Finite Group Databasebeta

← #11884483

Subgroups — #11884483

Order 1152.

1080 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595428C211yesmaximal, characteristic, complemented
2C2×#63949C211yesmaximal, characteristic, complemented
3C2×#63798C211yesmaximal, characteristic, complemented
4#10594524C211yesmaximal, characteristic, complemented
5#10592511C211yesmaximal, characteristic, complemented
6C3×#4810C211yesmaximal, characteristic, complemented
7C3×#4798C211yesmaximal, characteristic, complemented
8#10591656C211yesmaximal, characteristic, complemented
9#10591619C211yesmaximal, characteristic, complemented
10#10590907C211yesmaximal, characteristic, complemented
11#10590823C211yesmaximal, characteristic, complemented
12#10590753C211yesmaximal, characteristic, complemented
13#10590598C211yesmaximal, characteristic, complemented
14#10590499C211yesmaximal, characteristic, complemented
15#10590454C211yesmaximal, characteristic, complemented
16#80628—31nomaximal
17#80128—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×#3802C2211yescharacteristic
20C2×#3799C2211yescharacteristic, complemented
21C2×#3796C2211yescharacteristic
22#64155C2211yescharacteristic
23C2×#3755C2211yescharacteristic, complemented
24C2×#3743C2211yescharacteristic
25#64104C2211yescharacteristic
26C3×#947C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic, complemented
29C2×C3×D24C2211yescharacteristic
30C2×C3×#204C2211yescharacteristic
31C3×#895C2211yescharacteristic, complemented
32C3×#887C2211yescharacteristic, complemented
33#63949—24no—
34#63922—21no—
35D3×(C2×D3)⋊C4—21no—
36#63911—21no—
37#63911C2211yescharacteristic, complemented
38#63910—21no—
39#63908C2211yescharacteristic
40#63905—21no—
41C4×#626C2211yescharacteristic
42Dic3×D12C2211yescharacteristic
43#63886—21no—
44#63885—21no—
45#63880—21no—
46C2×#3715C2211yescharacteristic
47C2×#3714C2211yescharacteristic
48C2×#3714C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic, complemented
51#63798—24no—
52C32×#103C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54#63634C2211yescharacteristic, complemented
55C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic
59#63566C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63557C2211yescharacteristic
62#63554C2211yescharacteristic, complemented
63#5829—31no—
64C2×#950—31no—
65C2×#919—31no—
66C2×#914—31no—
67C2×#911—31no—
68#5676—31no—
69#5599—31no—
70#5577—31no—
71C3×#464—31no—
72C3×#449—31no—
73#5187—31no—
74#5176—31no—
75#5173—31no—
76#5172—31no—
77#5150—31no—
78#5058—31no—
79#5038—31no—
80#5026—31no—
81#4843—31no—
82#4836—31no—
83#4812—31no—
84#4812—31no—
85#4812—61no—
86#4810D311yescharacteristic, complemented
87#4798D311yescharacteristic, complemented
88#4775—31no—
89#4773—31no—
90#4773—31no—
91#4757—31no—
92#4734—31no—
93#4730—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C3×#239—22no—
100C3×#239—41no—
101C2×C3×D12—21no—
102C2×C3×D12—21no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#626D411yescharacteristic
114C2×#625—21no—
