Finite Group Databasebeta

← C101×#17255 #38799406

Subgroups — C101×#17255 #38799406

Order 25856.

1382 conjugacy classes of subgroups.

The subgroup lattice has 1102 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#1443C211yesmaximal, characteristic, complemented
2C101×#1443C211yesmaximal, characteristic, complemented
3C101×#1442C211yesmaximal, characteristic, complemented
4C101×#1442C211yesmaximal, characteristic, complemented
5C101×#1440C211yesmaximal, characteristic, complemented
6C101×#1440C211yesmaximal, characteristic, complemented
7C101×#1440C211yesmaximal, characteristic, complemented
8C101×#1440C211yesmaximal, characteristic, complemented
9C101×#1439C211yesmaximal, characteristic, complemented
10C101×#1439C211yesmaximal, characteristic, complemented
11C101×#1439C211yesmaximal, characteristic, complemented
12C101×#1439C211yesmaximal, characteristic, complemented
13C101×#1438C211yesmaximal, characteristic
14C101×#1438C211yesmaximal, characteristic
15C101×#1438C211yesmaximal, characteristic
16C23×D4×C101C2211yescharacteristic
17C22×C4⋊C4×C101C2211yescharacteristic
18C22×C4⋊C4×C101C2211yescharacteristic
19C22×C22⋊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×C22⋊C4×C101C2211yescharacteristic
27C22×C22⋊C4×C101C2211yescharacteristic
28C22×C22⋊C4×C101C2211yescharacteristic
29C22×C22⋊C4×C101C2211yescharacteristic
30C22×C22⋊C4×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
51C25×C101C2311yescharacteristic
52C25×C101C2311yescharacteristic
53C22×D4×C101—22no—
54C22×D4×C101—22no—
55C22×D4×C101—22no—
56C22×D4×C101—41no—
57C22×D4×C101—41no—
58C22×D4×C101—41no—
59C22×D4×C101—41no—
60C23×C4×C101C2311yescharacteristic
61C23×C4×C101C2311yescharacteristic
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
73C2×C4⋊C4×C101—41no—
74C2×C4⋊C4×C101—41no—
75C2×C4⋊C4×C101—41no—
76C2×C4⋊C4×C101—41no—
77C2×C4⋊C4×C101—41no—
78C2×C4⋊C4×C101—41no—
79C2×C22⋊C4×C101—22no—
80C2×C22⋊C4×C101—22no—
81C2×C22⋊C4×C101—22no—
82C2×C22⋊C4×C101—22no—
83C2×C22⋊C4×C101—22no—
84C2×C22⋊C4×C101—22no—
85C2×C22⋊C4×C101—22no—
86C2×C22⋊C4×C101—22no—
87C2×C22⋊C4×C101—41no—
88C2×C22⋊C4×C101—41no—
89C2×C22⋊C4×C101—41no—
90C2×C22⋊C4×C101—41no—
91C2×C22⋊C4×C101—41no—
92C2×C22⋊C4×C101—41no—
93C2×C22⋊C4×C101—41no—
94C2×C22⋊C4×C101—41no—
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×C101—41no—
102C2×C22⋊C4×C101—41no—
103C2×C22⋊C4×C101—41no—
104C2×C22⋊C4×C101—41no—
105C2×C22⋊C4×C101—41no—
106C2×C22⋊C4×C101—41no—
107C2×C22⋊C4×C101—41no—
108C2×C22⋊C4×C101—41no—
109C2×C22⋊C4×C101—41no—
110C2×C22⋊C4×C101—41no—
111C2×C22⋊C4×C101—41no—
112C2×C22⋊C4×C101—41no—
113C2×C22⋊C4×C101—41no—
114C2×C22⋊C4×C101—41no—
115#95×C101—22no—
116#95×C101—22no—
117#95×C101—22no—
118#95×C101—22no—
119#95×C101—41no—
120#95×C101—41no—
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—
133#95×C101—41no—
134#95×C101—41no—
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×C101—21no—
146C24×C101—21no—
147C24×C101—21no—
148C24×C101—21no—
