Finite Group Databasebeta

← C101×#27036 #38809187

Subgroups — C101×#27036 #38809187

Order 25856.

708 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#2497C211yesmaximal, characteristic
2C101×#2360C211yesmaximal, characteristic
3C101×#2072C211yesmaximal, characteristic, complemented
4C101×#2068C211yesmaximal, characteristic, complemented
5C101×#2036C211yesmaximal, characteristic
6C101×#2036C211yesmaximal, characteristic
7C101×#1947C211yesmaximal, characteristic, complemented
8C101×#1942C211yesmaximal, characteristic, complemented
9C101×#1923C211yesmaximal, characteristic
10C101×#1921C211yesmaximal, characteristic, complemented
11C101×#1921C211yesmaximal, characteristic, complemented
12C101×#1863C211yesmaximal, characteristic, complemented
13C101×#1852C211yesmaximal, characteristic
14C101×#1824C211yesmaximal, characteristic
15C4×#103×C101C211yesmaximal, characteristic, complemented
16C2×C22⋊Q8×C101C2211yescharacteristic
17C2×C4×Q8×C101C2211yescharacteristic
18C22×C4⋊C4×C101C2211yescharacteristic
19C2×#107×C101C2211yescharacteristic
20C2×#107×C101C2211yescharacteristic
21C2×#107×C101C2211yescharacteristic
22C2×#107×C101C2211yescharacteristic
23C2×C4⋊C8×C101C2211yescharacteristic
24C2×#103×C101C2211yescharacteristic
25C2×#103×C101C2211yescharacteristic
26C2×#103×C101C2211yescharacteristic
27C2×#103×C101C2211yescharacteristic
28C2×C22⋊C8×C101C2211yescharacteristic
29C2×C22⋊C8×C101C2211yescharacteristic
30C2×C4×C8×C101C2211yescharacteristic
31#400×C101—21no—
32#396×C101—21no—
33#391×C101C2211yescharacteristic
34#389×C101—21no—
35#389×C101C2211yescharacteristic
36#389×C101C2211yescharacteristic
37#389×C101C2211yescharacteristic
38#388×C101—21no—
39#387×C101—21no—
40#387×C101—21no—
41#385×C101—21no—
42#384×C101C2211yescharacteristic
43#380×C101C2211yescharacteristic
44#380×C101C2211yescharacteristic
45C4×C4⋊C4×C101C2211yescharacteristic
46C4×C4⋊C4×C101C2211yescharacteristic
47C4×C22⋊C4×C101—21no—
48C4×C22⋊C4×C101C2211yescharacteristic
49#340×C101C2211yescharacteristic
50#340×C101C2211yescharacteristic
51#340×C101C2211yescharacteristic
52#340×C101C2211yescharacteristic
53#340×C101C2211yescharacteristic
54#340×C101C2211yescharacteristic
55#340×C101C2211yescharacteristic
56#340×C101C2211yescharacteristic
57#336×C101C2211yescharacteristic
58#336×C101C2211yescharacteristic
59C22×Q8×C101C2311yescharacteristic
60C23×C4×C101—21no—
61C23×C4×C101C2311yescharacteristic
62C22×C8×C101C2311yescharacteristic
63C22×C8×C101C2311yescharacteristic
64C22×C8×C101C2311yescharacteristic
65C22×C8×C101C2311yescharacteristic
66C22⋊Q8×C101—22no—
67C22⋊Q8×C101—22no—
68C4×Q8×C101—22no—
69C4×Q8×C101—41no—
70C2×C4⋊C4×C101—21no—
71C2×C4⋊C4×C101—22no—
72C2×C4⋊C4×C101—21no—
73C2×C4⋊C4×C101—21no—
74C2×C4⋊C4×C101—21no—
75C2×C4⋊C4×C101—21no—
76C2×C4⋊C4×C101—21no—
77C2×C4⋊C4×C101—21no—
78C2×C4⋊C4×C101—21no—
79C2×C4⋊C4×C101—41no—
80C2×C4⋊C4×C101C2311yescharacteristic
