Finite Group Databasebeta

← C101×#14114 #38796265

Subgroups — C101×#14114 #38796265

Order 25856.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#388×C101C211yesmaximal, characteristic
2C2×#388×C101C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C101C211yesmaximal, characteristic
4C101×#1442C211yesmaximal, characteristic, complemented
5C101×#1441C211yesmaximal, characteristic, complemented
6C101×#1439C211yesmaximal, characteristic
7C101×#1439C211yesmaximal, characteristic
8C101×#1436C211yesmaximal, characteristic, complemented
9C101×#1436C211yesmaximal, characteristic, complemented
10C101×#1436C211yesmaximal, characteristic, complemented
11C101×C4⋊#95C211yesmaximal, characteristic, complemented
12C101×#1434C211yesmaximal, characteristic, complemented
13C101×C22⋊#95C211yesmaximal, characteristic
14C101×C22⋊#95C211yesmaximal, characteristic
15C4×#95×C101C211yesmaximal, characteristic, complemented
16C24×C4×C101C2211yescharacteristic
17C22×C4⋊C4×C101C2211yescharacteristic
18C22×C4⋊C4×C101C2211yescharacteristic
19C22×C4⋊C4×C101C2211yescharacteristic
20C22×C4⋊C4×C101C2211yescharacteristic
21C22×C22⋊C4×C101C2211yescharacteristic
22C22×C22⋊C4×C101C2211yescharacteristic
23C22×C22⋊C4×C101C2211yescharacteristic
24C22×C22⋊C4×C101C2211yescharacteristic
25C22×C22⋊C4×C101C2211yescharacteristic
26C22×C22⋊C4×C101C2211yescharacteristic
27C22×C42×C101C2211yescharacteristic
28C22×C42×C101C2211yescharacteristic
29C22×C42×C101C2211yescharacteristic
30C22×C42×C101C2211yescharacteristic
31#388×C101—24no—
32#388×C101C418yescomplemented
33C4×C22⋊C4×C101—24no—
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
53C2×#95×C101C2211yescharacteristic
54C25×C101C2311yescharacteristic
55C23×C4×C101—22no—
56C23×C4×C101—22no—
57C23×C4×C101—22no—
58C23×C4×C101—22no—
59C23×C4×C101—22no—
60C23×C4×C101—41no—
61C23×C4×C101—41no—
62C23×C4×C101C2311yescharacteristic
63C23×C4×C101C2311yescharacteristic
64C23×C4×C101C2311yescharacteristic
65C23×C4×C101C2311yescharacteristic
66C23×C4×C101C2311yescharacteristic
67C23×C4×C101C2311yescharacteristic
68C23×C4×C101C2311yescharacteristic
69C23×C4×C101C2311yescharacteristic
70C23×C4×C101C2311yescharacteristic
71C23×C4×C101C2311yescharacteristic
72C23×C4×C101C2311yescharacteristic
73C23×C4×C101C2311yescharacteristic
74C23×C4×C101C2311yescharacteristic
75C23×C4×C101C2311yescharacteristic
76C2×C4⋊C4×C101—22no—
77C2×C4⋊C4×C101—22no—
78C2×C4⋊C4×C101—22no—
79C2×C4⋊C4×C101—22no—
80C2×C4⋊C4×C101—22no—
81C2×C4⋊C4×C101—41no—
82C2×C4⋊C4×C101—41no—
83C2×C4⋊C4×C101—41no—
84C2×C4⋊C4×C101—41no—
85C2×C4⋊C4×C101—41no—
86C2×C4⋊C4×C101—41no—
87C2×C4⋊C4×C101C2×C414yescomplemented
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—41no—
96C2×C22⋊C4×C101—41no—
97C2×C22⋊C4×C101—41no—
98C2×C22⋊C4×C101—41no—
99C2×C22⋊C4×C101—41no—
100C2×C22⋊C4×C101—41no—
101C2×C22⋊C4×C101C2×C414yes—
102C2×C22⋊C4×C101C2×C414yes—
103C2×C22⋊C4×C101C2×C414yes—
104C2×C22⋊C4×C101D414yes—
105C2×C22⋊C4×C101Q814yes—
106C2×C42×C101—22no—
107C2×C42×C101—22no—
108C2×C42×C101—22no—
109C2×C42×C101—22no—
110C2×C42×C101—22no—
111C2×C42×C101—22no—
112C2×C42×C101—41no—
113C2×C42×C101—41no—
114C2×C42×C101—41no—
115C2×C42×C101—41no—
116C2×C42×C101—41no—
117C2×C42×C101C2×C414yescomplemented
118#95×C101—22no—
119#95×C101—22no—
120#95×C101—22no—
