Finite Group Databasebeta

← #11885763

Subgroups — #11885763

Order 1152.

1339 conjugacy classes of subgroups.

The subgroup lattice has 1015 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595297C211yesmaximal, characteristic, complemented
2C2×#63926C211yesmaximal, characteristic, complemented
3C2×D3×D24C211yesmaximal, characteristic, complemented
4#10594621C211yesmaximal, characteristic, complemented
5#10592472C211yesmaximal, characteristic, complemented
6C3×#4786C211yesmaximal, characteristic, complemented
7C3×#4775C211yesmaximal, characteristic, complemented
8#10591515C211yesmaximal, characteristic, complemented
9#10591482C211yesmaximal, characteristic, complemented
10#10590945C211yesmaximal, characteristic, complemented
11#10590765C211yesmaximal, characteristic, complemented
12#10590720C211yesmaximal, characteristic, complemented
13#10590595C211yesmaximal, characteristic, complemented
14#10590509C211yesmaximal, characteristic, complemented
15#10590456C211yesmaximal, characteristic, complemented
16#80729—31nomaximal
17#80350—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic, complemented
19C2×#3811—21no—
20C2×#3802C2211yescharacteristic, complemented
21C2×D3×D12—21no—
22C2×D3×D12C2211yescharacteristic, complemented
23C2×D3×D12C2211yescharacteristic, complemented
24C2×#3753C2211yescharacteristic, complemented
25C2×#3745C2211yescharacteristic, complemented
26#64104C2211yescharacteristic, complemented
27C3×#940C2211yescharacteristic, complemented
28C3×#938C2211yescharacteristic, complemented
29C2×C3×#213C2211yescharacteristic, complemented
30C2×C3×#213C2211yescharacteristic, complemented
31C2×C3×D24C2211yescharacteristic, complemented
32C2×C3×D3×C8C2211yescharacteristic, complemented
33C3×#895C2211yescharacteristic, complemented
34C3×#893C2211yescharacteristic, complemented
35#63983—21no—
36#63981—21no—
37#63958—21no—
38#63926—24no—
39#63923—21no—
40#63922—21no—
41#63916C2211yescharacteristic, complemented
42#63911C2211yescharacteristic, complemented
43#63906—21no—
44C4×#626C2211yescharacteristic
45#63894C2211yescharacteristic, complemented
46C2×#3714C2211yescharacteristic
47C2×#3714C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic, complemented
50C2×#3710C2211yescharacteristic, complemented
51D3×D24—24no—
52C32×#102C2211yescharacteristic, complemented
53#63647C2211yescharacteristic, complemented
54#63636C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58C3×#807C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62Dic3×C3⋊C8C2211yescharacteristic, complemented
63C2×D3×D8—31no—
64C2×D3×D8—31no—
65C2×D3×D8—31no—
66C22×D24—31no—
67#5717—31no—
68#5609—31no—
69#5609—31no—
70D4×D12—31no—
71C3×#466—31no—
72C3×#459—31no—
73#5156—31no—
74#5156—31no—
75#5151—31no—
76C8×#67—31no—
