Finite Group Databasebeta

← C101×#9360 #38791511

Subgroups — C101×#9360 #38791511

Order 25856.

538 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3038C211yesmaximal, characteristic
2C101×#2991C211yesmaximal, characteristic, complemented
3C101×#1965C211yesmaximal, characteristic, complemented
4C101×#1545C211yesmaximal, characteristic, complemented
5C101×#1489C211yesmaximal, characteristic, complemented
6C101×#1309C211yesmaximal, characteristic, complemented
7C101×#1299C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C101C412yes—
9C2×#127×C101C2211yescharacteristic
10C4×#41×C101C2211yescharacteristic
11#460×C101—21no—
12#460×C101—21no—
13#459×C101—21no—
14#459×C101—21no—
15C8×Q8×C101—21no—
16#436×C101—22no—
17#436×C101—21no—
18#431×C101—21no—
19#431×C101C2211yescharacteristic
20#423×C101—21no—
21#423×C101C2211yescharacteristic
22#423×C101C2211yescharacteristic
23#423×C101C2211yescharacteristic
24#418×C101C412yes—
25C2×#100×C101—22no—
26C4×M16×C101C2211yescharacteristic
27#331×C101—21no—
28#331×C101—21no—
29Q8⋊C8×C101—21no—
30D4⋊C8×C101—21no—
31C2×#41×C101C2×C411yescharacteristic
32C22×D4×C101—21no—
33C22×D4×C101—21no—
34C22×D4×C101C2×C412yes—
35AGL(1,ℤ/8)×C101—44no—
36C2×SD16×C101—22no—
37C2×D8×C101—22no—
38C2×M16×C101—22no—
39C2×M16×C101—21no—
40C2×M16×C101—21no—
41C2×M16×C101C2×C412yes—
42C2×M16×C101D412yes—
43#127×C101—21no—
44#127×C101—21no—
45#127×C101—21no—
46#127×C101—21no—
47C4×Q8×C101D411yescharacteristic
48C4×Q8×C101D411yescharacteristic
49C4×D4×C101—21no—
50C4×D4×C101—21no—
51C4×D4×C101D411yescharacteristic
52C4×D4×C101D411yescharacteristic
53#117×C101—21no—
54#117×C101C2×C411yescharacteristic
55C2×C42×C101—21no—
56C2×C42×C101C2311yescharacteristic
57C4⋊C8×C101—22no—
58C4⋊C8×C101—21no—
59C4⋊C8×C101—21no—
60C4⋊C8×C101—21no—
61C4⋊C8×C101—21no—
62C4⋊C8×C101—21no—
63C4⋊C8×C101—21no—
64C4⋊C8×C101D411yescharacteristic
65C4⋊C8×C101D411yescharacteristic
66#102×C101—22no—
67#102×C101—22no—
68#100×C101—44no—
69C22⋊C8×C101—22no—
70C22⋊C8×C101—21no—
71#97×C101—21no—
72C4×C8×C101—22no—
73C4×C8×C101—21no—
74C4×C8×C101—21no—
75C24×C101—22no—
76#41×C101—22no—
77#41×C101—41no—
78C2×Q8×C101C22⋊C411yescharacteristic
79C2×D4×C101—21no—
80C2×D4×C101—22no—
81C2×D4×C101—22no—
82C2×D4×C101—42no—
83C2×D4×C101—42no—
84C2×D4×C101—42no—
85C2×D4×C101—42no—
86C2×D4×C101—41no—
87C2×D4×C101—41no—
88C2×D4×C101—41no—
89C2×D4×C101—41no—
90C2×D4×C101—81no—
91C2×D4×C101—81no—
92C2×D4×C101C22⋊C411yescharacteristic
93C22×C4×C101—21no—
94C22×C4×C101—21no—
95C22×C4×C101—21no—
96C22×C4×C101C22×C411yescharacteristic
97C22×C4×C101C2×D411yescharacteristic
98C22×C4×C101#4111yescharacteristic
99SD16×C101—44no—
100D8×C101—44no—
101M16×C101—22no—
102M16×C101—41no—
103M16×C101—42no—
104M16×C101—42no—
105M16×C101—82no—
106M16×C101—81no—
107C2×C8×C101—22no—
108C2×C8×C101—21no—
109C2×C8×C101—22no—
110C2×C8×C101—21no—
111C2×C8×C101—41no—
112C2×C8×C101—41no—
113C4⋊C4×C101—21no—
114C4⋊C4×C101—21no—
115C4⋊C4×C101C22⋊C411yescharacteristic
116C4⋊C4×C101C22⋊C411yescharacteristic
117C22⋊C4×C101—21no—
118C22⋊C4×C101—21no—
119C22⋊C4×C101—21no—
120C42×C101—21no—
121C42×C101—21no—
122C42×C101—21no—
123C42×C101C2×D411yescharacteristic
124C42×C101C2×D411yescharacteristic
125C42×C101C2×D411yescharacteristic
