Finite Group Databasebeta

← C101×#9215 #38791366

Subgroups — C101×#9215 #38791366

Order 25856.

578 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#476×C101C211yesmaximal, characteristic
2C2×C8×D4×C101C211yesmaximal, characteristic
3C101×#1990C211yesmaximal, characteristic, complemented
4C101×#1802C211yesmaximal, characteristic
5C2×#333×C101C211yesmaximal, characteristic, complemented
6C101×#1296C211yesmaximal, characteristic, complemented
7C101×#1277C211yesmaximal, characteristic, complemented
8C23×C8×C101—21no—
9C2×C4⋊Q8×C101C2211yescharacteristic
10C2×C4×D4×C101C2211yescharacteristic
11#476×C101—22no—
12#476×C101C414yescomplemented
13C8×D4×C101—22no—
14C8×D4×C101—22no—
15C2×#106×C101—21no—
16C2×C4⋊C8×C101C2211yescharacteristic
17C2×C4⋊C8×C101C2211yescharacteristic
18C2×C4⋊C8×C101C2211yescharacteristic
19C2×#102×C101—21no—
20C2×#102×C101—21no—
21C2×C22⋊C8×C101—21no—
22C2×C4×C8×C101C2211yescharacteristic
23#384×C101C2211yescharacteristic
24#340×C101—21no—
25#340×C101—21no—
26#340×C101—21no—
27#333×C101—22no—
28C22×Q8×C101—21no—
29C22×D4×C101D411yescharacteristic
30C23×C4×C101—21no—
31C22×C8×C101—24no—
32C22×C8×C101—21no—
33C22×C8×C101—21no—
34C22×C8×C101—21no—
35C22×C8×C101—42no—
36C22×C8×C101—42no—
37C22×C8×C101D411yescharacteristic
38C22×C8×C101D411yescharacteristic
39C4⋊Q8×C101—21no—
40C4⋊Q8×C101—21no—
41C4⋊Q8×C101—21no—
42C4⋊Q8×C101C2×C412yes—
43C4×D4×C101—21no—
44C4×D4×C101—21no—
45C4×D4×C101C2×C412yes—
46C4×D4×C101D412yes—
47C2×C4⋊C4×C101—21no—
48C2×C4⋊C4×C101—21no—
49C2×C4⋊C4×C101—21no—
50C2×C4⋊C4×C101—21no—
51C2×C4⋊C4×C101—21no—
52C2×C4⋊C4×C101D411yescharacteristic
53C2×C22⋊C4×C101—21no—
54C2×C42×C101C2311yescharacteristic
55#106×C101—24no—
56C4⋊C8×C101—21no—
57C4⋊C8×C101—21no—
58C4⋊C8×C101—21no—
59C4⋊C8×C101—21no—
60C4⋊C8×C101C2×C412yes—
61C4⋊C8×C101D412yes—
62#102×C101—24no—
63#102×C101—42no—
64C22⋊C8×C101—24no—
65C4×C8×C101—21no—
66C4×C8×C101—21no—
67C24×C101—21no—
68C2×Q8×C101—22no—
69C2×Q8×C101—41no—
70C2×Q8×C101—81no—
71C2×Q8×C101—81no—
72C2×D4×C101—21no—
73C2×D4×C101—21no—
74C2×D4×C101—21no—
75C2×D4×C101C22⋊C412yes—
76C2×D4×C101SD1612yes—
77C2×D4×C101Q1612yes—
78C22×C4×C101—21no—
79C22×C4×C101—22no—
80C22×C4×C101—22no—
81C22×C4×C101—41no—
82C22×C4×C101—41no—
83C22×C4×C101—41no—
84C22×C4×C101—41no—
85C22×C4×C101—41no—
86C22×C4×C101—41no—
87C22×C4×C101C2×D411yescharacteristic
88C22×C4×C101C2×D411yescharacteristic
89C22×C4×C101#4111yescharacteristic
90C2×C8×C101—21no—
91C2×C8×C101—21no—
92C2×C8×C101—22no—
93C2×C8×C101—21no—
94C2×C8×C101—22no—
95C2×C8×C101—21no—
96C2×C8×C101—21no—
97C2×C8×C101—48no—
98C2×C8×C101—41no—
99C2×C8×C101—41no—
100C2×C8×C101—41no—
101C2×C8×C101—41no—
102C2×C8×C101—41no—
103C2×C8×C101—41no—
104C2×C8×C101—41no—
105C2×C8×C101SD1612yes—
106C4⋊C4×C101—21no—
107C4⋊C4×C101—22no—
108C4⋊C4×C101—22no—
109C4⋊C4×C101—41no—
110C4⋊C4×C101—41no—
111C4⋊C4×C101—41no—
112C4⋊C4×C101—41no—
113C4⋊C4×C101—41no—
114C4⋊C4×C101—41no—
115C4⋊C4×C101—81no—
116C4⋊C4×C101C22⋊C412yes—
117C22⋊C4×C101—22no—
118C22⋊C4×C101—22no—
119C42×C101C22×C411yescharacteristic
120C42×C101C2×D411yescharacteristic
121C42×C101C2×D411yescharacteristic
122C42×C101#4111yescharacteristic
123C23×C101—22no—
124C23×C101—22no—
125C23×C101—22no—
126C23×C101—41no—
127C23×C101—41no—
128C23×C101—41no—
129C23×C101—41no—
130C23×C101#12111yescharacteristic
131Q8×C101—82no—
132Q8×C101—82no—
133D4×C101—22no—
134D4×C101—22no—
135D4×C101—22no—
136D4×C101#10314yes—
137C2×C4×C101—21no—
