Finite Group Databasebeta

← #72222740

Subgroups — #72222740

Order 2304.

1516 conjugacy classes of subgroups.

The subgroup lattice has 791 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11899423C211yesmaximal, characteristic
2C3×#82007C211yesmaximal, characteristic
3#11857306C211yesmaximal, characteristic
4#11795946C211yesmaximal, characteristic, complemented
5#11795942C214yesmaximal, complemented
6C3×#71425C211yesmaximal, characteristic, complemented
7C2×#10589106C211yesmaximal, characteristic, complemented
8D3×#4512C214yesmaximal, complemented
9C2×#10589378C211yesmaximal, characteristic, complemented
10#10947848—31nomaximal
11#10947847—31nomaximal
12C2×C3×#901C2211yescharacteristic
13#10594958C411yescharacteristic
14C2×#63815C411yescharacteristic
15C2×C32×M32C2211yescharacteristic
16C2×#63642C2211yescharacteristic
17C2×#63639C2211yescharacteristic
18C3×#5101C2211yescharacteristic
19C2×C3×#812C2211yescharacteristic
20C2×C3×#812C2211yescharacteristic
21C3×#4907C414yescomplemented
22C3×D3×M32C2214yes—
23C3×#4901C414yescomplemented
24#10591060C411yescharacteristic
25#10591057C411yescharacteristic
26#10590908C412yes—
27#10590693C2212yes—
28Dic3×ΓL(1,𝔽25)C412yes—
29D3×#815C2212yes—
30#10590622C414yescomplemented
31#10590621C414yescomplemented
32D3×#812C2214yes—
33#10589378C2212yes—
34#10589378C2212yes—
35C3×#4512C2214yes—
36#10589106C2212yes—
37#10589106C2212yes—
38#10589105C2214yes—
39C3×#3407—31no—
40#83782—31no—
41#83780—31no—
42#82007—31no—
43#82007D311yescharacteristic
44#78550—31no—
45C3×#2110—31no—
46#71425—31no—
47#71425—34no—
48#71425D311yescharacteristic, complemented
49C2×#4512—31no—
50C2×#4512—31no—
51C2×#4512—34no—
52C2×#4512—31no—
53C2×#4512—31no—
54C2×#4512—61no—
55#69884—31no—
56#69087—34no—
57D3×#347—34no—
58C2×C3×#235C2×C411yescharacteristic
59C22×C32×C8C2311yescharacteristic
60C2×C4×C3⋊Dic3C2×C411yescharacteristic
61C22×C3⋊(C3⋊C8)C2×C411yescharacteristic
62C3×#926C2×C411yescharacteristic
63C2×C3×#208C2×C411yescharacteristic
64C2×C3×#208C2×C411yescharacteristic
65C3×#901C2×C412yes—
66C3×#901C2×C412yes—
67C3×#901C2×C412yes—
68C3×#901C2×C412yes—
69C2×C3×ΓL(1,𝔽25)C2×C412yes—
70C2×C3×D3×C8C2312yes—
71#67⋊Dic3—22no—
72#63898—21no—
73C4×D3×Dic3C2×C412yes—
74#63855C2×C412yes—
75#63843—21no—
76C2×#3711C2×C412yes—
77#63815—22no—
78#63815—22no—
79C2×D3×C3⋊C8C2×C412yes—
80C32×M32C2×C412yescomplemented
81C32×M32C2312yes—
82C2×C32×C16C2×C412yescomplemented
83#63642C2×C411yescharacteristic
84#63642C2×C411yescharacteristic
85#63642C2311yescharacteristic
86#63642C2311yescharacteristic
87#63639C2×C412yescomplemented
88#63639C2312yes—
89C2×C3⋊(C3⋊C16)C2×C412yescomplemented
90C3×#815C2312yes—
91C3×C8×Dic3C2×C412yes—
92C3×#812C2×C412yescomplemented
93C3×#812C2×C412yescomplemented
