Finite Group Databasebeta

← #11884275

Subgroups — #11884275

Order 1152.

1149 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
1C2×#64141C211yesmaximal, characteristic, complemented
2C3×#5806C211yesmaximal, characteristic, complemented
3C2×#63935C211yesmaximal, characteristic, complemented
4#10594834C211yesmaximal, characteristic, complemented
5C3×#5218C211yesmaximal, characteristic, complemented
6#10591521C211yesmaximal, characteristic, complemented
7#10591491C211yesmaximal, characteristic, complemented
8#10591489C211yesmaximal, characteristic, complemented
9#10591463C211yesmaximal, characteristic, complemented
10#10591460C211yesmaximal, characteristic, complemented
11#10591432C211yesmaximal, characteristic, complemented
12#10591404C211yesmaximal, characteristic, complemented
13#10591189C211yesmaximal, characteristic, complemented
14#10591184C211yesmaximal, characteristic, complemented
15#10591151C211yesmaximal, characteristic, complemented
16#83503—31nomaximal
17#80157—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C2×#3828C2211yescharacteristic
20C2×C3×#237C2211yescharacteristic
21C2×#3799C2211yescharacteristic, complemented
22C2×#3754C2211yescharacteristic
23C2×#3754C2211yescharacteristic
24#64141—24no—
25C2×#3753C2211yescharacteristic
26C2×#3753C2211yescharacteristic
27C2×#3748C2211yescharacteristic
28C3×#953—21no—
29C2×C3×#217—21no—
30C3×#939—21no—
31C3×#938C2211yescharacteristic
32C3×#936C2211yescharacteristic
33C3×#935—21no—
34C3×D4×Dic3C2211yescharacteristic
35C2×C3×#214C2211yescharacteristic
36C2×C3×#214C2211yescharacteristic
37C3×C4×#67C2211yescharacteristic
38C3×#924C2211yescharacteristic
39C3×#924C2211yescharacteristic
40#63975—21no—
41#63958—21no—
42#63935—24no—
43#63894C2211yescharacteristic, complemented
44#63883—21no—
45#63866C2211yescharacteristic, complemented
46#63857C2211yescharacteristic, complemented
47#63853—21no—
48C2×#3719C2211yescharacteristic, complemented
49C2×#3718C2211yescharacteristic, complemented
50C2×#3717C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52C3×#832C2211yescharacteristic
53C3×#832C2211yescharacteristic
54C3×#830C2211yescharacteristic
55#63574C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C3×#546—31no—
64C2×#950—31no—
65#5806D311yescharacteristic, complemented
66C2×#932—31no—
67C2×#932—31no—
68C2×#932—61no—
69C2×#916—31no—
70#5631—31no—
71#5551—31no—
72C3×#450—31no—
73#5239—31no—
74#5218D311yescharacteristic, complemented
75#5172—31no—
76#5167—31no—
77#5162—31no—
78#5060—31no—
79#5057—31no—
80#5052—31no—
81#5052—31no—
82#5047—31no—
83#5041—31no—
84#5037—31no—
85#5019—31no—
86#5014—31no—
87#5011—31no—
88#4787—31no—
89#4785—31no—
90#4783—31no—
91#4778—31no—
92#4733—31no—
93#4728—31no—
94C24×C32—21no—
95C2×C32×D4—22no—
96C2×C32×D4—21no—
97C2×C32×D4—41no—
98C2×C32×D4C2311yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C2×#638—21no—
102#3828—22no—
103#3828—41no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3—21no—
106C2×#634C2311yescharacteristic
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C2×C3×#67D411yescharacteristic
