Finite Group Databasebeta

← #11884262

Subgroups — #11884262

Order 1152.

1146 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596295C211yesmaximal, characteristic, complemented
2C2×C3×#950C211yesmaximal, characteristic, complemented
3C2×#63927C211yesmaximal, characteristic, complemented
4#10595070C211yesmaximal, characteristic, complemented
5C3×#5238C211yesmaximal, characteristic, complemented
6#10591652C211yesmaximal, characteristic, complemented
7#10591611C211yesmaximal, characteristic, complemented
8#10591600C211yesmaximal, characteristic, complemented
9#10591569C211yesmaximal, characteristic, complemented
10#10591476C211yesmaximal, characteristic, complemented
11#10591466C211yesmaximal, characteristic, complemented
12#10591436C211yesmaximal, characteristic, complemented
13#10591175C211yesmaximal, characteristic, complemented
14#10591173C211yesmaximal, characteristic, complemented
15#10591157C211yesmaximal, characteristic, complemented
16#83921—31nomaximal
17#80122—31nomaximal
18C2×C32×#41C2211yescharacteristic, complemented
19C2×#3830C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C2×#3802C2211yescharacteristic
22#64155C2211yescharacteristic
23#64153C2211yescharacteristic, complemented
24#64148—21no—
25#64144—21no—
26D4×C3⋊Dic3C2211yescharacteristic, complemented
27#64138—21no—
28C4×#638C2211yescharacteristic
29#64133C2211yescharacteristic, complemented
30C2×#3750—21no—
31C3×#950—24no—
32C2×C3×#216C2211yescharacteristic, complemented
33C2×C3×#215C2211yescharacteristic
34C2×C3×#215C2211yescharacteristic
35C2×C3×#214C2211yescharacteristic, complemented
36C2×C3×#213C2211yescharacteristic
37C2×C3×#213C2211yescharacteristic
38C3×#930C2211yescharacteristic
39C22×C3×C3⋊C8C2211yescharacteristic, complemented
40#63983—21no—
41#63970—21no—
42#63927—24no—
43D3×(C2×D3)⋊C4—21no—
44#63905—21no—
45#63898C2211yescharacteristic
46#63871C2211yescharacteristic
47#63863C2211yescharacteristic
48C2×#3719C2211yescharacteristic, complemented
49C2×#3716C2211yescharacteristic
50C2×#3716C2211yescharacteristic
51C2×#3712C2211yescharacteristic
52C3×#835C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic, complemented
54C3×#830C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61#63557C2211yescharacteristic
62#63555C2211yescharacteristic, complemented
63C2×C3×#135—31no—
64#5829—31no—
65#5824—31no—
66#5824—31no—
67#5824—61no—
68C2×#950D311yescharacteristic, complemented
69C2×#911—31no—
70C2×#911—31no—
71#5612—31no—
72C3×#449—31no—
73#5239—31no—
74#5238D311yescharacteristic, complemented
75#5190—31no—
76#5189—31no—
77#5173—31no—
78#5169—31no—
79#5169—31no—
80#5167—31no—
81#5165—31no—
82#5162—31no—
83#5153—31no—
84#5152—31no—
85#5114—31no—
86#5111—31no—
87#5041—31no—
88#4818—31no—
89#4816—31no—