81C2×C4⋊C4×C101C2311yescharacteristic
82C2×C4⋊C4×C101C2311yescharacteristic
83C2×C4⋊C4×C101C2311yescharacteristic
84C2×C4⋊C4×C101C2311yescharacteristic
85C2×C4⋊C4×C101C2311yescharacteristic
86C2×C4⋊C4×C101C2311yescharacteristic
87C2×C22⋊C4×C101—21no—
88C2×C22⋊C4×C101—21no—
89C2×C22⋊C4×C101—21no—
90C2×C22⋊C4×C101D411yescharacteristic
91C2×C22⋊C4×C101D411yescharacteristic
92C2×C42×C101—21no—
93C2×C42×C101—21no—
94C2×C42×C101—21no—
95C2×C42×C101C2311yescharacteristic
96C2×C42×C101C2311yescharacteristic
97#107×C101—22no—
98#107×C101—22no—
99#107×C101—22no—
100#107×C101—41no—
101C4⋊C8×C101—22no—
102#103×C101—22no—
103#103×C101—22no—
104#103×C101—22no—
105#103×C101—41no—
106C22⋊C8×C101—22no—
107C22⋊C8×C101—41no—
108C4×C8×C101—41no—
109#95×C101—21no—
110#95×C101—21no—
111#95×C101—21no—
112#95×C101—21no—
113#95×C101—21no—
114#95×C101—21no—
115#95×C101—21no—
116#95×C101—21no—
117#95×C101—21no—
118#95×C101D411yescharacteristic
119#95×C101D411yescharacteristic
120C24×C101C2×D411yescharacteristic
121C2×Q8×C101—21no—
122C2×Q8×C101—21no—
123C2×Q8×C101—21no—
124C2×Q8×C101—21no—
125C2×Q8×C101—21no—
126C2×Q8×C101#4112yes—
127C22×C4×C101—21no—
128C22×C4×C101—21no—
129C22×C4×C101—21no—
130C22×C4×C101—21no—
131C22×C4×C101—21no—
132C22×C4×C101—21no—
133C22×C4×C101—21no—
134C22×C4×C101—21no—
135C22×C4×C101—21no—
136C22×C4×C101—21no—
137C22×C4×C101—21no—
138C22×C4×C101—21no—
139C22×C4×C101—21no—
140C22×C4×C101—21no—
141C22×C4×C101—42no—
142C22×C4×C101—42no—
143C22×C4×C101—81no—
144C22×C4×C101C2×D411yescharacteristic
145C22×C4×C101C2×D411yescharacteristic
146C22×C4×C101C2×D411yescharacteristic
147C22×C4×C101C2×D411yescharacteristic
148C22×C4×C101C2×D411yescharacteristic
149C22×C4×C101C2411yescharacteristic
150C2×C8×C101—21no—
151C2×C8×C101—21no—
152C2×C8×C101—21no—
153C2×C8×C101—21no—
154C2×C8×C101—21no—
155C2×C8×C101—21no—
156C2×C8×C101—21no—
157C2×C8×C101—21no—
158C2×C8×C101—21no—
159C2×C8×C101—21no—
160C2×C8×C101—21no—
161C2×C8×C101#4112yes—
162C4⋊C4×C101—24no—
163C4⋊C4×C101—21no—
164C4⋊C4×C101—21no—
165C4⋊C4×C101—21no—
166C4⋊C4×C101—21no—
167C4⋊C4×C101—21no—
168C4⋊C4×C101—21no—
169C4⋊C4×C101—21no—
170C4⋊C4×C101—21no—
171C4⋊C4×C101—21no—
172C4⋊C4×C101—21no—
173C4⋊C4×C101—21no—
174C4⋊C4×C101—21no—
175C4⋊C4×C101—42no—
176C4⋊C4×C101—42no—
177C4⋊C4×C101—42no—
178C4⋊C4×C101—81no—
179C4⋊C4×C101—81no—
180C4⋊C4×C101—81no—
181C4⋊C4×C101—81no—
182C4⋊C4×C101#4112yes—
183C4⋊C4×C101#4112yes—
184C22⋊C4×C101—24no—
185C22⋊C4×C101—41no—
186C22⋊C4×C101—81no—
187C22⋊C4×C101—81no—
188C22⋊C4×C101Q1614yes—
189C42×C101—21no—
190C42×C101—21no—
191C42×C101—21no—
192C42×C101—21no—
193C42×C101—42no—
194C42×C101—81no—
195C42×C101—81no—
196C23×C101—21no—
197C23×C101—21no—
198C23×C101—21no—
199C23×C101—21no—
200C23×C101—21no—
201C23×C101—21no—
202C23×C101C2×Q1612yes—
203C23×C101C22×D411yescharacteristic
204Q8×C101—22no—
205Q8×C101—22no—
206Q8×C101—41no—
