Finite Group Databasebeta

← C101×#17616 #38799767

Subgroups — C101×#17616 #38799767

Order 25856.

918 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3507C211yesmaximal, characteristic
2C101×#2982C211yesmaximal, characteristic, complemented
3C101×#2356C211yesmaximal, characteristic, complemented
4C101×#1521C214yesmaximal, complemented
5C101×#1518C211yesmaximal, characteristic, complemented
6C101×#1517C211yesmaximal, characteristic
7C101×#1503C211yesmaximal, characteristic, complemented
8C101×#1502C211yesmaximal, characteristic
9C101×#1500C214yesmaximal, complemented
10#559×C101C412yescomplemented
11#557×C101C412yescomplemented
12#556×C101—22no—
13#556×C101C412yescomplemented
14#554×C101C412yescomplemented
15#552×C101—22no—
16#539×C101—22no—
17#536×C101—21no—
18#533×C101C2211yescharacteristic
19#532×C101C2211yescharacteristic
20#529×C101C2214yes—
21#520×C101—21no—
22C2×C4×Q8×C101C2211yescharacteristic
23C8×Q8×C101—22no—
24C8×Q8×C101—22no—
25#431×C101C2214yes—
26#431×C101C2211yescharacteristic
27#431×C101C2211yescharacteristic
28#391×C101—21no—
29#387×C101—22no—
30#383×C101C2212yes—
31#382×C101C2211yescharacteristic
32C4×C4⋊C4×C101—21no—
33C4×C4⋊C4×C101C2211yescharacteristic
34#376×C101C2212yes—
35#328×C101C2212yes—
36#328×C101C2214yes—
37#328×C101C2212yes—
38#327×C101C2212yes—
39#327×C101C2214yes—
40#327×C101C2212yes—
41C2×#41×C101—21no—
42C22×Q8×C101D411yescharacteristic
43C4⋊Q8×C101—22no—
44C4⋊Q8×C101C2×C411yescharacteristic
45C4⋊Q8×C101C2×C411yescharacteristic
46C4⋊Q8×C101C2×C411yescharacteristic
47#127×C101C2×C411yescharacteristic
48#126×C101—24no—
49#126×C101—24no—
50#125×C101—24no—
51#125×C101—21no—
52#125×C101C2×C414yes—
53#124×C101—22no—
54#124×C101—21no—
55#124×C101C2×C414yes—
56#123×C101—24no—
57#123×C101—24no—
58C22⋊Q8×C101—22no—
59C22⋊Q8×C101—22no—
60C22⋊Q8×C101—21no—
61C22⋊Q8×C101—24no—
62C22⋊Q8×C101C2312yes—
63#121×C101—21no—
64#121×C101C2312yes—
65C4×Q8×C101—22no—
66C4×Q8×C101—21no—
67C4×Q8×C101C2×C414yes—
68C4×Q8×C101C2×C412yes—
69C4×Q8×C101C2×C412yes—
70C4×Q8×C101C2×C412yes—
71C4×Q8×C101D412yes—
72C4×Q8×C101D412yes—
73C4×D4×C101—24no—
74C4×D4×C101—22no—
75C4×D4×C101—21no—
76C4×D4×C101C2×C414yes—
77C4×D4×C101C2×C412yes—
78#117×C101—21no—
79#117×C101—22no—
80#117×C101—24no—
81C2×C4⋊C4×C101—22no—
82C2×C4⋊C4×C101—21no—
83C2×C4⋊C4×C101—21no—
84C2×C4⋊C4×C101D411yescharacteristic
85C2×C4⋊C4×C101D412yes—
86C2×C42×C101—22no—
87C2×C42×C101—21no—
88C2×C42×C101C2312yes—
89C2×C42×C101C2311yescharacteristic
90C4⋊C8×C101—24no—
91C4⋊C8×C101—21no—
92C4⋊C8×C101—21no—
93C22⋊C8×C101C2312yes—
94C22⋊C8×C101C2312yes—
95C4×C8×C101—24no—
96C4×C8×C101—21no—
97C4×C8×C101—21no—
98#95×C101—22no—
99#95×C101—22no—
100#95×C101—21no—
101#95×C101—22no—
102#95×C101C2311yescharacteristic
103#95×C101C2312yes—
104#95×C101C2311yescharacteristic
105#41×C101—42no—
106#41×C101—42no—
107C2×Q8×C101—21no—
108C2×Q8×C101—21no—
109C2×Q8×C101—22no—
110C2×Q8×C101—22no—
111C2×Q8×C101C22⋊C412yes—