121#95×C101—22no—
122#95×C101—22no—
123#95×C101—22no—
124#95×C101—22no—
125#95×C101—22no—
126#95×C101—22no—
127#95×C101—22no—
128#95×C101—22no—
129#95×C101—22no—
130#95×C101—22no—
131#95×C101—41no—
132#95×C101—41no—
133#95×C101—41no—
134#95×C101—41no—
135#95×C101—41no—
136#95×C101C2×C414yescomplemented
137#95×C101C2×C414yescomplemented
138C24×C101—21no—
139C24×C101—21no—
140C24×C101—21no—
141C24×C101—21no—
142C24×C101—21no—
143C24×C101—21no—
144C24×C101—21no—
145C24×C101—21no—
146C24×C101—21no—
147C24×C101—21no—
148C24×C101—21no—
149C24×C101—21no—
150C24×C101C22×C412yes—
151C24×C101C2×D412yes—
152C24×C101C2×Q812yes—
153C24×C101C2411yescharacteristic
154C22×C4×C101—21no—
155C22×C4×C101—21no—
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—28no—
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—44no—
236C22×C4×C101—44no—
237C22×C4×C101—44no—
238C22×C4×C101—44no—
239C22×C4×C101—44no—
240C22×C4×C101—44no—
241C22×C4×C101C22×C412yes—
242C22×C4×C101C22×C412yes—
243C22×C4×C101C22×C412yes—
244C22×C4×C101C22×C412yes—
245C22×C4×C101C22×C412yes—
246C22×C4×C101C22×C412yes—
247C22×C4×C101C2×D412yes—
248C22×C4×C101C2×D412yes—
249C22×C4×C101C2×Q812yes—
250C22×C4×C101C2×Q812yes—
251C22×C4×C101#4112yes—
252C22×C4×C101#4112yes—
253C22×C4×C101#4112yes—
254C22×C4×C101#4112yes—
255C22×C4×C101#4112yes—
256C22×C4×C101#4112yes—
257C22×C4×C101#4112yes—
258C22×C4×C101#4112yes—
259C4⋊C4×C101—44no—
260C4⋊C4×C101—44no—
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×C101C4⋊C4116yescomplemented
269C42×C101—44no—
270C42×C101—44no—
271C42×C101—44no—
272C42×C101—44no—
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—22no—
289C23×C101—22no—
290C23×C101—22no—
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×C101—41no—
305C23×C101—41no—
306C23×C101—41no—
307C23×C101C2×C4⋊C414yes—
308C23×C101C23×C411yescharacteristic
309C23×C101C22×D411yescharacteristic
310C23×C101C22×Q811yescharacteristic
311C23×C101C2×#4111yescharacteristic
312C23×C101C2×#4111yescharacteristic
313C23×C101C2×#4111yescharacteristic
314C23×C101C2×#4111yescharacteristic
315C23×C101C2×#4111yescharacteristic
316C23×C101C2×#4111yescharacteristic
317C23×C101C2×#4111yescharacteristic
318C23×C101C2×#4111yescharacteristic
319C23×C101H(5,𝔽2)11yescharacteristic
320C23×C101H(5,𝔽2)11yescharacteristic
321C23×C101H(5,𝔽2)11yescharacteristic
322C23×C101H(5,𝔽2)11yescharacteristic
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—22no—
352C2×C4×C101—22no—
353C2×C4×C101—22no—
354C2×C4×C101—22no—
355C2×C4×C101—22no—
356C2×C4×C101—22no—
357C2×C4×C101—22no—
358C2×C4×C101—22no—
359C2×C4×C101—22no—
360C2×C4×C101—22no—
361C2×C4×C101—22no—
362C2×C4×C101—22no—
363C2×C4×C101—22no—
364C2×C4×C101—22no—
365C2×C4×C101—22no—
366C2×C4×C101—22no—
367C2×C4×C101—22no—
368C2×C4×C101—416no—
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×C101C2×C4⋊C414yes—
420C2×C4×C101C2×C4⋊C414yes—
421C2×C4×C101#12614yes—
422C22×C101—24no—
423C22×C101—24no—
424C22×C101—24no—
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×C101—42no—
436C22×C101—42no—
437C22×C101C22×C4⋊C411yescharacteristic
438C22×C101C4×#4111yescharacteristic
439C22×C101C4×#4111yescharacteristic
440C22×C101C4×#4111yescharacteristic
441C22×C101C4×#4111yescharacteristic
442C22×C101#51811yescharacteristic
