Finite Group Databasebeta

← C101×#13405 #38795556

Subgroups — C101×#13405 #38795556

Order 25856.

386 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#473×C101C211yesmaximal, characteristic
2C101×#2155C211yesmaximal, characteristic, complemented
3C101×#2141C211yesmaximal, characteristic, complemented
4C101×#2141C211yesmaximal, characteristic, complemented
5C101×#2117C211yesmaximal, characteristic
6C101×#1812C211yesmaximal, characteristic
7C101×#1389C211yesmaximal, 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
16#427×C101C2211yescharacteristic
17#427×C101C2211yescharacteristic
18C2×#101×C101—21no—
19#410×C101—21no—
20#365×C101—22no—
21#358×C101—22no—
22#358×C101—22no—
23#350×C101—22no—
24H(3,ℤ/4)×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×C101D411yescharacteristic
44C22×C8×C101—21no—
45C22×C8×C101C2311yescharacteristic
46#117×C101—21no—
47#117×C101—21no—
48M32×C101—21no—
49M32×C101—21no—
50M32×C101—21no—
51M32×C101—21no—
52C2×C16×C101—21no—
53C2×C16×C101D412yes—
54#108×C101—21no—
55#108×C101D412yes—
56#107×C101—21no—
57#107×C101—21no—
58#106×C101—21no—
59#106×C101—21no—
60#101×C101—24no—
61#99×C101—42no—
62#41×C101—21no—
63#41×C101—21no—
64#41×C101—21no—
65#41×C101—21no—
66C2×Q8×C101—22no—
67C2×Q8×C101—41no—
68C2×Q8×C101—41no—
69C2×Q8×C101—41no—
70C2×Q8×C101—41no—
71C2×Q8×C101—41no—
72C2×Q8×C101SD1611yescharacteristic
73C2×D4×C101—21no—
74C2×D4×C101SD1611yescharacteristic
75C22×C4×C101—21no—
76C22×C4×C101—41no—
77C22×C4×C101C2×D411yescharacteristic
78Q16×C101—22no—
79Q16×C101—22no—
80Q16×C101—44no—
81Q16×C101—41no—
82Q16×C101—41no—
83SD16×C101—44no—
84M16×C101—21no—
85M16×C101—22no—
86M16×C101—21no—
87M16×C101—41no—
88M16×C101—41no—
89M16×C101—41no—
90C2×C8×C101—21no—
91C2×C8×C101—41no—
92C2×C8×C101—41no—
93C2×C8×C101—41no—
94C2×C8×C101C2×D411yescharacteristic
95C2×C8×C101C2×D411yescharacteristic
96C2×C8×C101C2×D411yescharacteristic
97C2×C8×C101#4111yescharacteristic
98C2×C8×C101#4111yescharacteristic
99C2×C8×C101#4111yescharacteristic
100C4⋊C4×C101—41no—
101C4⋊C4×C101—41no—
102C22⋊C4×C101—41no—
103C22⋊C4×C101—41no—
104C42×C101—41no—
105C42×C101—41no—
106C16×C101—22no—
107C16×C101—41no—
108C23×C101—21no—
109C23×C101AGL(1,ℤ/8)11yescharacteristic
110Q8×C101—21no—
111Q8×C101—21no—
112Q8×C101—42no—
113Q8×C101—42no—
114Q8×C101—81no—
115Q8×C101—81no—
116D4×C101—21no—
117D4×C101—21no—
118D4×C101—41no—
119D4×C101—41no—
120C2×C4×C101—21no—
121C2×C4×C101—41no—
122C2×C4×C101—41no—
123C2×C4×C101—42no—
124C2×C4×C101—81no—
125C2×C4×C101—81no—
126C2×C4×C101—81no—
127C2×C4×C101—81no—
128C2×C4×C101#12011yescharacteristic
129C2×C4×C101#12111yescharacteristic
130C2×C4×C101#12311yescharacteristic
131C2×C4×C101C2×SD1611yescharacteristic
132C2×C4×C101#13511yescharacteristic
133C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
134C8×C101—41no—
135C8×C101—42no—
136C8×C101#12111yescharacteristic
137C8×C101#12111yescharacteristic
138C8×C101#12311yescharacteristic
139C8×C101#12411yescharacteristic
140C22×C101—41no—
141C22×C101—41no—
142C22×C101—81no—
143C22×C101#44911yescharacteristic
144C22×C101#46911yescharacteristic
145C22×C101#48111yescharacteristic
146C4×C101—41no—
147C4×C101—82no—
148C4×C101—161no—
149C4×C101—161no—
150C4×C101#39411yescharacteristic
151C4×C101#45011yescharacteristic
152C4×C101#46511yescharacteristic
153C4×C101#48211yescharacteristic
154#13405C10111yesmaximal, characteristic, direct product factor, Sylow
155C2×C101—21no—
156C2×C101—21no—
