Finite Group Databasebeta

← #11884261

Subgroups — #11884261

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64159C211yesmaximal, characteristic, complemented
2C3×#5824C211yesmaximal, characteristic, complemented
3C2×#63925C211yesmaximal, characteristic, complemented
4#10595078C211yesmaximal, characteristic, complemented
5C3×#5238C211yesmaximal, characteristic, complemented
6#10591651C211yesmaximal, characteristic, complemented
7#10591605C211yesmaximal, characteristic, complemented
8#10591598C211yesmaximal, characteristic, complemented
9#10591565C211yesmaximal, characteristic, complemented
10#10591468C211yesmaximal, characteristic, complemented
11#10591463C211yesmaximal, characteristic, complemented
12#10591404C211yesmaximal, characteristic, complemented
13#10591184C211yesmaximal, characteristic, complemented
14#10591179C211yesmaximal, characteristic, complemented
15#10591158C211yesmaximal, characteristic, complemented
16#83522—31nomaximal
17#80122—31nomaximal
18C2×C32×#41C2211yescharacteristic, complemented
19C2×#3828C2211yescharacteristic
20C2×C3×#237C2211yescharacteristic
21C2×D3×D12C2211yescharacteristic
22#64159—24no—
23C2×#3756C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic
25C2×#3754C2211yescharacteristic, complemented
26C2×#3753C2211yescharacteristic
27C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
28C3×#946C2211yescharacteristic
29C3×#944C2211yescharacteristic, complemented
30C2×C3×#215C2211yescharacteristic
31C3×#939—21no—
32C3×#935—21no—
33C3×D4×Dic3C2211yescharacteristic, complemented
34C2×C3×#213C2211yescharacteristic
35C3×#930C2211yescharacteristic
36C3×#929—21no—
37C3×C4×#67C2211yescharacteristic
38C3×#924C2211yescharacteristic, complemented
39C2×C3×Dic3⋊C4—21no—
40#63983—21no—
41#63958—21no—
42#63925—24no—
43#63921—21no—
44#63894C2211yescharacteristic
45#63860C2211yescharacteristic
46#63857C2211yescharacteristic
47#63853—21no—
48C2×#3719C2211yescharacteristic, complemented
49C2×#3717C2211yescharacteristic
50C2×#3715C2211yescharacteristic
51C2×#3711C2211yescharacteristic
52C3×#835C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic, complemented
54C3×#830C2211yescharacteristic, complemented
55#63574C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic, complemented
63C3×#547—31no—
64#5824D311yescharacteristic, complemented
65C2×#950—31no—
66C2×#950—31no—
67C2×#950—61no—
68C2×#949—31no—
69C2×#911—31no—
70#5612—31no—
71#5550—31no—
72C3×#449—31no—
73#5239—31no—
74#5238D311yescharacteristic, complemented
75#5169—31no—
76#5167—31no—
77#5153—31no—
78#5086—31no—
79#5083—31no—
80#5052—31no—
81#5048—31no—
82#5047—31no—
83#5046—31no—
84#5041—31no—
85#5016—31no—
86#5014—31no—
87#5011—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—
103#3828—22no—
104#3828—41no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3—21no—
107C2×#634C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67D411yescharacteristic
111C22×C3×Dic3—21no—
112C22×C3×Dic3—21no—
113C3×#237—22no—
114C3×#237—41no—
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×Dic6C2311yescharacteristic