126C42×C101#4111yescharacteristic
127C23×C101—21no—
128C23×C101—44no—
129C23×C101—42no—
130C23×C101—82no—
131C23×C101—82no—
132C23×C101C4×D411yescharacteristic
133Q8×C101—21no—
134Q8×C101#10012yescomplemented
135D4×C101—21no—
136D4×C101—21no—
137D4×C101—42no—
138D4×C101—42no—
139D4×C101—42no—
140D4×C101—82no—
141D4×C101—82no—
142D4×C101—82no—
143D4×C101—81no—
144D4×C101—81no—
145D4×C101—81no—
146D4×C101—81no—
147C2×C4×C101—21no—
148C2×C4×C101—21no—
149C2×C4×C101—21no—
150C2×C4×C101—21no—
151C2×C4×C101—21no—
152C2×C4×C101—21no—
153C2×C4×C101—21no—
154C2×C4×C101—21no—
155C2×C4×C101—21no—
156C2×C4×C101—42no—
157C2×C4×C101—41no—
158C2×C4×C101—41no—
159C2×C4×C101—41no—
160C2×C4×C101—41no—
161C2×C4×C101C2×C22⋊C411yescharacteristic
162C2×C4×C101C4×D411yescharacteristic
163C2×C4×C101#12011yescharacteristic
164C2×C4×C101#12111yescharacteristic
165C2×C4×C101#12111yescharacteristic
166C2×C4×C101#12311yescharacteristic
167C8×C101—42no—
168C8×C101—42no—
169C8×C101—42no—
170C8×C101—41no—
171C8×C101—41no—
172C8×C101—81no—
173C22×C101—21no—
174C22×C101—21no—
175C22×C101—21no—
176C22×C101—41no—
177C22×C101—41no—
178C22×C101—41no—
179C22×C101—82no—
180C22×C101—82no—
181C22×C101—82no—
182C22×C101—164no—
183C22×C101#38611yescharacteristic
184C4×C101—21no—
185C4×C101—21no—
186C4×C101—22no—
187C4×C101—21no—
188C4×C101—41no—
189C4×C101—41no—
190C4×C101C2×#10011yescharacteristic
191C4×C101#41311yescharacteristic
192C4×C101#45311yescharacteristic
193C4×C101#45411yescharacteristic
194C4×C101#47111yescharacteristic
195C4×C101#47211yescharacteristic
196#9360C10111yesmaximal, characteristic, direct product factor, Sylow
197C2×C101—41no—
198C2×C101—81no—
199C2×C101—162no—
200C2×C101#188311yescharacteristic
201C2×C101#190011yescharacteristic
202C2×C101#190711yescharacteristic
203#3038C2×C10111yescharacteristic
204#2991C2×C10111yescharacteristic, complemented
205#1965C2×C10111yescharacteristic, complemented
206#1545C2×C10111yescharacteristic, complemented
207#1489C2×C10111yescharacteristic, complemented
208#1309C2×C10111yescharacteristic, complemented
209#1299C2×C10111yescharacteristic, complemented
210C101#936011yescharacteristic, direct product factor, Sylow
211C2×AGL(1,ℤ/8)C4×C10112yes—
212C2×#127C22×C10111yescharacteristic
213C4×#41C22×C10111yescharacteristic
214#460—21no—
215#460—21no—
216#459—21no—
217#459—21no—
218C8×Q8—21no—
219#436—22no—
220#436—21no—
221#431—21no—
222#431C22×C10111yescharacteristic
223#423—21no—
224#423C22×C10111yescharacteristic
225#423C22×C10111yescharacteristic
226#423C22×C10111yescharacteristic
227#418C4×C10112yes—
228C2×#100—22no—
229C4×M16C22×C10111yescharacteristic
230#331—21no—
231#331—21no—
232Q8⋊C8—21no—
233D4⋊C8—21no—
234C2×#41C2×C4×C10111yescharacteristic
235C22×D4—21no—
236C22×D4—21no—
237C22×D4C2×C4×C10112yes—
238AGL(1,ℤ/8)—44no—
239C2×SD16—22no—
240C2×D8—22no—
241C2×M16—22no—
242C2×M16—21no—
243C2×M16—21no—
244C2×M16C2×C4×C10112yes—
245C2×M16D4×C10112yes—
246#127—21no—
247#127—21no—
248#127—21no—
249#127—21no—
250C4×Q8D4×C10111yescharacteristic
251C4×Q8D4×C10111yescharacteristic
252C4×D4—21no—
253C4×D4—21no—
254C4×D4D4×C10111yescharacteristic
255C4×D4D4×C10111yescharacteristic
256#117—21no—
257#117C2×C4×C10111yescharacteristic