110C22×C3×Dic3—21no—
111C22×C3×Dic3—21no—
112C3×#237—22no—
113C3×#237—41no—
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#626—21no—
118C2×#624—21no—
119C2×#624—21no—
120#3799—22no—
121#3799—41no—
122#3754—22no—
123#3754—22no—
124#3753—22no—
125#3753D414yescomplemented
126#3748—22no—
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C3×#217—21no—
130C3×#217—21no—
131C3×#217—21no—
132C3×#217—21no—
133C3×#217—21no—
134C3×#217—21no—
135C3×#217D411yescharacteristic
136C3×#214—22no—
137C3×#214—41no—
138C3×(C2×D3)⋊C4D411yescharacteristic
139C3×C4⋊Dic3C2311yescharacteristic
140C3×C4⋊Dic3C2311yescharacteristic
141C3×Dic3⋊C4—21no—
142C3×Dic3⋊C4—21no—
143C3×Dic3⋊C4D411yescharacteristic
144C3×C4×Dic3C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147Dic3⋊Dic3—21no—
148Dic3⋊Dic3—21no—
149Dic3⋊Dic3—21no—
150#3722—21no—
151(C2×D3)⋊Dic3—21no—
152#3719—41no—
153#3718—22no—
154#3717—22no—
155D3×C3⋊C8—22no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C22×C3×D4—21no—
159C22×C3×D4C2×D311yescharacteristic
160C22×C3×D4C2×D311yescharacteristic
161C2×#239—31no—
162C2×#237C2×D311yescharacteristic
163C2×#235—31no—
164C2×#235—31no—
165C2×#235—31no—
166C2×#235—61no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C3×#124—31no—
170C3×#123—61no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8—31no—
173C3×#121—31no—
174C3×#121—61no—
175C3×#120—61no—
176C3×C4×D4—31no—
177C3×C4×D4—31no—
178C2×C3×C22⋊C4—61no—
179#953—21no—
180C2×#217—21no—
181#950—64no—
182#944—31no—
183C2×#216—31no—
184C2×#216—31no—
185C2×#216—31no—
186C2×#215—31no—
187#939—21no—
188#938—61no—
189#938C2×D311yescharacteristic
190#936C2×D311yescharacteristic
191#935—21no—
192D4×Dic3C2×D311yescharacteristic
193C2×#214—31no—
194C2×#214—31no—
195C2×#214—31no—
196C2×#214—31no—
197C2×#214—61no—
198C2×#214—61no—
199C2×#214C2×D311yescharacteristic
200C2×#214C2×D311yescharacteristic
201#932—64no—
202#932—64no—
203#932—68no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213—31no—
207C2×#213—31no—
208C2×#213—61no—
209C2×#213—61no—
210C4×#67C2×D311yescharacteristic
211#924—31no—
212#924C2×D311yescharacteristic
213#924C2×D311yescharacteristic
214C2×#208—31no—
215C2×#208—31no—
216C2×#208—61no—
217C22×C3⋊C8—31no—
218#916—64no—
219C2×Dic12—31no—
220C2×#204—31no—
221C2×D3×C8—31no—
222#897—31no—
223#894—61no—
224#893—31no—
225D3×C4⋊C4—61no—
226D3×C4⋊C4—61no—
227#884—61no—
228#883—61no—
229#883—61no—
230#883—61no—
231C4×D12—31no—
232#869—31no—
233C3×#102—31no—
234C3×#102—31no—
235C3×C22⋊C8—31no—
236#835—31no—
237#835—31no—
238#832C2×D311yescharacteristic
239#832C2×D311yescharacteristic
240#830—31no—
241#830C2×D311yescharacteristic
242#821—31no—
243(C2×D3)⋊C8—31no—
244#816—31no—
245#815—31no—
246Dic3⋊C8—31no—
247#810—31no—
248#810—31no—
249#810—31no—
250#809—31no—
251#808—31no—
252#808—31no—
253C4⋊(C3⋊C8)—31no—
254#803—31no—
255C23×C32—21no—
256C23×C32—21no—
257C23×C32—42no—
258C23×C32—42no—
259C23×C32—81no—
260C23×C32C2×D411yescharacteristic
261C22×C3⋊D3—21no—
262C22×C3×D3C2×D411yescharacteristic
263C32×D4—21no—
264C32×D4—21no—