443C22×C101#51811yescharacteristic
444C22×C101#52511yescharacteristic
445C22×C101#52511yescharacteristic
446C22×C101C2×#12611yescharacteristic
447C22×C101#52911yescharacteristic
448C22×C101#52911yescharacteristic
449C22×C101#52911yescharacteristic
450C22×C101#53311yescharacteristic
451C22×C101#53311yescharacteristic
452C22×C101#53811yescharacteristic
453C22×C101#53811yescharacteristic
454C22×C101#54011yescharacteristic
455C22×C101#54011yescharacteristic
456C22×C101#54611yescharacteristic
457C22×C101#54611yescharacteristic
458C22×C101#54611yescharacteristic
459C22×C101#54611yescharacteristic
460C22×C101#55111yescharacteristic
461C22×C101#55111yescharacteristic
462C22×C101#55111yescharacteristic
463C22×C101#55311yescharacteristic
464C22×C101#55311yescharacteristic
465C22×C101#55411yescharacteristic
466C22×C101#55411yescharacteristic
467C22×C101#55411yescharacteristic
468C22×C101#55411yescharacteristic
469C22×C101#55511yescharacteristic
470C22×C101#55511yescharacteristic
471C22×C101#55911yescharacteristic
472C4×C101—24no—
473C4×C101—24no—
474C4×C101—24no—
475C4×C101—42no—
476C4×C101—42no—
477C4×C101—42no—
478C4×C101—42no—
479C4×C101—42no—
480C4×C101—42no—
481C4×C101—42no—
482C4×C101—42no—
483C4×C101—42no—
484C4×C101—81no—
485C4×C101—81no—
486#14114C10111yesmaximal, characteristic, direct product factor, Sylow
487C2×C101—44no—
488C2×C101#229611yescharacteristic
489C2×C101C4×#12611yescharacteristic
490C2×C101#233311yescharacteristic
491C2×C101#234911yescharacteristic
492C2×C101#234911yescharacteristic
493C2×C101#237211yescharacteristic
494C2×C101#237411yescharacteristic
495C2×C101#245711yescharacteristic
496C2×C101#245911yescharacteristic
497C2×C101#247611yescharacteristic
498C2×C101#248011yescharacteristic
499C2×C101#249711yescharacteristic
500C2×C101#252211yescharacteristic
501C2×C101#257411yescharacteristic
502C2×C101#258911yescharacteristic
503C2×#388C2×C10111yescharacteristic
504C2×#388C2×C10111yescharacteristic
505C2×C4×C22⋊C4C2×C10111yescharacteristic
506#1442C2×C10111yescharacteristic, complemented
507#1441C2×C10111yescharacteristic, complemented
508#1439C2×C10111yescharacteristic
509#1439C2×C10111yescharacteristic
510#1436C2×C10111yescharacteristic, complemented
511#1436C2×C10111yescharacteristic, complemented
512#1436C2×C10111yescharacteristic, complemented
513C4⋊#95C2×C10111yescharacteristic, complemented
514#1434C2×C10111yescharacteristic, complemented
515C22⋊#95C2×C10111yescharacteristic
516C22⋊#95C2×C10111yescharacteristic
517C4×#95C2×C10111yescharacteristic, complemented
518C101#1411411yescharacteristic, direct product factor, Sylow
519C24×C4C22×C10111yescharacteristic
520C22×C4⋊C4C22×C10111yescharacteristic
521C22×C4⋊C4C22×C10111yescharacteristic
522C22×C4⋊C4C22×C10111yescharacteristic
523C22×C4⋊C4C22×C10111yescharacteristic
524C22×C22⋊C4C22×C10111yescharacteristic
525C22×C22⋊C4C22×C10111yescharacteristic
526C22×C22⋊C4C22×C10111yescharacteristic
527C22×C22⋊C4C22×C10111yescharacteristic
528C22×C22⋊C4C22×C10111yescharacteristic
529C22×C22⋊C4C22×C10111yescharacteristic
530C22×C42C22×C10111yescharacteristic
531C22×C42C22×C10111yescharacteristic
532C22×C42C22×C10111yescharacteristic
533C22×C42C22×C10111yescharacteristic
534#388—24no—
535#388C4×C10118yescomplemented
536C4×C22⋊C4—24no—
