Finite Group Databasebeta

← C101×#9014 #38791165

Subgroups — C101×#9014 #38791165

Order 25856.

756 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 756 conjugacy classes of subgroups — too many to draw. Only its 150 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
1C2×#395×C101C211yesmaximal, characteristic
2C101×#2313C211yesmaximal, characteristic
3C101×#1787C212yesmaximal
4C2×#324×C101C211yesmaximal, characteristic
5C101×#1294C212yesmaximal
6C23×Q8×C101C2211yescharacteristic
7C22×C4⋊C4×C101—21no—
8C22×C4⋊C4×C101C2211yescharacteristic
9C2×#103×C101—24no—
10C2×C22⋊C8×C101C2212yes—
11#395×C101—22no—
12#395×C101C414yescomplemented
13#387×C101—24no—
14#381×C101—21no—
15#380×C101C2212yes—
16C4×C22⋊C4×C101—21no—
17C2×#95×C101—21no—
18C2×#95×C101C2211yescharacteristic
19#324×C101—22no—
20C22×Q8×C101—21no—
21C22×Q8×C101—22no—
22C22×Q8×C101—22no—
23C22×Q8×C101—44no—
24C22×Q8×C101C2×C412yes—
25C23×C4×C101—21no—
26C23×C4×C101—21no—
27C23×C4×C101D411yescharacteristic
28C23×C4×C101D411yescharacteristic
29C23×C4×C101C2311yescharacteristic
30C22×C8×C101—22no—
31C2×C4⋊C4×C101—22no—
32C2×C4⋊C4×C101—22no—
33C2×C4⋊C4×C101—24no—
34C2×C4⋊C4×C101—44no—
35C2×C4⋊C4×C101C2×C412yes—
36C2×C4⋊C4×C101D412yes—
37C2×C4⋊C4×C101D414yes—
38C2×C22⋊C4×C101—22no—
39C2×C42×C101—22no—
40#103×C101—48no—
41C22⋊C8×C101—22no—
42C22⋊C8×C101—22no—
43#95×C101—22no—
44#95×C101—24no—
45#95×C101—24no—
46#95×C101—21no—
47#95×C101—22no—
48#95×C101C2×C412yes—
49C24×C101C2×D411yescharacteristic
50C2×Q8×C101—28no—
51C2×Q8×C101—24no—
52C2×Q8×C101—44no—
53C2×Q8×C101—44no—
54C2×Q8×C101—44no—
55C2×Q8×C101—48no—
56C2×Q8×C101—42no—
57C22×C4×C101—24no—
58C22×C4×C101—24no—
59C22×C4×C101—22no—
60C22×C4×C101—22no—
61C22×C4×C101—21no—
62C22×C4×C101—21no—
63C22×C4×C101—21no—
64C22×C4×C101—22no—
65C22×C4×C101—22no—
66C22×C4×C101—21no—
67C22×C4×C101—24no—
68C22×C4×C101—42no—
69C22×C4×C101—42no—
70C22×C4×C101—42no—
71C22×C4×C101—41no—
72C22×C4×C101—41no—
73C22×C4×C101—42no—
74C22×C4×C101—42no—
75C22×C4×C101C22⋊C412yes—
76C22×C4×C101C22⋊C412yes—
77C22×C4×C101C22×C411yescharacteristic
78C22×C4×C101C2×D412yes—
79C22×C4×C101C2×D411yescharacteristic
80C22×C4×C101#4112yes—
81C2×C8×C101—44no—
82C2×C8×C101—42no—
83C4⋊C4×C101—24no—
84C4⋊C4×C101—24no—
85C4⋊C4×C101—44no—
86C4⋊C4×C101—48no—
87C22⋊C4×C101—42no—
88C22⋊C4×C101—42no—
89C42×C101—82no—
90C23×C101—22no—
91C23×C101—22no—
92C23×C101C2×C22⋊C411yescharacteristic
93C23×C101#12011yescharacteristic
94C23×C101#12311yescharacteristic
95C23×C101#13512yes—
96C23×C101#13712yes—
97Q8×C101—28no—
98Q8×C101—48no—
99Q8×C101—44no—
100C2×C4×C101—24no—
101C2×C4×C101—24no—
102C2×C4×C101—24no—
103C2×C4×C101—22no—
104C2×C4×C101—22no—
105C2×C4×C101—22no—
106C2×C4×C101—22no—
107C2×C4×C101—41no—
108C2×C4×C101—41no—
109C2×C4×C101—42no—
110C2×C4×C101—42no—
111C2×C4×C101—48no—
112C2×C4×C101—42no—
113C2×C4×C101—44no—
114C2×C4×C101—42no—
115C2×C4×C101—42no—
116C2×C4×C101—42no—
117C2×C4×C101—42no—
118C2×C4×C101—44no—
119C2×C4×C101—42no—
120C2×C4×C101—42no—
121C2×C4×C101—44no—
122C2×C4×C101—44no—
123C2×C4×C101—44no—
124C2×C4×C101—81no—
125C2×C4×C101C4×D412yes—
126C2×C4×C101#12112yes—
127C8×C101—82no—
128C22×C101—24no—
129C22×C101—24no—
130C22×C101—21no—
131C22×C101—21no—
132C22×C101—21no—
133C22×C101—21no—
134C22×C101#38611yescharacteristic
135C22×C101#41611yescharacteristic
136C22×C101#41911yescharacteristic
137C22×C101#45212yes—
138C22×C101#45612yes—
139C22×C101B(4,𝔽2)12yes—
140C22×C101#48512yes—
141C4×C101—22no—
142C4×C101—22no—
143C4×C101—44no—
144C4×C101—42no—
145C4×C101—44no—
146C4×C101—42no—
