Finite Group Databasebeta

← #11884014

Subgroups — #11884014

Order 1152.

1241 conjugacy classes of subgroups.

The subgroup lattice has 953 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×C3⋊D3C211yesmaximal, characteristic, complemented
2#10595414C211yesmaximal, characteristic, complemented
3C2×#63939C211yesmaximal, characteristic, complemented
4#10595297C211yesmaximal, characteristic, complemented
5C3×#5172C211yesmaximal, characteristic, complemented
6C3×#5163C211yesmaximal, characteristic, complemented
7#10591592C211yesmaximal, characteristic, complemented
8#10591540C211yesmaximal, characteristic, complemented
9#10591469C211yesmaximal, characteristic, complemented
10#10591462C211yesmaximal, characteristic, complemented
11#10591456C211yesmaximal, characteristic, complemented
12#10590946C211yesmaximal, characteristic, complemented
13#10590860C211yesmaximal, characteristic, complemented
14#10590839C211yesmaximal, characteristic, complemented
15#10590737C211yesmaximal, characteristic, complemented
16#80404—31nomaximal
17#80121—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic, complemented
19C2×D4×C3⋊D3C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic, complemented
21C2×#3811—21no—
22C2×D3×D12C2211yescharacteristic
23C2×C32×SD16C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic
25C2×#3754C2211yescharacteristic, complemented
26SD16×C3⋊D3—24no—
27C2×#3744C2211yescharacteristic
28C2×C8×C3⋊D3C2211yescharacteristic, complemented
29C3×Q8×Dic3C2211yescharacteristic, complemented
30C2×C3×#215C2211yescharacteristic, complemented
31C3×#940C2211yescharacteristic
32C3×#938C2211yescharacteristic
33C2×C3×#213C2211yescharacteristic, complemented
34#63983—21no—
35#63981—21no—
36#63958—21no—
37#63939—24no—
38#63916—21no—
39#63916C2211yescharacteristic
40#63916C2211yescharacteristic, complemented
41C4×#626—21no—
42C4×#626C2211yescharacteristic
43#63894C2211yescharacteristic
44#63860—21no—
45#63860C2211yescharacteristic, complemented
46#63857—21no—
47#63857C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic
50C2×#3713C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52C3×#835C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic, complemented
54C3×#821C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×Dic3⋊C8C2211yescharacteristic, complemented
58#63576C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63564C2211yescharacteristic
61#63557C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63#5831—31no—
64C2×#949—31no—
65C2×#914—31no—
66C2×D3×SD16—31no—
67C2×D3×SD16—31no—
68C2×D3×SD16—61no—
69#5717—31no—
70#5609—31no—
71#5576—31no—
72C3×#460—31no—
73C3×#449—31no—
74#5172D311yescharacteristic, complemented
75#5170—31no—
76#5163D311yescharacteristic, complemented
77#5156—31no—
78#5154—31no—
79#5074—31no—
80#5042—31no—
81#5026—31no—
82#4844—31no—
83#4836—31no—
84#4817—31no—
85#4806—31no—
86#4787—31no—
87#4780—31no—
88#4776—31no—
