Finite Group Databasebeta

← #11884308

Subgroups — #11884308

Order 1152.

1062 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#914C211yesmaximal, characteristic, complemented
2#10595358C211yesmaximal, characteristic, complemented
3#10595229C211yesmaximal, characteristic, complemented
4C2×#63810C211yesmaximal, characteristic, complemented
5#10592870C211yesmaximal, characteristic, complemented
6C3×#5167C211yesmaximal, characteristic, complemented
7#10591656C211yesmaximal, characteristic, complemented
8#10591597C211yesmaximal, characteristic, complemented
9#10591564C211yesmaximal, characteristic, complemented
10#10591520C211yesmaximal, characteristic, complemented
11#10591458C211yesmaximal, characteristic, complemented
12#10591431C211yesmaximal, characteristic, complemented
13#10590854C211yesmaximal, characteristic, complemented
14#10590771C211yesmaximal, characteristic, complemented
15#10590736C211yesmaximal, characteristic, complemented
16#83954—31nomaximal
17#81882—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×#3796C2211yescharacteristic
21C2×#3796C2211yescharacteristic, complemented
22C2×C32×SD16C2211yescharacteristic
23#64155C2211yescharacteristic, complemented
24#64147C2211yescharacteristic
25C2×C8×C3⋊D3C2211yescharacteristic, complemented
26C3×#944C2211yescharacteristic, complemented
27C2×C3×#216C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic
29C3×#936C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C3×#914—24no—
33C2×C3×Dic12C2211yescharacteristic, complemented
34C2×C3×D24C2211yescharacteristic
35C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
36#63977—21no—
37#63971—21no—
38#63969—21no—
39D3×#217—21no—
40C4×#626C2211yescharacteristic
41Dic3×D12C2211yescharacteristic
42Dic3×D12C2211yescharacteristic, complemented
43#63886—21no—
44#63884—21no—
45D3×Dic3⋊C4—21no—
46#63856C2211yescharacteristic
47#63856C2211yescharacteristic
48#63850—21no—
49C2×#3715C2211yescharacteristic
50C2×#3715C2211yescharacteristic, complemented
51#63810—24no—
52#63662C2211yescharacteristic, complemented
53#63659C2211yescharacteristic
54#63644C2211yescharacteristic, complemented
55C3×#815C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic, complemented
61#63557C2211yescharacteristic, complemented
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
63C2×C3×AGL(1,ℤ/8)—31no—
64#5824—31no—
65#5806—31no—
66C2×#919—31no—
67C2×#914D311yescharacteristic, complemented
68C2×#912—31no—
69#5726—31no—
70#5676—31no—
71C3×#497—31no—
72#5239—31no—
73#5218—31no—
74#5189—31no—
75#5187—31no—
76#5187—31no—
77#5173—31no—
78#5172—31no—
79#5171—31no—
80#5171—31no—
81#5171—61no—
82#5169—31no—
83#5167D311yescharacteristic, complemented
84#5162—31no—
85#5158—31no—
86#5153—31no—
87#5152—31no—
88#5137—31no—
89#5127—31no—
90#5083—31no—
91#5057—31no—
92#4711—31no—
93#4706—31no—
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×C3×#67—21no—
100C3×#239—22no—
101C3×#239—41no—
102C3×D3×D4—22no—
103C3×D3×D4—41no—
