Finite Group Databasebeta

← C101×#8673 #38790824

Subgroups — C101×#8673 #38790824

Order 25856.

386 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#2965C211yesmaximal, characteristic
2C4×#108×C101C211yesmaximal, characteristic, complemented
3C101×#1567C211yesmaximal, characteristic, complemented
4C101×#1489C212yesmaximal
5C101×#1299C212yesmaximal, complemented
6C4×#41×C101C2211yescharacteristic
7#446×C101C411yescharacteristic
8#446×C101C411yescharacteristic
9#436×C101C411yescharacteristic
10#436×C101C411yescharacteristic
11#435×C101—21no—
12#435×C101—21no—
13#431×C101—21no—
14#431×C101C2211yescharacteristic
15C2×#108×C101—21no—
16#423×C101C2212yes—
17C4×M16×C101—21no—
18C4×M16×C101C2212yes—
19C2×C4×C8×C101C2211yescharacteristic
20#341×C101—21no—
21#335×C101—21no—
22#335×C101—21no—
23Q8⋊C8×C101—22no—
24D4⋊C8×C101—22no—
25C2×#41×C101Q811yescharacteristic
26C2×M16×C101—21no—
27C2×M16×C101—21no—
28C2×M16×C101—22no—
29C2×M16×C101—22no—
30C22×C8×C101D411yescharacteristic
31C22×C8×C101D411yescharacteristic
32C4×Q8×C101C2×C411yescharacteristic
33C4×Q8×C101D411yescharacteristic
34C4×D4×C101—21no—
35C4×D4×C101—21no—
36C4×D4×C101C2×C411yescharacteristic
37C4×D4×C101D411yescharacteristic
38#117×C101—21no—
39#117×C101Q811yescharacteristic
40C2×C42×C101—21no—
41C2×C42×C101C2311yescharacteristic
42#108×C101—24no—
43C4⋊C8×C101—21no—
44C4⋊C8×C101—21no—
45C4⋊C8×C101—22no—
46C4⋊C8×C101—22no—
47C4⋊C8×C101C2×C411yescharacteristic
48C4⋊C8×C101C2×C411yescharacteristic
49C22⋊C8×C101—21no—
50C22⋊C8×C101—21no—
51C22⋊C8×C101—21no—
52#97×C101—21no—
53#97×C101—21no—
54#97×C101—22no—
55C4×C8×C101—21no—
56C4×C8×C101—22no—
57C4×C8×C101C2×C411yescharacteristic
58C4×C8×C101C2×C411yescharacteristic
59C4×C8×C101D411yescharacteristic
60C4×C8×C101D411yescharacteristic
61#41×C101—42no—
62C2×Q8×C101C4⋊C411yescharacteristic
63C2×D4×C101—21no—
64C2×D4×C101C4⋊C411yescharacteristic
65C22×C4×C101—21no—
66C22×C4×C101—21no—
67C22×C4×C101—21no—
68C22×C4×C101C2×D411yescharacteristic
69C22×C4×C101C2×Q811yescharacteristic
70C22×C4×C101#4111yescharacteristic
71M16×C101—24no—
72M16×C101—42no—
73M16×C101—42no—
74M16×C101—42no—
75M16×C101—82no—
76C2×C8×C101—22no—
77C2×C8×C101—21no—
78C2×C8×C101—21no—
79C2×C8×C101—41no—
80C2×C8×C101—42no—
81C2×C8×C101—42no—
82C2×C8×C101C22⋊C411yescharacteristic
83C2×C8×C101C22⋊C411yescharacteristic
84C2×C8×C101C22⋊C411yescharacteristic
85C2×C8×C101C22⋊C411yescharacteristic
86C4⋊C4×C101—21no—
87C4⋊C4×C101—21no—
88C4⋊C4×C101C4⋊C411yescharacteristic
89C4⋊C4×C101C4⋊C411yescharacteristic
90C22⋊C4×C101—21no—
91C22⋊C4×C101—21no—
92C22⋊C4×C101—21no—
93C42×C101—21no—
94C42×C101—21no—
95C42×C101—21no—
96C42×C101C22×C411yescharacteristic
97C42×C101C2×D411yescharacteristic
98C42×C101C2×D411yescharacteristic
99C42×C101#4111yescharacteristic
100C23×C101—21no—
101C23×C101C22⋊Q811yescharacteristic
102Q8×C101—22no—
103D4×C101—22no—
104D4×C101—42no—
105C2×C4×C101—21no—
106C2×C4×C101—21no—
107C2×C4×C101—22no—
108C2×C4×C101—21no—
109C2×C4×C101—21no—
110C2×C4×C101—21no—
111C2×C4×C101—21no—
112C2×C4×C101—21no—
113C2×C4×C101—42no—
114C2×C4×C101—41no—
115C2×C4×C101—41no—
116C2×C4×C101—41no—
117C2×C4×C101—41no—
118C2×C4×C101C2×C22⋊C411yescharacteristic
119C2×C4×C101C2×C4⋊C411yescharacteristic
120C2×C4×C101#11711yescharacteristic
121C2×C4×C101#12111yescharacteristic
122C2×C4×C101#12111yescharacteristic
123C2×C4×C101C22⋊Q811yescharacteristic
124C8×C101—21no—
125C8×C101—21no—
126C8×C101—21no—
127C8×C101—44no—
128C8×C101—41no—
129C8×C101—41no—
130C8×C101—82no—
131C8×C101#10412yes—
132C22×C101—21no—
133C22×C101—21no—
134C22×C101—21no—
135C22×C101—41no—
136C22×C101—41no—
137C22×C101—41no—
138C22×C101#38011yescharacteristic
139C4×C101—21no—
140C4×C101—21no—
141C4×C101—21no—
142C4×C101—41no—
143C4×C101—41no—
144C4×C101—41no—
145C4×C101C2×#10411yescharacteristic
146C4×C101#42111yescharacteristic
147C4×C101#43012yes—
148C4×C101#47211yescharacteristic
149C4×C101#47311yescharacteristic
150#8673C10111yesmaximal, characteristic, direct product factor, Sylow
151C2×C101—41no—
152C2×C101—81no—
153C2×C101#180611yescharacteristic