265C32×D4—21no—
266C32×D4—42no—
267C32×D4C2×D412yes—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4C2×D411yescharacteristic
271C2×C32×C4C2411yescharacteristic
272#638—42no—
273C2×C3⋊Dic3—21no—
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)C2×D412yes—
276C4×C3⋊D3—42no—
277#634—21no—
278#634—21no—
279C3×#67—41no—
280C3×#67—42no—
281C3×#67—81no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—42no—
287C2×C3×Dic3—81no—
288C2×C3×Dic3C2×D411yescharacteristic
289C2×C3×Dic3C2×D411yescharacteristic
290C2×C3×Dic3C2×D411yescharacteristic
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297#626—42no—
298#624—42no—
299#624—42no—
300C3⋊(C3⋊C8)—21no—
301C3⋊(C3⋊C8)C2×D412yes—
302C3×C3⋊C8—21no—
303C3×C3⋊C8—21no—
304C2×AGL(1,ℤ/8)—91no—
305C2×#135—91no—
306#547—91no—
307#546—31no—
308#497—91no—
309#470—91no—
310#465—91no—
311#463—91no—
312#461—91no—
313#452—91no—
314#452—91no—
315#450—31no—
316#449—91no—
317#442—91no—
318#435—91no—
319C24×C3—21no—
320C24×C3—21no—
321C24×C3—41no—
322C3×#41—62no—
323C3×#41—121no—
324C2×C3×Q8—31no—
325C2×C3×Q8—31no—
326C2×C3×D4—24no—
327C2×C3×D4—22no—
328C2×C3×D4—22no—
329C2×C3×D4—21no—
330C2×C3×D4—21no—
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4—31no—
334C2×C3×D4—41no—
335C2×C3×D4—41no—
336C2×C3×D4—41no—
337C2×C3×D4—42no—
338C2×C3×D4—61no—
339C2×C3×D4—61no—
340C2×C3×D4C22×D311yescharacteristic
341C2×C3×D4C22×D311yescharacteristic
342C2×C3×D4C22×D311yescharacteristic
343C2×C3×D4C22×D311yescharacteristic
344C22×C3×C4—21no—
345C22×C3×C4—31no—
346C22×C3×C4—61no—
347C22×C3×C4—61no—
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C2×#67—21no—
351C2×#67—21no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—121no—
356C2×#67#6711yescharacteristic
357C22×Dic3—21no—
358C22×Dic3—21no—
359#239—62no—
360#239—121no—
361#237—22no—
362#237—41no—
363#235—62no—
364#235—62no—
365#235—62no—
366#235—64no—
367#235—121no—
368#235—121no—
369#235—121no—
370#235—122no—
371C2×D12—31no—
372C2×D12—31no—
373C2×D12—61no—
374C2×D12—61no—
375C2×C4×D3—61no—
376C2×C4×D3—61no—
377C2×C4×D3—61no—
378C2×C4×D3—61no—
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3—121no—
382C2×C4×D3C22×D311yescharacteristic
383C2×Dic6—31no—
384C2×Dic6—31no—
385C2×Dic6—61no—
386C2×Dic6C22×D311yescharacteristic
387C2×Dic6C22×D311yescharacteristic
388C3×SD16—62no—
389C3×SD16—121no—
390C2×C3×C8—31no—
391C2×C3×C8—31no—
392C3×C4⋊C4—31no—
393C3×C4⋊C4—31no—
394C3×C4⋊C4—31no—
395C3×C4⋊C4—61no—
396C3×C4⋊C4—61no—
397C3×C22⋊C4—31no—
398C3×C22⋊C4—31no—
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C22⋊C4—61no—
403C3×C22⋊C4—61no—
404C3×C22⋊C4—61no—
405C3×C42—31no—
406#217—21no—
407#217—21no—
408#217—21no—
409#217—21no—
410#217—21no—
411#217—21no—
412#217—61no—
413#217#6711yescharacteristic
414#216—62no—
415#216—62no—
416#216—121no—
417#215—62no—
418#214—22no—
419#214—41no—
420#214—62no—
421#214—62no—
422#214—64no—
423#214—64no—
424#214—62no—
425#214—62no—
426#213—34no—
427#213—34no—
428#213—64no—
429#213—62no—
430#213—62no—
431#213—64no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4#6711yescharacteristic
