Finite Group Databasebeta

← C101×#15586 #38797737

Subgroups — C101×#15586 #38797737

Order 25856.

1494 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#393×C101C211yesmaximal, characteristic
2C2×#388×C101C211yesmaximal, characteristic
3C101×#1446C211yesmaximal, characteristic, complemented
4C101×#1446C211yesmaximal, characteristic, complemented
5C101×#1445C211yesmaximal, characteristic, complemented
6C101×#1443C211yesmaximal, characteristic, complemented
7C101×#1442C211yesmaximal, characteristic, complemented
8C101×#1442C211yesmaximal, characteristic, complemented
9C101×#1440C211yesmaximal, characteristic
10C101×#1439C211yesmaximal, characteristic
11C101×#1436C211yesmaximal, characteristic, complemented
12C101×#1434C211yesmaximal, characteristic, complemented
13C101×C22⋊#95C211yesmaximal, characteristic
14C101×C22⋊#95C211yesmaximal, characteristic
15C101×C22⋊#95C211yesmaximal, characteristic
16C23×Q8×C101C2211yescharacteristic
17C24×C4×C101C2211yescharacteristic
18C22×C4⋊C4×C101C2211yescharacteristic
19C22×C4⋊C4×C101C2211yescharacteristic
20C22×C22⋊C4×C101C2211yescharacteristic
21C22×C22⋊C4×C101C2211yescharacteristic
22C22×C22⋊C4×C101C2211yescharacteristic
23C22×C22⋊C4×C101C2211yescharacteristic
24C22×C22⋊C4×C101C2211yescharacteristic
25C22×C22⋊C4×C101C2211yescharacteristic
26C22×C42×C101C2211yescharacteristic
27#393×C101—24no—
28#388×C101—24no—
29C2×#95×C101C2211yescharacteristic
30C2×#95×C101C2211yescharacteristic
31C2×#95×C101C2211yescharacteristic
32C2×#95×C101C2211yescharacteristic
33C2×#95×C101C2211yescharacteristic
34C2×#95×C101C2211yescharacteristic
35C2×#95×C101C2211yescharacteristic
36C2×#95×C101C2211yescharacteristic
37C2×#95×C101C2211yescharacteristic
38C2×#95×C101C2211yescharacteristic
39C2×#95×C101C2211yescharacteristic
40C2×#95×C101C2211yescharacteristic
41C2×#95×C101C2211yescharacteristic
42C2×#95×C101C2211yescharacteristic
43C2×#95×C101C2211yescharacteristic
44C2×#95×C101C2211yescharacteristic
45C2×#95×C101C2211yescharacteristic
46C2×#95×C101C2211yescharacteristic
47C2×#95×C101C2211yescharacteristic
48C2×#95×C101C2211yescharacteristic
49C2×#95×C101C2211yescharacteristic
50C2×#95×C101C2211yescharacteristic
51C2×#95×C101C2211yescharacteristic
52C2×#95×C101C2211yescharacteristic
53C25×C101C2311yescharacteristic
54C22×Q8×C101—22no—
55C22×Q8×C101—22no—
56C22×Q8×C101—22no—
57C22×Q8×C101—41no—
58C22×Q8×C101—41no—
59C22×Q8×C101—41no—
60C22×Q8×C101—41no—
61C23×C4×C101—22no—
62C23×C4×C101—22no—
63C23×C4×C101—22no—
64C23×C4×C101—41no—
65C23×C4×C101—41no—
66C23×C4×C101—41no—
67C23×C4×C101—41no—
68C23×C4×C101C2311yescharacteristic
69C23×C4×C101C2311yescharacteristic
70C23×C4×C101C2311yescharacteristic
71C23×C4×C101C2311yescharacteristic
72C23×C4×C101C2311yescharacteristic
73C23×C4×C101C2311yescharacteristic
74C23×C4×C101C2311yescharacteristic
75C23×C4×C101C2311yescharacteristic
76C23×C4×C101C2311yescharacteristic
77C23×C4×C101C2311yescharacteristic
