Finite Group Databasebeta

← #11884277

Subgroups — #11884277

Order 1152.

1094 conjugacy classes of subgroups.

The subgroup lattice has 903 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5806C211yesmaximal, characteristic, complemented
2C2×C3×#932C211yesmaximal, characteristic, complemented
3C2×#63933C211yesmaximal, characteristic, complemented
4#10594887C211yesmaximal, characteristic, complemented
5#10592917C211yesmaximal, characteristic, complemented
6#10591519C211yesmaximal, characteristic, complemented
7#10591499C211yesmaximal, characteristic, complemented
8#10591491C211yesmaximal, characteristic, complemented
9#10591489C211yesmaximal, characteristic, complemented
10#10591461C211yesmaximal, characteristic, complemented
11#10591431C211yesmaximal, characteristic, complemented
12#10591430C211yesmaximal, characteristic, complemented
13#10591170C211yesmaximal, characteristic, complemented
14#10591147C211yesmaximal, characteristic, complemented
15#10591121C211yesmaximal, characteristic, complemented
16#83954—31nomaximal
17#83503—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C2×#3795C2211yescharacteristic, complemented
22C2×#3754C2211yescharacteristic
23C2×#3754C2211yescharacteristic
24#64133C2211yescharacteristic
25C3×#953—21no—
26C2×C3×#217—21no—
27C3×#939—21no—
28C3×#938C2211yescharacteristic
29C3×#936C2211yescharacteristic
30C3×#935—21no—
31C3×D4×Dic3C2211yescharacteristic
32C2×C3×#214C2211yescharacteristic
33C2×C3×#214C2211yescharacteristic
34C3×#932—24no—
35C2×C3×#213C2211yescharacteristic
36C2×C3×#213C2211yescharacteristic
37C3×C4×#67C2211yescharacteristic
38C3×#924C2211yescharacteristic
39C2×C3×#208C2211yescharacteristic
40#63970—21no—
41#63969—21no—
42#63933—24no—
43#63905—21no—
44Dic3×D12C2211yescharacteristic, complemented
45D3×Dic3⋊C4—21no—
46#63866C2211yescharacteristic, complemented
47#63856C2211yescharacteristic, complemented
48C2×#3719C2211yescharacteristic, complemented
49C2×#3718C2211yescharacteristic, complemented
50C2×#3715C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63659C2211yescharacteristic
53#63659C2211yescharacteristic
54#63657C2211yescharacteristic
55#63573C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64C3×#546—31no—
65#5824—31no—
66C2×#950—31no—
67#5806D311yescharacteristic, complemented
68C2×#932D311yescharacteristic, complemented
69C2×#912—31no—
70#5551—31no—
71#5239—31no—
72#5239—31no—
73#5218—31no—
74#5218—31no—
75#5218—61no—
76#5173—31no—
77#5171—31no—
78#5167—31no—
79#5162—31no—
80#5158—31no—
81#5153—31no—
82#5152—31no—
83#5137—31no—
84#5127—31no—
85#5060—31no—
86#5057—31no—
87#5052—31no—
88#5047—31no—
89#5041—31no—
90#5037—31no—
91#5019—31no—
92#5014—31no—
93#5011—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×#634C2311yescharacteristic
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67D411yescharacteristic
106C22×C3×Dic3—21no—
107C22×C3×Dic3—21no—
108C3×#237—22no—
109C3×#237—41no—