258C2×C42—21no—
259C2×C42C23×C10111yescharacteristic
260C4⋊C8—22no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8D4×C10111yescharacteristic
268C4⋊C8D4×C10111yescharacteristic
269#102—22no—
270#102—22no—
271#100—44no—
272C22⋊C8—22no—
273C22⋊C8—21no—
274#97—21no—
275C4×C8—22no—
276C4×C8—21no—
277C4×C8—21no—
278C24—22no—
279#41—22no—
280#41—41no—
281C2×Q8C22⋊C4×C10111yescharacteristic
282C2×D4—21no—
283C2×D4—22no—
284C2×D4—22no—
285C2×D4—42no—
286C2×D4—42no—
287C2×D4—42no—
288C2×D4—42no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—81no—
294C2×D4—81no—
295C2×D4C22⋊C4×C10111yescharacteristic
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4C22×C4×C10111yescharacteristic
300C22×C4C2×D4×C10111yescharacteristic
301C22×C4#41×C10111yescharacteristic
302SD16—44no—
303D8—44no—
304M16—22no—
305M16—41no—
306M16—42no—
307M16—42no—
308M16—82no—
309M16—81no—
310C2×C8—22no—
311C2×C8—21no—
312C2×C8—22no—
313C2×C8—21no—
314C2×C8—41no—
315C2×C8—41no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4C22⋊C4×C10111yescharacteristic
319C4⋊C4C22⋊C4×C10111yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C42—21no—
324C42—21no—
325C42—21no—
326C42C2×D4×C10111yescharacteristic
327C42C2×D4×C10111yescharacteristic
328C42C2×D4×C10111yescharacteristic
329C42#41×C10111yescharacteristic
330C23—21no—
331C23—44no—
332C23—42no—
333C23—82no—
334C23—82no—
335C23C4×D4×C10111yescharacteristic
336Q8—21no—
337Q8#100×C10112yescomplemented
338D4—21no—
339D4—21no—
340D4—42no—
341D4—42no—
342D4—42no—
343D4—82no—
344D4—82no—
345D4—82no—
346D4—81no—
347D4—81no—
348D4—81no—
349D4—81no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4C2×C22⋊C4×C10111yescharacteristic
365C2×C4C4×D4×C10111yescharacteristic
366C2×C4#120×C10111yescharacteristic
367C2×C4#121×C10111yescharacteristic
368C2×C4#121×C10111yescharacteristic
369C2×C4#123×C10111yescharacteristic
370C8—42no—
371C8—42no—
372C8—42no—
373C8—41no—
374C8—41no—
375C8—81no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—82no—
383C22—82no—
384C22—82no—
385C22—164no—
386C22#386×C10111yescharacteristic
387C4—21no—
388C4—21no—
389C4—22no—
390C4—21no—
391C4—41no—
392C4—41no—
393C4C2×#100×C10111yescharacteristic
394C4#413×C10111yescharacteristic
395C4#453×C10111yescharacteristic
396C4#454×C10111yescharacteristic
397C4#471×C10111yescharacteristic
398C4#472×C10111yescharacteristic
399C2—41no—
400C2—81no—
401C2—162no—
402C2C101×#188311yescharacteristic
403C2C101×#190011yescharacteristic
404C2C101×#190711yescharacteristic
subgroupG/H
center, socleC22×C101#386
commutatorC22×C4C22×C4×C101
Frattini, cosocleC2×C42C23×C101
prime radicalC101×#3038C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#2991C2semidirect
3. C101×#1965C2semidirect
4. C101×#1545C2semidirect
5. C101×#1489C2semidirect
6. C101×#1309C2semidirect
7. C101×#1299C2semidirect
134. Q8×C101#100semidirect
196. #9360C101direct (N × H)
204. #2991C2×C101semidirect
205. #1965C2×C101semidirect
206. #1545C2×C101semidirect
207. #1489C2×C101semidirect
208. #1309C2×C101semidirect
209. #1299C2×C101semidirect
210. C101#9360direct (N × H)
337. Q8#100×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#30382
C101×#29912
C101×#19652
C101×#15452
C101×#14892
C101×#13092
C101×#12992
#9360101