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
554C2×#95C22×C10111yescharacteristic
555C2×#95C22×C10111yescharacteristic
556C2×#95C22×C10111yescharacteristic
557C25C23×C10111yescharacteristic
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—22no—
561C23×C4—22no—
562C23×C4—22no—
563C23×C4—41no—
564C23×C4—41no—
565C23×C4C23×C10111yescharacteristic
566C23×C4C23×C10111yescharacteristic
567C23×C4C23×C10111yescharacteristic
568C23×C4C23×C10111yescharacteristic
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
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—41no—
585C2×C4⋊C4—41no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4C2×C4×C10114yescomplemented
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—41no—
599C2×C22⋊C4—41no—
600C2×C22⋊C4—41no—
601C2×C22⋊C4—41no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4C2×C4×C10114yes—
605C2×C22⋊C4C2×C4×C10114yes—
606C2×C22⋊C4C2×C4×C10114yes—
607C2×C22⋊C4D4×C10114yes—
608C2×C22⋊C4Q8×C10114yes—
609C2×C42—22no—
610C2×C42—22no—
611C2×C42—22no—
612C2×C42—22no—
613C2×C42—22no—
614C2×C42—22no—
615C2×C42—41no—
616C2×C42—41no—
617C2×C42—41no—
618C2×C42—41no—
619C2×C42—41no—
620C2×C42C2×C4×C10114yescomplemented
621#95—22no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—22no—
629#95—22no—
630#95—22no—
631#95—22no—
632#95—22no—
633#95—22no—
634#95—41no—
635#95—41no—
636#95—41no—
637#95—41no—
638#95—41no—
639#95C2×C4×C10114yescomplemented
640#95C2×C4×C10114yescomplemented
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C22×C4×C10112yes—
654C24C2×D4×C10112yes—
655C24C2×Q8×C10112yes—
656C24C24×C10111yescharacteristic
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—28no—
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—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4C22×C4×C10112yes—
745C22×C4C22×C4×C10112yes—
746C22×C4C22×C4×C10112yes—
747C22×C4C22×C4×C10112yes—
748C22×C4C22×C4×C10112yes—
749C22×C4C22×C4×C10112yes—
750C22×C4C2×D4×C10112yes—
751C22×C4C2×D4×C10112yes—
752C22×C4C2×Q8×C10112yes—
753C22×C4C2×Q8×C10112yes—
754C22×C4#41×C10112yes—
755C22×C4#41×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—
764C4⋊C4—44no—
765C4⋊C4—44no—
766C22⋊C4—28no—
767C22⋊C4—44no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—44no—
771C22⋊C4C4⋊C4×C101116yescomplemented
772C42—44no—
773C42—44no—
774C42—44no—
775C42—44no—
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—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C2×C4⋊C4×C10114yes—
811C23C23×C4×C10111yescharacteristic
812C23C22×D4×C10111yescharacteristic
813C23C22×Q8×C10111yescharacteristic
814C23C2×#41×C10111yescharacteristic
815C23C2×#41×C10111yescharacteristic
816C23C2×#41×C10111yescharacteristic
817C23C2×#41×C10111yescharacteristic
818C23C2×#41×C10111yescharacteristic
819C23C2×#41×C10111yescharacteristic
820C23C2×#41×C10111yescharacteristic
821C23C2×#41×C10111yescharacteristic
822C23H(5,𝔽2)×C10111yescharacteristic
823C23H(5,𝔽2)×C10111yescharacteristic
824C23H(5,𝔽2)×C10111yescharacteristic
825C23H(5,𝔽2)×C10111yescharacteristic
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—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—416no—
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—
921C2×C4—41no—
922C2×C4C2×C4⋊C4×C10114yes—
923C2×C4C2×C4⋊C4×C10114yes—