89#4775—31no—
90#4775—31no—
91#4773—31no—
92#4731—31no—
93#4728—31no—
94C23×C3⋊D3—21no—
95C22×D32—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×#638—21no—
99Q8×C3⋊D3—22no—
100Q8×C3⋊D3—41no—
101D4×C3⋊D3—22no—
102D4×C3⋊D3—41no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4×C3⋊D3—21no—
105C2×C4×C3⋊D3C2311yescharacteristic
106C2×#634—21no—
107C2×#634C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67—21no—
111C3×#239—22no—
112C3×#239—41no—
113C2×C3×D12—21no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3C2311yescharacteristic
118#3811—44no—
119C2×#626—21no—
120C2×#626—21no—
121C2×#626—21no—
122C2×#626D411yescharacteristic
123C2×#624—21no—
124D3×D12—22no—
125D3×D12—41no—
126C32×SD16—22no—
127C2×C32×C8C2311yescharacteristic
128#3755D414yescomplemented
129#3754—22no—
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131#3744—22no—
132C8×C3⋊D3—22no—
133C3×#217—21no—
134C3×#215—22no—
135C3×#213—41no—
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×C4⋊Dic3C2311yescharacteristic
139C3×C4×Dic3—21no—
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3D411yescharacteristic
145#3722—21no—
146#3722D411yescharacteristic
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3D411yescharacteristic
153#3716—41no—
154#3714—22no—
155#3713—22no—
156#3711—22no—
157#3265—91noSylow
158C2×C3×#41—31no—
159C2×#239C2×D311yescharacteristic, complemented
160C2×D3×Q8—31no—
161C2×D3×Q8—31no—
162C2×D3×Q8—61no—
163C2×D3×D4—31no—
164C2×D3×D4—31no—
165C2×D3×D4—31no—
166C2×D3×D4—61no—
167C2×D3×D4—61no—
168C2×D3×D4—61no—
169C22×D12—31no—
170C2×C3×SD16—21no—
171C2×C3×SD16—31no—
172C2×C3×SD16C2×D311yescharacteristic, complemented
173C2×C3×SD16C2×D311yescharacteristic, complemented
174C2×C3×D8—31no—
175C3×#127—31no—
176C3×#121—31no—
177C3×C4×Q8—31no—
178#949—64no—
179Q8×Dic3C2×D311yescharacteristic, complemented
180C2×#215—31no—
181C2×#215—31no—
182C2×#215—61no—
183C2×#215C2×D311yescharacteristic, complemented
184#940C2×D311yescharacteristic
185#938—31no—
186#938—31no—
187#938—61no—
188#938—61no—
189#938C2×D311yescharacteristic
190#937—61no—
191#937—61no—
192#937—61no—
193#936—31no—
194#936—61no—
195C2×#214—31no—
196C2×#214—31no—
197C2×#214—31no—
198C2×#214—61no—
199C2×#213—31no—
200C2×#213—31no—
201C2×#213—31no—
202C2×#213C2×D311yescharacteristic, complemented
203C4×#67—31no—
204C4×#67—61no—
205#924—31no—
206#924—61no—
207C2×#208—31no—
208#914—64no—
209D3×SD16—64no—
210D3×SD16—64no—
211D3×SD16—68no—
212C2×D24—31no—
213C2×#204—31no—
214C2×#204—31no—
215C2×#204—31no—
216C2×#204—61no—
217C2×ΓL(1,𝔽25)—31no—
218C2×D3×C8—31no—
219C2×D3×C8—31no—
220C2×D3×C8—61no—
221#897—31no—
222#897—61no—
223#895—31no—
224#895—31no—
225#895—61no—
226#893—31no—
227#884—61no—
228#882—61no—
229#875—31no—
230#875—61no—
231C4×D12—31no—
232C4×D12—31no—
233C4×D12—61no—
234C3×C4⋊C8—31no—
235C3×#103—31no—
236C3×#102—31no—
237C3×#102—31no—
238C3×#102—31no—
239C3×C22⋊C8—31no—
