Finite Group Databasebeta

← C101×#19060 #38801211

Subgroups — C101×#19060 #38801211

Order 25856.

822 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3553C211yesmaximal, characteristic
2C101×#3238C212yesmaximal, complemented
3C2×#491×C101C211yesmaximal, characteristic, complemented
4C101×#1664C214yesmaximal, complemented
5C101×#1663C212yesmaximal, complemented
6C101×#1662C212yesmaximal, complemented
7C101×#1534C211yesmaximal, characteristic, complemented
8C101×#1532C212yesmaximal, complemented
9#564×C101C2211yescharacteristic
10#563×C101C2212yes—
11#562×C101C2211yescharacteristic
12#554×C101—22no—
13#553×C101—22no—
14#552×C101—22no—
15#541×C101—22no—
16#539×C101—22no—
17#539×C101—22no—
18C2×C4⋊Q8×C101C2211yescharacteristic
19#529×C101C2212yes—
20C2×#125×C101C2211yescharacteristic
21#501×C101C2214yes—
22#491×C101—22no—
23#491×C101C2212yes—
24#491×C101C2212yes—
25#489×C101C2214yes—
26#483×C101—22no—
27#480×C101—22no—
28#477×C101—22no—
29#476×C101—22no—
30#432×C101C2212yes—
31C2×#103×C101—22no—
32C2×#97×C101C2211yescharacteristic
33#330×C101C2212yes—
34#330×C101C2214yes—
35#330×C101C2212yes—
36#329×C101C2214yes—
37C22×Q8×C101—21no—
38C22×C8×C101—21no—
39C4⋊Q8×C101—22no—
40C4⋊Q8×C101—22no—
41C4⋊Q8×C101—21no—
42C4⋊Q8×C101C2312yes—
43#126×C101—22no—
44#126×C101—22no—
45#126×C101—22no—
46#126×C101—22no—
47#126×C101—22no—
48#125×C101—22no—
49#125×C101—22no—
50#125×C101—22no—
51#125×C101—22no—
52#125×C101—22no—
53#125×C101—22no—
54#125×C101D412yes—
55#125×C101C2311yescharacteristic
56#125×C101C2311yescharacteristic
57#125×C101C2312yes—
58#124×C101C2312yes—
59#123×C101—22no—
60#123×C101—22no—
61#123×C101—22no—
62#123×C101—22no—
63#123×C101—22no—
64C22⋊Q8×C101—22no—
65C22⋊Q8×C101—22no—
66C22⋊Q8×C101—22no—
67C22⋊Q8×C101—22no—
68C22⋊Q8×C101—22no—
69C22⋊Q8×C101—22no—
70C22⋊Q8×C101D412yes—
71#121×C101—22no—
72#121×C101—22no—
73#121×C101D412yes—
74C4×Q8×C101—22no—
75C4×Q8×C101D412yes—
76C4×D4×C101—22no—
77C4×D4×C101—22no—
78C4×D4×C101—22no—
79C4×D4×C101—22no—
80C4×D4×C101D412yes—
81#117×C101—22no—
82#117×C101—22no—
83C2×C4⋊C4×C101—22no—
84C2×C4⋊C4×C101—22no—
85C2×C4⋊C4×C101—22no—
86C2×C4⋊C4×C101D412yes—
87C2×C42×C101C2311yescharacteristic
88#107×C101—24no—
89#106×C101—24no—
90C4⋊C8×C101—22no—
91#103×C101—24no—
92#103×C101—24no—
93#103×C101—24no—
94#102×C101—24no—
95C22⋊C8×C101—22no—
96#97×C101—21no—
97#97×C101C2312yes—
98#97×C101C2314yes—
99C2×Q8×C101—22no—
100C2×Q8×C101—22no—
101C2×Q8×C101—44no—
102C2×Q8×C101—41no—
103C2×Q8×C101C2×D412yes—
104C2×D4×C101—22no—
105C2×D4×C101—22no—
106C2×D4×C101C2×D412yes—
107C22×C4×C101—22no—
108C22×C4×C101—22no—
109C22×C4×C101—22no—
110C22×C4×C101—22no—
111C22×C4×C101—41no—
112C22×C4×C101C2×D411yescharacteristic
113C22×C4×C101C2×D412yes—
114C2×C8×C101—22no—
115C2×C8×C101—24no—
116C2×C8×C101—42no—
117C4⋊C4×C101—22no—
118C4⋊C4×C101—22no—
119C4⋊C4×C101—22no—
120C4⋊C4×C101—22no—
121C4⋊C4×C101—22no—
122C4⋊C4×C101—22no—
123C4⋊C4×C101—22no—
124C4⋊C4×C101—22no—
125C4⋊C4×C101—22no—
