Finite Group Databasebeta

← C101×#8953 #38791104

Subgroups — C101×#8953 #38791104

Order 25856.

514 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#2988C211yesmaximal, characteristic
2C4×#137×C101C211yesmaximal, characteristic
3C101×#1984C211yesmaximal, characteristic, complemented
4C101×#1479C211yesmaximal, characteristic, complemented
5C101×#1476C211yesmaximal, characteristic
6C101×#1283C211yesmaximal, characteristic, complemented
7C101×#1278C211yesmaximal, characteristic, complemented
8C2×#137×C101C411yescharacteristic
9C4×#41×C101C2211yescharacteristic
10C2×C4×Q8×C101C2211yescharacteristic
11C8×Q8×C101—21no—
12#441×C101—21no—
13#440×C101—21no—
14C4×Q16×C101—21no—
15C4×SD16×C101—21no—
16C8×D4×C101—22no—
17C8×D4×C101—21no—
18#431×C101—21no—
19#431×C101C2211yescharacteristic
20#431×C101C2211yescharacteristic
21#428×C101C411yescharacteristic
22C2×C4⋊C8×C101—21no—
23C2×C4⋊C8×C101C2211yescharacteristic
24#419×C101C411yescharacteristic
25#417×C101C411yescharacteristic
26C4×M16×C101C2211yescharacteristic
27C2×C4×C8×C101C2211yescharacteristic
28#336×C101—22no—
29Q8⋊C8×C101—21no—
30Q8⋊C8×C101—21no—
31Q8⋊C8×C101—21no—
32D4⋊C8×C101—21no—
33C2×#41×C101C2×C411yescharacteristic
34C22×Q8×C101C2×C411yescharacteristic
35#137×C101—22no—
36#137×C101C814yescomplemented
37C2×Q16×C101—21no—
38C2×SD16×C101—21no—
39C2×M16×C101C2×C411yescharacteristic
40C2×M16×C101C2×C411yescharacteristic
41C22×C8×C101—21no—
42C22×C8×C101—22no—
43C22×C8×C101D412yes—
44C4×Q8×C101—21no—
45C4×Q8×C101—21no—
46C4×Q8×C101—21no—
47C4×Q8×C101—21no—
48C4×Q8×C101D411yescharacteristic
49C4×Q8×C101D411yescharacteristic
50C4×D4×C101—21no—
51C4×D4×C101—21no—
52C4×D4×C101D411yescharacteristic
53C4×D4×C101D411yescharacteristic
54#117×C101—21no—
55#117×C101C2×C411yescharacteristic
56C2×C4⋊C4×C101—21no—
57C2×C4⋊C4×C101C2×C411yescharacteristic
58C2×C42×C101—21no—
59C2×C42×C101—21no—
60C2×C42×C101C2311yescharacteristic
61#107×C101—21no—
62#106×C101—21no—
63C4⋊C8×C101—22no—
64C4⋊C8×C101—21no—
65C4⋊C8×C101—21no—
66C4⋊C8×C101—21no—
67C4⋊C8×C101D411yescharacteristic
68C4⋊C8×C101D411yescharacteristic
69#103×C101—21no—
70#103×C101—21no—
71#103×C101—21no—
72#102×C101—21no—
73C22⋊C8×C101—22no—
74C22⋊C8×C101—21no—
75C22⋊C8×C101—21no—
76#97×C101—21no—
77C4×C8×C101—22no—
78C4×C8×C101—21no—
79C4×C8×C101—21no—
80C4×C8×C101—21no—
81C4×C8×C101—21no—
82C4×C8×C101—21no—
83#41×C101—21no—
84#41×C101—21no—
85#41×C101C2×C812yes—
86#41×C101M1612yes—
87C2×Q8×C101—21no—
88C2×Q8×C101—21no—
89C2×Q8×C101—21no—
90C2×Q8×C101—21no—
91C2×Q8×C101—21no—
92C2×Q8×C101C22⋊C411yescharacteristic
93C2×Q8×C101C2×C812yescomplemented
94C2×D4×C101—21no—
95C2×D4×C101C22⋊C411yescharacteristic
96C22×C4×C101—21no—
97C22×C4×C101—21no—
98C22×C4×C101—21no—