240#835C2×D311yescharacteristic, complemented
241#832C2×D311yescharacteristic, complemented
242#821—31no—
243#821C2×D311yescharacteristic, complemented
244#821C2×D311yescharacteristic, complemented
245(C2×D3)⋊C8—31no—
246(C2×D3)⋊C8—31no—
247(C2×D3)⋊C8C2×D311yescharacteristic, complemented
248#816—31no—
249#815—31no—
250Dic3⋊C8C2×D311yescharacteristic, complemented
251#810—31no—
252#809—31no—
253#807—31no—
254#807—31no—
255#803—31no—
256C23×C32—21no—
257C22×C3⋊D3—21no—
258C22×C3⋊D3—42no—
259C22×C3⋊D3—42no—
260C22×C3⋊D3—81no—
261C22×C3⋊D3C2×D411yescharacteristic
262C22×C3×D3—21no—
263C22×C3×D3—21no—
264C22×C3×D3C2×D411yescharacteristic
265C2×D32—42no—
266C2×D32—42no—
267C2×D32—81no—
268C32×Q8—21no—
269C32×Q8C2×D412yescomplemented
270C32×D4—21no—
271C32×D4—21no—
272C2×C32×C4—21no—
273C2×C32×C4C2411yescharacteristic
274#638—42no—
275C2×C3⋊Dic3—21no—
276C2×C3⋊Dic3C2×D411yescharacteristic
277C4⋊(C3⋊D3)—21no—
278C4⋊(C3⋊D3)C2×D412yes—
279C4×C3⋊D3—21no—
280C4×C3⋊D3—21no—
281C4×C3⋊D3—42no—
282#634—21no—
283#634—21no—
284#634—42no—
285C3×#67—42no—
286C3×#67—42no—
287C3×#67—81no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3C2×D411yescharacteristic
291C2×C3×Dic3C2×D411yescharacteristic
292C2×C3×Dic3C2×D411yescharacteristic
293C3×D12—21no—
294C3×D12—21no—
295C3×D12—21no—
296C3×D12—21no—
297C3×D12—42no—
298C3×C4×D3—21no—
299C3×C4×D3—21no—
300C3×C4×D3—42no—
301#626—22no—
302#626—42no—
303#626—42no—
304#626—42no—
305#624—42no—
306C32×C8—21no—
307C3⋊(C3⋊C8)C2×D412yescomplemented
308C3×C3⋊C8—21no—
309C3×C3⋊C8—21no—
310C2×AGL(1,ℤ/8)—91no—
311C22×SD16—91no—
312#548—91no—
313D42—91no—
314#496—91no—
315#468—91no—
316#466—91no—
317#463—91no—
318#460—31no—
319#450—91no—
320#449—31no—
321#448—91no—
322#447—91no—
323#440—91no—
324#435—91no—
325C23×D3—61no—
326C23×D3—61no—
327C23×D3—61no—
328C23×D3—61no—
329C23×D3—121no—
330C3×#41—62no—
331C3×#41—121no—
332C2×C3×Q8—21no—
333C2×C3×Q8C22×D311yescharacteristic
334C2×C3×Q8C22×D311yescharacteristic
335C2×C3×D4—21no—
336C2×C3×D4—31no—
337C2×C3×D4—31no—
338C2×C3×D4—61no—
339C2×C3×D4—61no—
340C2×C3×D4—61no—
341C2×C3×D4—61no—
342C2×C3×D4C22×D311yescharacteristic
343C2×C3×D4C22×D311yescharacteristic
344C22×C3×C4—31no—
345C22×C3×C4—61no—
346C2×#67—21no—
347C2×#67—21no—
348C2×#67—21no—
349C2×#67—31no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—121no—
356#239—22no—
357#239—41no—
358D3×Q8—64no—
359D3×Q8—62no—
360D3×Q8—62no—
361D3×Q8—121no—
362D3×Q8—121no—
363D3×Q8—122no—
364D3×D4—62no—
365D3×D4—62no—
366D3×D4—62no—
367D3×D4—64no—
368D3×D4—121no—
369D3×D4—121no—
370D3×D4—121no—
371D3×D4—122no—
372D3×D4—124no—
373D3×D4—124no—
374C2×D12—21no—
375C2×D12—31no—
376C2×D12—31no—
377C2×D12—31no—
378C2×D12—61no—
379C2×D12—62no—
380C2×D12—61no—
381C2×D12—61no—
382C2×D12—61no—
383C2×D12—121no—
384C2×D12C22×D311yescharacteristic
385C2×D12C22×D311yescharacteristic
386C2×C4×D3—21no—
387C2×C4×D3—31no—
388C2×C4×D3—31no—
389C2×C4×D3—61no—
390C2×C4×D3—61no—
