Finite Group Databasebeta

← C101×#9283 #38791434

Subgroups — C101×#9283 #38791434

Order 25856.

448 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3207C211yesmaximal, characteristic
2C101×#2981C211yesmaximal, characteristic, complemented
3C101×#1530C211yesmaximal, characteristic, complemented
4C101×#1530C211yesmaximal, characteristic, complemented
5C101×#1496C211yesmaximal, characteristic, complemented
6C101×#1287C211yesmaximal, characteristic, complemented
7C101×#1275C211yesmaximal, characteristic, complemented
8#532×C101C2211yescharacteristic
9#532×C101C2211yescharacteristic
10#493×C101C411yescharacteristic
11#492×C101C411yescharacteristic
12#487×C101C411yescharacteristic
13#486×C101C411yescharacteristic
14#463×C101—22no—
15#449×C101—22no—
16#436×C101—21no—
17#435×C101—22no—
18C8×D4×C101—21no—
19#432×C101C2211yescharacteristic
20#432×C101C2211yescharacteristic
21#431×C101C2211yescharacteristic
22#431×C101C2211yescharacteristic
23#408×C101—22no—
24C2×#97×C101C2211yescharacteristic
25#329×C101—22no—
26#329×C101—22no—
27D4⋊C8×C101—21no—
28D4⋊C8×C101—21no—
29C2×#41×C101—21no—
30C2×#41×C101D412yes—
31C2×SD16×C101—22no—
32C2×D8×C101—22no—
33C2×M16×C101—22no—
34C22×C8×C101—21no—
35C22×C8×C101—22no—
36C4⋊Q8×C101C2×C411yescharacteristic
37C4⋊Q8×C101C2×C411yescharacteristic
38#127×C101C2×C411yescharacteristic
39#127×C101C2×C411yescharacteristic
40#124×C101—21no—
41#124×C101D412yes—
42#121×C101—21no—
43#121×C101—21no—
44#121×C101—21no—
45#121×C101—21no—
46C4×D4×C101—21no—
47C4×D4×C101—21no—
48C4×D4×C101—21no—
49C4×D4×C101—21no—
50C2×C42×C101C2311yescharacteristic
51C4⋊C8×C101—21no—
52C4⋊C8×C101—21no—
53C4⋊C8×C101—21no—
54C4⋊C8×C101—21no—
55#103×C101—22no—
56#102×C101—22no—
57C22⋊C8×C101—22no—
58C22⋊C8×C101—22no—
59C22⋊C8×C101—21no—
60C22⋊C8×C101—21no—
61C22⋊C8×C101—21no—
62C22⋊C8×C101—21no—
63#97×C101—21no—
64#97×C101—21no—
65#97×C101—21no—
66#97×C101D412yes—
67C4×C8×C101C2×C411yescharacteristic
68C4×C8×C101C2×C411yescharacteristic
69C4×C8×C101D411yescharacteristic
70C4×C8×C101D411yescharacteristic
71#41×C101—82no—
72#41×C101—82no—
73C2×Q8×C101—21no—
74C2×Q8×C101C22⋊C412yes—
75C2×D4×C101—22no—
76C2×D4×C101—21no—
77C2×D4×C101—21no—
78C2×D4×C101—21no—
79C2×D4×C101—21no—
80C2×D4×C101—21no—
81C2×D4×C101—41no—
82C2×D4×C101C22⋊C412yes—
83C22×C4×C101—22no—
84C22×C4×C101—41no—
85C22×C4×C101C2×D411yescharacteristic
86C22×C4×C101#4111yescharacteristic
87C22×C4×C101#4111yescharacteristic
88SD16×C101—82no—
89D8×C101—82no—
90M16×C101—82no—
91C2×C8×C101—22no—
92C2×C8×C101—21no—
93C2×C8×C101—21no—
94C2×C8×C101—21no—
95C2×C8×C101—21no—
96C2×C8×C101—22no—
97C2×C8×C101—41no—
98C2×C8×C101—41no—
99C2×C8×C101—41no—
100C2×C8×C101—82no—
101C4⋊C4×C101—21no—
102C4⋊C4×C101—21no—
103C4⋊C4×C101—21no—
104C4⋊C4×C101—21no—
105C22⋊C4×C101—22no—
106C22⋊C4×C101—22no—
107C22⋊C4×C101—41no—
108C22⋊C4×C101—41no—
109C42×C101C22×C411yescharacteristic