77#5073—31no—
78#5036—31no—
79#5036—31no—
80C4×#213—31no—
81#4883—31no—
82#4872—31no—
83#4843—31no—
84#4834—31no—
85#4786—31no—
86#4786D311yescharacteristic, complemented
87#4775—31no—
88#4775D311yescharacteristic, complemented
89#4773—31no—
90#4773—31no—
91#4773—31no—
92#4773—31no—
93#4773—61no—
94C23×C3⋊D3—21no—
95C22×D32—21no—
96C22×D32—21no—
97C22×D32—21no—
98C2×C32×D4C2311yescharacteristic
99C2×#638—21no—
100D4×C3⋊D3—22no—
101D4×C3⋊D3—41no—
102C2×C4⋊(C3⋊D3)—21no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3C2311yescharacteristic
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C2×C3×D12—21no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2311yescharacteristic
115#3811—44no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#626—21no—
119C2×#626—21no—
120C2×#626—21no—
121C2×#626D411yescharacteristic
122C2×#625—21no—
123C2×#624—21no—
124#3802—22no—
125#3802—41no—
126D3×D12—22no—
127D3×D12—22no—
128D3×D12—41no—
129D3×D12—41no—
130D3×D12—44no—
131C2×C32×C8C2311yescharacteristic
132C32×C4⋊C4C2311yescharacteristic
133#3753—41no—
134#3752—21no—
135C2×C3⋊(C3⋊C8)C2311yescharacteristic
136#3745—22no—
137C3×#217—21no—
138C3×#213—22no—
139C3×#213—22no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4—21no—
142C3×C4⋊Dic3C2311yescharacteristic
143C3×C4×Dic3C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C3×D24—22no—
147C3×D3×C8—22no—
148Dic3⋊Dic3D411yescharacteristic
149#3722—21no—
150#3722D411yescharacteristic
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3D411yescharacteristic
153#3714—22no—
154#3714—22no—
155#3714D414yescomplemented
156#3713—41no—
157#3710—22no—
158D4×D8—91noSylow
159C2×D3×D4—31no—
160C2×D3×D4—31no—
161C2×D3×D4—31no—
162C2×D3×D4—31no—
163C2×D3×D4—31no—
164C2×D3×D4—31no—
165C2×D3×D4—61no—
166C2×D3×D4—61no—
167C2×D3×D4—61no—
168C2×D3×D4—61no—
169C22×D12—31no—
170C22×D12—31no—
171C22×D12—61no—
172C2×C3×D8—31no—
173C2×C3×D8—31no—
174C2×C3×D8—31no—
175C22×C3×C8—31no—
176C3×#127—31no—
177C3×#121—31no—
178C3×#121—31no—
179C3×C4×D4—31no—
180#940—31no—
181#940C2×D311yescharacteristic, complemented
182#938—31no—
183#938—61no—
184#938C2×D311yescharacteristic, complemented
185#937—61no—
186#937—61no—
187#937—61no—
188#937—61no—
189C2×#213—31no—
190C2×#213—31no—
191C2×#213—31no—
192C2×#213—31no—
193C2×#213—31no—
194C2×#213—31no—
195C2×#213—31no—
196C2×#213—61no—
197C2×#213C2×D311yescharacteristic, complemented
198C2×#213C2×D311yescharacteristic, complemented
199#930—61no—
200C4×#67—31no—
201D3×D8—64no—
202D3×D8—64no—
203D3×D8—64no—
204C2×D24—31no—
205C2×D24—31no—
206C2×D24—31no—
207C2×D24—31no—
208C2×D24—31no—
209C2×D24—61no—
210C2×D24—64no—
211C2×D24C2×D311yescharacteristic, complemented
212C2×D3×C8—31no—
213C2×D3×C8—31no—
214C2×D3×C8C2×D311yescharacteristic, complemented
