Finite Group Databasebeta

← #11884002

Subgroups — #11884002

Order 1152.

1152 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63795C211yesmaximal, characteristic, complemented
2C2×D3×#204C211yesmaximal, characteristic, complemented
3#10594618C211yesmaximal, characteristic, complemented
4#10594525C211yesmaximal, characteristic, complemented
5#10592588C211yesmaximal, characteristic, complemented
6C3×#4886C211yesmaximal, characteristic, complemented
7C3×#4883C211yesmaximal, characteristic, complemented
8#10590887C211yesmaximal, characteristic, complemented
9#10590722C211yesmaximal, characteristic, complemented
10#10590613C211yesmaximal, characteristic, complemented
11#10590603C211yesmaximal, characteristic, complemented
12#10590596C211yesmaximal, characteristic, complemented
13#10590595C211yesmaximal, characteristic, complemented
14#10590553C211yesmaximal, characteristic, complemented
15#10590540C211yesmaximal, characteristic, complemented
16#80834—31nomaximal
17#80727—31nomaximal
18C2×#3802—21no—
19C2×D3×D12C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×#3795C2211yescharacteristic, complemented
22C2×D3×Dic6C2211yescharacteristic, complemented
23C2×#3744C2211yescharacteristic
24#64102C2211yescharacteristic
25#64096C2211yescharacteristic, complemented
26C2×C3×D24C2211yescharacteristic, complemented
27C2×C3×#204C2211yescharacteristic, complemented
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
29C2×C3×D3×C8C2211yescharacteristic, complemented
30C3×#897C2211yescharacteristic, complemented
31C3×#895C2211yescharacteristic
32C3×#895C2211yescharacteristic
33C3×#895C2211yescharacteristic, complemented
34#63922—21no—
35#63922—21no—
36#63915—21no—
37#63914C2211yescharacteristic
38#63912—21no—
39C4×#625C2211yescharacteristic
40#63899—21no—
41#63898—21no—
42#63885—21no—
43#63863C2211yescharacteristic, complemented
44C2×#3717C2211yescharacteristic
45C2×#3716C2211yescharacteristic, complemented
46C2×#3716C2211yescharacteristic, complemented
47C2×#3715C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic
49C2×#3713C2211yescharacteristic, complemented
50#63795—24no—
51D3×#204—24no—
52C32×#107C2211yescharacteristic, complemented
53#63642C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55#63636C2211yescharacteristic
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59C3×#809C2211yescharacteristic, complemented
60#63572C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×D3×SD16—31no—
64C2×#911—31no—
65C2×#908—31no—
66C22×#204—31no—
67#5633—31no—
68#5609—31no—
69#5609—31no—
70#5598—31no—
71C3×#468—31no—
72C3×#466—31no—
73#5176—31no—
74#5154—31no—
75#5127—31no—
76#5111—31no—
77#5046—31no—
78#5040—31no—
79#5037—31no—
80#5036—31no—
81#4889—31no—
82#4889—31no—
83#4889—61no—
84#4886D311yescharacteristic, complemented
85#4883D311yescharacteristic, complemented
86#4819—31no—
87#4806—31no—
88#4787—31no—
89#4781—31no—
90#4776—31no—
91#4773—31no—
92#4762—31no—
93#4762—31no—
94C22×D32—21no—
95C22×D32—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×#634C2311yescharacteristic
99C2×C3×D12—21no—
100C2×C3×D12—21no—
101C2×C3×D12—21no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#627—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#625—21no—