94C3×#812C2312yes—
95C3×#812C2312yes—
96C2×C3×C3⋊C16C2×C412yescomplemented
97C2×C3×C3⋊C16C2×C412yescomplemented
98C3×#798C2×C418yescomplemented
99C3×D3×C16C2×C418yescomplemented
100#63555C2×C412yes—
101#63554C2×C412yes—
102#63553C2×C412yes—
103Dic3×C3⋊C8C2×C412yes—
104#63543C2×C418yescomplemented
105D3×C3⋊C16C2×C418yescomplemented
106#33329—91noSylow
107C2×C3×#131—31no—
108Dic3×#41—31no—
109C2×#948—31no—
110C2×#907—31no—
111C2×#901C2×D311yescharacteristic
112#5522—31no—
113C3×#504—34no—
114C3×#504—34no—
115C2×C3×M32—21no—
116C2×C3×M32—31no—
117C2×C3×M32—31no—
118C2×C3×M32—34no—
119C2×C3×M32C2×D311yescharacteristic
120C2×C3×M32C2×D311yescharacteristic
121C3×#405—31no—
122#5140—34no—
123#5140—34no—
124#5122—31no—
125#5122—32no—
126Dic3×M16—31no—
127Dic3×M16—31no—
128Dic3×M16—32no—
129#5101—32no—
130#5101C2×D311yescharacteristic
131C2×#815—31no—
132C2×#815—31no—
133C2×#815—32no—
134C2×#815—61no—
135C2×#812—31no—
136C2×#812—31no—
137C2×#812—34no—
138C2×#812—61no—
139C2×#812C2×D311yescharacteristic
140C2×#812C2×D311yescharacteristic
141#4997—31no—
142#4907—34no—
143#4907Dic314yescomplemented
144D3×M32—34no—
145D3×M32C2×D314yes—
146#4901—34no—
147#4901Dic314yescomplemented
148#4708—32no—
149D3×#97—32no—
150#4689—32no—
151C4×ΓL(1,𝔽25)—32no—
152C3×#347—34no—
153#4512—32no—
154#4512—32no—
155#4512—32no—
156#4512—32no—
157#4512—34no—
158#4512—32no—
159#4512—32no—
160#4512—32no—
161#4512—32no—
162#4512—62no—
163#4512—62no—
164#4512C2×D314yes—
165#4466—34no—
166C22×C32×C4C22×C411yescharacteristic
167C22×C3⋊Dic3—21no—
168C2×C3×#67M1612yes—
169C3×#235C4212yes—
170C3×#235C4212yes—
171C3×#235M1612yes—
172C3×#235M1612yes—
173C2×C3×D12M1611yescharacteristic
174C2×C3×C4×D3C22×C412yes—
175C2×C3×Dic6M1611yescharacteristic
176C2×D3×Dic3—22no—
177C2×C32×C8C22×C411yescharacteristic
178C2×C32×C8C22×C411yescharacteristic
179C2×C32×C8C22×C411yescharacteristic
180C2×C32×C8C22×C411yescharacteristic
181C2×C32×C8C22×C411yescharacteristic
182C2×C32×C8C2411yescharacteristic
183C4×C3⋊Dic3—21no—
184C4×C3⋊Dic3C22×C411yescharacteristic
185C4×C3⋊Dic3C22×C411yescharacteristic
186C2×C3⋊(C3⋊C8)—21no—
187C2×C3⋊(C3⋊C8)—21no—
188C2×C3⋊(C3⋊C8)C22×C411yescharacteristic
189C2×C3⋊(C3⋊C8)C22×C411yescharacteristic
190C3×#217—21no—
191C3×C4⋊Dic3—21no—
192C3×C4×Dic3C22×C412yes—
193C3×#208—21no—
194C3×#208—21no—
195C3×#208C4212yes—
196C3×#208C4212yes—
197C2×C3×C3⋊C8C22×C412yes—
198C2×C3×C3⋊C8C22×C412yes—
199C3×ΓL(1,𝔽25)C4214yes—
200C3×ΓL(1,𝔽25)C4214yes—
201C3×D3×C8C22×C414yes—
202C3×D3×C8C22×C414yes—
203Dic3⋊Dic3—22no—
204(C2×D3)⋊Dic3—22no—
205Dic32—22no—
206#3711—24no—
207D3×C3⋊C8—24no—
208C32×C16C22×C414yes—
209C3⋊(C3⋊C16)C22×C414yes—
210C3×C3⋊C16C22×C414yes—
211C3×C3⋊C16C22×C414yes—
212#3407—31no—
213#3407—91no—