924C2×C4#126×C10114yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C22×C4⋊C4×C10111yescharacteristic
941C22C4×#41×C10111yescharacteristic
942C22C4×#41×C10111yescharacteristic
943C22C4×#41×C10111yescharacteristic
944C22C4×#41×C10111yescharacteristic
945C22#518×C10111yescharacteristic
946C22#518×C10111yescharacteristic
947C22#525×C10111yescharacteristic
948C22#525×C10111yescharacteristic
949C22C2×#126×C10111yescharacteristic
950C22#529×C10111yescharacteristic
951C22#529×C10111yescharacteristic
952C22#529×C10111yescharacteristic
953C22#533×C10111yescharacteristic
954C22#533×C10111yescharacteristic
955C22#538×C10111yescharacteristic
956C22#538×C10111yescharacteristic
957C22#540×C10111yescharacteristic
958C22#540×C10111yescharacteristic
959C22#546×C10111yescharacteristic
960C22#546×C10111yescharacteristic
961C22#546×C10111yescharacteristic
962C22#546×C10111yescharacteristic
963C22#551×C10111yescharacteristic
964C22#551×C10111yescharacteristic
965C22#551×C10111yescharacteristic
966C22#553×C10111yescharacteristic
967C22#553×C10111yescharacteristic
968C22#554×C10111yescharacteristic
969C22#554×C10111yescharacteristic
970C22#554×C10111yescharacteristic
971C22#554×C10111yescharacteristic
972C22#555×C10111yescharacteristic
973C22#555×C10111yescharacteristic
974C22#559×C10111yescharacteristic
975C4—24no—
976C4—24no—
977C4—24no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—81no—
988C4—81no—
989C2—44no—
990C2C101×#229611yescharacteristic
991C2C4×#126×C10111yescharacteristic
992C2C101×#233311yescharacteristic
993C2C101×#234911yescharacteristic
994C2C101×#234911yescharacteristic
995C2C101×#237211yescharacteristic
996C2C101×#237411yescharacteristic
997C2C101×#245711yescharacteristic
998C2C101×#245911yescharacteristic
999C2C101×#247611yescharacteristic
1000C2C101×#248011yescharacteristic
1001C2C101×#249711yescharacteristic
1002C2C101×#252211yescharacteristic
1003C2C101×#257411yescharacteristic
1004C2C101×#258911yescharacteristic
subgroupG/H
center, socleC24×C101C24
commutatorC23C23×C4×C101
Frattini, cosocleC24C24×C101
prime radicalC25×C101C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C101 ◁ G

Complements

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

NH ≅ G/Ntype
4. C101×#1442C2semidirect
5. C101×#1441C2semidirect
8. C101×#1436C2semidirect
9. C101×#1436C2semidirect
10. C101×#1436C2semidirect
11. C101×C4⋊#95C2semidirect
12. C101×#1434C2semidirect
15. C4×#95×C101C2semidirect
32. #388×C101C4semidirect
87. C2×C4⋊C4×C101C2×C4semidirect
117. C2×C42×C101C2×C4semidirect
136. #95×C101C2×C4semidirect
137. #95×C101C2×C4semidirect
268. C22⋊C4×C101C4⋊C4semidirect
486. #14114C101direct (N × H)
506. #1442C2×C101semidirect
507. #1441C2×C101semidirect
510. #1436C2×C101semidirect
511. #1436C2×C101semidirect
512. #1436C2×C101semidirect
513. C4⋊#95C2×C101semidirect
514. #1434C2×C101semidirect
517. C4×#95C2×C101semidirect
518. C101#14114direct (N × H)
535. #388C4×C101semidirect
590. C2×C4⋊C4C2×C4×C101semidirect
620. C2×C42C2×C4×C101semidirect
639. #95C2×C4×C101semidirect
640. #95C2×C4×C101semidirect
771. C22⋊C4C4⋊C4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#388×C1012
C2×C4×C22⋊C4×C1012
C101×#14422
C101×#14412
C101×#14392
C101×#14362
C101×C4⋊#952
C101×#14342
C101×C22⋊#952
C4×#95×C1012
#14114101