Finite Group Databasebeta

← #11884326

Subgroups — #11884326

Order 1152.

1062 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595427C211yesmaximal, characteristic, complemented
2C2×#63949C211yesmaximal, characteristic, complemented
3C2×#63794C211yesmaximal, characteristic, complemented
4#10594530C211yesmaximal, characteristic, complemented
5#10592518C211yesmaximal, characteristic, complemented
6C3×#4816C211yesmaximal, characteristic, complemented
7C3×#4808C211yesmaximal, characteristic, complemented
8#10591657C211yesmaximal, characteristic, complemented
9#10591629C211yesmaximal, characteristic, complemented
10#10590967C211yesmaximal, characteristic, complemented
11#10590748C211yesmaximal, characteristic, complemented
12#10590724C211yesmaximal, characteristic, complemented
13#10590596C211yesmaximal, characteristic, complemented
14#10590577C211yesmaximal, characteristic, complemented
15#10590462C211yesmaximal, characteristic, complemented
16#80921—31nomaximal
17#80264—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21C2×#3799C2211yescharacteristic, complemented
22#64156C2211yescharacteristic
23C2×#3755C2211yescharacteristic, complemented
24C2×#3745C2211yescharacteristic
25#64102C2211yescharacteristic, complemented
26C3×#946C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic, complemented
28C2×C3×#216C2211yescharacteristic, complemented
29C2×C3×#204C2211yescharacteristic
30C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
31C3×#897C2211yescharacteristic
32C3×#897C2211yescharacteristic, complemented
33#63949—24no—
34#63922—21no—
35D3×(C2×D3)⋊C4—21no—
36#63912—21no—
37#63909C2211yescharacteristic
38C4×#625C2211yescharacteristic
39#63900—21no—
40#63898C2211yescharacteristic
41#63886—21no—
42#63873C2211yescharacteristic, complemented
43#63854—21no—
44#63854—21no—
45#63850—21no—
46C2×#3717C2211yescharacteristic
47C2×#3717C2211yescharacteristic
48C2×#3715C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic, complemented
51#63794—24no—
52C32×#103C2211yescharacteristic, complemented
53#63641C2211yescharacteristic, complemented
54#63636C2211yescharacteristic
55C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
56C3×#816C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63555C2211yescharacteristic, complemented
63#5829—31no—
64C2×#950—31no—
65C2×#919—31no—
66C2×#914—31no—
67C2×#908—31no—
68#5631—31no—
69#5631—31no—
70#5630—31no—
71C3×#470—31no—
72C3×#452—31no—
73#5190—31no—
74#5190—31no—
75#5187—31no—
76#5162—31no—
77#5127—31no—
78#5048—31no—
79#5047—31no—
80#5046—31no—
81#4869—31no—
82#4864—31no—
83#4819—31no—
84#4819—31no—
85#4819—61no—
86#4818—31no—
87#4816D311yescharacteristic, complemented
88#4810—31no—
89#4808D311yescharacteristic, complemented
90#4785—31no—
91#4776—31no—
92#4734—31no—
93#4730—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C3×#239—22no—
100C3×#239—41no—
101C2×C3×D12—21no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#626—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#625D411yescharacteristic
113C2×#624—21no—
114C2×#624—21no—
115C2×D3×Dic3—21no—
116D3×D12—22no—
117D3×D12—41no—
118#3799—22no—
119#3799—22no—
120#3799—41no—
121#3799—41no—
122C2×C32×C8C2311yescharacteristic
123C32×C4⋊C4C2311yescharacteristic
124#3755—22no—
125#3752—21no—
126#3752—21no—
127#3752—21no—
128C4×C3⋊Dic3C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130#3745—22no—
131C3×#216—22no—
132C3×#216—41no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3—21no—
138C3×C4⋊Dic3C2311yescharacteristic
139C3×Dic3⋊C4—21no—
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×#204—22no—
143C3×ΓL(1,𝔽25)—22no—
144#3724—21no—