214#2875—91no—
215#2110—31no—
216#2110—94no—
217#2110—91no—
218C2×#347—94no—
219C2×#347—91no—
220C2×#347—91no—
221C2×C3×#41—31no—
222C2×#235C4×D311yescharacteristic
223C3×#131—32no—
224C3×#131—32no—
225C3×#131—32no—
226C3×#131—32no—
227C2×C3×M16—31no—
228C2×C3×M16—31no—
229C2×C3×M16—32no—
230C22×C3×C8—21no—
231C22×C3×C8—32no—
232C22×C3×C8C22×D311yescharacteristic
233C22×C3×C8C22×D311yescharacteristic
234C3×#117—31no—
235#948—62no—
236#948—62no—
237Q8×Dic3—61no—
238D4×Dic3—61no—
239D4×Dic3—62no—
240#926—32no—
241#926C4×D311yescharacteristic
242C2×C4×Dic3—31no—
243C2×C4×Dic3—31no—
244C2×C4×Dic3—32no—
245C2×C4×Dic3—61no—
246C2×#208—32no—
247C2×#208C4×D311yescharacteristic
248C2×#208C4×D311yescharacteristic
249C22×C3⋊C8—31no—
250C22×C3⋊C8—31no—
251C22×C3⋊C8—32no—
252C22×C3⋊C8—61no—
253#907—62no—
254#907—62no—
255#901C4×D312yes—
256#901C4×D312yes—
257#901C2×Dic312yes—
258#901C2×Dic312yes—
259C2×ΓL(1,𝔽25)—32no—
260C2×ΓL(1,𝔽25)C4×D312yes—
261C2×D3×C8—32no—
262C2×D3×C8C22×D312yes—
263#893—61no—
264#887—61no—
265#67⋊C4—62no—
266#872—32no—
267C42×D3—32no—
268C3×M32—22no—
269C3×M32—22no—
270C3×M32—32no—
271C3×M32—32no—
272C3×M32—32no—
273C3×M32—32no—
274C3×M32—38no—
275C3×M32C4×D312yescomplemented
276C3×M32C2×Dic312yescomplemented
277C3×M32C22×D312yes—
278C3×M32C22×D312yes—
279C2×C3×C16—22no—
280C2×C3×C16—32no—
281C2×C3×C16—32no—
282C2×C3×C16—38no—
283C2×C3×C16C4×D312yescomplemented
284C2×C3×C16C2×Dic312yescomplemented
285C3×#97—32no—
286C3×C4×C8—32no—
287#815—31no—
288#815—31no—
289#815—31no—
290#815—31no—
291#815—31no—
292#815—31no—
293#815—31no—
294#815—31no—
295#815—32no—
296#815—32no—
297#815—32no—
298#815—61no—
299#815—61no—
300#815—61no—
301#815—61no—
302#815C22×D312yes—
303C8×Dic3—32no—
304C8×Dic3—32no—
305C8×Dic3—32no—
306C8×Dic3C4×D312yes—
307#812—32no—
308#812—32no—
309#812—32no—
310#812—32no—
311#812—38no—
312#812—62no—
313#812—62no—
314#812C4×D312yescomplemented
315#812C2×Dic312yescomplemented
316#812C22×D312yes—
317#812C22×D312yes—
318C2×C3⋊C16—32no—
319C2×C3⋊C16—32no—
320C2×C3⋊C16—38no—
321C2×C3⋊C16—62no—
322C2×C3⋊C16C4×D312yescomplemented
323C2×C3⋊C16C2×Dic312yescomplemented
324#803—32no—
325C4×C3⋊C8—32no—
326#798—38no—
327#798C2×Dic318yescomplemented
328D3×C16—38no—
329D3×C16C2×Dic318yescomplemented
330C23×C32C2×M1611yescharacteristic
331C22×C3×D3C2×M1612yes—
332C2×C32×C4C2×C4211yescharacteristic
333C2×C32×C4C2×C4211yescharacteristic
334C2×C32×C4C2×M1611yescharacteristic
335C2×C32×C4C2×M1611yescharacteristic
336C2×C32×C4C2×M1611yescharacteristic
337C2×C32×C4C23×C411yescharacteristic
338C2×C3⋊Dic3—21no—
339C2×C3⋊Dic3—21no—
340C2×C3⋊Dic3—81no—
341C3×#67#9714yes—
342C3×#67#9714yes—
343C2×C3×Dic3—22no—
344C2×C3×Dic3C2×M1612yes—
345C3×D12#9712yes—
346C3×D12#9712yes—
