Finite Group Databasebeta

← C101×#13305 #38795456

Subgroups — C101×#13305 #38795456

Order 25856.

618 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×SD32×C101C211yesmaximal, characteristic, complemented
2C2×#467×C101C211yesmaximal, characteristic, complemented
3C2×#466×C101C211yesmaximal, characteristic
4C2×#358×C101C211yesmaximal, characteristic, complemented
5C2×#357×C101C211yesmaximal, characteristic, complemented
6C2×C22⋊C16×C101C211yesmaximal, characteristic, complemented
7C101×#1380C211yesmaximal, characteristic, complemented
8C22×Q16×C101C2211yescharacteristic
9C22×D8×C101C2211yescharacteristic
10C23×C8×C101C2211yescharacteristic
11C2×C22⋊Q8×C101—21no—
12C2×#121×C101—21no—
13C2×SD32×C101—22no—
14C2×SD32×C101—22no—
15C2×SD32×C101—22no—
16C22×C16×C101C2211yescharacteristic
17C22×C16×C101C2211yescharacteristic
18#467×C101—22no—
19#467×C101—22no—
20#466×C101—22no—
21#466×C101—22no—
22C2×#107×C101C2211yescharacteristic
23C2×#107×C101C2211yescharacteristic
24C2×#103×C101—21no—
25C2×#102×C101—21no—
26#358×C101—22no—
27#357×C101—22no—
28C22⋊C16×C101—22no—
29C22×Q8×C101—21no—
30C22×D4×C101—21no—
31C22×D4×C101—41no—
32C23×C4×C101D411yescharacteristic
33C2×Q16×C101—21no—
34C2×Q16×C101—21no—
35C2×Q16×C101—21no—
36C2×Q16×C101—21no—
37C2×Q16×C101—21no—
38C2×Q16×C101D412yescomplemented
39C2×D8×C101—21no—
40C2×D8×C101—21no—
41C2×D8×C101—21no—
42C2×D8×C101—21no—
43C2×D8×C101—21no—
44C2×D8×C101D412yes—
45C22×C8×C101—21no—
46C22×C8×C101—21no—
47C22×C8×C101—21no—
48C22×C8×C101—21no—
49C22×C8×C101—21no—
50C22×C8×C101—21no—
51C22×C8×C101D411yescharacteristic
52C22×C8×C101C2311yescharacteristic
53C22⋊Q8×C101—24no—
54C22⋊Q8×C101—42no—
55#121×C101—24no—
56#121×C101—42no—
57C2×C4⋊C4×C101—21no—
58C2×C4⋊C4×C101—21no—
59C2×C4⋊C4×C101—41no—
60C2×C22⋊C4×C101—41no—
61C2×C22⋊C4×C101—41no—
62SD32×C101—28no—
63C2×C16×C101—21no—
64C2×C16×C101—21no—
65C2×C16×C101—21no—
66C2×C16×C101—21no—
67C2×C16×C101—21no—
68C2×C16×C101D412yescomplemented
69#107×C101—21no—
70#107×C101—21no—
71#107×C101D412yes—
72#107×C101D412yescomplemented
73#103×C101—24no—
74#102×C101—24no—
75C24×C101—41no—
76C24×C101D811yescharacteristic
77C2×Q8×C101—22no—
78C2×Q8×C101—41no—
79C2×Q8×C101—41no—
80C2×Q8×C101—41no—
81C2×Q8×C101—41no—
82C2×Q8×C101—41no—
83C2×D4×C101—22no—
84C2×D4×C101—44no—
85C2×D4×C101—41no—
86C2×D4×C101—41no—
87C2×D4×C101—41no—
88C2×D4×C101—41no—
89C2×D4×C101—41no—
90C2×D4×C101—82no—
91C2×D4×C101—82no—
92C22×C4×C101—21no—
93C22×C4×C101—21no—
94C22×C4×C101—21no—
95C22×C4×C101—21no—
96C22×C4×C101—21no—
97C22×C4×C101—21no—
98C22×C4×C101—41no—
99C22×C4×C101—41no—
100C22×C4×C101—41no—
101C22×C4×C101D811yescharacteristic
102C22×C4×C101C2×D411yescharacteristic
103Q16×C101—22no—
104Q16×C101—22no—
105Q16×C101—41no—
106Q16×C101—41no—
107D8×C101—22no—
108D8×C101—22no—
109D8×C101—41no—
110D8×C101—41no—
111C2×C8×C101—21no—
112C2×C8×C101—21no—
113C2×C8×C101—21no—
114C2×C8×C101—41no—
115C2×C8×C101—41no—
116C2×C8×C101—41no—
117C2×C8×C101—41no—
118C2×C8×C101C2×D411yescharacteristic
119C2×C8×C101C2×D411yescharacteristic
120C2×C8×C101C2×D411yescharacteristic
121C2×C8×C101C2×D411yescharacteristic
122C2×C8×C101C2×D411yescharacteristic
123C2×C8×C101#4111yescharacteristic
124C4⋊C4×C101—22no—
125C4⋊C4×C101—22no—
126C4⋊C4×C101—44no—
127C4⋊C4×C101—41no—
128C4⋊C4×C101—41no—
129C22⋊C4×C101—44no—
130C22⋊C4×C101—44no—
131C16×C101—22no—
132C16×C101—41no—
133C23×C101—21no—
134C23×C101—21no—
135C23×C101—21no—
136C23×C101—21no—
137C23×C101—21no—
138C23×C101—21no—
139C23×C101—42no—
140C23×C101—81no—
141C23×C101—81no—
142C23×C101—81no—
143C23×C101—81no—
144C23×C101—81no—
145C23×C101—81no—
146C23×C101SD3212yescomplemented