90#4785—31no—
91#4783—31no—
92#4733—31no—
93#4730—31no—
94C22×D32—21no—
95C32×#41—22no—
96C32×#41—41no—
97C2×C32×Q8C2311yescharacteristic
98C2×C32×D4—21no—
99C2×C32×D4C2311yescharacteristic
100C22×C32×C4—21no—
101C22×C32×C4C2311yescharacteristic
102C2×#638—21no—
103C2×#638D411yescharacteristic
104C22×C3⋊Dic3—21no—
105C22×C3⋊Dic3—21no—
106#3830—22no—
107#3830—41no—
108C2×C4×C3⋊D3C2311yescharacteristic
109C2×#634C2311yescharacteristic
110C2×C3×#67—21no—
111C2×C3×#67—21no—
112C3×#235—22no—
113C3×#235—41no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3—21no—
117C2×C3×Dic6C2311yescharacteristic
118C2×#625—21no—
119C2×D3×Dic3—21no—
120#3802—22no—
121#3802—41no—
122#3757—21no—
123#3757—21no—
124#3757D411yescharacteristic
125#3752—21no—
126#3752D411yescharacteristic
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128#3750—21no—
129#3750—21no—
130#3750—21no—
131#3750—21no—
132#3750D411yescharacteristic
133C4×C3⋊Dic3C2311yescharacteristic
134C3×#216—22no—
135C3×#215—22no—
136C3×#215—41no—
137C3×#214—22no—
138C3×#213—22no—
139C3×#213D414yescomplemented
140C3×(C2×D3)⋊C4—21no—
141C3×C4⋊Dic3C2311yescharacteristic
142C2×C3×C3⋊C8—22no—
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147Dic3⋊Dic3—21no—
148#3722—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152#3719—41no—
153#3716—22no—
154#3716—22no—
155#3712—22no—
156#3267—91noSylow
157C2×C3×#41—21no—
158C2×C3×#41—31no—
159C2×C3×#41C2×D311yescharacteristic, complemented
160C2×C3×#41C2×D311yescharacteristic, complemented
161C2×#237—31no—
162C2×#237—31no—
163C2×#237—61no—
164C2×D3×D4—31no—
165C2×D3×D4—31no—
166C2×#235C2×D311yescharacteristic
167C3×#135—64no—
168C2×C3×Q16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×D8—31no—
173C2×C3×D8—31no—
174C22×C3×C8—31no—
175C3×#121—31no—
176#950—24no—
177#947—31no—
178#946—31no—
179#946—31no—
180#946—31no—
181#946—61no—
182#944—31no—
183#944—31no—
184#944—61no—
185C2×#216—31no—
186C2×#216C2×D311yescharacteristic, complemented
187C2×#215C2×D311yescharacteristic
188C2×#215C2×D311yescharacteristic
189#939—61no—
190#939—61no—
191#939—61no—
192#939—62no—
193#938—61no—
194#937—61no—
195#937—61no—
196#936—31no—
197#935—61no—
198#935—61no—
199#935—62no—
200D4×Dic3—31no—
201D4×Dic3—31no—
202D4×Dic3—31no—
203D4×Dic3—61no—
204C2×#214—31no—
205C2×#214—31no—
206C2×#214C2×D311yescharacteristic, complemented
207C2×#213C2×D311yescharacteristic
208C2×#213C2×D311yescharacteristic
209#930C2×D311yescharacteristic
210#929—61no—
211#929—61no—
212#929—61no—
213#929—62no—
214C4×#67—31no—
215C4×#67—31no—
216C4×#67—61no—
217C2×(C2×D3)⋊C4—61no—
218#924—31no—
219#924—31no—
220#924—61no—
221C2×Dic3⋊C4—61no—
222C2×Dic3⋊C4—61no—
223C2×Dic3⋊C4—62no—
224C22×C3⋊C8C2×D311yescharacteristic, complemented
225#911—64no—
226#911—64no—
