Finite Group Databasebeta

← C101×#25481 #38807632

Subgroups — C101×#25481 #38807632

Order 25856.

770 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#474×C101C211yesmaximal, characteristic
2C2×#446×C101C211yesmaximal, characteristic, complemented
3C101×#2580C211yesmaximal, characteristic
4C101×#2567C211yesmaximal, characteristic, complemented
5C101×#2087C211yesmaximal, characteristic, complemented
6C101×#2086C211yesmaximal, characteristic, complemented
7C101×#2067C211yesmaximal, characteristic
8C101×#2065C211yesmaximal, characteristic
9C101×#1993C211yesmaximal, characteristic, complemented
10C101×#1949C211yesmaximal, characteristic, complemented
11C101×#1944C211yesmaximal, characteristic, complemented
12C101×#1942C211yesmaximal, characteristic, complemented
13C101×#1936C211yesmaximal, characteristic
14C101×#1934C211yesmaximal, characteristic
15C101×#1762C211yesmaximal, characteristic
16C2×C4⋊Q8×C101C2211yescharacteristic
17C2×C4×Q8×C101C2211yescharacteristic
18C2×C4×D4×C101C2211yescharacteristic
19#474×C101—24no—
20#446×C101—24no—
21C2×#107×C101C2211yescharacteristic
22C2×#107×C101C2211yescharacteristic
23C2×#107×C101C2211yescharacteristic
24C2×#106×C101C2211yescharacteristic
25C2×C4⋊C8×C101C2211yescharacteristic
26C2×C4⋊C8×C101C2211yescharacteristic
27C2×C4⋊C8×C101C2211yescharacteristic
28C2×#102×C101C2211yescharacteristic
29C2×#102×C101C2211yescharacteristic
30C2×#102×C101C2211yescharacteristic
31C2×#102×C101C2211yescharacteristic
32C2×#97×C101C2211yescharacteristic
33C2×#97×C101C2211yescharacteristic
34C2×C4×C8×C101C2211yescharacteristic
35#399×C101—21no—
36#395×C101—21no—
37#395×C101—21no—
38#393×C101—21no—
39#391×C101—21no—
40#390×C101C2211yescharacteristic
41#390×C101C2211yescharacteristic
42#389×C101C2211yescharacteristic
43#389×C101C2211yescharacteristic
44#389×C101C2211yescharacteristic
45#389×C101C2211yescharacteristic
46#389×C101C2211yescharacteristic
47#389×C101C2211yescharacteristic
48#385×C101—21no—
49#385×C101—21no—
50#384×C101—21no—
51#382×C101C2211yescharacteristic
52C4×C4⋊C4×C101C2211yescharacteristic
53#340×C101C2211yescharacteristic
54#340×C101C2211yescharacteristic
55#340×C101C2211yescharacteristic
56#340×C101C2211yescharacteristic
57#340×C101C2211yescharacteristic
58#340×C101C2211yescharacteristic
59#340×C101C2211yescharacteristic
60#340×C101C2211yescharacteristic
61C22×Q8×C101—21no—
62C22×Q8×C101D411yescharacteristic
63C22×D4×C101C2311yescharacteristic
64C23×C4×C101—21no—
65C22×C8×C101C2311yescharacteristic
66C22×C8×C101C2311yescharacteristic
67C22×C8×C101C2311yescharacteristic
68C22×C8×C101C2311yescharacteristic
69C4⋊Q8×C101—22no—
70C4⋊Q8×C101—22no—
71C4×Q8×C101—22no—
72C4×Q8×C101—22no—
73C4×D4×C101—22no—
74C4×D4×C101—22no—
75C2×C4⋊C4×C101—21no—
76C2×C4⋊C4×C101—21no—
77C2×C4⋊C4×C101—21no—
78C2×C4⋊C4×C101—21no—
79C2×C4⋊C4×C101—21no—
80C2×C4⋊C4×C101—21no—
81C2×C4⋊C4×C101—21no—
82C2×C4⋊C4×C101D411yescharacteristic
