Finite Group Databasebeta

← C101×#19198 #38801349

Subgroups — C101×#19198 #38801349

Order 25856.

726 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3206C211yesmaximal, characteristic, complemented
2C101×#3205C211yesmaximal, characteristic
3C2×#486×C101C211yesmaximal, characteristic, complemented
4C101×#2931C211yesmaximal, characteristic, complemented
5C101×#1701C214yesmaximal, complemented
6C101×#1681C214yesmaximal, complemented
7C101×#1564C211yesmaximal, characteristic, complemented
8C101×#1549C211yesmaximal, characteristic, complemented
9C101×#1545C211yesmaximal, characteristic, complemented
10C2×#131×C101—21no—
11#532×C101C2211yescharacteristic
12C2×C4⋊Q8×C101C2211yescharacteristic
13C2×#127×C101C2211yescharacteristic
14#493×C101—21no—
15#492×C101—21no—
16#487×C101—21no—
17#486×C101—21no—
18#486×C101—21no—
19#486×C101—21no—
20#486×C101C2212yes—
21#486×C101C2212yes—
22#461×C101C2214yescomplemented
23#459×C101C2214yes—
24#448×C101—22no—
25#447×C101—22no—
26#436×C101—21no—
27#436×C101C2212yescomplemented
28C8×D4×C101—21no—
29C8×D4×C101C2212yescomplemented
30#431×C101C2211yescharacteristic
31#431×C101C2211yescharacteristic
32#423×C101C2211yescharacteristic
33C2×#102×C101—21no—
34C2×#102×C101—21no—
35#408×C101—21no—
36C2×C4×C8×C101C2211yescharacteristic
37#335×C101C2212yescomplemented
38#334×C101C2212yescomplemented
39#332×C101C2214yescomplemented
40#331×C101C2214yes—
41C2×#41×C101—21no—
42C22×Q8×C101—21no—
43C22×D4×C101—21no—
44C22×D4×C101—21no—
45C22×D4×C101—21no—
46C2×SD16×C101—24no—
47C2×D8×C101—24no—
48#131×C101—44no—
49C2×M16×C101—21no—
50C2×M16×C101—22no—
51C22×C8×C101—22no—
52C22×C8×C101D411yescharacteristic
53C22×C8×C101D411yescharacteristic
54C4⋊Q8×C101—21no—
55C4⋊Q8×C101—21no—
56C4⋊Q8×C101—21no—
57C4⋊Q8×C101D411yescharacteristic
58C4⋊Q8×C101C2312yes—
59#127×C101—21no—
60#127×C101—21no—
61#127×C101—21no—
62#127×C101D411yescharacteristic
63#127×C101C2312yes—
64#124×C101—21no—
65#121×C101—21no—
66#121×C101D412yes—
67C4×D4×C101—21no—
68C4×D4×C101C2312yes—
69C2×C4⋊C4×C101—21no—
70C2×C4⋊C4×C101—21no—
71C2×C42×C101C2311yescharacteristic
72C4⋊C8×C101—21no—
73C4⋊C8×C101C2312yes—
74C4⋊C8×C101C2312yes—
75C4⋊C8×C101C2312yes—
76#103×C101—24no—
77#102×C101—22no—
78#102×C101—22no—
79#102×C101—22no—
80#102×C101—22no—
81#102×C101—24no—
82C22⋊C8×C101—21no—
83C22⋊C8×C101—21no—
84C22⋊C8×C101—22no—
85C22⋊C8×C101—22no—
86C4×C8×C101—21no—
87C4×C8×C101—21no—
88C4×C8×C101D411yescharacteristic
89C4×C8×C101D411yescharacteristic
90C4×C8×C101C2311yescharacteristic
91C4×C8×C101C2311yescharacteristic
92C24×C101—41no—
93#41×C101—42no—
94#41×C101—42no—
95C2×Q8×C101—21no—
96C2×Q8×C101—22no—
97C2×Q8×C101—41no—
98C2×Q8×C101—82no—
99C2×D4×C101—22no—
100C2×D4×C101—21no—
101C2×D4×C101—21no—
102C2×D4×C101—22no—