227C2×Dic12—31no—
228C2×#204—31no—
229C2×#204—31no—
230C2×ΓL(1,𝔽25)—31no—
231C2×ΓL(1,𝔽25)—31no—
232#897—31no—
233#893—31no—
234#883—61no—
235D3×C22⋊C4—61no—
236C3×#103—31no—
237C3×#102—31no—
238C3×C22⋊C8—31no—
239#835—31no—
240#835C2×D311yescharacteristic, complemented
241#832—31no—
242#832—31no—
243#832C2×D311yescharacteristic, complemented
244#830C2×D311yescharacteristic, complemented
245#821—31no—
246#821—31no—
247(C2×D3)⋊C8—31no—
248(C2×D3)⋊C8—31no—
249#817—31no—
250#816—31no—
251#816—31no—
252#815—31no—
253#815—31no—
254Dic3⋊C8—31no—
255Dic3⋊C8—31no—
256#810—31no—
257#808—31no—
258C23×C32—21no—
259C23×C32C2×D411yescharacteristic
260C22×C3⋊D3C2×D411yescharacteristic
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C2×D32—42no—
264C2×D32—42no—
265C2×D32—81no—
266C32×Q8—21no—
267C32×Q8—21no—
268C32×D4—21no—
269C32×D4—42no—
270C32×D4C2×D412yes—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—42no—
275C2×C32×C4C2×D411yescharacteristic
276C2×C32×C4C2411yescharacteristic
277#638—41no—
278#638—42no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3—21no—
281C2×C3⋊Dic3—42no—
282C2×C3⋊Dic3—42no—
283C2×C3⋊Dic3C2×D411yescharacteristic
284C2×C3⋊Dic3C2×D411yescharacteristic
285C2×C3⋊Dic3C2×D411yescharacteristic
286C4×C3⋊D3—21no—
287C4×C3⋊D3—21no—
288#634—21no—
289#634—21no—
290C3×#67—42no—
291C3×#67—81no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C3×D12—21no—
295C3×D12—21no—
296C3×D12—21no—
297C3×D12C2×D412yes—
298C3×C4×D3—42no—
299C3×Dic6—21no—
300C3×Dic6—21no—
301#625—42no—
302D3×Dic3—81no—
303C3×C3⋊C8—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8—21no—
306C3×C3⋊C8C2×D412yes—
307C2×AGL(1,ℤ/8)—91no—
308C2×#135—31no—
309#547—91no—
310#546—91no—
311#497—91no—
312#470—91no—
313#465—91no—
314#463—91no—
315#461—91no—
316#452—91no—
317#452—91no—
318#450—91no—
319#449—31no—
320#442—91no—
321#435—91no—
322C23×D3—61no—
323C23×D3—61no—
324C3×#41—22no—
325C3×#41—22no—
326C3×#41—42no—
327C3×#41—41no—
328C3×#41—41no—
329C3×#41—42no—
330C3×#41—62no—
331C3×#41—121no—
332C2×C3×Q8—21no—
333C2×C3×Q8—31no—
334C2×C3×Q8C22×D311yescharacteristic
335C2×C3×Q8C22×D311yescharacteristic
336C2×C3×D4—22no—
337C2×C3×D4—21no—
338C2×C3×D4—21no—
339C2×C3×D4—21no—
340C2×C3×D4—31no—
341C2×C3×D4—31no—
342C2×C3×D4—61no—
343C2×C3×D4—61no—
344C2×C3×D4C22×D311yescharacteristic
345C2×C3×D4C22×D311yescharacteristic
346C22×C3×C4—22no—
347C22×C3×C4—21no—
348C22×C3×C4—21no—
349C22×C3×C4—21no—
350C22×C3×C4—61no—
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C22×D311yescharacteristic
353C2×#67—21no—
354C2×#67—21no—
355C2×#67—31no—
356C2×#67—31no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67—61no—
361C2×#67—61no—
362C2×#67—62no—
363C22×Dic3—61no—
364C22×Dic3—61no—
365C22×Dic3—61no—
366C22×Dic3—61no—