112C2×#625—21no—
113C2×#625—21no—
114C2×#625D411yescharacteristic
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117#3802—44no—
118D3×D12—22no—
119D3×D12—22no—
120D3×D12—41no—
121D3×D12—41no—
122#3795—22no—
123#3795—41no—
124D3×Dic6—22no—
125D3×Dic6—41no—
126C2×C32×C8C2311yescharacteristic
127C32×C4⋊C4C2311yescharacteristic
128C32×C4⋊C4C2311yescharacteristic
129#3752—21no—
130#3750—21no—
131C4×C3⋊Dic3—21no—
132C4×C3⋊Dic3C2311yescharacteristic
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134#3744D414yescomplemented
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×C4⋊Dic3—21no—
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×D24—22no—
143C3×#204—22no—
144C3×ΓL(1,𝔽25)—22no—
145C3×D3×C8—22no—
146#3724D411yescharacteristic
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3D411yescharacteristic
150(C2×D3)⋊Dic3D411yescharacteristic
151#3717—22no—
152#3716—22no—
153#3716—22no—
154#3715—41no—
155#3714—22no—
156#3713—41no—
157#3265—91noSylow
158C2×D3×Q8—31no—
159C2×#237—31no—
160C2×D3×D4—31no—
161C2×D3×D4—31no—
162C2×D3×D4—61no—
163C2×D3×D4—61no—
164C2×#235—31no—
165C22×D12—31no—
166C22×D12—31no—
167C22×Dic6—31no—
168C2×C3×SD16—31no—
169C2×C3×D8—31no—
170C2×C3×M16—31no—
171C22×C3×C8—31no—
172C3×C22⋊Q8—31no—
173C3×#121—31no—
174C3×#121—31no—
175C3×#121—31no—
176#947—31no—
177C2×#215—31no—
178C2×#215—31no—
179#940—31no—
180#940—31no—
181#939—61no—
182#937—61no—
183#937—61no—
184#936—31no—
185D4×Dic3—61no—
186C2×#214—31no—
187C2×#214—31no—
188C2×#214—31no—
189C2×#213—31no—
190C2×#213—31no—
191C2×#213—31no—
192C4×#67—31no—
193C4×#67—31no—
194D3×SD16—64no—
195#911—64no—
196#908—64no—
197C2×D24—31no—
198C2×D24C2×D311yescharacteristic, complemented
199C2×#204—31no—
200C2×#204—31no—
201C2×#204—31no—
202C2×#204—31no—
203C2×#204—31no—
204C2×#204—61no—
205C2×#204—64no—
206C2×#204C2×D311yescharacteristic, complemented
207C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
208C2×D3×C8C2×D311yescharacteristic, complemented
209#897C2×D311yescharacteristic, complemented
210#896—61no—
211#895C2×D311yescharacteristic
212#895C2×D311yescharacteristic
213#895C2×D311yescharacteristic, complemented
214#893—31no—
215#893—31no—
216#893—61no—
217#893—61no—
218#887—31no—
219#887—31no—
220#887—61no—
221#885—61no—
222#885—61no—
223#884—61no—
224#884—61no—
225#884—61no—
226#882—61no—
227#882—61no—
228#878—61no—
229C3×#107—21no—
230C3×#107C2×D311yescharacteristic, complemented
231C3×#107C2×D311yescharacteristic, complemented
232C3×#103—31no—
233C3×#102—31no—
234C3×#102—31no—
235C3×#102—31no—
236#830—31no—
237#830—31no—
238(C2×D3)⋊C8—31no—
239(C2×D3)⋊C8—31no—
240#815—31no—
241#815—31no—
242#815—61no—
243Dic3⋊C8—31no—
244Dic3⋊C8—31no—
245#810—31no—
246#810—31no—
247#810—61no—
248#810C2×D311yescharacteristic, complemented
249#809—31no—
250#809—31no—
251#809—61no—
252#809C2×D311yescharacteristic, complemented
253#809C2×D311yescharacteristic, complemented
254#809C2×D311yescharacteristic, complemented
255C22×C3⋊D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3C2×D411yescharacteristic
260C22×C3×D3C2×D411yescharacteristic
261C2×D32—42no—
262C2×D32—42no—
263C2×D32—42no—
264C2×D32—42no—
265C2×D32—81no—