215#895—31no—
216#895—31no—
217#895—31no—
218#895—61no—
219#895C2×D311yescharacteristic, complemented
220#893—31no—
221#893C2×D311yescharacteristic, complemented
222#884—61no—
223#884—61no—
224#882—61no—
225#882—61no—
226#882—61no—
227#882—61no—
228#874—31no—
229C4×D12—31no—
230C4×D12—31no—
231C3×#107—31no—
232C3×C4⋊C8—31no—
233C3×#102—21no—
234C3×#102—31no—
235C3×#102—31no—
236C3×#102C2×D311yescharacteristic, complemented
237C3×#102C2×D311yescharacteristic, complemented
238#832—31no—
239#830—31no—
240#821—31no—
241#821C2×D311yescharacteristic, complemented
242(C2×D3)⋊C8—31no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8—31no—
245(C2×D3)⋊C8—61no—
246Dic3⋊C8C2×D311yescharacteristic, complemented
247C8×Dic3—31no—
248#809—31no—
249#809—31no—
250#809—31no—
251#809—31no—
252#809—61no—
253#809C2×D311yescharacteristic, complemented
254#807C2×D311yescharacteristic, complemented
255C4×C3⋊C8—31no—
256C23×C32—21no—
257C22×C3⋊D3—21no—
258C22×C3⋊D3—21no—
259C22×C3⋊D3—42no—
260C22×C3⋊D3—42no—
261C22×C3⋊D3—81no—
262C22×C3⋊D3C2×D411yescharacteristic
263C22×C3×D3—21no—
264C22×C3×D3—21no—
265C22×C3×D3—21no—
266C22×C3×D3C2×D411yescharacteristic
267C2×D32—42no—
268C2×D32—42no—
269C2×D32—42no—
270C2×D32—42no—
271C2×D32—42no—
272C2×D32—42no—
273C2×D32—81no—
274C2×D32—81no—
275C2×D32—81no—
276C32×D4—21no—
277C32×D4—21no—
278C2×C32×C4—21no—
279C2×C32×C4C2411yescharacteristic
280#638—42no—
281C2×C3⋊Dic3C2×D411yescharacteristic
282C4⋊(C3⋊D3)—21no—
283C4⋊(C3⋊D3)—21no—
284C4⋊(C3⋊D3)—21no—
285C4⋊(C3⋊D3)—42no—
286C4⋊(C3⋊D3)C2×D412yescomplemented
287C4×C3⋊D3—21no—
288C4×C3⋊D3—21no—
289C3×#67—42no—
290C3×#67—42no—
291C3×#67—81no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3C2×D411yescharacteristic
294C2×C3×Dic3C2×D411yescharacteristic
295C2×C3×Dic3C2×D411yescharacteristic
296C3×D12—21no—
297C3×D12—21no—
298C3×D12—21no—
299C3×D12—21no—
300C3×D12—21no—
301C3×D12—42no—
302C3×D12C2×D412yescomplemented
303C3×C4×D3—21no—
304C3×C4×D3—21no—
305C3×C4×D3—42no—
306#626—42no—
307#626—42no—
308#626—42no—
309#626—42no—
310#626—81no—
311#626D814yescomplemented
312#625—42no—
313#624—42no—
314C32×C8—21no—
315C3⋊(C3⋊C8)—21no—
316C3×C3⋊C8—21no—
317C3×C3⋊C8C2×D412yescomplemented
318C22×D8—91no—
319C22×D8—91no—
320D42—91no—
321D42—91no—
322#493—91no—
323#466—31no—
324#466—91no—
325#459—31no—
326#459—91no—
327#447—91no—
328#447—91no—
329#447—91no—
330#447—91no—
331C4×D8—91no—
332C8×D4—91no—
333C23×D3—61no—
334C23×D3—61no—
335C23×D3—61no—
336C23×D3—61no—
337C23×D3—61no—
338C23×D3—61no—
339C23×D3—61no—
340C23×D3—61no—
341C23×D3—121no—
342C2×C3×D4—21no—
343C2×C3×D4—31no—
344C2×C3×D4—31no—
345C2×C3×D4—31no—
346C2×C3×D4—61no—
347C2×C3×D4—61no—
348C2×C3×D4—61no—
349C2×C3×D4—61no—
350C2×C3×D4C22×D311yescharacteristic
