Finite Group Databasebeta

← C101×#25949 #38808100

Subgroups — C101×#25949 #38808100

Order 25856.

1202 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×#3501C211yesmaximal, characteristic, complemented
2C101×#2561C212yesmaximal, complemented
3C101×#2534C211yesmaximal, characteristic
4C101×#2030C212yesmaximal, complemented
5C101×#2029C212yesmaximal, complemented
6C101×#1996C212yesmaximal, complemented
7C101×#1890C212yesmaximal, complemented
8C101×#1889C212yesmaximal
9C4×#99×C101C211yesmaximal, characteristic, complemented
10#554×C101—22no—
11#554×C101—24no—
12D4×Q8×C101—22no—
13#544×C101—21no—
14#543×C101—21no—
15#543×C101C2212yes—
16#533×C101—21no—
17C2×#123×C101C2211yescharacteristic
18C2×C22⋊Q8×C101—21no—
19C2×C22⋊Q8×C101C2212yes—
20C2×#120×C101C2211yescharacteristic
21#518×C101C2212yes—
22C2×C4×D4×C101C2211yescharacteristic
23C22×C22⋊C4×C101C2211yescharacteristic
24C2×#99×C101C2212yes—
25#397×C101—22no—
26#396×C101—21no—
27#394×C101—21no—
28#393×C101—22no—
29#388×C101—24no—
30#388×C101—21no—
31#386×C101—21no—
32#381×C101C2214yes—
33#381×C101C2211yescharacteristic
34#380×C101C2211yescharacteristic
35#379×C101C2214yes—
36#379×C101C2211yescharacteristic
37C4×C22⋊C4×C101C2212yes—
38#342×C101C2214yes—
39#342×C101C2214yes—
40#342×C101C2212yes—
41C25×C101C2311yescharacteristic
42C22×Q8×C101—21no—
43C22×Q8×C101D412yescomplemented
44C22×D4×C101—21no—
45C22×D4×C101C2311yescharacteristic
46C23×C4×C101D411yescharacteristic
47C23×C4×C101C2311yescharacteristic
48C23×C4×C101C2311yescharacteristic
49C4⋊Q8×C101—21no—
50C4⋊Q8×C101—21no—
51C4⋊Q8×C101—24no—
52#125×C101—22no—
53#125×C101—24no—
54#123×C101—24no—
55C22⋊Q8×C101—22no—
56C22⋊Q8×C101—22no—
57C22⋊Q8×C101—24no—
58C22⋊Q8×C101—24no—
59C22⋊Q8×C101—22no—
60C22⋊Q8×C101—22no—
61C22⋊Q8×C101—22no—
62C22⋊Q8×C101—22no—
63C22⋊Q8×C101—22no—
64C22⋊Q8×C101—22no—
65C22⋊Q8×C101—24no—
66C22⋊Q8×C101—24no—
67#120×C101—24no—
68C4×Q8×C101—22no—
69C4×Q8×C101—22no—
70C4×D4×C101—22no—
71C4×D4×C101—22no—
72C4×D4×C101—24no—
73C4×D4×C101—24no—
74#117×C101—22no—
75C2×C4⋊C4×C101—21no—
76C2×C4⋊C4×C101—22no—
77C2×C4⋊C4×C101—21no—
78C2×C4⋊C4×C101—21no—
79C2×C4⋊C4×C101D411yescharacteristic
80C2×C4⋊C4×C101D412yescomplemented
81C2×C4⋊C4×C101D414yescomplemented
82C2×C22⋊C4×C101—22no—
83C2×C22⋊C4×C101—21no—
84C2×C22⋊C4×C101—21no—
85C2×C22⋊C4×C101—21no—
86C2×C22⋊C4×C101—22no—
87C2×C22⋊C4×C101—24no—
88C2×C22⋊C4×C101—21no—
89C2×C22⋊C4×C101—22no—
90C2×C22⋊C4×C101—21no—
91C2×C22⋊C4×C101—21no—
92C2×C22⋊C4×C101—24no—
93C2×C22⋊C4×C101D411yescharacteristic
94C2×C22⋊C4×C101C2314yes—
95C2×C22⋊C4×C101C2311yescharacteristic
96C2×C22⋊C4×C101C2311yescharacteristic
97C2×C22⋊C4×C101C2311yescharacteristic
98C2×C22⋊C4×C101C2314yes—
99C2×C42×C101—22no—
100C2×C42×C101D411yescharacteristic
101#99×C101—24no—
102#95×C101—21no—
103#95×C101—22no—
104#95×C101—24no—
105#95×C101—21no—
106#95×C101—24no—
107#95×C101—21no—
108C24×C101—22no—
109C24×C101—21no—
110C24×C101—22no—
111C24×C101—22no—
112C24×C101—42no—
113C24×C101—81no—
114C24×C101C2×D411yescharacteristic
115C24×C101C2411yescharacteristic
116C2×Q8×C101—22no—
117C2×Q8×C101—22no—
118C2×Q8×C101—22no—
119C2×Q8×C101—22no—
120C2×Q8×C101—82no—
121C2×Q8×C101—82no—
122C2×D4×C101—22no—
123C2×D4×C101—22no—