110C42×C101C2×D411yescharacteristic
111C42×C101C2×D411yescharacteristic
112C42×C101C2×D411yescharacteristic
113C23×C101—22no—
114C23×C101—41no—
115C23×C101#12311yescharacteristic
116Q8×C101—42no—
117Q8×C101—81no—
118D4×C101—42no—
119D4×C101—42no—
120D4×C101—41no—
121D4×C101—41no—
122D4×C101—41no—
123D4×C101—41no—
124D4×C101—81no—
125D4×C101—81no—
126D4×C101—82no—
127D4×C101—82no—
128C2×C4×C101—21no—
129C2×C4×C101—21no—
130C2×C4×C101—22no—
131C2×C4×C101—41no—
132C2×C4×C101—41no—
133C2×C4×C101—42no—
134C2×C4×C101—42no—
135C2×C4×C101—41no—
136C2×C4×C101—82no—
137C2×C4×C101C2×C22⋊C411yescharacteristic
138C2×C4×C101C4×D411yescharacteristic
139C2×C4×C101C4×D411yescharacteristic
140C2×C4×C101#12011yescharacteristic
141C2×C4×C101#12111yescharacteristic
142C2×C4×C101#12111yescharacteristic
143C8×C101—42no—
144C8×C101—41no—
145C8×C101—42no—
146C8×C101—41no—
147C8×C101—41no—
148C8×C101—41no—
149C8×C101—81no—
150C22×C101—21no—
151C22×C101—21no—
152C22×C101—21no—
153C22×C101—42no—
154C22×C101—42no—
155C22×C101—42no—
156C22×C101—81no—
157C22×C101—81no—
158C22×C101—81no—
159C22×C101#38611yescharacteristic
160C4×C101—21no—
161C4×C101—21no—
162C4×C101—21no—
163C4×C101—21no—
164C4×C101—21no—
165C4×C101—42no—
166C4×C101—81no—
167C4×C101#44311yescharacteristic
168C4×C101#44411yescharacteristic
169#9283C10111yesmaximal, characteristic, direct product factor, Sylow
170C2×C101—41no—
171C2×C101—82no—
172C2×C101—161no—
173C2×C101#187611yescharacteristic
174C2×C101#190311yescharacteristic
175C2×C101#191111yescharacteristic
176#3207C2×C10111yescharacteristic
177#2981C2×C10111yescharacteristic, complemented
178#1530C2×C10111yescharacteristic, complemented
179#1530C2×C10111yescharacteristic, complemented
180#1496C2×C10111yescharacteristic, complemented
181#1287C2×C10111yescharacteristic, complemented
182#1275C2×C10111yescharacteristic, complemented
183C101#928311yescharacteristic, direct product factor, Sylow
184#532C22×C10111yescharacteristic
185#532C22×C10111yescharacteristic
186#493C4×C10111yescharacteristic
187#492C4×C10111yescharacteristic
188#487C4×C10111yescharacteristic
189#486C4×C10111yescharacteristic
190#463—22no—
191#449—22no—
192#436—21no—
193#435—22no—
194C8×D4—21no—
195#432C22×C10111yescharacteristic
196#432C22×C10111yescharacteristic
197#431C22×C10111yescharacteristic
198#431C22×C10111yescharacteristic
199#408—22no—
200C2×#97C22×C10111yescharacteristic
201#329—22no—
202#329—22no—
203D4⋊C8—21no—
204D4⋊C8—21no—
205C2×#41—21no—
206C2×#41D4×C10112yes—
207C2×SD16—22no—
208C2×D8—22no—
209C2×M16—22no—
210C22×C8—21no—
211C22×C8—22no—
212C4⋊Q8C2×C4×C10111yescharacteristic
213C4⋊Q8C2×C4×C10111yescharacteristic
214#127C2×C4×C10111yescharacteristic
215#127C2×C4×C10111yescharacteristic
216#124—21no—
217#124D4×C10112yes—
218#121—21no—
219#121—21no—
220#121—21no—
221#121—21no—
222C4×D4—21no—
223C4×D4—21no—
224C4×D4—21no—
