Finite Group Databasebeta

← C101×#9295 #38791446

Subgroups — C101×#9295 #38791446

Order 25856.

594 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3208C211yesmaximal, characteristic
2C101×#2328C211yesmaximal, characteristic
3C101×#1995C211yesmaximal, characteristic, complemented
4C101×#1545C211yesmaximal, characteristic
5C101×#1518C211yesmaximal, characteristic, complemented
6C101×#1286C211yesmaximal, characteristic, complemented
7C101×#1274C211yesmaximal, characteristic, complemented
8#533×C101C2211yescharacteristic
9C2×#127×C101C2211yescharacteristic
10C2×C4×D4×C101—21no—
11#492×C101C412yescomplemented
12#486×C101C412yescomplemented
13#460×C101—22no—
14#450×C101—22no—
15#431×C101C2211yescharacteristic
16#431×C101C2211yescharacteristic
17#423×C101C2211yescharacteristic
18#390×C101—21no—
19#386×C101—22no—
20#386×C101—22no—
21#382×C101C2211yescharacteristic
22#376×C101C2211yescharacteristic
23#339×C101—21no—
24#339×C101—21no—
25#331×C101—22no—
26#328×C101—22no—
27C22×D4×C101—21no—
28C22×D4×C101—21no—
29C22×D4×C101D412yes—
30C23×C4×C101—22no—
31C2×SD16×C101—24no—
32C2×M16×C101—21no—
33C4⋊Q8×C101C2×C411yescharacteristic, complemented
34C4⋊Q8×C101C2×C411yescharacteristic, complemented
35#127×C101—21no—
36#127×C101—21no—
37#127×C101C2×C412yes—
38#127×C101D412yes—
39#125×C101—21no—
40C22⋊Q8×C101—21no—
41C22⋊Q8×C101—21no—
42C4×Q8×C101—21no—
43C4×Q8×C101—21no—
44C4×D4×C101—42no—
45C4×D4×C101—42no—
46#117×C101—21no—
47C2×C4⋊C4×C101—21no—
48C2×C22⋊C4×C101—22no—
49C2×C22⋊C4×C101—22no—
50C2×C22⋊C4×C101—22no—
51C2×C42×C101D411yescharacteristic
52C2×C42×C101D411yescharacteristic
53C2×C42×C101C2311yescharacteristic
54C4⋊C8×C101—21no—
55C4⋊C8×C101—21no—
56C4⋊C8×C101—21no—
57C4⋊C8×C101—21no—
58#102×C101—24no—
59C22⋊C8×C101—21no—
60C22⋊C8×C101—21no—
61C4×C8×C101—21no—
62C4×C8×C101C2×C412yescomplemented
63#95×C101—21no—
64#95×C101—21no—
65#95×C101—21no—
66#95×C101D412yes—
67C24×C101—22no—
68C2×Q8×C101—21no—
69C2×Q8×C101—21no—
70C2×D4×C101—22no—
71C2×D4×C101—22no—
72C2×D4×C101—22no—
73C2×D4×C101—22no—
74C2×D4×C101—22no—
75C2×D4×C101—41no—
76C2×D4×C101—41no—
77C2×D4×C101—41no—
78C2×D4×C101—41no—
79C2×D4×C101—82no—
80C2×D4×C101—82no—
81C2×D4×C101C22⋊C414yes—
82C22×C4×C101—21no—
83C22×C4×C101—21no—
84C22×C4×C101—22no—
85C22×C4×C101—44no—
86C22×C4×C101—82no—
87C22×C4×C101—82no—
88C22×C4×C101C2×D411yescharacteristic
89C22×C4×C101C2×D411yescharacteristic
90C22×C4×C101C2×D411yescharacteristic
91SD16×C101—84no—
92M16×C101—41no—
93M16×C101—41no—
94C2×C8×C101—22no—
95C2×C8×C101—41no—
96C2×C8×C101—41no—
97C4⋊C4×C101—21no—
98C4⋊C4×C101—21no—
99C4⋊C4×C101—21no—
100C4⋊C4×C101—21no—
101C4⋊C4×C101—41no—
102C4⋊C4×C101—41no—
103C4⋊C4×C101—41no—
104C4⋊C4×C101—41no—
105C22⋊C4×C101—44no—
106C22⋊C4×C101—41no—
107C22⋊C4×C101—82no—
108C22⋊C4×C101—82no—
109C42×C101—21no—
110C42×C101—21no—
111C42×C101—21no—
112C42×C101—41no—
113C42×C101SD1612yescomplemented
114C42×C101C22×C411yescharacteristic
115C42×C101C2×D411yescharacteristic
116C42×C101#4111yescharacteristic
117C42×C101#4111yescharacteristic
118C23×C101—24no—
119C23×C101—42no—
120C23×C101—42no—
121C23×C101—42no—
122C23×C101—42no—
123C23×C101—42no—
124C23×C101—42no—
125C23×C101#12011yescharacteristic
126Q8×C101—42no—