145#3724—21no—
146#3724D411yescharacteristic
147#3722—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3D411yescharacteristic
150(C2×D3)⋊Dic3D411yescharacteristic
151#3717—22no—
152#3717—41no—
153#3715—22no—
154#3714D414yescomplemented
155D3×C3⋊C8—22no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C2×#239—31no—
159C2×#239—31no—
160C2×#239C2×D311yescharacteristic
161C2×D3×D4—31no—
162C2×#235—31no—
163C2×#235—31no—
164C22×D12—31no—
165C2×C3×Q16—31no—
166C2×C3×Q16—31no—
167C2×C3×SD16—31no—
168C2×C3×M16—31no—
169C3×C22⋊Q8—31no—
170C3×C22⋊Q8—31no—
171C3×C22⋊Q8—31no—
172#950—64no—
173#947—31no—
174#947—31no—
175#947—61no—
176#946C2×D311yescharacteristic
177#944—31no—
178#944—31no—
179C2×#216C2×D311yescharacteristic, complemented
180C2×#216C2×D311yescharacteristic, complemented
181C2×#215—31no—
182C2×#215—31no—
183C2×#215—31no—
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—61no—
187#939—61no—
188#937—61no—
189D4×Dic3—31no—
190C2×#214—31no—
191C2×#213—31no—
192#930—31no—
193#929—61no—
194C4×#67—31no—
195C4×#67—31no—
196C2×(C2×D3)⋊C4—61no—
197C22×C3⋊C8—31no—
198#919—64no—
199#914—64no—
200#908—64no—
201C2×D24—31no—
202C2×D24—31no—
203C2×D24—31no—
204C2×D24—61no—
205C2×#204—31no—
206C2×#204—31no—
207C2×#204C2×D311yescharacteristic
208C2×ΓL(1,𝔽25)C2×D311yescharacteristic
209C2×D3×C8—31no—
210#897C2×D311yescharacteristic
211#897C2×D311yescharacteristic, complemented
212#895—31no—
213#895—61no—
214#894—61no—
215#894—61no—
216#894—61no—
217#893—31no—
218#893—31no—
219#893—31no—
220#893—61no—
221D3×C4⋊C4—61no—
222D3×C4⋊C4—61no—
223#884—61no—
224#884—61no—
225#883—61no—
226#883—61no—
227#882—61no—
228D3×C22⋊C4—61no—
229C3×#106—31no—
230C3×#103—21no—
231C3×#103—31no—
232C3×#103C2×D311yescharacteristic, complemented
233C3×#103C2×D311yescharacteristic, complemented
234C3×#102—31no—
235C3×C22⋊C8—31no—
236#835—31no—
237#830—31no—
238#821—31no—
239(C2×D3)⋊C8—31no—
240(C2×D3)⋊C8C2×D311yescharacteristic, complemented
241#816C2×D311yescharacteristic, complemented
242#815—31no—
243#815—31no—
244Dic3⋊C8—31no—
245Dic3⋊C8—31no—
246Dic3⋊C8—61no—
247#810—31no—
248#809—31no—
249#809—31no—
250#809—31no—
251#809—61no—
252#809C2×D311yescharacteristic
253#808C2×D311yescharacteristic, complemented
254C22×C3⋊D3—21no—
255C22×C3⋊D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3C2×D411yescharacteristic
258C22×C3×D3C2×D411yescharacteristic
259C2×D32—42no—
260C2×D32—42no—
261C2×D32—81no—
262C32×Q8—21no—
263C32×Q8—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4C2411yescharacteristic
267C2×C3⋊Dic3C2×D411yescharacteristic
268C2×C3⋊Dic3C2×D411yescharacteristic
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)C2×D412yes—
273C4×C3⋊D3—42no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C3×D12—21no—
280C3×D12—42no—
281C3×D12C2×D412yes—
282C3×C4×D3—21no—
283C3×C4×D3—21no—
284C3×C4×D3—21no—
285C3×C4×D3—21no—
286C3×C4×D3—42no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291#626—42no—
292#626—42no—
293#626—42no—
294#626—81no—
295#625—41no—
296#624—42no—
297#624—42no—
298D3×Dic3—81no—
299C32×C8—21no—
300C3⋊(C3⋊C8)—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yes—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—91no—
305#547—91no—
306#546—91no—
307#497—91no—
308#470—31no—
309#465—91no—
310#463—91no—
311#461—91no—
312#452—31no—
313#452—91no—
314#450—91no—
315#449—91no—
316#442—91no—
317#435—91no—
318C23×D3—61no—
319C23×D3—61no—
320C3×#41—62no—
321C3×#41—121no—
322C2×C3×Q8—21no—
323C2×C3×Q8—31no—
324C2×C3×Q8—31no—
325C2×C3×Q8C22×D311yescharacteristic
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×D4—31no—