124C2×D4×C101—42no—
125C2×D4×C101—42no—
126C2×D4×C101—81no—
127C2×D4×C101#4114yes—
128C22×C4×C101—22no—
129C22×C4×C101—22no—
130C22×C4×C101—21no—
131C22×C4×C101—21no—
132C22×C4×C101—22no—
133C22×C4×C101—24no—
134C22×C4×C101—21no—
135C22×C4×C101—21no—
136C22×C4×C101—21no—
137C22×C4×C101—22no—
138C22×C4×C101—22no—
139C22×C4×C101—81no—
140C22×C4×C101—81no—
141C22×C4×C101C2×D411yescharacteristic
142C22×C4×C101C2×D411yescharacteristic
143C22×C4×C101C2×D411yescharacteristic
144C22×C4×C101C2×D414yes—
145C22×C4×C101C2×D414yes—
146C22×C4×C101C2×D411yescharacteristic
147C22×C4×C101C2×D412yes—
148C22×C4×C101C2×D412yes—
149C22×C4×C101C2×D411yescharacteristic
150C4⋊C4×C101—22no—
151C4⋊C4×C101—24no—
152C4⋊C4×C101—22no—
153C4⋊C4×C101—22no—
154C4⋊C4×C101—24no—
155C4⋊C4×C101—22no—
156C4⋊C4×C101—24no—
157C4⋊C4×C101—22no—
158C4⋊C4×C101—22no—
159C4⋊C4×C101—22no—
160C4⋊C4×C101—24no—
161C4⋊C4×C101—42no—
162C4⋊C4×C101—81no—
163C22⋊C4×C101—24no—
164C22⋊C4×C101—24no—
165C22⋊C4×C101—22no—
166C22⋊C4×C101—24no—
167C22⋊C4×C101—22no—
168C22⋊C4×C101—24no—
169C22⋊C4×C101—22no—
170C22⋊C4×C101—22no—
171C22⋊C4×C101—24no—
172C22⋊C4×C101—48no—
173C22⋊C4×C101—42no—
174C22⋊C4×C101—42no—
175C22⋊C4×C101—41no—
176C22⋊C4×C101—41no—
177C22⋊C4×C101—42no—
178C22⋊C4×C101—42no—
179C22⋊C4×C101—81no—
180C22⋊C4×C101—84no—
181C42×C101—24no—
182C42×C101—21no—
183C42×C101—21no—
184C42×C101—82no—
185C23×C101—21no—
186C23×C101—21no—
187C23×C101—24no—
188C23×C101—22no—
189C23×C101—41no—
190C23×C101—41no—
191C23×C101—41no—
192C23×C101—41no—
193C23×C101—44no—
194C23×C101—41no—
195C23×C101—41no—
196C23×C101—42no—
197C23×C101—41no—
198C23×C101—41no—
199C23×C101—41no—
200C23×C101—41no—
201C23×C101—44no—
202C23×C101—84no—
203C23×C101—84no—
204C23×C101#12412yes—
205C23×C101C22×D411yescharacteristic
206C23×C101C22×D412yes—
207C23×C101C2×#4112yes—
208C23×C1012−1+412yes—
209Q8×C101—44no—
210Q8×C101—82no—
211Q8×C101—82no—
212Q8×C101—82no—
213D4×C101—28no—
214D4×C101—84no—
215C2×C4×C101—21no—
216C2×C4×C101—21no—
217C2×C4×C101—21no—
218C2×C4×C101—24no—
219C2×C4×C101—24no—
220C2×C4×C101—21no—
221C2×C4×C101—42no—
222C2×C4×C101—41no—
223C2×C4×C101—41no—
224C2×C4×C101—42no—
225C2×C4×C101—42no—
226C2×C4×C101—44no—
227C2×C4×C101—41no—
228C2×C4×C101—41no—
229C2×C4×C101—44no—
230C2×C4×C101—44no—
231C2×C4×C101—44no—
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—44no—
242C2×C4×C101—44no—
243C2×C4×C101—81no—
244C2×C4×C101—82no—
245C2×C4×C101—82no—
246C2×C4×C101#12011yescharacteristic
247C2×C4×C101#12011yescharacteristic
248C2×C4×C101#12012yes—
249C2×C4×C101#12412yes—
250C22×C101—22no—
251C22×C101—21no—
252C22×C101—22no—
253C22×C101—21no—
254C22×C101—22no—
255C22×C101—42no—
256C22×C101—42no—
257C22×C101—42no—
258C22×C101—42no—
259C22×C101—48no—
260C22×C101—42no—
261C22×C101—41no—
262C22×C101—41no—
263C22×C101—42no—
264C22×C101—81no—
265C22×C101—81no—
266C22×C101—84no—
267C22×C101—81no—
268C22×C101—81no—
269C22×C101—81no—
270C22×C101C2×#12011yescharacteristic
271C22×C101C2×#12411yescharacteristic
272C22×C101#53611yescharacteristic
273C22×C101#54814yes—
274C4×C101—22no—
275C4×C101—21no—
276C4×C101—21no—
277C4×C101—22no—
278C4×C101—44no—
279C4×C101—41no—
280C4×C101—41no—
281C4×C101—44no—
282C4×C101—81no—
283C4×C101—84no—
