Finite Group Databasebeta

← C2×C127×C22⋊#95 #44577424

Subgroups — C2×C127×C22⋊#95 #44577424

Order 32512.

7630 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×C4×C127C211yesmaximal, characteristic
2C23×C22⋊C4×C127C212yesmaximal
3C22×#95×C127C214yesmaximal, complemented
4C127×C22⋊#95C218yesmaximal, direct product factor
5C26×C127C2211yescharacteristic
6C24×C4×C127—28no—
7C24×C4×C127—216no—
8C24×C4×C127C418yescomplemented
9C24×C4×C127C2214yes—
10C24×C4×C127C2214yes—
11C24×C4×C127C2212yes—
12C22×C22⋊C4×C127—28no—
13C22×C22⋊C4×C127—28no—
14C22×C22⋊C4×C127C4116yescomplemented
15C22×C22⋊C4×C127C2218yes—
16C2×#95×C127—216no—
17C2×#95×C127C22116yescomplemented
18C25×C127—28no—
19C25×C127—28no—
20C25×C127C2×C418yes—
21C25×C127C2×C414yes—
22C25×C127D414yes—
23C25×C127D418yes—
24C25×C127Q814yes—
25C25×C127C2312yes—
26C25×C127C2311yescharacteristic
27C23×C4×C127—2128no—
28C23×C4×C127—232no—
29C23×C4×C127—216no—
30C23×C4×C127—28no—
31C23×C4×C127—28no—
32C23×C4×C127—264no—
33C23×C4×C127—232no—
34C23×C4×C127—28no—
35C23×C4×C127—28no—
36C23×C4×C127—216no—
37C23×C4×C127—216no—
38C23×C4×C127C2×C418yes—
39C23×C4×C127C2×C4116yescomplemented
40C23×C4×C127C2×C4116yescomplemented
41C23×C4×C127D4116yes—
42C23×C4×C127C2318yes—
43C23×C4×C127C2314yes—
44C2×C22⋊C4×C127—264no—
45C2×C22⋊C4×C127—216no—
46C2×C22⋊C4×C127—216no—
47C2×C22⋊C4×C127C2×C4132yescomplemented
48#95×C127—232no—
49C24×C127—216no—
50C24×C127—216no—
51C24×C127—264no—
52C24×C127—232no—
53C24×C127—232no—
54C24×C127—232no—
55C24×C127—232no—
56C24×C127—28no—
57C24×C127—28no—
58C24×C127C42116yes—
59C24×C127C22⋊C4132yes—
60C24×C127C22⋊C4116yes—
61C24×C127C4⋊C4116yes—
62C24×C127C4⋊C4132yes—
63C24×C127C22×C418yes—
64C24×C127C22×C414yes—
65C24×C127C22×C412yes—
66C24×C127C22×C414yes—
67C24×C127C2×D414yes—
68C24×C127C2×D418yes—
69C24×C127C2×D414yes—
70C24×C127C2×D412yes—
71C24×C127C2×D418yes—
72C24×C127C2×Q814yes—
73C24×C127C2×Q812yes—
74C24×C127#4118yes—
75C24×C127C2411yescharacteristic
76C22×C4×C127—2128no—
77C22×C4×C127—2256no—
78C22×C4×C127—216no—
79C22×C4×C127—216no—
80C22×C4×C127—232no—
81C22×C4×C127—264no—
82C22×C4×C127—28no—
83C22×C4×C127—28no—
84C22×C4×C127—264no—
85C22×C4×C127—232no—
86C22×C4×C127—264no—
87C22×C4×C127—216no—
88C22×C4×C127—28no—
89C22×C4×C127—28no—
90C22×C4×C127—216no—
91C22×C4×C127—416no—
92C22×C4×C127—432no—
93C22×C4×C127—416no—
94C22×C4×C127C22⋊C4132yescomplemented
95C22×C4×C127C22×C418yes—
96C22×C4×C127C22×C4116yescomplemented
97C22×C4×C127C2×D4116yes—
98C22⋊C4×C127—264no—
99C23×C127—28no—
100C23×C127—28no—
101C23×C127—232no—
102C23×C127—216no—
