Finite Group Databasebeta

← C101×#9982 #38792133

Subgroups — C101×#9982 #38792133

Order 25856.

722 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 722 conjugacy classes of subgroups — too many to draw. Only its 98 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×#3007C212yesmaximal
2C101×#2817C211yesmaximal, characteristic, complemented
3C101×#1782C211yesmaximal, characteristic
4C101×#1511C212yesmaximal, complemented
5C101×#1306C211yesmaximal, characteristic, complemented
6C22×#41×C101C2211yescharacteristic
7C2×#137×C101—22no—
8C2×C22⋊Q8×C101C2212yes—
9#452×C101—24no—
10#451×C101—22no—
11#450×C101—22no—
12#417×C101—22no—
13C2×#99×C101—22no—
14#407×C101C2212yes—
15#400×C101—22no—
16#397×C101—22no—
17#395×C101—22no—
18#381×C101C2211yescharacteristic
19#381×C101C2211yescharacteristic
20#328×C101—24no—
21C2×#41×C101—22no—
22C2×#41×C101—22no—
23C2×#41×C101—44no—
24C22×Q8×C101D412yes—
25C22×Q8×C101D411yescharacteristic
26C22×D4×C101—21no—
27C22×D4×C101D411yescharacteristic
28C23×C4×C101—21no—
29C23×C4×C101C2311yescharacteristic
30#137×C101—48no—
31C2×Q16×C101—24no—
32C2×SD16×C101—24no—
33C2×M16×C101—22no—
34C22⋊Q8×C101—22no—
35C22⋊Q8×C101—22no—
36C22⋊Q8×C101—22no—
37C22⋊Q8×C101—22no—
38C2×C4⋊C4×C101—22no—
39C2×C4⋊C4×C101—22no—
40C2×C4⋊C4×C101D412yes—
41C2×C22⋊C4×C101—22no—
42C2×C22⋊C4×C101—21no—
43C2×C22⋊C4×C101D412yes—
44#103×C101—24no—
45#102×C101—24no—
46#99×C101—44no—
47C22⋊C8×C101—22no—
48C22⋊C8×C101D414yes—
49#95×C101—24no—
50#95×C101—22no—
51#95×C101—22no—
52#95×C101—22no—
53C24×C101—21no—
54C24×C101C2×D411yescharacteristic
55#41×C101—28no—
56#41×C101—44no—
57#41×C101—44no—
58#41×C101—44no—
59C2×Q8×C101—22no—
60C2×Q8×C101—22no—
61C2×Q8×C101—22no—
62C2×Q8×C101—42no—
63C2×Q8×C101—44no—
64C2×D4×C101—24no—
65C2×D4×C101—22no—
66C2×D4×C101—42no—
67C2×D4×C101—42no—
68C2×D4×C101—41no—
69C2×D4×C101—41no—
70C22×C4×C101—21no—
71C22×C4×C101—22no—
72C22×C4×C101—22no—
73C22×C4×C101—22no—
74C22×C4×C101—42no—
75C22×C4×C101—42no—
76C22×C4×C101—42no—
77C22×C4×C101—42no—
78C22×C4×C101—41no—
79C22×C4×C101C2×D412yes—
80C22×C4×C101C2×D411yescharacteristic
81C22×C4×C101C2×D412yes—
82C22×C4×C101#4111yescharacteristic
83Q16×C101—48no—
84SD16×C101—48no—
85M16×C101—44no—
86C2×C8×C101—24no—
87C4⋊C4×C101—22no—
88C4⋊C4×C101—22no—
89C4⋊C4×C101—42no—
90C4⋊C4×C101—42no—
91C4⋊C4×C101—82no—
92C22⋊C4×C101—42no—
93C22⋊C4×C101—42no—
94C22⋊C4×C101—42no—
95C22⋊C4×C101—42no—
96C23×C101—22no—
97C23×C101—22no—
98C23×C101—42no—
99C23×C101—41no—
100C23×C101—41no—
101C23×C101—82no—
102C23×C101#12011yescharacteristic
103C23×C101#12111yescharacteristic
104C23×C101#12711yescharacteristic
105Q8×C101—24no—
106Q8×C101—42no—
107Q8×C101—44no—
108Q8×C101—82no—
109D4×C101—24no—
110D4×C101—42no—
111D4×C101—44no—
112D4×C101—44no—
113C2×C4×C101—24no—
114C2×C4×C101—22no—
115C2×C4×C101—41no—
116C2×C4×C101—41no—
117C2×C4×C101—42no—
118C2×C4×C101—48no—
119C2×C4×C101—41no—
120C2×C4×C101—41no—
121C2×C4×C101—44no—
122C2×C4×C101—44no—
123C2×C4×C101—42no—
124C2×C4×C101—42no—
125C2×C4×C101—42no—
126C2×C4×C101—44no—
127C2×C4×C101—81no—
128C2×C4×C101—82no—
129C2×C4×C101#12012yes—
130C2×C4×C101#12112yes—
131C8×C101—44no—
132C22×C101—22no—
133C22×C101—22no—
134C22×C101—22no—
135C22×C101—21no—
136C22×C101—21no—
137C22×C101—42no—
138C22×C101—82no—
139C22×C101—82no—
140C22×C101—82no—
141C22×C101—82no—
142C22×C101#39211yescharacteristic
143C22×C101B(4,𝔽2)12yes—
144C4×C101—22no—
145C4×C101—22no—
146C4×C101—42no—
147C4×C101—82no—
148C4×C101—82no—
149C4×C101—82no—
150C4×C101—161no—