391C2×C4×D3—61no—
392C2×C4×D3—61no—
393C2×C4×D3—61no—
394C2×C4×D3—121no—
395C2×C4×D3C22×D311yescharacteristic
396C2×Dic6—31no—
397C2×Dic6—31no—
398C2×Dic6—61no—
399C2×Dic6—61no—
400C2×Dic6—61no—
401C2×Dic6—121no—
402C3×SD16—24no—
403C3×SD16—22no—
404C3×SD16—22no—
405C3×SD16—62no—
406C3×D8—121no—
407C2×C3×C8—21no—
408C2×C3×C8—31no—
409C2×C3×C8—31no—
410C2×C3×C8C22×D311yescharacteristic
411C2×C3×C8C22×D311yescharacteristic
412C3×C4⋊C4—31no—
413C3×C4⋊C4—31no—
414C3×C4⋊C4—61no—
415C3×C22⋊C4—61no—
416C3×C42—31no—
417C3×C42—61no—
418#217—21no—
419#217—31no—
420#217—61no—
421#217—61no—
422#217—61no—
423#217—61no—
424#217—61no—
425#215—22no—
426#215—34no—
427#215—34no—
428#215—64no—
429#214—62no—
430#214—62no—
431#214—64no—
432#214—121no—
433#213—41no—
434#213—62no—
435#213—62no—
436#213—62no—
437(C2×D3)⋊C4—31no—
438(C2×D3)⋊C4—31no—
439(C2×D3)⋊C4—31no—
440(C2×D3)⋊C4—61no—
441(C2×D3)⋊C4—61no—
442(C2×D3)⋊C4—61no—
443(C2×D3)⋊C4—61no—
444(C2×D3)⋊C4—61no—
445(C2×D3)⋊C4—61no—
446(C2×D3)⋊C4—61no—
447C4⋊Dic3—21no—
448C4⋊Dic3—31no—
449C4⋊Dic3—61no—
450C4⋊Dic3C22×D311yescharacteristic
451C4⋊Dic3C22×D311yescharacteristic
452Dic3⋊C4—31no—
453Dic3⋊C4—61no—
454C4×Dic3—21no—
455C4×Dic3C22×D311yescharacteristic
456#208—62no—
457C2×C3⋊C8—31no—
458C2×C3⋊C8—31no—
459C2×C3⋊C8—61no—
460C2×C3⋊C8C22×D311yescharacteristic
461C2×C3⋊C8C22×D311yescharacteristic
462D24—62no—
463#204—62no—
464#204—62no—
465#204—64no—
466#204—121no—
467ΓL(1,𝔽25)—62no—
468D3×C8—62no—
469D3×C8—62no—
470D3×C8—64no—
471C22×C32—41no—
472C22×C32—41no—
473C22×C32—41no—
474C22×C32C22×D411yescharacteristic
475C2×C3⋊D3—21no—
476C2×C3⋊D3—21no—
477C2×C3⋊D3—22no—
478C2×C3⋊D3—41no—
479C2×C3⋊D3—41no—
480C2×C3⋊D3—84no—
481C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
482C2×C3×D3—21no—
483C2×C3×D3—21no—
484C2×C3×D3—21no—
485C2×C3×D3—41no—
486C2×C3×D3—41no—
487C2×C3×D3—41no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C2×C3×D3—41no—
491D32—84no—
492C32×C4—22no—
493C32×C4C22×D411yescharacteristic
494C32×C4H(5,𝔽2)11yescharacteristic
495C3⋊Dic3—21no—
496C3⋊Dic3—41no—
497C3×Dic3—21no—
498C3×Dic3—21no—
499C3×Dic3—21no—
500C3×Dic3—41no—
501C3×Dic3—41no—
502C2×#41—31no—
503C22×Q8—91no—
504C22×D4—91no—
505C22×D4—91no—
506C22×D4—181no—
507AGL(1,ℤ/8)—184no—
508C2×SD16—31no—
509C2×SD16—91no—
510C2×SD16—91no—
511C2×SD16—91no—
512C2×SD16—91no—
513C2×SD16—184no—
514C2×SD16D3211yescharacteristic, complemented
515C2×D8—31no—
516C2×D8—91no—
517C2×D8—91no—
518C2×M16—91no—
519C22×C8—91no—
520#127—31no—
521#124—91no—
522#124—181no—
523C22⋊Q8—91no—
524C22⋊Q8—181no—
525#121—31no—
526#121—91no—
527#121—91no—
528#121—181no—
529#121—181no—
530#120—181no—
531#120—181no—
532C4×Q8—31no—
533C4×D4—91no—
534C4×D4—91no—
535C4×D4—181no—
536#107—91no—
537C4⋊C8—31no—
538#103—31no—
539#103—91no—
540#102—31no—
541#102—31no—
542#102—31no—
543#102—91no—
544C22⋊C8—31no—
545C22⋊C8—91no—
546#97—91no—
547C23×C3—21no—
548C23×C3—21no—
549C23×C3—31no—
