Finite Group Databasebeta

← C101×#7803 #38789954

Subgroups — C101×#7803 #38789954

Order 25856.

338 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 94 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×#2810C211yesmaximal, characteristic
2C101×#2099C211yesmaximal, characteristic
3C101×#2084C211yesmaximal, characteristic
4C101×#2083C211yesmaximal, characteristic
5C101×#1271C211yesmaximal, characteristic
6C101×#1271C211yesmaximal, characteristic
7C101×#1271C211yesmaximal, characteristic
8C2×#107×C101—21no—
9C2×#106×C101—21no—
10#400×C101—21no—
11#400×C101—21no—
12#400×C101—21no—
13#389×C101C2211yescharacteristic
14#389×C101C2211yescharacteristic
15#389×C101C2211yescharacteristic
16#387×C101—21no—
17#387×C101—21no—
18#387×C101—21no—
19#384×C101C2211yescharacteristic
20#340×C101—21no—
21#340×C101—21no—
22#340×C101—21no—
23#340×C101—21no—
24#336×C101C2211yescharacteristic
25#336×C101C2211yescharacteristic
26#336×C101C2211yescharacteristic
27C22×C8×C101—21no—
28C22×C8×C101—21no—
29C22×C8×C101—21no—
30C2×C4⋊C4×C101—21no—
31C2×C4⋊C4×C101—21no—
32C2×C4⋊C4×C101—21no—
33C2×C4⋊C4×C101—21no—
34C2×C4⋊C4×C101—21no—
35C2×C4⋊C4×C101—21no—
36C2×C4⋊C4×C101D411yescharacteristic
37C2×C4⋊C4×C101D411yescharacteristic
38C2×C4⋊C4×C101D411yescharacteristic
39C2×C4⋊C4×C101D411yescharacteristic
40C2×C4⋊C4×C101D411yescharacteristic
41C2×C4⋊C4×C101D411yescharacteristic
42C2×C42×C101—21no—
43C2×C42×C101C2311yescharacteristic
44#107×C101—42no—
45#106×C101—42no—
46#95×C101—21no—
47#95×C101—21no—
48#95×C101—21no—
49#95×C101—21no—
50#95×C101—21no—
51#95×C101—21no—
52#95×C101—21no—
53#95×C101—21no—
54#95×C101—21no—
55#95×C101—21no—
56C22×C4×C101—21no—
57C22×C4×C101—21no—
58C22×C4×C101—21no—
59C22×C4×C101—21no—
60C22×C4×C101—21no—
61C22×C4×C101—21no—
62C22×C4×C101—41no—
63C22×C4×C101C2×D411yescharacteristic
64C22×C4×C101C2×D411yescharacteristic
65C22×C4×C101C2×D411yescharacteristic
66C2×C8×C101—22no—
67C2×C8×C101—22no—
68C2×C8×C101—41no—
69C2×C8×C101—41no—
70C2×C8×C101—41no—
71C2×C8×C101—41no—
72C2×C8×C101—41no—
73C2×C8×C101—41no—
74C2×C8×C101—41no—
75C4⋊C4×C101—21no—
76C4⋊C4×C101—21no—
77C4⋊C4×C101—21no—
78C4⋊C4×C101—21no—
79C4⋊C4×C101—21no—
80C4⋊C4×C101—21no—
81C4⋊C4×C101—41no—
82C4⋊C4×C101—41no—
83C4⋊C4×C101—41no—
84C4⋊C4×C101—42no—
85C4⋊C4×C101—41no—
86C4⋊C4×C101—41no—
87C4⋊C4×C101—41no—
88C4⋊C4×C101—41no—
89C4⋊C4×C101—41no—
90C4⋊C4×C101—41no—
91C4⋊C4×C101—41no—
92C4⋊C4×C101—41no—
93C4⋊C4×C101—41no—
94C4⋊C4×C101—41no—
95C42×C101—41no—
96C42×C101—81no—
97C23×C101#12011yescharacteristic
98C2×C4×C101—21no—
99C2×C4×C101—21no—
100C2×C4×C101—21no—
101C2×C4×C101—21no—
102C2×C4×C101—21no—
103C2×C4×C101—21no—
104C2×C4×C101—41no—
105C2×C4×C101—41no—
106C2×C4×C101—41no—
107C2×C4×C101—41no—
108C2×C4×C101—41no—
109C2×C4×C101—41no—
110C2×C4×C101—41no—
111C2×C4×C101—41no—
112C2×C4×C101—41no—
113C2×C4×C101—41no—
114C2×C4×C101—41no—
115C2×C4×C101—41no—
116C2×C4×C101—41no—
117C2×C4×C101—41no—
118C2×C4×C101—41no—
119C2×C4×C101—41no—
120C2×C4×C101—41no—
121C2×C4×C101—41no—
122C2×C4×C101—81no—
123C2×C4×C101—81no—
124C2×C4×C101—81no—
125C2×C4×C101#13511yescharacteristic
126C2×C4×C101#13511yescharacteristic
127C2×C4×C101#13511yescharacteristic
128C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C101#13711yescharacteristic
131C8×C101—42no—
132C8×C101—42no—
133C8×C101—81no—
134C22×C101#44911yescharacteristic
135C22×C101#44911yescharacteristic
136C22×C101#45211yescharacteristic
