Finite Group Databasebeta

← C101×#25064 #38807215

Subgroups — C101×#25064 #38807215

Order 25856.

694 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#2580C211yesmaximal, characteristic
2C101×#2355C211yesmaximal, characteristic, complemented
3C101×#2093C211yesmaximal, characteristic
4C101×#2092C211yesmaximal, characteristic
5C101×#2085C211yesmaximal, characteristic, complemented
6C101×#2084C211yesmaximal, characteristic, complemented
7C101×#1984C211yesmaximal, characteristic, complemented
8C101×#1949C211yesmaximal, characteristic, complemented
9C101×#1926C211yesmaximal, characteristic
10C101×#1926C211yesmaximal, characteristic
11C101×#1921C211yesmaximal, characteristic, complemented
12C101×#1918C211yesmaximal, characteristic, complemented
13C101×#1846C211yesmaximal, characteristic, complemented
14C101×#1804C211yesmaximal, characteristic
15C4×#102×C101C211yesmaximal, characteristic
16C2×C4×Q8×C101C2211yescharacteristic
17C2×C4×D4×C101C2211yescharacteristic
18C2×#107×C101C2211yescharacteristic
19C2×#107×C101C2211yescharacteristic
20C2×#107×C101C2211yescharacteristic
21C2×#106×C101C2211yescharacteristic
22C2×#106×C101C2211yescharacteristic
23C2×#106×C101C2211yescharacteristic
24C2×C4⋊C8×C101C2211yescharacteristic
25C2×#102×C101C2211yescharacteristic
26C2×#102×C101C2211yescharacteristic
27C2×#102×C101C2211yescharacteristic
28C2×#102×C101C2211yescharacteristic
29C2×C4×C8×C101C2211yescharacteristic
30#399×C101—21no—
31#393×C101—21no—
32#391×C101—21no—
33#390×C101C2211yescharacteristic
34#390×C101C2211yescharacteristic
35#389×C101C2211yescharacteristic
36#389×C101C2211yescharacteristic
37#387×C101—21no—
38#387×C101—21no—
39#385×C101—21no—
40#385×C101—21no—
41#384×C101C2211yescharacteristic
42#382×C101C2211yescharacteristic
43#382×C101C2211yescharacteristic
44#382×C101C2211yescharacteristic
45C4×C4⋊C4×C101—21no—
46C4×C4⋊C4×C101C2211yescharacteristic
47C4×C4⋊C4×C101C2211yescharacteristic
48C4×C4⋊C4×C101C2211yescharacteristic
49#340×C101C2211yescharacteristic
50#340×C101C2211yescharacteristic
51#340×C101C2211yescharacteristic
52#340×C101C2211yescharacteristic
53#340×C101C2211yescharacteristic
54#340×C101C2211yescharacteristic
55#336×C101C2211yescharacteristic
56#336×C101C2211yescharacteristic
57#336×C101C2211yescharacteristic
58#336×C101C2211yescharacteristic
59C22×Q8×C101D411yescharacteristic
60C22×D4×C101C2311yescharacteristic
61C23×C4×C101—21no—
62C22×C8×C101C2311yescharacteristic
63C22×C8×C101C2311yescharacteristic
64C22×C8×C101C2311yescharacteristic
65C22×C8×C101C2311yescharacteristic
66C4×Q8×C101—22no—
67C4×Q8×C101—22no—
68C4×D4×C101—22no—
69C4×D4×C101—22no—
70C2×C4⋊C4×C101—21no—
71C2×C4⋊C4×C101—21no—
72C2×C4⋊C4×C101—21no—
73C2×C4⋊C4×C101—21no—
74C2×C4⋊C4×C101D411yescharacteristic
75C2×C4⋊C4×C101D411yescharacteristic
76C2×C4⋊C4×C101D411yescharacteristic
77C2×C4⋊C4×C101C2311yescharacteristic
78C2×C4⋊C4×C101C2311yescharacteristic
79C2×C4⋊C4×C101C2311yescharacteristic
80C2×C4⋊C4×C101C2311yescharacteristic
81C2×C4⋊C4×C101C2311yescharacteristic
82C2×C4⋊C4×C101C2311yescharacteristic
83C2×C4⋊C4×C101C2311yescharacteristic
84C2×C22⋊C4×C101—21no—
85C2×C22⋊C4×C101—21no—
86C2×C22⋊C4×C101—21no—
87C2×C22⋊C4×C101—21no—
88C2×C22⋊C4×C101—21no—
89C2×C42×C101—21no—
90C2×C42×C101—21no—
91C2×C42×C101—21no—
92C2×C42×C101C2311yescharacteristic
93C2×C42×C101C2311yescharacteristic
94C2×C42×C101C2311yescharacteristic
95#107×C101—22no—
96#107×C101—22no—