149C24×C101—21no—
150C24×C101—21no—
151C24×C101—21no—
152C24×C101—21no—
153C24×C101—21no—
154C24×C101—21no—
155C24×C101—21no—
156C24×C101—21no—
157C24×C101—21no—
158C24×C101—21no—
159C24×C101—21no—
160C24×C101—21no—
161C24×C101—21no—
162C24×C101—21no—
163C24×C101#4112yes—
164C24×C101#4112yes—
165C24×C101C2411yescharacteristic
166C2×D4×C101—44no—
167C2×D4×C101—44no—
168C2×D4×C101—44no—
169C2×D4×C101—44no—
170C2×D4×C101—44no—
171C2×D4×C101—44no—
172C2×D4×C101—44no—
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—21no—
245C22×C4×C101—21no—
246C22×C4×C101—21no—
247C22×C4×C101—21no—
248C22×C4×C101—21no—
249C22×C4×C101—21no—
250C22×C4×C101—21no—
251C22×C4×C101—21no—
252C22×C4×C101—21no—
253C22×C4×C101—21no—
254C22×C4×C101—21no—
255C22×C4×C101—21no—
256C22×C4×C101—21no—
257C22×C4×C101—21no—
258C22×C4×C101—21no—
259C22×C4×C101—21no—
260C22×C4×C101—21no—
261C22×C4×C101#4112yes—
262C22×C4×C101#4112yes—
263C22×C4×C101#4112yes—
264C4⋊C4×C101—44no—
265C4⋊C4×C101—44no—
266C22⋊C4×C101—44no—
267C22⋊C4×C101—44no—
268C22⋊C4×C101—44no—
269C22⋊C4×C101—44no—
270C22⋊C4×C101—44no—
271C22⋊C4×C101—44no—
272C22⋊C4×C101—44no—
273C22⋊C4×C101—44no—
274C22⋊C4×C101—44no—
275C22⋊C4×C101—44no—
276C22⋊C4×C101—44no—
277C22⋊C4×C101—44no—
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—22no—
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×C101—41no—
308C23×C101—41no—
309C23×C101—41no—
310C23×C101—41no—
311C23×C101—41no—
312C23×C101—41no—
313C23×C101—41no—
314C23×C101—41no—
315C23×C101—41no—
316C23×C101—41no—
317C23×C101—41no—
318C23×C101—41no—
319C23×C101—41no—
320C23×C101—41no—
321C23×C101—41no—
322C23×C101—41no—
323C23×C101—41no—
324C23×C101—41no—
325C23×C101—41no—
326C23×C101—41no—
327C23×C101—41no—
328C23×C101—41no—
329C23×C101—41no—
330C23×C101—41no—
331C23×C101—41no—
332C23×C101—41no—
333C23×C101—41no—
334C23×C101—41no—
335C23×C101—41no—
336C23×C101—41no—
337C23×C101—41no—
338C23×C101—41no—
339C23×C101—41no—
340C23×C101—41no—
341C23×C101—41no—
342C23×C101—41no—
343C23×C101—41no—
344C23×C101—41no—
345C23×C101—41no—
346C23×C101—41no—
347C23×C101—41no—
348C23×C101C2×#4111yescharacteristic
349C23×C101C2×#4111yescharacteristic
350C23×C101C2×#4111yescharacteristic
351C23×C101C2×#4111yescharacteristic
352C23×C101C2×#4111yescharacteristic
353C23×C101H(5,𝔽2)11yescharacteristic
354C23×C101H(5,𝔽2)11yescharacteristic
355C23×C101H(5,𝔽2)11yescharacteristic
356C23×C101H(5,𝔽2)11yescharacteristic
357C23×C101H(5,𝔽2)11yescharacteristic
358C23×C101H(5,𝔽2)11yescharacteristic
359C23×C101H(5,𝔽2)11yescharacteristic
360C23×C101H(5,𝔽2)11yescharacteristic
361C23×C101H(5,𝔽2)11yescharacteristic
362C23×C1012−1+411yescharacteristic
363D4×C101—416no—
364C2×C4×C101—22no—
365C2×C4×C101—22no—
366C2×C4×C101—22no—
367C2×C4×C101—22no—
368C2×C4×C101—22no—
369C2×C4×C101—22no—
370C2×C4×C101—22no—
371C2×C4×C101—22no—
372C2×C4×C101—22no—
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—
420C2×C4×C101—41no—
421C2×C4×C101—41no—
422C2×C4×C101—41no—
423C2×C4×C101—41no—