104C2×C3×D12—21no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×#626—21no—
112C2×#626—21no—
113C2×#626D411yescharacteristic
114C2×D3×Dic3—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117C2×D3×Dic3—21no—
118#3796—22no—
119#3796—22no—
120#3796—41no—
121#3796—41no—
122C32×SD16—22no—
123C2×C32×C8C2311yescharacteristic
124#3757—21no—
125#3752—21no—
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128#3750—21no—
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C8×C3⋊D3—22no—
131C3×#217—21no—
132C3×#217—21no—
133C3×#216—41no—
134C3×#215—22no—
135C3×#214—41no—
136C3×#213—22no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×Dic12—22no—
143C3×D24D414yescomplemented
144C3×ΓL(1,𝔽25)—22no—
145#3724—21no—
146#3724—21no—
147Dic3⋊Dic3D411yescharacteristic
148#3722D411yescharacteristic
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3—21no—
153(C2×D3)⋊Dic3D411yescharacteristic
154#3715—22no—
155#3715—22no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C22×C3×D4—31no—
159C2×#239—31no—
160C2×#239—31no—
161C2×#239C2×D311yescharacteristic
162C2×#237—31no—
163C2×#237—31no—
164C2×D3×D4C2×D311yescharacteristic
165C3×AGL(1,ℤ/8)—64no—
166C2×C3×Q16—31no—
167C2×C3×Q16—31no—
168C2×C3×SD16—21no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16C2×D311yescharacteristic
172C2×C3×SD16C2×D311yescharacteristic
173C2×C3×D8—31no—
174C2×C3×D8—31no—
175C2×C3×M16—31no—
176C3×C4⋊Q8—31no—
177C3×#124—31no—
178#953—61no—
179C2×#217—61no—
180#946—31no—
181#946—31no—
182#946—31no—
183#946—31no—
184#946—61no—
185#944C2×D311yescharacteristic, complemented
186C2×#216C2×D311yescharacteristic, complemented
187C2×#215—31no—
188C2×#215—31no—
189C2×#215C2×D311yescharacteristic
190#939—61no—
191#939—61no—
192#938—31no—
193#938—31no—
194#938—61no—
195#936C2×D311yescharacteristic
196#935—61no—
197#935—61no—
198D4×Dic3—31no—
199D4×Dic3—31no—
200C2×#214—31no—
201C2×#214—31no—
202C2×#214C2×D311yescharacteristic
203C2×#213C2×D311yescharacteristic
204#929—61no—
205C4×#67—31no—
206#924—31no—
207#924—31no—
208C2×Dic3⋊C4—61no—
209#919—64no—
210#914—24no—
211#912—64no—
212C2×Dic12C2×D311yescharacteristic, complemented
213C2×D24C2×D311yescharacteristic
214C2×ΓL(1,𝔽25)C2×D311yescharacteristic
215C2×D3×C8—31no—
216C2×D3×C8—31no—
217C2×D3×C8—61no—
218#895—61no—
219#894—61no—
220#894—61no—
221D3×C4⋊C4—61no—
222#884—61no—
223#883—61no—
224#882—61no—
225D3×C22⋊C4—61no—
226C4×D12—31no—
227C4×D12—31no—
228C4×D12—31no—
229C3×#97—31no—
230#835—31no—
231#835—31no—
232#835—31no—
233#835—31no—
234#835—61no—
235#832—31no—
236#832—31no—
237#832—31no—
238#832—31no—
239#832—61no—
240#830—31no—
241#821—31no—
242#821—31no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8—31no—
245(C2×D3)⋊C8—31no—
246#817—31no—
247#817—31no—
248#817—61no—
249#816—31no—
250#816—31no—
251#815C2×D311yescharacteristic, complemented
252Dic3⋊C8—31no—
253C4⋊(C3⋊C8)—31no—
254C23×C32—21no—
255C22×C3⋊D3C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3—81no—