147C23×C101C2×D811yescharacteristic
148Q8×C101—42no—
149Q8×C101—42no—
150Q8×C101—81no—
151Q8×C101—81no—
152D4×C101—42no—
153D4×C101—42no—
154D4×C101—88no—
155D4×C101—81no—
156D4×C101—81no—
157C2×C4×C101—21no—
158C2×C4×C101—21no—
159C2×C4×C101—21no—
160C2×C4×C101—41no—
161C2×C4×C101—41no—
162C2×C4×C101—41no—
163C2×C4×C101—41no—
164C2×C4×C101—42no—
165C2×C4×C101—42no—
166C2×C4×C101—42no—
167C2×C4×C101—81no—
168C2×C4×C101—81no—
169C2×C4×C101—81no—
170C2×C4×C101—81no—
171C2×C4×C101—81no—
172C2×C4×C101—81no—
173C2×C4×C101#12011yescharacteristic
174C2×C4×C101#12011yescharacteristic
175C2×C4×C101#12111yescharacteristic
176C2×C4×C101#13511yescharacteristic
177C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
179C8×C101—41no—
180C8×C101#12011yescharacteristic
181C8×C101#12111yescharacteristic
182C8×C101#12111yescharacteristic
183C8×C101#12711yescharacteristic
184C22×C101—22no—
185C22×C101—22no—
186C22×C101—22no—
187C22×C101—41no—
188C22×C101—41no—
189C22×C101—41no—
190C22×C101—41no—
191C22×C101—82no—
192C22×C101—82no—
193C22×C101—82no—
194C22×C101—161no—
195C22×C101—161no—
196C22×C101—161no—
197C22×C101—161no—
198C22×C101#44711yescharacteristic
199C22×C101#44711yescharacteristic
200C22×C101#46611yescharacteristic
201C22×C101C2×SD3211yescharacteristic
202C22×C101#50811yescharacteristic
203C22×C101#50911yescharacteristic
204C22×C101#51011yescharacteristic
205C4×C101—41no—
206C4×C101—82no—
207C4×C101—82no—
208C4×C101—82no—
209C4×C101#39211yescharacteristic
210C4×C101#44911yescharacteristic
211C4×C101#44911yescharacteristic
212C4×C101#46911yescharacteristic
213#13305C10111yesmaximal, characteristic, direct product factor, Sylow
214C2×C101—42no—
215C2×C101—162no—
216C2×C101#199911yescharacteristic
217C2×C101#218511yescharacteristic
218C2×C101#218611yescharacteristic
219C2×C101#218711yescharacteristic
220C2×C101#218911yescharacteristic
221C2×C101#221711yescharacteristic
222C2×C101#222011yescharacteristic
223C22×SD32C2×C10111yescharacteristic, complemented
224C2×#467C2×C10111yescharacteristic, complemented
225C2×#466C2×C10111yescharacteristic
226C2×#358C2×C10111yescharacteristic, complemented
227C2×#357C2×C10111yescharacteristic, complemented
228C2×C22⋊C16C2×C10111yescharacteristic, complemented
229#1380C2×C10111yescharacteristic, complemented
230C101#1330511yescharacteristic, direct product factor, Sylow
231C22×Q16C22×C10111yescharacteristic
232C22×D8C22×C10111yescharacteristic
233C23×C8C22×C10111yescharacteristic
234C2×C22⋊Q8—21no—
235C2×#121—21no—
236C2×SD32—22no—
237C2×SD32—22no—
238C2×SD32—22no—
239C22×C16C22×C10111yescharacteristic
240C22×C16C22×C10111yescharacteristic
241#467—22no—
242#467—22no—
243#466—22no—
244#466—22no—
245C2×#107C22×C10111yescharacteristic
246C2×#107C22×C10111yescharacteristic
247C2×#103—21no—
248C2×#102—21no—
249#358—22no—
250#357—22no—
251C22⋊C16—22no—
252C22×Q8—21no—
253C22×D4—21no—
254C22×D4—41no—
255C23×C4D4×C10111yescharacteristic
256C2×Q16—21no—
257C2×Q16—21no—
258C2×Q16—21no—
259C2×Q16—21no—
260C2×Q16—21no—
261C2×Q16D4×C10112yescomplemented
262C2×D8—21no—
263C2×D8—21no—
264C2×D8—21no—
265C2×D8—21no—
266C2×D8—21no—
267C2×D8D4×C10112yes—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8D4×C10111yescharacteristic
275C22×C8C23×C10111yescharacteristic
276C22⋊Q8—24no—
277C22⋊Q8—42no—
278#121—24no—
279#121—42no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—41no—
283C2×C22⋊C4—41no—
284C2×C22⋊C4—41no—
285SD32—28no—
286C2×C16—21no—
287C2×C16—21no—
288C2×C16—21no—
289C2×C16—21no—
290C2×C16—21no—
291C2×C16D4×C10112yescomplemented
292#107—21no—
293#107—21no—
294#107D4×C10112yes—
295#107D4×C10112yescomplemented
296#103—24no—
297#102—24no—
298C24—41no—