127Q8×C101—81no—
128D4×C101—44no—
129D4×C101—42no—
130D4×C101—42no—
131D4×C101—42no—
132D4×C101—42no—
133D4×C101—82no—
134D4×C101—82no—
135D4×C101—82no—
136C2×C4×C101—22no—
137C2×C4×C101—41no—
138C2×C4×C101—41no—
139C2×C4×C101—41no—
140C2×C4×C101—41no—
141C2×C4×C101—41no—
142C2×C4×C101—41no—
143C2×C4×C101—42no—
144C2×C4×C101—42no—
145C2×C4×C101—41no—
146C2×C4×C101—41no—
147C2×C4×C101—42no—
148C2×C4×C101—41no—
149C2×C4×C101—88no—
150C2×C4×C101C2×C22⋊C411yescharacteristic
151C2×C4×C101C4×D411yescharacteristic
152C2×C4×C101C4×D411yescharacteristic
153C2×C4×C101#12111yescharacteristic
154C2×C4×C101#12111yescharacteristic
155C2×C4×C101#12311yescharacteristic
156C2×C4×C101C2×SD1611yescharacteristic
157C2×C4×C101#13511yescharacteristic
158C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C101#13711yescharacteristic
160C8×C101—42no—
161C8×C101—81no—
162C8×C101—81no—
163C22×C101—21no—
164C22×C101—21no—
165C22×C101—44no—
166C22×C101—44no—
167C22×C101—44no—
168C22×C101—82no—
169C22×C101—82no—
170C22×C101—82no—
171C22×C101—82no—
172C22×C101#38611yescharacteristic
173C22×C101#45011yescharacteristic
174C22×C101#45211yescharacteristic
175C4×C101—21no—
176C4×C101—21no—
177C4×C101—21no—
178C4×C101—21no—
179C4×C101—42no—
180C4×C101—81no—
181C4×C101—82no—
182C4×C101—81no—
183C4×C101—81no—
184C4×C101C4×SD1611yescharacteristic
185C4×C101#44011yescharacteristic
186C4×C101#46111yescharacteristic
187C4×C101#46311yescharacteristic
188#9295C10111yesmaximal, characteristic, direct product factor, Sylow
189C2×C101—21no—
190C2×C101—21no—
191C2×C101—84no—
192C2×C101#187711yescharacteristic
193C2×C101#190411yescharacteristic
194C2×C101#191111yescharacteristic
195#3208C2×C10111yescharacteristic
196#2328C2×C10111yescharacteristic
197#1995C2×C10111yescharacteristic, complemented
198#1545C2×C10111yescharacteristic
199#1518C2×C10111yescharacteristic, complemented
200#1286C2×C10111yescharacteristic, complemented
201#1274C2×C10111yescharacteristic, complemented
202C101#929511yescharacteristic, direct product factor, Sylow
203#533C22×C10111yescharacteristic
204C2×#127C22×C10111yescharacteristic
205C2×C4×D4—21no—
206#492C4×C10112yescomplemented
207#486C4×C10112yescomplemented
208#460—22no—
209#450—22no—
210#431C22×C10111yescharacteristic
211#431C22×C10111yescharacteristic
212#423C22×C10111yescharacteristic
213#390—21no—
214#386—22no—
215#386—22no—
216#382C22×C10111yescharacteristic
217#376C22×C10111yescharacteristic
218#339—21no—
219#339—21no—
220#331—22no—
221#328—22no—
222C22×D4—21no—
223C22×D4—21no—
224C22×D4D4×C10112yes—
225C23×C4—22no—
226C2×SD16—24no—
227C2×M16—21no—
228C4⋊Q8C2×C4×C10111yescharacteristic, complemented
229C4⋊Q8C2×C4×C10111yescharacteristic, complemented
230#127—21no—
231#127—21no—
232#127C2×C4×C10112yes—
233#127D4×C10112yes—
234#125—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×D4—42no—
240C4×D4—42no—
241#117—21no—
242C2×C4⋊C4—21no—
243C2×C22⋊C4—22no—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—22no—
246C2×C42D4×C10111yescharacteristic
247C2×C42D4×C10111yescharacteristic
248C2×C42C23×C10111yescharacteristic
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253#102—24no—
254C22⋊C8—21no—
255C22⋊C8—21no—
256C4×C8—21no—