99C22×C4×C101—21no—
100C22×C4×C101—21no—
101C22×C4×C101C22×C411yescharacteristic
102C22×C4×C101C2×D411yescharacteristic
103C22×C4×C101#4111yescharacteristic
104Q16×C101—24no—
105SD16×C101—24no—
106M16×C101—21no—
107M16×C101—21no—
108M16×C101—21no—
109M16×C101C2×C812yescomplemented
110C2×C8×C101—21no—
111C2×C8×C101—22no—
112C2×C8×C101—21no—
113C2×C8×C101—21no—
114C2×C8×C101—22no—
115C2×C8×C101—21no—
116C2×C8×C101—41no—
117C2×C8×C101—41no—
118C2×C8×C101—42no—
119C2×C8×C101—41no—
120C2×C8×C101—82no—
121C4⋊C4×C101—21no—
122C4⋊C4×C101—21no—
123C4⋊C4×C101—21no—
124C4⋊C4×C101—21no—
125C4⋊C4×C101—41no—
126C4⋊C4×C101—41no—
127C4⋊C4×C101C22⋊C411yescharacteristic
128C4⋊C4×C101C22⋊C411yescharacteristic
129C22⋊C4×C101—21no—
130C22⋊C4×C101—21no—
131C22⋊C4×C101—21no—
132C42×C101—21no—
133C42×C101—21no—
134C42×C101—21no—
135C42×C101—41no—
136C42×C101—41no—
137C42×C101C2×D411yescharacteristic
138C42×C101C2×D411yescharacteristic
139C42×C101C2×D411yescharacteristic
140C42×C101#4111yescharacteristic
141C23×C101—21no—
142C23×C101C4×D411yescharacteristic
143Q8×C101—21no—
144Q8×C101—22no—
145Q8×C101—22no—
146Q8×C101—41no—
147Q8×C101—41no—
148Q8×C101C22⋊C812yes—
149D4×C101—22no—
150D4×C101—22no—
151D4×C101—21no—
152D4×C101C22⋊C812yes—
153C2×C4×C101—21no—
154C2×C4×C101—22no—
155C2×C4×C101—22no—
156C2×C4×C101—21no—
157C2×C4×C101—21no—
158C2×C4×C101—21no—
159C2×C4×C101—21no—
160C2×C4×C101—22no—
161C2×C4×C101—41no—
162C2×C4×C101—41no—
163C2×C4×C101—41no—
164C2×C4×C101—41no—
165C2×C4×C101—41no—
166C2×C4×C101—42no—
167C2×C4×C101—41no—
168C2×C4×C101—81no—
169C2×C4×C101C2×C22⋊C411yescharacteristic
170C2×C4×C101C4×D411yescharacteristic
171C2×C4×C101#12011yescharacteristic
172C2×C4×C101#12111yescharacteristic
173C2×C4×C101#12111yescharacteristic
174C2×C4×C101#12311yescharacteristic
175C2×C4×C101C22×C811yescharacteristic
176C2×C4×C101C2×M1611yescharacteristic
177C2×C4×C101#13111yescharacteristic
178C2×C4×C101#13111yescharacteristic
179C8×C101—22no—
180C8×C101—42no—
181C8×C101—41no—
182C8×C101—42no—
183C8×C101—41no—
184C8×C101—41no—
185C8×C101—81no—
186C22×C101—21no—
187C22×C101—21no—
188C22×C101—22no—
189C22×C101—41no—
190C22×C101—41no—
191C22×C101#38611yescharacteristic
192C22×C101C8×D411yescharacteristic
193C22×C101#43511yescharacteristic
194C4×C101—22no—
195C4×C101—21no—
196C4×C101—21no—
197C4×C101—21no—
198C4×C101—42no—
199C4×C101—41no—
200C4×C101—41no—
201C4×C101—81no—
202C4×C101C2×C22⋊C811yescharacteristic
203C4×C101#40811yescharacteristic
204C4×C101C8×D411yescharacteristic
205C4×C101#43511yescharacteristic
206C4×C101#45511yescharacteristic
207C4×C101#45611yescharacteristic
208#8953C10111yesmaximal, characteristic, direct product factor, Sylow
209C2×C101—21no—
210C2×C101—21no—