110C3×#235—22no—
111C3×#235—41no—
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#625—21no—
118C2×D3×Dic3—21no—
119C2×D3×Dic3—21no—
120#3795—22no—
121#3795—41no—
122#3757—21no—
123#3754—22no—
124#3754—41no—
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126#3750—21no—
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×#217D411yescharacteristic
135C3×#214—22no—
136C3×#214—22no—
137C3×#213—22no—
138C3×#213D414yescomplemented
139C3×(C2×D3)⋊C4D411yescharacteristic
140C3×C4⋊Dic3C2311yescharacteristic
141C3×Dic3⋊C4—21no—
142C3×Dic3⋊C4D411yescharacteristic
143C3×C4×Dic3C2311yescharacteristic
144C3×#208—22no—
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147#3724—21no—
148Dic3⋊Dic3—21no—
149Dic3⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152#3719—22no—
153#3718—41no—
154#3715—22no—
155D3×C3⋊C8—22no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C22×C3×D4—21no—
160C22×C3×D4C2×D311yescharacteristic
161C22×C3×D4C2×D311yescharacteristic
162C2×#237—31no—
163C2×#237C2×D311yescharacteristic
164C2×#235—31no—
165C2×#235C2×D311yescharacteristic
166C3×AGL(1,ℤ/8)—64no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C2×C3×D8—31no—
170C2×C3×D8—31no—
171C2×C3×M16—31no—
172C3×#124—31no—
173C3×#123—61no—
174C3×C22⋊Q8—31no—
175C3×#121—31no—
176C3×#121—61no—
177C3×#120—61no—
178C3×C4×D4—31no—
179C3×C4×D4—31no—
180C2×C3×C22⋊C4—61no—
181#953—21no—
182C2×#217—21no—
183#950—64no—
184#946—31no—
185#944—31no—
186C2×#216—31no—
187C2×#216—31no—
188C2×#216—31no—
189C2×#215—31no—
190#939—21no—
191#939—61no—
192#938—61no—
193#938C2×D311yescharacteristic
194#936C2×D311yescharacteristic
195#935—21no—
196#935—61no—
197D4×Dic3—31no—
198D4×Dic3C2×D311yescharacteristic
199C2×#214—31no—
200C2×#214—31no—
201C2×#214—31no—
202C2×#214—31no—
203C2×#214—31no—
204C2×#214—61no—
205C2×#214—61no—
206C2×#214C2×D311yescharacteristic
207C2×#214C2×D311yescharacteristic
208#932—24no—
209C2×#213C2×D311yescharacteristic
210C2×#213C2×D311yescharacteristic
211#929—61no—
212C4×#67C2×D311yescharacteristic
213#924—31no—
214#924—31no—
215#924—31no—
216#924—61no—
217#924C2×D311yescharacteristic
218C2×Dic3⋊C4—61no—
219C2×#208C2×D311yescharacteristic
220C22×C3⋊C8—31no—
221#912—64no—
222C2×Dic12—31no—
223C2×D3×C8—31no—
224D3×C4⋊C4—61no—
225#883—61no—
226#883—61no—
227C4×D12—31no—
228#869—31no—
229#835—31no—
230#835—31no—
231#832—31no—
232#832—31no—
233#832—31no—
234#832—31no—
235#832—31no—
236#832—61no—
237#832—61no—
238#830—31no—
239#830—31no—
240#830—31no—
241#830—61no—
242(C2×D3)⋊C8—31no—
243#817—31no—
244#816—31no—
245#816—31no—
246#815—31no—
247Dic3⋊C8—31no—
248#810—31no—
249#810—31no—
250#809—31no—
251#808—31no—
252C4⋊(C3⋊C8)—31no—
253#803—31no—
254C23×C32—21no—
255C23×C32—21no—
256C23×C32—42no—
257C23×C32—42no—
258C23×C32—81no—
259C23×C32C2×D411yescharacteristic
260C22×C3×D3—21no—
261C22×C3×D3C2×D411yescharacteristic
262C32×D4—21no—
263C32×D4—21no—
264C32×D4—21no—
265C32×D4—42no—