137C22×C101#45411yescharacteristic
138C22×C101#45611yescharacteristic
139C22×C101#45611yescharacteristic
140C22×C101#45811yescharacteristic
141C4×C101—21no—
142C4×C101—21no—
143C4×C101—21no—
144C4×C101—21no—
145C4×C101—21no—
146C4×C101—21no—
147C4×C101—81no—
148C4×C101—81no—
149C4×C101—81no—
150C4×C101—81no—
151C4×C101—81no—
152C4×C101—81no—
153C4×C101—161no—
154#7803C10111yesmaximal, characteristic, direct product factor, Sylow
155C2×C101#160911yescharacteristic
156C2×C101#160911yescharacteristic
157C2×C101#161511yescharacteristic
158C2×C101#162811yescharacteristic
159C2×C101#165011yescharacteristic
160C2×C101#165211yescharacteristic
161C2×C101#166311yescharacteristic
162#2810C2×C10111yescharacteristic
163#2099C2×C10111yescharacteristic
164#2084C2×C10111yescharacteristic
165#2083C2×C10111yescharacteristic
166#1271C2×C10111yescharacteristic
167#1271C2×C10111yescharacteristic
168#1271C2×C10111yescharacteristic
169C101#780311yescharacteristic, direct product factor, Sylow
170C2×#107—21no—
171C2×#106—21no—
172#400—21no—
173#400—21no—
174#400—21no—
175#389C22×C10111yescharacteristic
176#389C22×C10111yescharacteristic
177#389C22×C10111yescharacteristic
178#387—21no—
179#387—21no—
180#387—21no—
181#384C22×C10111yescharacteristic
182#340—21no—
183#340—21no—
184#340—21no—
185#340—21no—
186#336C22×C10111yescharacteristic
187#336C22×C10111yescharacteristic
188#336C22×C10111yescharacteristic
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4D4×C10111yescharacteristic
199C2×C4⋊C4D4×C10111yescharacteristic
200C2×C4⋊C4D4×C10111yescharacteristic
201C2×C4⋊C4D4×C10111yescharacteristic
202C2×C4⋊C4D4×C10111yescharacteristic
203C2×C4⋊C4D4×C10111yescharacteristic
204C2×C42—21no—
205C2×C42C23×C10111yescharacteristic
206#107—42no—
207#106—42no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—41no—
225C22×C4C2×D4×C10111yescharacteristic
226C22×C4C2×D4×C10111yescharacteristic
227C22×C4C2×D4×C10111yescharacteristic
228C2×C8—22no—
229C2×C8—22no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—42no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C42—41no—
258C42—81no—
259C23#120×C10111yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4#135×C10111yescharacteristic
288C2×C4#135×C10111yescharacteristic
289C2×C4#135×C10111yescharacteristic
290C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
291C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
292C2×C4#137×C10111yescharacteristic
293C8—42no—
294C8—42no—
295C8—81no—
296C22#449×C10111yescharacteristic
297C22#449×C10111yescharacteristic
298C22#452×C10111yescharacteristic
299C22#454×C10111yescharacteristic
300C22#456×C10111yescharacteristic
301C22#456×C10111yescharacteristic
302C22#458×C10111yescharacteristic
303C4—21no—
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—81no—
310C4—81no—
311C4—81no—
312C4—81no—
313C4—81no—
314C4—81no—
315C4—161no—
316C2C101×#160911yescharacteristic
317C2C101×#160911yescharacteristic
318C2C101×#161511yescharacteristic
319C2C101×#162811yescharacteristic
320C2C101×#165011yescharacteristic
321C2C101×#165211yescharacteristic
322C2C101×#166311yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C101#120
commutator, Frattini, cosocleC2×C42C23×C101
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
154. #7803C101direct (N × H)
169. C101#7803direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#28102
C101×#20992
C101×#20842
C101×#20832
C101×#12712
#7803101