Finite Group Databasebeta

← C101×#13231 #38795382

Subgroups — C101×#13231 #38795382

Order 25856.

468 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3058C211yesmaximal, characteristic
2C101×#2128C212yesmaximal, complemented
3C101×#2122C212yesmaximal, complemented
4C101×#1812C211yesmaximal, characteristic, complemented
5C101×#1757C211yesmaximal, characteristic, complemented
6C22×D8×C101C411yescharacteristic, complemented
7C2×#131×C101C2211yescharacteristic
8#535×C101C2212yes—
9#469×C101—21no—
10#469×C101—21no—
11#466×C101—21no—
12#466×C101—21no—
13#427×C101—21no—
14#427×C101C411yescharacteristic, complemented
15#418×C101C412yescomplemented
16#413×C101C2211yescharacteristic
17#410×C101C2212yes—
18#410×C101C2211yescharacteristic
19#405×C101—21no—
20#353×C101—24no—
21AΣL(1,𝔽16)×C101—24no—
22#344×C101—21no—
23H(3,ℤ/4)×C101—21no—
24C2×#41×C101C2311yescharacteristic
25C22×D4×C101C2×C412yes—
26C2×D8×C101—21no—
27C2×D8×C101—21no—
28C2×D8×C101—41no—
29C2×D8×C101—41no—
30#131×C101—41no—
31#131×C101—41no—
32C2×M16×C101—21no—
33C2×M16×C101C2×C411yescharacteristic
34C2×M16×C101D411yescharacteristic
35C2×M16×C101D411yescharacteristic
36C22×C8×C101C2×C411yescharacteristic
37C22×C8×C101D411yescharacteristic
38C22×C8×C101D411yescharacteristic
39#127×C101—22no—
40#124×C101—22no—
41#121×C101—22no—
42#121×C101—22no—
43#120×C101—22no—
44#120×C101—22no—
45#117×C101—21no—
46#117×C101—22no—
47#117×C101C2×C412yes—
48#107×C101—21no—
49#107×C101—41no—
50#106×C101—21no—
51#106×C101—41no—
52#102×C101—22no—
53#102×C101—22no—
54#101×C101—21no—
55#100×C101D412yes—
56#99×C101—21no—
57#99×C101—22no—
58#99×C101—22no—
59#99×C101D412yes—
60#97×C101—41no—
61C4×C8×C101—41no—
62C24×C101—22no—
63#41×C101—41no—
64#41×C101—41no—
65C2×Q8×C101#4111yescharacteristic
66C2×D4×C101—22no—
67C2×D4×C101—22no—
68C2×D4×C101—42no—
69C2×D4×C101—42no—
70C2×D4×C101—42no—
71C2×D4×C101—42no—
72C2×D4×C101C2×D411yescharacteristic
73C2×D4×C101C2×D411yescharacteristic
74C2×D4×C101#4111yescharacteristic
75C22×C4×C101C22×C411yescharacteristic
76C22×C4×C101C2×D411yescharacteristic
77C22×C4×C101C2×D411yescharacteristic
78D8×C101—42no—
79D8×C101—41no—
80D8×C101—41no—
81M16×C101—22no—
82M16×C101—41no—
83M16×C101—41no—
84M16×C101—41no—
85M16×C101—41no—
86C2×C8×C101—21no—
87C2×C8×C101—21no—
88C2×C8×C101—21no—
89C2×C8×C101—21no—
90C2×C8×C101—21no—
91C2×C8×C101—21no—
92C2×C8×C101—41no—
93C2×C8×C101C22⋊C411yescharacteristic
94C2×C8×C101C22⋊C411yescharacteristic
95C2×C8×C101C22⋊C411yescharacteristic
96C2×C8×C101C22⋊C411yescharacteristic
97C4⋊C4×C101—22no—
98C4⋊C4×C101—41no—
99C4⋊C4×C101—42no—
100C22⋊C4×C101—22no—
101C22⋊C4×C101—22no—
102C22⋊C4×C101—42no—
103C22⋊C4×C101—42no—
104C22⋊C4×C101—42no—
105C42×C101—22no—
106C42×C101—41no—
107C42×C101—42no—