266C2×D32—81no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4C2411yescharacteristic
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3C2×D411yescharacteristic
272C2×C3⋊Dic3C2×D411yescharacteristic
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)C2×D412yes—
275C4×C3⋊D3—42no—
276#634—21no—
277#634C2×D412yescomplemented
278C2×C3×Dic3—21no—
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—42no—
288C3×D12—42no—
289C3×D12—42no—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296#627—42no—
297#626—42no—
298#626—42no—
299#625—22no—
300#625—42no—
301#625—42no—
302#625—81no—
303D3×Dic3—42no—
304D3×Dic3—42no—
305C32×C8C2×D412yescomplemented
306C3⋊(C3⋊C8)—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8—21no—
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—91no—
311#548—91no—
312D42—91no—
313#496—91no—
314#468—31no—
315#466—31no—
316#463—91no—
317#460—91no—
318#450—91no—
319#449—91no—
320#448—91no—
321#447—91no—
322#440—91no—
323#435—91no—
324C23×D3—61no—
325C23×D3—61no—
326C23×D3—61no—
327C23×D3—61no—
328C2×C3×Q8—31no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C2×#67—31no—
338C2×#67—31no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C22×Dic3—61no—
348C22×Dic3—61no—
349D3×Q8—62no—
350D3×Q8—121no—
351#237—62no—
352#237—121no—
353D3×D4—62no—
354D3×D4—62no—
355D3×D4—121no—
356D3×D4—121no—
357D3×D4—124no—
358D3×D4—124no—
359#235—62no—
360#235—121no—
361C2×D12—21no—
362C2×D12—21no—
363C2×D12—21no—
364C2×D12—31no—
365C2×D12—31no—
366C2×D12—61no—
367C2×D12—62no—
368C2×D12—62no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12—121no—
372C2×D12—121no—
373C2×D12C22×D311yescharacteristic
374C2×D12C22×D311yescharacteristic
375C2×D12C22×D311yescharacteristic
376C2×C4×D3—61no—
377C2×C4×D3—61no—
378C2×C4×D3—61no—
379C2×C4×D3—61no—
380C2×C4×D3—121no—
381C2×C4×D3C22×D311yescharacteristic
382C2×C4×D3C22×D311yescharacteristic
383C2×Dic6—31no—
384C2×Dic6—31no—
385C2×Dic6—61no—
386C2×Dic6—62no—
387C2×Dic6—61no—
388C2×Dic6—61no—
389C2×Dic6—121no—
390C2×Dic6C22×D311yescharacteristic
391C3×SD16—62no—
392C3×D8—62no—
393C3×M16—62no—
394C2×C3×C8—21no—
395C2×C3×C8—31no—
396C2×C3×C8—31no—
397C2×C3×C8—62no—
398C2×C3×C8C22×D311yescharacteristic
399C2×C3×C8C22×D311yescharacteristic
400C3×C4⋊C4—21no—
401C3×C4⋊C4—21no—
402C3×C4⋊C4—61no—
403C3×C4⋊C4C22×D311yescharacteristic
404C3×C4⋊C4C22×D311yescharacteristic
405C3×C4⋊C4C22×D311yescharacteristic
406C3×C4⋊C4C22×D311yescharacteristic
407C3×C22⋊C4—61no—
408C3×C22⋊C4—61no—
409C3×C22⋊C4—61no—
410C3×C22⋊C4—61no—
411#217—31no—
412#217—31no—
413#217—61no—
414#217—61no—
415#215—62no—
416#215—121no—
417#214—62no—
418#214—62no—
419#214—121no—
420#213—62no—
421#213—121no—
422#213—121no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—21no—
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—21no—
427(C2×D3)⋊C4—31no—
428(C2×D3)⋊C4—31no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—121no—
434C4⋊Dic3—21no—
435Dic3⋊C4—31no—
436Dic3⋊C4—31no—
437Dic3⋊C4—61no—
438Dic3⋊C4—61no—
439Dic3⋊C4—121no—
440C4×Dic3—31no—
441C4×Dic3—31no—
442C4×Dic3—61no—
443C4×Dic3—61no—
444C4×Dic3—61no—
445C4×Dic3—121no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—31no—
