Finite Group Databasebeta

← C101×#12705 #38794856

Subgroups — C101×#12705 #38794856

Order 25856.

1186 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 1186 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3484C211yesmaximal, characteristic
2C101×#2121C214yesmaximal, complemented
3C101×#1783C211yesmaximal, characteristic, complemented
4C101×#1781C211yesmaximal, characteristic, complemented
5C2×H(5,𝔽2)×C101C411yescharacteristic, complemented
6C23×D4×C101C2211yescharacteristic
7#546×C101—24no—
8D42×C101—24no—
9#535×C101—21no—
10#534×C101—21no—
11#534×C101C2212yes—
12#525×C101—21no—
13C2×#120×C101—21no—
14C2×#120×C101C412yescomplemented
15#518×C101C411yescharacteristic, complemented
16C2×#100×C101—21no—
17C2×#100×C101C2212yescomplemented
18C2×#99×C101—21no—
19C2×#99×C101C2212yescomplemented
20#407×C101—21no—
21#379×C101—21no—
22#352×C101—24no—
23AΣL(1,𝔽16)×C101—24no—
24C25×C101C2×C411yescharacteristic
25C25×C101D411yescharacteristic
26H(5,𝔽2)×C101—42no—
27H(5,𝔽2)×C101—42no—
28C2×#41×C101—21no—
29C2×#41×C101—22no—
30C22×D4×C101—21no—
31C22×D4×C101—22no—
32C22×D4×C101—22no—
33C22×D4×C101—22no—
34C22×D4×C101—24no—
35C22×D4×C101—42no—
36C22×D4×C101—42no—
37C22×D4×C101C2×C411yescharacteristic
38C22×D4×C101C2×C412yes—
39C22×D4×C101D411yescharacteristic
40C22×D4×C101D411yescharacteristic
41C22×D4×C101C2311yescharacteristic
42C23×C4×C101D411yescharacteristic
43C2×M16×C101—22no—
44#127×C101—22no—
45#124×C101—22no—
46#123×C101—22no—
47#123×C101—22no—
48#123×C101D414yes—
49C22⋊Q8×C101—22no—
50#121×C101—22no—
51#121×C101—24no—
52#121×C101—24no—
53#121×C101—24no—
54#120×C101—24no—
55#120×C101—22no—
56#120×C101—22no—
57#120×C101—22no—
58#120×C101—22no—
59#120×C101—24no—
60#120×C101D414yes—
61C4×D4×C101—24no—
62C4×D4×C101—24no—
63#117×C101—21no—
64C2×C22⋊C4×C101—22no—
65C2×C22⋊C4×C101—21no—
66C2×C22⋊C4×C101—22no—
67C2×C22⋊C4×C101—22no—
68C2×C22⋊C4×C101—42no—
69C2×C22⋊C4×C101C2×C412yes—
70#100×C101—24no—
71#100×C101—42no—
72#99×C101—24no—
73#99×C101—42no—
74C22⋊C8×C101—42no—
75C24×C101—21no—
76C24×C101—22no—
77C24×C101—22no—
78C24×C101—22no—
79C24×C101—41no—
80C24×C101—41no—
81C24×C101—41no—
82C24×C101—82no—
83C24×C101—82no—
84C24×C101C22⋊C411yescharacteristic
85C24×C101C22⋊C411yescharacteristic
86C24×C101C22⋊C411yescharacteristic
87C24×C101C22⋊C412yescomplemented
88C24×C101C22×C411yescharacteristic
89C24×C101C2×D411yescharacteristic
90#41×C101—42no—
91#41×C101—48no—
92#41×C101—42no—
93C2×Q8×C101—21no—
94C2×D4×C101—22no—
95C2×D4×C101—22no—
96C2×D4×C101—24no—
97C2×D4×C101—22no—
98C2×D4×C101—21no—
99C2×D4×C101—22no—
100C2×D4×C101—22no—
101C2×D4×C101—22no—
102C2×D4×C101—22no—
103C2×D4×C101—24no—
104C2×D4×C101—24no—
105C2×D4×C101—22no—
106C2×D4×C101—22no—
107C2×D4×C101—22no—
108C2×D4×C101—41no—
109C2×D4×C101—41no—
110C2×D4×C101—41no—
111C2×D4×C101—41no—
112C2×D4×C101—416no—