103C2×D4×C101—22no—
104C2×D4×C101—22no—
105C2×D4×C101—41no—
106C2×D4×C101—41no—
107C2×D4×C101—41no—
108C2×D4×C101—42no—
109C2×D4×C101—42no—
110C2×D4×C101—82no—
111C2×D4×C101—82no—
112C2×D4×C101C2×D412yes—
113C22×C4×C101—22no—
114C22×C4×C101—41no—
115C22×C4×C101C2×D411yescharacteristic
116C22×C4×C101C2×D411yescharacteristic
117C22×C4×C101#4111yescharacteristic
118SD16×C101—84no—
119D8×C101—84no—
120M16×C101—44no—
121M16×C101—42no—
122C2×C8×C101—22no—
123C2×C8×C101—22no—
124C2×C8×C101—22no—
125C2×C8×C101—22no—
126C2×C8×C101—22no—
127C2×C8×C101—44no—
128C2×C8×C101C2×D411yescharacteristic
129C2×C8×C101C2×D411yescharacteristic
130C2×C8×C101C2×D411yescharacteristic
131C2×C8×C101C2×D411yescharacteristic
132C4⋊C4×C101—21no—
133C4⋊C4×C101—22no—
134C4⋊C4×C101—22no—
135C4⋊C4×C101—41no—
136C4⋊C4×C101—41no—
137C4⋊C4×C101C2×D412yes—
138C22⋊C4×C101—22no—
139C22⋊C4×C101—22no—
140C42×C101C2×D411yescharacteristic
141C42×C101C2×D411yescharacteristic
142C42×C101#4111yescharacteristic
143C42×C101C2411yescharacteristic
144C23×C101—22no—
145C23×C101—42no—
146C23×C101—82no—
147C23×C101—82no—
148C23×C101—82no—
149C23×C101#12111yescharacteristic
150Q8×C101—42no—
151Q8×C101—44no—
152Q8×C101—82no—
153D4×C101—24no—
154D4×C101—44no—
155D4×C101—42no—
156D4×C101—42no—
157D4×C101—44no—
158D4×C101—42no—
159D4×C101—42no—
160D4×C101—82no—
161D4×C101—82no—
162D4×C101—82no—
163D4×C101—82no—
164C2×C4×C101—22no—
165C2×C4×C101—22no—
166C2×C4×C101—22no—
167C2×C4×C101—42no—
168C2×C4×C101—42no—
169C2×C4×C101—42no—
170C2×C4×C101—82no—
171C2×C4×C101#12111yescharacteristic
172C2×C4×C101#12111yescharacteristic
173C2×C4×C101#12111yescharacteristic
174C2×C4×C101#13512yes—
175C2×C4×C101AGL(1,ℤ/8)12yes—
176C2×C4×C101C22×D411yescharacteristic
177C2×C4×C101C22×D411yescharacteristic
178C2×C4×C101C2×#4111yescharacteristic
179C8×C101—21no—
180C8×C101—21no—
181C8×C101—21no—
182C8×C101—21no—
183C8×C101—42no—
184C8×C101—42no—
185C8×C101—42no—
186C22×C101—21no—
187C22×C101—21no—
188C22×C101—42no—
189C22×C101—42no—
190C22×C101—42no—
191C22×C101—82no—
192C22×C101—82no—
193C22×C101—82no—
194C22×C101—164no—
195C22×C101#46312yes—
196C22×C101C2×#12111yescharacteristic
197C4×C101—21no—
198C4×C101—21no—
199C4×C101—42no—
200C4×C101—82no—
201C4×C101#46312yes—
202C4×C101#47112yes—
203C4×C101C2×#13511yescharacteristic
204C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
205C4×C101#57612yes—
206#19198C10111yesmaximal, characteristic, direct product factor, Sylow
207C2×C101—22no—
208C2×C101—82no—
209C2×C101—162no—
210C2×C101C2×#46311yescharacteristic
211C2×C101#305811yescharacteristic
212C2×C101C2×#47111yescharacteristic
213#3206C2×C10111yescharacteristic, complemented
214#3205C2×C10111yescharacteristic
215C2×#486C2×C10111yescharacteristic, complemented