138C2×C4×C101—21no—
139C2×C4×C101—22no—
140C2×C4×C101—41no—
141C2×C4×C101—41no—
142C2×C4×C101—42no—
143C2×C4×C101—42no—
144C2×C4×C101—42no—
145C2×C4×C101—42no—
146C2×C4×C101—42no—
147C2×C4×C101—81no—
148C2×C4×C101—81no—
149C2×C4×C101—81no—
150C2×C4×C101—81no—
151C2×C4×C101—81no—
152C2×C4×C101C2×C22⋊C411yescharacteristic
153C2×C4×C101C4×D411yescharacteristic
154C2×C4×C101C4×D411yescharacteristic
155C2×C4×C101#12011yescharacteristic
156C2×C4×C101#12111yescharacteristic
157C2×C4×C101#12311yescharacteristic
158C2×C4×C101C2×SD1611yescharacteristic
159C2×C4×C101C2×SD1611yescharacteristic
160C2×C4×C101C2×Q1611yescharacteristic
161C2×C4×C101#13511yescharacteristic
162C2×C4×C101#13511yescharacteristic
163C2×C4×C101#13511yescharacteristic
164C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C101#13711yescharacteristic
166C8×C101—22no—
167C8×C101—42no—
168C8×C101—42no—
169C8×C101—41no—
170C8×C101—81no—
171C22×C101—24no—
172C22×C101—42no—
173C22×C101—42no—
174C22×C101—42no—
175C22×C101—42no—
176C22×C101—42no—
177C22×C101—42no—
178C22×C101#38611yescharacteristic
179C22×C101#46111yescharacteristic
180C22×C101#46311yescharacteristic
181C22×C101#46511yescharacteristic
182C22×C101#46711yescharacteristic
183C22×C101#47111yescharacteristic
184C22×C101#47211yescharacteristic
185C4×C101—21no—
186C4×C101—21no—
187C4×C101—42no—
188C4×C101—82no—
189C4×C101—161no—
190C4×C101C2×#10311yescharacteristic
191C4×C101#41611yescharacteristic
192C4×C101C4×SD1611yescharacteristic
193C4×C101#44011yescharacteristic
194C4×C101#45011yescharacteristic
195C4×C101#45211yescharacteristic
196C4×C101#46511yescharacteristic
197C4×C101#46711yescharacteristic
198#9215C10111yesmaximal, characteristic, direct product factor, Sylow
199C2×C101—44no—
200C2×C101#167111yescharacteristic
201C2×C101#167511yescharacteristic
202C2×C101#167711yescharacteristic
203C2×C101#168311yescharacteristic
204C2×C101#187711yescharacteristic
205C2×C101#189211yescharacteristic
206C2×C101#190711yescharacteristic
207C2×#476C2×C10111yescharacteristic
208C2×C8×D4C2×C10111yescharacteristic
209#1990C2×C10111yescharacteristic, complemented
210#1802C2×C10111yescharacteristic
211C2×#333C2×C10111yescharacteristic, complemented
212#1296C2×C10111yescharacteristic, complemented
213#1277C2×C10111yescharacteristic, complemented
214C101#921511yescharacteristic, direct product factor, Sylow
215C23×C8—21no—
216C2×C4⋊Q8C22×C10111yescharacteristic
217C2×C4×D4C22×C10111yescharacteristic
218#476—22no—
219#476C4×C10114yescomplemented
220C8×D4—22no—
221C8×D4—22no—
222C2×#106—21no—
223C2×C4⋊C8C22×C10111yescharacteristic
224C2×C4⋊C8C22×C10111yescharacteristic
225C2×C4⋊C8C22×C10111yescharacteristic
226C2×#102—21no—
227C2×#102—21no—
228C2×C22⋊C8—21no—
229C2×C4×C8C22×C10111yescharacteristic
230#384C22×C10111yescharacteristic
231#340—21no—
232#340—21no—
233#340—21no—
234#333—22no—
235C22×Q8—21no—
236C22×D4D4×C10111yescharacteristic
237C23×C4—21no—
238C22×C8—24no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—42no—
243C22×C8—42no—
244C22×C8D4×C10111yescharacteristic
245C22×C8D4×C10111yescharacteristic
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8C2×C4×C10112yes—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4C2×C4×C10112yes—
253C4×D4D4×C10112yes—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4D4×C10111yescharacteristic
260C2×C22⋊C4—21no—
261C2×C42C23×C10111yescharacteristic
262#106—24no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8C2×C4×C10112yes—
