Finite Group Databasebeta

← #11884260

Subgroups — #11884260

Order 1152.

1081 conjugacy classes of subgroups.

The subgroup lattice has 901 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5824C211yesmaximal, characteristic, complemented
2C2×C3×#950C211yesmaximal, characteristic, complemented
3C2×#63925C211yesmaximal, characteristic, complemented
4#10595067C211yesmaximal, characteristic, complemented
5#10592937C211yesmaximal, characteristic, complemented
6#10591651C211yesmaximal, characteristic, complemented
7#10591638C211yesmaximal, characteristic, complemented
8#10591608C211yesmaximal, characteristic, complemented
9#10591564C211yesmaximal, characteristic, complemented
10#10591471C211yesmaximal, characteristic, complemented
11#10591461C211yesmaximal, characteristic, complemented
12#10591430C211yesmaximal, characteristic, complemented
13#10591177C211yesmaximal, characteristic, complemented
14#10591170C211yesmaximal, characteristic, complemented
15#10591155C211yesmaximal, characteristic, complemented
16#83921—31nomaximal
17#83522—31nomaximal
18C2×C32×#41C2211yescharacteristic, complemented
19C2×C3×#237C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C2×D3×D12C2211yescharacteristic
22C2×#3755C2211yescharacteristic
23C2×#3753C2211yescharacteristic
24#64139C2211yescharacteristic
25C3×#950—24no—
26C3×#946C2211yescharacteristic
27C3×#944C2211yescharacteristic, complemented
28C2×C3×#216C2211yescharacteristic, complemented
29C2×C3×#215C2211yescharacteristic
30C3×#939—21no—
31C3×#935—21no—
32C3×D4×Dic3C2211yescharacteristic, complemented
33C2×C3×#214C2211yescharacteristic, complemented
34C2×C3×#213C2211yescharacteristic
35C3×#929—21no—
36C3×C4×#67C2211yescharacteristic
37C3×#924C2211yescharacteristic, complemented
38C2×C3×Dic3⋊C4—21no—
39C22×C3×C3⋊C8C2211yescharacteristic, complemented
40#63983—21no—
41#63971—21no—
42#63925—24no—
43D3×(C2×D3)⋊C4—21no—
44Dic3×D12C2211yescharacteristic
45#63864C2211yescharacteristic
46#63856C2211yescharacteristic
47#63850—21no—
48C2×#3718C2211yescharacteristic, complemented
49C2×#3717C2211yescharacteristic
50C2×#3715C2211yescharacteristic
51C2×#3711C2211yescharacteristic
52#63662C2211yescharacteristic, complemented
53#63659C2211yescharacteristic, complemented
54#63657C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic, complemented
63C2×C3×#135—31no—
64C3×#547—31no—
65#5829—31no—
66#5824D311yescharacteristic, complemented
67C2×#950D311yescharacteristic, complemented
68C2×#949—31no—
69C2×#911—31no—
70#5550—31no—
71#5239—31no—
72#5239—31no—
73#5238—31no—
74#5238—31no—
75#5238—61no—
76#5190—31no—
77#5189—31no—
78#5173—31no—
79#5169—31no—
80#5165—31no—
81#5162—31no—
82#5152—31no—
83#5114—31no—
84#5111—31no—
85#5086—31no—
86#5083—31no—
87#5052—31no—
88#5048—31no—
89#5047—31no—
90#5046—31no—
91#5016—31no—
92#5014—31no—
93#5011—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×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67D411yescharacteristic
107C22×C3×Dic3—21no—
108C22×C3×Dic3—21no—
109C3×#237—22no—
110C3×#237—41no—
111C3×#235—22no—
112C3×#235—41no—
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×C3×Dic6C2311yescharacteristic
