Dic3—121no—
515C2×Dic3—121no—
516C2×Dic3—241no—
517C2×Dic3C2×#6711yescharacteristic
518C2×Dic3C2×#6711yescharacteristic
519C2×Dic3C2×#6711yescharacteristic
520D12—21no—
521D12C2×Dic612yes—
522C4×D3—81no—
523C4×D3—81no—
524C4×D3—241no—
525C4×D3C2×Dic612yes—
526C4×D3#23512yes—
527Dic6—81no—
528Dic6—241no—
529Dic6—241no—
530C3×C8—61no—
531C3×C8—61no—
532C3⋊C8—21no—
533C3⋊C8—21no—
534C3⋊C8—61no—
535C3⋊C8—61no—
536C3⋊C8—61no—
537C3⋊C8—61no—
538C3⋊C8—121no—
539C3⋊C8—121no—
540C2×C32—42no—
541C2×C32C2×C22⋊Q811yescharacteristic
542C2×C32#57611yescharacteristic
543C2×C32#57711yescharacteristic
544C3×D3—22no—
545C3×D3—42no—
546C24—61no—
547C2×Q8—61no—
548C2×Q8—181no—
549C2×D4—34no—
550C2×D4—31no—
551C2×D4—62no—
552C2×D4—61no—
553C2×D4C2×D3211yescharacteristic
554C22×C4—21no—
555C22×C4—31no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—181no—
560M16—182no—
561C2×C8—31no—
562C2×C8—31no—
563C2×C8—91no—
564C2×C8—91no—
565C2×C8—182no—
566C4⋊C4—31no—
567C4⋊C4—31no—
568C4⋊C4—31no—
569C4⋊C4—31no—
570C4⋊C4—31no—
571C4⋊C4—61no—
572C4⋊C4—91no—
573C4⋊C4—91no—
574C4⋊C4—181no—
575C4⋊C4—181no—
576C4⋊C4—181no—
577C4⋊C4—181no—
578C4⋊C4—181no—
579C4⋊C4—181no—
580C4⋊C4C2×D3211yescharacteristic
581C22⋊C4—21no—
582C22⋊C4—31no—
583C22⋊C4—31no—
584C22⋊C4—61no—
585C22⋊C4—61no—
586C22⋊C4—61no—
587C22⋊C4—61no—
588C22⋊C4—181no—
589C42—31no—
590C42—61no—
591C42—181no—
592C42C2×D3211yescharacteristic
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—21no—
596C22×C3—32no—
597C22×C3—42no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—61no—
603C22×C3—61no—
604C22×C3—62no—
605C22×C3—81no—
606C22×C3—81no—
607C22×C3—121no—
608C22×C3—121no—
609C22×C3—244no—
610C22×C3C2×D3×D411yescharacteristic
611C22×C3C22×#6711yescharacteristic
612C2×D3—21no—
613C2×D3—21no—
614C2×D3—22no—
615C2×D3—41no—
616C2×D3—41no—
617C2×D3—84no—
618C2×D3#92412yes—
619C3×C4—21no—
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—32no—
626C3×C4—41no—
627C3×C4—41no—
628C3×C4—41no—
629C3×C4—41no—
630C3×C4—61no—
631C3×C4—61no—
632C3×C4—81no—
633C3×C4—121no—
634C3×C4—121no—
635C3×C4—121no—
636C3×C4C22×Dic611yescharacteristic
637C3×C4C2×#23511yescharacteristic
638C3×C4C2×D3×Q811yescharacteristic
639C3×C4D3×#4111yescharacteristic
640Dic3—21no—
641Dic3—21no—
642Dic3—41no—
643Dic3—41no—
644Dic3—41no—
645Dic3—121no—
646Dic3—121no—
647Dic3—121no—
648Dic3—121no—
649Dic3—241no—
650Dic3—241no—
651Dic3#92412yes—
652C32#308111yescharacteristic, complemented, Sylow
653C23—21no—
654C23—31no—
655C23—64no—
656C23—61no—
657C23—241no—
658C23—241no—
659Q8—241no—
660Q8—721no—
661D4—21no—
662D4—32no—
663D4—64no—
664D4—61no—
665D4D3×Dic612yes—
666C2×C4—21no—
667C2×C4—31no—
668C2×C4—32no—
669C2×C4—32no—
670C2×C4—31no—
671C2×C4—31no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—81no—
676C2×C4—181no—
677C2×C4—181no—
678C2×C4—241no—
679C2×C4—241no—
680C2×C4—241no—
681C2×C4—721no—
682C2×C4D3×#6711yescharacteristic
683C2×C4D3×#6711yescharacteristic
684C2×C4C22×D3211yescharacteristic
685C8—61no—
686C8—61no—
687C8—181no—
688C8—181no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—42no—
693C2×C3—42no—
694C2×C3—62no—
695C2×C3—82no—
696C2×C3—122no—
697C2×C3D3×C22⋊Q811yescharacteristic
698C2×C3#576211yescharacteristic
699C2×C3#577411yescharacteristic
700C2×C3C2×#92411yescharacteristic
701C2×C3#583511yescharacteristic
702C2×C3#583611yescharacteristic
703D3—22no—
704D3—42no—
705C22—22no—
706C22—32no—
707C22—41no—
708C22—41no—
709C22—61no—
710C22—61no—
711C22—62no—
712C22—121no—
713C22—121no—
714C22—244no—
715C22C2×D3×#6711yescharacteristic
716C4—21no—
717C4—21no—
718C4—32no—
719C4—41no—
720C4—61no—
721C4—61no—
722C4—121no—
723C4—121no—
724C4—121no—
725C4—361no—
726C4—361no—
727C4C2×D3×Dic611yescharacteristic
728C4D3×#23511yescharacteristic
729C3—21no—
730C3#8106211yescharacteristic, complemented
731C3#8253911yescharacteristic, complemented
732C2—42no—
733C2—62no—
734C2—122no—
735C2D3×#92411yescharacteristic
736C2#1059510511yescharacteristic
737C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
hypercenterC4×D4D32
hypocenterC32#3081
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10593954C2semidirect
3. #10592708C2semidirect
4. C3×#5008C2semidirect
7. #10591410C2semidirect
8. #10591409C2semidirect
9. #10590572C2semidirect
10. #10590558C2semidirect
11. #10590545C2semidirect
12. #10590437C2semidirect
13. #10590324C2semidirect
14. #10590271C2semidirect
15. #10590269C2semidirect
20. #64079C22semidirect
30. C3×#869C22semidirect
31. #63918C22semidirect
35. #63869C22semidirect
43. #63635C22semidirect
44. #63634C22semidirect
45. C4⋊(C3⋊(C3⋊C8))C22semidirect
48. C3×#808C22semidirect
49. C3×#808C22semidirect
50. C3×C4⋊(C3⋊C8)C22semidirect
51. #63576C22semidirect
52. #63576C22semidirect
53. #63575C22semidirect
54. #63573C22semidirect
55. Dic3⋊(C3⋊C8)C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
76. #5008D3semidirect
98. C3×D3×D4Q8semidirect
187. #869C2×D3semidirect
217. #808C2×D3semidirect
218. #808C2×D3semidirect
232. C4⋊(C3⋊C8)C2×D3semidirect
305. D3×D4Dic6semidirect
652. C32#3081semidirect
730. C3#81062semidirect
731. C3#82539semidirect

Maximal subgroups

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

subgroupindex
C3×#55452
#105939542
#105927082
C3×#50082
#105914212
D3×#8322
#105914102
#105914092
#105905722
#105905582
#105905452
#105904372
#105903242
#105902712
#105902692
#825393
#810623