347C3×C4×D3C2×C4214yes—
348C3×C4×D3C2×M1614yes—
349C3×Dic6#9712yes—
350C3×Dic6#9712yes—
351D3×Dic3—82no—
352C32×C8C2×C4211yescharacteristic
353C32×C8C2×C4211yescharacteristic
354C32×C8C23×C411yescharacteristic
355C32×C8C23×C411yescharacteristic
356C3⋊(C3⋊C8)—21no—
357C3⋊(C3⋊C8)—21no—
358C3×C3⋊C8—22no—
359C3×C3⋊C8C2×C4214yes—
360C2×#131—31no—
361C2×#131—91no—
362C4×#41—91no—
363#504—34no—
364#504—34no—
365#504—94no—
366#504—94no—
367C2×M32—31no—
368C2×M32—31no—
369C2×M32—34no—
370C2×M32—94no—
371C2×M32—91no—
372C2×M32D3211yescharacteristic
373#405—31no—
374#405—92no—
375#405—92no—
376#405—91no—
377C4×M16—92no—
378C4×M16—91no—
379C2×#97—92no—
380C2×#97—91no—
381#347—34no—
382#347—94no—
383#347—92no—
384#347—92no—
385#347—92no—
386#347—92no—
387C3×#41—32no—
388C3×#41—32no—
389C3×#41—32no—
390C3×#41—32no—
391C2×C3×Q8—31no—
392C2×C3×D4—32no—
393C2×C3×D4—31no—
394C22×C3×C4—21no—
395C22×C3×C4—32no—
396C22×C3×C4C2×C4×D311yescharacteristic
397C22×C3×C4C2×C4×D311yescharacteristic
398C2×#67ΓL(1,𝔽25)12yes—
399C22×Dic3—62no—
400C22×Dic3—61no—
401C22×Dic3—61no—
402C22×Dic3—121no—
403#235ΓL(1,𝔽25)12yes—
404#235ΓL(1,𝔽25)12yes—
405#235C4×Dic312yes—
406#235C4×Dic312yes—
407C2×D12ΓL(1,𝔽25)11yescharacteristic
408C2×C4×D3—62no—
409C2×C4×D3C2×C4×D312yes—
410C2×Dic6ΓL(1,𝔽25)11yescharacteristic
411C3×M16—32no—
412C3×M16—32no—
413C3×M16—34no—
414C3×M16—34no—
415C3×M16—61no—
416C3×M16—61no—
417C2×C3×C8—21no—
418C2×C3×C8—21no—
419C2×C3×C8—21no—
420C2×C3×C8—21no—
421C2×C3×C8—21no—
422C2×C3×C8—21no—
423C2×C3×C8—32no—
424C2×C3×C8—34no—
425C2×C3×C8—34no—
426C2×C3×C8—32no—
427C2×C3×C8C2×C4×D311yescharacteristic
428C2×C3×C8C2×C4×D311yescharacteristic
429C2×C3×C8C2×C4×D311yescharacteristic
430C2×C3×C8C2×C4×D311yescharacteristic
431C2×C3×C8C2×C4×D311yescharacteristic
432C2×C3×C8C2×C4×D311yescharacteristic
433C2×C3×C8C2×C4×D311yescharacteristic
434C2×C3×C8C2×C4×D311yescharacteristic
435C2×C3×C8C22×Dic311yescharacteristic
436C2×C3×C8C22×Dic311yescharacteristic
437C2×C3×C8C23×D311yescharacteristic
438C2×C3×C8C23×D311yescharacteristic
439C3×C4⋊C4—61no—
440C3×C22⋊C4—61no—
441C3×C42—32no—
442#217—21no—
443#217—62no—
444(C2×D3)⋊C4—62no—
445C4⋊Dic3—21no—
446C4⋊Dic3—62no—
447Dic3⋊C4—62no—
448C4×Dic3—31no—
449C4×Dic3—31no—
450C4×Dic3—31no—
451C4×Dic3—31no—
452C4×Dic3—61no—
453C4×Dic3—61no—
454C4×Dic3—62no—
455C4×Dic3—61no—
456C4×Dic3—61no—
457C4×Dic3—62no—
458C4×Dic3—121no—
459C4×Dic3C2×C4×D312yes—
460#208—21no—
461#208—21no—
462#208—64no—
463#208C4×Dic312yes—
464#208C4×Dic312yes—
465C2×C3⋊C8—31no—
466C2×C3⋊C8—31no—
467C2×C3⋊C8—31no—
468C2×C3⋊C8—31no—
469C2×C3⋊C8—61no—
470C2×C3⋊C8—61no—
471C2×C3⋊C8—64no—
472C2×C3⋊C8—61no—
473C2×C3⋊C8—61no—
474C2×C3⋊C8—61no—
475C2×C3⋊C8—61no—
476C2×C3⋊C8—121no—
477C2×C3⋊C8—121no—