78C23×C4×C101C2311yescharacteristic
79C23×C4×C101C2311yescharacteristic
80C23×C4×C101C2311yescharacteristic
81C23×C4×C101C2311yescharacteristic
82C2×C4⋊C4×C101—22no—
83C2×C4⋊C4×C101—22no—
84C2×C4⋊C4×C101—22no—
85C2×C4⋊C4×C101—41no—
86C2×C4⋊C4×C101—41no—
87C2×C4⋊C4×C101—41no—
88C2×C22⋊C4×C101—22no—
89C2×C22⋊C4×C101—22no—
90C2×C22⋊C4×C101—22no—
91C2×C22⋊C4×C101—22no—
92C2×C22⋊C4×C101—22no—
93C2×C22⋊C4×C101—22no—
94C2×C22⋊C4×C101—22no—
95C2×C22⋊C4×C101—22no—
96C2×C22⋊C4×C101—22no—
97C2×C22⋊C4×C101—22no—
98C2×C22⋊C4×C101—41no—
99C2×C22⋊C4×C101—41no—
100C2×C22⋊C4×C101—41no—
101C2×C22⋊C4×C101—41no—
102C2×C22⋊C4×C101—41no—
103C2×C22⋊C4×C101—41no—
104C2×C22⋊C4×C101D414yes—
105C2×C22⋊C4×C101Q814yescomplemented
106C2×C42×C101—22no—
107C2×C42×C101—22no—
108C2×C42×C101—41no—
109#95×C101—22no—
110#95×C101—22no—
111#95×C101—22no—
112#95×C101—22no—
113#95×C101—22no—
114#95×C101—22no—
115#95×C101—22no—
116#95×C101—22no—
117#95×C101—22no—
118#95×C101—22no—
119#95×C101—22no—
120#95×C101—22no—
121#95×C101—41no—
122#95×C101—41no—
123#95×C101—41no—
124#95×C101—41no—
125#95×C101—41no—
126#95×C101—41no—
127#95×C101—41no—
128#95×C101—41no—
129#95×C101—41no—
130#95×C101—41no—
131#95×C101—41no—
132#95×C101—41no—
133C24×C101—21no—
134C24×C101—21no—
135C24×C101—21no—
136C24×C101—21no—
137C24×C101—21no—
138C24×C101—21no—
139C24×C101—21no—
140C24×C101—21no—
141C24×C101—21no—
142C24×C101—21no—
143C24×C101—21no—
144C24×C101—21no—
145C24×C101C2×D412yes—
146C24×C101C2×Q812yes—
147C24×C101#4112yes—
148C24×C101C2411yescharacteristic
149C2×Q8×C101—44no—
150C2×Q8×C101—44no—
151C2×Q8×C101—44no—
152C2×Q8×C101—44no—
153C2×Q8×C101—44no—
154C2×Q8×C101—44no—
155C2×Q8×C101—44no—
156C22×C4×C101—21no—
157C22×C4×C101—21no—
158C22×C4×C101—21no—
159C22×C4×C101—21no—
160C22×C4×C101—21no—
161C22×C4×C101—21no—
162C22×C4×C101—21no—
163C22×C4×C101—21no—
164C22×C4×C101—21no—
165C22×C4×C101—21no—
166C22×C4×C101—21no—
167C22×C4×C101—21no—
168C22×C4×C101—21no—
169C22×C4×C101—21no—
170C22×C4×C101—21no—
171C22×C4×C101—21no—
172C22×C4×C101—21no—
173C22×C4×C101—21no—
174C22×C4×C101—21no—
175C22×C4×C101—21no—
176C22×C4×C101—21no—
177C22×C4×C101—21no—
178C22×C4×C101—21no—
179C22×C4×C101—21no—
180C22×C4×C101—21no—
181C22×C4×C101—21no—
182C22×C4×C101—21no—
183C22×C4×C101—21no—
184C22×C4×C101—21no—
185C22×C4×C101—21no—
186C22×C4×C101—21no—
187C22×C4×C101—21no—
188C22×C4×C101—21no—
189C22×C4×C101—21no—
190C22×C4×C101—21no—
191C22×C4×C101—21no—
192C22×C4×C101—21no—
193C22×C4×C101—21no—
194C22×C4×C101—21no—
195C22×C4×C101—21no—
196C22×C4×C101—21no—
197C22×C4×C101—21no—
198C22×C4×C101—21no—
199C22×C4×C101—21no—
200C22×C4×C101—21no—
201C22×C4×C101—21no—
202C22×C4×C101—21no—
203C22×C4×C101—21no—
204C22×C4×C101—21no—
205C22×C4×C101—21no—
206C22×C4×C101—21no—
207C22×C4×C101—21no—
208C22×C4×C101—21no—
209C22×C4×C101—21no—
210C22×C4×C101—21no—
211C22×C4×C101—21no—
212C22×C4×C101—21no—
213C22×C4×C101—21no—
214C22×C4×C101—21no—
215C22×C4×C101—21no—
216C22×C4×C101—21no—