115C2×#625—21no—
116C2×#624—21no—
117C2×D3×Dic3—21no—
118C2×D3×Dic3—21no—
119#3802—22no—
120#3802—41no—
121#3799—22no—
122#3799—41no—
123#3796—22no—
124#3796—41no—
125C2×C32×C8C2311yescharacteristic
126C32×C4⋊C4C2311yescharacteristic
127#3755—22no—
128#3752—21no—
129#3752—21no—
130C4⋊(C3⋊Dic3)C2311yescharacteristic
131#3750—21no—
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133#3743—22no—
134C3×#216—22no—
135C3×#215—41no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×C4×Dic3—21no—
141C3×C4×Dic3C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C3×D24—22no—
145C3×#204—22no—
146Dic3⋊Dic3D411yescharacteristic
147#3722D411yescharacteristic
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3D411yescharacteristic
151#3715D414yescomplemented
152#3714—22no—
153#3714—41no—
154#3713—22no—
155D3×C3⋊C8—22no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C2×#239—31no—
159C2×#239—31no—
160C2×#239C2×D311yescharacteristic
161C2×#237—31no—
162C2×D3×D4—31no—
163C2×D3×D4—31no—
164C2×#235—31no—
165C2×C3×Q16—31no—
166C2×C3×SD16—31no—
167C2×C3×SD16—31no—
168C2×C3×D8—31no—
169C3×#124—31no—
170C3×#121—31no—
171C3×C4×Q8—31no—
172#950—64no—
173#947C2×D311yescharacteristic
174#946—31no—
175#946—31no—
176#946—61no—
177C2×#216C2×D311yescharacteristic, complemented
178C2×#215—31no—
179C2×#215—31no—
180C2×#215—31no—
181C2×#215—61no—
182C2×#215C2×D311yescharacteristic, complemented
183#940—31no—
184#940—61no—
185#939—61no—
186#939—61no—
187#938—31no—
188#937—61no—
189D4×Dic3—31no—
190C2×#214—31no—
191C2×#213—31no—
192C2×#213—31no—
193C2×#213—31no—
194C2×#213—31no—
195#930—31no—
196#929—61no—
197C4×#67—31no—
198C2×(C2×D3)⋊C4—61no—
199C22×C3⋊C8—31no—
200#919—64no—
201#914—64no—
202#911—64no—
203C2×D24—31no—
204C2×D24—31no—
205C2×D24C2×D311yescharacteristic
206C2×#204C2×D311yescharacteristic
207C2×ΓL(1,𝔽25)—31no—
208C2×ΓL(1,𝔽25)—31no—
209C2×ΓL(1,𝔽25)—61no—
210C2×D3×C8—31no—
211#895—31no—
212#895—31no—
213#895—61no—
214#895—61no—
215#895—61no—
216#895C2×D311yescharacteristic, complemented
217#887C2×D311yescharacteristic, complemented
218#884—61no—
219#884—61no—
220#883—61no—
221#882—61no—
222#67⋊C4—61no—
223D3×C22⋊C4—61no—
224#874—31no—
225#874—61no—
226C4×D12—31no—
227C4×D12—31no—
228C4×D12—61no—
229C3×C4⋊C8—31no—
230C3×#103—21no—
231C3×#103C2×D311yescharacteristic, complemented
232C3×#103C2×D311yescharacteristic, complemented
233C3×#102—31no—
234C3×#102—31no—
235C3×C22⋊C8—31no—
236#835—31no—
237#832—31no—
238#821—31no—
239#821—31no—
240#821—31no—
241#821—61no—
242(C2×D3)⋊C8—31no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8C2×D311yescharacteristic, complemented
245#816—31no—
246#815—31no—
247Dic3⋊C8C2×D311yescharacteristic, complemented
248#809C2×D311yescharacteristic
249#809C2×D311yescharacteristic
250#807—31no—
251#807—31no—
252#807—61no—
253#803—31no—
254C22×C3⋊D3—21no—
255C22×C3⋊D3C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—42no—
261C2×D32—42no—
262C2×D32—81no—
263C32×Q8—21no—
264C32×Q8—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2411yescharacteristic