424C2×C4×C101—41no—
425C2×C4×C101—41no—
426C2×C4×C101—41no—
427C2×C4×C101—41no—
428C2×C4×C101—41no—
429C2×C4×C101—41no—
430C2×C4×C101—41no—
431C2×C4×C101—41no—
432C2×C4×C101—41no—
433C2×C4×C101—41no—
434C2×C4×C101—41no—
435C2×C4×C101—41no—
436C2×C4×C101—41no—
437C2×C4×C101—41no—
438C2×C4×C101—41no—
439C2×C4×C101—41no—
440C2×C4×C101—41no—
441C2×C4×C101—41no—
442C2×C4×C101—41no—
443C2×C4×C101—41no—
444C2×C4×C101—41no—
445C2×C4×C101—41no—
446C2×C4×C101—41no—
447C2×C4×C101—41no—
448C2×C4×C101—41no—
449C2×C4×C101—41no—
450C2×C4×C101—41no—
451C2×C4×C101—41no—
452C2×C4×C101—41no—
453C2×C4×C101—41no—
454C2×C4×C101—41no—
455C22×C101—42no—
456C22×C101—42no—
457C22×C101—42no—
458C22×C101—42no—
459C22×C101—42no—
460C22×C101—42no—
461C22×C101—42no—
462C22×C101—42no—
463C22×C101—42no—
464C22×C101—42no—
465C22×C101—42no—
466C22×C101—42no—
467C22×C101—42no—
468C22×C101—42no—
469C22×C101—81no—
470C22×C101—81no—
471C22×C101—81no—
472C22×C101—81no—
473C22×C101—81no—
474C22×C101—81no—
475C22×C101—81no—
476C22×C101—81no—
477C22×C101—81no—
478C22×C101—81no—
479C22×C101—81no—
480C22×C101—81no—
481C22×C101—81no—
482C22×C101—81no—
483C22×C101—81no—
484C22×C101—81no—
485C22×C101#53811yescharacteristic
486C22×C101#53811yescharacteristic
487C22×C101#53811yescharacteristic
488C22×C101#53811yescharacteristic
489C22×C101#53811yescharacteristic
490C22×C101#53811yescharacteristic
491C22×C101#53811yescharacteristic
492C22×C101#53811yescharacteristic
493C22×C101#53811yescharacteristic
494C22×C101#53911yescharacteristic
495C22×C101#53911yescharacteristic
496C22×C101#54011yescharacteristic
497C22×C101#54011yescharacteristic
498C22×C101#54011yescharacteristic
499C22×C101#54211yescharacteristic
500C22×C101#55111yescharacteristic
501C22×C101#55111yescharacteristic
502C22×C101#55111yescharacteristic
503C22×C101#55111yescharacteristic
504C22×C101#55211yescharacteristic
505C22×C101#55311yescharacteristic
506C22×C101#55311yescharacteristic
507C22×C101#55311yescharacteristic
508C22×C101#55511yescharacteristic
509C22×C101#55911yescharacteristic
510C22×C101#56011yescharacteristic
511C22×C101#56011yescharacteristic
512C22×C101#56011yescharacteristic
513C22×C101#56011yescharacteristic
514C22×C101#56011yescharacteristic
515C22×C101#56011yescharacteristic
516C22×C101H(3,𝔽4)11yescharacteristic
517C22×C101#56211yescharacteristic
518C22×C101#56211yescharacteristic
519C22×C101#56211yescharacteristic
520C4×C101—42no—
521C4×C101—42no—
522C4×C101—42no—
523C4×C101—81no—
524C4×C101—81no—
525C4×C101—81no—
526C4×C101—81no—
527C4×C101—81no—
528C4×C101—81no—
529C4×C101—81no—
530C4×C101—81no—
531C4×C101—81no—
532C4×C101—81no—
533#17255C10111yesmaximal, characteristic, direct product factor, Sylow
534C2×C101—82no—
535C2×C101—82no—
536C2×C101#273611yescharacteristic
537C2×C101#274311yescharacteristic
538C2×C101#274911yescharacteristic
539C2×C101#275611yescharacteristic
540C2×C101#276111yescharacteristic
541C2×C101#277811yescharacteristic
542C2×C101#278111yescharacteristic