261C22×C3×D3C2×D411yescharacteristic
262C32×Q8—21no—
263C32×Q8—21no—
264C32×D4—21no—
265C32×D4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2411yescharacteristic
268#638—81no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3C2×D411yescharacteristic
272C4×C3⋊D3—21no—
273C4×C3⋊D3—21no—
274C3×#67—42no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—42no—
283C3×D12C2×D412yes—
284C3×D12C2×D412yes—
285C3×C4×D3—21no—
286C3×C4×D3—21no—
287C3×C4×D3—42no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292#626—41no—
293#626—42no—
294#626—42no—
295D3×Dic3—42no—
296D3×Dic3—42no—
297D3×Dic3—42no—
298D3×Dic3—81no—
299C32×C8C2×D412yes—
300C3⋊(C3⋊C8)—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C2×AGL(1,ℤ/8)—31no—
304C2×#135—91no—
305#547—91no—
306#546—91no—
307#497—31no—
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—61no—
319C23×D3—21no—
320C3×#41—62no—
321C3×#41—121no—
322C2×C3×Q8—21no—
323C2×C3×Q8—31no—
324C2×C3×Q8—31no—
325C2×C3×Q8C22×D311yescharacteristic
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×D4—21no—
328C2×C3×D4—31no—
329C2×C3×D4—31no—
330C2×C3×D4—61no—
331C2×C3×D4—61no—
332C2×C3×D4—62no—
333C2×C3×D4—121no—
334C2×C3×D4C22×D311yescharacteristic
335C2×C3×D4C22×D311yescharacteristic
336C22×C3×C4—31no—
337C22×C3×C4—61no—
338C2×#67—21no—
339C2×#67—31no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—121no—
345C22×Dic3—61no—
346C22×Dic3—61no—
347C22×Dic3—61no—
348C22×Dic3—61no—
349#239—22no—
350#239—41no—
351#239—62no—
352#239—62no—
353#239—121no—
354#239—121no—
355#237—62no—
356#237—62no—
357#237—121no—
358#237—121no—
359D3×D4—22no—
360D3×D4—41no—
361C2×D12—21no—
362C2×D12—31no—
363C2×D12—61no—
364C2×D12—61no—
365C2×D12C22×D311yescharacteristic
366C2×D12C22×D311yescharacteristic
367C2×C4×D3—21no—
368C2×C4×D3—31no—
369C2×C4×D3—31no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—61no—
374C2×C4×D3—61no—
375C2×C4×D3C22×D311yescharacteristic
376C2×Dic6C22×D311yescharacteristic
377C2×Dic6C22×D311yescharacteristic
378C3×Q16—62no—
379C3×Q16—121no—
380C3×SD16—22no—
381C3×SD16—22no—
382C3×SD16—42no—
383C3×SD16—62no—
384C3×SD16—121no—
385C3×D8—34no—
386C3×D8—62no—
387C3×M16—62no—
388C2×C3×C8—21no—
389C2×C3×C8—31no—
390C2×C3×C8—31no—
391C2×C3×C8C22×D311yescharacteristic
392C2×C3×C8C22×D311yescharacteristic
393C3×C4⋊C4—61no—
394C3×C4⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C22⋊C4—61no—
397C3×C42—31no—
398#217—21no—
399#217—21no—
400#217—31no—
401#217—61no—
402#217—61no—
403#217—61no—
404#217—61no—
405#217—61no—
406#217—61no—
407#217—121no—
408#216—41no—
409#215—22no—
410#215—62no—
411#215—62no—
412#214—41no—
413#214—62no—
414#214—62no—
415#213—22no—
416(C2×D3)⋊C4—31no—
417(C2×D3)⋊C4—31no—
418(C2×D3)⋊C4—31no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—121no—
426C4⋊Dic3—31no—
427C4⋊Dic3—31no—
428C4⋊Dic3—31no—
429C4⋊Dic3—31no—
430C4⋊Dic3—31no—
431C4⋊Dic3—61no—
432C4⋊Dic3—61no—
433Dic3⋊C4—21no—
434Dic3⋊C4—21no—