351C2×C3×D4C22×D311yescharacteristic
352C22×C3×C4—31no—
353C22×C3×C4—61no—
354C2×#67—21no—
355C2×#67—21no—
356C2×#67—21no—
357C2×#67—31no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67—61no—
361C2×#67—61no—
362C2×#67—61no—
363C2×#67—61no—
364C2×#67—61no—
365C2×#67—61no—
366C2×#67—61no—
367C2×#67—121no—
368D3×D4—62no—
369D3×D4—62no—
370D3×D4—62no—
371D3×D4—62no—
372D3×D4—62no—
373D3×D4—62no—
374D3×D4—122no—
375D3×D4—121no—
376D3×D4—121no—
377D3×D4—124no—
378D3×D4—121no—
379D3×D4—121no—
380D3×D4—121no—
381D3×D4—121no—
382D3×D4—124no—
383D3×D4—124no—
384D3×D4—122no—
385C2×D12—21no—
386C2×D12—31no—
387C2×D12—31no—
388C2×D12—31no—
389C2×D12—31no—
390C2×D12—31no—
391C2×D12—61no—
392C2×D12—61no—
393C2×D12—62no—
394C2×D12—62no—
395C2×D12—61no—
396C2×D12—61no—
397C2×D12—61no—
398C2×D12—61no—
399C2×D12—61no—
400C2×D12—61no—
401C2×D12—61no—
402C2×D12—121no—
403C2×D12—121no—
404C2×D12—121no—
405C2×D12—124no—
406C2×D12C22×D311yescharacteristic
407C2×D12C22×D311yescharacteristic
408C2×D12C22×D311yescharacteristic
409C2×C4×D3—21no—
410C2×C4×D3—31no—
411C2×C4×D3—31no—
412C2×C4×D3—61no—
413C2×C4×D3—61no—
414C2×C4×D3—61no—
415C2×C4×D3C22×D311yescharacteristic
416C3×D8—62no—
417C3×D8—62no—
418C3×D8—62no—
419C2×C3×C8—21no—
420C2×C3×C8—31no—
421C2×C3×C8—31no—
422C2×C3×C8—62no—
423C2×C3×C8C22×D311yescharacteristic
424C2×C3×C8C22×D311yescharacteristic
425C3×C4⋊C4—21no—
426C3×C4⋊C4—31no—
427C3×C4⋊C4C22×D311yescharacteristic
428C3×C4⋊C4C22×D311yescharacteristic
429C3×C22⋊C4—61no—
430C3×C22⋊C4—61no—
431C3×C22⋊C4—61no—
432C3×C42—31no—
433#217—21no—
434#217—31no—
435#217—61no—
436#213—22no—
437#213—22no—
438#213—34no—
439#213—62no—
440#213—62no—
441#213—121no—
442#213—121no—
443#213—121no—
444#213—121no—
445#213—122no—
446(C2×D3)⋊C4—21no—
447(C2×D3)⋊C4—21no—
448(C2×D3)⋊C4—31no—
449(C2×D3)⋊C4—31no—
450(C2×D3)⋊C4—31no—
451(C2×D3)⋊C4—61no—
452(C2×D3)⋊C4—61no—
453(C2×D3)⋊C4—61no—
454(C2×D3)⋊C4—61no—
455(C2×D3)⋊C4—61no—
456(C2×D3)⋊C4—121no—
457C4⋊Dic3—31no—
458C4⋊Dic3C22×D311yescharacteristic
459Dic3⋊C4—31no—
460C4×Dic3C22×D311yescharacteristic
461C2×C3⋊C8—31no—
462C2×C3⋊C8—31no—
463C2×C3⋊C8—61no—
464C2×C3⋊C8C22×D311yescharacteristic
465C2×C3⋊C8C22×D311yescharacteristic
466D24—22no—
467D24—34no—
468D24—62no—
469D24—62no—
470D24—62no—
471D24—62no—
472D24—122no—
473D3×C8—22no—
474D3×C8—62no—
475D3×C8—62no—
476C22×C32—41no—
477C22×C32—41no—
478C22×C32—41no—
479C22×C32C22×D411yescharacteristic
480C2×C3⋊D3—21no—
481C2×C3⋊D3—21no—
482C2×C3⋊D3—22no—
483C2×C3⋊D3—41no—
484C2×C3⋊D3—41no—
485C2×C3⋊D3—41no—
486C2×C3⋊D3—41no—
487C2×C3⋊D3—41no—
488C2×C3⋊D3—84no—
489C2×C3⋊D3C2×D812yescomplemented
490C2×C3×D3—21no—
491C2×C3×D3—21no—
492C2×C3×D3—22no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496C2×C3×D3—41no—
497C2×C3×D3—41no—
