Finite Group Databasebeta

← C101×#8841 #38790992

Subgroups — C101×#8841 #38790992

Order 25856.

440 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#2989C211yesmaximal, characteristic
2C101×#1842C211yesmaximal, characteristic, complemented
3C4×#104×C101C211yesmaximal, characteristic
4C101×#1565C211yesmaximal, characteristic, complemented
5C101×#1477C211yesmaximal, characteristic
6C101×#1283C211yesmaximal, characteristic, complemented
7C101×#1276C211yesmaximal, characteristic, complemented
8C4×#41×C101C2211yescharacteristic
9#446×C101—21no—
10#436×C101—21no—
11#435×C101—22no—
12#432×C101—21no—
13#431×C101C2211yescharacteristic
14#431×C101C2211yescharacteristic
15#423×C101—21no—
16C2×C4⋊C8×C101—22no—
17C2×C4⋊C8×C101C2211yescharacteristic
18C2×C4⋊C8×C101C2211yescharacteristic
19C2×#104×C101C411yescharacteristic
20C2×#104×C101C411yescharacteristic
21C4×M16×C101C2211yescharacteristic
22C43×C101C2211yescharacteristic
23#339×C101C411yescharacteristic
24#339×C101C411yescharacteristic
25#335×C101—21no—
26#334×C101—21no—
27Q8⋊C8×C101—21no—
28D4⋊C8×C101—21no—
29C2×#41×C101C2×C411yescharacteristic
30C2×M16×C101—22no—
31C2×M16×C101C2×C411yescharacteristic
32C2×M16×C101C2×C411yescharacteristic
33C22×C8×C101—21no—
34C22×C8×C101D412yes—
35C4×Q8×C101D411yescharacteristic
36C4×Q8×C101Q811yescharacteristic
37C4×D4×C101—21no—
38C4×D4×C101—21no—
39C4×D4×C101D411yescharacteristic
40C4×D4×C101Q811yescharacteristic
41#117×C101—21no—
42#117×C101C2×C411yescharacteristic
43C2×C42×C101—21no—
44C2×C42×C101—21no—
45C2×C42×C101—21no—
46C2×C42×C101C2×C411yescharacteristic
47C2×C42×C101C2×C411yescharacteristic
48C2×C42×C101C2311yescharacteristic
49C4⋊C8×C101—22no—
50C4⋊C8×C101—21no—
51C4⋊C8×C101—21no—
52C4⋊C8×C101—21no—
53C4⋊C8×C101—21no—
54C4⋊C8×C101—21no—
55C4⋊C8×C101—44no—
56C4⋊C8×C101D411yescharacteristic
57C4⋊C8×C101D411yescharacteristic
58#104×C101—22no—
59#104×C101—22no—
60C22⋊C8×C101—22no—
61C22⋊C8×C101—21no—
62C22⋊C8×C101—21no—
63#97×C101—22no—
64#97×C101—21no—
65C4×C8×C101—21no—
66C4×C8×C101—21no—
67C4×C8×C101—21no—
68#41×C101—21no—
69#41×C101—21no—
70#41×C101—21no—
71#41×C101—21no—
72C2×Q8×C101C4⋊C411yescharacteristic
73C2×D4×C101—21no—
74C2×D4×C101C4⋊C411yescharacteristic
75C22×C4×C101—21no—
76C22×C4×C101—21no—
77C22×C4×C101—21no—
78C22×C4×C101—21no—
79C22×C4×C101—21no—
80C22×C4×C101C22×C411yescharacteristic
81C22×C4×C101C2×D411yescharacteristic
82C22×C4×C101#4111yescharacteristic
83M16×C101—21no—
84M16×C101—21no—
85M16×C101—21no—
86M16×C101—82no—
87M16×C101M1612yescomplemented
88C2×C8×C101—21no—
89C2×C8×C101—21no—
90C2×C8×C101—21no—
91C2×C8×C101—21no—
92C2×C8×C101—22no—
93C2×C8×C101—42no—
94C2×C8×C101—42no—
95C2×C8×C101—41no—
96C2×C8×C101—41no—
97C4⋊C4×C101—21no—
98C4⋊C4×C101—21no—
99C4⋊C4×C101C4⋊C411yescharacteristic
100C4⋊C4×C101C4⋊C411yescharacteristic
101C22⋊C4×C101—21no—
102C22⋊C4×C101—21no—
103C22⋊C4×C101—21no—
104C42×C101—22no—
105C42×C101—22no—
106C42×C101—21no—
107C42×C101—21no—
108C42×C101—21no—
109C42×C101—21no—
110C42×C101—21no—
111C42×C101—21no—
112C42×C101—42no—
113C42×C101M1612yescomplemented
114C42×C101C2×D411yescharacteristic
115C42×C101C2×D411yescharacteristic
116C42×C101C2×Q811yescharacteristic
117C42×C101#4111yescharacteristic
118C23×C101—21no—