126C4⋊C4×C101—22no—
127C4⋊C4×C101—22no—
128C4⋊C4×C101—22no—
129C4⋊C4×C101—22no—
130C4⋊C4×C101—22no—
131C4⋊C4×C101—22no—
132C4⋊C4×C101—24no—
133C4⋊C4×C101—42no—
134C4⋊C4×C101C2×D412yes—
135C4⋊C4×C101C2×D412yes—
136C4⋊C4×C101C2×D412yes—
137C4⋊C4×C101C2×D412yes—
138C22⋊C4×C101—22no—
139C22⋊C4×C101—22no—
140C22⋊C4×C101—22no—
141C22⋊C4×C101—22no—
142C22⋊C4×C101—22no—
143C22⋊C4×C101—22no—
144C22⋊C4×C101—22no—
145C22⋊C4×C101—22no—
146C22⋊C4×C101—22no—
147C42×C101—22no—
148C42×C101—22no—
149C42×C101—22no—
150C42×C101C2×D411yescharacteristic
151C42×C101C2×D412yes—
152C42×C101C2411yescharacteristic
153C23×C101—22no—
154C23×C101#12011yescharacteristic
155Q8×C101—42no—
156Q8×C101—44no—
157Q8×C101—82no—
158Q8×C101—82no—
159D4×C101—42no—
160D4×C101—44no—
161D4×C101—82no—
162C2×C4×C101—22no—
163C2×C4×C101—22no—
164C2×C4×C101—22no—
165C2×C4×C101—22no—
166C2×C4×C101—22no—
167C2×C4×C101—22no—
168C2×C4×C101—42no—
169C2×C4×C101—42no—
170C2×C4×C101—82no—
171C2×C4×C101—82no—
172C2×C4×C101—82no—
173C2×C4×C101—82no—
174C2×C4×C101—82no—
175C2×C4×C101#12012yes—
176C2×C4×C101#12011yescharacteristic
177C2×C4×C101C22×D411yescharacteristic
178C2×C4×C101C22×D412yes—
179C8×C101—44no—
180C8×C101—42no—
181C22×C101—22no—
182C22×C101—42no—
183C22×C101—42no—
184C22×C101—42no—
185C22×C101#45412yes—
186C22×C101C2×#12011yescharacteristic
187C4×C101—21no—
188C4×C101—21no—
189C4×C101—22no—
190C4×C101—22no—
191C4×C101—42no—
192C4×C101—42no—
193C4×C101—42no—
194C4×C101—42no—
195C4×C101—42no—
196C4×C101—82no—
197#19060C10111yesmaximal, characteristic, direct product factor, Sylow
198C2×C101—22no—
199C2×C101—82no—
200C2×C101C2×#45411yescharacteristic
201C2×C101#302212yes—
202#3553C2×C10111yescharacteristic
203#3238C2×C10112yescomplemented
204C2×#491C2×C10111yescharacteristic, complemented
205#1664C2×C10114yescomplemented
206#1663C2×C10112yescomplemented
207#1662C2×C10112yescomplemented
208#1534C2×C10111yescharacteristic, complemented
209#1532C2×C10112yescomplemented
210C101#1906011yescharacteristic, direct product factor, Sylow
211#564C22×C10111yescharacteristic
212#563C22×C10112yes—
213#562C22×C10111yescharacteristic
214#554—22no—
215#553—22no—
216#552—22no—
217#541—22no—
218#539—22no—
219#539—22no—
220C2×C4⋊Q8C22×C10111yescharacteristic
221#529C22×C10112yes—
222C2×#125C22×C10111yescharacteristic
223#501C22×C10114yes—
224#491—22no—
225#491C22×C10112yes—
226#491C22×C10112yes—
227#489C22×C10114yes—
228#483—22no—
229#480—22no—
230#477—22no—
231#476—22no—
232#432C22×C10112yes—
233C2×#103—22no—
234C2×#97C22×C10111yescharacteristic
235#330C22×C10112yes—
236#330C22×C10114yes—
237#330C22×C10112yes—
238#329C22×C10114yes—
239C22×Q8—21no—
240C22×C8—21no—
241C4⋊Q8—22no—
242C4⋊Q8—22no—
243C4⋊Q8—21no—
244C4⋊Q8C23×C10112yes—
245#126—22no—
246#126—22no—
247#126—22no—
248#126—22no—
249#126—22no—
250#125—22no—
251#125—22no—
252#125—22no—
253#125—22no—
254#125—22no—
255#125—22no—
256#125D4×C10112yes—
257#125C23×C10111yescharacteristic
258#125C23×C10111yescharacteristic
