Finite Group Databasebeta

← #11889231

Subgroups — #11889231

Order 1152.

899 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5806C211yesmaximal, characteristic
2#10594841C211yesmaximal, characteristic, complemented
3#10592914C211yesmaximal, characteristic, complemented
4C3×#5218C211yesmaximal, characteristic, complemented
5#10591499C211yesmaximal, characteristic, complemented
6#10591488C211yesmaximal, characteristic, complemented
7#10591461C211yesmaximal, characteristic, complemented
8#10591442C211yesmaximal, characteristic, complemented
9#10591440C211yesmaximal, characteristic, complemented
10#10591423C211yesmaximal, characteristic, complemented
11#10591420C211yesmaximal, characteristic, complemented
12#10591408C211yesmaximal, characteristic, complemented
13#10591189C211yesmaximal, characteristic, complemented
14#10591151C211yesmaximal, characteristic, complemented
15#10591127C211yesmaximal, characteristic, complemented
16#83497—31nomaximal
17#80162—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20#64135C2211yescharacteristic
21C2×#3748C2211yescharacteristic
22C3×#953—21no—
23C2×C3×#217—21no—
24C3×#939—21no—
25C3×#938C2211yescharacteristic
26C3×#936C2211yescharacteristic
27C3×#935—21no—
28C3×D4×Dic3C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic
31C3×C4×#67C2211yescharacteristic
32C3×#924C2211yescharacteristic
33C3×#924C2211yescharacteristic
34#63959—21no—
35#63956—21no—
36#63918C2211yescharacteristic, complemented
37#63862—21no—
38#63856C2211yescharacteristic, complemented
39Dic3×Dic6C2211yescharacteristic, complemented
40#63841C2211yescharacteristic, complemented
41#63838—21no—
42C2×#3718C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63659C2211yescharacteristic
45#63659C2211yescharacteristic
46#63659C2211yescharacteristic
47#63659C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic
51#63575C2211yescharacteristic, complemented
52#63574C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61C3×#546—31no—
62#5806D311yescharacteristic
63#5641—31no—
64#5542—31no—
65C3×#450—31no—
66#5239—31no—
67#5233—31no—
68#5218D311yescharacteristic, complemented
69#5215—31no—
70#5215—31no—
71#5215—61no—
72#5173—31no—
73#5171—31no—
74#5166—31no—
75#5164—31no—
76#5055—31no—
77#5054—31no—
78#5052—31no—
79#5052—31no—
80#5045—31no—
81#5041—31no—
82#5035—31no—
83#5018—31no—
84#5011—31no—
85#5008—31no—
86#4784—31no—
87#4772—31no—
88#4765—31no—
89#4761—31no—
90#4728—31no—
91#4723—31no—
92C24×C32—21no—
93C2×C32×D4—22no—
94C2×C32×D4—21no—
95C2×C32×D4—41no—
96C2×C32×D4C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67D411yescharacteristic
102C22×C3×Dic3—21no—
103C22×C3×Dic3—21no—
104C3×#237—22no—
105C3×#237—41no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#627—21no—
110#3757—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4×C3⋊Dic3—21no—
114#3748—41no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#217—21no—
123C3×#217D411yescharacteristic
124C3×#214—22no—
125C3×#214—41no—
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
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—
140Dic32—21no—
141Dic32—21no—
142#3718—41no—
143D3×C3⋊C8—41no—
144#3311—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—21no—
147C22×C3×D4C2×D311yescharacteristic
148C22×C3×D4C2×D311yescharacteristic
149C2×#237C2×D311yescharacteristic
150C2×C3×SD16—31no—
151C2×C3×SD16—31no—
152C3×#124—31no—
153C3×#123—61no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×#121—31no—
157C3×#121—61no—
158C3×#120—61no—
159C3×C4×D4—31no—
160C3×C4×D4—31no—
161C2×C3×C22⋊C4—61no—
162#953—21no—
163C2×#217—21no—
164#946—31no—
165Q8×Dic3—31no—
166C2×#216—31no—
167C2×#216—31no—
168#939—21no—
169#938C2×D311yescharacteristic