151#9982C10111yesmaximal, characteristic, direct product factor, Sylow
152C2×C101—22no—
153C2×C101—41no—
154C2×C101—41no—
155C2×C101—82no—
156C2×C101#200912yes—
157C2×C101#202111yescharacteristic
158#3007C2×C10112yes—
159#2817C2×C10111yescharacteristic, complemented
160#1782C2×C10111yescharacteristic
161#1511C2×C10112yescomplemented
162#1306C2×C10111yescharacteristic, complemented
163C101#998211yescharacteristic, direct product factor, Sylow
164C22×#41C22×C10111yescharacteristic
165C2×#137—22no—
166C2×C22⋊Q8C22×C10112yes—
167#452—24no—
168#451—22no—
169#450—22no—
170#417—22no—
171C2×#99—22no—
172#407C22×C10112yes—
173#400—22no—
174#397—22no—
175#395—22no—
176#381C22×C10111yescharacteristic
177#381C22×C10111yescharacteristic
178#328—24no—
179C2×#41—22no—
180C2×#41—22no—
181C2×#41—44no—
182C22×Q8D4×C10112yes—
183C22×Q8D4×C10111yescharacteristic
184C22×D4—21no—
185C22×D4D4×C10111yescharacteristic
186C23×C4—21no—
187C23×C4C23×C10111yescharacteristic
188#137—48no—
189C2×Q16—24no—
190C2×SD16—24no—
191C2×M16—22no—
192C22⋊Q8—22no—
193C22⋊Q8—22no—
194C22⋊Q8—22no—
195C22⋊Q8—22no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4D4×C10112yes—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—21no—
201C2×C22⋊C4D4×C10112yes—
202#103—24no—
203#102—24no—
204#99—44no—
205C22⋊C8—22no—
206C22⋊C8D4×C10114yes—
207#95—24no—
208#95—22no—
209#95—22no—
210#95—22no—
211C24—21no—
212C24C2×D4×C10111yescharacteristic
213#41—28no—
214#41—44no—
215#41—44no—
216#41—44no—
217C2×Q8—22no—
218C2×Q8—22no—
219C2×Q8—22no—
220C2×Q8—42no—
221C2×Q8—44no—
222C2×D4—24no—
223C2×D4—22no—
224C2×D4—42no—
225C2×D4—42no—
226C2×D4—41no—
227C2×D4—41no—
228C22×C4—21no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—41no—
237C22×C4C2×D4×C10112yes—
238C22×C4C2×D4×C10111yescharacteristic
239C22×C4C2×D4×C10112yes—
240C22×C4#41×C10111yescharacteristic
241Q16—48no—
242SD16—48no—
243M16—44no—
244C2×C8—24no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C4⋊C4—82no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—42no—
253C22⋊C4—42no—
254C23—22no—
255C23—22no—
256C23—42no—
257C23—41no—
258C23—41no—
259C23—82no—
260C23#120×C10111yescharacteristic
261C23#121×C10111yescharacteristic
262C23#127×C10111yescharacteristic
263Q8—24no—
264Q8—42no—
265Q8—44no—
266Q8—82no—
267D4—24no—
268D4—42no—
269D4—44no—
270D4—44no—
271C2×C4—24no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—48no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—44no—
280C2×C4—44no—
281C2×C4—42no—
282C2×C4—44no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—81no—
286C2×C4—82no—
287C2×C4#120×C10112yes—
288C2×C4#121×C10112yes—
289C8—44no—
290C22—22no—
291C22—22no—
292C22—22no—
293C22—21no—
294C22—21no—
295C22—42no—
296C22—82no—
297C22—82no—
298C22—82no—
299C22—82no—
300C22#392×C10111yescharacteristic
301C22B(4,𝔽2)×C10112yes—
302C4—22no—
303C4—22no—
304C4—42no—
305C4—82no—
306C4—82no—
307C4—82no—
308C4—161no—
309C2—22no—
310C2—41no—
311C2—41no—
312C2—82no—
313C2C101×#200912yes—
314C2C101×#202111yescharacteristic
subgroupG/H
center, socleC22×C101#392
commutator, Frattini, cosocleC23×C4C23×C101
prime radicalC22×#41×C101C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C23×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#2817C2semidirect
4. C101×#1511C2semidirect
5. C101×#1306C2semidirect
151. #9982C101direct (N × H)
159. #2817C2×C101semidirect
161. #1511C2×C101semidirect
162. #1306C2×C101semidirect
163. C101#9982direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#30072
C101×#28172
C101×#17822
C101×#15112
C101×#13062
#9982101