266C32×D4C2×D412yes—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2411yescharacteristic
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—21no—
273#634—21no—
274#634—21no—
275C3×#67—41no—
276C3×#67—42no—
277C3×#67—42no—
278C3×#67—81no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—42no—
283C2×C3×Dic3—81no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C3×D12—21no—
288C3×D12C2×D412yes—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×C4×D3—42no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296#625—42no—
297D3×Dic3—42no—
298D3×Dic3—42no—
299C3⋊(C3⋊C8)—21no—
300C3⋊(C3⋊C8)—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yes—
303C2×AGL(1,ℤ/8)—31no—
304C2×#135—91no—
305#547—91no—
306#546—31no—
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—
318C24×C3—21no—
319C24×C3—21no—
320C24×C3—41no—
321C3×#41—62no—
322C3×#41—62no—
323C3×#41—121no—
324C3×#41—121no—
325C2×C3×Q8—31no—
326C2×C3×Q8—31no—
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—31no—
335C2×C3×D4—41no—
336C2×C3×D4—42no—
337C2×C3×D4—41no—
338C2×C3×D4—41no—
339C2×C3×D4—42no—
340C2×C3×D4—61no—
341C2×C3×D4—61no—
342C2×C3×D4—61no—
343C2×C3×D4C22×D311yescharacteristic
344C2×C3×D4C22×D311yescharacteristic
345C2×C3×D4C22×D311yescharacteristic
346C2×C3×D4C22×D311yescharacteristic
347C22×C3×C4—21no—
348C22×C3×C4—31no—
349C22×C3×C4—61no—
350C22×C3×C4—61no—
351C22×C3×C4—61no—
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C2×#67—21no—
355C2×#67—21no—
356C2×#67—21no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67#6711yescharacteristic
360C22×Dic3—21no—
361C22×Dic3—21no—
362C22×Dic3—61no—
363C22×Dic3—61no—
364#237—22no—
365#237—41no—
366#237—62no—
367#237—121no—
368#235—22no—
369#235—41no—
370#235—62no—
371#235—121no—
372C2×D12C22×D311yescharacteristic
373C2×C4×D3—21no—
374C2×C4×D3—61no—
375C2×C4×D3—61no—
376C2×C4×D3C22×D311yescharacteristic
377C2×Dic6—31no—
378C2×Dic6—31no—
379C2×Dic6—61no—
380C2×Dic6C22×D311yescharacteristic
381C2×Dic6C22×D311yescharacteristic
382C3×SD16—62no—
383C3×SD16—62no—
384C3×D8—34no—
385C3×D8—62no—
386C3×M16—62no—
387C2×C3×C8—31no—
388C2×C3×C8—31no—
389C3×C4⋊C4—31no—
390C3×C4⋊C4—31no—
391C3×C4⋊C4—61no—
392C3×C22⋊C4—31no—
393C3×C22⋊C4—31no—
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399C3×C42—31no—
400#217—21no—
401#217—21no—
402#217—21no—
403#217—21no—
404#217—21no—
405#217—61no—
406#217—61no—
407#217—61no—
408#217—61no—
409#217—121no—
410#217#6711yescharacteristic
411#216—62no—
412#216—121no—
413#216—121no—
414#215—62no—
415#214—22no—
416#214—22no—
417#214—62no—
418#214—62no—
419#214—62no—
420#214—122no—
421#214—121no—
422#214—121no—
423#214—122no—
424#213—22no—
425#213#6714yescomplemented
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4#6711yescharacteristic
429C4⋊Dic3—31no—
430C4⋊Dic3—31no—
431C4⋊Dic3—61no—
432C4⋊Dic3—61no—
433C4⋊Dic3—61no—
434C4⋊Dic3C22×D311yescharacteristic
435Dic3⋊C4—21no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438Dic3⋊C4—61no—