119C23×C101C4×D411yescharacteristic
120Q8×C101—21no—
121Q8×C101—21no—
122D4×C101—21no—
123D4×C101—21no—
124D4×C101—41no—
125D4×C101—41no—
126C2×C4×C101—22no—
127C2×C4×C101—22no—
128C2×C4×C101—22no—
129C2×C4×C101—21no—
130C2×C4×C101—21no—
131C2×C4×C101—22no—
132C2×C4×C101—21no—
133C2×C4×C101—21no—
134C2×C4×C101—21no—
135C2×C4×C101—41no—
136C2×C4×C101—41no—
137C2×C4×C101—41no—
138C2×C4×C101—41no—
139C2×C4×C101—41no—
140C2×C4×C101—41no—
141C2×C4×C101—41no—
142C2×C4×C101—81no—
143C2×C4×C101C2×C4⋊C411yescharacteristic
144C2×C4×C101C4×D411yescharacteristic
145C2×C4×C101#12011yescharacteristic
146C2×C4×C101C22⋊Q811yescharacteristic
147C2×C4×C101C22⋊Q811yescharacteristic
148C2×C4×C101#12311yescharacteristic
149C2×C4×C101C2×M1611yescharacteristic
150C2×C4×C101C2×M1611yescharacteristic
151C2×C4×C101#13111yescharacteristic
152C2×C4×C101#13111yescharacteristic
153C8×C101—22no—
154C8×C101—41no—
155C8×C101—42no—
156C8×C101—41no—
157C8×C101—41no—
158C8×C101—81no—
159C8×C101—81no—
160C22×C101—21no—
161C22×C101—21no—
162C22×C101—41no—
163C22×C101—41no—
164C22×C101—41no—
165C22×C101#38511yescharacteristic
166C22×C101#43511yescharacteristic
167C22×C101#43611yescharacteristic
168C4×C101—24no—
169C4×C101—21no—
170C4×C101—21no—
171C4×C101—21no—
172C4×C101—42no—
173C4×C101—41no—
174C4×C101—41no—
175C4×C101—41no—
176C4×C101#42311yescharacteristic
177C4×C101#42411yescharacteristic
178C4×C101#43511yescharacteristic
179C4×C101#43611yescharacteristic
180C4×C101#45311yescharacteristic
181C4×C101#45611yescharacteristic
182#8841C10111yesmaximal, characteristic, direct product factor, Sylow
183C2×C101—21no—
184C2×C101—21no—
185C2×C101—81no—
186C2×C101#185111yescharacteristic
187C2×C101#185911yescharacteristic
188C2×C101#186111yescharacteristic
189#2989C2×C10111yescharacteristic
190#1842C2×C10111yescharacteristic, complemented
191C4×#104C2×C10111yescharacteristic
192#1565C2×C10111yescharacteristic, complemented
193#1477C2×C10111yescharacteristic
194#1283C2×C10111yescharacteristic, complemented
195#1276C2×C10111yescharacteristic, complemented
196C101#884111yescharacteristic, direct product factor, Sylow
197C4×#41C22×C10111yescharacteristic
198#446—21no—
199#436—21no—
200#435—22no—
201#432—21no—
202#431C22×C10111yescharacteristic
203#431C22×C10111yescharacteristic
204#423—21no—
205C2×C4⋊C8—22no—
206C2×C4⋊C8C22×C10111yescharacteristic
207C2×C4⋊C8C22×C10111yescharacteristic
208C2×#104C4×C10111yescharacteristic
209C2×#104C4×C10111yescharacteristic
210C4×M16C22×C10111yescharacteristic
211C43C22×C10111yescharacteristic
212#339C4×C10111yescharacteristic
213#339C4×C10111yescharacteristic
214#335—21no—
215#334—21no—
216Q8⋊C8—21no—
217D4⋊C8—21no—
218C2×#41C2×C4×C10111yescharacteristic
219C2×M16—22no—
220C2×M16C2×C4×C10111yescharacteristic
221C2×M16C2×C4×C10111yescharacteristic
222C22×C8—21no—
223C22×C8D4×C10112yes—
224C4×Q8D4×C10111yescharacteristic
225C4×Q8Q8×C10111yescharacteristic
226C4×D4—21no—
227C4×D4—21no—
228C4×D4D4×C10111yescharacteristic
229C4×D4Q8×C10111yescharacteristic
230#117—21no—
231#117C2×C4×C10111yescharacteristic
232C2×C42—21no—
233C2×C42—21no—
234C2×C42—21no—
235C2×C42C2×C4×C10111yescharacteristic
236C2×C42C2×C4×C10111yescharacteristic
237C2×C42C23×C10111yescharacteristic