435Dic3⋊C4—31no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438Dic3⋊C4—61no—
439Dic3⋊C4—61no—
440Dic3⋊C4—61no—
441Dic3⋊C4—61no—
442Dic3⋊C4—121no—
443C4×Dic3C22×D311yescharacteristic
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—61no—
447C2×C3⋊C8C22×D311yescharacteristic
448C2×C3⋊C8C22×D311yescharacteristic
449Dic12—22no—
450D24#6714yescomplemented
451ΓL(1,𝔽25)—22no—
452D3×C8—62no—
453D3×C8—62no—
454D3×C8—122no—
455C22×C32—41no—
456C22×C32—41no—
457C22×C32—41no—
458C22×C32C22×D411yescharacteristic
459C2×C3⋊D3—21no—
460C2×C3⋊D3—21no—
461C2×C3⋊D3—21no—
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—84no—
472C32×C4—41no—
473C32×C4C22×D411yescharacteristic
474C32×C4H(5,𝔽2)11yescharacteristic
475C3⋊Dic3—21no—
476C3⋊Dic3—41no—
477C3⋊Dic3—41no—
478C3×Dic3—21no—
479C3×Dic3—21no—
480C3×Dic3—21no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C2×#41—31no—
484C2×#41—91no—
485C2×#41—91no—
486C22×D4—31no—
487AGL(1,ℤ/8)—64no—
488#135—184no—
489C2×Q16—31no—
490C2×Q16—31no—
491C2×SD16—31no—
492C2×SD16—31no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16D3211yescharacteristic
496C2×D8—31no—
497C2×D8—31no—
498C2×M16—31no—
499C22×C8—91no—
500C4⋊Q8—31no—
501#124—31no—
502#123—181no—
503#123—181no—
504#123—181no—
505C22⋊Q8—91no—
506C22⋊Q8—91no—
507C22⋊Q8—91no—
508#121—91no—
509#121—181no—
510#121—181no—
511#120—181no—
512C4×D4—91no—
513C4×D4—91no—
514C4×D4—91no—
515C2×C4⋊C4—181no—
516C2×C22⋊C4—181no—
517#106—91no—
518C4⋊C8—91no—
519#103—91no—
520#103—91no—
521#103—91no—
522#102—91no—
523#102—91no—
524#102—91no—
525C22⋊C8—91no—
526C22⋊C8—91no—
527#97—31no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—31no—
531C23×C3—41no—
532C23×C3—61no—
533C23×C3—61no—
534C23×C3—122no—
535C23×C3—122no—
536C23×C3—241no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—31no—
540C22×D3—31no—
541C22×D3—42no—
542C22×D3—42no—
543C22×D3—61no—
544C22×D3—81no—
545C22×D3D3×D411yescharacteristic
546C3×Q8—21no—
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—21no—
550C3×Q8—41no—
551C3×Q8—41no—
552C3×Q8—61no—
553C3×Q8—61no—
554C3×Q8—61no—
555C3×Q8—61no—
556C3×D4—21no—
557C3×D4—21no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—32no—
561C3×D4—32no—
562C3×D4—41no—
563C3×D4—41no—
564C3×D4—61no—
565C3×D4—61no—
566C3×D4—122no—
567C3×D4—122no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—31no—
572C2×C3×C4—31no—
573C2×C3×C4—31no—
574C2×C3×C4—41no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—122no—
580C2×C3×C4C23×D311yescharacteristic
581C2×C3×C4C23×D311yescharacteristic
582#67—42no—
583#67—121no—
584#67—122no—
585#67—122no—
586#67—241no—
587#67—241no—
588#67—242no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—31no—
592C2×Dic3—31no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—121no—
599C2×Dic3—121no—
600C2×Dic3—122no—
601C2×Dic3—122no—
602C2×Dic3—122no—
603C2×Dic3—241no—
604C2×Dic3D3×D411yescharacteristic
605C2×Dic3D3×D411yescharacteristic
606C2×Dic3D3×D411yescharacteristic
607D12—21no—
608D12—21no—
609D12—42no—
