Finite Group Databasebeta

← #11888606

Subgroups — #11888606

Order 1152.

840 conjugacy classes of subgroups.

The subgroup lattice has 789 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5514C211yesmaximal, characteristic, complemented
2#10594887C211yesmaximal, characteristic, complemented
3#10592670C211yesmaximal, characteristic, complemented
4C3×#4966C211yesmaximal, characteristic, complemented
5#10591176C211yesmaximal, characteristic, complemented
6#10591161C211yesmaximal, characteristic, complemented
7#10591147C211yesmaximal, characteristic, complemented
8#10590613C211yesmaximal, characteristic, complemented
9#10590608C211yesmaximal, characteristic, complemented
10#10590562C211yesmaximal, characteristic, complemented
11#10590559C211yesmaximal, characteristic, complemented
12#10590519C211yesmaximal, characteristic, complemented
13#10590514C211yesmaximal, characteristic, complemented
14#10590469C211yesmaximal, characteristic, complemented
15#10590455C211yesmaximal, characteristic, complemented
16#83615—31nomaximal
17#78895—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21#64133C2211yescharacteristic
22C3×#930—21no—
23C3×#930C2211yescharacteristic
24C3×C4×#67—21no—
25C3×C4×#67C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27C3×#898—21no—
28C3×#895C2211yescharacteristic
29C3×#894—21no—
30C3×#893C2211yescharacteristic
31C3×#892C2211yescharacteristic
32C3×#890C2211yescharacteristic
33#63970—21no—
34#63969—21no—
35#63905—21no—
36Dic3×D12C2211yescharacteristic
37D3×Dic3⋊C4—21no—
38#63866C2211yescharacteristic
39#63856C2211yescharacteristic
40C2×#3716C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63657C2211yescharacteristic
45#63637C2211yescharacteristic
46#63637C2211yescharacteristic
47#63635C2211yescharacteristic
48#63635C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×#809C2211yescharacteristic
53#63575C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63565C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic
61C3×#553—31no—
62#5824—31no—
63#5551—31no—
64#5514D311yescharacteristic, complemented
65C3×#417—31no—
66#5238—31no—
67#5134—31no—
68#5127—31no—
69#5069—31no—
70#5066—31no—
71#5042—31no—
72#5041—31no—
73#5037—31no—
74#5037—31no—
75#5019—31no—
76#5014—31no—
77#5011—31no—
78#5002—31no—
79#4996—31no—
80#4971—31no—
81#4971—31no—
82#4971—61no—
83#4966D311yescharacteristic, complemented
84#4818—31no—
85#4814—31no—
86#4807—31no—
87#4797—31no—
88#4785—31no—
89#4781—31no—
90#4772—31no—
91#4766—31no—
92C22×C32×C4—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C2×C3×#67D411yescharacteristic
98C3×#235—22no—
99C3×#235—41no—
100C2×C3×D12—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#625—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3795—22no—
111#3795—41no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3757—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217D411yescharacteristic
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×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4D411yescharacteristic
130C3×C4×Dic3—21no—
131C3×C4×Dic3C2311yescharacteristic
132C3×#208—41no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140#3716—41no—
141#3715—41no—
142#3713—22no—
143D3×C3⋊C8—41no—
144#3307—91noSylow
145C2×C3×#41—31no—
146C2×#237—31no—
147C2×#235—31no—
148C2×#235C2×D311yescharacteristic
149C2×C3×M16—31no—
150C3×#126—61no—
151C3×#125—31no—
152C3×#123—61no—
153C3×#121—31no—
154C3×#121—31no—
155C3×#121—61no—
156C3×C4×D4—31no—