113C2×D4×C101—48no—
114C2×D4×C101—42no—
115C2×D4×C101—42no—
116C2×D4×C101—42no—
117C2×D4×C101—42no—
118C2×D4×C101—84no—
119C2×D4×C101—84no—
120C2×D4×C101C2×D414yes—
121C22×C4×C101—21no—
122C22×C4×C101—22no—
123C22×C4×C101—22no—
124C22×C4×C101—22no—
125C22×C4×C101—22no—
126C22×C4×C101—22no—
127C22×C4×C101—41no—
128C22×C4×C101—42no—
129C22×C4×C101C22⋊C411yescharacteristic
130C22×C4×C101C22⋊C412yescomplemented
131C22×C4×C101C2×D411yescharacteristic
132M16×C101—42no—
133M16×C101—42no—
134C2×C8×C101—42no—
135C4⋊C4×C101—22no—
136C4⋊C4×C101—24no—
137C22⋊C4×C101—24no—
138C22⋊C4×C101—22no—
139C22⋊C4×C101—24no—
140C22⋊C4×C101—22no—
141C22⋊C4×C101—24no—
142C22⋊C4×C101—24no—
143C22⋊C4×C101—42no—
144C22⋊C4×C101—42no—
145C22⋊C4×C101—84no—
146C22⋊C4×C101C22⋊C414yescomplemented
147C42×C101—22no—
148C23×C101—21no—
149C23×C101—21no—
150C23×C101—21no—
151C23×C101—21no—
152C23×C101—21no—
153C23×C101—21no—
154C23×C101—21no—
155C23×C101—21no—
156C23×C101—21no—
157C23×C101—21no—
158C23×C101—22no—
159C23×C101—21no—
160C23×C101—21no—
161C23×C101—42no—
162C23×C101—44no—
163C23×C101—44no—
164C23×C101—44no—
165C23×C101—44no—
166C23×C101—44no—
167C23×C101—42no—
168C23×C101—42no—
169C23×C101—82no—
170C23×C101—82no—
171C23×C101—82no—
172C23×C101—81no—
173C23×C101—81no—
174C23×C101—81no—
175C23×C101—81no—
176C23×C101—82no—
177C23×C101—82no—
178C23×C101—82no—
179C23×C101—82no—
180C23×C101—82no—
181C23×C101—82no—
182C23×C101—82no—
183C23×C101—82no—
184C23×C101#9912yes—
185C23×C101C2×C22⋊C412yes—
186C23×C101C2×C22⋊C411yescharacteristic
187C23×C101#12012yes—
188Q8×C101—42no—
189D4×C101—28no—
190D4×C101—44no—
191D4×C101—44no—
192D4×C101—44no—
193D4×C101—42no—
194D4×C101—44no—
195D4×C101—44no—
196D4×C101—48no—
197D4×C101—42no—
198D4×C101—42no—
199D4×C101—84no—
200D4×C101—84no—
201C2×C4×C101—21no—
202C2×C4×C101—21no—
203C2×C4×C101—21no—
204C2×C4×C101—21no—
205C2×C4×C101—24no—
206C2×C4×C101—22no—
207C2×C4×C101—44no—
208C2×C4×C101—44no—
209C2×C4×C101—42no—
210C2×C4×C101—42no—
211C2×C4×C101—82no—
212C2×C4×C101—82no—
213C2×C4×C101—82no—
214C2×C4×C101—84no—
215C2×C4×C101#9912yes—
216C2×C4×C101#12012yes—
217C8×C101—82no—
218C22×C101—22no—
219C22×C101—22no—
220C22×C101—22no—
221C22×C101—22no—
222C22×C101—22no—
223C22×C101—22no—
224C22×C101—41no—
225C22×C101—42no—
226C22×C101—42no—
227C22×C101—42no—
228C22×C101—42no—
229C22×C101—42no—
230C22×C101—41no—
231C22×C101—41no—
232C22×C101—41no—
233C22×C101—44no—
234C22×C101—42no—
235C22×C101—41no—
236C22×C101—42no—
237C22×C101—41no—
238C22×C101—81no—
239C22×C101—81no—
240C22×C101—81no—
241C22×C101—81no—
242C22×C101—81no—
243C22×C101—81no—
244C22×C101—88no—
245C22×C101—88no—
246C22×C101—162no—
247C22×C101—162no—
248C22×C101#37911yescharacteristic
249C22×C101C2×#9911yescharacteristic
250C22×C101C2×#9911yescharacteristic
251C4×C101—22no—
252C4×C101—22no—