225C4×D4—21no—
226C2×C42C23×C10111yescharacteristic
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231#103—22no—
232#102—22no—
233C22⋊C8—22no—
234C22⋊C8—22no—
235C22⋊C8—21no—
236C22⋊C8—21no—
237C22⋊C8—21no—
238C22⋊C8—21no—
239#97—21no—
240#97—21no—
241#97—21no—
242#97D4×C10112yes—
243C4×C8C2×C4×C10111yescharacteristic
244C4×C8C2×C4×C10111yescharacteristic
245C4×C8D4×C10111yescharacteristic
246C4×C8D4×C10111yescharacteristic
247#41—82no—
248#41—82no—
249C2×Q8—21no—
250C2×Q8C22⋊C4×C10112yes—
251C2×D4—22no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4C22⋊C4×C10112yes—
259C22×C4—22no—
260C22×C4—41no—
261C22×C4C2×D4×C10111yescharacteristic
262C22×C4#41×C10111yescharacteristic
263C22×C4#41×C10111yescharacteristic
264SD16—82no—
265D8—82no—
266M16—82no—
267C2×C8—22no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—22no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—82no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C22⋊C4—22no—
282C22⋊C4—22no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C42C22×C4×C10111yescharacteristic
286C42C2×D4×C10111yescharacteristic
287C42C2×D4×C10111yescharacteristic
288C42C2×D4×C10111yescharacteristic
289C23—22no—
290C23—41no—
291C23#123×C10111yescharacteristic
292Q8—42no—
293Q8—81no—
294D4—42no—
295D4—42no—
296D4—41no—
297D4—41no—
298D4—41no—
299D4—41no—
300D4—81no—
301D4—81no—
302D4—82no—
303D4—82no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—82no—
313C2×C4C2×C22⋊C4×C10111yescharacteristic
314C2×C4C4×D4×C10111yescharacteristic
315C2×C4C4×D4×C10111yescharacteristic
316C2×C4#120×C10111yescharacteristic
317C2×C4#121×C10111yescharacteristic
318C2×C4#121×C10111yescharacteristic
319C8—42no—
320C8—41no—
321C8—42no—
322C8—41no—
323C8—41no—
324C8—41no—
325C8—81no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—42no—
330C22—42no—
331C22—42no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22#386×C10111yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—42no—
342C4—81no—
343C4#443×C10111yescharacteristic
344C4#444×C10111yescharacteristic
345C2—41no—
346C2—82no—
347C2—161no—
348C2C101×#187611yescharacteristic
349C2C101×#190311yescharacteristic
350C2C101×#191111yescharacteristic
subgroupG/H
center, socleC22×C101#386
commutatorC42C22×C4×C101
Frattini, cosocleC2×C42C23×C101
prime radicalC101×#3207C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#2981C2semidirect
3. C101×#1530C2semidirect
4. C101×#1530C2semidirect
5. C101×#1496C2semidirect
6. C101×#1287C2semidirect
7. C101×#1275C2semidirect
169. #9283C101direct (N × H)
177. #2981C2×C101semidirect
178. #1530C2×C101semidirect
179. #1530C2×C101semidirect
180. #1496C2×C101semidirect
181. #1287C2×C101semidirect
182. #1275C2×C101semidirect
183. C101#9283direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#32072
C101×#29812
C101×#15302
C101×#14962
C101×#12872
C101×#12752
#9283101