436C4⋊Dic3—61no—
437C4⋊Dic3—61no—
438C4⋊Dic3—61no—
439C4⋊Dic3C22×D311yescharacteristic
440C4⋊Dic3C22×D311yescharacteristic
441Dic3⋊C4—21no—
442Dic3⋊C4—21no—
443Dic3⋊C4—61no—
444Dic3⋊C4—61no—
445Dic3⋊C4—61no—
446Dic3⋊C4#6711yescharacteristic
447C4×Dic3C22×D311yescharacteristic
448#208—62no—
449#208—62no—
450#208—64no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—31no—
454C2×C3⋊C8—31no—
455C2×C3⋊C8—61no—
456C2×C3⋊C8—61no—
457C2×C3⋊C8—62no—
458C2×C3⋊C8C22×D311yescharacteristic
459C2×C3⋊C8C22×D311yescharacteristic
460Dic12—121no—
461#204—62no—
462D3×C8—62no—
463C22×C32—21no—
464C22×C32—22no—
465C22×C32—21no—
466C22×C32—21no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32—41no—
470C22×C32—41no—
471C22×C32—41no—
472C22×C32—84no—
473C22×C32C22×D411yescharacteristic
474C2×C3⋊D3—22no—
475C2×C3⋊D3—41no—
476C2×C3⋊D3—41no—
477C2×C3×D3—21no—
478C2×C3×D3—21no—
479C2×C3×D3—21no—
480C32×C4—21no—
481C32×C4C22×D411yescharacteristic
482C32×C4H(5,𝔽2)11yescharacteristic
483C3⋊Dic3—41no—
484C3×Dic3—21no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—41no—
488C3×Dic3—41no—
489C3×Dic3—41no—
490C3×Dic3—41no—
491C2×#41—31no—
492C2×#41—91no—
493C2×#41—91no—
494C22×D4D3211yescharacteristic
495AGL(1,ℤ/8)—184no—
496#135—184no—
497C2×Q16—91no—
498C2×Q16—91no—
499C2×SD16—31no—
500C2×SD16—31no—
501C2×SD16—91no—
502C2×SD16—91no—
503C2×SD16—91no—
504C2×D8—91no—
505C2×D8—91no—
506C2×M16—91no—
507C22×C8—91no—
508C4⋊Q8—91no—
509#124—31no—
510#123—61no—
511#123—181no—
512#123—181no—
513C22⋊Q8—31no—
514C22⋊Q8—31no—
515C22⋊Q8—91no—
516#121—31no—
517#121—61no—
518#121—181no—
519#120—61no—
520C4×D4—31no—
521C4×D4—31no—
522C4×D4—91no—
523C2×C4⋊C4—181no—
524C2×C22⋊C4—61no—
525#106—91no—
526C4⋊C8—91no—
527#103—91no—
528#103—91no—
529#103—91no—
530#102—31no—
531#102—31no—
532#102—91no—
533C22⋊C8—31no—
534C22⋊C8—91no—
535#97—91no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—31no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—42no—
545C23×C3—42no—
546C23×C3—44no—
547C23×C3—42no—
548C23×C3—42no—
549C23×C3—82no—
550C23×C3—81no—
551C23×C3—81no—
552C23×C3—82no—
553C23×C3D3×D411yescharacteristic
554C23×C3C2×#6711yescharacteristic
555C22×D3—61no—
556C22×D3—61no—
557C22×D3—121no—
558C22×D3C2×#6711yescharacteristic
559C3×Q8—61no—
560C3×Q8—61no—
561C3×Q8—61no—
562C3×Q8—61no—
563C3×D4—22no—
564C3×D4—21no—
565C3×D4—21no—
566C3×D4—21no—
567C3×D4—21no—
568C3×D4—21no—
569C3×D4—21no—
570C3×D4—22no—
571C3×D4—41no—
572C3×D4—41no—
573C3×D4—42no—
574C3×D4—42no—
575C3×D4—44no—
576C3×D4—121no—
577C3×D4—122no—
578C3×D4—241no—
579C3×D4D3×D412yes—
580C3×D4D3×D412yes—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—31no—
590C2×C3×C4—31no—
591C2×C3×C4—31no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—122no—
599C2×C3×C4—241no—
600C2×C3×C4D3×D411yescharacteristic
601C2×C3×C4C2×#6711yescharacteristic
602C2×C3×C4C23×D311yescharacteristic
603C2×C3×C4C23×D311yescharacteristic
604#67—41no—
605#67—42no—
606#67—81no—
607#67—122no—
608#67—122no—
609#67—122no—
610#67—124no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—42no—