157C3×C4×D4—31no—
158C3×C4×D4—61no—
159C3×#117—31no—
160C2×C3×C4⋊C4—21no—
161C2×C3×C4⋊C4C2×D311yescharacteristic
162C2×C3×C4⋊C4C2×D311yescharacteristic
163#946—31no—
164#944—31no—
165C2×#215—31no—
166#939—61no—
167#938—61no—
168#935—61no—
169D4×Dic3—31no—
170C2×#214—31no—
171C2×#214—31no—
172C2×#213—31no—
173C2×#213—31no—
174#930—21no—
175#930C2×D311yescharacteristic
176#929—61no—
177C4×#67—21no—
178C4×#67C2×D311yescharacteristic
179#924—31no—
180#924—31no—
181#924—31no—
182#924—61no—
183C2×Dic3⋊C4—61no—
184C2×#208C2×D311yescharacteristic
185C22×C3⋊C8—31no—
186C2×#204—31no—
187C2×D3×C8—31no—
188#898—21no—
189#895C2×D311yescharacteristic
190#894—21no—
191#893C2×D311yescharacteristic
192#892C2×D311yescharacteristic
193D3×C4⋊C4—61no—
194#890C2×D311yescharacteristic
195#883—61no—
196#883—61no—
197C4×D12—31no—
198#869—31no—
199C3×#103—31no—
200C3×#103—31no—
201C3×#102—31no—
202C3×#102—31no—
203#835—31no—
204#832—31no—
205#832—31no—
206#830—31no—
207#830—31no—
208#830—31no—
209#830—61no—
210#821—31no—
211(C2×D3)⋊C8—31no—
212#818—31no—
213#816—31no—
214#815—31no—
215Dic3⋊C8—31no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—31no—
220#810—31no—
221#810—31no—
222#810—61no—
223#810—61no—
224#810C2×D311yescharacteristic
225#810C2×D311yescharacteristic
226#809—31no—
227#809C2×D311yescharacteristic
228#809C2×D311yescharacteristic
229#808—31no—
230#808—31no—
231#808—31no—
232#808—31no—
233#808—61no—
234#808—61no—
235#807—31no—
236C4⋊(C3⋊C8)—31no—
237#803—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—81no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251#634—21no—
252#634—21no—
253C3×#67—41no—
254C3×#67—42no—
255C3×#67—42no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—81no—
265C3×D12#4112yes—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—42no—
269C3×C4×D3—81no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272#625—42no—
273D3×Dic3—42no—
274D3×Dic3—42no—
275C3⋊(C3⋊C8)—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#553—31no—
280#547—91no—
281#491—91no—
282#485—91no—
283#483—91no—
284#478—91no—
285#468—91no—
286#465—91no—
287#461—91no—
288#449—91no—
289#449—91no—
290#442—91no—
291#435—91no—
292#417—31no—
293#416—91no—
294C3×#41—62no—
295C3×#41—121no—
296C2×C3×Q8—31no—
297C2×C3×D4—31no—
298C2×C3×D4—31no—
299C2×C3×D4—31no—
300C2×C3×D4—61no—
301C2×C3×D4—61no—
302C2×C3×D4—61no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—31no—
307C22×C3×C4—41no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C2×#67—21no—
313C2×#67—21no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67#6711yescharacteristic
317C22×Dic3—61no—
318C22×Dic3—61no—
319#237—62no—
320#237—121no—
321#235—22no—
322#235—41no—
323#235—62no—
324#235—121no—
325C2×D12—21no—
326C2×D12C22×D311yescharacteristic
327C2×D12C22×D311yescharacteristic
328C2×C4×D3—21no—
329C2×C4×D3—21no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—61no—
336C2×Dic6C22×D311yescharacteristic
337C3×M16—121no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—41no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C22⋊C4—31no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C42—31no—
360C3×C42—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—121no—
366#217#6711yescharacteristic
367#215—121no—
368#214—121no—
369#214—121no—
370#213—62no—
371#213—62no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4#6711yescharacteristic
379C4⋊Dic3—21no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—21no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—121no—