550C23×C3—41no—
551C23×C3—61no—
552C23×C3—61no—
553C22×D3—21no—
554C22×D3—21no—
555C22×D3—31no—
556C22×D3—31no—
557C22×D3—61no—
558C22×D3—61no—
559C22×D3—61no—
560C22×D3—121no—
561C22×D3—122no—
562C22×D3—122no—
563C22×D3—122no—
564C22×D3—122no—
565C22×D3—122no—
566C22×D3—122no—
567C22×D3—122no—
568C22×D3—122no—
569C22×D3—124no—
570C22×D3—242no—
571C22×D3—241no—
572C22×D3—241no—
573C22×D3—241no—
574C22×D3—241no—
575C22×D3—242no—
576C22×D3D3×D411yescharacteristic
577C3×Q8—21no—
578C3×Q8—21no—
579C3×Q8—22no—
580C3×Q8—41no—
581C3×Q8D3×D412yescomplemented
582C3×Q8D3×D412yescomplemented
583C3×D4—22no—
584C3×D4—21no—
585C3×D4—21no—
586C3×D4—21no—
587C3×D4—21no—
588C3×D4—41no—
589C3×D4—61no—
590C3×D4—61no—
591C3×D4—61no—
592C3×D4—61no—
593C3×D4—122no—
594C3×D4—122no—
595C3×D4—122no—
596C3×D4—241no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—31no—
601C2×C3×C4—31no—
602C2×C3×C4—31no—
603C2×C3×C4—41no—
604C2×C3×C4—61no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—122no—
609C2×C3×C4C23×D311yescharacteristic
610C2×C3×C4C23×D311yescharacteristic
611#67—42no—
612#67—42no—
613#67—62no—
614#67—81no—
615#67—122no—
616#67—122no—
617#67—122no—
618#67—122no—
619#67—122no—
620#67—124no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—31no—
624C2×Dic3—31no—
625C2×Dic3—61no—
626C2×Dic3—61no—
627C2×Dic3—61no—
628C2×Dic3—121no—
629C2×Dic3D3×D411yescharacteristic
630C2×Dic3D3×D411yescharacteristic
631C2×Dic3D3×D411yescharacteristic
632D12—21no—
633D12—21no—
634D12—21no—
635D12—21no—
636D12—32no—
637D12—32no—
638D12—42no—
639D12—62no—
640D12—62no—
641D12—61no—
642D12—61no—
643D12—121no—
644D12—122no—
645D12—122no—
646D12—122no—
647C4×D3—21no—
648C4×D3—21no—
649C4×D3—42no—
650C4×D3—62no—
651C4×D3—62no—
652C4×D3—61no—
653C4×D3—61no—
654C4×D3—61no—
655C4×D3—61no—
656C4×D3—122no—
657C4×D3—122no—
658C4×D3—122no—
659C4×D3—122no—
660C4×D3—124no—
661Dic6—62no—
662Dic6—61no—
663Dic6—61no—
664Dic6—61no—
665Dic6—61no—
666Dic6—121no—
667Dic6—122no—
668Dic6—122no—
669Dic6—124no—
670C3×C8—22no—
671C3×C8—21no—
672C3×C8—21no—
673C3×C8—61no—
674C3×C8—61no—
675C3⋊C8—21no—
676C3⋊C8—21no—
677C3⋊C8—32no—
678C3⋊C8—32no—
679C3⋊C8—62no—
680C2×C32—81no—
681C2×C32D4211yescharacteristic
682C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
683C2×C32#57711yescharacteristic
684C3⋊D3—22no—
685C3⋊D3—42no—
686C3×D3—41no—
687C3×D3—81no—
688C3×D3—81no—
689C24—181no—
690C24—181no—
691#41—62no—
692#41—121no—
693C2×Q8—91no—
694C2×Q8—181no—
695C2×Q8—182no—
696C2×Q8—361no—
697C2×Q8C2×D3211yescharacteristic
698C2×D4—31no—
699C2×D4—31no—
700C2×D4—61no—
701C2×D4—61no—
702C2×D4—61no—
703C2×D4—61no—
704C2×D4—91no—
705C2×D4—91no—
706C2×D4—181no—
707C2×D4—182no—
708C2×D4—181no—
709C2×D4—181no—
710C2×D4—181no—
711C2×D4—182no—
712C2×D4—361no—
713C2×D4—361no—
714C2×D4—364no—
715C2×D4C2×D3211yescharacteristic
716C22×C4—31no—
717C22×C4—61no—
718C22×C4—91no—
719C22×C4—181no—
720C22×C4—181no—
721SD16—22no—
722SD16—62no—