616C2×Dic3—61no—
617C2×Dic3—61no—
618C2×Dic3—81no—
619C2×Dic3—121no—
620C2×Dic3C2×#6711yescharacteristic
621C2×Dic3C2×#6711yescharacteristic
622C2×Dic3C2×#6711yescharacteristic
623D12—32no—
624D12—32no—
625D12—62no—
626D12—61no—
627D12—61no—
628D12—121no—
629D12—122no—
630C4×D3—21no—
631C4×D3—21no—
632C4×D3—122no—
633C4×D3—122no—
634C4×D3—122no—
635C4×D3—122no—
636C4×D3—122no—
637C4×D3—122no—
638C4×D3—124no—
639Dic6—21no—
640Dic6—21no—
641Dic6—21no—
642Dic6—21no—
643Dic6—62no—
644Dic6—61no—
645Dic6—61no—
646Dic6—61no—
647Dic6—61no—
648Dic6—121no—
649C3×C8—61no—
650C3×C8—61no—
651C3⋊C8—21no—
652C3⋊C8—21no—
653C3⋊C8—32no—
654C3⋊C8—32no—
655C3⋊C8—62no—
656C3⋊C8—62no—
657C3⋊C8—61no—
658C3⋊C8—61no—
659C2×C32—41no—
660C2×C32—42no—
661C2×C32—81no—
662C2×C32D4211yescharacteristic
663C2×C32#57511yescharacteristic
664C2×C32#57711yescharacteristic
665C3⋊D3—42no—
666C3×D3—41no—
667C24—21no—
668#41—62no—
669#41—121no—
670#41—182no—
671#41—182no—
672#41—361no—
673#41—361no—
674C2×Q8—31no—
675C2×Q8—31no—
676C2×Q8—91no—
677C2×D4—22no—
678C2×D4—21no—
679C2×D4—31no—
680C2×D4—41no—
681C2×D4—61no—
682C2×D4—61no—
683C2×D4—91no—
684C2×D4—181no—
685C2×D4—181no—
686C2×D4C2×D3211yescharacteristic
687C2×D4C2×D3211yescharacteristic
688C22×C4—31no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—181no—
692C22×C4—181no—
693C22×C4—181no—
694C22×C4C2×D3211yescharacteristic
695Q16—182no—
696Q16—361no—
697SD16—62no—
698SD16—121no—
699SD16—182no—
700SD16—182no—
701SD16—182no—
702D8—94no—
703D8—182no—
704M16—182no—
705C2×C8—31no—
706C2×C8—31no—
707C2×C8—91no—
708C2×C8—91no—
709C2×C8—182no—
710C4⋊C4—31no—
711C4⋊C4—31no—
712C4⋊C4—31no—
713C4⋊C4—61no—
714C4⋊C4—61no—
715C4⋊C4—181no—
716C4⋊C4—181no—
717C4⋊C4—181no—
718C22⋊C4—31no—
719C22⋊C4—31no—
720C22⋊C4—61no—
721C22⋊C4—61no—
722C22⋊C4—61no—
723C22⋊C4—61no—
724C22⋊C4—61no—
725C22⋊C4—61no—
726C22⋊C4—181no—
727C22⋊C4—181no—
728C42—31no—
729C22×C3—22no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—22no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—22no—
738C22×C3—21no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—42no—
742C22×C3—42no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—61no—
754C22×C3—61no—
755C22×C3—61no—
756C22×C3—81no—
757C22×C3—81no—
758C22×C3—81no—
759C22×C3—81no—
760C22×C3—84no—
761C22×C3—84no—
762C22×C3—88no—
763C22×C3C2×D3×D411yescharacteristic
764C22×C3C22×#6711yescharacteristic
765C2×D3—21no—
766C2×D3—21no—
767C2×D3—21no—
768C2×D3—62no—
769C2×D3—62no—
770C2×D3—122no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—241no—
776C2×D3—241no—
777C3×C4—22no—
778C3×C4—21no—
779C3×C4—21no—
780C3×C4—21no—
781C3×C4—21no—
782C3×C4—61no—
783C3×C4—61no—
784C3×C4—61no—
785C3×C4—121no—
786C3×C4—121no—
787C3×C4—121no—
788C3×C4—121no—
789C3×C4C2×D3×D411yescharacteristic
790C3×C4C2×D3×D411yescharacteristic
791C3×C4#100411yescharacteristic
792C3×C4#100411yescharacteristic
793Dic3—21no—
794Dic3—21no—
795Dic3—21no—
796Dic3—41no—
797Dic3—41no—
798Dic3—41no—
799Dic3—41no—
800Dic3—122no—
801Dic3—121no—
802Dic3—121no—
803C32#326711yescharacteristic, complemented, Sylow