112C2×Q8×C101C22⋊C412yes—
113C2×Q8×C101C22×C412yes—
114C2×D4×C101—22no—
115C2×D4×C101—21no—
116C2×D4×C101—21no—
117C2×D4×C101C22×C412yes—
118C22×C4×C101—21no—
119C22×C4×C101—22no—
120C22×C4×C101—24no—
121C22×C4×C101—22no—
122C22×C4×C101—21no—
123C22×C4×C101C2×D412yes—
124C22×C4×C101C2×D412yes—
125C22×C4×C101C2×D411yescharacteristic
126C22×C4×C101C2×D411yescharacteristic
127C22×C4×C101C2411yescharacteristic
128C2×C8×C101—22no—
129C2×C8×C101—22no—
130C4⋊C4×C101—21no—
131C4⋊C4×C101—24no—
132C4⋊C4×C101—21no—
133C4⋊C4×C101—24no—
134C4⋊C4×C101—21no—
135C4⋊C4×C101—21no—
136C4⋊C4×C101—22no—
137C4⋊C4×C101—24no—
138C4⋊C4×C101—22no—
139C4⋊C4×C101—42no—
140C4⋊C4×C101—42no—
141C4⋊C4×C101C22⋊C412yes—
142C4⋊C4×C101C22⋊C412yes—
143C4⋊C4×C101C22⋊C414yes—
144C4⋊C4×C101C22⋊C414yes—
145C4⋊C4×C101C22×C412yes—
146C4⋊C4×C101C22×C412yes—
147C22⋊C4×C101—22no—
148C22⋊C4×C101—24no—
149C22⋊C4×C101—24no—
150C22⋊C4×C101—22no—
151C22⋊C4×C101—24no—
152C22⋊C4×C101—22no—
153C42×C101—24no—
154C42×C101—22no—
155C42×C101—44no—
156C42×C101—42no—
157C42×C101C22×C411yescharacteristic
158C42×C101C22×C414yes—
159C42×C101C22×C411yescharacteristic
160C42×C101C2×D414yes—
161C42×C101C2×D411yescharacteristic
162C42×C101C2×D411yescharacteristic
163C23×C101—22no—
164C23×C101C22×D411yescharacteristic
165Q8×C101—24no—
166Q8×C101—24no—
167Q8×C101—42no—
168Q8×C101—42no—
169Q8×C101—81no—
170D4×C101—42no—
171D4×C101—42no—
172D4×C101—42no—
173D4×C101—42no—
174D4×C101—81no—
175C2×C4×C101—22no—
176C2×C4×C101—22no—
177C2×C4×C101—22no—
178C2×C4×C101—22no—
179C2×C4×C101—22no—
180C2×C4×C101—22no—
181C2×C4×C101—42no—
182C2×C4×C101—41no—
183C2×C4×C101—41no—
184C2×C4×C101—41no—
185C2×C4×C101—41no—
186C2×C4×C101—44no—
187C2×C4×C101—42no—
188C2×C4×C101—41no—
189C2×C4×C101—41no—
190C2×C4×C101—42no—
191C2×C4×C101—41no—
192C2×C4×C101—42no—
193C2×C4×C101—84no—
194C2×C4×C101C2×C22⋊C414yes—
195C2×C4×C101C2×C22⋊C414yes—
196C2×C4×C101C2×C22⋊C411yescharacteristic
197C2×C4×C101C2×C22⋊C411yescharacteristic
198C2×C4×C101C2×C22⋊C411yescharacteristic
199C2×C4×C101C2×C22⋊C411yescharacteristic
200C2×C4×C101#13512yes—
201C2×C4×C101#13512yes—
202C2×C4×C101C23×C411yescharacteristic
203C2×C4×C101C22×D411yescharacteristic
204C8×C101—42no—
205C8×C101—42no—
206C22×C101—21no—
207C22×C101—21no—
208C22×C101—42no—
209C22×C101—42no—
210C22×C101—42no—
211C22×C101C22×C22⋊C411yescharacteristic
212C22×C101C2×#13511yescharacteristic
213C22×C101C2×#13511yescharacteristic
214C4×C101—21no—
215C4×C101—21no—
216C4×C101—24no—
217C4×C101—24no—
218C4×C101—21no—
219C4×C101—21no—
220C4×C101—42no—
221C4×C101—42no—
222C4×C101—42no—
223C4×C101—42no—
224C4×C101—81no—
225C4×C101—82no—
226C4×C101#41612yes—
227C4×C101#41612yes—
228#17616C10111yesmaximal, characteristic, direct product factor, Sylow
229C2×C101—21no—
230C2×C101—21no—
231C2×C101—82no—
232C2×C101#288411yescharacteristic
233C2×C101C2×#41611yescharacteristic
234C2×C101#290111yescharacteristic