543C2×C101#279611yescharacteristic
544C2×C101#279711yescharacteristic
545C2×C101#280311yescharacteristic
546C2×C101#282411yescharacteristic
547C2×C101#282511yescharacteristic
548C2×C101#282611yescharacteristic
549C2×C101#282811yescharacteristic
550C2×C101#282911yescharacteristic
551#1443C2×C10111yescharacteristic, complemented
552#1443C2×C10111yescharacteristic, complemented
553#1442C2×C10111yescharacteristic, complemented
554#1442C2×C10111yescharacteristic, complemented
555#1440C2×C10111yescharacteristic, complemented
556#1440C2×C10111yescharacteristic, complemented
557#1440C2×C10111yescharacteristic, complemented
558#1440C2×C10111yescharacteristic, complemented
559#1439C2×C10111yescharacteristic, complemented
560#1439C2×C10111yescharacteristic, complemented
561#1439C2×C10111yescharacteristic, complemented
562#1439C2×C10111yescharacteristic, complemented
563#1438C2×C10111yescharacteristic
564#1438C2×C10111yescharacteristic
565#1438C2×C10111yescharacteristic
566C101#1725511yescharacteristic, direct product factor, Sylow
567C23×D4C22×C10111yescharacteristic
568C22×C4⋊C4C22×C10111yescharacteristic
569C22×C4⋊C4C22×C10111yescharacteristic
570C22×C22⋊C4C22×C10111yescharacteristic
571C22×C22⋊C4C22×C10111yescharacteristic
572C22×C22⋊C4C22×C10111yescharacteristic
573C22×C22⋊C4C22×C10111yescharacteristic
574C22×C22⋊C4C22×C10111yescharacteristic
575C22×C22⋊C4C22×C10111yescharacteristic
576C22×C22⋊C4C22×C10111yescharacteristic
577C22×C22⋊C4C22×C10111yescharacteristic
578C22×C22⋊C4C22×C10111yescharacteristic
579C22×C22⋊C4C22×C10111yescharacteristic
580C22×C22⋊C4C22×C10111yescharacteristic
581C22×C22⋊C4C22×C10111yescharacteristic
582C2×#95C22×C10111yescharacteristic
583C2×#95C22×C10111yescharacteristic
584C2×#95C22×C10111yescharacteristic
585C2×#95C22×C10111yescharacteristic
586C2×#95C22×C10111yescharacteristic
587C2×#95C22×C10111yescharacteristic
588C2×#95C22×C10111yescharacteristic
589C2×#95C22×C10111yescharacteristic
590C2×#95C22×C10111yescharacteristic
591C2×#95C22×C10111yescharacteristic
592C2×#95C22×C10111yescharacteristic
593C2×#95C22×C10111yescharacteristic
594C2×#95C22×C10111yescharacteristic
595C2×#95C22×C10111yescharacteristic
596C2×#95C22×C10111yescharacteristic
597C2×#95C22×C10111yescharacteristic
598C2×#95C22×C10111yescharacteristic
599C2×#95C22×C10111yescharacteristic
600C2×#95C22×C10111yescharacteristic
601C2×#95C22×C10111yescharacteristic
602C25C23×C10111yescharacteristic
603C25C23×C10111yescharacteristic
604C22×D4—22no—
605C22×D4—22no—
606C22×D4—22no—
607C22×D4—41no—
608C22×D4—41no—
609C22×D4—41no—
610C22×D4—41no—
611C23×C4C23×C10111yescharacteristic
612C23×C4C23×C10111yescharacteristic
613C23×C4C23×C10111yescharacteristic
614C23×C4C23×C10111yescharacteristic
615C23×C4C23×C10111yescharacteristic
616C23×C4C23×C10111yescharacteristic
617C23×C4C23×C10111yescharacteristic
618C23×C4C23×C10111yescharacteristic
619C23×C4C23×C10111yescharacteristic
620C23×C4C23×C10111yescharacteristic