328C2×C3×D4—61no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—61no—
332C2×#67—31no—
333C2×#67—31no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C22×Dic3—61no—
339#239—22no—
340#239—41no—
341#239—62no—
342#239—62no—
343#239—121no—
344#239—121no—
345D3×D4—62no—
346D3×D4—121no—
347#235—62no—
348#235—62no—
349#235—121no—
350#235—121no—
351C2×D12—21no—
352C2×D12—31no—
353C2×D12—31no—
354C2×D12—31no—
355C2×D12—31no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—62no—
359C2×D12—61no—
360C2×D12—61no—
361C2×D12—61no—
362C2×D12—61no—
363C2×D12—121no—
364C2×D12C22×D311yescharacteristic
365C2×C4×D3—21no—
366C2×C4×D3—61no—
367C2×C4×D3—61no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—121no—
374C2×C4×D3C22×D311yescharacteristic
375C2×C4×D3C22×D311yescharacteristic
376C2×Dic6C22×D311yescharacteristic
377C2×Dic6C22×D311yescharacteristic
378C3×Q16—62no—
379C3×Q16—121no—
380C3×SD16—62no—
381C3×M16—62no—
382C2×C3×C8—21no—
383C2×C3×C8—31no—
384C2×C3×C8—31no—
385C2×C3×C8C22×D311yescharacteristic
386C2×C3×C8C22×D311yescharacteristic
387C3×C4⋊C4—21no—
388C3×C4⋊C4—31no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4—61no—
391C3×C4⋊C4—61no—
392C3×C4⋊C4C22×D311yescharacteristic
393C3×C4⋊C4C22×D311yescharacteristic
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C22⋊C4—61no—
397#217—31no—
398#217—31no—
399#217—61no—
400#216—22no—
401#216—41no—
402#215—62no—
403#215—62no—
404#215—62no—
405#215—62no—
406#215—122no—
407#215—121no—
408#214—62no—
409#213—34no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—21no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—31no—
414(C2×D3)⋊C4—31no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—121no—
425(C2×D3)⋊C4—121no—
426(C2×D3)⋊C4—121no—
427C4⋊Dic3—21no—
428C4⋊Dic3—21no—
429C4⋊Dic3C22×D311yescharacteristic
430Dic3⋊C4—21no—
431Dic3⋊C4—31no—
432Dic3⋊C4—31no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437C4×Dic3—31no—
438C4×Dic3—31no—
439C4×Dic3—61no—
440C2×C3⋊C8—31no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—61no—
443C2×C3⋊C8—62no—
444C2×C3⋊C8C22×D311yescharacteristic
445C2×C3⋊C8C22×D311yescharacteristic
446D24—34no—
447D24—62no—
448D24—62no—
449D24—122no—
450#204—22no—
451#204—62no—
452#204—121no—
453ΓL(1,𝔽25)—22no—
454D3×C8—62no—
455C22×C32C22×D411yescharacteristic
456C2×C3⋊D3—22no—
457C2×C3⋊D3—41no—
458C2×C3⋊D3—41no—
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3⋊D3—41no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—22no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471D32—84no—
472C32×C4—41no—
473C32×C4—41no—
474C32×C4C22×D411yescharacteristic
475C32×C4H(5,𝔽2)11yescharacteristic
476C3⋊Dic3—21no—
477C3⋊Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—21no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C2×#41—31no—
484C2×#41—91no—
485C2×#41—91no—
486C22×D4—91no—
487AGL(1,ℤ/8)—184no—
488#135—184no—
489C2×Q16—31no—
490C2×Q16—31no—
491C2×SD16—31no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×D8—91no—
497C2×D8—91no—
498C2×M16—31no—
499C22×C8—91no—
500C4⋊Q8—91no—
501#124—91no—
502#123—181no—
503#123—181no—
504#123—181no—
505C22⋊Q8—31no—
506C22⋊Q8—31no—
507C22⋊Q8—31no—
508#121—91no—
509#121—181no—
510#121—181no—
511#120—181no—
512C4×D4—91no—
513C4×D4—91no—
514C4×D4—91no—
515C2×C4⋊C4—181no—
516C2×C22⋊C4—181no—
517#106—31no—
518C4⋊C8—91no—
519#103—31no—
520#103—91no—
521#103D3211yescharacteristic, complemented
522#102—31no—
523#102—91no—
524#102—91no—
525C22⋊C8—31no—
526C22⋊C8—91no—
527#97—91no—
528C23×C3—31no—
529C23×C3—31no—
530C23×C3—61no—
531C22×D3—21no—
532C22×D3—61no—
533C22×D3—61no—
534C22×D3—61no—
535C22×D3—61no—
536C22×D3—121no—
537C22×D3—121no—