235#3507C2×C10111yescharacteristic
236#2982C2×C10111yescharacteristic, complemented
237#2356C2×C10111yescharacteristic, complemented
238#1521C2×C10114yescomplemented
239#1518C2×C10111yescharacteristic, complemented
240#1517C2×C10111yescharacteristic
241#1503C2×C10111yescharacteristic, complemented
242#1502C2×C10111yescharacteristic
243#1500C2×C10114yescomplemented
244C101#1761611yescharacteristic, direct product factor, Sylow
245#559C4×C10112yescomplemented
246#557C4×C10112yescomplemented
247#556—22no—
248#556C4×C10112yescomplemented
249#554C4×C10112yescomplemented
250#552—22no—
251#539—22no—
252#536—21no—
253#533C22×C10111yescharacteristic
254#532C22×C10111yescharacteristic
255#529C22×C10114yes—
256#520—21no—
257C2×C4×Q8C22×C10111yescharacteristic
258C8×Q8—22no—
259C8×Q8—22no—
260#431C22×C10114yes—
261#431C22×C10111yescharacteristic
262#431C22×C10111yescharacteristic
263#391—21no—
264#387—22no—
265#383C22×C10112yes—
266#382C22×C10111yescharacteristic
267C4×C4⋊C4—21no—
268C4×C4⋊C4C22×C10111yescharacteristic
269#376C22×C10112yes—
270#328C22×C10112yes—
271#328C22×C10114yes—
272#328C22×C10112yes—
273#327C22×C10112yes—
274#327C22×C10114yes—
275#327C22×C10112yes—
276C2×#41—21no—
277C22×Q8D4×C10111yescharacteristic
278C4⋊Q8—22no—
279C4⋊Q8C2×C4×C10111yescharacteristic
280C4⋊Q8C2×C4×C10111yescharacteristic
281C4⋊Q8C2×C4×C10111yescharacteristic
282#127C2×C4×C10111yescharacteristic
283#126—24no—
284#126—24no—
285#125—24no—
286#125—21no—
287#125C2×C4×C10114yes—
288#124—22no—
289#124—21no—
290#124C2×C4×C10114yes—
291#123—24no—
292#123—24no—
293C22⋊Q8—22no—
294C22⋊Q8—22no—
295C22⋊Q8—21no—
296C22⋊Q8—24no—
297C22⋊Q8C23×C10112yes—
298#121—21no—
299#121C23×C10112yes—
300C4×Q8—22no—
301C4×Q8—21no—
302C4×Q8C2×C4×C10114yes—
303C4×Q8C2×C4×C10112yes—
304C4×Q8C2×C4×C10112yes—
305C4×Q8C2×C4×C10112yes—
306C4×Q8D4×C10112yes—
307C4×Q8D4×C10112yes—
308C4×D4—24no—
309C4×D4—22no—
310C4×D4—21no—
311C4×D4C2×C4×C10114yes—
312C4×D4C2×C4×C10112yes—
313#117—21no—
314#117—22no—
315#117—24no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4D4×C10111yescharacteristic
320C2×C4⋊C4D4×C10112yes—
321C2×C42—22no—
322C2×C42—21no—
323C2×C42C23×C10112yes—
324C2×C42C23×C10111yescharacteristic
325C4⋊C8—24no—
326C4⋊C8—21no—
327C4⋊C8—21no—
328C22⋊C8C23×C10112yes—
329C22⋊C8C23×C10112yes—
330C4×C8—24no—
331C4×C8—21no—
332C4×C8—21no—
333#95—22no—
334#95—22no—
335#95—21no—
336#95—22no—
337#95C23×C10111yescharacteristic
338#95C23×C10112yes—
339#95C23×C10111yescharacteristic
340#41—42no—
341#41—42no—
342C2×Q8—21no—
343C2×Q8—21no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8C22⋊C4×C10112yes—
347C2×Q8C22⋊C4×C10112yes—
348C2×Q8C22×C4×C10112yes—
349C2×D4—22no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4C22×C4×C10112yes—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—24no—
356C22×C4—22no—
357C22×C4—21no—
358C22×C4C2×D4×C10112yes—
359C22×C4C2×D4×C10112yes—
360C22×C4C2×D4×C10111yescharacteristic