207Q8×C101—41no—
208C2×C4×C101—21no—
209C2×C4×C101—21no—
210C2×C4×C101—21no—
211C2×C4×C101—21no—
212C2×C4×C101—22no—
213C2×C4×C101—22no—
214C2×C4×C101—21no—
215C2×C4×C101—21no—
216C2×C4×C101—22no—
217C2×C4×C101—21no—
218C2×C4×C101—21no—
219C2×C4×C101—21no—
220C2×C4×C101—21no—
221C2×C4×C101—21no—
222C2×C4×C101—21no—
223C2×C4×C101—21no—
224C2×C4×C101—41no—
225C2×C4×C101—41no—
226C2×C4×C101—41no—
227C2×C4×C101—41no—
228C2×C4×C101—41no—
229C2×C4×C101—41no—
230C2×C4×C101—41no—
231C2×C4×C101—41no—
232C2×C4×C101—41no—
233C2×C4×C101—41no—
234C2×C4×C101—41no—
235C2×C4×C101—41no—
236C2×C4×C101—41no—
237C2×C4×C101—41no—
238C2×C4×C101—41no—
239C2×C4×C101—41no—
240C2×C4×C101—41no—
241C2×C4×C101—41no—
242C2×C4×C101—41no—
243C2×C4×C101—41no—
244C2×C4×C101—41no—
245C2×C4×C101—41no—
246C2×C4×C101—41no—
247C2×C4×C101—41no—
248C2×C4×C101—41no—
249C2×C4×C101—84no—
250C2×C4×C101C2×Q1612yes—
251C2×C4×C101C2×Q1612yes—
252C2×C4×C101C2×#4111yescharacteristic
253C2×C4×C101C2×#4111yescharacteristic
254C2×C4×C101C2×#4111yescharacteristic
255C2×C4×C101C2×#4111yescharacteristic
256C2×C4×C101H(5,𝔽2)11yescharacteristic
257C2×C4×C1012−1+411yescharacteristic
258C8×C101—22no—
259C8×C101—41no—
260C8×C101—41no—
261C8×C101—41no—
262C22×C101—22no—
263C22×C101—22no—
264C22×C101—22no—
265C22×C101—41no—
266C22×C101—41no—
267C22×C101—41no—
268C22×C101—41no—
269C22×C101#52511yescharacteristic
270C22×C101#54611yescharacteristic
271C22×C101#54711yescharacteristic
272C22×C101C22×Q1611yescharacteristic
273C22×C101#57511yescharacteristic
274C22×C101#57611yescharacteristic
275C22×C101#57711yescharacteristic
276C4×C101—22no—
277C4×C101—22no—
278C4×C101—41no—
279C4×C101—42no—
280C4×C101—41no—
281C4×C101—42no—
282C4×C101—41no—
283C4×C101—42no—
284C4×C101—81no—
285C4×C101—81no—
286C4×C101—81no—
287C4×C101—81no—
288C4×C101—81no—
289C4×C101#52911yescharacteristic
290C4×C101#53911yescharacteristic
291C4×C101#55311yescharacteristic
292C4×C101#55611yescharacteristic
293#27036C10111yesmaximal, characteristic, direct product factor, Sylow
294C2×C101—42no—
295C2×C101#246611yescharacteristic
296C2×C101#310411yescharacteristic
297C2×C101#311911yescharacteristic
298C2×C101#329911yescharacteristic
299C2×C101#331911yescharacteristic
300C2×C101#333811yescharacteristic
301C2×C101#335111yescharacteristic
302#2497C2×C10111yescharacteristic
303#2360C2×C10111yescharacteristic
304#2072C2×C10111yescharacteristic, complemented
305#2068C2×C10111yescharacteristic, complemented
306#2036C2×C10111yescharacteristic
307#2036C2×C10111yescharacteristic
308#1947C2×C10111yescharacteristic, complemented
309#1942C2×C10111yescharacteristic, complemented
310#1923C2×C10111yescharacteristic
311#1921C2×C10111yescharacteristic, complemented
312#1921C2×C10111yescharacteristic, complemented
313#1863C2×C10111yescharacteristic, complemented
314#1852C2×C10111yescharacteristic
315#1824C2×C10111yescharacteristic