217C22×C4×C101—21no—
218C22×C4×C101—21no—
219C22×C4×C101—21no—
220C22×C4×C101—21no—
221C22×C4×C101—21no—
222C22×C4×C101—21no—
223C22×C4×C101—21no—
224C22×C4×C101—21no—
225C22×C4×C101—21no—
226C22×C4×C101—21no—
227C22×C4×C101—21no—
228C22×C4×C101—21no—
229C22×C4×C101—21no—
230C22×C4×C101—21no—
231C22×C4×C101—21no—
232C22×C4×C101—21no—
233C22×C4×C101—21no—
234C22×C4×C101—21no—
235C22×C4×C101—21no—
236C22×C4×C101—21no—
237C22×C4×C101—21no—
238C22×C4×C101—21no—
239C22×C4×C101—21no—
240C22×C4×C101—21no—
241C22×C4×C101—21no—
242C22×C4×C101—21no—
243C22×C4×C101—21no—
244C22×C4×C101—44no—
245C22×C4×C101—44no—
246C22×C4×C101—44no—
247C22×C4×C101—44no—
248C22×C4×C101—44no—
249C22×C4×C101—44no—
250C22×C4×C101—44no—
251C22×C4×C101C2×D412yes—
252C22×C4×C101C2×D412yes—
253C22×C4×C101C2×Q812yes—
254C22×C4×C101C2×Q812yes—
255C22×C4×C101#4112yes—
256C22×C4×C101#4112yes—
257C22×C4×C101#4112yes—
258C22×C4×C101#4112yes—
259C22×C4×C101#4112yes—
260C22×C4×C101#4112yes—
261C4⋊C4×C101—44no—
262C4⋊C4×C101—44no—
263C22⋊C4×C101—28no—
264C22⋊C4×C101—44no—
265C22⋊C4×C101—44no—
266C22⋊C4×C101—44no—
267C22⋊C4×C101—44no—
268C22⋊C4×C101—44no—
269C42×C101—44no—
270C23×C101—22no—
271C23×C101—22no—
272C23×C101—22no—
273C23×C101—22no—
274C23×C101—22no—
275C23×C101—22no—
276C23×C101—22no—
277C23×C101—22no—
278C23×C101—22no—
279C23×C101—22no—
280C23×C101—22no—
281C23×C101—22no—
282C23×C101—22no—
283C23×C101—22no—
284C23×C101—22no—
285C23×C101—22no—
286C23×C101—22no—
287C23×C101—22no—
288C23×C101—41no—
289C23×C101—41no—
290C23×C101—41no—
291C23×C101—41no—
292C23×C101—41no—
293C23×C101—41no—
294C23×C101—41no—
295C23×C101—41no—
296C23×C101—41no—
297C23×C101—41no—
298C23×C101—41no—
299C23×C101—41no—
300C23×C101—41no—
301C23×C101—41no—
302C23×C101—41no—
303C23×C101—41no—
304C23×C101C22⋊Q814yes—
305C23×C101C22×D411yescharacteristic
306C23×C101C22×Q811yescharacteristic
307C23×C101C2×#4111yescharacteristic
308C23×C101C2×#4111yescharacteristic
309C23×C101C2×#4111yescharacteristic
310C23×C101C2×#4111yescharacteristic
311C23×C101C2×#4111yescharacteristic
312C23×C101C2×#4111yescharacteristic
313C23×C101C2×#4111yescharacteristic
314C23×C101H(5,𝔽2)11yescharacteristic
315C23×C101H(5,𝔽2)11yescharacteristic
316C23×C101H(5,𝔽2)11yescharacteristic
317C23×C101H(5,𝔽2)11yescharacteristic
318C23×C101H(5,𝔽2)11yescharacteristic
319C23×C1012−1+411yescharacteristic
320Q8×C101—416no—
321C2×C4×C101—22no—
322C2×C4×C101—22no—
323C2×C4×C101—22no—
324C2×C4×C101—22no—
325C2×C4×C101—22no—
326C2×C4×C101—22no—
327C2×C4×C101—22no—
328C2×C4×C101—22no—
329C2×C4×C101—22no—
330C2×C4×C101—22no—
331C2×C4×C101—22no—
332C2×C4×C101—22no—
333C2×C4×C101—22no—
334C2×C4×C101—22no—
335C2×C4×C101—22no—
336C2×C4×C101—22no—
337C2×C4×C101—22no—
338C2×C4×C101—22no—
339C2×C4×C101—22no—
340C2×C4×C101—22no—
341C2×C4×C101—22no—
342C2×C4×C101—22no—
343C2×C4×C101—22no—
344C2×C4×C101—22no—
345C2×C4×C101—22no—
346C2×C4×C101—22no—
347C2×C4×C101—22no—
348C2×C4×C101—22no—
349C2×C4×C101—22no—