498C2×C3×D3—41no—
499C2×C3×D3—41no—
500C2×C3×D3—41no—
501C2×C3×D3C2×D812yescomplemented
502D32—84no—
503D32—84no—
504D32—84no—
505C32×C4—41no—
506C32×C4C22×D411yescharacteristic
507C32×C4H(5,𝔽2)11yescharacteristic
508C3⋊Dic3—21no—
509C3×Dic3—21no—
510C3×Dic3—21no—
511C3×Dic3—41no—
512C3×Dic3C2×D812yescomplemented
513C22×D4—91no—
514C22×D4—91no—
515C22×D4—91no—
516C22×D4—91no—
517C22×D4—181no—
518C22×D4—181no—
519C2×D8—31no—
520C2×D8—31no—
521C2×D8—31no—
522C2×D8—91no—
523C2×D8—91no—
524C2×D8—91no—
525C2×D8—91no—
526C2×D8—91no—
527C2×D8—91no—
528C2×D8—184no—
529C2×D8—184no—
530C22×C8—31no—
531C22×C8—91no—
532#127—31no—
533#127—91no—
534#121—31no—
535#121—31no—
536#121—91no—
537#121—91no—
538#121—181no—
539#121—181no—
540#120—181no—
541#120—181no—
542#120—181no—
543#120—181no—
544C4×D4—31no—
545C4×D4—91no—
546C4×D4—91no—
547#107—31no—
548C4⋊C8—31no—
549#102—31no—
550#102—31no—
551#102—91no—
552#102—91no—
553#102—91no—
554#102D3211yescharacteristic, complemented
555C22⋊C8—91no—
556C22⋊C8—91no—
557C4×C8—91no—
558C23×C3—21no—
559C23×C3—21no—
560C23×C3—31no—
561C23×C3—41no—
562C23×C3—61no—
563C23×C3—61no—
564C23×C3—61no—
565C22×D3—21no—
566C22×D3—21no—
567C22×D3—21no—
568C22×D3—31no—
569C22×D3—31no—
570C22×D3—61no—
571C22×D3—61no—
572C22×D3—61no—
573C22×D3—61no—
574C22×D3—61no—
575C22×D3—121no—
576C22×D3—121no—
577C22×D3—122no—
578C22×D3—122no—
579C22×D3—122no—
580C22×D3—122no—
581C22×D3—122no—
582C22×D3—122no—
583C22×D3—122no—
584C22×D3—122no—
585C22×D3—122no—
586C22×D3—122no—
587C22×D3—122no—
588C22×D3—122no—
589C22×D3—122no—
590C22×D3—122no—
591C22×D3—124no—
592C22×D3—122no—
593C22×D3—122no—
594C22×D3—242no—
595C22×D3—241no—
596C22×D3—241no—
597C22×D3—241no—
598C22×D3—241no—
599C22×D3—241no—
600C22×D3—241no—
601C22×D3—241no—
602C22×D3—241no—
603C22×D3—242no—
604C22×D3D3×D411yescharacteristic
605C3×D4—22no—
606C3×D4—21no—
607C3×D4—21no—
608C3×D4—21no—
609C3×D4—21no—
610C3×D4—32no—
611C3×D4—41no—
612C3×D4—61no—
613C3×D4—61no—
614C3×D4—61no—
615C3×D4—61no—
616C3×D4—61no—
617C3×D4—122no—
618C3×D4—122no—
619C3×D4—122no—
620C3×D4—241no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—31no—
625C2×C3×C4—31no—
626C2×C3×C4—31no—
627C2×C3×C4—41no—
628C2×C3×C4—61no—
629C2×C3×C4—61no—
630C2×C3×C4—61no—
631C2×C3×C4—122no—
632C2×C3×C4C23×D311yescharacteristic
633C2×C3×C4C23×D311yescharacteristic
634#67—34no—
635#67—42no—
636#67—42no—
637#67—81no—
638#67—122no—
639#67—122no—
640#67—122no—
641#67—122no—
642#67—122no—
643#67—122no—
644#67—122no—
645#67—124no—
646#67—122no—
647#67—241no—
648C2×Dic3—21no—
649C2×Dic3—31no—
650C2×Dic3—31no—
651C2×Dic3—61no—
652C2×Dic3D3×D411yescharacteristic
653C2×Dic3D3×D411yescharacteristic
654C2×Dic3D3×D411yescharacteristic
655D12—21no—
656D12—21no—
657D12—21no—
658D12—21no—