170#936—61no—
171#936C2×D311yescharacteristic
172#935—21no—
173D4×Dic3C2×D311yescharacteristic
174C2×#214C2×D311yescharacteristic
175C2×#214C2×D311yescharacteristic
176C4×#67C2×D311yescharacteristic
177#926—31no—
178#926—31no—
179#926—31no—
180#926—61no—
181#924—31no—
182#924C2×D311yescharacteristic
183#924C2×D311yescharacteristic
184C2×#208—31no—
185C2×#208—31no—
186C2×#208—61no—
187C22×C3⋊C8—31no—
188C2×D3×C8—31no—
189#898—61no—
190#892—31no—
191#888—31no—
192#887—61no—
193#887—61no—
194#885—61no—
195#879—61no—
196#879—61no—
197#879—61no—
198#869—31no—
199C4×Dic6—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×C22⋊C8—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#832—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—61no—
216#832—61no—
217#832—61no—
218#832—61no—
219#832C2×D311yescharacteristic
220#832C2×D311yescharacteristic
221#830—31no—
222#830C2×D311yescharacteristic
223(C2×D3)⋊C8—31no—
224#818—31no—
225#817—31no—
226#816—31no—
227#816—31no—
228#815—31no—
229Dic3⋊C8—31no—
230#810—31no—
231#810—31no—
232#808—31no—
233#808—31no—
234#808—31no—
235#807—31no—
236C4⋊(C3⋊C8)—31no—
237#803—31no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—42no—
241C23×C32—42no—
242C23×C32—81no—
243C23×C32C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4—21no—
247C32×D4—21no—
248C32×D4—42no—
249C32×D4#4112yes—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C3×#67—41no—
257C3×#67—42no—
258C3×#67—81no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—42no—
264C2×C3×Dic3—81no—
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274#627—42no—
275C3⋊(C3⋊C8)—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#556—91no—
280#546—31no—
281#489—91no—
282#485—91no—
283#482—91no—
284#476—91no—
285#470—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—31no—
290#440—91no—
291#435—91no—
292#418—91no—
293#416—91no—
294C24×C3—21no—
295C24×C3—21no—
296C24×C3—41no—
297C3×#41—62no—
298C3×#41—121no—
299C2×C3×Q8—31no—
300C2×C3×Q8—31no—
301C2×C3×D4—24no—
302C2×C3×D4—22no—
303C2×C3×D4—22no—
304C2×C3×D4—21no—
305C2×C3×D4—21no—
306C2×C3×D4—21no—
307C2×C3×D4—21no—
308C2×C3×D4—31no—
309C2×C3×D4—41no—
310C2×C3×D4—41no—
311C2×C3×D4—41no—
312C2×C3×D4—42no—
313C2×C3×D4—61no—
314C2×C3×D4—61no—
315C2×C3×D4C22×D311yescharacteristic
316C2×C3×D4C22×D311yescharacteristic
317C2×C3×D4C22×D311yescharacteristic
318C2×C3×D4C22×D311yescharacteristic
319C22×C3×C4—21no—
320C22×C3×C4—31no—
321C22×C3×C4—61no—
322C22×C3×C4—61no—
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C2×#67—21no—
326C2×#67—21no—
327C2×#67#6711yescharacteristic
328C22×Dic3—21no—
329C22×Dic3—21no—
330#237—22no—
331#237—41no—
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6—61no—
334C2×Dic6—61no—
335C2×Dic6C22×D311yescharacteristic
336C2×Dic6C22×D311yescharacteristic
337C3×SD16—62no—
338C3×SD16—121no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C42—31no—
355#217—21no—
356#217—21no—
357#217—21no—
358#217—21no—
359#217—21no—
360#217—21no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—121no—
366#217#6711yescharacteristic
367#216—121no—
368#216—121no—
369#214—22no—
370#214—41no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4#6711yescharacteristic
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4#6711yescharacteristic
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—121no—
398C4×Dic3C22×D311yescharacteristic
399#208—121no—
400#208—121no—
401#208—122no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—121no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411D3×C8—121no—
412C22×C32—21no—
413C22×C32—22no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—84no—
422C22×C32C22×D411yescharacteristic