316C4×#103C2×C10111yescharacteristic, complemented
317C101#2703611yescharacteristic, direct product factor, Sylow
318C2×C22⋊Q8C22×C10111yescharacteristic
319C2×C4×Q8C22×C10111yescharacteristic
320C22×C4⋊C4C22×C10111yescharacteristic
321C2×#107C22×C10111yescharacteristic
322C2×#107C22×C10111yescharacteristic
323C2×#107C22×C10111yescharacteristic
324C2×#107C22×C10111yescharacteristic
325C2×C4⋊C8C22×C10111yescharacteristic
326C2×#103C22×C10111yescharacteristic
327C2×#103C22×C10111yescharacteristic
328C2×#103C22×C10111yescharacteristic
329C2×#103C22×C10111yescharacteristic
330C2×C22⋊C8C22×C10111yescharacteristic
331C2×C22⋊C8C22×C10111yescharacteristic
332C2×C4×C8C22×C10111yescharacteristic
333#400—21no—
334#396—21no—
335#391C22×C10111yescharacteristic
336#389—21no—
337#389C22×C10111yescharacteristic
338#389C22×C10111yescharacteristic
339#389C22×C10111yescharacteristic
340#388—21no—
341#387—21no—
342#387—21no—
343#385—21no—
344#384C22×C10111yescharacteristic
345#380C22×C10111yescharacteristic
346#380C22×C10111yescharacteristic
347C4×C4⋊C4C22×C10111yescharacteristic
348C4×C4⋊C4C22×C10111yescharacteristic
349C4×C22⋊C4—21no—
350C4×C22⋊C4C22×C10111yescharacteristic
351#340C22×C10111yescharacteristic
352#340C22×C10111yescharacteristic
353#340C22×C10111yescharacteristic
354#340C22×C10111yescharacteristic
355#340C22×C10111yescharacteristic
356#340C22×C10111yescharacteristic
357#340C22×C10111yescharacteristic
358#340C22×C10111yescharacteristic
359#336C22×C10111yescharacteristic
360#336C22×C10111yescharacteristic
361C22×Q8C23×C10111yescharacteristic
362C23×C4—21no—
363C23×C4C23×C10111yescharacteristic
364C22×C8C23×C10111yescharacteristic
365C22×C8C23×C10111yescharacteristic
366C22×C8C23×C10111yescharacteristic
367C22×C8C23×C10111yescharacteristic
368C22⋊Q8—22no—
369C22⋊Q8—22no—
370C4×Q8—22no—
371C4×Q8—41no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—41no—
382C2×C4⋊C4C23×C10111yescharacteristic
383C2×C4⋊C4C23×C10111yescharacteristic
384C2×C4⋊C4C23×C10111yescharacteristic
385C2×C4⋊C4C23×C10111yescharacteristic
386C2×C4⋊C4C23×C10111yescharacteristic
387C2×C4⋊C4C23×C10111yescharacteristic
388C2×C4⋊C4C23×C10111yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4D4×C10111yescharacteristic
393C2×C22⋊C4D4×C10111yescharacteristic
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42C23×C10111yescharacteristic
398C2×C42C23×C10111yescharacteristic
399#107—22no—
400#107—22no—
401#107—22no—
402#107—41no—
403C4⋊C8—22no—
404#103—22no—
405#103—22no—
406#103—22no—
407#103—41no—
408C22⋊C8—22no—
409C22⋊C8—41no—
410C4×C8—41no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95D4×C10111yescharacteristic
421#95D4×C10111yescharacteristic
422C24C2×D4×C10111yescharacteristic
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8#41×C10112yes—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—81no—
446C22×C4C2×D4×C10111yescharacteristic