118C2×#626—21no—
119C2×D3×Dic3—21no—
120D3×D12—22no—
121D3×D12—41no—
122#3755—41no—
123#3753—22no—
124#3752—21no—
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#217—21no—
129C3×#217—21no—
130C3×#217D411yescharacteristic
131C3×#216—22no—
132C3×#215—22no—
133C3×#214—22no—
134C3×#213D414yescomplemented
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×C4⋊Dic3C2311yescharacteristic
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4—21no—
141C3×Dic3⋊C4—21no—
142C3×Dic3⋊C4D411yescharacteristic
143C3×C4×Dic3C2311yescharacteristic
144C2×C3×C3⋊C8—22no—
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147#3724—21no—
148#3722—21no—
149#3722—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152#3718—41no—
153#3717—22no—
154#3715—22no—
155#3711—22no—
156#3267—91noSylow
157C2×C3×#41—21no—
158C2×C3×#41—31no—
159C2×C3×#41—31no—
160C2×C3×#41C2×D311yescharacteristic, complemented
161C2×C3×#41C2×D311yescharacteristic, complemented
162C2×#237C2×D311yescharacteristic
163C2×D3×D4—31no—
164C2×#235C2×D311yescharacteristic
165C22×D12—31no—
166C3×#135—64no—
167C2×C3×Q16—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×D8—31no—
171C22×C3×C8—31no—
172C3×C4⋊Q8—31no—
173C3×#123—61no—
174C3×#123—61no—
175C3×C22⋊Q8—31no—
176C3×C22⋊Q8—31no—
177C3×#121—61no—
178C3×C4×D4—31no—
179C3×C4×D4—31no—
180C2×C3×C4⋊C4—61no—
181#950—24no—
182#949—64no—
183#947—31no—
184#946—31no—
185#946C2×D311yescharacteristic
186#944C2×D311yescharacteristic, complemented
187C2×#216—31no—
188C2×#216—31no—
189C2×#216C2×D311yescharacteristic, complemented
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—31no—
193C2×#215—31no—
194C2×#215—61no—
195C2×#215C2×D311yescharacteristic
196#939—21no—
197#939—61no—
198#937—61no—
199#937—61no—
200#935—21no—
201D4×Dic3—31no—
202D4×Dic3C2×D311yescharacteristic, complemented
203C2×#214—31no—
204C2×#214C2×D311yescharacteristic, complemented
205C2×#213—31no—
206C2×#213—31no—
207C2×#213—61no—
208C2×#213C2×D311yescharacteristic
209#930—31no—
210#930—31no—
211#930—61no—
212#929—21no—
213#929—61no—
214C4×#67C2×D311yescharacteristic
215C2×(C2×D3)⋊C4—61no—
216#924—31no—
217#924C2×D311yescharacteristic, complemented
218C2×Dic3⋊C4—21no—
219C2×#208—31no—
220C22×C3⋊C8C2×D311yescharacteristic, complemented
221#911—64no—
222C2×#204—31no—
223C2×ΓL(1,𝔽25)—31no—
224#894—61no—
225#884—61no—
226D3×C22⋊C4—61no—
227#875—31no—
228C4×D12—31no—
229#835—31no—
230#835—31no—
231#835—31no—
232#835—31no—
233#835—61no—
234#832—31no—
235#832—31no—
236#832—31no—
237#832—61no—
238#830—31no—
239#830—31no—
240#830—31no—
241#830—61no—
242#821—31no—
243(C2×D3)⋊C8—31no—
244#817—31no—
245#816—31no—
246#815—31no—
247Dic3⋊C8—31no—
248#810—31no—
249#809—31no—
250#809—31no—
251#808—31no—
252C4⋊(C3⋊C8)—31no—
253#803—31no—
254C23×C32—21no—
255C23×C32C2×D411yescharacteristic
256C22×C3⋊D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3C2×D411yescharacteristic
259C2×D32—42no—
260C2×D32—42no—
261C2×D32—81no—
262C32×Q8—21no—
263C32×Q8—21no—
264C32×D4—21no—
265C32×D4—42no—
266C32×D4C2×D412yes—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—42no—