97#107×C101—41no—
98#106×C101—41no—
99#106×C101—41no—
100#106×C101—41no—
101C4⋊C8×C101—22no—
102#102×C101—22no—
103#102×C101—41no—
104#102×C101—41no—
105#102×C101Q814yescomplemented
106C4×C8×C101—22no—
107#95×C101—21no—
108#95×C101—21no—
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—
118C24×C101—21no—
119C2×Q8×C101—22no—
120C2×Q8×C101—22no—
121C2×Q8×C101—41no—
122C2×D4×C101—21no—
123C2×D4×C101—21no—
124C2×D4×C101—21no—
125C2×D4×C101—21no—
126C2×D4×C101—21no—
127C2×D4×C101C2×Q812yes—
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—42no—
136C22×C4×C101—81no—
137C22×C4×C101—81no—
138C22×C4×C101C2×D411yescharacteristic
139C22×C4×C101C2×D411yescharacteristic
140C22×C4×C101C2×D411yescharacteristic
141C22×C4×C101C2×D411yescharacteristic
142C22×C4×C101C2×D411yescharacteristic
143C22×C4×C101C2×D411yescharacteristic
144C22×C4×C101C2411yescharacteristic
145C2×C8×C101—21no—
146C2×C8×C101—21no—
147C2×C8×C101—21no—
148C2×C8×C101—21no—
149C2×C8×C101—21no—
150C2×C8×C101—21no—
151C2×C8×C101—21no—
152C2×C8×C101—21no—
153C2×C8×C101—21no—
154C2×C8×C101—21no—
155C2×C8×C101C2×Q812yes—
156C2×C8×C101#4112yes—
157C4⋊C4×C101—22no—
158C4⋊C4×C101—22no—
159C4⋊C4×C101—22no—
160C4⋊C4×C101—21no—
161C4⋊C4×C101—21no—
162C4⋊C4×C101—21no—
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—42no—
174C4⋊C4×C101—81no—
175C4⋊C4×C101—81no—
176C4⋊C4×C101—81no—
177C4⋊C4×C101C2×Q812yes—
178C22⋊C4×C101—42no—
179C22⋊C4×C101—42no—
180C22⋊C4×C101—42no—
181C22⋊C4×C101—81no—
182C22⋊C4×C101—81no—
183C42×C101—21no—
184C42×C101—21no—
185C42×C101—21no—
186C42×C101—21no—
187C42×C101—42no—
188C42×C101—81no—
189C42×C101—81no—
190C42×C101#4112yes—
191C42×C101#4112yes—
192C23×C101—22no—
193C23×C101—41no—
194C23×C101—41no—
195C23×C101—41no—
196C23×C101—41no—
197C23×C101—41no—
198C23×C101—41no—
199C23×C101C22×D411yescharacteristic
200Q8×C101—44no—
201D4×C101—22no—
202D4×C101—22no—
203D4×C101—41no—
204D4×C101—41no—
205C2×C4×C101—21no—
206C2×C4×C101—21no—
207C2×C4×C101—21no—
208C2×C4×C101—21no—
209C2×C4×C101—21no—
210C2×C4×C101—21no—
211C2×C4×C101—21no—
212C2×C4×C101—21no—
213C2×C4×C101—21no—
214C2×C4×C101—22no—
215C2×C4×C101—21no—
216C2×C4×C101—21no—
217C2×C4×C101—21no—
218C2×C4×C101—21no—
219C2×C4×C101—21no—
220C2×C4×C101—21no—
221C2×C4×C101—41no—
222C2×C4×C101—41no—
223C2×C4×C101—41no—
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—84no—
242C2×C4×C101#12312yes—
243C2×C4×C101#12312yes—
244C2×C4×C101#13512yes—
245C2×C4×C101C22×Q811yescharacteristic
246C2×C4×C101C2×#4111yescharacteristic
247C2×C4×C101C2×#4111yescharacteristic
248C2×C4×C101C2×#4111yescharacteristic
249C2×C4×C101H(5,𝔽2)11yescharacteristic
250C2×C4×C1012−1+411yescharacteristic
251C8×C101—22no—
252C8×C101—22no—
253C8×C101—41no—
254C8×C101—41no—
255C22×C101—42no—
256C22×C101—42no—
257C22×C101—42no—
258C22×C101—81no—
259C22×C101—81no—
260C22×C101—81no—
261C22×C101—81no—
262C22×C101C2×#12311yescharacteristic
263C22×C101D4×Q811yescharacteristic
264C22×C101#55011yescharacteristic
265C22×C101C2×#13511yescharacteristic
266C22×C101#57511yescharacteristic
267C22×C101#57611yescharacteristic
268C22×C101#57711yescharacteristic
269C4×C101—22no—
270C4×C101—22no—
271C4×C101—22no—
272C4×C101—41no—
273C4×C101—41no—
274C4×C101—41no—
275C4×C101—42no—
276C4×C101—81no—
277C4×C101—81no—
278C4×C101—81no—
279C4×C101—81no—
280C4×C101—81no—
281C4×C101—81no—
282C4×C101#53311yescharacteristic
283C4×C101#54211yescharacteristic