253C4×C101—44no—
254C4×C101—42no—
255C4×C101—162no—
256#12705C10111yesmaximal, characteristic, direct product factor, Sylow
257C2×C101—21no—
258C2×C101—21no—
259C2×C101—21no—
260C2×C101—42no—
261C2×C101—42no—
262C2×C101—42no—
263C2×C101—42no—
264C2×C101—81no—
265C2×C101—82no—
266C2×C101#178111yescharacteristic
267#3484C2×C10111yescharacteristic
268#2121C2×C10114yescomplemented
269#1783C2×C10111yescharacteristic, complemented
270#1781C2×C10111yescharacteristic, complemented
271C101#1270511yescharacteristic, direct product factor, Sylow
272C2×H(5,𝔽2)C4×C10111yescharacteristic, complemented
273C23×D4C22×C10111yescharacteristic
274#546—24no—
275D42—24no—
276#535—21no—
277#534—21no—
278#534C22×C10112yes—
279#525—21no—
280C2×#120—21no—
281C2×#120C4×C10112yescomplemented
282#518C4×C10111yescharacteristic, complemented
283C2×#100—21no—
284C2×#100C22×C10112yescomplemented
285C2×#99—21no—
286C2×#99C22×C10112yescomplemented
287#407—21no—
288#379—21no—
289#352—24no—
290AΣL(1,𝔽16)—24no—
291C25C2×C4×C10111yescharacteristic
292C25D4×C10111yescharacteristic
293H(5,𝔽2)—42no—
294H(5,𝔽2)—42no—
295C2×#41—21no—
296C2×#41—22no—
297C22×D4—21no—
298C22×D4—22no—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—24no—
302C22×D4—42no—
303C22×D4—42no—
304C22×D4C2×C4×C10111yescharacteristic
305C22×D4C2×C4×C10112yes—
306C22×D4D4×C10111yescharacteristic
307C22×D4D4×C10111yescharacteristic
308C22×D4C23×C10111yescharacteristic
309C23×C4D4×C10111yescharacteristic
310C2×M16—22no—
311#127—22no—
312#124—22no—
313#123—22no—
314#123—22no—
315#123D4×C10114yes—
316C22⋊Q8—22no—
317#121—22no—
318#121—24no—
319#121—24no—
320#121—24no—
321#120—24no—
322#120—22no—
323#120—22no—
324#120—22no—
325#120—22no—
326#120—24no—
327#120D4×C10114yes—
328C4×D4—24no—
329C4×D4—24no—
330#117—21no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4C2×C4×C10112yes—
337#100—24no—
338#100—42no—
339#99—24no—
340#99—42no—
341C22⋊C8—42no—
342C24—21no—
343C24—22no—
344C24—22no—
345C24—22no—
346C24—41no—
347C24—41no—
348C24—41no—
349C24—82no—
350C24—82no—
351C24C22⋊C4×C10111yescharacteristic
352C24C22⋊C4×C10111yescharacteristic
353C24C22⋊C4×C10111yescharacteristic
354C24C22⋊C4×C10112yescomplemented
355C24C22×C4×C10111yescharacteristic
356C24C2×D4×C10111yescharacteristic
357#41—42no—
358#41—48no—
359#41—42no—
360C2×Q8—21no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—24no—
364C2×D4—22no—
365C2×D4—21no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—24no—
371C2×D4—24no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—416no—
380C2×D4—48no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—84no—
386C2×D4—84no—
387C2×D4C2×D4×C10114yes—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—41no—
395C22×C4—42no—
396C22×C4C22⋊C4×C10111yescharacteristic
397C22×C4C22⋊C4×C10112yescomplemented