271C2×C32×C4C2×D411yescharacteristic
272C2×C32×C4C2411yescharacteristic
273#638—81no—
274C2×C3⋊Dic3—21no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—21no—
277C3×#67—41no—
278C3×#67—42no—
279C3×#67—42no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—42no—
284C2×C3×Dic3—42no—
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C3×D12—21no—
289C3×D12C2×D412yes—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—42no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297#626—42no—
298D3×Dic3—81no—
299C3⋊(C3⋊C8)—21no—
300C3⋊(C3⋊C8)—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yes—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—31no—
305#547—31no—
306#546—91no—
307#497—91no—
308#470—91no—
309#465—91no—
310#463—91no—
311#461—91no—
312#452—91no—
313#452—91no—
314#450—91no—
315#449—91no—
316#442—91no—
317#435—91no—
318C23×D3—61no—
319C23×D3—61no—
320C3×#41—22no—
321C3×#41—22no—
322C3×#41—42no—
323C3×#41—41no—
324C3×#41—41no—
325C3×#41—42no—
326C3×#41—62no—
327C3×#41—62no—
328C3×#41—121no—
329C3×#41—121no—
330C2×C3×Q8—21no—
331C2×C3×Q8—31no—
332C2×C3×Q8—31no—
333C2×C3×Q8C22×D311yescharacteristic
334C2×C3×Q8C22×D311yescharacteristic
335C2×C3×D4—21no—
336C2×C3×D4—21no—
337C2×C3×D4—21no—
338C2×C3×D4—31no—
339C2×C3×D4—31no—
340C2×C3×D4—41no—
341C2×C3×D4—61no—
342C2×C3×D4—61no—
343C2×C3×D4C22×D311yescharacteristic
344C2×C3×D4C22×D311yescharacteristic
345C22×C3×C4—21no—
346C22×C3×C4—21no—
347C22×C3×C4—21no—
348C22×C3×C4—31no—
349C22×C3×C4—41no—
350C22×C3×C4—61no—
351C22×C3×C4—61no—
352C22×C3×C4—61no—
353C22×C3×C4C22×D311yescharacteristic
354C22×C3×C4C22×D311yescharacteristic
355C2×#67—21no—
356C2×#67—21no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67—121no—
361C2×#67#6711yescharacteristic
362C22×Dic3—21no—
363C22×Dic3—21no—
364C22×Dic3—61no—
365#237—22no—
366#237—41no—
367D3×D4—62no—
368D3×D4—121no—
369#235—22no—
370#235—41no—
371C2×D12—31no—
372C2×D12—31no—
373C2×D12—61no—
374C2×D12—62no—
375C2×D12—61no—
376C2×D12—121no—
377C2×D12C22×D311yescharacteristic
378C2×C4×D3—21no—
379C2×C4×D3—61no—
380C2×C4×D3C22×D311yescharacteristic
381C2×Dic6C22×D311yescharacteristic
382C2×Dic6C22×D311yescharacteristic
383C3×Q16—62no—
384C3×SD16—62no—
385C3×SD16—62no—
386C3×D8—34no—
387C2×C3×C8—31no—
388C2×C3×C8—31no—
389C2×C3×C8—62no—
390C3×C4⋊C4—31no—
391C3×C4⋊C4—31no—
392C3×C4⋊C4—61no—
393C3×C4⋊C4—61no—
394C3×C4⋊C4—61no—
395C3×C4⋊C4—61no—
396C3×C22⋊C4—31no—
397C3×C22⋊C4—31no—
398C3×C22⋊C4—61no—
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C42—31no—
402#217—21no—
403#217—21no—
404#217—61no—
405#217—61no—
406#217#6711yescharacteristic
407#216—22no—
408#216—121no—
409#216—121no—
410#215—22no—
411#215—62no—
412#215—62no—
413#215—121no—
414#215—121no—
415#215—122no—
416#214—22no—
417#214—62no—
418#213—62no—
419#213—62no—
420#213—122no—
421#213#6714yescomplemented
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—121no—
432(C2×D3)⋊C4#6711yescharacteristic
433C4⋊Dic3—31no—
434C4⋊Dic3—31no—
435C4⋊Dic3—61no—
436C4⋊Dic3C22×D311yescharacteristic
437Dic3⋊C4—21no—
438Dic3⋊C4—21no—
439Dic3⋊C4—21no—
440Dic3⋊C4—21no—
441Dic3⋊C4—61no—