211C2×C101—42no—
212C2×C101#186911yescharacteristic
213C2×C101#188111yescharacteristic
214C2×C101#188211yescharacteristic
215#2988C2×C10111yescharacteristic
216C4×#137C2×C10111yescharacteristic
217#1984C2×C10111yescharacteristic, complemented
218#1479C2×C10111yescharacteristic, complemented
219#1476C2×C10111yescharacteristic
220#1283C2×C10111yescharacteristic, complemented
221#1278C2×C10111yescharacteristic, complemented
222C101#895311yescharacteristic, direct product factor, Sylow
223C2×#137C4×C10111yescharacteristic
224C4×#41C22×C10111yescharacteristic
225C2×C4×Q8C22×C10111yescharacteristic
226C8×Q8—21no—
227#441—21no—
228#440—21no—
229C4×Q16—21no—
230C4×SD16—21no—
231C8×D4—22no—
232C8×D4—21no—
233#431—21no—
234#431C22×C10111yescharacteristic
235#431C22×C10111yescharacteristic
236#428C4×C10111yescharacteristic
237C2×C4⋊C8—21no—
238C2×C4⋊C8C22×C10111yescharacteristic
239#419C4×C10111yescharacteristic
240#417C4×C10111yescharacteristic
241C4×M16C22×C10111yescharacteristic
242C2×C4×C8C22×C10111yescharacteristic
243#336—22no—
244Q8⋊C8—21no—
245Q8⋊C8—21no—
246Q8⋊C8—21no—
247D4⋊C8—21no—
248C2×#41C2×C4×C10111yescharacteristic
249C22×Q8C2×C4×C10111yescharacteristic
250#137—22no—
251#137C8×C10114yescomplemented
252C2×Q16—21no—
253C2×SD16—21no—
254C2×M16C2×C4×C10111yescharacteristic
255C2×M16C2×C4×C10111yescharacteristic
256C22×C8—21no—
257C22×C8—22no—
258C22×C8D4×C10112yes—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×Q8—21no—
263C4×Q8D4×C10111yescharacteristic
264C4×Q8D4×C10111yescharacteristic
265C4×D4—21no—
266C4×D4—21no—
267C4×D4D4×C10111yescharacteristic
268C4×D4D4×C10111yescharacteristic
269#117—21no—
270#117C2×C4×C10111yescharacteristic
271C2×C4⋊C4—21no—
272C2×C4⋊C4C2×C4×C10111yescharacteristic
273C2×C42—21no—
274C2×C42—21no—
275C2×C42C23×C10111yescharacteristic
276#107—21no—
277#106—21no—
278C4⋊C8—22no—
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8D4×C10111yescharacteristic
283C4⋊C8D4×C10111yescharacteristic
284#103—21no—
285#103—21no—
286#103—21no—
287#102—21no—
288C22⋊C8—22no—
289C22⋊C8—21no—
290C22⋊C8—21no—
291#97—21no—
292C4×C8—22no—
293C4×C8—21no—
294C4×C8—21no—
295C4×C8—21no—
296C4×C8—21no—
297C4×C8—21no—
298#41—21no—
299#41—21no—
300#41C2×C8×C10112yes—
301#41M16×C10112yes—
302C2×Q8—21no—
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8C22⋊C4×C10111yescharacteristic
308C2×Q8C2×C8×C10112yescomplemented
309C2×D4—21no—
310C2×D4C22⋊C4×C10111yescharacteristic
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4C22×C4×C10111yescharacteristic
317C22×C4C2×D4×C10111yescharacteristic
318C22×C4#41×C10111yescharacteristic
319Q16—24no—
320SD16—24no—
321M16—21no—
322M16—21no—
323M16—21no—
324M16C2×C8×C10112yescomplemented
325C2×C8—21no—