83C2×C4⋊C4×C101D411yescharacteristic
84C2×C4⋊C4×C101D411yescharacteristic
85C2×C4⋊C4×C101C2311yescharacteristic
86C2×C4⋊C4×C101C2311yescharacteristic
87C2×C4⋊C4×C101C2311yescharacteristic
88C2×C4⋊C4×C101C2311yescharacteristic
89C2×C4⋊C4×C101C2311yescharacteristic
90C2×C4⋊C4×C101C2311yescharacteristic
91C2×C4⋊C4×C101C2311yescharacteristic
92C2×C22⋊C4×C101—21no—
93C2×C22⋊C4×C101—21no—
94C2×C22⋊C4×C101—21no—
95C2×C22⋊C4×C101—21no—
96C2×C22⋊C4×C101—21no—
97C2×C42×C101—21no—
98C2×C42×C101C2311yescharacteristic
99C2×C42×C101C2311yescharacteristic
100C2×C42×C101C2311yescharacteristic
101#107×C101—22no—
102#107×C101—22no—
103#107×C101—22no—
104#106×C101—22no—
105C4⋊C8×C101—22no—
106C4⋊C8×C101—22no—
107C4⋊C8×C101D414yes—
108#102×C101—22no—
109#102×C101—22no—
110#102×C101—22no—
111#102×C101Q814yescomplemented
112#97×C101—22no—
113#97×C101—22no—
114C4×C8×C101—22no—
115#95×C101—21no—
116#95×C101—21no—
117#95×C101—21no—
118#95×C101—21no—
119#95×C101—21no—
120#95×C101—21no—
121#95×C101—21no—
122#95×C101—21no—
123#95×C101—21no—
124C24×C101—21no—
125C2×Q8×C101—22no—
126C2×Q8×C101—22no—
127C2×Q8×C101—41no—
128C2×Q8×C101—42no—
129C2×Q8×C101—81no—
130C2×Q8×C101—81no—
131C2×D4×C101—21no—
132C2×D4×C101—21no—
133C2×D4×C101—21no—
134C2×D4×C101—21no—
135C2×D4×C101—21no—
136C2×D4×C101C2×Q812yes—
137C22×C4×C101—21no—
138C22×C4×C101—21no—
139C22×C4×C101—21no—
140C22×C4×C101—21no—
141C22×C4×C101—21no—
142C22×C4×C101—21no—
143C22×C4×C101—21no—
144C22×C4×C101—42no—
145C22×C4×C101—81no—
146C22×C4×C101—81no—
147C22×C4×C101C2×D411yescharacteristic
148C22×C4×C101C2×D411yescharacteristic
149C22×C4×C101C2×D411yescharacteristic
150C22×C4×C101C2×D411yescharacteristic
151C22×C4×C101C2×D411yescharacteristic
152C22×C4×C101C2×D411yescharacteristic
153C22×C4×C101C2411yescharacteristic
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—21no—
162C2×C8×C101—21no—
163C2×C8×C101C2×D412yes—
164C2×C8×C101C2×D412yes—
165C2×C8×C101C2×Q812yes—
166C4⋊C4×C101—22no—
167C4⋊C4×C101—22no—
168C4⋊C4×C101—22no—
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—21no—
176C4⋊C4×C101—21no—
177C4⋊C4×C101—21no—
178C4⋊C4×C101—21no—
179C4⋊C4×C101—21no—
180C4⋊C4×C101—21no—
181C4⋊C4×C101—42no—
182C4⋊C4×C101—81no—
183C4⋊C4×C101—81no—
184C4⋊C4×C101—81no—
185C4⋊C4×C101—81no—
186C4⋊C4×C101—81no—
187C4⋊C4×C101—81no—
188C4⋊C4×C101C2×Q812yes—
189C4⋊C4×C101#4112yes—
190C22⋊C4×C101—42no—
191C22⋊C4×C101—42no—
192C22⋊C4×C101—42no—
193C22⋊C4×C101—81no—
194C22⋊C4×C101—81no—
195C42×C101—21no—
196C42×C101—21no—
197C42×C101—21no—
198C42×C101—21no—
199C42×C101—42no—
200C42×C101C2×D412yes—
201C42×C101#4112yes—
202C23×C101—22no—
203C23×C101—41no—
204C23×C101—41no—
205C23×C101—41no—
206C23×C101—41no—
207C23×C101—41no—
208C23×C101—41no—
209C23×C101C22×D411yescharacteristic
210Q8×C101—44no—
211Q8×C101—84no—
212D4×C101—22no—
213D4×C101—22no—
214D4×C101—41no—
215D4×C101—41no—
216C2×C4×C101—21no—