621C23×C4C23×C10111yescharacteristic
622C23×C4C23×C10111yescharacteristic
623C23×C4C23×C10111yescharacteristic
624C2×C4⋊C4—41no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4—41no—
628C2×C4⋊C4—41no—
629C2×C4⋊C4—41no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—41no—
639C2×C22⋊C4—41no—
640C2×C22⋊C4—41no—
641C2×C22⋊C4—41no—
642C2×C22⋊C4—41no—
643C2×C22⋊C4—41no—
644C2×C22⋊C4—41no—
645C2×C22⋊C4—41no—
646C2×C22⋊C4—41no—
647C2×C22⋊C4—41no—
648C2×C22⋊C4—41no—
649C2×C22⋊C4—41no—
650C2×C22⋊C4—41no—
651C2×C22⋊C4—41no—
652C2×C22⋊C4—41no—
653C2×C22⋊C4—41no—
654C2×C22⋊C4—41no—
655C2×C22⋊C4—41no—
656C2×C22⋊C4—41no—
657C2×C22⋊C4—41no—
658C2×C22⋊C4—41no—
659C2×C22⋊C4—41no—
660C2×C22⋊C4—41no—
661C2×C22⋊C4—41no—
662C2×C22⋊C4—41no—
663C2×C22⋊C4—41no—
664C2×C22⋊C4—41no—
665C2×C22⋊C4—41no—
666#95—22no—
667#95—22no—
668#95—22no—
669#95—22no—
670#95—41no—
671#95—41no—
672#95—41no—
673#95—41no—
674#95—41no—
675#95—41no—
676#95—41no—
677#95—41no—
678#95—41no—
679#95—41no—
680#95—41no—
681#95—41no—
682#95—41no—
683#95—41no—
684#95—41no—
685#95—41no—
686C24—21no—
687C24—21no—
688C24—21no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24—21no—
704C24—21no—
705C24—21no—
706C24—21no—
707C24—21no—
708C24—21no—
709C24—21no—
710C24—21no—
711C24—21no—
712C24—21no—
713C24—21no—
714C24#41×C10112yes—
715C24#41×C10112yes—
716C24C24×C10111yescharacteristic
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—44no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
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—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4#41×C10112yes—
813C22×C4#41×C10112yes—
814C22×C4#41×C10112yes—
815C4⋊C4—44no—
816C4⋊C4—44no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—44no—
820C22⋊C4—44no—
821C22⋊C4—44no—
822C22⋊C4—44no—
823C22⋊C4—44no—
824C22⋊C4—44no—
825C22⋊C4—44no—
826C22⋊C4—44no—
827C22⋊C4—44no—
828C22⋊C4—44no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23C2×#41×C10111yescharacteristic
900C23C2×#41×C10111yescharacteristic
901C23C2×#41×C10111yescharacteristic
902C23C2×#41×C10111yescharacteristic
903C23C2×#41×C10111yescharacteristic
904C23H(5,𝔽2)×C10111yescharacteristic
905C23H(5,𝔽2)×C10111yescharacteristic
906C23H(5,𝔽2)×C10111yescharacteristic
907C23H(5,𝔽2)×C10111yescharacteristic
908C23H(5,𝔽2)×C10111yescharacteristic
909C23H(5,𝔽2)×C10111yescharacteristic
910C23H(5,𝔽2)×C10111yescharacteristic
911C23H(5,𝔽2)×C10111yescharacteristic
912C23H(5,𝔽2)×C10111yescharacteristic
913C232−1+4×C10111yescharacteristic
914D4—416no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C22—42no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—42no—
1012C22—42no—
1013C22—42no—
1014C22—42no—
1015C22—42no—
1016C22—42no—
1017C22—42no—
1018C22—42no—
1019C22—42no—
1020C22—81no—
1021C22—81no—
1022C22—81no—
1023C22—81no—
1024C22—81no—
1025C22—81no—
1026C22—81no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—81no—
1031C22—81no—
1032C22—81no—
1033C22—81no—
1034C22—81no—
1035C22—81no—