154C2×C101#181111yescharacteristic
155C2×C101#181611yescharacteristic
156#2965C2×C10111yescharacteristic
157C4×#108C2×C10111yescharacteristic, complemented
158#1567C2×C10111yescharacteristic, complemented
159#1489C2×C10112yes—
160#1299C2×C10112yescomplemented
161C101#867311yescharacteristic, direct product factor, Sylow
162C4×#41C22×C10111yescharacteristic
163#446C4×C10111yescharacteristic
164#446C4×C10111yescharacteristic
165#436C4×C10111yescharacteristic
166#436C4×C10111yescharacteristic
167#435—21no—
168#435—21no—
169#431—21no—
170#431C22×C10111yescharacteristic
171C2×#108—21no—
172#423C22×C10112yes—
173C4×M16—21no—
174C4×M16C22×C10112yes—
175C2×C4×C8C22×C10111yescharacteristic
176#341—21no—
177#335—21no—
178#335—21no—
179Q8⋊C8—22no—
180D4⋊C8—22no—
181C2×#41Q8×C10111yescharacteristic
182C2×M16—21no—
183C2×M16—21no—
184C2×M16—22no—
185C2×M16—22no—
186C22×C8D4×C10111yescharacteristic
187C22×C8D4×C10111yescharacteristic
188C4×Q8C2×C4×C10111yescharacteristic
189C4×Q8D4×C10111yescharacteristic
190C4×D4—21no—
191C4×D4—21no—
192C4×D4C2×C4×C10111yescharacteristic
193C4×D4D4×C10111yescharacteristic
194#117—21no—
195#117Q8×C10111yescharacteristic
196C2×C42—21no—
197C2×C42C23×C10111yescharacteristic
198#108—24no—
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—22no—
202C4⋊C8—22no—
203C4⋊C8C2×C4×C10111yescharacteristic
204C4⋊C8C2×C4×C10111yescharacteristic
205C22⋊C8—21no—
206C22⋊C8—21no—
207C22⋊C8—21no—
208#97—21no—
209#97—21no—
210#97—22no—
211C4×C8—21no—
212C4×C8—22no—
213C4×C8C2×C4×C10111yescharacteristic
214C4×C8C2×C4×C10111yescharacteristic
215C4×C8D4×C10111yescharacteristic
216C4×C8D4×C10111yescharacteristic
217#41—42no—
218C2×Q8C4⋊C4×C10111yescharacteristic
219C2×D4—21no—
220C2×D4C4⋊C4×C10111yescharacteristic
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4C2×D4×C10111yescharacteristic
225C22×C4C2×Q8×C10111yescharacteristic
226C22×C4#41×C10111yescharacteristic
227M16—24no—
228M16—42no—
229M16—42no—
230M16—42no—
231M16—82no—
232C2×C8—22no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—41no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8C22⋊C4×C10111yescharacteristic
239C2×C8C22⋊C4×C10111yescharacteristic
240C2×C8C22⋊C4×C10111yescharacteristic
241C2×C8C22⋊C4×C10111yescharacteristic
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4C4⋊C4×C10111yescharacteristic
245C4⋊C4C4⋊C4×C10111yescharacteristic
246C22⋊C4—21no—
247C22⋊C4—21no—
248C22⋊C4—21no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42C22×C4×C10111yescharacteristic
253C42C2×D4×C10111yescharacteristic
254C42C2×D4×C10111yescharacteristic
255C42#41×C10111yescharacteristic
256C23—21no—
257C23C22⋊Q8×C10111yescharacteristic
258Q8—22no—
259D4—22no—
260D4—42no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4C2×C22⋊C4×C10111yescharacteristic
275C2×C4C2×C4⋊C4×C10111yescharacteristic
276C2×C4#117×C10111yescharacteristic
277C2×C4#121×C10111yescharacteristic
278C2×C4#121×C10111yescharacteristic
279C2×C4C22⋊Q8×C10111yescharacteristic
280C8—21no—
281C8—21no—
282C8—21no—
283C8—44no—
284C8—41no—
285C8—41no—
286C8—82no—
287C8#104×C10112yes—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22#380×C10111yescharacteristic
295C4—21no—
296C4—21no—
297C4—21no—
298C4—41no—
299C4—41no—
300C4—41no—
301C4C2×#104×C10111yescharacteristic
302C4#421×C10111yescharacteristic
303C4#430×C10112yes—
304C4#472×C10111yescharacteristic
305C4#473×C10111yescharacteristic
306C2—41no—
307C2—81no—
308C2C101×#180611yescharacteristic
309C2C101×#181111yescharacteristic
310C2C101×#181611yescharacteristic
subgroupG/H
centerC2×C4×C101#121
commutatorC42C22×C4×C101
Frattini, cosocleC2×C42C23×C101
socleC22×C101#380
prime radicalC2×#41×C101Q8
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×#108×C101C2semidirect
3. C101×#1567C2semidirect
5. C101×#1299C2semidirect
150. #8673C101direct (N × H)
157. C4×#108C2×C101semidirect
158. #1567C2×C101semidirect
160. #1299C2×C101semidirect
161. C101#8673direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#29652
C4×#108×C1012
C101×#15672
C101×#14892
C101×#12992
#8673101