478C2×C3⋊C8C2×C4×D312yes—
479C2×C3⋊C8C2×C4×D312yes—
480ΓL(1,𝔽25)—64no—
481ΓL(1,𝔽25)C4×Dic314yes—
482ΓL(1,𝔽25)C4×Dic314yes—
483D3×C8—64no—
484D3×C8C2×C4×D314yes—
485D3×C8C22×Dic314yes—
486C3×C16—24no—
487C3×C16—34no—
488C3×C16—34no—
489C3×C16C2×C4×D314yes—
490C3×C16C22×Dic314yes—
491C3⋊C16—34no—
492C3⋊C16—34no—
493C3⋊C16—64no—
494C3⋊C16C2×C4×D314yes—
495C3⋊C16C22×Dic314yes—
496C22×C32—41no—
497C22×C32C2×#9711yescharacteristic
498C22×C32C2×#9711yescharacteristic
499C22×C32C22×M1611yescharacteristic
500C2×C3×D3—42no—
501C2×C3×D3C2×#9714yes—
502C32×C4C2×#9711yescharacteristic
503C32×C4C2×#9711yescharacteristic
504C32×C4C22×C4211yescharacteristic
505C32×C4C22×M1611yescharacteristic
506C3⋊Dic3—41no—
507C3⋊Dic3—41no—
508C3×Dic3—42no—
509C3×Dic3C2×#9714yes—
510C2×#41—31no—
511#131—32no—
512#131—32no—
513#131—32no—
514#131—32no—
515#131—182no—
516#131—182no—
517C2×M16—31no—
518C2×M16—31no—
519C2×M16—32no—
520C2×M16—92no—
521C22×C8—32no—
522C22×C8—92no—
523C22×C8—91no—
524C22×C8C2×D3211yescharacteristic
525C4×Q8—181no—
526C4×D4—182no—
527C4×D4—181no—
528#117—31no—
529#117—92no—
530C2×C42—92no—
531C2×C42—91no—
532M32—32no—
533M32—32no—
534M32—32no—
535M32—32no—
536M32—38no—
537M32—98no—
538M32—92no—
539M32—92no—
540M32D3×Dic312yescomplemented
541M32C2×D3212yes—
542C2×C16—32no—
543C2×C16—32no—
544C2×C16—38no—
545C2×C16—98no—
546C2×C16—92no—
547C2×C16D3×Dic312yescomplemented
548#97—32no—
549#97—92no—
550#97—92no—
551#97—91no—
552#97—91no—
553#97—91no—
554#97—91no—
555C4×C8—32no—
556C4×C8—92no—
557C4×C8—92no—
558C23×C3—21no—
559C23×C3—32no—
560C23×C3C2×ΓL(1,𝔽25)11yescharacteristic
561C23×C3D3×M1611yescharacteristic
562C22×D3C2×ΓL(1,𝔽25)12yes—
563C3×Q8—32no—
564C3×Q8—32no—
565C3×D4—34no—
566C3×D4—34no—
567C3×D4—32no—
568C3×D4—32no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—32no—
576C2×C3×C4—34no—
577C2×C3×C4—34no—
578C2×C3×C4—62no—
579C2×C3×C4C42×D311yescharacteristic
580C2×C3×C4C42×D311yescharacteristic
581C2×C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
582C2×C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
583C2×C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
584C2×C3×C4D3×M1611yescharacteristic
585C2×C3×C4D3×M1611yescharacteristic
586C2×C3×C4D3×M1611yescharacteristic
587C2×C3×C4C2×C4×Dic311yescharacteristic
588C2×C3×C4C2×C4×Dic311yescharacteristic
589C2×C3×C4C22×C4×D311yescharacteristic
590C2×C3×C4C22×C4×D311yescharacteristic
591#67#81514yes—
592#67#81514yes—
593C2×Dic3—22no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—121no—
599C2×Dic3—121no—
600C2×Dic3—242no—
601C2×Dic3—241no—
602C2×Dic3—241no—
603C2×Dic3—242no—
604C2×Dic3C2×ΓL(1,𝔽25)12yes—
605D12#81512yes—
606D12#81512yes—
607C4×D3—242no—
608C4×D3C2×ΓL(1,𝔽25)14yes—
609C4×D3C2×C4×Dic314yes—