367C22×Dic3—61no—
368C22×Dic3—62no—
369C22×Dic3—62no—
370#237—62no—
371#237—62no—
372#237—122no—
373#237—121no—
374#237—121no—
375#237—122no—
376D3×D4—62no—
377D3×D4—62no—
378D3×D4—121no—
379D3×D4—121no—
380#235—22no—
381#235—41no—
382C2×D12C22×D311yescharacteristic
383C2×D12C22×D311yescharacteristic
384C2×C4×D3—21no—
385C2×C4×D3—31no—
386C2×C4×D3—31no—
387C2×C4×D3—61no—
388C2×C4×D3—61no—
389C2×Dic6—31no—
390C2×Dic6—31no—
391C2×Dic6—61no—
392C2×Dic6C22×D311yescharacteristic
393C3×Q16—62no—
394C3×SD16—62no—
395C3×SD16—62no—
396C3×SD16—121no—
397C3×D8—34no—
398C3×D8—62no—
399C2×C3×C8—31no—
400C2×C3×C8—31no—
401C2×C3×C8—31no—
402C2×C3×C8—31no—
403C2×C3×C8—62no—
404C3×C4⋊C4—31no—
405C3×C22⋊C4—61no—
406#217—31no—
407#217—31no—
408#217—61no—
409#217—61no—
410#217—61no—
411#217—61no—
412#217—61no—
413#217—61no—
414#217—62no—
415#217—62no—
416#217—61no—
417#217—61no—
418#216—22no—
419#216—121no—
420#215—22no—
421#215—41no—
422#214—22no—
423#214—62no—
424#214—62no—
425#213—22no—
426#213#6714yescomplemented
427(C2×D3)⋊C4—21no—
428(C2×D3)⋊C4—31no—
429(C2×D3)⋊C4—31no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—62no—
439C4⋊Dic3—31no—
440C4⋊Dic3—31no—
441C4⋊Dic3—61no—
442C4⋊Dic3—61no—
443C4⋊Dic3C22×D311yescharacteristic
444Dic3⋊C4—31no—
445Dic3⋊C4—31no—
446Dic3⋊C4—61no—
447Dic3⋊C4—61no—
448Dic3⋊C4—61no—
449Dic3⋊C4—61no—
450Dic3⋊C4—61no—
451Dic3⋊C4—61no—
452Dic3⋊C4—61no—
453Dic3⋊C4—61no—
454Dic3⋊C4—62no—
455Dic3⋊C4—62no—
456Dic3⋊C4—62no—
457Dic3⋊C4—62no—
458Dic3⋊C4—61no—
459Dic3⋊C4—61no—
460C4×Dic3—31no—
461C4×Dic3—31no—
462C4×Dic3—61no—
463C2×C3⋊C8—22no—
464C2×C3⋊C8C22×D311yescharacteristic
465C2×C3⋊C8C22×D311yescharacteristic
466C2×C3⋊C8C22×D311yescharacteristic
467C2×C3⋊C8C22×D311yescharacteristic
468Dic12—121no—
469#204—62no—
470#204—62no—
471ΓL(1,𝔽25)—62no—
472ΓL(1,𝔽25)—62no—
473C22×C32—22no—
474C22×C32—21no—
475C22×C32—21no—
476C22×C32—21no—
477C22×C32—41no—
478C22×C32—41no—
479C22×C32C22×D411yescharacteristic
480C2×C3⋊D3—21no—
481C2×C3⋊D3—21no—
482C2×C3⋊D3—21no—
483C2×C3×D3—22no—
484C2×C3×D3—41no—
485C2×C3×D3—41no—
486C2×C3×D3—41no—
487C2×C3×D3—41no—
488C2×C3×D3—41no—
489D32—84no—
490C32×C4—21no—
491C32×C4—41no—
492C32×C4C22×D411yescharacteristic
493C32×C4H(5,𝔽2)11yescharacteristic
494C3⋊Dic3—21no—
495C3⋊Dic3—21no—
496C3⋊Dic3—21no—
497C3⋊Dic3—41no—
498C3⋊Dic3—41no—
499C3×Dic3—41no—
500C3×Dic3—41no—
501C2×#41—31no—
502C2×#41—91no—
503C2×#41D3211yescharacteristic, complemented
504C22×D4—91no—
505AGL(1,ℤ/8)—184no—
506#135—64no—
507C2×Q16—31no—
508C2×Q16—91no—
509C2×SD16—31no—
510C2×SD16—31no—
511C2×SD16—31no—
512C2×SD16—91no—
513C2×SD16—91no—
514C2×D8—31no—
515C2×D8—31no—
516C2×M16—91no—
517C22×C8—31no—
518C4⋊Q8—91no—
519#124—91no—
520#123—181no—
521#123—181no—
522#123—181no—
523C22⋊Q8—91no—