1036C22#538×C10111yescharacteristic
1037C22#538×C10111yescharacteristic
1038C22#538×C10111yescharacteristic
1039C22#538×C10111yescharacteristic
1040C22#538×C10111yescharacteristic
1041C22#538×C10111yescharacteristic
1042C22#538×C10111yescharacteristic
1043C22#538×C10111yescharacteristic
1044C22#538×C10111yescharacteristic
1045C22#539×C10111yescharacteristic
1046C22#539×C10111yescharacteristic
1047C22#540×C10111yescharacteristic
1048C22#540×C10111yescharacteristic
1049C22#540×C10111yescharacteristic
1050C22#542×C10111yescharacteristic
1051C22#551×C10111yescharacteristic
1052C22#551×C10111yescharacteristic
1053C22#551×C10111yescharacteristic
1054C22#551×C10111yescharacteristic
1055C22#552×C10111yescharacteristic
1056C22#553×C10111yescharacteristic
1057C22#553×C10111yescharacteristic
1058C22#553×C10111yescharacteristic
1059C22#555×C10111yescharacteristic
1060C22#559×C10111yescharacteristic
1061C22#560×C10111yescharacteristic
1062C22#560×C10111yescharacteristic
1063C22#560×C10111yescharacteristic
1064C22#560×C10111yescharacteristic
1065C22#560×C10111yescharacteristic
1066C22#560×C10111yescharacteristic
1067C22H(3,𝔽4)×C10111yescharacteristic
1068C22#562×C10111yescharacteristic
1069C22#562×C10111yescharacteristic
1070C22#562×C10111yescharacteristic
1071C4—42no—
1072C4—42no—
1073C4—42no—
1074C4—81no—
1075C4—81no—
1076C4—81no—
1077C4—81no—
1078C4—81no—
1079C4—81no—
1080C4—81no—
1081C4—81no—
1082C4—81no—
1083C4—81no—
1084C2—82no—
1085C2—82no—
1086C2C101×#273611yescharacteristic
1087C2C101×#274311yescharacteristic
1088C2C101×#274911yescharacteristic
1089C2C101×#275611yescharacteristic
1090C2C101×#276111yescharacteristic
1091C2C101×#277811yescharacteristic
1092C2C101×#278111yescharacteristic
1093C2C101×#279611yescharacteristic
1094C2C101×#279711yescharacteristic
1095C2C101×#280311yescharacteristic
1096C2C101×#282411yescharacteristic
1097C2C101×#282511yescharacteristic
1098C2C101×#282611yescharacteristic
1099C2C101×#282811yescharacteristic
1100C2C101×#282911yescharacteristic
subgroupG/H
center, socleC24×C101C24
commutator, Frattini, cosocleC24C24×C101
prime radicalC23×D4×C101C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#1443C2semidirect
2. C101×#1443C2semidirect
3. C101×#1442C2semidirect
4. C101×#1442C2semidirect
5. C101×#1440C2semidirect
6. C101×#1440C2semidirect
7. C101×#1440C2semidirect
8. C101×#1440C2semidirect
9. C101×#1439C2semidirect
10. C101×#1439C2semidirect
11. C101×#1439C2semidirect
12. C101×#1439C2semidirect
533. #17255C101direct (N × H)
551. #1443C2×C101semidirect
552. #1443C2×C101semidirect
553. #1442C2×C101semidirect
554. #1442C2×C101semidirect
555. #1440C2×C101semidirect
556. #1440C2×C101semidirect
557. #1440C2×C101semidirect
558. #1440C2×C101semidirect
559. #1439C2×C101semidirect
560. #1439C2×C101semidirect
561. #1439C2×C101semidirect
562. #1439C2×C101semidirect
566. C101#17255direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#14432
C101×#14422
C101×#14402
C101×#14392
C101×#14382
#17255101