659D12—21no—
660D12—34no—
661D12—32no—
662D12—32no—
663D12—42no—
664D12—62no—
665D12—61no—
666D12—61no—
667D12—61no—
668D12—61no—
669D12—61no—
670D12—61no—
671D12—121no—
672D12—121no—
673D12—121no—
674D12—122no—
675D12—122no—
676D12—122no—
677D12—122no—
678D12—122no—
679D12—122no—
680D12—242no—
681D12—241no—
682D12D3×D412yescomplemented
683C4×D3—21no—
684C4×D3—21no—
685C4×D3—42no—
686C4×D3—61no—
687C4×D3—61no—
688C4×D3—61no—
689C4×D3—61no—
690C4×D3—121no—
691C4×D3—121no—
692C4×D3—122no—
693C4×D3—122no—
694C3×C8—21no—
695C3×C8—21no—
696C3×C8—32no—
697C3×C8—41no—
698C3×C8—61no—
699C3⋊C8—21no—
700C3⋊C8—61no—
701C3⋊C8—61no—
702C3⋊C8—121no—
703C3⋊C8D3×D412yescomplemented
704C2×C32—81no—
705C2×C32D4211yescharacteristic
706C2×C32C22×D811yescharacteristic
707C2×C32#57611yescharacteristic
708C3⋊D3—22no—
709C3⋊D3—42no—
710C3⋊D3—81no—
711C3×D3—22no—
712C3×D3—42no—
713C3×D3—81no—
714C3×D3—81no—
715C24—181no—
716C24—181no—
717C24—181no—
718C24—181no—
719C2×D4—31no—
720C2×D4—31no—
721C2×D4—31no—
722C2×D4—61no—
723C2×D4—61no—
724C2×D4—61no—
725C2×D4—61no—
726C2×D4—91no—
727C2×D4—91no—
728C2×D4—91no—
729C2×D4—181no—
730C2×D4—181no—
731C2×D4—181no—
732C2×D4—181no—
733C2×D4—181no—
734C2×D4—182no—
735C2×D4—182no—
736C2×D4—181no—
737C2×D4—181no—
738C2×D4—181no—
739C2×D4—182no—
740C2×D4—182no—
741C2×D4—361no—
742C2×D4—361no—
743C2×D4—364no—
744C2×D4—361no—
745C2×D4—361no—
746C2×D4—364no—
747C2×D4C2×D3211yescharacteristic
748C22×C4—31no—
749C22×C4—61no—
750C22×C4—91no—
751C22×C4—181no—
752D8—62no—
753D8—62no—
754D8—62no—
755D8—94no—
756D8—182no—
757D8—182no—
758D8—182no—
759D8—361no—
760D8—361no—
761C2×C8—31no—
762C2×C8—31no—
763C2×C8—62no—
764C2×C8—91no—
765C2×C8—182no—
766C2×C8C2×D3211yescharacteristic
767C4⋊C4—31no—
768C4⋊C4—91no—
769C4⋊C4C2×D3211yescharacteristic
770C22⋊C4—61no—
771C22⋊C4—61no—
772C22⋊C4—61no—
773C22⋊C4—91no—
774C22⋊C4—91no—
775C22⋊C4—181no—
776C22⋊C4—181no—
777C22⋊C4—181no—
778C42—31no—
779C22×C3—21no—
780C22×C3—32no—
781C22×C3—42no—
782C22×C3—41no—
783C22×C3—41no—
784C22×C3—41no—
785C22×C3—41no—
786C22×C3—41no—
787C22×C3—41no—
788C22×C3—61no—
789C22×C3—61no—
790C22×C3—62no—
791C22×C3—81no—
792C22×C3—81no—
793C22×C3—121no—
794C22×C3—121no—
795C22×C3—121no—
796C22×C3—121no—
797C22×C3—121no—
798C22×C3—121no—
799C22×C3—121no—
800C22×C3—121no—
801C22×C3C2×D3×D411yescharacteristic
802C22×C3C2×D3×D411yescharacteristic
803C2×D3—21no—
804C2×D3—21no—
805C2×D3—22no—
806C2×D3—32no—
807C2×D3—32no—
808C2×D3—41no—
809C2×D3—41no—
810C2×D3—41no—
811C2×D3—41no—
812C2×D3—41no—
813C2×D3—41no—
814C2×D3—41no—
815C2×D3—41no—
816C2×D3—62no—
817C2×D3—61no—
818C2×D3—61no—
819C2×D3—61no—
820C2×D3—61no—
821C2×D3—62no—
822C2×D3—62no—
823C2×D3—121no—
824C2×D3—121no—
825C2×D3—122no—
826C2×D3—121no—
827C2×D3—121no—