259#125C23×C10112yes—
260#124C23×C10112yes—
261#123—22no—
262#123—22no—
263#123—22no—
264#123—22no—
265#123—22no—
266C22⋊Q8—22no—
267C22⋊Q8—22no—
268C22⋊Q8—22no—
269C22⋊Q8—22no—
270C22⋊Q8—22no—
271C22⋊Q8—22no—
272C22⋊Q8D4×C10112yes—
273#121—22no—
274#121—22no—
275#121D4×C10112yes—
276C4×Q8—22no—
277C4×Q8D4×C10112yes—
278C4×D4—22no—
279C4×D4—22no—
280C4×D4—22no—
281C4×D4—22no—
282C4×D4D4×C10112yes—
283#117—22no—
284#117—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4D4×C10112yes—
289C2×C42C23×C10111yescharacteristic
290#107—24no—
291#106—24no—
292C4⋊C8—22no—
293#103—24no—
294#103—24no—
295#103—24no—
296#102—24no—
297C22⋊C8—22no—
298#97—21no—
299#97C23×C10112yes—
300#97C23×C10114yes—
301C2×Q8—22no—
302C2×Q8—22no—
303C2×Q8—44no—
304C2×Q8—41no—
305C2×Q8C2×D4×C10112yes—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4C2×D4×C10112yes—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—41no—
314C22×C4C2×D4×C10111yescharacteristic
315C22×C4C2×D4×C10112yes—
316C2×C8—22no—
317C2×C8—24no—
318C2×C8—42no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—24no—
335C4⋊C4—42no—
336C4⋊C4C2×D4×C10112yes—
337C4⋊C4C2×D4×C10112yes—
338C4⋊C4C2×D4×C10112yes—
339C4⋊C4C2×D4×C10112yes—
340C22⋊C4—22no—
341C22⋊C4—22no—
342C22⋊C4—22no—
343C22⋊C4—22no—
344C22⋊C4—22no—
345C22⋊C4—22no—
346C22⋊C4—22no—
347C22⋊C4—22no—
348C22⋊C4—22no—
349C42—22no—
350C42—22no—
351C42—22no—
352C42C2×D4×C10111yescharacteristic
353C42C2×D4×C10112yes—
354C42C24×C10111yescharacteristic
355C23—22no—
356C23#120×C10111yescharacteristic
357Q8—42no—
358Q8—44no—
359Q8—82no—
360Q8—82no—
361D4—42no—
362D4—44no—
363D4—82no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—82no—
373C2×C4—82no—
374C2×C4—82no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4#120×C10112yes—
378C2×C4#120×C10111yescharacteristic
379C2×C4C22×D4×C10111yescharacteristic
380C2×C4C22×D4×C10112yes—
381C8—42no—
382C8—44no—
383C22—22no—
384C22—42no—
385C22—42no—
386C22—42no—
387C22#454×C10112yes—
388C22C2×#120×C10111yescharacteristic
389C4—21no—
390C4—21no—
391C4—22no—
392C4—22no—
393C4—42no—
394C4—42no—
395C4—42no—
396C4—42no—
397C4—42no—
398C4—82no—
399C2—22no—
400C2—82no—
401C2C2×#454×C10111yescharacteristic
402C2C101×#302212yes—
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC42C24×C101
prime radicalC101×#3553C2
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
2. C101×#3238C2semidirect
3. C2×#491×C101C2semidirect
4. C101×#1664C2semidirect
5. C101×#1663C2semidirect
6. C101×#1662C2semidirect
7. C101×#1534C2semidirect
8. C101×#1532C2semidirect
197. #19060C101direct (N × H)
203. #3238C2×C101semidirect
204. C2×#491C2×C101semidirect
205. #1664C2×C101semidirect
206. #1663C2×C101semidirect
207. #1662C2×C101semidirect
208. #1534C2×C101semidirect
209. #1532C2×C101semidirect
210. C101#19060direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#35532
C101×#32382
C2×#491×C1012
C101×#16642
C101×#16632
C101×#16622
C101×#15342
C101×#15322
#19060101