118C2×#626—21no—
119C2×#624—21no—
120D3×D12—22no—
121D3×D12—41no—
122#3756—22no—
123#3755—22no—
124#3754—22no—
125#3753D414yescomplemented
126C2×C3⋊(C3⋊C8)—22no—
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C3×#217—21no—
130C3×#217—21no—
131C3×#217D411yescharacteristic
132C3×#215—41no—
133C3×#213—22no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×C4⋊Dic3C2311yescharacteristic
138C3×C4⋊Dic3C2311yescharacteristic
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4—21no—
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—
148#3722—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152#3719—41no—
153#3717—22no—
154#3715—22no—
155#3711—22no—
156#3267—91noSylow
157C2×C3×#41—21no—
158C2×C3×#41—31no—
159C2×C3×#41C2×D311yescharacteristic, complemented
160C2×C3×#41C2×D311yescharacteristic, complemented
161C2×#237C2×D311yescharacteristic
162C2×D3×D4—31no—
163C2×#235—31no—
164C2×#235—31no—
165C2×#235—61no—
166C22×D12—31no—
167C2×C3×SD16—31no—
168C2×C3×D8—31no—
169C3×C4⋊Q8—31no—
170C3×#123—61no—
171C3×#123—61no—
172C3×C22⋊Q8—31no—
173C3×C22⋊Q8—31no—
174C3×#121—31no—
175C3×#121—61no—
176C3×C4×D4—31no—
177C3×C4×D4—31no—
178C2×C3×C4⋊C4—61no—
179#950—64no—
180#950—64no—
181#950—68no—
182#949—64no—
183#946C2×D311yescharacteristic
184#944C2×D311yescharacteristic, complemented
185C2×#216—31no—
186C2×#216—31no—
187C2×#216—31no—
188C2×#216—61no—
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—31no—
193C2×#215—61no—
194C2×#215C2×D311yescharacteristic
195#939—21no—
196#938—61no—
197#937—61no—
198#937—61no—
199#936—31no—
200#935—21no—
201D4×Dic3C2×D311yescharacteristic, complemented
202C2×#214—31no—
203C2×#214—31no—
204C2×#214—31no—
205C2×#214—61no—
206C2×#213—31no—
207C2×#213—31no—
208C2×#213—61no—
209C2×#213C2×D311yescharacteristic
210#930C2×D311yescharacteristic
211#929—21no—
212C4×#67C2×D311yescharacteristic
213#924—31no—
214#924C2×D311yescharacteristic, complemented
215C2×Dic3⋊C4—21no—
216C2×#208—31no—
217C22×C3⋊C8—31no—
218C22×C3⋊C8—31no—
219C22×C3⋊C8—61no—
220#911—64no—
221C2×Dic12—31no—
222C2×#204—31no—
223C2×ΓL(1,𝔽25)—31no—
224#897—31no—
225#894—61no—
226#893—31no—
227#884—61no—
228#883—61no—
229D3×C22⋊C4—61no—
230D3×C22⋊C4—61no—
231#875—31no—
232C4×D12—31no—
233C3×#103—31no—
234C3×#102—31no—
235C3×C22⋊C8—31no—
236#835—31no—
237#835C2×D311yescharacteristic, complemented
238#832—31no—
239#832C2×D311yescharacteristic, complemented
240#830—31no—
241#830C2×D311yescharacteristic, complemented
242#821—31no—
243(C2×D3)⋊C8—31no—
244#816—31no—
245#815—31no—
246Dic3⋊C8—31no—
247#810—31no—
248#810—31no—
249#809—31no—
250#809—31no—
251#808—31no—
252#808—31no—
253C4⋊(C3⋊C8)—31no—
254#803—31no—
255C23×C32—21no—
256C23×C32C2×D411yescharacteristic
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—
265C32×D4—21no—
266C32×D4—42no—
267C32×D4C2×D412yes—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—42no—
272C2×C32×C4C2×D411yescharacteristic
273C2×C32×C4C2411yescharacteristic
274#638—42no—
275C2×C3⋊Dic3—21no—