350C2×C4×C101—22no—
351C2×C4×C101—416no—
352C2×C4×C101—41no—
353C2×C4×C101—41no—
354C2×C4×C101—41no—
355C2×C4×C101—41no—
356C2×C4×C101—41no—
357C2×C4×C101—41no—
358C2×C4×C101—41no—
359C2×C4×C101—41no—
360C2×C4×C101—41no—
361C2×C4×C101—41no—
362C2×C4×C101—41no—
363C2×C4×C101—41no—
364C2×C4×C101—41no—
365C2×C4×C101—41no—
366C2×C4×C101—41no—
367C2×C4×C101—41no—
368C2×C4×C101—41no—
369C2×C4×C101—41no—
370C2×C4×C101—41no—
371C2×C4×C101—41no—
372C2×C4×C101—41no—
373C2×C4×C101—41no—
374C2×C4×C101—41no—
375C2×C4×C101—41no—
376C2×C4×C101—41no—
377C2×C4×C101—41no—
378C2×C4×C101—41no—
379C2×C4×C101—41no—
380C2×C4×C101—41no—
381C2×C4×C101—41no—
382C2×C4×C101—41no—
383C2×C4×C101—41no—
384C2×C4×C101—41no—
385C2×C4×C101—41no—
386C2×C4×C101—41no—
387C2×C4×C101—41no—
388C2×C4×C101—41no—
389C2×C4×C101—41no—
390C2×C4×C101—41no—
391C2×C4×C101—41no—
392C2×C4×C101—41no—
393C2×C4×C101—41no—
394C2×C4×C101—41no—
395C2×C4×C101—41no—
396C2×C4×C101—41no—
397C2×C4×C101—41no—
398C2×C4×C101—41no—
399C2×C4×C101—41no—
400C2×C4×C101—41no—
401C2×C4×C101—41no—
402C2×C4×C101—41no—
403C2×C4×C101—41no—
404C2×C4×C101—41no—
405C2×C4×C101—41no—
406C2×C4×C101—41no—
407C2×C4×C101—41no—
408C2×C4×C101—41no—
409C2×C4×C101—41no—
410C2×C4×C101—41no—
411C2×C4×C101—41no—
412C2×C4×C101—41no—
413C2×C4×C101—41no—
414C2×C4×C101—41no—
415C2×C4×C101—41no—
416C2×C4×C101—41no—
417C2×C4×C101—41no—
418C2×C4×C101—41no—
419C2×C4×C101—41no—
420C22×C101—24no—
421C22×C101—24no—
422C22×C101—24no—
423C22×C101—42no—
424C22×C101—42no—
425C22×C101—42no—
426C22×C101—42no—
427C22×C101—42no—
428C22×C101—42no—
429C22×C101—42no—
430C22×C101—42no—
431C22×C101—42no—
432C22×C101—42no—
433C22×C101—42no—
434C22×C101—42no—
435C22×C101C2×C22⋊Q811yescharacteristic
436C22×C101#52911yescharacteristic
437C22×C101#52911yescharacteristic
438C22×C101#52911yescharacteristic
439C22×C101#53211yescharacteristic
440C22×C101#53311yescharacteristic
441C22×C101#53411yescharacteristic
442C22×C101#53811yescharacteristic
443C22×C101#53811yescharacteristic
444C22×C101#53811yescharacteristic
445C22×C101#53811yescharacteristic
446C22×C101#53811yescharacteristic
447C22×C101#54211yescharacteristic
448C22×C101#54211yescharacteristic
449C22×C101#54411yescharacteristic
450C22×C101#54611yescharacteristic
451C22×C101#54611yescharacteristic
452C22×C101#54611yescharacteristic
453C22×C101#54711yescharacteristic
454C22×C101#55111yescharacteristic
455C22×C101#55111yescharacteristic
456C22×C101#55111yescharacteristic
457C22×C101#55111yescharacteristic
458C22×C101#55111yescharacteristic
459C22×C101#55111yescharacteristic
460C22×C101#55211yescharacteristic
461C22×C101#55411yescharacteristic
462C22×C101#55411yescharacteristic
463C22×C101#55411yescharacteristic
464C22×C101#55411yescharacteristic
465C22×C101#55511yescharacteristic
466C22×C101#55611yescharacteristic
467C22×C101#55911yescharacteristic
468C22×C101H(3,𝔽4)11yescharacteristic
469C22×C101#56211yescharacteristic
470C4×C101—42no—