442Dic3⋊C4—61no—
443Dic3⋊C4#6711yescharacteristic
444C4×Dic3C22×D311yescharacteristic
445#208—62no—
446C2×C3⋊C8—22no—
447C2×C3⋊C8—31no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—61no—
452C2×C3⋊C8—61no—
453C2×C3⋊C8C22×D311yescharacteristic
454C2×C3⋊C8C22×D311yescharacteristic
455#204—62no—
456ΓL(1,𝔽25)—62no—
457C22×C32—22no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32—41no—
462C22×C32—41no—
463C22×C32C22×D411yescharacteristic
464C2×C3⋊D3—41no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3×D3—22no—
468C2×C3×D3—21no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473D32—84no—
474C32×C4—21no—
475C32×C4—41no—
476C32×C4C22×D411yescharacteristic
477C32×C4H(5,𝔽2)11yescharacteristic
478C3⋊Dic3—41no—
479C3×Dic3—21no—
480C3×Dic3—21no—
481C3×Dic3—21no—
482C3×Dic3—41no—
483C3×Dic3—41no—
484C3×Dic3—41no—
485C2×#41—31no—
486C2×#41—31no—
487C2×#41D3211yescharacteristic, complemented
488C22×D4—91no—
489AGL(1,ℤ/8)—184no—
490#135—64no—
491C2×Q16—31no—
492C2×Q16—91no—
493C2×SD16—31no—
494C2×SD16—31no—
495C2×SD16—91no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×D8—31no—
499C2×D8—91no—
500C2×M16—91no—
501C22×C8—31no—
502C4⋊Q8—31no—
503#124—91no—
504#123—61no—
505#123—61no—
506#123—181no—
507C22⋊Q8—31no—
508C22⋊Q8—31no—
509C22⋊Q8—91no—
510#121—61no—
511#121—91no—
512#121—181no—
513#120—181no—
514C4×D4—31no—
515C4×D4—31no—
516C4×D4—91no—
517C2×C4⋊C4—61no—
518C2×C22⋊C4—181no—
519#106—91no—
520C4⋊C8—91no—
521#103—91no—
522#103—91no—
523#103—91no—
524#102—91no—
525#102—91no—
526#102—91no—
527C22⋊C8—91no—
528C22⋊C8—91no—
529#97—91no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—31no—
534C23×C3—41no—
535C23×C3—61no—
536C23×C3D3×D411yescharacteristic
537C23×C3C2×#6711yescharacteristic
538C22×D3—21no—
539C22×D3—61no—
540C22×D3—61no—
541C22×D3—121no—
542C22×D3—122no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—241no—
547C22×D3—241no—
548C22×D3C2×#6711yescharacteristic
549C3×Q8—22no—
550C3×Q8—21no—
551C3×Q8—21no—
552C3×Q8—21no—
553C3×Q8—21no—
554C3×Q8—41no—
555C3×Q8—61no—
556C3×Q8—61no—
557C3×Q8—61no—
558C3×Q8—61no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—22no—
562C3×D4—32no—
563C3×D4—41no—
564C3×D4—42no—
565C3×D4—42no—
566C3×D4—44no—
567C3×D4—61no—
568C3×D4—121no—
569C3×D4—122no—
570C3×D4—122no—
571C3×D4D3×D412yes—
572C3×D4C2×#6712yes—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—31no—
582C2×C3×C4—31no—
583C2×C3×C4—31no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—42no—
588C2×C3×C4—42no—
589C2×C3×C4—44no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—122no—
596C2×C3×C4—122no—
597C2×C3×C4—122no—
598C2×C3×C4D3×D411yescharacteristic
599C2×C3×C4C2×#6711yescharacteristic
600C2×C3×C4C23×D311yescharacteristic
601C2×C3×C4C23×D311yescharacteristic
602#67—41no—
603#67—42no—
604#67—42no—
605#67—122no—
606#67—241no—
607#67—241no—
608#67—242no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—42no—
613C2×Dic3—42no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—121no—
617C2×Dic3—241no—
618C2×Dic3C2×#6711yescharacteristic
619C2×Dic3C2×#6711yescharacteristic
620C2×Dic3C2×#6711yescharacteristic