108C23×C101—42no—
109C23×C101—82no—
110C23×C101—162no—
111C23×C101C4×D411yescharacteristic
112C23×C101#12111yescharacteristic
113C23×C101#12711yescharacteristic
114Q8×C101—41no—
115D4×C101—41no—
116D4×C101—41no—
117D4×C101—41no—
118D4×C101—42no—
119D4×C101—42no—
120D4×C101—82no—
121D4×C101—162no—
122D4×C101—162no—
123C2×C4×C101—21no—
124C2×C4×C101—21no—
125C2×C4×C101—21no—
126C2×C4×C101—21no—
127C2×C4×C101—21no—
128C2×C4×C101—21no—
129C2×C4×C101—42no—
130C2×C4×C101—42no—
131C2×C4×C101—82no—
132C2×C4×C101C2×C22⋊C411yescharacteristic
133C2×C4×C101C4×D411yescharacteristic
134C2×C4×C101#12111yescharacteristic
135C2×C4×C101#12411yescharacteristic
136C8×C101—21no—
137C8×C101—21no—
138C8×C101—21no—
139C8×C101—42no—
140C8×C101#9911yescharacteristic
141C8×C101#9911yescharacteristic
142C22×C101—21no—
143C22×C101—21no—
144C22×C101—21no—
145C22×C101—41no—
146C22×C101—41no—
147C22×C101—41no—
148C22×C101—82no—
149C22×C101—82no—
150C22×C101—82no—
151C22×C101—164no—
152C22×C101#39011yescharacteristic
153C4×C101—21no—
154C4×C101—21no—
155C4×C101—21no—
156C4×C101—82no—
157C4×C101—82no—
158C4×C101—162no—
159C4×C101C2×#9911yescharacteristic
160C4×C101#41011yescharacteristic
161#13231C10111yesmaximal, characteristic, direct product factor, Sylow
162C2×C101—21no—
163C2×C101—41no—
164C2×C101—41no—
165C2×C101—41no—
166C2×C101—162no—
167C2×C101#196411yescharacteristic
168#3058C2×C10111yescharacteristic
169#2128C2×C10112yescomplemented
170#2122C2×C10112yescomplemented
171#1812C2×C10111yescharacteristic, complemented
172#1757C2×C10111yescharacteristic, complemented
173C101#1323111yescharacteristic, direct product factor, Sylow
174C22×D8C4×C10111yescharacteristic, complemented
175C2×#131C22×C10111yescharacteristic
176#535C22×C10112yes—
177#469—21no—
178#469—21no—
179#466—21no—
180#466—21no—
181#427—21no—
182#427C4×C10111yescharacteristic, complemented
183#418C4×C10112yescomplemented
184#413C22×C10111yescharacteristic
185#410C22×C10112yes—
186#410C22×C10111yescharacteristic
187#405—21no—
188#353—24no—
189AΣL(1,𝔽16)—24no—
190#344—21no—
191H(3,ℤ/4)—21no—
192C2×#41C23×C10111yescharacteristic
193C22×D4C2×C4×C10112yes—
194C2×D8—21no—
195C2×D8—21no—
196C2×D8—41no—
197C2×D8—41no—
198#131—41no—
199#131—41no—
200C2×M16—21no—
201C2×M16C2×C4×C10111yescharacteristic
202C2×M16D4×C10111yescharacteristic
203C2×M16D4×C10111yescharacteristic
204C22×C8C2×C4×C10111yescharacteristic
205C22×C8D4×C10111yescharacteristic
206C22×C8D4×C10111yescharacteristic
207#127—22no—
208#124—22no—
209#121—22no—
210#121—22no—
211#120—22no—
212#120—22no—
213#117—21no—
214#117—22no—
215#117C2×C4×C10112yes—
216#107—21no—
217#107—41no—
218#106—21no—
219#106—41no—
220#102—22no—
221#102—22no—
222#101—21no—
223#100D4×C10112yes—
224#99—21no—
225#99—22no—
226#99—22no—