216#2931C2×C10111yescharacteristic, complemented
217#1701C2×C10114yescomplemented
218#1681C2×C10114yescomplemented
219#1564C2×C10111yescharacteristic, complemented
220#1549C2×C10111yescharacteristic, complemented
221#1545C2×C10111yescharacteristic, complemented
222C101#1919811yescharacteristic, direct product factor, Sylow
223C2×#131—21no—
224#532C22×C10111yescharacteristic
225C2×C4⋊Q8C22×C10111yescharacteristic
226C2×#127C22×C10111yescharacteristic
227#493—21no—
228#492—21no—
229#487—21no—
230#486—21no—
231#486—21no—
232#486—21no—
233#486C22×C10112yes—
234#486C22×C10112yes—
235#461C22×C10114yescomplemented
236#459C22×C10114yes—
237#448—22no—
238#447—22no—
239#436—21no—
240#436C22×C10112yescomplemented
241C8×D4—21no—
242C8×D4C22×C10112yescomplemented
243#431C22×C10111yescharacteristic
244#431C22×C10111yescharacteristic
245#423C22×C10111yescharacteristic
246C2×#102—21no—
247C2×#102—21no—
248#408—21no—
249C2×C4×C8C22×C10111yescharacteristic
250#335C22×C10112yescomplemented
251#334C22×C10112yescomplemented
252#332C22×C10114yescomplemented
253#331C22×C10114yes—
254C2×#41—21no—
255C22×Q8—21no—
256C22×D4—21no—
257C22×D4—21no—
258C22×D4—21no—
259C2×SD16—24no—
260C2×D8—24no—
261#131—44no—
262C2×M16—21no—
263C2×M16—22no—
264C22×C8—22no—
265C22×C8D4×C10111yescharacteristic
266C22×C8D4×C10111yescharacteristic
267C4⋊Q8—21no—
268C4⋊Q8—21no—
269C4⋊Q8—21no—
270C4⋊Q8D4×C10111yescharacteristic
271C4⋊Q8C23×C10112yes—
272#127—21no—
273#127—21no—
274#127—21no—
275#127D4×C10111yescharacteristic
276#127C23×C10112yes—
277#124—21no—
278#121—21no—
279#121D4×C10112yes—
280C4×D4—21no—
281C4×D4C23×C10112yes—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C42C23×C10111yescharacteristic
285C4⋊C8—21no—
286C4⋊C8C23×C10112yes—
287C4⋊C8C23×C10112yes—
288C4⋊C8C23×C10112yes—
289#103—24no—
290#102—22no—
291#102—22no—
292#102—22no—
293#102—22no—
294#102—24no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C22⋊C8—22no—
298C22⋊C8—22no—
299C4×C8—21no—
300C4×C8—21no—
301C4×C8D4×C10111yescharacteristic
302C4×C8D4×C10111yescharacteristic
303C4×C8C23×C10111yescharacteristic
304C4×C8C23×C10111yescharacteristic
305C24—41no—
306#41—42no—
307#41—42no—
308C2×Q8—21no—
309C2×Q8—22no—
310C2×Q8—41no—
311C2×Q8—82no—
312C2×D4—22no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—22no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—42no—
322C2×D4—42no—
323C2×D4—82no—
324C2×D4—82no—
325C2×D4C2×D4×C10112yes—
326C22×C4—22no—
327C22×C4—41no—
328C22×C4C2×D4×C10111yescharacteristic
329C22×C4C2×D4×C10111yescharacteristic
330C22×C4#41×C10111yescharacteristic
331SD16—84no—
332D8—84no—
333M16—44no—
334M16—42no—
335C2×C8—22no—
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—22no—
339C2×C8—22no—
340C2×C8—44no—
341C2×C8C2×D4×C10111yescharacteristic
