Finite Group Databasebeta

← C2×#14271041 #16821909

Subgroups — C2×#14271041 #16821909

Order 3712.

1576 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D116C211yesmaximal, characteristic
2C23×C4×D29C211yesmaximal, characteristic, complemented
3C22×#90781C211yesmaximal, characteristic, complemented
4C22×#90781C211yesmaximal, characteristic, complemented
5C22×#90781C211yesmaximal, characteristic, complemented
6#14271041C218yesmaximal, direct product factor
7C2×#11745179C211yesmaximal, characteristic, complemented
8C2×C29×#95C211yesmaximal, characteristic, complemented
9C24×D29C2211yescharacteristic
10C24×D29C2211yescharacteristic
11C23×C4×C29C2211yescharacteristic
12C23×C4×C29C2211yescharacteristic
13C23×C4×C29C2211yescharacteristic
14C23×Dic29C2211yescharacteristic
15C23×Dic29C2211yescharacteristic
16C22×D116—24no—
17C22×D116—24no—
18C22×D116C418yescomplemented
19C22×D116C2214yes—
20C22×C4×D29—24no—
21C22×C4×D29—24no—
22C22×C4×D29—24no—
23C22×C4×D29C2214yescomplemented
24C2×#90781—24no—
25C2×#90781—24no—
26C2×#90781—24no—
27C2×#90781C2214yescomplemented
28C2×#90781C2214yescomplemented
29C2×#90781C2214yescomplemented
30C29×#95C2214yescomplemented
31#11745179C2214yescomplemented
32C24×C29C2311yescharacteristic
33C23×D29—22no—
34C23×D29—22no—
35C23×D29—22no—
36C23×D29—22no—
37C23×D29—22no—
38C23×D29—22no—
39C23×D29—22no—
40C23×D29—22no—
41C23×D29—22no—
42C23×D29—22no—
43C23×D29C2×C414yes—
44C23×D29C2×C414yescomplemented
45C23×D29D414yes—
46C23×D29D414yes—
47C23×D29C2312yes—
48C23×D29C2312yes—
49C22×C4×C29—22no—
50C22×C4×C29—22no—
51C22×C4×C29—22no—
52C22×C4×C29—22no—
53C22×C4×C29—22no—
54C22×C4×C29—22no—
55C22×C4×C29—22no—
56C22×C4×C29C2×C414yescomplemented
57C22×C4×C29D414yescomplemented
58C22×C4×C29C2312yes—
59C22×C4×C29C2312yes—
60C22×C4×C29C2312yes—
61C22×Dic29—22no—
62C22×Dic29—22no—
63C22×Dic29—22no—
64C22×Dic29—22no—
65C22×Dic29—22no—
66C22×Dic29D414yescomplemented
67C22×Dic29C2312yes—
68C22×Dic29C2312yes—
69C2×D116—232no—
70C2×D116—28no—
71C2×D116—28no—
72C2×D116C2×C4116yescomplemented
73C2×C4×D29—232no—
74C2×C4×D29—28no—
75C2×C4×D29—28no—
76C2×C4×D29—28no—
77#90781—28no—
78#90781—28no—
79#90781—28no—
80C23×C29C22×C412yes—
81C23×C29C2×D412yes—
82C23×C29C2×D412yes—
83C23×C29C2×D412yes—
84C23×C29C2×D412yes—
85C23×C29#4112yes—
86C23×C29#4112yes—
87C23×C29C2411yescharacteristic
88C22×D29—28no—
89C22×D29—28no—
90C22×D29—28no—
91C22×D29—28no—
92C22×D29—28no—
93C22×D29—28no—
94C22×D29—22no—
95C22×D29—22no—
96C22×D29—22no—
97C22×D29—22no—
98C22×D29—28no—
99C22×D29—28no—
100C22×D29—28no—
101C22×D29—22no—
102C22×D29—22no—
103C22×D29—22no—
104C22×D29—22no—
105C22×D29—22no—
106C22×D29—22no—
107C22×D29—44no—
108C22×D29—44no—
109C22×D29—44no—
110C22×D29—44no—
111C22×D29C22⋊C4116yescomplemented
112C22×D29C22×C414yes—
113C22×D29C22×C414yescomplemented
114C22×D29C2×D414yes—
115C22×D29C2×D414yes—
116C2×C4×C29—28no—
117C2×C4×C29—28no—
118C2×C4×C29—22no—
119C2×C4×C29—22no—
120C2×C4×C29—22no—
121C2×C4×C29—22no—
122C2×C4×C29—22no—
123C2×C4×C29—22no—
124C2×C4×C29—22no—
125C2×C4×C29—44no—