284C4×C101—81no—
285C4×C101—81no—
286#25949C10111yesmaximal, characteristic, direct product factor, Sylow
287C2×C101—21no—
288C2×C101—24no—
289C2×C101—21no—
290C2×C101—42no—
291C2×C101—82no—
292C2×C101#243611yescharacteristic
293C2×C101#302511yescharacteristic
294C2×C101#302611yescharacteristic
295#3501C2×C10111yescharacteristic, complemented
296#2561C2×C10112yescomplemented
297#2534C2×C10111yescharacteristic
298#2030C2×C10112yescomplemented
299#2029C2×C10112yescomplemented
300#1996C2×C10112yescomplemented
301#1890C2×C10112yescomplemented
302#1889C2×C10112yes—
303C4×#99C2×C10111yescharacteristic, complemented
304C101#2594911yescharacteristic, direct product factor, Sylow
305#554—24no—
306#554—22no—
307D4×Q8—22no—
308#544—21no—
309#543—21no—
310#543C22×C10112yes—
311#533—21no—
312C2×#123C22×C10111yescharacteristic
313C2×C22⋊Q8—21no—
314C2×C22⋊Q8C22×C10112yes—
315C2×#120C22×C10111yescharacteristic
316#518C22×C10112yes—
317C2×C4×D4C22×C10111yescharacteristic
318C22×C22⋊C4C22×C10111yescharacteristic
319C2×#99C22×C10112yes—
320#397—22no—
321#396—21no—
322#394—21no—
323#393—22no—
324#388—24no—
325#388—21no—
326#386—21no—
327#381C22×C10114yes—
328#381C22×C10111yescharacteristic
329#380C22×C10111yescharacteristic
330#379C22×C10114yes—
331#379C22×C10111yescharacteristic
332C4×C22⋊C4C22×C10112yes—
333#342C22×C10114yes—
334#342C22×C10114yes—
335#342C22×C10112yes—
336C25C23×C10111yescharacteristic
337C22×Q8—21no—
338C22×Q8D4×C10112yescomplemented
339C22×D4—21no—
340C22×D4C23×C10111yescharacteristic
341C23×C4D4×C10111yescharacteristic
342C23×C4C23×C10111yescharacteristic
343C23×C4C23×C10111yescharacteristic
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8—24no—
347#125—22no—
348#125—24no—
349#123—24no—
350C22⋊Q8—22no—
351C22⋊Q8—22no—
352C22⋊Q8—24no—
353C22⋊Q8—24no—
354C22⋊Q8—22no—
355C22⋊Q8—22no—
356C22⋊Q8—22no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C22⋊Q8—22no—
360C22⋊Q8—24no—
361C22⋊Q8—24no—
362#120—24no—
363C4×Q8—22no—
364C4×Q8—22no—
365C4×D4—22no—
366C4×D4—22no—
367C4×D4—24no—
368C4×D4—24no—
369#117—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4D4×C10111yescharacteristic
375C2×C4⋊C4D4×C10114yescomplemented
376C2×C4⋊C4D4×C10112yescomplemented
377C2×C22⋊C4—22no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4D4×C10111yescharacteristic
389C2×C22⋊C4C23×C10111yescharacteristic
390C2×C22⋊C4C23×C10111yescharacteristic
391C2×C22⋊C4C23×C10114yes—
392C2×C22⋊C4C23×C10111yescharacteristic
393C2×C22⋊C4C23×C10114yes—
394C2×C42—22no—
395C2×C42D4×C10111yescharacteristic
396#99—24no—
397#95—22no—
398#95—21no—
399#95—21no—
400#95—24no—
401#95—21no—
402#95—24no—
403C24—22no—
404C24—21no—
405C24—22no—
406C24—22no—
407C24—42no—
408C24—81no—
409C24C2×D4×C10111yescharacteristic
410C24C24×C10111yescharacteristic
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—82no—
416C2×Q8—82no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—42no—
420C2×D4—42no—
421C2×D4—81no—
422C2×D4#41×C10114yes—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—81no—
435C22×C4—81no—
436C22×C4C2×D4×C10111yescharacteristic
437C22×C4C2×D4×C10111yescharacteristic
438C22×C4C2×D4×C10111yescharacteristic
439C22×C4C2×D4×C10114yes—
440C22×C4C2×D4×C10114yes—