610D12—121no—
611D12—122no—
612D12—122no—
613D12C2×#6712yes—
614D12C2×#6712yes—
615C4×D3—21no—
616C4×D3—21no—
617C4×D3—42no—
618C4×D3—61no—
619C4×D3—61no—
620C4×D3—61no—
621C4×D3—61no—
622C4×D3—121no—
623C4×D3—121no—
624C4×D3—122no—
625C4×D3—122no—
626C4×D3—122no—
627C4×D3—241no—
628Dic6—21no—
629Dic6—21no—
630Dic6—21no—
631Dic6—21no—
632C3×C8—22no—
633C3×C8—61no—
634C3×C8—61no—
635C3×C8D3×D412yes—
636C3×C8C2×#6712yes—
637C3⋊C8—21no—
638C3⋊C8—21no—
639C3⋊C8—61no—
640C3⋊C8—61no—
641C3⋊C8—121no—
642C2×C32—81no—
643C2×C32D4211yescharacteristic
644C2×C32#57511yescharacteristic
645C2×C32#57711yescharacteristic
646C3⋊D3—41no—
647C3×D3—41no—
648C3×D3—42no—
649C3×D3—42no—
650C24—61no—
651#41—62no—
652#41—121no—
653#41—182no—
654#41—182no—
655#41—361no—
656#41—361no—
657C2×Q8—31no—
658C2×Q8—31no—
659C2×Q8C2×D3211yescharacteristic
660C2×D4—31no—
661C2×D4—31no—
662C2×D4—61no—
663C2×D4—61no—
664C2×D4—62no—
665C2×D4—91no—
666C2×D4—121no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4—181no—
670C2×D4C2×D3211yescharacteristic
671C22×C4—31no—
672C22×C4—61no—
673C22×C4—91no—
674C22×C4—181no—
675C22×C4—181no—
676C22×C4—181no—
677C22×C4—181no—
678Q16—62no—
679Q16—121no—
680SD16—22no—
681SD16—62no—
682SD16—121no—
683SD16—182no—
684SD16—182no—
685D8—34no—
686D8—62no—
687M16—62no—
688C2×C8—31no—
689C2×C8—31no—
690C2×C8—91no—
691C2×C8—182no—
692C2×C8C2×D3211yescharacteristic
693C4⋊C4—61no—
694C4⋊C4—61no—
695C4⋊C4—91no—
696C4⋊C4—91no—
697C4⋊C4—91no—
698C4⋊C4—181no—
699C4⋊C4—181no—
700C4⋊C4—181no—
701C22⋊C4—61no—
702C22⋊C4—61no—
703C22⋊C4—91no—
704C22⋊C4—91no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C22⋊C4—181no—
711C42—31no—
712C22×C3—21no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—62no—
720C22×C3—62no—
721C22×C3—61no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—81no—
725C22×C3—81no—
726C22×C3—81no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3—244no—
732C22×C3C2×D3×D411yescharacteristic
733C22×C3C2×D3×D411yescharacteristic
734C2×D3—21no—
735C2×D3—21no—
736C2×D3—21no—
737C2×D3—22no—
738C2×D3—22no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—62no—
744C2×D3—61no—
745C2×D3—61no—
746C2×D3—61no—
747C2×D3—61no—
748C2×D3—61no—
749C2×D3—61no—
750C2×D3—84no—
751C2×D3—121no—
752C2×D3—121no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—41no—
756C3×C4—41no—
757C3×C4—61no—
758C3×C4—61no—
759C3×C4—61no—
760C3×C4—81no—
761C3×C4—121no—
762C3×C4—121no—
763C3×C4C2×D3×D411yescharacteristic
764C3×C4#100411yescharacteristic
765C3×C4#100411yescharacteristic
766C3×C4C22×#6711yescharacteristic
767Dic3—21no—
768Dic3—21no—
769Dic3—21no—
770Dic3—41no—
771Dic3—41no—
772Dic3—61no—
773Dic3—61no—
774Dic3—121no—
775Dic3—121no—
776Dic3—121no—
777Dic3—121no—
778Dic3—121no—
779Dic3—241no—
780Dic3—241no—
781C32#326711yescharacteristic, complemented, Sylow
782C23—21no—
783C23—31no—
784C23—61no—
785C23—61no—
786C23—91no—
787C23—122no—
788C23—122no—
789C23—241no—
790Q8—21no—
791Q8—21no—
792Q8—61no—
793Q8—61no—