238C4⋊C8—22no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—44no—
245C4⋊C8D4×C10111yescharacteristic
246C4⋊C8D4×C10111yescharacteristic
247#104—22no—
248#104—22no—
249C22⋊C8—22no—
250C22⋊C8—21no—
251C22⋊C8—21no—
252#97—22no—
253#97—21no—
254C4×C8—21no—
255C4×C8—21no—
256C4×C8—21no—
257#41—21no—
258#41—21no—
259#41—21no—
260#41—21no—
261C2×Q8C4⋊C4×C10111yescharacteristic
262C2×D4—21no—
263C2×D4C4⋊C4×C10111yescharacteristic
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4C22×C4×C10111yescharacteristic
270C22×C4C2×D4×C10111yescharacteristic
271C22×C4#41×C10111yescharacteristic
272M16—21no—
273M16—21no—
274M16—21no—
275M16—82no—
276M16M16×C10112yescomplemented
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—22no—
282C2×C8—42no—
283C2×C8—42no—
284C2×C8—41no—
285C2×C8—41no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4C4⋊C4×C10111yescharacteristic
289C4⋊C4C4⋊C4×C10111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C42—22no—
294C42—22no—
295C42—21no—
296C42—21no—
297C42—21no—
298C42—21no—
299C42—21no—
300C42—21no—
301C42—42no—
302C42M16×C10112yescomplemented
303C42C2×D4×C10111yescharacteristic
304C42C2×D4×C10111yescharacteristic
305C42C2×Q8×C10111yescharacteristic
306C42#41×C10111yescharacteristic
307C23—21no—
308C23C4×D4×C10111yescharacteristic
309Q8—21no—
310Q8—21no—
311D4—21no—
312D4—21no—
313D4—41no—
314D4—41no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—81no—
332C2×C4C2×C4⋊C4×C10111yescharacteristic
333C2×C4C4×D4×C10111yescharacteristic
334C2×C4#120×C10111yescharacteristic
335C2×C4C22⋊Q8×C10111yescharacteristic
336C2×C4C22⋊Q8×C10111yescharacteristic
337C2×C4#123×C10111yescharacteristic
338C2×C4C2×M16×C10111yescharacteristic
339C2×C4C2×M16×C10111yescharacteristic
340C2×C4#131×C10111yescharacteristic
341C2×C4#131×C10111yescharacteristic
342C8—22no—
343C8—41no—
344C8—42no—
345C8—41no—
346C8—41no—
347C8—81no—
348C8—81no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22#385×C10111yescharacteristic
355C22#435×C10111yescharacteristic
356C22#436×C10111yescharacteristic
357C4—24no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—42no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4#423×C10111yescharacteristic
366C4#424×C10111yescharacteristic
367C4#435×C10111yescharacteristic
368C4#436×C10111yescharacteristic
369C4#453×C10111yescharacteristic
370C4#456×C10111yescharacteristic
371C2—21no—
372C2—21no—
373C2—81no—
374C2C101×#185111yescharacteristic
375C2C101×#185911yescharacteristic
376C2C101×#186111yescharacteristic
subgroupG/H
centerC2×C4×C101#120
commutatorC22×C4C22×C4×C101
Frattini, cosocleC2×C42C23×C101
socleC22×C101#385
prime radicalC2×#41×C101C2×C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#1842C2semidirect
4. C101×#1565C2semidirect
6. C101×#1283C2semidirect
7. C101×#1276C2semidirect
87. M16×C101M16semidirect
113. C42×C101M16semidirect
182. #8841C101direct (N × H)
190. #1842C2×C101semidirect
192. #1565C2×C101semidirect
194. #1283C2×C101semidirect
195. #1276C2×C101semidirect
196. C101#8841direct (N × H)
276. M16M16×C101semidirect
302. C42M16×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#29892
C101×#18422
C4×#104×C1012
C101×#15652
C101×#14772
C101×#12832
C101×#12762
#8841101