441C22×C4C2×D4×C10111yescharacteristic
442C22×C4C2×D4×C10112yes—
443C22×C4C2×D4×C10112yes—
444C22×C4C2×D4×C10111yescharacteristic
445C4⋊C4—22no—
446C4⋊C4—24no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—24no—
450C4⋊C4—22no—
451C4⋊C4—24no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—24no—
456C4⋊C4—42no—
457C4⋊C4—81no—
458C22⋊C4—24no—
459C22⋊C4—24no—
460C22⋊C4—22no—
461C22⋊C4—24no—
462C22⋊C4—22no—
463C22⋊C4—24no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—24no—
467C22⋊C4—48no—
468C22⋊C4—42no—
469C22⋊C4—42no—
470C22⋊C4—41no—
471C22⋊C4—41no—
472C22⋊C4—42no—
473C22⋊C4—42no—
474C22⋊C4—81no—
475C22⋊C4—84no—
476C42—24no—
477C42—21no—
478C42—21no—
479C42—82no—
480C23—21no—
481C23—21no—
482C23—24no—
483C23—22no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—44no—
489C23—41no—
490C23—41no—
491C23—42no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—44no—
497C23—84no—
498C23—84no—
499C23#124×C10112yes—
500C23C22×D4×C10111yescharacteristic
501C23C22×D4×C10112yes—
502C23C2×#41×C10112yes—
503C232−1+4×C10112yes—
504Q8—44no—
505Q8—82no—
506Q8—82no—
507Q8—82no—
508D4—28no—
509D4—84no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—21no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—44no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—44no—
525C2×C4—44no—
526C2×C4—44no—
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—44no—
537C2×C4—44no—
538C2×C4—81no—
539C2×C4—82no—
540C2×C4—82no—
541C2×C4#120×C10111yescharacteristic
542C2×C4#120×C10111yescharacteristic
543C2×C4#120×C10112yes—
544C2×C4#124×C10112yes—
545C22—22no—
546C22—21no—
547C22—22no—
548C22—21no—
549C22—22no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—48no—
555C22—42no—
556C22—41no—
557C22—41no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—84no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22C2×#120×C10111yescharacteristic
566C22C2×#124×C10111yescharacteristic
567C22#536×C10111yescharacteristic
568C22#548×C10114yes—
569C4—22no—
570C4—21no—
571C4—21no—
572C4—22no—
573C4—44no—
574C4—41no—
575C4—41no—
576C4—44no—
577C4—81no—
578C4—81no—
579C4—84no—
580C4—81no—
581C2—21no—
582C2—24no—
583C2—21no—
584C2—42no—
585C2—82no—
586C2C101×#243611yescharacteristic
587C2C101×#302511yescharacteristic
588C2C101×#302611yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC24C24×C101
prime radicalC2×#120×C101C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C23×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3501C2semidirect
2. C101×#2561C2semidirect
4. C101×#2030C2semidirect
5. C101×#2029C2semidirect
6. C101×#1996C2semidirect
7. C101×#1890C2semidirect
9. C4×#99×C101C2semidirect
43. C22×Q8×C101D4semidirect
80. C2×C4⋊C4×C101D4semidirect
81. C2×C4⋊C4×C101D4semidirect
286. #25949C101direct (N × H)
295. #3501C2×C101semidirect
296. #2561C2×C101semidirect
298. #2030C2×C101semidirect
299. #2029C2×C101semidirect
300. #1996C2×C101semidirect
301. #1890C2×C101semidirect
303. C4×#99C2×C101semidirect
304. C101#25949direct (N × H)
338. C22×Q8D4×C101semidirect
375. C2×C4⋊C4D4×C101semidirect
376. C2×C4⋊C4D4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#35012
C101×#25612
C101×#25342
C101×#20302
C101×#20292
C101×#19962
C101×#18902
C101×#18892
C4×#99×C1012
#25949101