342C2×C8C2×D4×C10111yescharacteristic
343C2×C8C2×D4×C10111yescharacteristic
344C2×C8C2×D4×C10111yescharacteristic
345C4⋊C4—21no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4C2×D4×C10112yes—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C42C2×D4×C10111yescharacteristic
354C42C2×D4×C10111yescharacteristic
355C42#41×C10111yescharacteristic
356C42C24×C10111yescharacteristic
357C23—22no—
358C23—42no—
359C23—82no—
360C23—82no—
361C23—82no—
362C23#121×C10111yescharacteristic
363Q8—42no—
364Q8—44no—
365Q8—82no—
366D4—24no—
367D4—44no—
368D4—42no—
369D4—42no—
370D4—42no—
371D4—42no—
372D4—44no—
373D4—82no—
374D4—82no—
375D4—82no—
376D4—82no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—82no—
384C2×C4#121×C10111yescharacteristic
385C2×C4#121×C10111yescharacteristic
386C2×C4#121×C10111yescharacteristic
387C2×C4#135×C10112yes—
388C2×C4AGL(1,ℤ/8)×C10112yes—
389C2×C4C22×D4×C10111yescharacteristic
390C2×C4C22×D4×C10111yescharacteristic
391C2×C4C2×#41×C10111yescharacteristic
392C8—21no—
393C8—21no—
394C8—21no—
395C8—21no—
396C8—42no—
397C8—42no—
398C8—42no—
399C22—21no—
400C22—21no—
401C22—42no—
402C22—42no—
403C22—42no—
404C22—82no—
405C22—82no—
406C22—82no—
407C22—164no—
408C22#463×C10112yes—
409C22C2×#121×C10111yescharacteristic
410C4—21no—
411C4—21no—
412C4—42no—
413C4—82no—
414C4#463×C10112yes—
415C4#471×C10112yes—
416C4C2×#135×C10111yescharacteristic
417C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
418C4#576×C10112yes—
419C2—22no—
420C2—82no—
421C2—162no—
422C2C2×#463×C10111yescharacteristic
423C2C101×#305811yescharacteristic
424C2C2×#471×C10111yescharacteristic
subgroupG/H
center, socleC22×C101C2×#121
commutator, Frattini, cosocleC42C24×C101
prime radicalC101×#3205C2
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
1. C101×#3206C2semidirect
3. C2×#486×C101C2semidirect
4. C101×#2931C2semidirect
5. C101×#1701C2semidirect
6. C101×#1681C2semidirect
7. C101×#1564C2semidirect
8. C101×#1549C2semidirect
9. C101×#1545C2semidirect
22. #461×C101C22semidirect
27. #436×C101C22semidirect
29. C8×D4×C101C22semidirect
37. #335×C101C22semidirect
38. #334×C101C22semidirect
39. #332×C101C22semidirect
206. #19198C101direct (N × H)
213. #3206C2×C101semidirect
215. C2×#486C2×C101semidirect
216. #2931C2×C101semidirect
217. #1701C2×C101semidirect
218. #1681C2×C101semidirect
219. #1564C2×C101semidirect
220. #1549C2×C101semidirect
221. #1545C2×C101semidirect
222. C101#19198direct (N × H)
235. #461C22×C101semidirect
240. #436C22×C101semidirect
242. C8×D4C22×C101semidirect
250. #335C22×C101semidirect
251. #334C22×C101semidirect
252. #332C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#32062
C101×#32052
C2×#486×C1012
C101×#29312
C101×#17012
C101×#16812
C101×#15642
C101×#15492
C101×#15452
#19198101