621D12—21no—
622D12—61no—
623D12—61no—
624D12—61no—
625D12—61no—
626D12—121no—
627D12—121no—
628D12—122no—
629D12C2×#6712yes—
630C4×D3—21no—
631C4×D3—21no—
632C4×D3—42no—
633C4×D3—241no—
634Dic6—21no—
635Dic6—21no—
636Dic6—21no—
637Dic6—21no—
638C3×C8—32no—
639C3×C8—61no—
640C3⋊C8—21no—
641C3⋊C8—61no—
642C3⋊C8—61no—
643C3⋊C8—61no—
644C3⋊C8—61no—
645C3⋊C8—121no—
646C3⋊C8—121no—
647C3⋊C8C2×#6712yes—
648C2×C32—41no—
649C2×C32—42no—
650C2×C32D4211yescharacteristic
651C2×C32#57511yescharacteristic
652C2×C32#57711yescharacteristic
653C3⋊D3—81no—
654C3×D3—41no—
655C3×D3—42no—
656C24—181no—
657#41—22no—
658#41—41no—
659#41—62no—
660#41—62no—
661#41—121no—
662#41—121no—
663C2×Q8—31no—
664C2×Q8—31no—
665C2×Q8C2×D3211yescharacteristic
666C2×D4—21no—
667C2×D4—31no—
668C2×D4—31no—
669C2×D4—61no—
670C2×D4—61no—
671C2×D4—91no—
672C2×D4—181no—
673C2×D4—182no—
674C2×D4—181no—
675C2×D4—361no—
676C2×D4C2×D3211yescharacteristic
677C22×C4—21no—
678C22×C4—31no—
679C22×C4—61no—
680C22×C4—61no—
681C22×C4—61no—
682C22×C4—181no—
683C22×C4C2×D3211yescharacteristic
684Q16—62no—
685Q16—361no—
686SD16—62no—
687SD16—62no—
688SD16—182no—
689SD16—182no—
690SD16—361no—
691D8—34no—
692D8—182no—
693M16—182no—
694C2×C8—31no—
695C2×C8—31no—
696C2×C8—62no—
697C2×C8—91no—
698C2×C8—91no—
699C4⋊C4—31no—
700C4⋊C4—31no—
701C4⋊C4—61no—
702C4⋊C4—61no—
703C4⋊C4—61no—
704C4⋊C4—61no—
705C4⋊C4—91no—
706C4⋊C4—181no—
707C22⋊C4—31no—
708C22⋊C4—31no—
709C22⋊C4—61no—
710C22⋊C4—61no—
711C22⋊C4—61no—
712C22⋊C4—181no—
713C22⋊C4—181no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C42—31no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—22no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—22no—
724C22×C3—21no—
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—41no—
728C22×C3—42no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—61no—
736C22×C3—61no—
737C22×C3—62no—
738C22×C3—61no—
739C22×C3—81no—
740C22×C3—81no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3C2×D3×D411yescharacteristic
744C22×C3C22×#6711yescharacteristic
745C2×D3—21no—
746C2×D3—22no—
747C2×D3—21no—
748C2×D3—21no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—121no—
754C2×D3—121no—
755C2×D3—121no—
756C2×D3—121no—
757C2×D3—241no—
758C2×D3—241no—
759C2×D3—241no—
760C2×D3—244no—
761C2×D3—244no—
762C3×C4—21no—
763C3×C4—21no—
764C3×C4—21no—
765C3×C4—21no—
766C3×C4—41no—
767C3×C4—42no—
768C3×C4—41no—
769C3×C4—41no—
770C3×C4—61no—
771C3×C4—61no—
772C3×C4—61no—
773C3×C4—121no—
774C3×C4—121no—
775C3×C4—121no—
776C3×C4C2×D3×D411yescharacteristic
777C3×C4#100411yescharacteristic
778C3×C4#100411yescharacteristic
779C3×C4C22×#6711yescharacteristic
780Dic3—21no—
781Dic3—21no—
782Dic3—21no—
783Dic3—41no—
784Dic3—41no—
785Dic3—41no—
786Dic3—121no—
787Dic3—121no—
788Dic3—241no—
789C32#326711yescharacteristic, complemented, Sylow
790C23—21no—
791C23—31no—
792C23—61no—
793C23—181no—
794C23—362no—
795C23—362no—
796C23—721no—
797C23D3×#6711yescharacteristic
798Q8—21no—
799Q8—21no—
800Q8—61no—
801Q8—61no—
802Q8—61no—
803Q8—61no—
804D4—21no—
805D4—32no—
806D4—42no—
807D4—61no—
808D4—121no—
809D4—122no—
810D4—122no—
811D4—181no—