103C23×C127—216no—
104C23×C127—216no—
105C23×C127—216no—
106C23×C127—264no—
107C23×C127—232no—
108C23×C127—264no—
109C23×C127—232no—
110C23×C127—2128no—
111C23×C127—2128no—
112C23×C127#95164yescomplemented
113C23×C127C2×C4218yes—
114C23×C127C2×C4214yes—
115C23×C127C2×C22⋊C4116yes—
116C23×C127C2×C22⋊C418yes—
117C23×C127C2×C22⋊C414yes—
118C23×C127C2×C22⋊C418yes—
119C23×C127C2×C22⋊C418yes—
120C23×C127C2×C4⋊C418yes—
121C23×C127C2×C4⋊C4116yes—
122C23×C127C2×C4⋊C414yes—
123C23×C127C2×C4⋊C418yes—
124C23×C127#11718yes—
125C23×C127C4×D4132yes—
126C23×C127#120116yes—
127C23×C127#121116yes—
128C23×C127C22⋊Q8116yes—
129C23×C127#123116yes—
130C23×C127C23×C411yescharacteristic
131C23×C127C23×C412yes—
132C23×C127C22×D412yes—
133C23×C127C22×D411yescharacteristic
134C23×C127C22×D414yes—
135C23×C127C22×Q811yescharacteristic
136C23×C127C2×#4114yes—
137C2×C4×C127—2128no—
138C2×C4×C127—28no—
139C2×C4×C127—28no—
140C2×C4×C127—232no—
141C2×C4×C127—264no—
142C2×C4×C127—216no—
143C2×C4×C127—232no—
144C2×C4×C127—48no—
145C2×C4×C127—416no—
146C2×C4×C127—48no—
147C2×C4×C127—464no—
148C2×C4×C127C2×C22⋊C4116yescomplemented
149C22×C127—2128no—
150C22×C127—216no—
151C22×C127—28no—
152C22×C127—216no—
153C22×C127—28no—
154C22×C127—232no—
155C22×C127—232no—
156C22×C127C2×#9518yes—
157C22×C127C2×#95116yescomplemented
158C22×C127C4×C22⋊C4116yes—
159C22×C127#37918yes—
160C22×C127#380116yes—
161C22×C127#38118yes—
162C22×C127#385132yes—
163C22×C127#386132yes—
164C22×C127C22×C4211yescharacteristic
165C22×C127C22×C22⋊C411yescharacteristic
166C22×C127C22×C22⋊C412yes—
167C22×C127C22×C22⋊C412yes—
168C22×C127C22×C4⋊C411yescharacteristic
169C22×C127C22×C4⋊C412yes—
170C22×C127C2×#11712yes—
171C22×C127C2×C4×D418yes—
172C22×C127C2×#12014yes—
173C22×C127C2×#12114yes—
174C22×C127C2×C22⋊Q814yes—
175C22×C127C2×#12314yes—
176C4×C127—216no—
177C4×C127—416no—
178C2×C22⋊#95C12711yesmaximal, characteristic, direct product factor, Sylow
179C2×C127—216no—
180C2×C127C22⋊#95116yesdirect product factor
181C2×C127C22×#9511yescharacteristic
182C2×C127C2×C4×C22⋊C412yes—
183C2×C127C2×#37911yescharacteristic
184C2×C127C2×#38012yes—
185C2×C127C2×#38111yescharacteristic
186C2×C127C2×#38514yes—
187C2×C127C2×#38614yes—
188C25×C4C2×C12711yescharacteristic
189C23×C22⋊C4C2×C12712yes—
190C22×#95C2×C12714yescomplemented
191C22⋊#95C2×C12718yesdirect product factor
192C127C2×C22⋊#9511yescharacteristic, direct product factor, Sylow
193C26C22×C12711yescharacteristic
194C24×C4—28no—
195C24×C4—216no—
196C24×C4C4×C12718yescomplemented
197C24×C4C22×C12714yes—
198C24×C4C22×C12714yes—
199C24×C4C22×C12712yes—