610Dic6#81512yes—
611Dic6#81512yes—
612C3×C8—21no—
613C3×C8—21no—
614C3×C8—21no—
615C3×C8—21no—
616C3×C8—34no—
617C3×C8—62no—
618C3×C8C42×D311yescharacteristic
619C3×C8C42×D311yescharacteristic
620C3×C8C2×C4×Dic311yescharacteristic
621C3×C8C2×C4×Dic311yescharacteristic
622C3×C8C22×C4×D311yescharacteristic
623C3×C8C22×C4×D311yescharacteristic
624C3×C8C22×C4×D311yescharacteristic
625C3×C8C23×Dic311yescharacteristic
626C3⋊C8—22no—
627C3⋊C8—61no—
628C3⋊C8—61no—
629C3⋊C8—61no—
630C3⋊C8—61no—
631C3⋊C8—121no—
632C3⋊C8—121no—
633C3⋊C8C2×C4×Dic314yes—
634C2×C32—21no—
635C2×C32—21no—
636C2×C32—21no—
637C2×C32C22×#9711yescharacteristic
638C3×D3—24no—
639#41—32no—
640#41—32no—
641#41—32no—
642#41—32no—
643C2×Q8—31no—
644C2×D4—32no—
645C2×D4—31no—
646C22×C4—32no—
647C22×C4—182no—
648C22×C4—181no—
649C22×C4C4×D3211yescharacteristic
650M16—32no—
651M16—32no—
652M16—34no—
653M16—34no—
654M16—61no—
655M16—61no—
656M16—184no—
657C2×C8—32no—
658C2×C8—34no—
659C2×C8—34no—
660C2×C8—32no—
661C2×C8—91no—
662C2×C8—91no—
663C2×C8—184no—
664C2×C8—181no—
665C2×C8—181no—
666C2×C8C4×D3211yescharacteristic
667C2×C8C4×D3211yescharacteristic
668C2×C8C4×D3211yescharacteristic
669C2×C8C2×D3×Dic311yescharacteristic
670C2×C8C2×D3×Dic311yescharacteristic
671C2×C8C22×D3211yescharacteristic
672C4⋊C4—61no—
673C4⋊C4—182no—
674C22⋊C4—61no—
675C22⋊C4—182no—
676C42—32no—
677C42—91no—
678C42—91no—
679C42—182no—
680C42—181no—
681C16—34no—
682C16—34no—
683C16—94no—
684C16C2×D3×Dic314yes—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—34no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—42no—
692C22×C3—122no—
693C22×C3D3×#9711yescharacteristic
694C22×C3D3×#9711yescharacteristic
695C22×C3C2×#81511yescharacteristic
696C22×C3C2×#81511yescharacteristic
697C22×C3C22×ΓL(1,𝔽25)11yescharacteristic
698C22×C3C2×D3×M1611yescharacteristic
699C2×D3—42no—
700C2×D3C2×#81514yes—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—34no—
706C3×C4—122no—
707C3×C4D3×#9711yescharacteristic
708C3×C4D3×#9711yescharacteristic
709C3×C4C2×#81511yescharacteristic
710C3×C4C2×#81511yescharacteristic
711C3×C4C2×C42×D311yescharacteristic
712C3×C4C22×ΓL(1,𝔽25)11yescharacteristic
713C3×C4C2×D3×M1611yescharacteristic
714C3×C4C22×C4×Dic311yescharacteristic
715Dic3—42no—
716Dic3—121no—
717Dic3—121no—
718Dic3—121no—
719Dic3—121no—
720Dic3—241no—
721Dic3—241no—
722Dic3C2×#81514yes—
723C32#3332911yescharacteristic, complemented, Sylow
724C23—32no—
725C23D3×ΓL(1,𝔽25)11yescharacteristic
726Q8—32no—
727Q8—32no—
728D4—34no—
729D4—34no—
730D4—32no—
731D4—32no—
732C2×C4—32no—
733C2×C4—34no—
734C2×C4—34no—
735C2×C4—62no—
736C2×C4—181no—
737C2×C4—181no—
738C2×C4—722no—
739C2×C4—721no—
740C2×C4D3×ΓL(1,𝔽25)11yescharacteristic
741C2×C4D3×ΓL(1,𝔽25)11yescharacteristic
