Finite Group Databasebeta

← C101×#12965 #38795116

Subgroups — C101×#12965 #38795116

Order 25856.

536 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2372C211yesmaximal, characteristic
2C2×#354×C101C211yesmaximal, characteristic
3C101×#1885C211yesmaximal, characteristic
4C101×#1867C212yesmaximal
5C101×#1390C212yesmaximal
6C2×#124×C101C2211yescharacteristic
7#518×C101C2211yescharacteristic
8#419×C101—21no—
9C2×#100×C101C2211yescharacteristic
10C2×#99×C101C2212yes—
11#391×C101—21no—
12#388×C101—22no—
13#386×C101C2212yes—
14#385×C101—22no—
15C4×C22⋊C4×C101—22no—
16#376×C101—21no—
17#354×C101C414yescomplemented
18#342×C101—22no—
19#339×C101—21no—
20C22×Q8×C101D411yescharacteristic
21C22×D4×C101C2311yescharacteristic
22C23×C4×C101D412yes—
23C2×M16×C101—21no—
24#124×C101—22no—
25#124×C101C2×C412yes—
26#124×C101Q812yes—
27C4×D4×C101—42no—
28#117×C101—21no—
29C2×C4⋊C4×C101—21no—
30C2×C4⋊C4×C101—42no—
31C2×C22⋊C4×C101—22no—
32C2×C22⋊C4×C101—22no—
33C2×C22⋊C4×C101—22no—
34C2×C22⋊C4×C101—22no—
35C2×C22⋊C4×C101D412yes—
36C2×C42×C101—22no—
37C2×C42×C101—21no—
38C2×C42×C101D411yescharacteristic
39#103×C101—42no—
40#100×C101—22no—
41#99×C101—22no—
42#99×C101C2×C414yes—
43#95×C101—21no—
44#95×C101—21no—
45#95×C101—22no—
46#95×C101—22no—
47#95×C101—42no—
48C24×C101C2×D412yes—
49C2×Q8×C101—21no—
50C2×Q8×C101—41no—
51C2×Q8×C101—41no—
52C2×Q8×C101C4⋊C412yescomplemented
53C2×D4×C101—41no—
54C2×D4×C101—41no—
55C2×D4×C101C22×C411yescharacteristic
56C2×D4×C101C2×Q811yescharacteristic
57C2×D4×C101#4112yes—
58C22×C4×C101—22no—
59C22×C4×C101—21no—
60C22×C4×C101—21no—
61C22×C4×C101—22no—
62C22×C4×C101—22no—
63C22×C4×C101—22no—
64C22×C4×C101—44no—
65C22×C4×C101—42no—
66C22×C4×C101—42no—
67C22×C4×C101C2×D411yescharacteristic
68M16×C101—41no—
69M16×C101—41no—
70C2×C8×C101—41no—
71C4⋊C4×C101—22no—
72C4⋊C4×C101—81no—
73C4⋊C4×C101—84no—
74C22⋊C4×C101—24no—
75C22⋊C4×C101—24no—
76C22⋊C4×C101—24no—
77C22⋊C4×C101—44no—
78C22⋊C4×C101—42no—
79C22⋊C4×C101—42no—
80C22⋊C4×C101—41no—
81C22⋊C4×C101—42no—
82C42×C101—21no—
83C42×C101—44no—
84C42×C101—41no—
85C42×C101—81no—
86C42×C101C4⋊C412yescomplemented
87C23×C101—22no—
88C23×C101—22no—
89C23×C101—42no—
90C23×C101—42no—
91C23×C101C4×D412yes—
92C23×C101#12011yescharacteristic
93C23×C101C22⋊Q812yes—
94Q8×C101—42no—
95Q8×C101—81no—
96D4×C101—41no—
97D4×C101—41no—
98D4×C101—42no—
99C2×C4×C101—21no—
100C2×C4×C101—21no—
101C2×C4×C101—24no—
102C2×C4×C101—22no—
103C2×C4×C101—22no—
104C2×C4×C101—42no—
105C2×C4×C101—42no—
106C2×C4×C101—42no—
107C2×C4×C101—41no—
108C2×C4×C101—41no—
109C2×C4×C101—44no—
110C2×C4×C101—42no—
111C2×C4×C101—44no—
112C2×C4×C101—42no—
113C2×C4×C101—42no—
114C2×C4×C101—42no—
115C2×C4×C101—82no—
116C2×C4×C101—82no—
117C2×C4×C101—82no—
118C2×C4×C101—82no—
119C2×C4×C101—82no—
120C2×C4×C101C2×C4⋊C411yescharacteristic
121C2×C4×C101#12311yescharacteristic
122C8×C101—81no—
123C22×C101—22no—
124C22×C101—22no—
125C22×C101—22no—
126C22×C101—42no—
127C22×C101—42no—
128C22×C101—42no—
129C22×C101—42no—
130C22×C101—82no—
131C22×C101#38511yescharacteristic
132C22×C101B(4,𝔽2)11yescharacteristic
133C22×C101#45811yescharacteristic
134C4×C101—21no—
135C4×C101—21no—
136C4×C101—42no—
137C4×C101—42no—
138C4×C101—44no—
139C4×C101—82no—
140C4×C101—84no—
141C4×C101—82no—
142#12965C10111yesmaximal, characteristic, direct product factor, Sylow
143C2×C101—21no—
144C2×C101—21no—
145C2×C101—42no—
146C2×C101—42no—