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—21no—
225C2×C4×C101—22no—
226C2×C4×C101—22no—
227C2×C4×C101—21no—
228C2×C4×C101—21no—
229C2×C4×C101—21no—
230C2×C4×C101—21no—
231C2×C4×C101—21no—
232C2×C4×C101—21no—
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—41no—
250C2×C4×C101—41no—
251C2×C4×C101—41no—
252C2×C4×C101—84no—
253C2×C4×C101#12112yes—
254C2×C4×C101#12112yes—
255C2×C4×C101#13712yes—
256C2×C4×C101C22×D411yescharacteristic
257C2×C4×C101C22×Q811yescharacteristic
258C2×C4×C101C2×#4111yescharacteristic
259C2×C4×C101C2×#4111yescharacteristic
260C2×C4×C1012−1+411yescharacteristic
261C2×C4×C1012−1+411yescharacteristic
262C8×C101—22no—
263C8×C101—22no—
264C8×C101—22no—
265C8×C101—41no—
266C22×C101—42no—
267C22×C101—42no—
268C22×C101—42no—
269C22×C101—81no—
270C22×C101—81no—
271C22×C101—81no—
272C22×C101—81no—
273C22×C101C2×#12111yescharacteristic
274C22×C101#54811yescharacteristic
275C22×C101D4×Q811yescharacteristic
276C22×C101C2×#13711yescharacteristic
277C22×C101#57511yescharacteristic
278C22×C101#57611yescharacteristic
279C22×C101#57611yescharacteristic
280C4×C101—22no—
281C4×C101—22no—
282C4×C101—22no—
283C4×C101—42no—
284C4×C101—42no—
285C4×C101—41no—
286C4×C101—41no—
287C4×C101—41no—
288C4×C101—81no—
289C4×C101—81no—
290C4×C101—81no—
291C4×C101—81no—
292C4×C101—81no—
293C4×C101#53311yescharacteristic
294C4×C101#54111yescharacteristic
295C4×C101#54711yescharacteristic
296C4×C101D4×Q811yescharacteristic
297#25481C10111yesmaximal, characteristic, direct product factor, Sylow
298C2×C101—82no—
299C2×C101#242911yescharacteristic
300C2×C101#305611yescharacteristic
301C2×C101#305811yescharacteristic
302C2×C101#337011yescharacteristic
303C2×C101#337511yescharacteristic
304C2×C101#338511yescharacteristic
305C2×C101#338911yescharacteristic
306C2×#474C2×C10111yescharacteristic
307C2×#446C2×C10111yescharacteristic, complemented
308#2580C2×C10111yescharacteristic
309#2567C2×C10111yescharacteristic, complemented
310#2087C2×C10111yescharacteristic, complemented
311#2086C2×C10111yescharacteristic, complemented
312#2067C2×C10111yescharacteristic
313#2065C2×C10111yescharacteristic
314#1993C2×C10111yescharacteristic, complemented
315#1949C2×C10111yescharacteristic, complemented
316#1944C2×C10111yescharacteristic, complemented
317#1942C2×C10111yescharacteristic, complemented
318#1936C2×C10111yescharacteristic
319#1934C2×C10111yescharacteristic
320#1762C2×C10111yescharacteristic
321C101#2548111yescharacteristic, direct product factor, Sylow
322C2×C4⋊Q8C22×C10111yescharacteristic
323C2×C4×Q8C22×C10111yescharacteristic
324C2×C4×D4C22×C10111yescharacteristic
325#474—24no—
326#446—24no—
327C2×#107C22×C10111yescharacteristic
328C2×#107C22×C10111yescharacteristic
329C2×#107C22×C10111yescharacteristic
330C2×#106C22×C10111yescharacteristic
331C2×C4⋊C8C22×C10111yescharacteristic
332C2×C4⋊C8C22×C10111yescharacteristic
333C2×C4⋊C8C22×C10111yescharacteristic