723SD16—94no—
724SD16—182no—
725SD16—182no—
726SD16—361no—
727D8—121no—
728D8—182no—
729D8—182no—
730M16—182no—
731C2×C8—31no—
732C2×C8—31no—
733C2×C8—91no—
734C2×C8—182no—
735C2×C8C2×D3211yescharacteristic
736C4⋊C4—31no—
737C4⋊C4—31no—
738C4⋊C4—61no—
739C4⋊C4—91no—
740C4⋊C4—181no—
741C22⋊C4—61no—
742C22⋊C4—91no—
743C22⋊C4—91no—
744C22⋊C4—181no—
745C22⋊C4—181no—
746C22⋊C4—181no—
747C22⋊C4—181no—
748C22⋊C4—181no—
749C22⋊C4—181no—
750C42—31no—
751C42—61no—
752C22×C3—21no—
753C22×C3—42no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—41no—
760C22×C3—61no—
761C22×C3—61no—
762C22×C3—61no—
763C22×C3—81no—
764C22×C3—81no—
765C22×C3—121no—
766C22×C3—121no—
767C22×C3—121no—
768C22×C3—121no—
769C22×C3—121no—
770C22×C3—121no—
771C22×C3C2×D3×D411yescharacteristic
772C22×C3C2×D3×D411yescharacteristic
773C2×D3—21no—
774C2×D3—21no—
775C2×D3—21no—
776C2×D3—32no—
777C2×D3—32no—
778C2×D3—41no—
779C2×D3—41no—
780C2×D3—41no—
781C2×D3—41no—
782C2×D3—41no—
783C2×D3—41no—
784C2×D3—62no—
785C2×D3—62no—
786C2×D3—62no—
787C2×D3—61no—
788C2×D3—61no—
789C2×D3—61no—
790C2×D3—61no—
791C2×D3—62no—
792C2×D3—62no—
793C2×D3—122no—
794C2×D3—121no—
795C2×D3—121no—
796C2×D3—121no—
797C2×D3—121no—
798C2×D3—241no—
799C2×D3—241no—
800C2×D3—244no—
801C2×D3—244no—
802C2×D3—244no—
803C2×D3—248no—
804C2×D3—244no—
805C3×C4—22no—
806C3×C4—22no—
807C3×C4—21no—
808C3×C4—21no—
809C3×C4—42no—
810C3×C4—61no—
811C3×C4—61no—
812C3×C4—61no—
813C3×C4—121no—
814C3×C4—121no—
815C3×C4C2×D3×D411yescharacteristic
816C3×C4C2×D3×D411yescharacteristic
817C3×C4#100411yescharacteristic
818C3×C4#100911yescharacteristic
819Dic3—21no—
820Dic3—21no—
821Dic3—21no—
822Dic3—41no—
823Dic3—41no—
824Dic3—62no—
825Dic3—61no—
826Dic3—61no—
827Dic3—122no—
828Dic3—121no—
829Dic3—121no—
830C32#326511yescharacteristic, complemented, Sylow
831C23—21no—
832C23—31no—
833C23—61no—
834C23—61no—
835C23—91no—
836C23—181no—
837C23—362no—
838C23—362no—
839C23—362no—
840C23—362no—
841C23—721no—
842C23—721no—
843Q8—21no—
844Q8—181no—
845Q8—181no—
846Q8—362no—
847Q8#381112yescomplemented
848D4—21no—
849D4—21no—
850D4—61no—
851D4—61no—
852D4—61no—
853D4—61no—
854D4—92no—
855D4—122no—
856D4—122no—
857D4—122no—
858D4—182no—
859D4—181no—
860D4—241no—
861D4—362no—
862D4—362no—
863D4—362no—
864D4—362no—
865C2×C4—21no—
866C2×C4—31no—
867C2×C4—31no—
868C2×C4—31no—
869C2×C4—61no—
870C2×C4—61no—
871C2×C4—61no—
872C2×C4—61no—
873C2×C4—91no—
874C2×C4—122no—
875C2×C4—181no—
876C2×C4—181no—
877C2×C4—181no—
878C2×C4—362no—
879C2×C4—362no—
880C2×C4C22×D3211yescharacteristic
881C8—21no—
882C8—61no—
883C8—61no—
884C8—92no—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—82no—
889C2×C3—81no—
890C2×C3—81no—
891C2×C3—121no—
892C2×C3—241no—
893C2×C3—241no—
894C2×C3#559011yescharacteristic
895C2×C3#560911yescharacteristic
896C2×C3#576211yescharacteristic
897C2×C3#577011yescharacteristic
898C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