147C2×C101#186711yescharacteristic
148C2×C101#219712yes—
149#2372C2×C10111yescharacteristic
150C2×#354C2×C10111yescharacteristic
151#1885C2×C10111yescharacteristic
152#1867C2×C10112yes—
153#1390C2×C10112yes—
154C101#1296511yescharacteristic, direct product factor, Sylow
155C2×#124C22×C10111yescharacteristic
156#518C22×C10111yescharacteristic
157#419—21no—
158C2×#100C22×C10111yescharacteristic
159C2×#99C22×C10112yes—
160#391—21no—
161#388—22no—
162#386C22×C10112yes—
163#385—22no—
164C4×C22⋊C4—22no—
165#376—21no—
166#354C4×C10114yescomplemented
167#342—22no—
168#339—21no—
169C22×Q8D4×C10111yescharacteristic
170C22×D4C23×C10111yescharacteristic
171C23×C4D4×C10112yes—
172C2×M16—21no—
173#124—22no—
174#124C2×C4×C10112yes—
175#124Q8×C10112yes—
176C4×D4—42no—
177#117—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—42no—
180C2×C22⋊C4—22no—
181C2×C22⋊C4—22no—
182C2×C22⋊C4—22no—
183C2×C22⋊C4—22no—
184C2×C22⋊C4D4×C10112yes—
185C2×C42—22no—
186C2×C42—21no—
187C2×C42D4×C10111yescharacteristic
188#103—42no—
189#100—22no—
190#99—22no—
191#99C2×C4×C10114yes—
192#95—21no—
193#95—21no—
194#95—22no—
195#95—22no—
196#95—42no—
197C24C2×D4×C10112yes—
198C2×Q8—21no—
199C2×Q8—41no—
200C2×Q8—41no—
201C2×Q8C4⋊C4×C10112yescomplemented
202C2×D4—41no—
203C2×D4—41no—
204C2×D4C22×C4×C10111yescharacteristic
205C2×D4C2×Q8×C10111yescharacteristic
206C2×D4#41×C10112yes—
207C22×C4—22no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—44no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4C2×D4×C10111yescharacteristic
217M16—41no—
218M16—41no—
219C2×C8—41no—
220C4⋊C4—22no—
221C4⋊C4—81no—
222C4⋊C4—84no—
223C22⋊C4—24no—
224C22⋊C4—24no—
225C22⋊C4—24no—
226C22⋊C4—44no—
227C22⋊C4—42no—
228C22⋊C4—42no—
229C22⋊C4—41no—
230C22⋊C4—42no—
231C42—21no—
232C42—44no—
233C42—41no—
234C42—81no—
235C42C4⋊C4×C10112yescomplemented
236C23—22no—
237C23—22no—
238C23—42no—
239C23—42no—
240C23C4×D4×C10112yes—
241C23#120×C10111yescharacteristic
242C23C22⋊Q8×C10112yes—
243Q8—42no—
244Q8—81no—
245D4—41no—
246D4—41no—
247D4—42no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—24no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—44no—
259C2×C4—42no—
260C2×C4—44no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—82no—
265C2×C4—82no—
266C2×C4—82no—
267C2×C4—82no—
268C2×C4—82no—
269C2×C4C2×C4⋊C4×C10111yescharacteristic
270C2×C4#123×C10111yescharacteristic
271C8—81no—
272C22—22no—
273C22—22no—
274C22—22no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—82no—
280C22#385×C10111yescharacteristic
281C22B(4,𝔽2)×C10111yescharacteristic
282C22#458×C10111yescharacteristic
283C4—21no—
284C4—21no—
285C4—42no—
286C4—44no—
287C4—42no—
288C4—82no—
289C4—84no—
290C4—82no—
291C2—21no—
292C2—21no—
293C2—42no—
294C2—42no—
295C2C101×#186711yescharacteristic
296C2C101×#219712yes—
subgroupG/H
center, socleC22×C101B(4,𝔽2)
commutatorC2×D4C22×C4×C101
Frattini, cosocleC22×D4C23×C101
prime radicalC22×D4×C101C23
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C23×C101 ◁ C22×D4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
17. #354×C101C4semidirect
52. C2×Q8×C101C4⋊C4semidirect
86. C42×C101C4⋊C4semidirect
142. #12965C101direct (N × H)
154. C101#12965direct (N × H)
166. #354C4×C101semidirect
201. C2×Q8C4⋊C4×C101semidirect
235. C42C4⋊C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#23722
C2×#354×C1012
C101×#18852
C101×#18672
C101×#13902
#12965101