471C4×C101—42no—
472C4×C101—42no—
473C4×C101—42no—
474C4×C101—42no—
475C4×C101—42no—
476C4×C101—42no—
477C4×C101—42no—
478C4×C101—42no—
479C4×C101—42no—
480C4×C101—81no—
481C4×C101—81no—
482C4×C101—81no—
483C4×C101—81no—
484#15586C10111yesmaximal, characteristic, direct product factor, Sylow
485C2×C101—44no—
486C2×C101#243811yescharacteristic
487C2×C101#245011yescharacteristic
488C2×C101#252111yescharacteristic
489C2×C101#252711yescharacteristic
490C2×C101#255711yescharacteristic
491C2×C101#256411yescharacteristic
492C2×C101#257211yescharacteristic
493C2×C101#257411yescharacteristic
494C2×C101#258911yescharacteristic
495C2×C101#268411yescharacteristic
496C2×C101#268611yescharacteristic
497C2×C101#273611yescharacteristic
498C2×C101#275111yescharacteristic
499C2×C101#276311yescharacteristic
500C2×C101#278811yescharacteristic
501C2×#393C2×C10111yescharacteristic
502C2×#388C2×C10111yescharacteristic
503#1446C2×C10111yescharacteristic, complemented
504#1446C2×C10111yescharacteristic, complemented
505#1445C2×C10111yescharacteristic, complemented
506#1443C2×C10111yescharacteristic, complemented
507#1442C2×C10111yescharacteristic, complemented
508#1442C2×C10111yescharacteristic, complemented
509#1440C2×C10111yescharacteristic
510#1439C2×C10111yescharacteristic
511#1436C2×C10111yescharacteristic, complemented
512#1434C2×C10111yescharacteristic, complemented
513C22⋊#95C2×C10111yescharacteristic
514C22⋊#95C2×C10111yescharacteristic
515C22⋊#95C2×C10111yescharacteristic
516C101#1558611yescharacteristic, direct product factor, Sylow
517C23×Q8C22×C10111yescharacteristic
518C24×C4C22×C10111yescharacteristic
519C22×C4⋊C4C22×C10111yescharacteristic
520C22×C4⋊C4C22×C10111yescharacteristic
521C22×C22⋊C4C22×C10111yescharacteristic
522C22×C22⋊C4C22×C10111yescharacteristic
523C22×C22⋊C4C22×C10111yescharacteristic
524C22×C22⋊C4C22×C10111yescharacteristic
525C22×C22⋊C4C22×C10111yescharacteristic
526C22×C22⋊C4C22×C10111yescharacteristic
527C22×C42C22×C10111yescharacteristic
528#393—24no—
529#388—24no—
530C2×#95C22×C10111yescharacteristic
531C2×#95C22×C10111yescharacteristic
532C2×#95C22×C10111yescharacteristic
533C2×#95C22×C10111yescharacteristic
534C2×#95C22×C10111yescharacteristic
535C2×#95C22×C10111yescharacteristic
536C2×#95C22×C10111yescharacteristic
537C2×#95C22×C10111yescharacteristic
538C2×#95C22×C10111yescharacteristic
539C2×#95C22×C10111yescharacteristic
540C2×#95C22×C10111yescharacteristic
541C2×#95C22×C10111yescharacteristic
542C2×#95C22×C10111yescharacteristic
543C2×#95C22×C10111yescharacteristic
544C2×#95C22×C10111yescharacteristic
545C2×#95C22×C10111yescharacteristic
546C2×#95C22×C10111yescharacteristic
547C2×#95C22×C10111yescharacteristic
548C2×#95C22×C10111yescharacteristic
549C2×#95C22×C10111yescharacteristic
550C2×#95C22×C10111yescharacteristic
551C2×#95C22×C10111yescharacteristic
552C2×#95C22×C10111yescharacteristic
553C2×#95C22×C10111yescharacteristic
554C25C23×C10111yescharacteristic