899C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
900D3—41no—
901D3—64no—
902D3—62no—
903D3—62no—
904D3—81no—
905D3—81no—
906D3—122no—
907D3—122no—
908D3—242no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—61no—
913C22—61no—
914C22—61no—
915C22—92no—
916C22—121no—
917C22—121no—
918C22—121no—
919C22—121no—
920C22—121no—
921C22—121no—
922C22—181no—
923C22—181no—
924C22—182no—
925C22—361no—
926C22—361no—
927C22—724no—
928C22—724no—
929C22D32×D411yescharacteristic
930C4—22no—
931C4—61no—
932C4—61no—
933C4—61no—
934C4—121no—
935C4—121no—
936C4—181no—
937C4—361no—
938C4#6431411yescharacteristic
939C4C2×#381111yescharacteristic
940C3—21no—
941C3#8012111yescharacteristic, complemented
942C3#8040411yescharacteristic, complemented
943C2—81no—
944C2—121no—
945C2—182no—
946C2—241no—
947C2—241no—
948C2—362no—
949C2#1059474011yescharacteristic
950C2#1059475311yescharacteristic
951C2#1059529211yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3265
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×SD16×C3⋊D3C2semidirect
2. #10595414C2semidirect
3. C2×#63939C2semidirect
4. #10595297C2semidirect
5. C3×#5172C2semidirect
6. C3×#5163C2semidirect
7. #10591592C2semidirect
8. #10591540C2semidirect
9. #10591469C2semidirect
10. #10591462C2semidirect
11. #10591456C2semidirect
12. #10590946C2semidirect
13. #10590860C2semidirect
14. #10590839C2semidirect
15. #10590737C2semidirect
18. C2×Q8×C3⋊D3C22semidirect
20. C2×C3×#239C22semidirect
23. C2×C32×SD16C22semidirect
25. C2×#3754C22semidirect
28. C2×C8×C3⋊D3C22semidirect
29. C3×Q8×Dic3C22semidirect
30. C2×C3×#215C22semidirect
33. C2×C3×#213C22semidirect
40. #63916C22semidirect
45. #63860C22semidirect
47. #63857C22semidirect
48. C2×#3716C22semidirect
50. C2×#3713C22semidirect
51. C2×#3711C22semidirect
52. C3×#835C22semidirect
53. C3×#832C22semidirect
54. C3×#821C22semidirect
55. C3×#821C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×Dic3⋊C8C22semidirect
58. #63576C22semidirect
59. #63567C22semidirect
61. #63557C22semidirect
62. #63554C22semidirect
74. #5172D3semidirect
76. #5163D3semidirect
128. #3755D4semidirect
159. C2×#239C2×D3semidirect
172. C2×C3×SD16C2×D3semidirect
173. C2×C3×SD16C2×D3semidirect
179. Q8×Dic3C2×D3semidirect
183. C2×#215C2×D3semidirect
202. C2×#213C2×D3semidirect
240. #835C2×D3semidirect
241. #832C2×D3semidirect
243. #821C2×D3semidirect
244. #821C2×D3semidirect
247. (C2×D3)⋊C8C2×D3semidirect
250. Dic3⋊C8C2×D3semidirect
269. C32×Q8C2×D4semidirect
307. C3⋊(C3⋊C8)C2×D4semidirect
481. C2×C3⋊D3AGL(1,ℤ/8)semidirect
514. C2×SD16D32semidirect
581. C3×Q8D3×D4semidirect
582. C3×Q8D3×D4semidirect
830. C32#3265semidirect
847. Q8#3811semidirect
941. C3#80121semidirect
942. C3#80404semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×C3⋊D32
#105954142
C2×#639392
#105952972
C3×#51722
C3×#51632
#105915922
#105915402
#105914692
#105914622
#105914562
#105909462
#105908602
#105908392
#105907372
#804043
#801213