334C2×#102C22×C10111yescharacteristic
335C2×#102C22×C10111yescharacteristic
336C2×#102C22×C10111yescharacteristic
337C2×#102C22×C10111yescharacteristic
338C2×#97C22×C10111yescharacteristic
339C2×#97C22×C10111yescharacteristic
340C2×C4×C8C22×C10111yescharacteristic
341#399—21no—
342#395—21no—
343#395—21no—
344#393—21no—
345#391—21no—
346#390C22×C10111yescharacteristic
347#390C22×C10111yescharacteristic
348#389C22×C10111yescharacteristic
349#389C22×C10111yescharacteristic
350#389C22×C10111yescharacteristic
351#389C22×C10111yescharacteristic
352#389C22×C10111yescharacteristic
353#389C22×C10111yescharacteristic
354#385—21no—
355#385—21no—
356#384—21no—
357#382C22×C10111yescharacteristic
358C4×C4⋊C4C22×C10111yescharacteristic
359#340C22×C10111yescharacteristic
360#340C22×C10111yescharacteristic
361#340C22×C10111yescharacteristic
362#340C22×C10111yescharacteristic
363#340C22×C10111yescharacteristic
364#340C22×C10111yescharacteristic
365#340C22×C10111yescharacteristic
366#340C22×C10111yescharacteristic
367C22×Q8—21no—
368C22×Q8D4×C10111yescharacteristic
369C22×D4C23×C10111yescharacteristic
370C23×C4—21no—
371C22×C8C23×C10111yescharacteristic
372C22×C8C23×C10111yescharacteristic
373C22×C8C23×C10111yescharacteristic
374C22×C8C23×C10111yescharacteristic
375C4⋊Q8—22no—
376C4⋊Q8—22no—
377C4×Q8—22no—
378C4×Q8—22no—
379C4×D4—22no—
380C4×D4—22no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4D4×C10111yescharacteristic
389C2×C4⋊C4D4×C10111yescharacteristic
390C2×C4⋊C4D4×C10111yescharacteristic
391C2×C4⋊C4C23×C10111yescharacteristic
392C2×C4⋊C4C23×C10111yescharacteristic
393C2×C4⋊C4C23×C10111yescharacteristic
394C2×C4⋊C4C23×C10111yescharacteristic
395C2×C4⋊C4C23×C10111yescharacteristic
396C2×C4⋊C4C23×C10111yescharacteristic
397C2×C4⋊C4C23×C10111yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C42—21no—
404C2×C42C23×C10111yescharacteristic
405C2×C42C23×C10111yescharacteristic
406C2×C42C23×C10111yescharacteristic
407#107—22no—
408#107—22no—
409#107—22no—
410#106—22no—
411C4⋊C8—22no—
412C4⋊C8—22no—
413C4⋊C8D4×C10114yes—
414#102—22no—
415#102—22no—
416#102—22no—
417#102Q8×C10114yescomplemented
418#97—22no—
419#97—22no—
420C4×C8—22no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430C24—21no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—41no—
434C2×Q8—42no—
435C2×Q8—81no—
436C2×Q8—81no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4C2×Q8×C10112yes—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—42no—
451C22×C4—81no—
452C22×C4—81no—
453C22×C4C2×D4×C10111yescharacteristic
454C22×C4C2×D4×C10111yescharacteristic
455C22×C4C2×D4×C10111yescharacteristic
456C22×C4C2×D4×C10111yescharacteristic
457C22×C4C2×D4×C10111yescharacteristic
458C22×C4C2×D4×C10111yescharacteristic
459C22×C4C24×C10111yescharacteristic
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8C2×D4×C10112yes—
470C2×C8C2×D4×C10112yes—