157C2×C101—21no—
158C2×C101—81no—
159C2×C101#203411yescharacteristic
160C2×#473C2×C10111yescharacteristic
161#2155C2×C10111yescharacteristic, complemented
162#2141C2×C10111yescharacteristic, complemented
163#2141C2×C10111yescharacteristic, complemented
164#2117C2×C10111yescharacteristic
165#1812C2×C10111yescharacteristic
166#1389C2×C10111yescharacteristic, complemented
167C101#1340511yescharacteristic, direct product factor, Sylow
168C2×#137—21no—
169C22×Q16C22×C10111yescharacteristic
170C2×#131C22×C10111yescharacteristic
171C2×M32C22×C10111yescharacteristic
172C2×M32C22×C10111yescharacteristic
173#473—22no—
174#473—22no—
175C2×#108C22×C10111yescharacteristic
176#427C22×C10111yescharacteristic
177#427C22×C10111yescharacteristic
178C2×#101—21no—
179#410—21no—
180#365—22no—
181#358—22no—
182#358—22no—
183#350—22no—
184H(3,ℤ/4)—21no—
185C2×#41D4×C10111yescharacteristic
186C22×Q8—21no—
187#137—24no—
188#137—42no—
189C2×Q16—21no—
190C2×Q16—21no—
191C2×Q16—21no—
192C2×Q16—21no—
193C2×Q16—21no—
194C2×Q16—41no—
195C2×Q16D4×C10112yes—
196C2×SD16—41no—
197#131—21no—
198#131—21no—
199#131—21no—
200#131—21no—
201C2×M16—21no—
202C2×M16—21no—
203C2×M16D4×C10111yescharacteristic
204C22×C8—21no—
205C22×C8C23×C10111yescharacteristic
206#117—21no—
207#117—21no—
208M32—21no—
209M32—21no—
210M32—21no—
211M32—21no—
212C2×C16—21no—
213C2×C16D4×C10112yes—
214#108—21no—
215#108D4×C10112yes—
216#107—21no—
217#107—21no—
218#106—21no—
219#106—21no—
220#101—24no—
221#99—42no—
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×Q8SD16×C10111yescharacteristic
233C2×D4—21no—
234C2×D4SD16×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—
250C2×C8—21no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8C2×D4×C10111yescharacteristic
255C2×C8C2×D4×C10111yescharacteristic
256C2×C8C2×D4×C10111yescharacteristic
257C2×C8#41×C10111yescharacteristic
258C2×C8#41×C10111yescharacteristic
259C2×C8#41×C10111yescharacteristic
260C4⋊C4—41no—
261C4⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C42—41no—
265C42—41no—
266C16—22no—
267C16—41no—
268C23—21no—
269C23AGL(1,ℤ/8)×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—81no—
287C2×C4—81no—
288C2×C4#120×C10111yescharacteristic
289C2×C4#121×C10111yescharacteristic
290C2×C4#123×C10111yescharacteristic
291C2×C4C2×SD16×C10111yescharacteristic
292C2×C4#135×C10111yescharacteristic
293C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
294C8—42no—
295C8—41no—
296C8#121×C10111yescharacteristic
297C8#121×C10111yescharacteristic
298C8#123×C10111yescharacteristic
299C8#124×C10111yescharacteristic
300C22—41no—
301C22—41no—
302C22—81no—
303C22#449×C10111yescharacteristic
304C22#469×C10111yescharacteristic
305C22#481×C10111yescharacteristic
306C4—41no—
307C4—82no—
308C4—161no—
309C4—161no—
310C4#394×C10111yescharacteristic
311C4#450×C10111yescharacteristic
312C4#465×C10111yescharacteristic
313C4#482×C10111yescharacteristic
314C2—21no—
315C2—21no—
316C2—21no—
317C2—81no—
318C2C101×#203411yescharacteristic
subgroupG/H
center, socleC2×C101#2034
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×#2155C2semidirect
3. C101×#2141C2semidirect
4. C101×#2141C2semidirect
7. C101×#1389C2semidirect
154. #13405C101direct (N × H)
161. #2155C2×C101semidirect
162. #2141C2×C101semidirect
163. #2141C2×C101semidirect
166. #1389C2×C101semidirect
167. C101#13405direct (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×#21552
C101×#21412
C101×#21172
C101×#18122
C101×#13892
#13405101