398C22×C4C2×D4×C10111yescharacteristic
399M16—42no—
400M16—42no—
401C2×C8—42no—
402C4⋊C4—22no—
403C4⋊C4—24no—
404C22⋊C4—24no—
405C22⋊C4—22no—
406C22⋊C4—24no—
407C22⋊C4—22no—
408C22⋊C4—24no—
409C22⋊C4—24no—
410C22⋊C4—42no—
411C22⋊C4—42no—
412C22⋊C4—84no—
413C22⋊C4C22⋊C4×C10114yescomplemented
414C42—22no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—22no—
426C23—21no—
427C23—21no—
428C23—42no—
429C23—44no—
430C23—44no—
431C23—44no—
432C23—44no—
433C23—44no—
434C23—42no—
435C23—42no—
436C23—82no—
437C23—82no—
438C23—82no—
439C23—81no—
440C23—81no—
441C23—81no—
442C23—81no—
443C23—82no—
444C23—82no—
445C23—82no—
446C23—82no—
447C23—82no—
448C23—82no—
449C23—82no—
450C23—82no—
451C23#99×C10112yes—
452C23C2×C22⋊C4×C10112yes—
453C23C2×C22⋊C4×C10111yescharacteristic
454C23#120×C10112yes—
455Q8—42no—
456D4—28no—
457D4—44no—
458D4—44no—
459D4—44no—
460D4—42no—
461D4—44no—
462D4—44no—
463D4—48no—
464D4—42no—
465D4—42no—
466D4—84no—
467D4—84no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—44no—
475C2×C4—44no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—82no—
479C2×C4—82no—
480C2×C4—82no—
481C2×C4—84no—
482C2×C4#99×C10112yes—
483C2×C4#120×C10112yes—
484C8—82no—
485C22—22no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—41no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—44no—
501C22—42no—
502C22—41no—
503C22—42no—
504C22—41no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—88no—
512C22—88no—
513C22—162no—
514C22—162no—
515C22#379×C10111yescharacteristic
516C22C2×#99×C10111yescharacteristic
517C22C2×#99×C10111yescharacteristic
518C4—22no—
519C4—22no—
520C4—44no—
521C4—42no—
522C4—162no—
523C2—21no—
524C2—21no—
525C2—21no—
526C2—42no—
527C2—42no—
528C2—42no—
529C2—42no—
530C2—81no—
531C2—82no—
532C2C101×#178111yescharacteristic
subgroupG/H
center, socleC2×C101#1781
commutatorC24C22×C4×C101
Frattini, cosocleC22×D4C23×C101
prime radicalC101×#3484C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C101 ◁ C23×C101 ◁ C23×D4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#2121C2semidirect
3. C101×#1783C2semidirect
4. C101×#1781C2semidirect
5. C2×H(5,𝔽2)×C101C4semidirect
14. C2×#120×C101C4semidirect
15. #518×C101C4semidirect
17. C2×#100×C101C22semidirect
19. C2×#99×C101C22semidirect
87. C24×C101C22⋊C4semidirect
130. C22×C4×C101C22⋊C4semidirect
146. C22⋊C4×C101C22⋊C4semidirect
256. #12705C101direct (N × H)
268. #2121C2×C101semidirect
269. #1783C2×C101semidirect
270. #1781C2×C101semidirect
271. C101#12705direct (N × H)
272. C2×H(5,𝔽2)C4×C101semidirect
281. C2×#120C4×C101semidirect
282. #518C4×C101semidirect
284. C2×#100C22×C101semidirect
286. C2×#99C22×C101semidirect
354. C24C22⋊C4×C101semidirect
397. C22×C4C22⋊C4×C101semidirect
413. C22⋊C4C22⋊C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#34842
C101×#21212
C101×#17832
C101×#17812
#12705101