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C32×C4—21no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—41no—
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C2×#41—31no—
439C22×D4D3211yescharacteristic
440C2×Q16—91no—
441C2×SD16—31no—
442C2×SD16—31no—
443C2×M16—91no—
444C22×C8—91no—
445C4⋊Q8—91no—
446#126—181no—
447#126—181no—
448#124—31no—
449#124—181no—
450#123—61no—
451C22⋊Q8—31no—
452C22⋊Q8—31no—
453C22⋊Q8—91no—
454#121—31no—
455#121—61no—
456#120—61no—
457C4×Q8—91no—
458C4×Q8—181no—
459C4×D4—31no—
460C4×D4—31no—
461#117—91no—
462#117—91no—
463C2×C22⋊C4—61no—
464#107—91no—
465#106—91no—
466#106—91no—
467C4⋊C8—91no—
468#103—91no—
469#103—91no—
470#103—91no—
471#103—91no—
472#102—31no—
473#102—31no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478C22⋊C8—31no—
479C22⋊C8—91no—
480#97—91no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—31no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—42no—
490C23×C3—42no—
491C23×C3—44no—
492C23×C3—42no—
493C23×C3—42no—
494C23×C3—82no—
495C23×C3—81no—
496C23×C3—81no—
497C23×C3—82no—
498C23×C3D3×D411yescharacteristic
499C23×C3C2×#6711yescharacteristic
500C22×D3C2×#6711yescharacteristic
501C3×Q8—61no—
502C3×Q8—61no—
503C3×Q8—61no—
504C3×Q8—61no—
505C3×D4—22no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—21no—
511C3×D4—21no—
512C3×D4—22no—
513C3×D4—41no—
514C3×D4—41no—
515C3×D4—42no—
516C3×D4—42no—
517C3×D4—44no—
518C3×D4—121no—
519C3×D4—122no—
520C3×D4—241no—
521C3×D4#23712yes—
522C3×D4#23712yes—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—31no—
532C2×C3×C4—31no—
533C2×C3×C4—31no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—122no—
541C2×C3×C4—241no—
542C2×C3×C4D3×D411yescharacteristic
543C2×C3×C4C2×#6711yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545C2×C3×C4C23×D311yescharacteristic
546#67—41no—
547#67—42no—
548#67—81no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—42no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—81no—
559C2×Dic3—121no—
560C2×Dic3—121no—
561C2×Dic3C2×#6711yescharacteristic
562C2×Dic3C2×#6711yescharacteristic
563C2×Dic3C2×#6711yescharacteristic
564C4×D3—21no—
565C4×D3—21no—
566Dic6—21no—
567Dic6—21no—
568Dic6—21no—
569Dic6—21no—
570Dic6—122no—
571Dic6—122no—
572C3×C8—61no—
573C3×C8—61no—
574C3⋊C8—21no—
575C3⋊C8—21no—
576C3⋊C8—61no—
577C3⋊C8—61no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—121no—
581C3⋊C8—121no—
582C2×C32—41no—
583C2×C32—42no—
584C2×C32—81no—
585C2×C32#54611yescharacteristic
586C2×C32#57511yescharacteristic
587C2×C32#57711yescharacteristic
588C3×D3—41no—
589C24—21no—
590#41—62no—
591#41—121no—
592C2×Q8—31no—
593C2×Q8—31no—
594C2×Q8—181no—
595C2×D4—22no—
596C2×D4—21no—
597C2×D4—31no—
598C2×D4—41no—
599C2×D4—61no—
600C2×D4—61no—
601C2×D4C2×D3211yescharacteristic
602C2×D4C2×D3211yescharacteristic
603C22×C4—31no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4C2×D3211yescharacteristic
607Q16—361no—
608SD16—62no—
609SD16—121no—
610M16—361no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—91no—
614C2×C8—91no—
615C2×C8—361no—
616C4⋊C4—31no—
617C4⋊C4—31no—
618C4⋊C4—31no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—91no—
622C4⋊C4—91no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C22⋊C4—31no—
627C22⋊C4—31no—
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C42—31no—
638C42—181no—
639C42—181no—
640C42—181no—
641C22×C3—22no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—22no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—22no—
650C22×C3—21no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—42no—
654C22×C3—42no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—61no—
666C22×C3—61no—
