Finite Group Databasebeta

← C101×#13390 #38795541

Subgroups — C101×#13390 #38795541

Order 25856.

382 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#473×C101C211yesmaximal, characteristic
2C101×#2161C211yesmaximal, characteristic, complemented
3C2×#362×C101C211yesmaximal, characteristic, complemented
4C2×#362×C101C211yesmaximal, characteristic, complemented
5C101×#2117C211yesmaximal, characteristic
6C101×#1813C211yesmaximal, characteristic
7C101×#1388C211yesmaximal, characteristic, complemented
8C2×#137×C101—21no—
9C22×Q16×C101C2211yescharacteristic
10C2×#131×C101C2211yescharacteristic
11C2×M32×C101C2211yescharacteristic
12C2×M32×C101C2211yescharacteristic
13#473×C101—22no—
14#473×C101—22no—
15C2×#108×C101C2211yescharacteristic
16C2×#108×C101C2211yescharacteristic
17C2×#108×C101C2211yescharacteristic
18#413×C101—21no—
19C2×#101×C101—21no—
20#368×C101—22no—
21#362×C101—22no—
22#362×C101—22no—
23#350×C101—22no—
24#338×C101—21no—
25C2×#41×C101D411yescharacteristic
26C22×Q8×C101—21no—
27#137×C101—24no—
28#137×C101—42no—
29C2×Q16×C101—21no—
30C2×Q16×C101—21no—
31C2×Q16×C101—21no—
32C2×Q16×C101—21no—
33C2×Q16×C101—21no—
34C2×Q16×C101—41no—
35C2×Q16×C101D412yes—
36C2×SD16×C101—41no—
37#131×C101—21no—
38#131×C101—21no—
39#131×C101—21no—
40#131×C101—21no—
41C2×M16×C101—21no—
42C2×M16×C101—21no—
43C2×M16×C101—21no—
44C2×M16×C101—21no—
45C2×M16×C101D411yescharacteristic
46C22×C8×C101—21no—
47C22×C8×C101C2311yescharacteristic
48M32×C101—21no—
49M32×C101—21no—
50M32×C101—21no—
51M32×C101D412yes—
52C2×C16×C101—21no—
53C2×C16×C101—21no—
54#108×C101—21no—
55#108×C101—21no—
56#108×C101—21no—
57#108×C101—21no—
58#108×C101—21no—
59#108×C101D412yes—
60#101×C101—24no—
61#101×C101—41no—
62#100×C101—41no—
63#41×C101—21no—
64#41×C101—21no—
65#41×C101—21no—
66#41×C101—21no—
67C2×Q8×C101—22no—
68C2×Q8×C101—41no—
69C2×Q8×C101—41no—
70C2×Q8×C101—41no—
71C2×Q8×C101—41no—
72C2×Q8×C101—41no—
73C2×Q8×C101D811yescharacteristic
74C2×D4×C101—21no—
75C2×D4×C101D811yescharacteristic
76C22×C4×C101—21no—
77C22×C4×C101—41no—
78C22×C4×C101C2×D411yescharacteristic
79Q16×C101—22no—
80Q16×C101—22no—
81Q16×C101—44no—
82Q16×C101—41no—
83Q16×C101—41no—
84SD16×C101—44no—
85M16×C101—21no—
86M16×C101—22no—
87M16×C101—21no—
88M16×C101—41no—
89M16×C101—41no—
90M16×C101—41no—
91M16×C101—41no—
92M16×C101—41no—
93M16×C101—41no—
94M16×C101—41no—
95C2×C8×C101—21no—
96C2×C8×C101—41no—
97C2×C8×C101—41no—
98C2×C8×C101—41no—
99C2×C8×C101—41no—
100C2×C8×C101—41no—
101C2×C8×C101C2×D411yescharacteristic
102C2×C8×C101C2×D411yescharacteristic
103C2×C8×C101C2×D411yescharacteristic
104C2×C8×C101#4111yescharacteristic
105C2×C8×C101#4111yescharacteristic
106C2×C8×C101#4111yescharacteristic
107C16×C101—22no—
108C16×C101—41no—
109C23×C101—21no—
110C23×C101#13711yescharacteristic
111Q8×C101—21no—
112Q8×C101—21no—
113Q8×C101—42no—
114Q8×C101—42no—
115Q8×C101—81no—
116Q8×C101—81no—
117D4×C101—21no—
118D4×C101—21no—
119D4×C101—41no—
120D4×C101—41no—
121C2×C4×C101—21no—
122C2×C4×C101—41no—
123C2×C4×C101—41no—
124C2×C4×C101—42no—
125C2×C4×C101—81no—
126C2×C4×C101—81no—
127C2×C4×C101#12011yescharacteristic
128C2×C4×C101#12111yescharacteristic
129C2×C4×C101#12311yescharacteristic
130C2×C4×C101C2×D811yescharacteristic
131C2×C4×C101#13511yescharacteristic
132C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
133C8×C101—41no—
134C8×C101—42no—
135C8×C101—81no—
136C8×C101—81no—
137C8×C101#12111yescharacteristic
138C8×C101#12111yescharacteristic
139C8×C101#12311yescharacteristic
140C8×C101#12411yescharacteristic
141C22×C101—41no—
142C22×C101—41no—
143C22×C101—81no—
144C22×C101#45211yescharacteristic
145C22×C101#46811yescharacteristic
146C22×C101#48011yescharacteristic
147C4×C101—41no—
148C4×C101—82no—
149C4×C101#39411yescharacteristic
150C4×C101#44711yescharacteristic
151C4×C101#46611yescharacteristic
152C4×C101#48211yescharacteristic
153#13390C10111yesmaximal, characteristic, direct product factor, Sylow
154C2×C101—21no—
155C2×C101—21no—
156C2×C101—21no—
157C2×C101—81no—