200C22×C22⋊C4—28no—
201C22×C22⋊C4—28no—
202C22×C22⋊C4C4×C127116yescomplemented
203C22×C22⋊C4C22×C12718yes—
204C2×#95—216no—
205C2×#95C22×C127116yescomplemented
206C25—28no—
207C25—28no—
208C25C2×C4×C12718yes—
209C25C2×C4×C12714yes—
210C25D4×C12714yes—
211C25D4×C12718yes—
212C25Q8×C12714yes—
213C25C23×C12712yes—
214C25C23×C12711yescharacteristic
215C23×C4—2128no—
216C23×C4—232no—
217C23×C4—216no—
218C23×C4—28no—
219C23×C4—28no—
220C23×C4—264no—
221C23×C4—232no—
222C23×C4—28no—
223C23×C4—28no—
224C23×C4—216no—
225C23×C4—216no—
226C23×C4C2×C4×C12718yes—
227C23×C4C2×C4×C127116yescomplemented
228C23×C4C2×C4×C127116yescomplemented
229C23×C4D4×C127116yes—
230C23×C4C23×C12718yes—
231C23×C4C23×C12714yes—
232C2×C22⋊C4—264no—
233C2×C22⋊C4—216no—
234C2×C22⋊C4—216no—
235C2×C22⋊C4C2×C4×C127132yescomplemented
236#95—232no—
237C24—216no—
238C24—216no—
239C24—264no—
240C24—232no—
241C24—232no—
242C24—232no—
243C24—232no—
244C24—28no—
245C24—28no—
246C24C42×C127116yes—
247C24C22⋊C4×C127132yes—
248C24C22⋊C4×C127116yes—
249C24C4⋊C4×C127116yes—
250C24C4⋊C4×C127132yes—
251C24C22×C4×C12718yes—
252C24C22×C4×C12714yes—
253C24C22×C4×C12712yes—
254C24C22×C4×C12714yes—
255C24C2×D4×C12714yes—
256C24C2×D4×C12718yes—
257C24C2×D4×C12714yes—
258C24C2×D4×C12712yes—
259C24C2×D4×C12718yes—
260C24C2×Q8×C12714yes—
261C24C2×Q8×C12712yes—
262C24#41×C12718yes—
263C24C24×C12711yescharacteristic
264C22×C4—2128no—
265C22×C4—2256no—
266C22×C4—216no—
267C22×C4—216no—
268C22×C4—232no—
269C22×C4—264no—
270C22×C4—28no—
271C22×C4—28no—
272C22×C4—264no—
273C22×C4—232no—
274C22×C4—264no—
275C22×C4—216no—
276C22×C4—28no—
277C22×C4—28no—
278C22×C4—216no—
279C22×C4—416no—
280C22×C4—432no—
281C22×C4—416no—
282C22×C4C22⋊C4×C127132yescomplemented
283C22×C4C22×C4×C12718yes—
284C22×C4C22×C4×C127116yescomplemented
285C22×C4C2×D4×C127116yes—
286C22⋊C4—264no—
287C23—28no—
288C23—28no—
289C23—232no—
290C23—216no—
291C23—216no—
292C23—216no—
293C23—216no—
294C23—264no—
295C23—232no—
296C23—264no—
297C23—232no—
298C23—2128no—
299C23—2128no—
300C23#95×C127164yescomplemented
301C23C2×C42×C12718yes—
302C23C2×C42×C12714yes—
303C23C2×C22⋊C4×C127116yes—
304C23C2×C22⋊C4×C12718yes—
305C23C2×C22⋊C4×C12714yes—
306C23C2×C22⋊C4×C12718yes—
307C23C2×C22⋊C4×C12718yes—
308C23C2×C4⋊C4×C12718yes—
309C23C2×C4⋊C4×C127116yes—
310C23C2×C4⋊C4×C12714yes—
311C23C2×C4⋊C4×C12718yes—
312C23#117×C12718yes—
313C23C4×D4×C127132yes—
314C23#120×C127116yes—
315C23#121×C127116yes—
316C23C22⋊Q8×C127116yes—
317C23#123×C127116yes—
318C23C23×C4×C12711yescharacteristic
319C23C23×C4×C12712yes—
320C23C22×D4×C12712yes—