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)C2×D412yes—
278C4×C3⋊D3—42no—
279#634—21no—
280#634—21no—
281C3×#67—41no—
282C3×#67—42no—
283C3×#67—81no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—42no—
288C2×C3×Dic3—42no—
289C2×C3×Dic3C2×D411yescharacteristic
290C2×C3×Dic3C2×D411yescharacteristic
291C2×C3×Dic3C2×D411yescharacteristic
292C3×D12—21no—
293C3×D12—21no—
294C3×C4×D3—21no—
295C3×C4×D3—21no—
296C3×Dic6—21no—
297C3×Dic6—21no—
298#626—42no—
299#624—81no—
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—31no—
307#546—91no—
308#497—91no—
309#470—91no—
310#465—91no—
311#463—91no—
312#461—91no—
313#452—91no—
314#452—91no—
315#450—91no—
316#449—31no—
317#442—91no—
318#435—91no—
319C23×D3—61no—
320C23×D3—61no—
321C3×#41—24no—
322C3×#41—22no—
323C3×#41—22no—
324C3×#41—41no—
325C3×#41—41no—
326C3×#41—42no—
327C3×#41—62no—
328C3×#41—121no—
329C2×C3×Q8—21no—
330C2×C3×Q8—31no—
331C2×C3×Q8C22×D311yescharacteristic
332C2×C3×Q8C22×D311yescharacteristic
333C2×C3×D4—21no—
334C2×C3×D4—21no—
335C2×C3×D4—21no—
336C2×C3×D4—31no—
337C2×C3×D4—31no—
338C2×C3×D4—41no—
339C2×C3×D4—61no—
340C2×C3×D4—61no—
341C2×C3×D4C22×D311yescharacteristic
342C2×C3×D4C22×D311yescharacteristic
343C22×C3×C4—21no—
344C22×C3×C4—21no—
345C22×C3×C4—21no—
346C22×C3×C4—31no—
347C22×C3×C4—41no—
348C22×C3×C4—61no—
349C22×C3×C4—61no—
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C2×#67—21no—
353C2×#67—21no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—121no—
358C2×#67#6711yescharacteristic
359C22×Dic3—21no—
360C22×Dic3—21no—
361#237—22no—
362#237—41no—
363D3×D4—62no—
364D3×D4—121no—
365#235—62no—
366#235—62no—
367#235—64no—
368#235—121no—
369#235—121no—
370#235—122no—
371C2×D12—31no—
372C2×D12—31no—
373C2×D12—61no—
374C2×D12—62no—
375C2×D12—61no—
376C2×D12—121no—
377C2×D12C22×D311yescharacteristic
378C2×C4×D3—61no—
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3—61no—
382C2×C4×D3—121no—
383C2×C4×D3C22×D311yescharacteristic
384C2×Dic6—31no—
385C2×Dic6—31no—
386C2×Dic6—61no—
387C2×Dic6C22×D311yescharacteristic
388C3×SD16—121no—
389C3×D8—62no—
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×C4⋊C4—61no—
398C3×C4⋊C4—61no—
399C3×C22⋊C4—31no—
400C3×C22⋊C4—31no—
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—61no—
409#217—61no—
410#217—61no—
411#217#6711yescharacteristic
412#216—62no—
413#216—62no—
414#216—64no—
415#216—121no—
416#215—41no—
417#215—62no—
418#215—62no—
419#215—62no—
420#215—62no—
421#215—64no—
422#214—62no—
423#214—64no—
424#214—62no—
425#214—62no—
426#213—22no—
427#213—34no—
428#213—34no—
429#213—64no—
430(C2×D3)⋊C4—21no—
431(C2×D3)⋊C4—21no—
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#6711yescharacteristic
438C4⋊Dic3—61no—
439C4⋊Dic3C22×D311yescharacteristic
440C4⋊Dic3C22×D311yescharacteristic
441Dic3⋊C4—21no—
442Dic3⋊C4—21no—
443Dic3⋊C4—21no—
444Dic3⋊C4—21no—
445Dic3⋊C4—61no—
446Dic3⋊C4#6711yescharacteristic
447C4×Dic3C22×D311yescharacteristic
448#208—62no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—61no—
454C2×C3⋊C8—61no—
455C2×C3⋊C8—62no—