126C2×C4×C29C22×C414yescomplemented
127C2×C4×C29C2×D414yescomplemented
128C2×Dic29—28no—
129C2×Dic29—22no—
130C2×Dic29—22no—
131C2×Dic29—22no—
132C2×Dic29—22no—
133C2×Dic29—22no—
134C2×Dic29—44no—
135C2×Dic29C2×D414yescomplemented
136D116—232no—
137C4×D29—232no—
138C2×#386—291nomaximal, Sylow
139C22×C29C2×C22⋊C414yes—
140C22×C29C4×D414yes—
141C22×C29C4×D414yes—
142C22×C29#12014yes—
143C22×C29#12114yes—
144C22×C29#12114yes—
145C22×C29#12314yes—
146C22×C29C23×C411yescharacteristic
147C22×C29C22×D411yescharacteristic
148C22×C29C22×D411yescharacteristic
149C22×C29C22×D411yescharacteristic
150C22×C29C22×D411yescharacteristic
151C22×C29C2×#4111yescharacteristic
152C22×C29C2×#4111yescharacteristic
153C2×D29—24no—
154C2×D29—24no—
155C2×D29—24no—
156C2×D29—24no—
157C2×D29—24no—
158C2×D29—24no—
159C2×D29—232no—
160C2×D29—24no—
161C2×D29—24no—
162C2×D29—24no—
163C2×D29—42no—
164C2×D29—42no—
165C2×D29—42no—
166C2×D29—42no—
167C2×D29—416no—
168C2×D29C2×C22⋊C418yescomplemented
169C4×C29—24no—
170C4×C29—24no—
171C4×C29—42no—
172Dic29—24no—
173Dic29—42no—
174C23×D4—291no—
175C24×C4—291no—
176C22×C22⋊C4—291no—
177C22×C22⋊C4—291no—
178C22×C22⋊C4—291no—
179#386—298no—
180C2×#95—291no—
181C2×#95D2911yescharacteristic, complemented
182C2×C29#38618yescomplemented
183C2×C29C22×C22⋊C411yescharacteristic
184C2×C29C2×C4×D411yescharacteristic
185C2×C29C2×C4×D411yescharacteristic
186C2×C29C2×#12011yescharacteristic
187C2×C29C2×#12111yescharacteristic
188C2×C29C2×#12111yescharacteristic
189C2×C29C2×#12311yescharacteristic
190D29—28no—
191D29—44no—
192C25—291no—
193C25—291no—
194C22×D4—298no—
195C22×D4—294no—
196C22×D4—584no—
197C22×D4—584no—
198C23×C4—291no—
199C23×C4—291no—
200C23×C4—294no—
201C23×C4—584no—
202C23×C4—584no—
203C23×C4—584no—
204C23×C4C2×D2911yescharacteristic
205C23×C4C2×D2911yescharacteristic
206C23×C4C2×D2911yescharacteristic
207C2×C22⋊C4—294no—
208C2×C22⋊C4—294no—
209C2×C22⋊C4—294no—
210C2×C22⋊C4—584no—
211C2×C22⋊C4—584no—
212C2×C22⋊C4—584no—
213#95—294no—
214#95C2×D2914yescomplemented
215C29C2×#38611yescharacteristic, complemented, Sylow
216C24—294no—
217C24—294no—
218C24—294no—
219C24—292no—
220C24—294no—
221C24—292no—
222C24—582no—
223C24—582no—
224C24—582no—
225C24—582no—
226C24—582no—
227C24—582no—
228C24—582no—
229C24—582no—
230C24—582no—
231C24—582no—
232C24C22×D2911yescharacteristic
233C2×D4—2916no—
234C2×D4—588no—
235C2×D4—588no—
236C2×D4—5832no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—294no—
245C22×C4—292no—
246C22×C4—292no—
247C22×C4—588no—
248C22×C4—588no—
249C22×C4—5832no—
250C22×C4—582no—
251C22×C4—582no—
252C22×C4—588no—
253C22×C4—582no—
254C22×C4—582no—
255C22×C4—582no—
256C22×C4C4×D2914yescomplemented
257C22×C4D11614yescomplemented
258C22×C4C22×D2912yes—
259C22×C4C22×D2912yes—
260C22×C4C22×D2912yes—
261C22⋊C4—588no—
262C22⋊C4—588no—
263C22⋊C4—588no—
264C23—294no—
265C23—294no—
266C23—294no—
267C23—2916no—
268C23—294no—
269C23—582no—
270C23—582no—
271C23—582no—
272C23—582no—
273C23—588no—
274C23—588no—
275C23—588no—
276C23—588no—
277C23—588no—
278C23—588no—