538C22×D3—122no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3—122no—
542C22×D3—241no—
543C22×D3—241no—
544C22×D3D3×D411yescharacteristic
545C22×D3D3×D411yescharacteristic
546C3×Q8—21no—
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—21no—
550C3×Q8—41no—
551C3×Q8—41no—
552C3×Q8—61no—
553C3×Q8—61no—
554C3×Q8—61no—
555C3×Q8—61no—
556C3×D4—32no—
557C3×D4—61no—
558C3×D4—122no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—31no—
565C2×C3×C4—31no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—122no—
576C2×C3×C4C23×D311yescharacteristic
577C2×C3×C4C23×D311yescharacteristic
578#67—122no—
579#67—122no—
580#67—122no—
581#67—121no—
582#67—121no—
583#67—241no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—31no—
588C2×Dic3—31no—
589C2×Dic3—31no—
590C2×Dic3—31no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—241no—
594C2×Dic3D3×D411yescharacteristic
595C2×Dic3D3×D411yescharacteristic
596D12—21no—
597D12—32no—
598D12—32no—
599D12—42no—
600D12—62no—
601D12—61no—
602D12—61no—
603D12—61no—
604D12—61no—
605D12—61no—
606D12—61no—
607D12—121no—
608D12—121no—
609D12—121no—
610D12—122no—
611D12—122no—
612D12—122no—
613D12—241no—
614D12D3×D412yes—
615C4×D3—21no—
616C4×D3—21no—
617C4×D3—21no—
618C4×D3—21no—
619C4×D3—42no—
620C4×D3—122no—
621C4×D3—122no—
622C4×D3—122no—
623C4×D3—122no—
624C4×D3—122no—
625C4×D3—122no—
626C4×D3—242no—
627C4×D3—241no—
628Dic6—21no—
629Dic6—21no—
630Dic6—21no—
631Dic6—21no—
632C3×C8—21no—
633C3×C8—21no—
634C3×C8—32no—
635C3×C8—41no—
636C3×C8—61no—
637C3⋊C8—21no—
638C3⋊C8—61no—
639C3⋊C8—61no—
640C3⋊C8—121no—
641C3⋊C8D3×D412yes—
642C2×C32D4211yescharacteristic
643C2×C32#57511yescharacteristic
644C2×C32#57711yescharacteristic
645C3⋊D3—42no—
646C3⋊D3—81no—
647C3×D3—41no—
648C3×D3—42no—
649C3×D3—41no—
650C24—181no—
651#41—62no—
652#41—121no—
653#41—182no—
654#41—182no—
655#41—361no—
656#41—361no—
657C2×Q8—31no—
658C2×Q8—31no—
659C2×Q8C2×D3211yescharacteristic
660C2×D4—31no—
661C2×D4—61no—
662C2×D4—91no—
663C2×D4—91no—
664C2×D4—91no—
665C2×D4—181no—
666C2×D4—182no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4—181no—
670C2×D4—361no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—61no—
674C22×C4—181no—
675C22×C4—181no—
676C22×C4—181no—
677C22×C4—181no—
678Q16—62no—
679Q16—121no—
680SD16—62no—
681SD16—182no—
682SD16—182no—
683SD16—182no—
684SD16—361no—
685D8—94no—
686D8—182no—
687M16—62no—
688C2×C8—31no—
689C2×C8—31no—
690C2×C8—91no—
691C2×C8—182no—
692C2×C8C2×D3211yescharacteristic
693C4⋊C4—31no—
694C4⋊C4—61no—
695C4⋊C4—61no—
696C4⋊C4—61no—
697C4⋊C4—91no—
698C4⋊C4—181no—
699C4⋊C4—181no—
700C4⋊C4C2×D3211yescharacteristic
701C22⋊C4—61no—
702C22⋊C4—61no—
703C22⋊C4—61no—
704C22⋊C4—91no—
705C22⋊C4—91no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C22⋊C4—181no—
711C42—91no—
712C22×C3—21no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—61no—
717C22×C3—61no—
718C22×C3—61no—
719C22×C3—62no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3C2×D3×D411yescharacteristic
723C22×C3C2×D3×D411yescharacteristic
724C2×D3—21no—
725C2×D3—21no—
726C2×D3—21no—
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—22no—
730C2×D3—21no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3—62no—
734C2×D3—62no—
735C2×D3—122no—
736C2×D3—121no—
737C2×D3—121no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—121no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—241no—
747C2×D3—241no—
748C2×D3—241no—
749C2×D3—241no—
750C2×D3—241no—
751C2×D3—244no—
752C2×D3—244no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—41no—
756C3×C4—41no—
757C3×C4—41no—
758C3×C4—41no—
759C3×C4—61no—
760C3×C4—61no—
761C3×C4—81no—