742C2×C4D3×ΓL(1,𝔽25)11yescharacteristic
743C2×C4C4×D3×Dic311yescharacteristic
744C2×C4C4×D3×Dic311yescharacteristic
745C2×C4C2×C4×D3211yescharacteristic
746C8—34no—
747C8—62no—
748C8—181no—
749C8—181no—
750C8C4×D3×Dic311yescharacteristic
751C8C4×D3×Dic311yescharacteristic
752C8C2×C4×D3211yescharacteristic
753C8C22×D3×Dic311yescharacteristic
754C2×C3—22no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—41no—
763C2×C3—41no—
764C2×C3—64no—
765C2×C3C2×D3×#9711yescharacteristic
766C2×C3C22×#81511yescharacteristic
767D3—24no—
768C22—34no—
769C22—41no—
770C22—122no—
771C22D3×#81511yescharacteristic
772C22D3×#81511yescharacteristic
773C22C2×D3×ΓL(1,𝔽25)11yescharacteristic
774C4—34no—
775C4—122no—
776C4—361no—
777C4—361no—
778C4D3×#81511yescharacteristic
779C4D3×#81511yescharacteristic
780C4C2×D3×ΓL(1,𝔽25)11yescharacteristic
781C4C2×C4×D3×Dic311yescharacteristic
782C3—21no—
783C3#1094784711yescharacteristic, complemented
784C3#1094784811yescharacteristic, complemented
785C2—21no—
786C2—21no—
787C2—21no—
788C2—64no—
789C2C2×D3×#81511yescharacteristic
subgroupG/H
centerC4C2×C4×D3×Dic3
commutatorC32×C4C22×C42
FrattiniC2×C8C22×D32
FittingC2×C32×M32C22
socleC2×C32C22×#97
prime radicalC2×C3×#235C2×C4
cosocleC2×C32×C8C24
hypercenterC2×M32D32
hypocenterC32#33329
LCSG ▷ C32×C4 ▷ C32
UCSC1 ◁ C4 ◁ C2×M32

Complements

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

NH ≅ G/Ntype
4. #11795946C2semidirect
5. #11795942C2semidirect
6. C3×#71425C2semidirect
7. C2×#10589106C2semidirect
8. D3×#4512C2semidirect
9. C2×#10589378C2semidirect
21. C3×#4907C4semidirect
23. C3×#4901C4semidirect
30. #10590622C4semidirect
31. #10590621C4semidirect
48. #71425D3semidirect
80. C32×M32C2×C4semidirect
82. C2×C32×C16C2×C4semidirect
87. #63639C2×C4semidirect
89. C2×C3⋊(C3⋊C16)C2×C4semidirect
92. C3×#812C2×C4semidirect
93. C3×#812C2×C4semidirect
96. C2×C3×C3⋊C16C2×C4semidirect
97. C2×C3×C3⋊C16C2×C4semidirect
98. C3×#798C2×C4semidirect
99. C3×D3×C16C2×C4semidirect
104. #63543C2×C4semidirect
105. D3×C3⋊C16C2×C4semidirect
143. #4907Dic3semidirect
147. #4901Dic3semidirect
275. C3×M32C4×D3semidirect
276. C3×M32C2×Dic3semidirect
283. C2×C3×C16C4×D3semidirect
284. C2×C3×C16C2×Dic3semidirect
314. #812C4×D3semidirect
315. #812C2×Dic3semidirect
322. C2×C3⋊C16C4×D3semidirect
323. C2×C3⋊C16C2×Dic3semidirect
327. #798C2×Dic3semidirect
329. D3×C16C2×Dic3semidirect
540. M32D3×Dic3semidirect
547. C2×C16D3×Dic3semidirect
723. C32#33329semidirect
783. C3#10947847semidirect
784. C3#10947848semidirect

Maximal subgroups

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

subgroupindex
#118994232
C3×#820072
#118573062
#117959462
#117959422
C3×#714252
C2×#105891062
D3×#45122
C2×#105893782
#109478483
#109478473