326C2×C8—22no—
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—22no—
330C2×C8—21no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—42no—
334C2×C8—41no—
335C2×C8—82no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4C22⋊C4×C10111yescharacteristic
343C4⋊C4C22⋊C4×C10111yescharacteristic
344C22⋊C4—21no—
345C22⋊C4—21no—
346C22⋊C4—21no—
347C42—21no—
348C42—21no—
349C42—21no—
350C42—41no—
351C42—41no—
352C42C2×D4×C10111yescharacteristic
353C42C2×D4×C10111yescharacteristic
354C42C2×D4×C10111yescharacteristic
355C42#41×C10111yescharacteristic
356C23—21no—
357C23C4×D4×C10111yescharacteristic
358Q8—21no—
359Q8—22no—
360Q8—22no—
361Q8—41no—
362Q8—41no—
363Q8C22⋊C8×C10112yes—
364D4—22no—
365D4—22no—
366D4—21no—
367D4C22⋊C8×C10112yes—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—22no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—81no—
384C2×C4C2×C22⋊C4×C10111yescharacteristic
385C2×C4C4×D4×C10111yescharacteristic
386C2×C4#120×C10111yescharacteristic
387C2×C4#121×C10111yescharacteristic
388C2×C4#121×C10111yescharacteristic
389C2×C4#123×C10111yescharacteristic
390C2×C4C22×C8×C10111yescharacteristic
391C2×C4C2×M16×C10111yescharacteristic
392C2×C4#131×C10111yescharacteristic
393C2×C4#131×C10111yescharacteristic
394C8—22no—
395C8—42no—
396C8—41no—
397C8—42no—
398C8—41no—
399C8—41no—
400C8—81no—
401C22—21no—
402C22—21no—
403C22—22no—
404C22—41no—
405C22—41no—
406C22#386×C10111yescharacteristic
407C22C8×D4×C10111yescharacteristic
408C22#435×C10111yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—22no—
413C4—41no—
414C4—41no—
415C4—42no—
416C4—81no—
417C4C2×C22⋊C8×C10111yescharacteristic
418C4#408×C10111yescharacteristic
419C4C8×D4×C10111yescharacteristic
420C4#435×C10111yescharacteristic
421C4#455×C10111yescharacteristic
422C4#456×C10111yescharacteristic
423C2—21no—
424C2—21no—
425C2—42no—
426C2C101×#186911yescharacteristic
427C2C101×#188111yescharacteristic
428C2C101×#188211yescharacteristic
subgroupG/H
centerC2×C4×C101#120
commutatorC2×C4C22×C8×C101
Frattini, cosocleC2×C42C23×C101
socleC22×C101#386
prime radicalC2×#41×C101C2×C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
3. C101×#1984C2semidirect
4. C101×#1479C2semidirect
6. C101×#1283C2semidirect
7. C101×#1278C2semidirect
36. #137×C101C8semidirect
93. C2×Q8×C101C2×C8semidirect
109. M16×C101C2×C8semidirect
208. #8953C101direct (N × H)
217. #1984C2×C101semidirect
218. #1479C2×C101semidirect
220. #1283C2×C101semidirect
221. #1278C2×C101semidirect
222. C101#8953direct (N × H)
251. #137C8×C101semidirect
308. C2×Q8C2×C8×C101semidirect
324. M16C2×C8×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#29882
C4×#137×C1012
C101×#19842
C101×#14792
C101×#14762
C101×#12832
C101×#12782
#8953101