667C22×C3—61no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—81no—
671C22×C3—81no—
672C22×C3—84no—
673C22×C3—84no—
674C22×C3—88no—
675C22×C3C2×D3×D411yescharacteristic
676C22×C3C22×#6711yescharacteristic
677C2×D3—21no—
678C2×D3—21no—
679C2×D3—21no—
680C3×C4—22no—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—61no—
686C3×C4—61no—
687C3×C4—61no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4—121no—
692C3×C4C2×#23711yescharacteristic
693C3×C4C2×#23711yescharacteristic
694C3×C4#100411yescharacteristic
695C3×C4#100411yescharacteristic
696Dic3—21no—
697Dic3—21no—
698Dic3—21no—
699Dic3—41no—
700Dic3—41no—
701Dic3—41no—
702Dic3—41no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706Dic3—121no—
707Dic3—241no—
708Dic3—241no—
709C32#331111yescharacteristic, complemented, Sylow
710C23—21no—
711C23—21no—
712C23—31no—
713C23—42no—
714C23—42no—
715C23—81no—
716C23D3×#6711yescharacteristic
717Q8—61no—
718Q8—61no—
719Q8—61no—
720Q8—61no—
721Q8—362no—
722D4—21no—
723D4—21no—
724D4—21no—
725D4—42no—
726D4—121no—
727D4—122no—
728D4—241no—
729D4#380512yes—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—31no—
733C2×C4—31no—
734C2×C4—31no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—122no—
742C2×C4—181no—
743C2×C4—181no—
744C2×C4—241no—
745C2×C4D3×#6711yescharacteristic
746C2×C4C22×D3211yescharacteristic
747C8—61no—
748C8—61no—
749C8—181no—
750C8—181no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—42no—
755C2×C3—41no—
756C2×C3—42no—
757C2×C3—41no—
758C2×C3—42no—
759C2×C3—82no—
760C2×C3—82no—
761C2×C3—81no—
762C2×C3—81no—
763C2×C3—121no—
764C2×C3#559111yescharacteristic
765C2×C3#576211yescharacteristic
766C2×C3#577311yescharacteristic
767C2×C3#580611yescharacteristic
768C2×C3#582211yescharacteristic
769C2×C3#583611yescharacteristic
770D3—41no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—22no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—61no—
781C22—61no—
782C22—61no—
783C22—84no—
784C22C2×D3×#6711yescharacteristic
785C4—21no—
786C4—61no—
787C4—61no—
788C4—61no—
789C4—121no—
790C4—121no—
791C4—121no—
792C4—121no—
793C4—361no—
794C4—361no—
795C4C2×#380511yescharacteristic
796C4#6433011yescharacteristic
797C3—21no—
798C3#8016211yescharacteristic, complemented
799C3#8349711yescharacteristic, complemented
800C2—41no—
801C2—42no—
802C2—81no—
803C2—121no—
804C2#1059509511yescharacteristic
805C2#1059510511yescharacteristic
806C2#1059549411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalC3×#5806C2
hypercenterC22×D4D32
hypocenterC32#3311
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10594841C2semidirect
3. #10592914C2semidirect
4. C3×#5218C2semidirect
5. #10591499C2semidirect
6. #10591488C2semidirect
7. #10591461C2semidirect
8. #10591442C2semidirect
9. #10591440C2semidirect
10. #10591423C2semidirect
11. #10591420C2semidirect
12. #10591408C2semidirect
13. #10591189C2semidirect
14. #10591151C2semidirect
15. #10591127C2semidirect
36. #63918C22semidirect
38. #63856C22semidirect
39. Dic3×Dic6C22semidirect
40. #63841C22semidirect
42. C2×#3718C22semidirect
43. C2×D3×C3⋊C8C22semidirect
51. #63575C22semidirect
52. #63574C22semidirect
53. #63573C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63566C22semidirect
56. #63566C22semidirect
57. #63565C22semidirect
58. #63565C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63554C22semidirect
68. #5218D3semidirect
709. C32#3311semidirect
798. C3#80162semidirect
799. C3#83497semidirect

Maximal subgroups

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

subgroupindex
C3×#58062
#105948412
#105929142
C3×#52182
#105914992
#105914882
#105914612
#105914422
#105914402
#105914232
#105914202
#105914082
#105911892
#105911512
#105911272
#834973
#801623