439Dic3⋊C4—61no—
440Dic3⋊C4—61no—
441Dic3⋊C4—61no—
442Dic3⋊C4—121no—
443Dic3⋊C4#6711yescharacteristic
444C4×Dic3C22×D311yescharacteristic
445#208—22no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—31no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—61no—
451C2×C3⋊C8—61no—
452C2×C3⋊C8—62no—
453C2×C3⋊C8C22×D311yescharacteristic
454C2×C3⋊C8C22×D311yescharacteristic
455Dic12—62no—
456D3×C8—62no—
457C22×C32—21no—
458C22×C32—22no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32—41no—
462C22×C32—41no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32—84no—
467C22×C32C22×D411yescharacteristic
468C2×C3×D3—22no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C32×C4—21no—
475C32×C4C22×D411yescharacteristic
476C32×C4H(5,𝔽2)11yescharacteristic
477C3⋊Dic3—41no—
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×#41—91no—
488C22×D4D3211yescharacteristic
489AGL(1,ℤ/8)—64no—
490#135—184no—
491C2×Q16—91no—
492C2×Q16—91no—
493C2×SD16—31no—
494C2×SD16—31no—
495C2×SD16—91no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×D8—31no—
499C2×D8—31no—
500C2×M16—31no—
501C22×C8—91no—
502C4⋊Q8—91no—
503#124—31no—
504#123—61no—
505#123—181no—
506#123—181no—
507C22⋊Q8—31no—
508C22⋊Q8—91no—
509C22⋊Q8—91no—
510#121—31no—
511#121—61no—
512#121—181no—
513#120—61no—
514C4×D4—31no—
515C4×D4—31no—
516C4×D4—91no—
517C2×C4⋊C4—181no—
518C2×C22⋊C4—61no—
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—21no—
534C23×C3—21no—
535C23×C3—31no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—42no—
539C23×C3—42no—
540C23×C3—42no—
541C23×C3—42no—
542C23×C3—44no—
543C23×C3—61no—
544C23×C3—82no—
545C23×C3—81no—
546C23×C3—81no—
547C23×C3—82no—
548C23×C3D3×D411yescharacteristic
549C23×C3C2×#6711yescharacteristic
550C22×D3—21no—
551C22×D3C2×#6711yescharacteristic
552C3×Q8—61no—
553C3×Q8—61no—
554C3×Q8—61no—
555C3×Q8—61no—
556C3×D4—22no—
557C3×D4—21no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—21no—
562C3×D4—21no—
563C3×D4—22no—
564C3×D4—32no—
565C3×D4—41no—
566C3×D4—41no—
567C3×D4—42no—
568C3×D4—42no—
569C3×D4—44no—
570C3×D4—61no—
571C3×D4—121no—
572C3×D4—122no—
573C3×D4—122no—
574C3×D4—241no—
575C3×D4D3×D412yes—
576C3×D4C2×#6712yes—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—31no—
584C2×C3×C4—31no—
585C2×C3×C4—31no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—122no—
594C2×C3×C4—122no—
595C2×C3×C4—241no—
596C2×C3×C4D3×D411yescharacteristic
597C2×C3×C4C2×#6711yescharacteristic
598C2×C3×C4C23×D311yescharacteristic
599C2×C3×C4C23×D311yescharacteristic
600#67—41no—
601#67—42no—
602#67—42no—
603#67—81no—
604#67—122no—
605#67—122no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—42no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—81no—
615C2×Dic3—121no—
616C2×Dic3—121no—
617C2×Dic3—122no—
618C2×Dic3—122no—
619C2×Dic3C2×#6711yescharacteristic
620C2×Dic3C2×#6711yescharacteristic
621C2×Dic3C2×#6711yescharacteristic