456C2×C3⋊C8—62no—
457C2×C3⋊C8—64no—
458C2×C3⋊C8C22×D311yescharacteristic
459C2×C3⋊C8C22×D311yescharacteristic
460Dic12—121no—
461#204—62no—
462ΓL(1,𝔽25)—62no—
463C22×C32—21no—
464C22×C32—22no—
465C22×C32—21no—
466C22×C32—21no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32C22×D411yescharacteristic
470C2×C3⋊D3—22no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3—41no—
473C2×C3×D3—21no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479D32—84no—
480C32×C4—21no—
481C32×C4—41no—
482C32×C4C22×D411yescharacteristic
483C32×C4H(5,𝔽2)11yescharacteristic
484C3⋊Dic3—41no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—41no—
489C3×Dic3—41no—
490C3×Dic3—41no—
491C2×#41—31no—
492C2×#41—91no—
493C2×#41D3211yescharacteristic, complemented
494C22×D4—91no—
495AGL(1,ℤ/8)—184no—
496#135—184no—
497C2×Q16—91no—
498C2×Q16—91no—
499C2×SD16—31no—
500C2×SD16—91no—
501C2×SD16—91no—
502C2×SD16—91no—
503C2×SD16—91no—
504C2×D8—31no—
505C2×D8—91no—
506C2×M16—91no—
507C22×C8—91no—
508C4⋊Q8—31no—
509#124—91no—
510#123—61no—
511#123—61no—
512#123—181no—
513C22⋊Q8—31no—
514C22⋊Q8—31no—
515C22⋊Q8—91no—
516#121—31no—
517#121—61no—
518#121—181no—
519#120—181no—
520C4×D4—31no—
521C4×D4—31no—
522C4×D4—91no—
523C2×C4⋊C4—61no—
524C2×C22⋊C4—181no—
525#106—91no—
526C4⋊C8—91no—
527#103—31no—
528#103—91no—
529#103—91no—
530#102—31no—
531#102—91no—
532#102—91no—
533C22⋊C8—31no—
534C22⋊C8—91no—
535#97—91no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—31no—
540C23×C3—41no—
541C23×C3—61no—
542C23×C3D3×D411yescharacteristic
543C23×C3C2×#6711yescharacteristic
544C22×D3—21no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—121no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—122no—
552C22×D3—241no—
553C22×D3—241no—
554C22×D3C2×#6711yescharacteristic
555C3×Q8—22no—
556C3×Q8—21no—
557C3×Q8—21no—
558C3×Q8—21no—
559C3×Q8—21no—
560C3×Q8—41no—
561C3×Q8—61no—
562C3×Q8—61no—
563C3×D4—21no—
564C3×D4—21no—
565C3×D4—22no—
566C3×D4—41no—
567C3×D4—42no—
568C3×D4—42no—
569C3×D4—44no—
570C3×D4—61no—
571C3×D4—61no—
572C3×D4—121no—
573C3×D4—122no—
574C3×D4—241no—
575C3×D4D3×D412yes—
576C3×D4D3×D412yes—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—31no—
588C2×C3×C4—31no—
589C2×C3×C4—31no—
590C2×C3×C4—41no—
591C2×C3×C4—42no—
592C2×C3×C4—42no—
593C2×C3×C4—44no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—122no—
600C2×C3×C4—122no—
601C2×C3×C4D3×D411yescharacteristic
602C2×C3×C4C2×#6711yescharacteristic
603C2×C3×C4C23×D311yescharacteristic
604C2×C3×C4C23×D311yescharacteristic
605#67—41no—
606#67—42no—
607#67—81no—
608#67—122no—
609#67—122no—
610#67—122no—
611#67—124no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—42no—
616C2×Dic3—42no—
617C2×Dic3—61no—
618C2×Dic3—61no—
619C2×Dic3—121no—
620C2×Dic3C2×#6711yescharacteristic
621C2×Dic3C2×#6711yescharacteristic
622C2×Dic3C2×#6711yescharacteristic
623D12—21no—
624D12—21no—
625D12—32no—
626D12—32no—
627D12—62no—
628D12—61no—
629D12—61no—
630D12—121no—
631D12—122no—
632C4×D3—21no—
633C4×D3—21no—
634C4×D3—122no—
635C4×D3—122no—
636C4×D3—124no—