524C22⋊Q8—91no—
525C22⋊Q8—91no—
526#121—31no—
527#121—181no—
528#121—181no—
529#120—181no—
530C4×D4—91no—
531C4×D4—91no—
532C4×D4—91no—
533C2×C4⋊C4—181no—
534C2×C22⋊C4—181no—
535#106—91no—
536C4⋊C8—91no—
537#103—31no—
538#103—91no—
539#103—91no—
540#102—31no—
541#102—91no—
542#102—91no—
543C22⋊C8—31no—
544C22⋊C8—91no—
545#97—91no—
546C23×C3—22no—
547C23×C3—21no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—61no—
551C23×C3—61no—
552C23×C3D3×D411yescharacteristic
553C23×C3D3×D411yescharacteristic
554C22×D3—21no—
555C22×D3—21no—
556C22×D3—31no—
557C22×D3—31no—
558C22×D3—61no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—122no—
562C22×D3—122no—
563C22×D3—241no—
564C22×D3—241no—
565C3×Q8—21no—
566C3×Q8—21no—
567C3×Q8—21no—
568C3×Q8—21no—
569C3×Q8—41no—
570C3×Q8—41no—
571C3×Q8—61no—
572C3×Q8—61no—
573C3×D4—22no—
574C3×D4—21no—
575C3×D4—21no—
576C3×D4—22no—
577C3×D4—32no—
578C3×D4—42no—
579C3×D4—42no—
580C3×D4—44no—
581C3×D4—61no—
582C3×D4—61no—
583C3×D4—61no—
584C3×D4—122no—
585C3×D4—241no—
586C3×D4D3×D412yes—
587C3×D4C2×#6712yes—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—22no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—42no—
600C2×C3×C4—42no—
601C2×C3×C4—44no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—122no—
605C2×C3×C4D3×D411yescharacteristic
606C2×C3×C4D3×D411yescharacteristic
607C2×C3×C4C23×D311yescharacteristic
608C2×C3×C4C23×D311yescharacteristic
609#67—42no—
610#67—81no—
611#67—122no—
612#67—122no—
613#67—121no—
614#67—121no—
615#67—122no—
616#67—122no—
617#67—122no—
618#67—124no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—31no—
622C2×Dic3—31no—
623C2×Dic3—31no—
624C2×Dic3—31no—
625C2×Dic3—31no—
626C2×Dic3—31no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—62no—
631C2×Dic3—62no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—61no—
635C2×Dic3—61no—
636C2×Dic3—122no—
637C2×Dic3—122no—
638C2×Dic3—124no—
639C2×Dic3—122no—
640C2×Dic3—122no—
641C2×Dic3—124no—
642C2×Dic3—241no—
643D12—21no—
644D12—21no—
645D12—21no—
646D12C2×#6712yes—
647C4×D3—42no—
648C4×D3—61no—
649C4×D3—61no—
650C4×D3—61no—
651C4×D3—61no—
652C4×D3—121no—
653C4×D3—121no—
654C4×D3—241no—
655Dic6—21no—
656Dic6—21no—
657Dic6—61no—
658Dic6—61no—
659Dic6—61no—
660Dic6—61no—
661Dic6—121no—
662Dic6—121no—
663C3×C8—32no—
664C3×C8—61no—
665C3×C8—61no—
666C3×C8—61no—
667C3⋊C8—21no—
668C3⋊C8—21no—
669C3⋊C8—21no—
670C3⋊C8C2×#6712yes—
671C2×C32—42no—
672C2×C32—41no—
673C2×C32D4211yescharacteristic
674C2×C32#57511yescharacteristic
675C2×C32#57711yescharacteristic
676C3⋊D3—41no—
677C3×D3—42no—
678C3×D3—81no—
679C24—181no—
680#41—22no—
681#41—41no—
682#41—62no—
683#41—121no—
684#41—182no—
685#41—361no—
686C2×Q8—31no—
687C2×Q8—91no—
688C2×Q8C2×D3211yescharacteristic
689C2×D4—21no—