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3C2×D411yescharacteristic
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—81no—
273C4×C3⋊D3—21no—
274C4×C3⋊D3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—42no—
285C3×D12—81no—
286C3×D12C2×D412yes—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—42no—
290C3×Dic6—21no—
291C3×Dic6C2×D412yes—
292#626—41no—
293#626—42no—
294#626—42no—
295#626—42no—
296#626—81no—
297#625—42no—
298#625—81no—
299#624—42no—
300D3×Dic3—42no—
301D3×Dic3—81no—
302C32×C8—21no—
303C3⋊(C3⋊C8)C2×D412yes—
304C3×C3⋊C8—21no—
305C3×C3⋊C8—21no—
306C2×AGL(1,ℤ/8)—91no—
307C2×#135—91no—
308#550—91no—
309#546—91no—
310#496—91no—
311#468—91no—
312#466—91no—
313#464—31no—
314#459—91no—
315#452—91no—
316#449—31no—
317#449—91no—
318#447—91no—
319#440—91no—
320#435—91no—
321C23×D3—61no—
322C23×D3—61no—
323C3×#41—62no—
324C3×#41—121no—
325C2×C3×Q8—21no—
326C2×C3×Q8—31no—
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C22×C3×C4—31no—
335C22×C3×C4—61no—
336C2×#67—31no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C22×Dic3—61no—
346C22×Dic3—61no—
347#239—22no—
348#239—41no—
349#239—62no—
350#239—62no—
351#239—121no—
352#239—121no—
353#237—62no—
354#237—121no—
355D3×D4—62no—
356D3×D4—62no—
357D3×D4—121no—
358D3×D4—121no—
359#235—62no—
360#235—121no—
361C2×D12—21no—
362C2×D12—21no—
363C2×D12—31no—
364C2×D12—31no—
365C2×D12—31no—
366C2×D12—61no—
367C2×D12—61no—
368C2×D12—61no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—61no—
373C2×D12—121no—
374C2×D12C22×D311yescharacteristic
375C2×D12C22×D311yescharacteristic
376C2×D12C22×D311yescharacteristic
377C2×C4×D3—21no—
378C2×C4×D3—31no—
379C2×C4×D3—31no—
380C2×C4×D3—61no—
381C2×C4×D3—61no—
382C2×C4×D3—61no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3C22×D311yescharacteristic
386C2×Dic6C22×D311yescharacteristic
387C3×Q16—62no—
388C3×SD16—62no—
389C3×SD16—121no—
390C3×D8—62no—
391C2×C3×C8—21no—
392C2×C3×C8—31no—
393C2×C3×C8—31no—
394C2×C3×C8C22×D311yescharacteristic
395C2×C3×C8C22×D311yescharacteristic
396C3×C4⋊C4—21no—
397C3×C4⋊C4—61no—
398C3×C4⋊C4C22×D311yescharacteristic
399C3×C4⋊C4C22×D311yescharacteristic
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C22⋊C4—61no—
403C3×C42—31no—
404C3×C42—61no—
405#217—31no—
406#217—61no—
407#217—61no—
408#216—22no—
409#215—34no—
410#215—41no—
411#215—62no—
412#215—62no—
413#215—122no—
414#214—34no—
415#213—62no—
416#213—62no—
417#213—62no—
418#213—121no—
419(C2×D3)⋊C4—21no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—31no—
423(C2×D3)⋊C4—31no—
424(C2×D3)⋊C4—31no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—121no—
432(C2×D3)⋊C4—121no—
433C4⋊Dic3—31no—
434C4⋊Dic3—31no—
435C4⋊Dic3—31no—
436C4⋊Dic3—61no—
437Dic3⋊C4—21no—
438Dic3⋊C4—31no—
439Dic3⋊C4—61no—
440Dic3⋊C4—61no—
441Dic3⋊C4—121no—
442C4×Dic3—21no—
443C4×Dic3C22×D311yescharacteristic
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—61no—
447C2×C3⋊C8—62no—
448C2×C3⋊C8C22×D311yescharacteristic
449C2×C3⋊C8C22×D311yescharacteristic