268C4⋊C8D4×C10112yes—
269#102—24no—
270#102—42no—
271C22⋊C8—24no—
272C4×C8—21no—
273C4×C8—21no—
274C24—21no—
275C2×Q8—22no—
276C2×Q8—41no—
277C2×Q8—81no—
278C2×Q8—81no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4C22⋊C4×C10112yes—
283C2×D4SD16×C10112yes—
284C2×D4Q16×C10112yes—
285C22×C4—21no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4C2×D4×C10111yescharacteristic
295C22×C4C2×D4×C10111yescharacteristic
296C22×C4#41×C10111yescharacteristic
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—22no—
300C2×C8—21no—
301C2×C8—22no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—48no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8SD16×C10112yes—
313C4⋊C4—21no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—81no—
323C4⋊C4C22⋊C4×C10112yes—
324C22⋊C4—22no—
325C22⋊C4—22no—
326C42C22×C4×C10111yescharacteristic
327C42C2×D4×C10111yescharacteristic
328C42C2×D4×C10111yescharacteristic
329C42#41×C10111yescharacteristic
330C23—22no—
331C23—22no—
332C23—22no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23#121×C10111yescharacteristic
338Q8—82no—
339Q8—82no—
340D4—22no—
341D4—22no—
342D4—22no—
343D4#103×C10114yes—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4C2×C22⋊C4×C10111yescharacteristic
360C2×C4C4×D4×C10111yescharacteristic
361C2×C4C4×D4×C10111yescharacteristic
362C2×C4#120×C10111yescharacteristic
363C2×C4#121×C10111yescharacteristic
364C2×C4#123×C10111yescharacteristic
365C2×C4C2×SD16×C10111yescharacteristic
366C2×C4C2×SD16×C10111yescharacteristic
367C2×C4C2×Q16×C10111yescharacteristic
368C2×C4#135×C10111yescharacteristic
369C2×C4#135×C10111yescharacteristic
370C2×C4#135×C10111yescharacteristic
371C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
372C2×C4#137×C10111yescharacteristic
373C8—22no—
374C8—42no—
375C8—42no—
376C8—41no—
377C8—81no—
378C22—24no—
379C22—42no—
380C22—42no—
381C22—42no—
382C22—42no—
383C22—42no—
384C22—42no—
385C22#386×C10111yescharacteristic
386C22#461×C10111yescharacteristic
387C22#463×C10111yescharacteristic
388C22#465×C10111yescharacteristic
389C22#467×C10111yescharacteristic
390C22#471×C10111yescharacteristic
391C22#472×C10111yescharacteristic
392C4—21no—
393C4—21no—
394C4—42no—
395C4—82no—
396C4—161no—
397C4C2×#103×C10111yescharacteristic
398C4#416×C10111yescharacteristic
399C4C4×SD16×C10111yescharacteristic
400C4#440×C10111yescharacteristic
401C4#450×C10111yescharacteristic
402C4#452×C10111yescharacteristic
403C4#465×C10111yescharacteristic
404C4#467×C10111yescharacteristic
405C2—44no—
406C2C101×#167111yescharacteristic
407C2C101×#167511yescharacteristic
408C2C101×#167711yescharacteristic
409C2C101×#168311yescharacteristic
410C2C101×#187711yescharacteristic
411C2C101×#189211yescharacteristic
412C2C101×#190711yescharacteristic
subgroupG/H
center, socleC23×C101#121
commutatorC42C22×C4×C101
Frattini, cosocleC2×C42C23×C101
prime radicalC22×D4×C101D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
3. C101×#1990C2semidirect
5. C2×#333×C101C2semidirect
6. C101×#1296C2semidirect
7. C101×#1277C2semidirect
12. #476×C101C4semidirect
198. #9215C101direct (N × H)
209. #1990C2×C101semidirect
211. C2×#333C2×C101semidirect
212. #1296C2×C101semidirect
213. #1277C2×C101semidirect
214. C101#9215direct (N × H)
219. #476C4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#476×C1012
C2×C8×D4×C1012
C101×#19902
C101×#18022
C2×#333×C1012
C101×#12962
C101×#12772
#9215101