471C2×C8C2×Q8×C10112yes—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—42no—
488C4⋊C4—81no—
489C4⋊C4—81no—
490C4⋊C4—81no—
491C4⋊C4—81no—
492C4⋊C4—81no—
493C4⋊C4—81no—
494C4⋊C4C2×Q8×C10112yes—
495C4⋊C4#41×C10112yes—
496C22⋊C4—42no—
497C22⋊C4—42no—
498C22⋊C4—42no—
499C22⋊C4—81no—
500C22⋊C4—81no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—42no—
506C42C2×D4×C10112yes—
507C42#41×C10112yes—
508C23—22no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23C22×D4×C10111yescharacteristic
516Q8—44no—
517Q8—84no—
518D4—22no—
519D4—22no—
520D4—41no—
521D4—41no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
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—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—84no—
559C2×C4#121×C10112yes—
560C2×C4#121×C10112yes—
561C2×C4#137×C10112yes—
562C2×C4C22×D4×C10111yescharacteristic
563C2×C4C22×Q8×C10111yescharacteristic
564C2×C4C2×#41×C10111yescharacteristic
565C2×C4C2×#41×C10111yescharacteristic
566C2×C42−1+4×C10111yescharacteristic
567C2×C42−1+4×C10111yescharacteristic
568C8—22no—
569C8—22no—
570C8—22no—
571C8—41no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22C2×#121×C10111yescharacteristic
580C22#548×C10111yescharacteristic
581C22D4×Q8×C10111yescharacteristic
582C22C2×#137×C10111yescharacteristic
583C22#575×C10111yescharacteristic
584C22#576×C10111yescharacteristic
585C22#576×C10111yescharacteristic
586C4—22no—
587C4—22no—
588C4—22no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—42no—
593C4—42no—
594C4—81no—
595C4—81no—
596C4—81no—
597C4—81no—
598C4—81no—
599C4#533×C10111yescharacteristic
600C4#541×C10111yescharacteristic
601C4#547×C10111yescharacteristic
602C4D4×Q8×C10111yescharacteristic
603C2—82no—
604C2C101×#242911yescharacteristic
605C2C101×#305611yescharacteristic
606C2C101×#305811yescharacteristic
607C2C101×#337011yescharacteristic
608C2C101×#337511yescharacteristic
609C2C101×#338511yescharacteristic
610C2C101×#338911yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC22×D4×C101C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C2×C4×Q8×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#446×C101C2semidirect
4. C101×#2567C2semidirect
5. C101×#2087C2semidirect
6. C101×#2086C2semidirect
9. C101×#1993C2semidirect
10. C101×#1949C2semidirect
11. C101×#1944C2semidirect
12. C101×#1942C2semidirect
111. #102×C101Q8semidirect
297. #25481C101direct (N × H)
307. C2×#446C2×C101semidirect
309. #2567C2×C101semidirect
310. #2087C2×C101semidirect
311. #2086C2×C101semidirect
314. #1993C2×C101semidirect
315. #1949C2×C101semidirect
316. #1944C2×C101semidirect
317. #1942C2×C101semidirect
321. C101#25481direct (N × H)
417. #102Q8×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#474×C1012
C2×#446×C1012
C101×#25802
C101×#25672
C101×#20872
C101×#20862
C101×#20672
C101×#20652
C101×#19932
C101×#19492
C101×#19442
C101×#19422
C101×#19362
C101×#19342
C101×#17622
#25481101