637C4×D3—241no—
638C4×D3—241no—
639Dic6—21no—
640Dic6—21no—
641Dic6—62no—
642Dic6—61no—
643Dic6—61no—
644Dic6—61no—
645Dic6—61no—
646Dic6—121no—
647C3×C8—61no—
648C3×C8—61no—
649C3⋊C8—21no—
650C3⋊C8—21no—
651C3⋊C8—32no—
652C3⋊C8—32no—
653C3⋊C8—62no—
654C3⋊C8—62no—
655C3⋊C8—61no—
656C3⋊C8—61no—
657C2×C32—41no—
658C2×C32—42no—
659C2×C32D4211yescharacteristic
660C2×C32#57511yescharacteristic
661C2×C32#57711yescharacteristic
662C3⋊D3—42no—
663C3×D3—41no—
664C3×D3—81no—
665C24—181no—
666#41—22no—
667#41—41no—
668#41—62no—
669#41—121no—
670#41—182no—
671#41—361no—
672C2×Q8—31no—
673C2×Q8—91no—
674C2×Q8C2×D3211yescharacteristic
675C2×D4—21no—
676C2×D4—31no—
677C2×D4—31no—
678C2×D4—61no—
679C2×D4—61no—
680C2×D4—91no—
681C2×D4—181no—
682C2×D4—182no—
683C2×D4—181no—
684C2×D4—361no—
685C2×D4C2×D3211yescharacteristic
686C22×C4—21no—
687C22×C4—31no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—181no—
691C22×C4—181no—
692C22×C4C2×D3211yescharacteristic
693Q16—182no—
694Q16—361no—
695SD16—121no—
696SD16—182no—
697SD16—182no—
698SD16—182no—
699SD16—182no—
700D8—62no—
701D8—94no—
702M16—182no—
703C2×C8—31no—
704C2×C8—31no—
705C2×C8—91no—
706C2×C8—91no—
707C2×C8—182no—
708C4⋊C4—31no—
709C4⋊C4—31no—
710C4⋊C4—31no—
711C4⋊C4—61no—
712C4⋊C4—61no—
713C4⋊C4—61no—
714C4⋊C4—61no—
715C4⋊C4—181no—
716C22⋊C4—31no—
717C22⋊C4—31no—
718C22⋊C4—61no—
719C22⋊C4—61no—
720C22⋊C4—61no—
721C22⋊C4—61no—
722C22⋊C4—181no—
723C22⋊C4—181no—
724C22⋊C4—181no—
725C22⋊C4—181no—
726C42—31no—
727C22×C3—22no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—22no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—22no—
736C22×C3—21no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—42no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—61no—
745C22×C3—61no—
746C22×C3—61no—
747C22×C3—81no—
748C22×C3—81no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3C2×D3×D411yescharacteristic
753C22×C3C22×#6711yescharacteristic
754C2×D3—21no—
755C2×D3—21no—
756C2×D3—21no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—62no—
761C2×D3—62no—
762C2×D3—122no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—241no—
768C2×D3—241no—
769C2×D3—244no—
770C2×D3—244no—
771C3×C4—22no—
772C3×C4—21no—
773C3×C4—21no—
774C3×C4—21no—
775C3×C4—21no—
776C3×C4—42no—
777C3×C4—41no—
778C3×C4—41no—
779C3×C4—61no—
780C3×C4—61no—
781C3×C4—61no—
782C3×C4—121no—
783C3×C4—121no—
784C3×C4—121no—
785C3×C4C2×D3×D411yescharacteristic
786C3×C4C2×D3×D411yescharacteristic
787C3×C4#100411yescharacteristic
788C3×C4#100411yescharacteristic
789Dic3—21no—
790Dic3—21no—
791Dic3—21no—
792Dic3—41no—
793Dic3—41no—
794Dic3—41no—
795Dic3—122no—
796Dic3—121no—
797Dic3—121no—
798C32#326711yescharacteristic, complemented, Sylow
799C23—21no—
800C23—31no—
801C23—61no—
802C23—181no—
803C23—362no—
804C23—362no—
805C23—721no—
806C23D3×#6711yescharacteristic
807Q8—21no—
808Q8—21no—
809Q8—61no—
810Q8—61no—
811Q8—181no—
812Q8—181no—
813D4—21no—
814D4—42no—
815D4—61no—
816D4—61no—
817D4—92no—
818D4—121no—
819D4—122no—
820D4—181no—
821D4—241no—
822D4—362no—
