Finite Group Databasebeta

← C2×#14271063 #16821946

Subgroups — C2×#14271063 #16821946

Order 3712.

1360 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊D29C211yesmaximal, characteristic
2C22×#90779C211yesmaximal, characteristic, complemented
3C22×C22⋊Dic29C211yesmaximal, characteristic, complemented
4C22×#90781C211yesmaximal, characteristic, complemented
5C22×#90781C211yesmaximal, characteristic, complemented
6C22×C4×Dic29C211yesmaximal, characteristic, complemented
7#14271063C218yesmaximal, direct product factor
8C22×C22⋊C4×C29C211yesmaximal, characteristic, complemented
9C25×C29C2211yescharacteristic
10C24×D29C2211yescharacteristic
11C23×C4×C29C2211yescharacteristic
12C23×C4×C29C2211yescharacteristic
13C22×C22⋊D29—24no—
14C22×C22⋊D29—24no—
15C22×C22⋊D29C418yescomplemented
16C22×C22⋊D29C2214yes—
17C23×Dic29C2211yescharacteristic
18C23×Dic29C2211yescharacteristic
19C23×Dic29C2211yescharacteristic
20C2×C22⋊C4×C29—24no—
21C2×C22⋊C4×C29C2214yescomplemented
22C2×C22⋊Dic29—24no—
23C2×C22⋊Dic29C2214yescomplemented
24C2×#90781—24no—
25C2×#90781—24no—
26C2×#90781C2214yescomplemented
27C2×#90781C2214yescomplemented
28C2×#90779—24no—
29C2×#90779C2214yescomplemented
30C2×C4×Dic29—24no—
31C2×C4×Dic29C2214yescomplemented
32C24×C29—22no—
33C24×C29—22no—
34C24×C29—22no—
35C24×C29—22no—
36C24×C29—22no—
37C24×C29—22no—
38C24×C29C2×C414yes—
39C24×C29C2312yes—
40C24×C29C2311yescharacteristic
41C23×D29—22no—
42C23×D29—22no—
43C23×D29—22no—
44C23×D29—22no—
45C23×D29—22no—
46C23×D29—22no—
47C23×D29C2×C414yes—
48C23×D29C2312yes—
49C22×C4×C29—22no—
50C22×C4×C29—22no—
51C22×C4×C29—22no—
52C22×C4×C29—22no—
53C22×C4×C29—22no—
54C22×C4×C29D414yescomplemented
55C22×C4×C29C2312yes—
56C22×C4×C29C2312yes—
57C2×C22⋊D29—232no—
58C2×C22⋊D29—28no—
59C2×C22⋊D29—28no—
60C2×C22⋊D29C2×C4116yescomplemented
61C22×Dic29—22no—
62C22×Dic29—22no—
63C22×Dic29—22no—
64C22×Dic29—22no—
65C22×Dic29—22no—
66C22×Dic29C2×C414yes—
67C22×Dic29D414yes—
68C22×Dic29D414yes—
69C22×Dic29D414yescomplemented
70C22×Dic29C2312yes—
71C22×Dic29C2312yes—
72C22×Dic29C2312yes—
73C22⋊C4×C29—28no—
74C22⋊Dic29—28no—
75#90781—28no—
76#90781—28no—
77#90779—28no—
78C4×Dic29—28no—
79C23×C29—28no—
80C23×C29—28no—
81C23×C29—28no—
82C23×C29—22no—
83C23×C29—22no—
84C23×C29—22no—
85C23×C29—22no—
86C23×C29—22no—
87C23×C29—22no—
88C23×C29—44no—
89C23×C29—44no—
90C23×C29—44no—
91C23×C29—44no—
92C23×C29C22×C414yes—
93C23×C29C22×C412yes—
94C23×C29C2×D412yes—
95C23×C29C2×D412yes—
96C23×C29C2×D412yes—
97C23×C29C2×D412yes—
98C23×C29#4112yes—
99C23×C29#4112yes—