762C3×C4—81no—
763C3×C4—121no—
764C3×C4—121no—
765C3×C4—121no—
766C3×C4C2×D3×D411yescharacteristic
767C3×C4C2×D3×D411yescharacteristic
768C3×C4#100411yescharacteristic
769C3×C4#100911yescharacteristic
770Dic3—21no—
771Dic3—21no—
772Dic3—41no—
773Dic3—41no—
774Dic3—41no—
775Dic3—61no—
776Dic3—61no—
777Dic3—61no—
778Dic3—61no—
779Dic3—121no—
780Dic3—121no—
781C32#326711yescharacteristic, complemented, Sylow
782C23—31no—
783C23—31no—
784C23—61no—
785C23—181no—
786C23—181no—
787C23—362no—
788C23—362no—
789C23—721no—
790Q8—21no—
791Q8—21no—
792Q8—61no—
793Q8—61no—
794Q8—61no—
795Q8—61no—
796D4—32no—
797D4—61no—
798D4—92no—
799D4—122no—
800D4—181no—
801D4—181no—
802D4—181no—
803D4—362no—
804D4—362no—
805D4—362no—
806D4—361no—
807D4—721no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—31no—
811C2×C4—31no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—91no—
820C2×C4—91no—
821C2×C4—122no—
822C2×C4—362no—
823C2×C4—362no—
824C2×C4—362no—
825C2×C4—721no—
826C2×C4C22×D3211yescharacteristic
827C8—21no—
828C8—32no—
829C8—61no—
830C8—181no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—122no—
835C2×C3—121no—
836C2×C3—121no—
837C2×C3#559011yescharacteristic
838C2×C3#560911yescharacteristic
839C2×C3#576811yescharacteristic
840C2×C3#577711yescharacteristic
841C2×C3#577811yescharacteristic
842C2×C3#577811yescharacteristic
843D3—41no—
844D3—41no—
845D3—42no—
846D3—122no—
847D3—122no—
848D3—242no—
849D3—241no—
850D3—241no—
851D3—481no—
852C22—61no—
853C22—61no—
854C22—61no—
855C22—61no—
856C22—61no—
857C22—61no—
858C22—62no—
859C22—121no—
860C22—121no—
861C22—182no—
862C22—361no—
863C22—361no—
864C22—361no—
865C22—361no—
866C22—361no—
867C22—724no—
868C22D32×D411yescharacteristic
869C4—41no—
870C4—41no—
871C4—61no—
872C4—61no—
873C4—121no—
874C4—121no—
875C4—121no—
876C4—181no—
877C4—181no—
878C4#6430711yescharacteristic
879C4D32×D411yescharacteristic
880C3—21no—
881C3#8026411yescharacteristic, complemented
882C3#8092111yescharacteristic, complemented
883C2—121no—
884C2—121no—
885C2—122no—
886C2—362no—
887C2—721no—
888C2#1059427511yescharacteristic
889C2#1059474611yescharacteristic
890C2#1059476711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595427C2semidirect
2. C2×#63949C2semidirect
3. C2×#63794C2semidirect
4. #10594530C2semidirect
5. #10592518C2semidirect
6. C3×#4816C2semidirect
7. C3×#4808C2semidirect
8. #10591657C2semidirect
9. #10591629C2semidirect
10. #10590967C2semidirect
11. #10590748C2semidirect
12. #10590724C2semidirect
13. #10590596C2semidirect
14. #10590577C2semidirect
15. #10590462C2semidirect
21. C2×#3799C22semidirect
23. C2×#3755C22semidirect
25. #64102C22semidirect
27. C2×C3×#216C22semidirect
28. C2×C3×#216C22semidirect
32. C3×#897C22semidirect
42. #63873C22semidirect
50. C2×D3×C3⋊C8C22semidirect
52. C32×#103C22semidirect
53. #63641C22semidirect
55. C3×(C2×D3)⋊C8C22semidirect
56. C3×#816C22semidirect
58. C3×#808C22semidirect
59. #63565C22semidirect
60. #63564C22semidirect
62. #63555C22semidirect
87. #4816D3semidirect
89. #4808D3semidirect
154. #3714D4semidirect
179. C2×#216C2×D3semidirect
180. C2×#216C2×D3semidirect
211. #897C2×D3semidirect
232. C3×#103C2×D3semidirect
233. C3×#103C2×D3semidirect
240. (C2×D3)⋊C8C2×D3semidirect
241. #816C2×D3semidirect
253. #808C2×D3semidirect
521. #103D32semidirect
781. C32#3267semidirect
881. C3#80264semidirect
882. C3#80921semidirect

Maximal subgroups

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

subgroupindex
#105954272
C2×#639492
C2×#637942
#105945302
#105925182
C3×#48162
C3×#48082
#105916572
#105916292
#105909672
#105907482
#105907242
#105905962
#105905772
#105904622
#809213
#802643