279C23—582no—
280C23—582no—
281C23—582no—
282C23—582no—
283C23—582no—
284C23—582no—
285C23—588no—
286C23—588no—
287C23—588no—
288C23—1164no—
289C23—1164no—
290C23—1164no—
291C23—1164no—
292C23C2×C4×D2912yes—
293C23C2×D11612yes—
294C23#9080512yes—
295C23D4×D2912yes—
296C23D4×D2912yes—
297C23D4×D2912yes—
298C23#9080912yes—
299C23C23×D2911yescharacteristic
300D4—5832no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—28no—
306C2×C4—28no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—44no—
311C2×C4—294no—
312C2×C4—5832no—
313C2×C4—582no—
314C2×C4—582no—
315C2×C4—588no—
316C2×C4—582no—
317C2×C4—582no—
318C2×C4—582no—
319C2×C4—1164no—
320C2×C4C2×C4×D2914yescomplemented
321C2×C4C2×D11614yescomplemented
322C22—298no—
323C22—5832no—
324C22—584no—
325C22—584no—
326C22—584no—
327C22—584no—
328C22—584no—
329C22—584no—
330C22—584no—
331C22—584no—
332C22—584no—
333C22—11616no—
334C22—1162no—
335C22—1162no—
336C22—1162no—
337C22—1162no—
338C22C4×D11614yes—
339C22C22⋊C4×D2914yes—
340C22#1174524414yes—
341C22#1174524614yes—
342C22#1174525514yes—
343C22#1174525614yes—
344C22#1174525714yes—
345C22C22×C4×D2911yescharacteristic
346C22C22×D11611yescharacteristic
347C22C2×#9080511yescharacteristic
348C22C2×D4×D2911yescharacteristic
349C22C2×D4×D2911yescharacteristic
350C22C2×D4×D2911yescharacteristic
351C22C2×#9080911yescharacteristic
352C4—24no—
353C4—24no—
354C4—42no—
355C4—584no—
356C4—1162no—
357C2—588no—
358C2—1164no—
359C2#1427104118yesdirect product factor
360C2C2×C22⋊C4×D2911yescharacteristic
361C2C2×#1174525511yescharacteristic
362C2C2×C4×D11611yescharacteristic
363C2C2×#1174524411yescharacteristic
364C2C2×#1174524611yescharacteristic
365C2C2×#1174525711yescharacteristic
366C2C2×#1174525611yescharacteristic
subgroupG/H
centerC24C22×D29
commutatorC22×C29C23×C4
FrattiniC23C23×D29
FittingC2×C29×#95C2
socleC24×C29C23
prime radicalC23×D116C2
cosocleC23×C29C24
hypercenterC2×#95D29
hypocenterC29C2×#386
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
2. C23×C4×D29C2semidirect
3. C22×#90781C2semidirect
4. C22×#90781C2semidirect
5. C22×#90781C2semidirect
6. #14271041C2direct (N × H)
7. C2×#11745179C2semidirect
8. C2×C29×#95C2semidirect
18. C22×D116C4semidirect
23. C22×C4×D29C22semidirect
27. C2×#90781C22semidirect
28. C2×#90781C22semidirect
29. C2×#90781C22semidirect
30. C29×#95C22semidirect
31. #11745179C22semidirect
44. C23×D29C2×C4semidirect
56. C22×C4×C29C2×C4semidirect
57. C22×C4×C29D4semidirect
66. C22×Dic29D4semidirect
72. C2×D116C2×C4semidirect
111. C22×D29C22⋊C4semidirect
113. C22×D29C22×C4semidirect
126. C2×C4×C29C22×C4semidirect
127. C2×C4×C29C2×D4semidirect
135. C2×Dic29C2×D4semidirect
168. C2×D29C2×C22⋊C4semidirect
181. C2×#95D29semidirect
182. C2×C29#386semidirect
214. #95C2×D29semidirect
215. C29C2×#386semidirect
256. C22×C4C4×D29semidirect
257. C22×C4D116semidirect
320. C2×C4C2×C4×D29semidirect
321. C2×C4C2×D116semidirect
359. C2#14271041direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D1162
C23×C4×D292
C22×#907812
#142710412
C2×#117451792
C2×C29×#952
C2×#38629