450D24—22no—
451D24—62no—
452D24—121no—
453#204—22no—
454ΓL(1,𝔽25)—62no—
455ΓL(1,𝔽25)—62no—
456ΓL(1,𝔽25)—122no—
457D3×C8—62no—
458C22×C32C22×D411yescharacteristic
459C2×C3⋊D3—21no—
460C2×C3⋊D3—21no—
461C2×C3⋊D3—21no—
462C2×C3⋊D3—41no—
463C2×C3⋊D3—41no—
464C2×C3⋊D3—41no—
465C2×C3×D3—22no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477D32—84no—
478C32×C4—41no—
479C32×C4—41no—
480C32×C4C22×D411yescharacteristic
481C32×C4H(5,𝔽2)11yescharacteristic
482C3⋊Dic3—21no—
483C3⋊Dic3—41no—
484C3×Dic3—22no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C2×#41—31no—
489C2×#41—91no—
490C2×#41—91no—
491C22×D4—91no—
492AGL(1,ℤ/8)—184no—
493#135—184no—
494C2×Q16—31no—
495C2×SD16—31no—
496C2×SD16—31no—
497C2×SD16—91no—
498C2×SD16—91no—
499C2×D8—31no—
500C2×D8—91no—
501C2×D8—91no—
502C2×D8—91no—
503C2×M16—91no—
504C22×C8—91no—
505#127—91no—
506#127—181no—
507#124—31no—
508#123—181no—
509C22⋊Q8—91no—
510#121—31no—
511#121—91no—
512#121—91no—
513#121—181no—
514#121—181no—
515#121—181no—
516#120—181no—
517C4×Q8—31no—
518C4×D4—91no—
519C4×D4—91no—
520C4×D4—181no—
521C2×C22⋊C4—181no—
522#107—91no—
523C4⋊C8—31no—
524#103—91no—
525#103D3211yescharacteristic, complemented
526#102—31no—
527#102—31no—
528#102—91no—
529#102—91no—
530C22⋊C8—31no—
531C22⋊C8—91no—
532#97—91no—
533C23×C3—31no—
534C23×C3—61no—
535C23×C3—61no—
536C23×C3—61no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—31no—
541C22×D3—31no—
542C22×D3—61no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—121no—
546C22×D3—122no—
547C22×D3—122no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—241no—
551C22×D3—241no—
552C22×D3D3×D411yescharacteristic
553C3×Q8—21no—
554C3×Q8—21no—
555C3×Q8—21no—
556C3×Q8—21no—
557C3×Q8—32no—
558C3×Q8—41no—
559C3×Q8—41no—
560C3×Q8—61no—
561C3×D4—32no—
562C3×D4—61no—
563C3×D4—61no—
564C3×D4—61no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—122no—
568C3×D4—241no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—31no—
575C2×C3×C4—31no—
576C2×C3×C4—31no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—122no—
583C2×C3×C4C23×D311yescharacteristic
584C2×C3×C4C23×D311yescharacteristic
585#67—121no—
586#67—122no—
587#67—122no—
588#67—122no—
589#67—122no—
590#67—122no—
591#67—241no—
592#67—241no—
593#67—241no—
594C2×Dic3—21no—
595C2×Dic3—31no—
596C2×Dic3—31no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—121no—
601C2×Dic3—122no—
602C2×Dic3—241no—
603C2×Dic3D3×D411yescharacteristic
604C2×Dic3D3×D411yescharacteristic
605C2×Dic3D3×D411yescharacteristic
606D12—21no—
607D12—21no—
608D12—21no—
609D12—21no—
610D12—21no—
611D12—42no—
612D12—61no—
613D12—61no—
614D12—61no—
615D12—61no—
616D12—81no—
617D12—121no—
618D12—121no—
619D12—121no—
620D12—122no—
621D12—122no—
622D12—122no—
623D12—241no—
624D12—241no—
625D12—241no—
626D12—242no—
627D12D3×D412yes—
628C4×D3—21no—
629C4×D3—21no—
630C4×D3—42no—
631C4×D3—61no—
632C4×D3—61no—
633C4×D3—61no—
634C4×D3—61no—
635C4×D3—121no—
636C4×D3—121no—
637C4×D3—122no—
638C4×D3—122no—
639C4×D3—122no—
640C4×D3—241no—