394Dic3⋊C4#6711yescharacteristic
395C4×Dic3—21no—
396C4×Dic3C22×D311yescharacteristic
397#208—41no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8—121no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407#204—121no—
408D3×C8—121no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32C22×D411yescharacteristic
413C2×C3×D3—22no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C32×C4—21no—
423C32×C4—41no—
424C32×C4—41no—
425C32×C4C2×#4111yescharacteristic
426C32×C4H(5,𝔽2)11yescharacteristic
427C3⋊Dic3—41no—
428C3⋊Dic3—41no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C2×#41—31no—
435C2×#41—91no—
436C2×SD16—91no—
437C2×SD16—91no—
438C2×D8—91no—
439C2×M16—31no—
440C22×C8—91no—
441C4⋊Q8—91no—
442#126—61no—
443#125—31no—
444#123—61no—
445#123—181no—
446#123—181no—
447C22⋊Q8—91no—
448C22⋊Q8—91no—
449#121—31no—
450#121—31no—
451#121—61no—
452#121—181no—
453C4×D4—31no—
454C4×D4—31no—
455C4×D4—61no—
456C4×D4—91no—
457#117—31no—
458C2×C4⋊C4—181no—
459C2×C4⋊C4D3211yescharacteristic
460#107—91no—
461#106—91no—
462#106—91no—
463C4⋊C8—91no—
464#103—31no—
465#103—31no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#102—31no—
471#102—31no—
472#102—91no—
473#102—91no—
474C22⋊C8—91no—
475C22⋊C8—91no—
476#97—91no—
477C23×C3—21no—
478C23×C3—31no—
479C23×C3—61no—
480C23×C3—61no—
481C23×C3D3×D411yescharacteristic
482C23×C3C2×#6711yescharacteristic
483C22×D3—21no—
484C22×D3—21no—
485C22×D3C2×#6711yescharacteristic
486C3×Q8—61no—
487C3×Q8—61no—
488C3×D4—32no—
489C3×D4—61no—
490C3×D4—61no—
491C3×D4—61no—
492C3×D4—121no—
493C3×D4—122no—
494C3×D4—122no—
495C3×D4—241no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
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—31no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—81no—
518C2×C3×C4—81no—
519C2×C3×C4—82no—
520C2×C3×C4—122no—
521C2×C3×C4—241no—
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4C2×#6711yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526#67—41no—
527#67—42no—
528#67—42no—
529#67—122no—
530#67—122no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—121no—
538C2×Dic3—121no—
539C2×Dic3—122no—
540C2×Dic3—122no—
541C2×Dic3C2×#6711yescharacteristic
542C2×Dic3C2×#6711yescharacteristic
543C2×Dic3C2×#6711yescharacteristic
544D12—21no—
545D12—21no—
546D12—21no—
547D12—81no—
548D12#23512yes—
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—42no—
552C4×D3—81no—
553C4×D3—122no—
554C4×D3—122no—
555Dic6—21no—
556Dic6—21no—
557Dic6—61no—
558Dic6—61no—
559Dic6—61no—
560Dic6—61no—
561Dic6—121no—
562Dic6—121no—
563C3×C8—61no—
564C3×C8—61no—
565C3⋊C8—21no—
566C3⋊C8—21no—
567C3⋊C8—61no—
568C3⋊C8—61no—
569C3⋊C8—61no—
570C3⋊C8—61no—
571C3⋊C8—121no—
572C3⋊C8—121no—
573C2×C32—41no—
574C2×C32#54611yescharacteristic
575C2×C32#57511yescharacteristic
576C2×C32#57711yescharacteristic
577C3×D3—41no—
578C3×D3—42no—
579C3×D3—81no—
580#41—62no—
581#41—121no—
582#41—182no—
583#41—361no—
584C2×Q8—31no—
585C2×Q8—91no—
586C2×D4—31no—
587C2×D4—31no—
588C2×D4—31no—
589C2×D4—61no—
590C2×D4—61no—
591C2×D4—61no—
592C2×D4—181no—
593C22×C4—21no—
594C22×C4—31no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—181no—
598C22×C4—181no—
599C22×C4C2×D3211yescharacteristic
600SD16—361no—
601SD16—361no—
602D8—182no—
603M16—121no—
604C2×C8—31no—
605C2×C8—31no—
606C2×C8—91no—
607C2×C8—91no—
608C2×C8—361no—
609C4⋊C4—21no—
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—91no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4C2×D3211yescharacteristic