227#99D4×C10112yes—
228#97—41no—
229C4×C8—41no—
230C24—22no—
231#41—41no—
232#41—41no—
233C2×Q8#41×C10111yescharacteristic
234C2×D4—22no—
235C2×D4—22no—
236C2×D4—42no—
237C2×D4—42no—
238C2×D4—42no—
239C2×D4—42no—
240C2×D4C2×D4×C10111yescharacteristic
241C2×D4C2×D4×C10111yescharacteristic
242C2×D4#41×C10111yescharacteristic
243C22×C4C22×C4×C10111yescharacteristic
244C22×C4C2×D4×C10111yescharacteristic
245C22×C4C2×D4×C10111yescharacteristic
246D8—42no—
247D8—41no—
248D8—41no—
249M16—22no—
250M16—41no—
251M16—41no—
252M16—41no—
253M16—41no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—21no—
260C2×C8—41no—
261C2×C8C22⋊C4×C10111yescharacteristic
262C2×C8C22⋊C4×C10111yescharacteristic
263C2×C8C22⋊C4×C10111yescharacteristic
264C2×C8C22⋊C4×C10111yescharacteristic
265C4⋊C4—22no—
266C4⋊C4—41no—
267C4⋊C4—42no—
268C22⋊C4—22no—
269C22⋊C4—22no—
270C22⋊C4—42no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C42—22no—
274C42—41no—
275C42—42no—
276C23—42no—
277C23—82no—
278C23—162no—
279C23C4×D4×C10111yescharacteristic
280C23#121×C10111yescharacteristic
281C23#127×C10111yescharacteristic
282Q8—41no—
283D4—41no—
284D4—41no—
285D4—41no—
286D4—42no—
287D4—42no—
288D4—82no—
289D4—162no—
290D4—162no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—82no—
300C2×C4C2×C22⋊C4×C10111yescharacteristic
301C2×C4C4×D4×C10111yescharacteristic
302C2×C4#121×C10111yescharacteristic
303C2×C4#124×C10111yescharacteristic
304C8—21no—
305C8—21no—
306C8—21no—
307C8—42no—
308C8#99×C10111yescharacteristic
309C8#99×C10111yescharacteristic
310C22—21no—
311C22—21no—
312C22—21no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—82no—
317C22—82no—
318C22—82no—
319C22—164no—
320C22#390×C10111yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—82no—
325C4—82no—
326C4—162no—
327C4C2×#99×C10111yescharacteristic
328C4#410×C10111yescharacteristic
329C2—21no—
330C2—41no—
331C2—41no—
332C2—41no—
333C2—162no—
334C2C101×#196411yescharacteristic
subgroupG/H
center, socleC2×C101#1964
commutatorC22×C4C22×C4×C101
Frattini, cosocleC2×#41C23×C101
prime radicalC101×#3058C2
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C101 ◁ C2×C4×C101 ◁ C2×#131×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#2128C2semidirect
3. C101×#2122C2semidirect
4. C101×#1812C2semidirect
5. C101×#1757C2semidirect
6. C22×D8×C101C4semidirect
14. #427×C101C4semidirect
15. #418×C101C4semidirect
161. #13231C101direct (N × H)
169. #2128C2×C101semidirect
170. #2122C2×C101semidirect
171. #1812C2×C101semidirect
172. #1757C2×C101semidirect
173. C101#13231direct (N × H)
174. C22×D8C4×C101semidirect
182. #427C4×C101semidirect
183. #418C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#30582
C101×#21282
C101×#21222
C101×#18122
C101×#17572
#13231101