641Dic6—21no—
642Dic6D3×D412yes—
643C3×C8—21no—
644C3×C8—21no—
645C3×C8—41no—
646C3×C8—61no—
647C3×C8—61no—
648C3⋊C8—21no—
649C3⋊C8—21no—
650C3⋊C8—32no—
651C3⋊C8—32no—
652C3⋊C8—62no—
653C2×C32D4211yescharacteristic
654C2×C32#57511yescharacteristic
655C2×C32#57611yescharacteristic
656C3⋊D3—41no—
657C3⋊D3—81no—
658C3×D3—42no—
659C3×D3—41no—
660C3×D3—81no—
661C3×D3—81no—
662C24—181no—
663#41—62no—
664#41—121no—
665#41—182no—
666#41—182no—
667#41—361no—
668#41—361no—
669C2×Q8—31no—
670C2×Q8C2×D3211yescharacteristic
671C2×D4—31no—
672C2×D4—31no—
673C2×D4—31no—
674C2×D4—61no—
675C2×D4—61no—
676C2×D4—91no—
677C2×D4—91no—
678C2×D4—181no—
679C2×D4—181no—
680C2×D4—181no—
681C2×D4—181no—
682C2×D4—181no—
683C2×D4—181no—
684C2×D4—182no—
685C2×D4—181no—
686C2×D4—361no—
687C22×C4—31no—
688C22×C4—61no—
689C22×C4—91no—
690C22×C4—181no—
691C22×C4—181no—
692C22×C4—181no—
693Q16—62no—
694SD16—62no—
695SD16—94no—
696SD16—121no—
697SD16—182no—
698D8—62no—
699D8—182no—
700D8—182no—
701D8—361no—
702M16—182no—
703C2×C8—31no—
704C2×C8—31no—
705C2×C8—91no—
706C2×C8—182no—
707C2×C8C2×D3211yescharacteristic
708C4⋊C4—61no—
709C4⋊C4—91no—
710C4⋊C4—91no—
711C4⋊C4—181no—
712C4⋊C4C2×D3211yescharacteristic
713C22⋊C4—61no—
714C22⋊C4—61no—
715C22⋊C4—61no—
716C22⋊C4—91no—
717C22⋊C4—91no—
718C22⋊C4—181no—
719C22⋊C4—181no—
720C22⋊C4—181no—
721C22⋊C4—181no—
722C42—31no—
723C42—61no—
724C22×C3—21no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—61no—
728C22×C3—62no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3—121no—
732C22×C3—121no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3C2×D3×D411yescharacteristic
738C22×C3C2×D3×D411yescharacteristic
739C2×D3—21no—
740C2×D3—21no—
741C2×D3—21no—
742C2×D3—22no—
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—61no—
752C2×D3—61no—
753C2×D3—61no—
754C2×D3—61no—
755C2×D3—61no—
756C2×D3—61no—
757C2×D3—121no—
758C2×D3—121no—
759C2×D3—121no—
760C2×D3—121no—
761C2×D3—121no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—241no—
767C2×D3—241no—
768C2×D3—241no—
769C2×D3—244no—
770C2×D3—244no—
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—41no—
774C3×C4—41no—
775C3×C4—41no—
776C3×C4—41no—
777C3×C4—61no—
778C3×C4—61no—
779C3×C4—62no—
780C3×C4—61no—
781C3×C4—81no—
782C3×C4—81no—
783C3×C4C2×D3×D411yescharacteristic
784C3×C4C2×D3×D411yescharacteristic
785C3×C4#100411yescharacteristic
786C3×C4#100911yescharacteristic
787Dic3—21no—
788Dic3—21no—
789Dic3—21no—
790Dic3—22no—
791Dic3—61no—
792Dic3—61no—
793Dic3—121no—
794Dic3—121no—
795Dic3—121no—
796Dic3—241no—
797C32#326811yescharacteristic, complemented, Sylow
798C23—31no—
799C23—61no—
800C23—61no—
801C23—61no—
802C23—91no—
803C23—181no—
804C23—362no—
805C23—362no—
806C23—721no—
807Q8—21no—
808Q8—21no—
809Q8—32no—
810Q8—61no—
811D4—32no—
812D4—61no—
813D4—61no—
814D4—61no—
815D4—61no—
816D4—61no—
817D4—122no—
818D4—181no—
819D4—181no—
820D4—241no—
821D4—361no—
822D4—362no—
823D4—362no—
824D4—362no—
825D4—362no—
826D4—721no—
827D4—721no—