812D4—181no—
813D4—362no—
814D4—721no—
815D4D3×#6712yes—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—31no—
820C2×C4—31no—
821C2×C4—31no—
822C2×C4—42no—
823C2×C4—61no—
824C2×C4—61no—
825C2×C4—61no—
826C2×C4—61no—
827C2×C4—61no—
828C2×C4—122no—
829C2×C4—122no—
830C2×C4—122no—
831C2×C4—181no—
832C2×C4—721no—
833C2×C4D3×#6711yescharacteristic
834C2×C4C22×D3211yescharacteristic
835C8—32no—
836C8—61no—
837C8—181no—
838C8—181no—
839C2×C3—21no—
840C2×C3—21no—
841C2×C3—21no—
842C2×C3—41no—
843C2×C3—42no—
844C2×C3—41no—
845C2×C3—42no—
846C2×C3—81no—
847C2×C3—82no—
848C2×C3—122no—
849C2×C3—121no—
850C2×C3#576811yescharacteristic
851C2×C3#577011yescharacteristic
852C2×C3D4×#6711yescharacteristic
853C2×C3D4×#6711yescharacteristic
854C2×C3#582211yescharacteristic
855C2×C3#583711yescharacteristic
856D3—41no—
857D3—42no—
858D3—241no—
859D3—241no—
860D3—481no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—22no—
865C22—41no—
866C22—41no—
867C22—61no—
868C22—61no—
869C22—61no—
870C22—62no—
871C22—121no—
872C22—121no—
873C22—361no—
874C22—361no—
875C22—361no—
876C22—724no—
877C22C2×D3×#6711yescharacteristic
878C4—21no—
879C4—41no—
880C4—61no—
881C4—61no—
882C4—61no—
883C4—121no—
884C4—121no—
885C4—121no—
886C4—361no—
887C4C2×D3×#6711yescharacteristic
888C4#6433011yescharacteristic
889C3—21no—
890C3#8352211yescharacteristic, complemented
891C3#8392111yescharacteristic, complemented
892C2—41no—
893C2—42no—
894C2—121no—
895C2—122no—
896C2—721no—
897C2#1059545311yescharacteristic
898C2#1059545711yescharacteristic
899C2#67211yescharacteristic
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. C3×#5824C2semidirect
2. C2×C3×#950C2semidirect
3. C2×#63925C2semidirect
4. #10595067C2semidirect
5. #10592937C2semidirect
6. #10591651C2semidirect
7. #10591638C2semidirect
8. #10591608C2semidirect
9. #10591564C2semidirect
10. #10591471C2semidirect
11. #10591461C2semidirect
12. #10591430C2semidirect
13. #10591177C2semidirect
14. #10591170C2semidirect
15. #10591155C2semidirect
18. C2×C32×#41C22semidirect
27. C3×#944C22semidirect
28. C2×C3×#216C22semidirect
32. C3×D4×Dic3C22semidirect
33. C2×C3×#214C22semidirect
37. C3×#924C22semidirect
39. C22×C3×C3⋊C8C22semidirect
48. C2×#3718C22semidirect
52. #63662C22semidirect
53. #63659C22semidirect
54. #63657C22semidirect
55. #63573C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63566C22semidirect
58. #63565C22semidirect
62. #63554C22semidirect
66. #5824D3semidirect
67. C2×#950D3semidirect
134. C3×#213D4semidirect
160. C2×C3×#41C2×D3semidirect
161. C2×C3×#41C2×D3semidirect
186. #944C2×D3semidirect
189. C2×#216C2×D3semidirect
202. D4×Dic3C2×D3semidirect
204. C2×#214C2×D3semidirect
217. #924C2×D3semidirect
220. C22×C3⋊C8C2×D3semidirect
421. #213#67semidirect
487. C2×#41D32semidirect
789. C32#3267semidirect
890. C3#83522semidirect
891. C3#83921semidirect

Maximal subgroups

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

subgroupindex
C3×#58242
C2×C3×#9502
C2×#639252
#105950672
#105929372
#105916512
#105916382
#105916082
#105915642
#105914712
#105914612
#105914302
#105911772
#105911702
#105911552
#839213
#835223