828C2×D3—121no—
829C2×D3—121no—
830C2×D3—121no—
831C2×D3—121no—
832C2×D3—121no—
833C2×D3—121no—
834C2×D3—121no—
835C2×D3—121no—
836C2×D3—241no—
837C2×D3—241no—
838C2×D3—241no—
839C2×D3—241no—
840C2×D3—241no—
841C2×D3—244no—
842C2×D3—244no—
843C2×D3—244no—
844C2×D3—244no—
845C2×D3—244no—
846C2×D3—244no—
847C2×D3—244no—
848C2×D3—244no—
849C2×D3—248no—
850C2×D3D3×D812yescomplemented
851C3×C4—21no—
852C3×C4—21no—
853C3×C4—32no—
854C3×C4—41no—
855C3×C4—41no—
856C3×C4—61no—
857C3×C4—61no—
858C3×C4—81no—
859C3×C4—121no—
860C3×C4C2×D3×D411yescharacteristic
861C3×C4C2×D3×D411yescharacteristic
862C3×C4#100911yescharacteristic
863C3×C4#100911yescharacteristic
864Dic3—21no—
865Dic3—21no—
866Dic3—41no—
867Dic3—61no—
868Dic3—61no—
869Dic3—121no—
870Dic3D3×D812yescomplemented
871C32D4×D811yescharacteristic, complemented, Sylow
872C23—21no—
873C23—31no—
874C23—61no—
875C23—61no—
876C23—61no—
877C23—91no—
878C23—181no—
879C23—181no—
880C23—362no—
881C23—362no—
882C23—362no—
883C23—362no—
884C23—362no—
885C23—362no—
886C23—362no—
887C23—362no—
888C23—721no—
889C23—721no—
890C23—721no—
891C23—721no—
892D4—21no—
893D4—21no—
894D4—32no—
895D4—61no—
896D4—61no—
897D4—61no—
898D4—61no—
899D4—61no—
900D4—94no—
901D4—92no—
902D4—122no—
903D4—122no—
904D4—122no—
905D4—181no—
906D4—181no—
907D4—181no—
908D4—241no—
909D4—362no—
910D4—362no—
911D4—362no—
912D4—362no—
913D4—362no—
914D4—362no—
915D4—362no—
916D4—721no—
917C2×C4—21no—
918C2×C4—31no—
919C2×C4—31no—
920C2×C4—31no—
921C2×C4—61no—
922C2×C4—61no—
923C2×C4—61no—
924C2×C4—91no—
925C2×C4—122no—
926C2×C4—181no—
927C2×C4—181no—
928C2×C4—362no—
929C2×C4C22×D3211yescharacteristic
930C8—21no—
931C8—32no—
932C8—61no—
933C8—181no—
934C2×C3—21no—
935C2×C3—21no—
936C2×C3—21no—
937C2×C3—62no—
938C2×C3—82no—
939C2×C3—81no—
940C2×C3—81no—
941C2×C3—122no—
942C2×C3—241no—
943C2×C3—241no—
944C2×C3#560911yescharacteristic
945C2×C3#560911yescharacteristic
946C2×C3C2×D3×D811yescharacteristic
947C2×C3C2×D3×D811yescharacteristic
948C2×C3#576911yescharacteristic
949C2×C3#577411yescharacteristic
950D3—22no—
951D3—42no—
952D3—62no—
953D3—62no—
954D3—81no—
955D3—81no—
956D3—122no—
957D3—122no—
958D3—122no—
959D3—242no—
960D3—241no—
961D3—241no—
962D3—481no—
963C22—32no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—61no—
968C22—61no—
969C22—62no—
970C22—92no—
971C22—121no—
972C22—121no—
973C22—121no—
974C22—121no—
975C22—121no—
976C22—121no—
977C22—121no—
978C22—121no—
979C22—181no—
980C22—181no—
981C22—182no—
982C22—361no—
983C22—361no—
984C22—361no—
985C22—361no—
986C22—361no—
987C22—724no—
988C22—724no—
989C22—724no—
990C22—724no—
991C22D32×D411yescharacteristic
992C4—32no—
993C4—41no—
994C4—61no—
995C4—61no—
996C4—121no—
997C4—181no—
998C4#6430811yescharacteristic
999C4D32×D411yescharacteristic