448C2×C3⋊C8—61no—
449C2×C3⋊C8C22×D311yescharacteristic
450C2×C3⋊C8C22×D311yescharacteristic
451D24—22no—
452D24—62no—
453#204—22no—
454#204—34no—
455#204—34no—
456#204—64no—
457#204—62no—
458#204—62no—
459#204—62no—
460ΓL(1,𝔽25)—22no—
461D3×C8—22no—
462C22×C32C22×D411yescharacteristic
463C2×C3⋊D3—22no—
464C2×C3⋊D3—41no—
465C2×C3⋊D3—41no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3AGL(1,ℤ/8)12yescomplemented
481D32—84no—
482D32—84no—
483C32×C4—41no—
484C32×C4—41no—
485C32×C4C22×D411yescharacteristic
486C32×C4H(5,𝔽2)11yescharacteristic
487C3⋊Dic3—22no—
488C3⋊Dic3—21no—
489C3⋊Dic3—21no—
490C3×Dic3—21no—
491C3×Dic3—21no—
492C3×Dic3—41no—
493C2×#41—91no—
494C22×Q8—91no—
495C22×D4—91no—
496C22×D4—91no—
497C22×D4—181no—
498AGL(1,ℤ/8)—184no—
499C2×SD16—31no—
500C2×SD16—91no—
501C2×SD16—91no—
502C2×SD16—91no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—184no—
506C2×D8—31no—
507C2×D8—91no—
508C2×D8—91no—
509C2×M16—31no—
510C22×C8—31no—
511#127—91no—
512#124—91no—
513#124—181no—
514C22⋊Q8—31no—
515C22⋊Q8—181no—
516#121—31no—
517#121—31no—
518#121—31no—
519#121—181no—
520#121—181no—
521#120—181no—
522#120—181no—
523C4×Q8—91no—
524C4×D4—91no—
525C4×D4—91no—
526C4×D4—181no—
527#107D3211yescharacteristic, complemented
528C4⋊C8—91no—
529#103—31no—
530#103—91no—
531#102—31no—
532#102—31no—
533#102—31no—
534#102—91no—
535C22⋊C8—91no—
536C22⋊C8—91no—
537#97—91no—
538C23×C3—31no—
539C23×C3—31no—
540C23×C3—61no—
541C23×C3—61no—
542C23×C3—61no—
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—121no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3—122no—
554C22×D3—122no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—241no—
558C22×D3—241no—
559C22×D3—241no—
560C22×D3—241no—
561C22×D3D3×D411yescharacteristic
562C22×D3D3×D411yescharacteristic
563C3×Q8—61no—
564C3×Q8—61no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—61no—
568C3×D4—61no—
569C3×D4—61no—
570C3×D4—61no—
571C3×D4—122no—
572C3×D4—122no—
573C3×D4—122no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—31no—
580C2×C3×C4—31no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4C23×D311yescharacteristic
589C2×C3×C4C23×D311yescharacteristic
590#67—62no—
591#67—62no—
592#67—122no—
593#67—122no—
594#67—122no—
595#67—122no—
596#67—122no—
597#67—122no—
598#67—241no—
599#67—241no—
600C2×Dic3—21no—
601C2×Dic3—31no—
602C2×Dic3—31no—
603C2×Dic3—31no—
604C2×Dic3—31no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—121no—
610C2×Dic3—122no—
611C2×Dic3—122no—
612C2×Dic3D3×D411yescharacteristic
613C2×Dic3D3×D411yescharacteristic
614D12—21no—
615D12—21no—
616D12—21no—
617D12—21no—
618D12—21no—
619D12—21no—
620D12—32no—
621D12—32no—
622D12—42no—
623D12—42no—
624D12—42no—
625D12—62no—
626D12—61no—
627D12—61no—
628D12—121no—
629D12—122no—
630D12—122no—
631C4×D3—21no—
632C4×D3—21no—
633C4×D3—21no—
634C4×D3—21no—
635C4×D3—122no—
636C4×D3—122no—
637C4×D3—122no—
638C4×D3—122no—
639C4×D3—242no—
640Dic6—21no—
641Dic6—21no—
642Dic6—32no—
643Dic6—32no—
644Dic6—62no—
645Dic6—61no—
646Dic6—61no—
647Dic6—121no—
648Dic6—122no—
649Dic6—122no—
650C3×C8—22no—
651C3×C8—61no—
652C3×C8—61no—
653C3×C8D3×D412yescomplemented
654C3×C8D3×D412yescomplemented
655C3⋊C8—21no—
656C3⋊C8—21no—