257C4×C8C2×C4×C10112yescomplemented
258#95—21no—
259#95—21no—
260#95—21no—
261#95D4×C10112yes—
262C24—22no—
263C2×Q8—21no—
264C2×Q8—21no—
265C2×D4—22no—
266C2×D4—22no—
267C2×D4—22no—
268C2×D4—22no—
269C2×D4—22no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—82no—
275C2×D4—82no—
276C2×D4C22⋊C4×C10114yes—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—44no—
281C22×C4—82no—
282C22×C4—82no—
283C22×C4C2×D4×C10111yescharacteristic
284C22×C4C2×D4×C10111yescharacteristic
285C22×C4C2×D4×C10111yescharacteristic
286SD16—84no—
287M16—41no—
288M16—41no—
289C2×C8—22no—
290C2×C8—41no—
291C2×C8—41no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C22⋊C4—44no—
301C22⋊C4—41no—
302C22⋊C4—82no—
303C22⋊C4—82no—
304C42—21no—
305C42—21no—
306C42—21no—
307C42—41no—
308C42SD16×C10112yescomplemented
309C42C22×C4×C10111yescharacteristic
310C42C2×D4×C10111yescharacteristic
311C42#41×C10111yescharacteristic
312C42#41×C10111yescharacteristic
313C23—24no—
314C23—42no—
315C23—42no—
316C23—42no—
317C23—42no—
318C23—42no—
319C23—42no—
320C23#120×C10111yescharacteristic
321Q8—42no—
322Q8—81no—
323D4—44no—
324D4—42no—
325D4—42no—
326D4—42no—
327D4—42no—
328D4—82no—
329D4—82no—
330D4—82no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—88no—
345C2×C4C2×C22⋊C4×C10111yescharacteristic
346C2×C4C4×D4×C10111yescharacteristic
347C2×C4C4×D4×C10111yescharacteristic
348C2×C4#121×C10111yescharacteristic
349C2×C4#121×C10111yescharacteristic
350C2×C4#123×C10111yescharacteristic
351C2×C4C2×SD16×C10111yescharacteristic
352C2×C4#135×C10111yescharacteristic
353C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
354C2×C4#137×C10111yescharacteristic
355C8—42no—
356C8—81no—
357C8—81no—
358C22—21no—
359C22—21no—
360C22—44no—
361C22—44no—
362C22—44no—
363C22—82no—
364C22—82no—
365C22—82no—
366C22—82no—
367C22#386×C10111yescharacteristic
368C22#450×C10111yescharacteristic
369C22#452×C10111yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—42no—
375C4—82no—
376C4—81no—
377C4—81no—
378C4—81no—
379C4C4×SD16×C10111yescharacteristic
380C4#440×C10111yescharacteristic
381C4#461×C10111yescharacteristic
382C4#463×C10111yescharacteristic
383C2—21no—
384C2—21no—
385C2—84no—
386C2C101×#187711yescharacteristic
387C2C101×#190411yescharacteristic
388C2C101×#191111yescharacteristic
subgroupG/H
center, socleC22×C101#386
commutatorC42C22×C4×C101
Frattini, cosocleC2×C42C23×C101
prime radicalC2×#127×C101C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
3. C101×#1995C2semidirect
5. C101×#1518C2semidirect
6. C101×#1286C2semidirect
7. C101×#1274C2semidirect
11. #492×C101C4semidirect
12. #486×C101C4semidirect
33. C4⋊Q8×C101C2×C4semidirect
34. C4⋊Q8×C101C2×C4semidirect
62. C4×C8×C101C2×C4semidirect
113. C42×C101SD16semidirect
188. #9295C101direct (N × H)
197. #1995C2×C101semidirect
199. #1518C2×C101semidirect
200. #1286C2×C101semidirect
201. #1274C2×C101semidirect
202. C101#9295direct (N × H)
206. #492C4×C101semidirect
207. #486C4×C101semidirect
228. C4⋊Q8C2×C4×C101semidirect
229. C4⋊Q8C2×C4×C101semidirect
257. C4×C8C2×C4×C101semidirect
308. C42SD16×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#32082
C101×#23282
C101×#19952
C101×#15452
C101×#15182
C101×#12862
C101×#12742
#9295101