284C4×C101#55211yescharacteristic
285C4×C101#55411yescharacteristic
286#25064C10111yesmaximal, characteristic, direct product factor, Sylow
287C2×C101—82no—
288C2×C101#242311yescharacteristic
289C2×C101#309111yescharacteristic
290C2×C101#309611yescharacteristic
291C2×C101#338111yescharacteristic
292C2×C101#338911yescharacteristic
293C2×C101#339611yescharacteristic
294C2×C101#340111yescharacteristic
295#2580C2×C10111yescharacteristic
296#2355C2×C10111yescharacteristic, complemented
297#2093C2×C10111yescharacteristic
298#2092C2×C10111yescharacteristic
299#2085C2×C10111yescharacteristic, complemented
300#2084C2×C10111yescharacteristic, complemented
301#1984C2×C10111yescharacteristic, complemented
302#1949C2×C10111yescharacteristic, complemented
303#1926C2×C10111yescharacteristic
304#1926C2×C10111yescharacteristic
305#1921C2×C10111yescharacteristic, complemented
306#1918C2×C10111yescharacteristic, complemented
307#1846C2×C10111yescharacteristic, complemented
308#1804C2×C10111yescharacteristic
309C4×#102C2×C10111yescharacteristic
310C101#2506411yescharacteristic, direct product factor, Sylow
311C2×C4×Q8C22×C10111yescharacteristic
312C2×C4×D4C22×C10111yescharacteristic
313C2×#107C22×C10111yescharacteristic
314C2×#107C22×C10111yescharacteristic
315C2×#107C22×C10111yescharacteristic
316C2×#106C22×C10111yescharacteristic
317C2×#106C22×C10111yescharacteristic
318C2×#106C22×C10111yescharacteristic
319C2×C4⋊C8C22×C10111yescharacteristic
320C2×#102C22×C10111yescharacteristic
321C2×#102C22×C10111yescharacteristic
322C2×#102C22×C10111yescharacteristic
323C2×#102C22×C10111yescharacteristic
324C2×C4×C8C22×C10111yescharacteristic
325#399—21no—
326#393—21no—
327#391—21no—
328#390C22×C10111yescharacteristic
329#390C22×C10111yescharacteristic
330#389C22×C10111yescharacteristic
331#389C22×C10111yescharacteristic
332#387—21no—
333#387—21no—
334#385—21no—
335#385—21no—
336#384C22×C10111yescharacteristic
337#382C22×C10111yescharacteristic
338#382C22×C10111yescharacteristic
339#382C22×C10111yescharacteristic
340C4×C4⋊C4—21no—
341C4×C4⋊C4C22×C10111yescharacteristic
342C4×C4⋊C4C22×C10111yescharacteristic
343C4×C4⋊C4C22×C10111yescharacteristic
344#340C22×C10111yescharacteristic
345#340C22×C10111yescharacteristic
346#340C22×C10111yescharacteristic
347#340C22×C10111yescharacteristic
348#340C22×C10111yescharacteristic
349#340C22×C10111yescharacteristic
350#336C22×C10111yescharacteristic
351#336C22×C10111yescharacteristic
352#336C22×C10111yescharacteristic
353#336C22×C10111yescharacteristic
354C22×Q8D4×C10111yescharacteristic
355C22×D4C23×C10111yescharacteristic
356C23×C4—21no—
357C22×C8C23×C10111yescharacteristic
358C22×C8C23×C10111yescharacteristic
359C22×C8C23×C10111yescharacteristic
360C22×C8C23×C10111yescharacteristic
361C4×Q8—22no—
362C4×Q8—22no—
363C4×D4—22no—
364C4×D4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4D4×C10111yescharacteristic
370C2×C4⋊C4D4×C10111yescharacteristic
371C2×C4⋊C4D4×C10111yescharacteristic
372C2×C4⋊C4C23×C10111yescharacteristic
373C2×C4⋊C4C23×C10111yescharacteristic
374C2×C4⋊C4C23×C10111yescharacteristic
375C2×C4⋊C4C23×C10111yescharacteristic
376C2×C4⋊C4C23×C10111yescharacteristic
377C2×C4⋊C4C23×C10111yescharacteristic
378C2×C4⋊C4C23×C10111yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42C23×C10111yescharacteristic
388C2×C42C23×C10111yescharacteristic
389C2×C42C23×C10111yescharacteristic
390#107—22no—
391#107—22no—
392#107—41no—
393#106—41no—