622D12—21no—
623D12C2×#6712yes—
624C4×D3—21no—
625C4×D3—21no—
626C4×D3—42no—
627C4×D3—122no—
628C4×D3—122no—
629Dic6—21no—
630Dic6—21no—
631Dic6—21no—
632Dic6—21no—
633Dic6—61no—
634Dic6—61no—
635Dic6—61no—
636Dic6—61no—
637Dic6—121no—
638Dic6—121no—
639C3×C8—32no—
640C3×C8—61no—
641C3⋊C8—21no—
642C3⋊C8—61no—
643C3⋊C8—61no—
644C3⋊C8—61no—
645C3⋊C8—61no—
646C3⋊C8—121no—
647C3⋊C8—121no—
648C3⋊C8C2×#6712yes—
649C2×C32—41no—
650C2×C32—42no—
651C2×C32—81no—
652C2×C32D4211yescharacteristic
653C2×C32#57511yescharacteristic
654C2×C32#57711yescharacteristic
655C3×D3—41no—
656C3×D3—42no—
657C24—21no—
658#41—62no—
659#41—62no—
660#41—121no—
661#41—121no—
662#41—182no—
663#41—361no—
664C2×Q8—31no—
665C2×Q8—31no—
666C2×Q8—91no—
667C2×D4—22no—
668C2×D4—21no—
669C2×D4—31no—
670C2×D4—31no—
671C2×D4—41no—
672C2×D4—61no—
673C2×D4—61no—
674C2×D4—61no—
675C2×D4—181no—
676C2×D4C2×D3211yescharacteristic
677C2×D4C2×D3211yescharacteristic
678C22×C4—31no—
679C22×C4—61no—
680C22×C4—61no—
681C22×C4—61no—
682C22×C4—181no—
683C22×C4—181no—
684C22×C4C2×D3211yescharacteristic
685Q16—182no—
686Q16—361no—
687SD16—62no—
688SD16—62no—
689SD16—182no—
690SD16—182no—
691SD16—361no—
692D8—34no—
693D8—62no—
694M16—62no—
695C2×C8—31no—
696C2×C8—31no—
697C2×C8—91no—
698C2×C8—91no—
699C2×C8—182no—
700C4⋊C4—31no—
701C4⋊C4—31no—
702C4⋊C4—61no—
703C4⋊C4—91no—
704C4⋊C4—181no—
705C4⋊C4—181no—
706C4⋊C4—181no—
707C4⋊C4—181no—
708C22⋊C4—31no—
709C22⋊C4—31no—
710C22⋊C4—61no—
711C22⋊C4—61no—
712C22⋊C4—61no—
713C22⋊C4—61no—
714C22⋊C4—61no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C22⋊C4—181no—
718C42—31no—
719C22×C3—22no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—22no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—22no—
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—42no—
732C22×C3—42no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—61no—
744C22×C3—61no—
745C22×C3—62no—
746C22×C3—61no—
747C22×C3—81no—
748C22×C3—81no—
749C22×C3—81no—
750C22×C3—81no—
751C22×C3—84no—
752C22×C3—84no—
753C22×C3—88no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3C2×D3×D411yescharacteristic
757C22×C3C22×#6711yescharacteristic
758C2×D3—21no—
759C2×D3—22no—
760C2×D3—21no—
761C2×D3—21no—
762C2×D3—41no—
763C2×D3—41no—
764C3×C4—21no—
765C3×C4—21no—
766C3×C4—21no—
767C3×C4—21no—
768C3×C4—41no—
769C3×C4—61no—
770C3×C4—61no—
771C3×C4—61no—
772C3×C4—121no—
773C3×C4—121no—
774C3×C4—121no—
775C3×C4C2×D3×D411yescharacteristic
776C3×C4#100411yescharacteristic
777C3×C4#100411yescharacteristic
778C3×C4C22×#6711yescharacteristic
779Dic3—21no—
780Dic3—21no—
781Dic3—21no—
782Dic3—41no—
783Dic3—41no—
784Dic3—41no—
785Dic3—121no—
786Dic3—121no—
787Dic3—121no—
788Dic3—121no—
789Dic3—241no—
790Dic3—241no—
791C32#326711yescharacteristic, complemented, Sylow
792C23—21no—
793C23—21no—
794C23—31no—
795C23—42no—
796C23—42no—
797C23—61no—
798C23—81no—
799C23D3×#6711yescharacteristic
800Q8—61no—
801Q8—61no—
802Q8—61no—
803Q8—61no—