100C23×C29C2411yescharacteristic
101C22×D29—28no—
102C22×D29—28no—
103C22×D29—28no—
104C22×D29—22no—
105C22×D29—22no—
106C22×D29—22no—
107C22×D29—22no—
108C22×D29—22no—
109C22×D29—22no—
110C22×D29—44no—
111C22×D29—44no—
112C22×D29—44no—
113C22×D29—44no—
114C22×D29C22×C414yes—
115C2×C4×C29—28no—
116C2×C4×C29—22no—
117C2×C4×C29—22no—
118C2×C4×C29—22no—
119C2×C4×C29—22no—
120C2×C4×C29—22no—
121C2×C4×C29—44no—
122C2×C4×C29C2×D414yescomplemented
123C22⋊D29—232no—
124C2×Dic29—28no—
125C2×Dic29—22no—
126C2×Dic29—22no—
127C2×Dic29—22no—
128C2×Dic29—22no—
129C2×Dic29—22no—
130C2×Dic29—44no—
131C2×Dic29C22⋊C4116yescomplemented
132C2×Dic29C22×C414yes—
133C2×Dic29C2×D414yes—
134C2×Dic29C2×D414yes—
135C2×Dic29C2×D414yescomplemented
136C2×#390—291nomaximal, Sylow
137C22×C29—24no—
138C22×C29—24no—
139C22×C29—24no—
140C22×C29—42no—
141C22×C29—42no—
142C22×C29—42no—
143C22×C29—42no—
144C22×C29—416no—
145C22×C29C2×C22⋊C414yes—
146C22×C29C4×D414yes—
147C22×C29C4×D414yes—
148C22×C29#12114yes—
149C22×C29#12114yes—
150C22×C29#12414yes—
151C22×C29#12714yes—
152C22×C29C23×C411yescharacteristic
153C22×C29C22×D411yescharacteristic
154C22×C29C22×D411yescharacteristic
155C22×C29C22×D411yescharacteristic
156C22×C29C22×D411yescharacteristic
157C22×C29C2×#4111yescharacteristic
158C22×C29C2×#4111yescharacteristic
159C2×D29—24no—
160C2×D29—24no—
161C2×D29—24no—
162C2×D29—42no—
163C2×D29—42no—
164C2×D29—42no—
165C2×D29—42no—
166C2×D29—416no—
167C4×C29—24no—
168C4×C29—42no—
169Dic29—24no—
170Dic29—42no—
171Dic29C2×C22⋊C418yescomplemented
172C23×D4—291no—
173C22×C4⋊C4—291no—
174C22×C22⋊C4—291no—
175C22×C22⋊C4—291no—
176C22×C22⋊C4—291no—
177C22×C22⋊C4D2911yescharacteristic, complemented
178C22×C42—291no—
179#390—298no—
180C2×C29—44no—
181C2×C29#39018yescomplemented
182C2×C29C22×C22⋊C411yescharacteristic
183C2×C29C2×C4×D411yescharacteristic
184C2×C29C2×C4×D411yescharacteristic
185C2×C29C2×#12111yescharacteristic
186C2×C29C2×#12111yescharacteristic
187C2×C29C2×#12411yescharacteristic
188C2×C29C2×#12711yescharacteristic
189D29—44no—
190C25—291no—
191C25C2×D2911yescharacteristic
192C22×D4—298no—
193C22×D4—294no—
194C22×D4—584no—
195C22×D4—584no—
196C23×C4—291no—
197C23×C4—291no—
198C23×C4—291no—
199C23×C4C2×D2911yescharacteristic
200C23×C4C2×D2911yescharacteristic
201C2×C4⋊C4—294no—
202C2×C4⋊C4—584no—
203C2×C22⋊C4—24no—
204C2×C22⋊C4—294no—
205C2×C22⋊C4—294no—
206C2×C22⋊C4—294no—
207C2×C22⋊C4—584no—
208C2×C22⋊C4—584no—
209C2×C22⋊C4—584no—
210C2×C22⋊C4C2×D2914yescomplemented
211C2×C42—294no—
212C2×C42—584no—
213C29C2×#39011yescharacteristic, complemented, Sylow