555C22×Q8—22no—
556C22×Q8—22no—
557C22×Q8—22no—
558C22×Q8—41no—
559C22×Q8—41no—
560C22×Q8—41no—
561C22×Q8—41no—
562C23×C4—22no—
563C23×C4—22no—
564C23×C4—22no—
565C23×C4—41no—
566C23×C4—41no—
567C23×C4—41no—
568C23×C4—41no—
569C23×C4C23×C10111yescharacteristic
570C23×C4C23×C10111yescharacteristic
571C23×C4C23×C10111yescharacteristic
572C23×C4C23×C10111yescharacteristic
573C23×C4C23×C10111yescharacteristic
574C23×C4C23×C10111yescharacteristic
575C23×C4C23×C10111yescharacteristic
576C23×C4C23×C10111yescharacteristic
577C23×C4C23×C10111yescharacteristic
578C23×C4C23×C10111yescharacteristic
579C23×C4C23×C10111yescharacteristic
580C23×C4C23×C10111yescharacteristic
581C23×C4C23×C10111yescharacteristic
582C23×C4C23×C10111yescharacteristic
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—41no—
589C2×C22⋊C4—22no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—41no—
600C2×C22⋊C4—41no—
601C2×C22⋊C4—41no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4—41no—
605C2×C22⋊C4D4×C10114yes—
606C2×C22⋊C4Q8×C10114yescomplemented
607C2×C42—22no—
608C2×C42—22no—
609C2×C42—41no—
610#95—22no—
611#95—22no—
612#95—22no—
613#95—22no—
614#95—22no—
615#95—22no—
616#95—22no—
617#95—22no—
618#95—22no—
619#95—22no—
620#95—22no—
621#95—22no—
622#95—41no—
623#95—41no—
624#95—41no—
625#95—41no—
626#95—41no—
627#95—41no—
628#95—41no—
629#95—41no—
630#95—41no—
631#95—41no—
632#95—41no—
633#95—41no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24C2×D4×C10112yes—
647C24C2×Q8×C10112yes—
648C24#41×C10112yes—
649C24C24×C10111yescharacteristic
650C2×Q8—44no—
651C2×Q8—44no—
652C2×Q8—44no—
653C2×Q8—44no—
654C2×Q8—44no—
655C2×Q8—44no—
656C2×Q8—44no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4C2×D4×C10112yes—
753C22×C4C2×D4×C10112yes—
754C22×C4C2×Q8×C10112yes—
755C22×C4C2×Q8×C10112yes—
756C22×C4#41×C10112yes—
757C22×C4#41×C10112yes—
758C22×C4#41×C10112yes—
759C22×C4#41×C10112yes—
760C22×C4#41×C10112yes—
761C22×C4#41×C10112yes—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C22⋊C4—28no—
765C22⋊C4—44no—
766C22⋊C4—44no—
767C22⋊C4—44no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C42—44no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23C22⋊Q8×C10114yes—
806C23C22×D4×C10111yescharacteristic
807C23C22×Q8×C10111yescharacteristic
808C23C2×#41×C10111yescharacteristic
809C23C2×#41×C10111yescharacteristic
810C23C2×#41×C10111yescharacteristic
811C23C2×#41×C10111yescharacteristic
812C23C2×#41×C10111yescharacteristic
813C23C2×#41×C10111yescharacteristic
814C23C2×#41×C10111yescharacteristic
815C23H(5,𝔽2)×C10111yescharacteristic
816C23H(5,𝔽2)×C10111yescharacteristic
817C23H(5,𝔽2)×C10111yescharacteristic
818C23H(5,𝔽2)×C10111yescharacteristic
819C23H(5,𝔽2)×C10111yescharacteristic
820C232−1+4×C10111yescharacteristic
821Q8—416no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—416no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C22—24no—
922C22—24no—