1000C3—21no—
1001C3#8035011yescharacteristic, complemented
1002C3#8072911yescharacteristic, complemented
1003C2—62no—
1004C2—81no—
1005C2—122no—
1006C2—182no—
1007C2—241no—
1008C2—241no—
1009C2—362no—
1010C2—721no—
1011C2#1059428411yescharacteristic
1012C2D32×D811yescharacteristic
1013C2#1059475511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32D4×D8
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595297C2semidirect
2. C2×#63926C2semidirect
3. C2×D3×D24C2semidirect
4. #10594621C2semidirect
5. #10592472C2semidirect
6. C3×#4786C2semidirect
7. C3×#4775C2semidirect
8. #10591515C2semidirect
9. #10591482C2semidirect
10. #10590945C2semidirect
11. #10590765C2semidirect
12. #10590720C2semidirect
13. #10590595C2semidirect
14. #10590509C2semidirect
15. #10590456C2semidirect
18. C2×D4×C3⋊D3C22semidirect
20. C2×#3802C22semidirect
22. C2×D3×D12C22semidirect
23. C2×D3×D12C22semidirect
24. C2×#3753C22semidirect
25. C2×#3745C22semidirect
26. #64104C22semidirect
27. C3×#940C22semidirect
28. C3×#938C22semidirect
29. C2×C3×#213C22semidirect
30. C2×C3×#213C22semidirect
31. C2×C3×D24C22semidirect
32. C2×C3×D3×C8C22semidirect
33. C3×#895C22semidirect
34. C3×#893C22semidirect
41. #63916C22semidirect
42. #63911C22semidirect
45. #63894C22semidirect
47. C2×#3714C22semidirect
48. C2×#3714C22semidirect
49. C2×#3713C22semidirect
50. C2×#3710C22semidirect
52. C32×#102C22semidirect
53. #63647C22semidirect
54. #63636C22semidirect
55. C3×#821C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#809C22semidirect
58. C3×#807C22semidirect
59. #63564C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. Dic3×C3⋊C8C22semidirect
86. #4786D3semidirect
88. #4775D3semidirect
155. #3714D4semidirect
181. #940C2×D3semidirect
184. #938C2×D3semidirect
197. C2×#213C2×D3semidirect
198. C2×#213C2×D3semidirect
211. C2×D24C2×D3semidirect
214. C2×D3×C8C2×D3semidirect
219. #895C2×D3semidirect
221. #893C2×D3semidirect
236. C3×#102C2×D3semidirect
237. C3×#102C2×D3semidirect
241. #821C2×D3semidirect
246. Dic3⋊C8C2×D3semidirect
253. #809C2×D3semidirect
254. #807C2×D3semidirect
286. C4⋊(C3⋊D3)C2×D4semidirect
302. C3×D12C2×D4semidirect
311. #626D8semidirect
317. C3×C3⋊C8C2×D4semidirect
489. C2×C3⋊D3C2×D8semidirect
501. C2×C3×D3C2×D8semidirect
512. C3×Dic3C2×D8semidirect
554. #102D32semidirect
682. D12D3×D4semidirect
703. C3⋊C8D3×D4semidirect
850. C2×D3D3×D8semidirect
870. Dic3D3×D8semidirect
871. C32D4×D8semidirect
1001. C3#80350semidirect
1002. C3#80729semidirect

Maximal subgroups

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

subgroupindex
#105952972
C2×#639262
C2×D3×D242
#105946212
#105924722
C3×#47862
C3×#47752
#105915152
#105914822
#105909452
#105907652
#105907202
#105905952
#105905092
#105904562
#807293
#803503