690C2×D4—31no—
691C2×D4—31no—
692C2×D4—61no—
693C2×D4—61no—
694C2×D4—91no—
695C2×D4—181no—
696C2×D4—182no—
697C2×D4—181no—
698C2×D4—361no—
699C2×D4C2×D3211yescharacteristic
700C22×C4—21no—
701C22×C4—61no—
702C22×C4—91no—
703C22×C4—181no—
704C22×C4—181no—
705C22×C4—181no—
706C22×C4C2×D3211yescharacteristic
707Q16—62no—
708Q16—361no—
709SD16—62no—
710SD16—62no—
711SD16—121no—
712SD16—182no—
713SD16—182no—
714D8—34no—
715D8—62no—
716M16—182no—
717C2×C8—31no—
718C2×C8—31no—
719C2×C8—31no—
720C2×C8—31no—
721C2×C8—62no—
722C4⋊C4—31no—
723C4⋊C4—91no—
724C4⋊C4—91no—
725C4⋊C4—181no—
726C4⋊C4—181no—
727C4⋊C4—181no—
728C4⋊C4—181no—
729C4⋊C4—181no—
730C22⋊C4—61no—
731C22⋊C4—91no—
732C22⋊C4—91no—
733C22⋊C4—181no—
734C22⋊C4—181no—
735C22⋊C4—181no—
736C22⋊C4—181no—
737C22⋊C4—181no—
738C22⋊C4—181no—
739C22⋊C4—181no—
740C42—91no—
741C22×C3—24no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—22no—
747C22×C3—21no—
748C22×C3—22no—
749C22×C3—21no—
750C22×C3—21no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—42no—
755C22×C3—42no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—41no—
760C22×C3—62no—
761C22×C3—121no—
762C22×C3—121no—
763C22×C3—121no—
764C22×C3—121no—
765C22×C3—121no—
766C22×C3C2×D3×D411yescharacteristic
767C22×C3C2×D3×D411yescharacteristic
768C2×D3—22no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—41no—
772C2×D3—41no—
773C2×D3—41no—
774C2×D3—61no—
775C2×D3—61no—
776C2×D3—61no—
777C2×D3—61no—
778C2×D3—61no—
779C2×D3—61no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—121no—
783C2×D3—244no—
784C2×D3—244no—
785C3×C4—21no—
786C3×C4—21no—
787C3×C4—21no—
788C3×C4—21no—
789C3×C4—41no—
790C3×C4—42no—
791C3×C4—41no—
792C3×C4—41no—
793C3×C4—121no—
794C3×C4—121no—
795C3×C4C2×D3×D411yescharacteristic
796C3×C4#100411yescharacteristic
797C3×C4#100411yescharacteristic
798C3×C4C22×#6711yescharacteristic
799Dic3—41no—
800Dic3—41no—
801Dic3—62no—
802Dic3—61no—
803Dic3—61no—
804Dic3—61no—
805Dic3—61no—
806Dic3—61no—
807Dic3—61no—
808Dic3—121no—
809Dic3—121no—
810Dic3—122no—
811Dic3—122no—
812Dic3—121no—
813Dic3—121no—
814Dic3—121no—
815Dic3—121no—
816C32#326711yescharacteristic, complemented, Sylow
817C23—21no—
818C23—61no—
819C23—61no—
820C23—91no—
821C23—362no—
822C23—362no—
823C23—721no—
824C23#381111yescharacteristic
825Q8—21no—
826Q8—21no—
827Q8—61no—
828Q8—61no—
829Q8—181no—
830Q8—181no—
831D4—21no—
832D4—32no—
833D4—42no—
834D4—61no—
835D4—61no—
836D4—61no—
837D4—122no—
838D4—241no—
839D4—361no—
840D4—362no—
841D4—362no—
842D4D3×#6712yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—42no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—91no—
850C2×C4—91no—
851C2×C4—91no—
852C2×C4—122no—
853C2×C4—181no—
854C2×C4—181no—
855C2×C4—181no—
856C2×C4—181no—
857C2×C4—362no—
858C2×C4—362no—