447C22×C4C2×D4×C10111yescharacteristic
448C22×C4C2×D4×C10111yescharacteristic
449C22×C4C2×D4×C10111yescharacteristic
450C22×C4C2×D4×C10111yescharacteristic
451C22×C4C24×C10111yescharacteristic
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8#41×C10112yes—
464C4⋊C4—24no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—42no—
478C4⋊C4—42no—
479C4⋊C4—42no—
480C4⋊C4—81no—
481C4⋊C4—81no—
482C4⋊C4—81no—
483C4⋊C4—81no—
484C4⋊C4#41×C10112yes—
485C4⋊C4#41×C10112yes—
486C22⋊C4—24no—
487C22⋊C4—41no—
488C22⋊C4—81no—
489C22⋊C4—81no—
490C22⋊C4Q16×C10114yes—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—42no—
496C42—81no—
497C42—81no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23C2×Q16×C10112yes—
505C23C22×D4×C10111yescharacteristic
506Q8—22no—
507Q8—22no—
508Q8—41no—
509Q8—41no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—84no—
552C2×C4C2×Q16×C10112yes—
553C2×C4C2×Q16×C10112yes—
554C2×C4C2×#41×C10111yescharacteristic
555C2×C4C2×#41×C10111yescharacteristic
556C2×C4C2×#41×C10111yescharacteristic
557C2×C4C2×#41×C10111yescharacteristic
558C2×C4H(5,𝔽2)×C10111yescharacteristic
559C2×C42−1+4×C10111yescharacteristic
560C8—22no—
561C8—41no—
562C8—41no—
563C8—41no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22#525×C10111yescharacteristic
572C22#546×C10111yescharacteristic
573C22#547×C10111yescharacteristic
574C22C22×Q16×C10111yescharacteristic
575C22#575×C10111yescharacteristic
576C22#576×C10111yescharacteristic
577C22#577×C10111yescharacteristic
578C4—22no—
579C4—22no—
580C4—41no—
581C4—42no—
582C4—41no—
583C4—42no—
584C4—41no—
585C4—42no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4#529×C10111yescharacteristic
592C4#539×C10111yescharacteristic
593C4#553×C10111yescharacteristic
594C4#556×C10111yescharacteristic
595C2—42no—
596C2C101×#246611yescharacteristic
597C2C101×#310411yescharacteristic
598C2C101×#311911yescharacteristic
599C2C101×#329911yescharacteristic
600C2C101×#331911yescharacteristic
601C2C101×#333811yescharacteristic
602C2C101×#335111yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC24×C101C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C4×C22⋊C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
3. C101×#2072C2semidirect
4. C101×#2068C2semidirect
7. C101×#1947C2semidirect
8. C101×#1942C2semidirect
10. C101×#1921C2semidirect
11. C101×#1921C2semidirect
12. C101×#1863C2semidirect
15. C4×#103×C101C2semidirect
293. #27036C101direct (N × H)
304. #2072C2×C101semidirect
305. #2068C2×C101semidirect
308. #1947C2×C101semidirect
309. #1942C2×C101semidirect
311. #1921C2×C101semidirect
312. #1921C2×C101semidirect
313. #1863C2×C101semidirect
316. C4×#103C2×C101semidirect
317. C101#27036direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#24972
C101×#23602
C101×#20722
C101×#20682
C101×#20362
C101×#19472
C101×#19422
C101×#19232
C101×#19212
C101×#18632
C101×#18522
C101×#18242
C4×#103×C1012
#27036101