794Q8—61no—
795Q8—61no—
796D4—21no—
797D4—21no—
798D4—32no—
799D4—32no—
800D4—61no—
801D4—61no—
802D4—122no—
803D4—122no—
804D4—361no—
805D4—362no—
806D4—362no—
807D4—721no—
808C2×C4—21no—
809C2×C4—31no—
810C2×C4—31no—
811C2×C4—31no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—91no—
817C2×C4—122no—
818C2×C4—181no—
819C2×C4—181no—
820C2×C4—181no—
821C2×C4—181no—
822C2×C4—362no—
823C2×C4—362no—
824C2×C4—362no—
825C2×C4—721no—
826C2×C4C22×D3211yescharacteristic
827C8—61no—
828C8—61no—
829C8—181no—
830C8D3×#6712yes—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—81no—
835C2×C3—81no—
836C2×C3—121no—
837C2×C3—122no—
838C2×C3—122no—
839C2×C3—161no—
840C2×C3#571711yescharacteristic
841C2×C3#577311yescharacteristic
842C2×C3#577511yescharacteristic
843C2×C3#577711yescharacteristic
844C2×C3#577811yescharacteristic
845C2×C3D4×#6711yescharacteristic
846D3—41no—
847D3—42no—
848D3—42no—
849D3—122no—
850D3—121no—
851D3—121no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—61no—
856C22—61no—
857C22—61no—
858C22—62no—
859C22—62no—
860C22—121no—
861C22—121no—
862C22—121no—
863C22—121no—
864C22—181no—
865C22—181no—
866C22—181no—
867C22—244no—
868C22D32×D411yescharacteristic
869C4—41no—
870C4—61no—
871C4—61no—
872C4—61no—
873C4—121no—
874C4—121no—
875C4—181no—
876C4—361no—
877C4—361no—
878C4#6431311yescharacteristic
879C4C2×D3×#6711yescharacteristic
880C3—21no—
881C3#8188211yescharacteristic, complemented
882C3#8395411yescharacteristic, complemented
883C2—81no—
884C2—121no—
885C2—122no—
886C2—122no—
887C2—361no—
888C2#1059474411yescharacteristic
889C2#1059475411yescharacteristic
890C2#1059529311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#914C2semidirect
2. #10595358C2semidirect
3. #10595229C2semidirect
4. C2×#63810C2semidirect
5. #10592870C2semidirect
6. C3×#5167C2semidirect
7. #10591656C2semidirect
8. #10591597C2semidirect
9. #10591564C2semidirect
10. #10591520C2semidirect
11. #10591458C2semidirect
12. #10591431C2semidirect
13. #10590854C2semidirect
14. #10590771C2semidirect
15. #10590736C2semidirect
21. C2×#3796C22semidirect
23. #64155C22semidirect
25. C2×C8×C3⋊D3C22semidirect
26. C3×#944C22semidirect
27. C2×C3×#216C22semidirect
33. C2×C3×Dic12C22semidirect
42. Dic3×D12C22semidirect
50. C2×#3715C22semidirect
52. #63662C22semidirect
54. #63644C22semidirect
55. C3×#815C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63566C22semidirect
58. #63566C22semidirect
60. #63563C22semidirect
61. #63557C22semidirect
67. C2×#914D3semidirect
83. #5167D3semidirect
143. C3×D24D4semidirect
185. #944C2×D3semidirect
186. C2×#216C2×D3semidirect
212. C2×Dic12C2×D3semidirect
251. #815C2×D3semidirect
450. D24#67semidirect
781. C32#3267semidirect
881. C3#81882semidirect
882. C3#83954semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9142
#105953582
#105952292
C2×#638102
#105928702
C3×#51672
#105916562
#105915972
#105915642
#105915202
#105914582
#105914312
#105908542
#105907712
#105907362
#839543
#818823