158C2×C101#203311yescharacteristic
159C2×#473C2×C10111yescharacteristic
160#2161C2×C10111yescharacteristic, complemented
161C2×#362C2×C10111yescharacteristic, complemented
162C2×#362C2×C10111yescharacteristic, complemented
163#2117C2×C10111yescharacteristic
164#1813C2×C10111yescharacteristic
165#1388C2×C10111yescharacteristic, complemented
166C101#1339011yescharacteristic, direct product factor, Sylow
167C2×#137—21no—
168C22×Q16C22×C10111yescharacteristic
169C2×#131C22×C10111yescharacteristic
170C2×M32C22×C10111yescharacteristic
171C2×M32C22×C10111yescharacteristic
172#473—22no—
173#473—22no—
174C2×#108C22×C10111yescharacteristic
175C2×#108C22×C10111yescharacteristic
176C2×#108C22×C10111yescharacteristic
177#413—21no—
178C2×#101—21no—
179#368—22no—
180#362—22no—
181#362—22no—
182#350—22no—
183#338—21no—
184C2×#41D4×C10111yescharacteristic
185C22×Q8—21no—
186#137—24no—
187#137—42no—
188C2×Q16—21no—
189C2×Q16—21no—
190C2×Q16—21no—
191C2×Q16—21no—
192C2×Q16—21no—
193C2×Q16—41no—
194C2×Q16D4×C10112yes—
195C2×SD16—41no—
196#131—21no—
197#131—21no—
198#131—21no—
199#131—21no—
200C2×M16—21no—
201C2×M16—21no—
202C2×M16—21no—
203C2×M16—21no—
204C2×M16D4×C10111yescharacteristic
205C22×C8—21no—
206C22×C8C23×C10111yescharacteristic
207M32—21no—
208M32—21no—
209M32—21no—
210M32D4×C10112yes—
211C2×C16—21no—
212C2×C16—21no—
213#108—21no—
214#108—21no—
215#108—21no—
216#108—21no—
217#108—21no—
218#108D4×C10112yes—
219#101—24no—
220#101—41no—
221#100—41no—
222#41—21no—
223#41—21no—
224#41—21no—
225#41—21no—
226C2×Q8—22no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8D8×C10111yescharacteristic
233C2×D4—21no—
234C2×D4D8×C10111yescharacteristic
235C22×C4—21no—
236C22×C4—41no—
237C22×C4C2×D4×C10111yescharacteristic
238Q16—22no—
239Q16—22no—
240Q16—44no—
241Q16—41no—
242Q16—41no—
243SD16—44no—
244M16—21no—
245M16—22no—
246M16—21no—
247M16—41no—
248M16—41no—
249M16—41no—
250M16—41no—
251M16—41no—
252M16—41no—
253M16—41no—
254C2×C8—21no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8C2×D4×C10111yescharacteristic
261C2×C8C2×D4×C10111yescharacteristic
262C2×C8C2×D4×C10111yescharacteristic
263C2×C8#41×C10111yescharacteristic
264C2×C8#41×C10111yescharacteristic
265C2×C8#41×C10111yescharacteristic
266C16—22no—
267C16—41no—
268C23—21no—
269C23#137×C10111yescharacteristic
270Q8—21no—
271Q8—21no—
272Q8—42no—
273Q8—42no—
274Q8—81no—
275Q8—81no—
276D4—21no—
277D4—21no—
278D4—41no—
279D4—41no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—42no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4#120×C10111yescharacteristic
287C2×C4#121×C10111yescharacteristic
288C2×C4#123×C10111yescharacteristic
289C2×C4C2×D8×C10111yescharacteristic
290C2×C4#135×C10111yescharacteristic
291C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
292C8—42no—
293C8—41no—
294C8—81no—
295C8—81no—
296C8#121×C10111yescharacteristic
297C8#121×C10111yescharacteristic
298C8#123×C10111yescharacteristic
299C8#124×C10111yescharacteristic
300C22—41no—
301C22—41no—
302C22—81no—
303C22#452×C10111yescharacteristic
304C22#468×C10111yescharacteristic
305C22#480×C10111yescharacteristic
306C4—41no—
307C4—82no—
308C4#394×C10111yescharacteristic
309C4#447×C10111yescharacteristic
310C4#466×C10111yescharacteristic
311C4#482×C10111yescharacteristic
312C2—21no—
313C2—21no—
314C2—21no—
315C2—81no—
316C2C101×#203311yescharacteristic
subgroupG/H
center, socleC2×C101#2033
commutator, Frattini, cosocleC22×C8C23×C101
prime radicalC2×#41×C101D4
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C101 ◁ C22×C4×C101 ◁ C2×#131×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#2161C2semidirect
3. C2×#362×C101C2semidirect
4. C2×#362×C101C2semidirect
7. C101×#1388C2semidirect
153. #13390C101direct (N × H)
160. #2161C2×C101semidirect
161. C2×#362C2×C101semidirect
162. C2×#362C2×C101semidirect
165. #1388C2×C101semidirect
166. C101#13390direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#473×C1012
C101×#21612
C2×#362×C1012
C101×#21172
C101×#18132
C101×#13882
#13390101