299C24D8×C10111yescharacteristic
300C2×Q8—22no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×D4—22no—
307C2×D4—44no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—82no—
314C2×D4—82no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4D8×C10111yescharacteristic
325C22×C4C2×D4×C10111yescharacteristic
326Q16—22no—
327Q16—22no—
328Q16—41no—
329Q16—41no—
330D8—22no—
331D8—22no—
332D8—41no—
333D8—41no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—21no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8C2×D4×C10111yescharacteristic
342C2×C8C2×D4×C10111yescharacteristic
343C2×C8C2×D4×C10111yescharacteristic
344C2×C8C2×D4×C10111yescharacteristic
345C2×C8C2×D4×C10111yescharacteristic
346C2×C8#41×C10111yescharacteristic
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—44no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C22⋊C4—44no—
353C22⋊C4—44no—
354C16—22no—
355C16—41no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—42no—
363C23—81no—
364C23—81no—
365C23—81no—
366C23—81no—
367C23—81no—
368C23—81no—
369C23SD32×C10112yescomplemented
370C23C2×D8×C10111yescharacteristic
371Q8—42no—
372Q8—42no—
373Q8—81no—
374Q8—81no—
375D4—42no—
376D4—42no—
377D4—88no—
378D4—81no—
379D4—81no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4#120×C10111yescharacteristic
397C2×C4#120×C10111yescharacteristic
398C2×C4#121×C10111yescharacteristic
399C2×C4#135×C10111yescharacteristic
400C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
401C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
402C8—41no—
403C8#120×C10111yescharacteristic
404C8#121×C10111yescharacteristic
405C8#121×C10111yescharacteristic
406C8#127×C10111yescharacteristic
407C22—22no—
408C22—22no—
409C22—22no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—82no—
415C22—82no—
416C22—82no—
417C22—161no—
418C22—161no—
419C22—161no—
420C22—161no—
421C22#447×C10111yescharacteristic
422C22#447×C10111yescharacteristic
423C22#466×C10111yescharacteristic
424C22C2×SD32×C10111yescharacteristic
425C22#508×C10111yescharacteristic
426C22#509×C10111yescharacteristic
427C22#510×C10111yescharacteristic
428C4—41no—
429C4—82no—
430C4—82no—
431C4—82no—
432C4#392×C10111yescharacteristic
433C4#449×C10111yescharacteristic
434C4#449×C10111yescharacteristic
435C4#469×C10111yescharacteristic
436C2—42no—
437C2—162no—
438C2C101×#199911yescharacteristic
439C2C101×#218511yescharacteristic
440C2C101×#218611yescharacteristic
441C2C101×#218711yescharacteristic
442C2C101×#218911yescharacteristic
443C2C101×#221711yescharacteristic
444C2C101×#222011yescharacteristic
subgroupG/H
center, socleC23×C101C2×D8
commutator, Frattini, cosocleC22×C8C23×C101
prime radicalC2×#466×C101C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C23×C4×C101 ◁ C23×C8×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×SD32×C101C2semidirect
2. C2×#467×C101C2semidirect
4. C2×#358×C101C2semidirect
5. C2×#357×C101C2semidirect
6. C2×C22⋊C16×C101C2semidirect
7. C101×#1380C2semidirect
38. C2×Q16×C101D4semidirect
68. C2×C16×C101D4semidirect
72. #107×C101D4semidirect
146. C23×C101SD32semidirect
213. #13305C101direct (N × H)
223. C22×SD32C2×C101semidirect
224. C2×#467C2×C101semidirect
226. C2×#358C2×C101semidirect
227. C2×#357C2×C101semidirect
228. C2×C22⋊C16C2×C101semidirect
229. #1380C2×C101semidirect
230. C101#13305direct (N × H)
261. C2×Q16D4×C101semidirect
291. C2×C16D4×C101semidirect
295. #107D4×C101semidirect
369. C23SD32×C101semidirect

Maximal subgroups

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

subgroupindex
C22×SD32×C1012
C2×#467×C1012
C2×#466×C1012
C2×#358×C1012
C2×#357×C1012
C2×C22⋊C16×C1012
C101×#13802
#13305101