657C3⋊C8—61no—
658C3⋊C8—61no—
659C3⋊C8—121no—
660C2×C32D4211yescharacteristic
661C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
662C2×C32#57711yescharacteristic
663C3⋊D3—42no—
664C3×D3—22no—
665C3×D3—41no—
666C3×D3—81no—
667C3×D3—81no—
668C3×D3—81no—
669C24—181no—
670C24—181no—
671#41—182no—
672#41—361no—
673C2×Q8—31no—
674C2×Q8—91no—
675C2×Q8—181no—
676C2×Q8—182no—
677C2×Q8—361no—
678C2×D4—31no—
679C2×D4—31no—
680C2×D4—31no—
681C2×D4—61no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4—91no—
685C2×D4—91no—
686C2×D4—181no—
687C2×D4—181no—
688C2×D4—182no—
689C2×D4—182no—
690C2×D4—181no—
691C2×D4—181no—
692C2×D4—181no—
693C2×D4—361no—
694C2×D4—361no—
695C2×D4—364no—
696C22×C4—31no—
697C22×C4—31no—
698C22×C4—181no—
699C22×C4—181no—
700C22×C4—181no—
701SD16—62no—
702SD16—94no—
703SD16—182no—
704SD16—182no—
705SD16—182no—
706SD16—361no—
707D8—62no—
708D8—182no—
709D8—361no—
710M16—62no—
711C2×C8—31no—
712C2×C8—31no—
713C2×C8—62no—
714C2×C8—91no—
715C2×C8C2×D3211yescharacteristic
716C4⋊C4—61no—
717C4⋊C4—91no—
718C4⋊C4—181no—
719C4⋊C4C2×D3211yescharacteristic
720C4⋊C4C2×D3211yescharacteristic
721C22⋊C4—61no—
722C22⋊C4—61no—
723C22⋊C4—61no—
724C22⋊C4—61no—
725C22⋊C4—91no—
726C22⋊C4—91no—
727C22⋊C4—181no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C42—91no—
731C42—181no—
732C22×C3—21no—
733C22×C3—32no—
734C22×C3—61no—
735C22×C3—61no—
736C22×C3—61no—
737C22×C3—61no—
738C22×C3—61no—
739C22×C3—121no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3C2×D3×D411yescharacteristic
749C22×C3C2×D3×D411yescharacteristic
750C2×D3—21no—
751C2×D3—21no—
752C2×D3—21no—
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—62no—
765C2×D3—62no—
766C2×D3—122no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—241no—
772C2×D3—241no—
773C2×D3—244no—
774C2×D3—244no—
775C2×D3—244no—
776C2×D3—244no—
777C2×D3#91112yescomplemented
778C3×C4—21no—
779C3×C4—21no—
780C3×C4—41no—
781C3×C4—41no—
782C3×C4—41no—
783C3×C4—41no—
784C3×C4—61no—
785C3×C4—61no—
786C3×C4—81no—
787C3×C4—81no—
788C3×C4—121no—
789C3×C4C2×D3×D411yescharacteristic
790C3×C4C2×D3×D411yescharacteristic
791C3×C4#100911yescharacteristic
792C3×C4#100911yescharacteristic
793Dic3—21no—
794Dic3—21no—
795Dic3—41no—
796Dic3—61no—
797Dic3—61no—
798Dic3—61no—
799Dic3—61no—
800Dic3—62no—
801Dic3—62no—
802Dic3—122no—
803Dic3—121no—
804Dic3—121no—
805C32#326511yescharacteristic, complemented, Sylow
806C23—31no—
807C23—31no—
808C23—61no—
809C23—61no—
810C23—61no—
811C23—181no—
812C23—362no—
813C23—362no—
814C23—362no—
815C23—362no—
816C23—721no—
817C23—721no—
818Q8—61no—
819Q8—61no—
820Q8—92no—
821Q8—181no—
822Q8—362no—
823D4—61no—
824D4—61no—
825D4—61no—
826D4—61no—
827D4—61no—
828D4—61no—
829D4—92no—
830D4—122no—
831D4—122no—
832D4—122no—
833D4—182no—
834D4—181no—
835D4—362no—
836D4—362no—
837D4—362no—
838D4—362no—
839D4—721no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—31no—
843C2×C4—31no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—91no—
850C2×C4—91no—
851C2×C4—181no—
852C2×C4—362no—
853C2×C4—362no—
854C2×C4—362no—
855C2×C4C22×D3211yescharacteristic
856C8—61no—
857C8—61no—
858C8—181no—
859C8#380212yescomplemented
860C2×C3—21no—
861C2×C3—21no—
862C2×C3—21no—