147C4×C101—84no—
148#9014C10111yesmaximal, characteristic, direct product factor, Sylow
149C2×C101—21no—
150C2×C101—21no—
151C2×C101—22no—
152C2×C101#160314yes—
153C2×C101#187311yescharacteristic
154C2×C101#188611yescharacteristic
155C2×C101#188911yescharacteristic
156C2×#395C2×C10111yescharacteristic
157#2313C2×C10111yescharacteristic
158#1787C2×C10112yes—
159C2×#324C2×C10111yescharacteristic
160#1294C2×C10112yes—
161C101#901411yescharacteristic, direct product factor, Sylow
162C23×Q8C22×C10111yescharacteristic
163C22×C4⋊C4—21no—
164C22×C4⋊C4C22×C10111yescharacteristic
165C2×#103—24no—
166C2×C22⋊C8C22×C10112yes—
167#395—22no—
168#395C4×C10114yescomplemented
169#387—24no—
170#381—21no—
171#380C22×C10112yes—
172C4×C22⋊C4—21no—
173C2×#95—21no—
174C2×#95C22×C10111yescharacteristic
175#324—22no—
176C22×Q8—21no—
177C22×Q8—22no—
178C22×Q8—22no—
179C22×Q8—44no—
180C22×Q8C2×C4×C10112yes—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4D4×C10111yescharacteristic
184C23×C4D4×C10111yescharacteristic
185C23×C4C23×C10111yescharacteristic
186C22×C8—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—24no—
190C2×C4⋊C4—44no—
191C2×C4⋊C4C2×C4×C10112yes—
192C2×C4⋊C4D4×C10112yes—
193C2×C4⋊C4D4×C10114yes—
194C2×C22⋊C4—22no—
195C2×C42—22no—
196#103—48no—
197C22⋊C8—22no—
198C22⋊C8—22no—
199#95—22no—
200#95—24no—
201#95—24no—
202#95—21no—
203#95—22no—
204#95C2×C4×C10112yes—
205C24C2×D4×C10111yescharacteristic
206C2×Q8—28no—
207C2×Q8—24no—
208C2×Q8—44no—
209C2×Q8—44no—
210C2×Q8—44no—
211C2×Q8—48no—
212C2×Q8—42no—
213C22×C4—24no—
214C22×C4—24no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—21no—
223C22×C4—24no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4C22⋊C4×C10112yes—
232C22×C4C22⋊C4×C10112yes—
233C22×C4C22×C4×C10111yescharacteristic
234C22×C4C2×D4×C10112yes—
235C22×C4C2×D4×C10111yescharacteristic
236C22×C4#41×C10112yes—
237C2×C8—44no—
238C2×C8—42no—
239C4⋊C4—24no—
240C4⋊C4—24no—
241C4⋊C4—44no—
242C4⋊C4—48no—
243C22⋊C4—42no—
244C22⋊C4—42no—
245C42—82no—
246C23—22no—
247C23—22no—
248C23C2×C22⋊C4×C10111yescharacteristic
249C23#120×C10111yescharacteristic
250C23#123×C10111yescharacteristic
251C23#135×C10112yes—
252C23#137×C10112yes—
253Q8—28no—
254Q8—48no—
255Q8—44no—
256C2×C4—24no—
257C2×C4—24no—
258C2×C4—24no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—44no—
269C2×C4—48no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—44no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—44no—
278C2×C4—44no—
279C2×C4—44no—
280C2×C4—81no—
281C2×C4C4×D4×C10112yes—
282C2×C4#121×C10112yes—
283C8—82no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—24no—
289C22—24no—
290C22#386×C10111yescharacteristic
291C22#416×C10111yescharacteristic
292C22#419×C10111yescharacteristic
293C22#452×C10112yes—
294C22#456×C10112yes—
295C22B(4,𝔽2)×C10112yes—
296C22#485×C10112yes—
297C4—22no—
298C4—22no—
299C4—44no—
300C4—44no—
301C4—42no—
302C4—42no—
303C4—84no—
304C2—21no—
305C2—21no—
306C2—22no—
307C2C101×#160314yes—
308C2C101×#187311yescharacteristic
309C2C101×#188611yescharacteristic
310C2C101×#188911yescharacteristic
subgroupG/H
center, socleC23×C101#120
commutatorC22×C4C22×C4×C101
Frattini, cosocleC23×C4C23×C101
prime radicalC24×C101C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C101 ◁ C23×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
12. #395×C101C4semidirect
148. #9014C101direct (N × H)
161. C101#9014direct (N × H)
168. #395C4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#395×C1012
C101×#23132
C101×#17872
C2×#324×C1012
C101×#12942
#9014101