823D4—362no—
824D4#381112yes—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—31no—
829C2×C4—31no—
830C2×C4—31no—
831C2×C4—42no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—122no—
838C2×C4—122no—
839C2×C4—181no—
840C2×C4—362no—
841C2×C4—721no—
842C2×C4D3×#6711yescharacteristic
843C2×C4C22×D3211yescharacteristic
844C8—61no—
845C8—61no—
846C8—92no—
847C8—181no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—42no—
852C2×C3—41no—
853C2×C3—42no—
854C2×C3—41no—
855C2×C3—42no—
856C2×C3—82no—
857C2×C3—121no—
858C2×C3—241no—
859C2×C3#559011yescharacteristic
860C2×C3#576811yescharacteristic
861C2×C3#577511yescharacteristic
862C2×C3D4×#6711yescharacteristic
863C2×C3#582211yescharacteristic
864C2×C3#583711yescharacteristic
865D3—41no—
866D3—81no—
867D3—122no—
868D3—122no—
869D3—242no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—22no—
874C22—41no—
875C22—41no—
876C22—61no—
877C22—61no—
878C22—61no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—182no—
883C22—361no—
884C22—361no—
885C22—724no—
886C22C2×D3×#6711yescharacteristic
887C4—21no—
888C4—41no—
889C4—61no—
890C4—61no—
891C4—61no—
892C4—121no—
893C4—121no—
894C4—121no—
895C4—361no—
896C4C2×#381111yescharacteristic
897C4#6433011yescharacteristic
898C3—21no—
899C3#8012211yescharacteristic, complemented
900C3#8352211yescharacteristic, complemented
901C2—41no—
902C2—42no—
903C2—121no—
904C2—241no—
905C2—362no—
906C2#1059545311yescharacteristic
907C2#1059545511yescharacteristic
908C2#1059552611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
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. C2×#64159C2semidirect
2. C3×#5824C2semidirect
3. C2×#63925C2semidirect
4. #10595078C2semidirect
5. C3×#5238C2semidirect
6. #10591651C2semidirect
7. #10591605C2semidirect
8. #10591598C2semidirect
9. #10591565C2semidirect
10. #10591468C2semidirect
11. #10591463C2semidirect
12. #10591404C2semidirect
13. #10591184C2semidirect
14. #10591179C2semidirect
15. #10591158C2semidirect
18. C2×C32×#41C22semidirect
23. C2×#3756C22semidirect
25. C2×#3754C22semidirect
27. C22×C3⋊(C3⋊C8)C22semidirect
29. C3×#944C22semidirect
33. C3×D4×Dic3C22semidirect
38. C3×#924C22semidirect
48. C2×#3719C22semidirect
52. C3×#835C22semidirect
53. C3×#832C22semidirect
54. C3×#830C22semidirect
55. #63574C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
58. #63565C22semidirect
62. #63554C22semidirect
64. #5824D3semidirect
74. #5238D3semidirect
125. #3753D4semidirect
159. C2×C3×#41C2×D3semidirect
160. C2×C3×#41C2×D3semidirect
184. #944C2×D3semidirect
201. D4×Dic3C2×D3semidirect
214. #924C2×D3semidirect
237. #835C2×D3semidirect
239. #832C2×D3semidirect
241. #830C2×D3semidirect
493. C2×#41D32semidirect
798. C32#3267semidirect
899. C3#80122semidirect
900. C3#83522semidirect

Maximal subgroups

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

subgroupindex
C2×#641592
C3×#58242
C2×#639252
#105950782
C3×#52382
#105916512
#105916052
#105915982
#105915652
#105914682
#105914632
#105914042
#105911842
#105911792
#105911582
#835223
#801223