804C23—21no—
805C23—21no—
806C23—31no—
807C23—42no—
808C23—42no—
809C23—81no—
810C23—181no—
811C23D3×#6711yescharacteristic
812Q8—61no—
813Q8—61no—
814Q8—61no—
815Q8—61no—
816Q8—181no—
817Q8—181no—
818D4—21no—
819D4—21no—
820D4—21no—
821D4—42no—
822D4—92no—
823D4—121no—
824D4—122no—
825D4—181no—
826D4—241no—
827D4—362no—
828D4—362no—
829D4#381112yes—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—31no—
833C2×C4—31no—
834C2×C4—31no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—122no—
842C2×C4—181no—
843C2×C4—241no—
844C2×C4—362no—
845C2×C4—362no—
846C2×C4—362no—
847C2×C4D3×#6711yescharacteristic
848C2×C4C22×D3211yescharacteristic
849C8—61no—
850C8—61no—
851C8—92no—
852C8—181no—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—21no—
856C2×C3—42no—
857C2×C3—41no—
858C2×C3—42no—
859C2×C3—41no—
860C2×C3—42no—
861C2×C3—82no—
862C2×C3—82no—
863C2×C3—81no—
864C2×C3—81no—
865C2×C3—121no—
866C2×C3#559011yescharacteristic
867C2×C3#576211yescharacteristic
868C2×C3#577311yescharacteristic
869C2×C3D4×#6711yescharacteristic
870C2×C3#582211yescharacteristic
871C2×C3#583611yescharacteristic
872D3—41no—
873D3—122no—
874D3—122no—
875D3—242no—
876C22—21no—
877C22—21no—
878C22—21no—
879C22—22no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—61no—
886C22—61no—
887C22—61no—
888C22—84no—
889C22—182no—
890C22—361no—
891C22—361no—
892C22C2×D3×#6711yescharacteristic
893C4—21no—
894C4—61no—
895C4—61no—
896C4—61no—
897C4—121no—
898C4—121no—
899C4—121no—
900C4—121no—
901C4—361no—
902C4C2×#381111yescharacteristic
903C4#6433011yescharacteristic
904C3—21no—
905C3#8015711yescharacteristic, complemented
906C3#8350311yescharacteristic, complemented
907C2—41no—
908C2—42no—
909C2—81no—
910C2—121no—
911C2—362no—
912C2#1059509511yescharacteristic
913C2#1059510511yescharacteristic
914C2#1059552611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64141C2semidirect
2. C3×#5806C2semidirect
3. C2×#63935C2semidirect
4. #10594834C2semidirect
5. C3×#5218C2semidirect
6. #10591521C2semidirect
7. #10591491C2semidirect
8. #10591489C2semidirect
9. #10591463C2semidirect
10. #10591460C2semidirect
11. #10591432C2semidirect
12. #10591404C2semidirect
13. #10591189C2semidirect
14. #10591184C2semidirect
15. #10591151C2semidirect
21. C2×#3799C22semidirect
43. #63894C22semidirect
45. #63866C22semidirect
46. #63857C22semidirect
48. C2×#3719C22semidirect
49. C2×#3718C22semidirect
50. C2×#3717C22semidirect
51. C2×D3×C3⋊C8C22semidirect
55. #63574C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
58. #63565C22semidirect
59. #63565C22semidirect
60. #63564C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
65. #5806D3semidirect
74. #5218D3semidirect
125. #3753D4semidirect
803. C32#3267semidirect
905. C3#80157semidirect
906. C3#83503semidirect

Maximal subgroups

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

subgroupindex
C2×#641412
C3×#58062
C2×#639352
#105948342
C3×#52182
#105915212
#105914912
#105914892
#105914632
#105914602
#105914322
#105914042
#105911892
#105911842
#105911512
#835033
#801573