863C2×C3—62no—
864C2×C3—121no—
865C2×C3—241no—
866C2×C3—241no—
867C2×C3—241no—
868C2×C3#560911yescharacteristic
869C2×C3#560911yescharacteristic
870C2×C3C2×#91111yescharacteristic
871C2×C3#577011yescharacteristic
872C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
873C2×C3#577811yescharacteristic
874D3—22no—
875D3—41no—
876D3—81no—
877D3—81no—
878D3—81no—
879D3—122no—
880D3—122no—
881D3—242no—
882C22—32no—
883C22—61no—
884C22—61no—
885C22—61no—
886C22—61no—
887C22—61no—
888C22—121no—
889C22—121no—
890C22—121no—
891C22—121no—
892C22—121no—
893C22—121no—
894C22—121no—
895C22—121no—
896C22—121no—
897C22—182no—
898C22—361no—
899C22—361no—
900C22—724no—
901C22—724no—
902C22D32×D411yescharacteristic
903C4—41no—
904C4—41no—
905C4—61no—
906C4—61no—
907C4—121no—
908C4—182no—
909C4—181no—
910C4—181no—
911C4C2×#380211yescharacteristic
912C4#6432011yescharacteristic
913C3—21no—
914C3#8072711yescharacteristic, complemented
915C3#8083411yescharacteristic, complemented
916C2—62no—
917C2—121no—
918C2—241no—
919C2—241no—
920C2—241no—
921C2—362no—
922C2#1059461811yescharacteristic
923C2D3×#91111yescharacteristic
924C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
hypercenter#107D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
1. C2×#63795C2semidirect
2. C2×D3×#204C2semidirect
3. #10594618C2semidirect
4. #10594525C2semidirect
5. #10592588C2semidirect
6. C3×#4886C2semidirect
7. C3×#4883C2semidirect
8. #10590887C2semidirect
9. #10590722C2semidirect
10. #10590613C2semidirect
11. #10590603C2semidirect
12. #10590596C2semidirect
13. #10590595C2semidirect
14. #10590553C2semidirect
15. #10590540C2semidirect
21. C2×#3795C22semidirect
22. C2×D3×Dic6C22semidirect
25. #64096C22semidirect
26. C2×C3×D24C22semidirect
27. C2×C3×#204C22semidirect
28. C2×C3×ΓL(1,𝔽25)C22semidirect
29. C2×C3×D3×C8C22semidirect
30. C3×#897C22semidirect
33. C3×#895C22semidirect
43. #63863C22semidirect
45. C2×#3716C22semidirect
46. C2×#3716C22semidirect
47. C2×#3715C22semidirect
49. C2×#3713C22semidirect
52. C32×#107C22semidirect
53. #63642C22semidirect
54. #63637C22semidirect
56. C3×#810C22semidirect
57. C3×#809C22semidirect
58. C3×#809C22semidirect
59. C3×#809C22semidirect
60. #63572C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
84. #4886D3semidirect
85. #4883D3semidirect
134. #3744D4semidirect
198. C2×D24C2×D3semidirect
206. C2×#204C2×D3semidirect
207. C2×ΓL(1,𝔽25)C2×D3semidirect
208. C2×D3×C8C2×D3semidirect
209. #897C2×D3semidirect
213. #895C2×D3semidirect
230. C3×#107C2×D3semidirect
231. C3×#107C2×D3semidirect
248. #810C2×D3semidirect
252. #809C2×D3semidirect
253. #809C2×D3semidirect
254. #809C2×D3semidirect
277. #634C2×D4semidirect
305. C32×C8C2×D4semidirect
480. C2×C3×D3AGL(1,ℤ/8)semidirect
527. #107D32semidirect
653. C3×C8D3×D4semidirect
654. C3×C8D3×D4semidirect
777. C2×D3#911semidirect
805. C32#3265semidirect
859. C8#3802semidirect
914. C3#80727semidirect
915. C3#80834semidirect

Maximal subgroups

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

subgroupindex
C2×#637952
C2×D3×#2042
#105946182
#105945252
#105925882
C3×#48862
C3×#48832
#105908872
#105907222
#105906132
#105906032
#105905962
#105905952
#105905532
#105905402
#808343
#807273