828D4—721no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—31no—
832C2×C4—31no—
833C2×C4—31no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—91no—
838C2×C4—122no—
839C2×C4—181no—
840C2×C4—181no—
841C2×C4—181no—
842C2×C4—362no—
843C2×C4—362no—
844C2×C4—721no—
845C2×C4C22×D3211yescharacteristic
846C8—21no—
847C8—61no—
848C8—61no—
849C8—92no—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3—122no—
854C2×C3—121no—
855C2×C3—241no—
856C2×C3—241no—
857C2×C3#559011yescharacteristic
858C2×C3#560911yescharacteristic
859C2×C3#576811yescharacteristic
860C2×C3#576911yescharacteristic
861C2×C3#577411yescharacteristic
862C2×C3#577711yescharacteristic
863D3—41no—
864D3—42no—
865D3—81no—
866D3—81no—
867D3—121no—
868D3—121no—
869D3—241no—
870D3—241no—
871D3—241no—
872D3—481no—
873C22—61no—
874C22—61no—
875C22—61no—
876C22—62no—
877C22—121no—
878C22—121no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—121no—
885C22—181no—
886C22—181no—
887C22—181no—
888C22—361no—
889C22—361no—
890C22—361no—
891C22—724no—
892C22D32×D411yescharacteristic
893C4—41no—
894C4—41no—
895C4—61no—
896C4—61no—
897C4—61no—
898C4—62no—
899C4—181no—
900C4—361no—
901C4#6430711yescharacteristic
902C4D32×D411yescharacteristic
903C3—21no—
904C3#8012811yescharacteristic, complemented
905C3#8062811yescharacteristic, complemented
906C2—121no—
907C2—122no—
908C2—241no—
909C2—241no—
910C2—361no—
911C2—721no—
912C2#1059427511yescharacteristic
913C2#1059475511yescharacteristic
914C2#1059476311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3268
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. #10595428C2semidirect
2. C2×#63949C2semidirect
3. C2×#63798C2semidirect
4. #10594524C2semidirect
5. #10592511C2semidirect
6. C3×#4810C2semidirect
7. C3×#4798C2semidirect
8. #10591656C2semidirect
9. #10591619C2semidirect
10. #10590907C2semidirect
11. #10590823C2semidirect
12. #10590753C2semidirect
13. #10590598C2semidirect
14. #10590499C2semidirect
15. #10590454C2semidirect
20. C2×#3799C22semidirect
23. C2×#3755C22semidirect
27. C2×C3×#216C22semidirect
28. C2×C3×#215C22semidirect
31. C3×#895C22semidirect
32. C3×#887C22semidirect
37. #63911C22semidirect
50. C2×D3×C3⋊C8C22semidirect
52. C32×#103C22semidirect
53. #63648C22semidirect
54. #63634C22semidirect
55. C3×(C2×D3)⋊C8C22semidirect
56. C3×Dic3⋊C8C22semidirect
59. #63566C22semidirect
60. #63563C22semidirect
62. #63554C22semidirect
86. #4810D3semidirect
87. #4798D3semidirect
151. #3715D4semidirect
177. C2×#216C2×D3semidirect
182. C2×#215C2×D3semidirect
216. #895C2×D3semidirect
217. #887C2×D3semidirect
231. C3×#103C2×D3semidirect
232. C3×#103C2×D3semidirect
244. (C2×D3)⋊C8C2×D3semidirect
247. Dic3⋊C8C2×D3semidirect
525. #103D32semidirect
797. C32#3268semidirect
904. C3#80128semidirect
905. C3#80628semidirect

Maximal subgroups

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

subgroupindex
#105954282
C2×#639492
C2×#637982
#105945242
#105925112
C3×#48102
C3×#47982
#105916562
#105916192
#105909072
#105908232
#105907532
#105905982
#105904992
#105904542
#806283
#801283