620C4⋊C4C2×D3211yescharacteristic
621C22⋊C4—31no—
622C22⋊C4—31no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C42—31no—
631C42—61no—
632C22×C3—22no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—62no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—121no—
651C22×C3C2×D3×D411yescharacteristic
652C22×C3C22×#6711yescharacteristic
653C2×D3—22no—
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—41no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—61no—
672C3×C4—61no—
673C3×C4—61no—
674C3×C4—81no—
675C3×C4—81no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4C2×#23511yescharacteristic
679C3×C4#100411yescharacteristic
680C3×C4D3×#4111yescharacteristic
681C3×C4#100911yescharacteristic
682Dic3—21no—
683Dic3—21no—
684Dic3—21no—
685Dic3—41no—
686Dic3—41no—
687Dic3—121no—
688Dic3—121no—
689Dic3—121no—
690Dic3—121no—
691Dic3—241no—
692Dic3—241no—
693C32#330711yescharacteristic, complemented, Sylow
694C23—31no—
695C23—61no—
696C23—61no—
697C23D3×#6711yescharacteristic
698Q8—61no—
699Q8—61no—
700Q8—181no—
701Q8—181no—
702D4—32no—
703D4—61no—
704D4—61no—
705D4—61no—
706D4—121no—
707D4—122no—
708D4—122no—
709D4—241no—
710D4—362no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—31no—
716C2×C4—31no—
717C2×C4—31no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—81no—
723C2×C4—122no—
724C2×C4—181no—
725C2×C4—181no—
726C2×C4—241no—
727C2×C4—362no—
728C2×C4—362no—
729C2×C4D3×#6711yescharacteristic
730C2×C4C22×D3211yescharacteristic
731C8—61no—
732C8—61no—
733C8—181no—
734C8—181no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—42no—
739C2×C3—41no—
740C2×C3—41no—
741C2×C3—121no—
742C2×C3—122no—
743C2×C3—241no—
744C2×C3#549011yescharacteristic
745C2×C3#577511yescharacteristic
746C2×C3#577711yescharacteristic
747C2×C3#582211yescharacteristic
748C2×C3#582911yescharacteristic
749C2×C3#583611yescharacteristic
750D3—42no—
751D3—41no—
752D3—81no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—61no—
757C22—61no—
758C22—61no—
759C22—62no—
760C22—121no—
761C22—121no—
762C22—121no—
763C22—121no—
764C22—121no—
765C22C2×D3×#6711yescharacteristic
766C4—21no—
767C4—41no—
768C4—41no—
769C4—61no—
770C4—61no—
771C4—61no—
772C4—121no—
773C4—121no—
774C4—361no—
775C4—361no—
776C4D3×#23511yescharacteristic
777C4#6430711yescharacteristic
778C3—21no—
779C3#7889511yescharacteristic, complemented
780C3#8361511yescharacteristic, complemented
781C2—41no—
782C2—121no—
783C2—122no—
784C2—241no—
785C2#1059506511yescharacteristic
786C2#1059510611yescharacteristic
787C2#1059531711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#3307
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#5514C2semidirect
2. #10594887C2semidirect
3. #10592670C2semidirect
4. C3×#4966C2semidirect
5. #10591176C2semidirect
6. #10591161C2semidirect
7. #10591147C2semidirect
8. #10590613C2semidirect
9. #10590608C2semidirect
10. #10590562C2semidirect
11. #10590559C2semidirect
12. #10590519C2semidirect
13. #10590514C2semidirect
14. #10590469C2semidirect
15. #10590455C2semidirect
64. #5514D3semidirect
83. #4966D3semidirect
693. C32#3307semidirect
779. C3#78895semidirect
780. C3#83615semidirect

Maximal subgroups

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

subgroupindex
C3×#55142
#105948872
#105926702
C3×#49662
#105911762
#105911612
#105911472
#105906132
#105906082
#105905622
#105905592
#105905192
#105905142
#105904692
#105904552
#836153
#788953