321C23C22×D4×C12711yescharacteristic
322C23C22×D4×C12714yes—
323C23C22×Q8×C12711yescharacteristic
324C23C2×#41×C12714yes—
325C2×C4—2128no—
326C2×C4—28no—
327C2×C4—28no—
328C2×C4—232no—
329C2×C4—264no—
330C2×C4—216no—
331C2×C4—232no—
332C2×C4—48no—
333C2×C4—416no—
334C2×C4—48no—
335C2×C4—464no—
336C2×C4C2×C22⋊C4×C127116yescomplemented
337C22—2128no—
338C22—216no—
339C22—28no—
340C22—216no—
341C22—28no—
342C22—232no—
343C22—232no—
344C22C2×#95×C12718yes—
345C22C2×#95×C127116yescomplemented
346C22C4×C22⋊C4×C127116yes—
347C22#379×C12718yes—
348C22#380×C127116yes—
349C22#381×C12718yes—
350C22#385×C127132yes—
351C22#386×C127132yes—
352C22C22×C42×C12711yescharacteristic
353C22C22×C22⋊C4×C12711yescharacteristic
354C22C22×C22⋊C4×C12712yes—
355C22C22×C22⋊C4×C12712yes—
356C22C22×C4⋊C4×C12711yescharacteristic
357C22C22×C4⋊C4×C12712yes—
358C22C2×#117×C12712yes—
359C22C2×C4×D4×C12718yes—
360C22C2×#120×C12714yes—
361C22C2×#121×C12714yes—
362C22C2×C22⋊Q8×C12714yes—
363C22C2×#123×C12714yes—
364C4—216no—
365C4—416no—
366C2—216no—
367C2C127×C22⋊#95116yesdirect product factor
368C2C22×#95×C12711yescharacteristic
369C2C2×C4×C22⋊C4×C12712yes—
370C2C2×#379×C12711yescharacteristic
371C2C2×#380×C12712yes—
372C2C2×#381×C12711yescharacteristic
373C2C2×#385×C12714yes—
374C2C2×#386×C12714yes—
subgroupG/H
center, socleC25×C127C23
commutatorC22C22×C42×C127
Frattini, cosocleC24C24×C127
prime radicalC26×C127C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C25×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C22×#95×C127C2semidirect
4. C127×C22⋊#95C2direct (N × H)
8. C24×C4×C127C4semidirect
14. C22×C22⋊C4×C127C4semidirect
17. C2×#95×C127C22semidirect
39. C23×C4×C127C2×C4semidirect
40. C23×C4×C127C2×C4semidirect
47. C2×C22⋊C4×C127C2×C4semidirect
94. C22×C4×C127C22⋊C4semidirect
96. C22×C4×C127C22×C4semidirect
112. C23×C127#95semidirect
148. C2×C4×C127C2×C22⋊C4semidirect
157. C22×C127C2×#95semidirect
178. C2×C22⋊#95C127direct (N × H)
180. C2×C127C22⋊#95direct (N × H)
190. C22×#95C2×C127semidirect
191. C22⋊#95C2×C127direct (N × H)
192. C127C2×C22⋊#95direct (N × H)
196. C24×C4C4×C127semidirect
202. C22×C22⋊C4C4×C127semidirect
205. C2×#95C22×C127semidirect
227. C23×C4C2×C4×C127semidirect
228. C23×C4C2×C4×C127semidirect
235. C2×C22⋊C4C2×C4×C127semidirect
282. C22×C4C22⋊C4×C127semidirect
284. C22×C4C22×C4×C127semidirect
300. C23#95×C127semidirect
336. C2×C4C2×C22⋊C4×C127semidirect
345. C22C2×#95×C127semidirect
367. C2C127×C22⋊#95direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C4×C1272
C23×C22⋊C4×C1272
C22×#95×C1272
C127×C22⋊#952
C2×C22⋊#95127