859C2×C4—721no—
860C2×C4#381111yescharacteristic
861C2×C4C22×D3211yescharacteristic
862C8—32no—
863C8—61no—
864C8—61no—
865C8—61no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—44no—
870C2×C3—41no—
871C2×C3—42no—
872C2×C3—41no—
873C2×C3—42no—
874C2×C3—81no—
875C2×C3—122no—
876C2×C3—241no—
877C2×C3#559011yescharacteristic
878C2×C3#576811yescharacteristic
879C2×C3#576811yescharacteristic
880C2×C3#577011yescharacteristic
881C2×C3#577511yescharacteristic
882C2×C3D4×#6711yescharacteristic
883D3—42no—
884D3—81no—
885D3—121no—
886D3—121no—
887D3—241no—
888C22—21no—
889C22—21no—
890C22—21no—
891C22—22no—
892C22—41no—
893C22—41no—
894C22—62no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—181no—
901C22—181no—
902C22—181no—
903C22—724no—
904C22C2×#381111yescharacteristic
905C4—21no—
906C4—41no—
907C4—121no—
908C4—121no—
909C4—181no—
910C4—181no—
911C4—181no—
912C4—361no—
913C4—361no—
914C4C2×D3×#6711yescharacteristic
915C4#6433011yescharacteristic
916C3—21no—
917C3#8012211yescharacteristic, complemented
918C3#8392111yescharacteristic, complemented
919C2—41no—
920C2—42no—
921C2—122no—
922C2—241no—
923C2—361no—
924C2#1059546011yescharacteristic
925C2#1059546211yescharacteristic
926C2#1059552611yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #10596295C2semidirect
2. C2×C3×#950C2semidirect
3. C2×#63927C2semidirect
4. #10595070C2semidirect
5. C3×#5238C2semidirect
6. #10591652C2semidirect
7. #10591611C2semidirect
8. #10591600C2semidirect
9. #10591569C2semidirect
10. #10591476C2semidirect
11. #10591466C2semidirect
12. #10591436C2semidirect
13. #10591175C2semidirect
14. #10591173C2semidirect
15. #10591157C2semidirect
18. C2×C32×#41C22semidirect
23. #64153C22semidirect
26. D4×C3⋊Dic3C22semidirect
29. #64133C22semidirect
32. C2×C3×#216C22semidirect
35. C2×C3×#214C22semidirect
39. C22×C3×C3⋊C8C22semidirect
48. C2×#3719C22semidirect
52. C3×#835C22semidirect
53. C3×#832C22semidirect
54. C3×#830C22semidirect
55. #63573C22semidirect
56. #63572C22semidirect
57. #63567C22semidirect
58. #63566C22semidirect
62. #63555C22semidirect
68. C2×#950D3semidirect
74. #5238D3semidirect
139. C3×#213D4semidirect
159. C2×C3×#41C2×D3semidirect
160. C2×C3×#41C2×D3semidirect
186. C2×#216C2×D3semidirect
206. C2×#214C2×D3semidirect
224. C22×C3⋊C8C2×D3semidirect
240. #835C2×D3semidirect
243. #832C2×D3semidirect
244. #830C2×D3semidirect
426. #213#67semidirect
503. C2×#41D32semidirect
816. C32#3267semidirect
917. C3#80122semidirect
918. C3#83921semidirect

Maximal subgroups

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

subgroupindex
#105962952
C2×C3×#9502
C2×#639272
#105950702
C3×#52382
#105916522
#105916112
#105916002
#105915692
#105914762
#105914662
#105914362
#105911752
#105911732
#105911572
#839213
#801223