361C22×C4C2×D4×C10111yescharacteristic
362C22×C4C24×C10111yescharacteristic
363C2×C8—22no—
364C2×C8—22no—
365C4⋊C4—21no—
366C4⋊C4—24no—
367C4⋊C4—21no—
368C4⋊C4—24no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—24no—
373C4⋊C4—22no—
374C4⋊C4—42no—
375C4⋊C4—42no—
376C4⋊C4C22⋊C4×C10112yes—
377C4⋊C4C22⋊C4×C10112yes—
378C4⋊C4C22⋊C4×C10114yes—
379C4⋊C4C22⋊C4×C10114yes—
380C4⋊C4C22×C4×C10112yes—
381C4⋊C4C22×C4×C10112yes—
382C22⋊C4—22no—
383C22⋊C4—24no—
384C22⋊C4—24no—
385C22⋊C4—22no—
386C22⋊C4—24no—
387C22⋊C4—22no—
388C42—24no—
389C42—22no—
390C42—44no—
391C42—42no—
392C42C22×C4×C10111yescharacteristic
393C42C22×C4×C10114yes—
394C42C22×C4×C10111yescharacteristic
395C42C2×D4×C10114yes—
396C42C2×D4×C10111yescharacteristic
397C42C2×D4×C10111yescharacteristic
398C23—22no—
399C23C22×D4×C10111yescharacteristic
400Q8—24no—
401Q8—24no—
402Q8—42no—
403Q8—42no—
404Q8—81no—
405D4—42no—
406D4—42no—
407D4—42no—
408D4—42no—
409D4—81no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—44no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—84no—
429C2×C4C2×C22⋊C4×C10114yes—
430C2×C4C2×C22⋊C4×C10114yes—
431C2×C4C2×C22⋊C4×C10111yescharacteristic
432C2×C4C2×C22⋊C4×C10111yescharacteristic
433C2×C4C2×C22⋊C4×C10111yescharacteristic
434C2×C4C2×C22⋊C4×C10111yescharacteristic
435C2×C4#135×C10112yes—
436C2×C4#135×C10112yes—
437C2×C4C23×C4×C10111yescharacteristic
438C2×C4C22×D4×C10111yescharacteristic
439C8—42no—
440C8—42no—
441C22—21no—
442C22—21no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22C22×C22⋊C4×C10111yescharacteristic
447C22C2×#135×C10111yescharacteristic
448C22C2×#135×C10111yescharacteristic
449C4—21no—
450C4—21no—
451C4—24no—
452C4—24no—
453C4—21no—
454C4—21no—
455C4—42no—
456C4—42no—
457C4—42no—
458C4—42no—
459C4—81no—
460C4—82no—
461C4#416×C10112yes—
462C4#416×C10112yes—
463C2—21no—
464C2—21no—
465C2—82no—
466C2C101×#288411yescharacteristic
467C2C2×#416×C10111yescharacteristic
468C2C101×#290111yescharacteristic
subgroupG/H
center, socleC22×C101C22×C22⋊C4
commutatorC2×C4C23×C4×C101
Frattini, cosocleC22×C4C24×C101
prime radical#532×C101C22
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C2×C4×Q8×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#2982C2semidirect
3. C101×#2356C2semidirect
4. C101×#1521C2semidirect
5. C101×#1518C2semidirect
7. C101×#1503C2semidirect
9. C101×#1500C2semidirect
10. #559×C101C4semidirect
11. #557×C101C4semidirect
13. #556×C101C4semidirect
14. #554×C101C4semidirect
228. #17616C101direct (N × H)
236. #2982C2×C101semidirect
237. #2356C2×C101semidirect
238. #1521C2×C101semidirect
239. #1518C2×C101semidirect
241. #1503C2×C101semidirect
243. #1500C2×C101semidirect
244. C101#17616direct (N × H)
245. #559C4×C101semidirect
246. #557C4×C101semidirect
248. #556C4×C101semidirect
249. #554C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#35072
C101×#29822
C101×#23562
C101×#15212
C101×#15182
C101×#15172
C101×#15032
C101×#15022
C101×#15002
#17616101