804Q8—181no—
805Q8—181no—
806D4—21no—
807D4—21no—
808D4—21no—
809D4—32no—
810D4—42no—
811D4—61no—
812D4—121no—
813D4—122no—
814D4—122no—
815D4—241no—
816D4—362no—
817D4D3×#6712yes—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—31no—
821C2×C4—31no—
822C2×C4—31no—
823C2×C4—61no—
824C2×C4—61no—
825C2×C4—61no—
826C2×C4—61no—
827C2×C4—61no—
828C2×C4—122no—
829C2×C4—122no—
830C2×C4—181no—
831C2×C4—181no—
832C2×C4—241no—
833C2×C4—362no—
834C2×C4—362no—
835C2×C4D3×#6711yescharacteristic
836C2×C4C22×D3211yescharacteristic
837C8—32no—
838C8—61no—
839C8—181no—
840C8—181no—
841C2×C3—21no—
842C2×C3—21no—
843C2×C3—21no—
844C2×C3—42no—
845C2×C3—41no—
846C2×C3—42no—
847C2×C3—41no—
848C2×C3—42no—
849C2×C3—82no—
850C2×C3—82no—
851C2×C3—81no—
852C2×C3—81no—
853C2×C3—122no—
854C2×C3—121no—
855C2×C3#577311yescharacteristic
856C2×C3#577511yescharacteristic
857C2×C3D4×#6711yescharacteristic
858C2×C3D4×#6711yescharacteristic
859C2×C3#582211yescharacteristic
860C2×C3#583611yescharacteristic
861D3—41no—
862D3—42no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—22no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—61no—
873C22—61no—
874C22—61no—
875C22—62no—
876C22—84no—
877C22—121no—
878C22—121no—
879C22C2×D3×#6711yescharacteristic
880C4—21no—
881C4—61no—
882C4—61no—
883C4—61no—
884C4—121no—
885C4—121no—
886C4—121no—
887C4—361no—
888C4—361no—
889C4C2×D3×#6711yescharacteristic
890C4#6433011yescharacteristic
891C3—21no—
892C3#8350311yescharacteristic, complemented
893C3#8395411yescharacteristic, complemented
894C2—41no—
895C2—42no—
896C2—81no—
897C2—121no—
898C2—122no—
899C2#1059509511yescharacteristic
900C2#1059510611yescharacteristic
901C2#67211yescharacteristic
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. C3×#5806C2semidirect
2. C2×C3×#932C2semidirect
3. C2×#63933C2semidirect
4. #10594887C2semidirect
5. #10592917C2semidirect
6. #10591519C2semidirect
7. #10591499C2semidirect
8. #10591491C2semidirect
9. #10591489C2semidirect
10. #10591461C2semidirect
11. #10591431C2semidirect
12. #10591430C2semidirect
13. #10591170C2semidirect
14. #10591147C2semidirect
15. #10591121C2semidirect
21. C2×#3795C22semidirect
44. Dic3×D12C22semidirect
46. #63866C22semidirect
47. #63856C22semidirect
48. C2×#3719C22semidirect
49. C2×#3718C22semidirect
50. C2×#3715C22semidirect
51. C2×D3×C3⋊C8C22semidirect
55. #63573C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
58. #63566C22semidirect
59. #63565C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
67. #5806D3semidirect
68. C2×#932D3semidirect
138. C3×#213D4semidirect
425. #213#67semidirect
791. C32#3267semidirect
892. C3#83503semidirect
893. C3#83954semidirect

Maximal subgroups

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

subgroupindex
C3×#58062
C2×C3×#9322
C2×#639332
#105948872
#105929172
#105915192
#105914992
#105914912
#105914892
#105914612
#105914312
#105914302
#105911702
#105911472
#105911212
#839543
#835033