923C22—24no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22C2×C22⋊Q8×C10111yescharacteristic
937C22#529×C10111yescharacteristic
938C22#529×C10111yescharacteristic
939C22#529×C10111yescharacteristic
940C22#532×C10111yescharacteristic
941C22#533×C10111yescharacteristic
942C22#534×C10111yescharacteristic
943C22#538×C10111yescharacteristic
944C22#538×C10111yescharacteristic
945C22#538×C10111yescharacteristic
946C22#538×C10111yescharacteristic
947C22#538×C10111yescharacteristic
948C22#542×C10111yescharacteristic
949C22#542×C10111yescharacteristic
950C22#544×C10111yescharacteristic
951C22#546×C10111yescharacteristic
952C22#546×C10111yescharacteristic
953C22#546×C10111yescharacteristic
954C22#547×C10111yescharacteristic
955C22#551×C10111yescharacteristic
956C22#551×C10111yescharacteristic
957C22#551×C10111yescharacteristic
958C22#551×C10111yescharacteristic
959C22#551×C10111yescharacteristic
960C22#551×C10111yescharacteristic
961C22#552×C10111yescharacteristic
962C22#554×C10111yescharacteristic
963C22#554×C10111yescharacteristic
964C22#554×C10111yescharacteristic
965C22#554×C10111yescharacteristic
966C22#555×C10111yescharacteristic
967C22#556×C10111yescharacteristic
968C22#559×C10111yescharacteristic
969C22H(3,𝔽4)×C10111yescharacteristic
970C22#562×C10111yescharacteristic
971C4—42no—
972C4—42no—
973C4—42no—
974C4—42no—
975C4—42no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—81no—
982C4—81no—
983C4—81no—
984C4—81no—
985C2—44no—
986C2C101×#243811yescharacteristic
987C2C101×#245011yescharacteristic
988C2C101×#252111yescharacteristic
989C2C101×#252711yescharacteristic
990C2C101×#255711yescharacteristic
991C2C101×#256411yescharacteristic
992C2C101×#257211yescharacteristic
993C2C101×#257411yescharacteristic
994C2C101×#258911yescharacteristic
995C2C101×#268411yescharacteristic
996C2C101×#268611yescharacteristic
997C2C101×#273611yescharacteristic
998C2C101×#275111yescharacteristic
999C2C101×#276311yescharacteristic
1000C2C101×#278811yescharacteristic
subgroupG/H
center, socleC24×C101C24
commutator, Frattini, cosocleC24C24×C101
prime radicalC25×C101C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C101 ◁ G

Complements

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

NH ≅ G/Ntype
3. C101×#1446C2semidirect
4. C101×#1446C2semidirect
5. C101×#1445C2semidirect
6. C101×#1443C2semidirect
7. C101×#1442C2semidirect
8. C101×#1442C2semidirect
11. C101×#1436C2semidirect
12. C101×#1434C2semidirect
105. C2×C22⋊C4×C101Q8semidirect
484. #15586C101direct (N × H)
503. #1446C2×C101semidirect
504. #1446C2×C101semidirect
505. #1445C2×C101semidirect
506. #1443C2×C101semidirect
507. #1442C2×C101semidirect
508. #1442C2×C101semidirect
511. #1436C2×C101semidirect
512. #1434C2×C101semidirect
516. C101#15586direct (N × H)
606. C2×C22⋊C4Q8×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#393×C1012
C2×#388×C1012
C101×#14462
C101×#14452
C101×#14432
C101×#14422
C101×#14402
C101×#14392
C101×#14362
C101×#14342
C101×C22⋊#952
#15586101