394#106—41no—
395#106—41no—
396C4⋊C8—22no—
397#102—22no—
398#102—41no—
399#102—41no—
400#102Q8×C10114yescomplemented
401C4×C8—22no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413C24—21no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—41no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4C2×Q8×C10112yes—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—42no—
431C22×C4—81no—
432C22×C4—81no—
433C22×C4C2×D4×C10111yescharacteristic
434C22×C4C2×D4×C10111yescharacteristic
435C22×C4C2×D4×C10111yescharacteristic
436C22×C4C2×D4×C10111yescharacteristic
437C22×C4C2×D4×C10111yescharacteristic
438C22×C4C2×D4×C10111yescharacteristic
439C22×C4C24×C10111yescharacteristic
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8C2×Q8×C10112yes—
451C2×C8#41×C10112yes—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—42no—
469C4⋊C4—81no—
470C4⋊C4—81no—
471C4⋊C4—81no—
472C4⋊C4C2×Q8×C10112yes—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—42no—
476C22⋊C4—81no—
477C22⋊C4—81no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—42no—
483C42—81no—
484C42—81no—
485C42#41×C10112yes—
486C42#41×C10112yes—
487C23—22no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23C22×D4×C10111yescharacteristic
495Q8—44no—
496D4—22no—
497D4—22no—
498D4—41no—
499D4—41no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
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—84no—
537C2×C4#123×C10112yes—
538C2×C4#123×C10112yes—
539C2×C4#135×C10112yes—
540C2×C4C22×Q8×C10111yescharacteristic
541C2×C4C2×#41×C10111yescharacteristic
542C2×C4C2×#41×C10111yescharacteristic
543C2×C4C2×#41×C10111yescharacteristic
544C2×C4H(5,𝔽2)×C10111yescharacteristic
545C2×C42−1+4×C10111yescharacteristic
546C8—22no—
547C8—22no—
548C8—41no—
549C8—41no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C2×#123×C10111yescharacteristic
558C22D4×Q8×C10111yescharacteristic
559C22#550×C10111yescharacteristic
560C22C2×#135×C10111yescharacteristic
561C22#575×C10111yescharacteristic
562C22#576×C10111yescharacteristic
563C22#577×C10111yescharacteristic
564C4—22no—
565C4—22no—
566C4—22no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—42no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4#533×C10111yescharacteristic
578C4#542×C10111yescharacteristic
579C4#552×C10111yescharacteristic
580C4#554×C10111yescharacteristic
581C2—82no—
582C2C101×#242311yescharacteristic
583C2C101×#309111yescharacteristic
584C2C101×#309611yescharacteristic
585C2C101×#338111yescharacteristic
586C2C101×#338911yescharacteristic
587C2C101×#339611yescharacteristic
588C2C101×#340111yescharacteristic
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. C101×#2355C2semidirect
5. C101×#2085C2semidirect
6. C101×#2084C2semidirect
7. C101×#1984C2semidirect
8. C101×#1949C2semidirect
11. C101×#1921C2semidirect
12. C101×#1918C2semidirect
13. C101×#1846C2semidirect
105. #102×C101Q8semidirect
286. #25064C101direct (N × H)
296. #2355C2×C101semidirect
299. #2085C2×C101semidirect
300. #2084C2×C101semidirect
301. #1984C2×C101semidirect
302. #1949C2×C101semidirect
305. #1921C2×C101semidirect
306. #1918C2×C101semidirect
307. #1846C2×C101semidirect
310. C101#25064direct (N × H)
400. #102Q8×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#25802
C101×#23552
C101×#20932
C101×#20922
C101×#20852
C101×#20842
C101×#19842
C101×#19492
C101×#19262
C101×#19212
C101×#19182
C101×#18462
C101×#18042
C4×#102×C1012
#25064101