214C24—22no—
215C24—22no—
216C24—22no—
217C24—22no—
218C24—22no—
219C24—22no—
220C24—294no—
221C24—292no—
222C24—582no—
223C24—582no—
224C24—582no—
225C24—582no—
226C24—582no—
227C24—582no—
228C24C4×D2914yes—
229C24C22×D2912yes—
230C24C22×D2911yescharacteristic
231C2×D4—2916no—
232C2×D4—588no—
233C2×D4—588no—
234C2×D4—5832no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—294no—
241C22×C4—294no—
242C22×C4—294no—
243C22×C4—292no—
244C22×C4—294no—
245C22×C4—292no—
246C22×C4—292no—
247C22×C4—582no—
248C22×C4—582no—
249C22×C4—582no—
250C22×C4—582no—
251C22×C4—582no—
252C22×C4C22⋊D2914yescomplemented
253C22×C4C22×D2912yes—
254C22×C4C22×D2912yes—
255C4⋊C4—588no—
256C22⋊C4—28no—
257C22⋊C4—588no—
258C22⋊C4—588no—
259C22⋊C4—588no—
260C42—588no—
261C23—28no—
262C23—22no—
263C23—22no—
264C23—22no—
265C23—22no—
266C23—22no—
267C23—22no—
268C23—28no—
269C23—28no—
270C23—44no—
271C23—44no—
272C23—44no—
273C23—44no—
274C23—294no—
275C23—588no—
276C23—582no—
277C23—582no—
278C23—582no—
279C23—582no—
280C23—582no—
281C23—582no—
282C23—588no—
283C23—588no—
284C23—1164no—
285C23—1164no—
286C23—1164no—
287C23—1164no—
288C23C2×C4×D2914yes—
289C23C2×C4×D2912yes—
290C23#9080512yes—
291C23D4×D2912yes—
292C23D4×D2912yes—
293C23D4×D2912yes—
294C23#9080712yes—
295C23C2×C22⋊D2912yes—
296C23C23×D2911yescharacteristic
297D4—5832no—
298C2×C4—28no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—44no—
305C2×C4—294no—
306C2×C4—294no—
307C2×C4—294no—
308C2×C4—2916no—
309C2×C4—294no—
310C2×C4—582no—
311C2×C4—582no—
312C2×C4—588no—
313C2×C4—582no—
314C2×C4—582no—
315C2×C4—582no—
316C2×C4—1164no—
317C2×C4C2×C22⋊D2914yescomplemented
318C22—24no—
319C22—24no—
320C22—24no—
321C22—416no—
322C22—42no—
323C22—42no—
324C22—42no—
325C22—42no—
326C22—584no—
327C22—584no—
328C22—584no—
329C22—11616no—
330C22—1162no—
331C22—1162no—
332C22—1162no—
333C22—1162no—
334C22C22⋊C4×D2914yes—
335C22#1174524314yes—
336C22#1174524614yes—
337C22#1174524714yes—
338C22C4×C22⋊D2914yes—
339C22#1174530114yes—
340C22#1174530214yes—
341C22C22×C4×D2911yescharacteristic
342C22C2×#9080511yescharacteristic
343C22C2×D4×D2911yescharacteristic
344C22C2×D4×D2911yescharacteristic
345C22C2×D4×D2911yescharacteristic
346C22C2×#9080711yescharacteristic
347C22C22×C22⋊D2911yescharacteristic
348C4—24no—
349C4—42no—
350C4—298no—
351C4—584no—
352C4—1162no—
353C2—44no—
354C2—1164no—
355C2#1427106318yesdirect product factor
356C2C2×C22⋊C4×D2911yescharacteristic
357C2C2×#1174524311yescharacteristic
358C2C2×C4×C22⋊D2911yescharacteristic
359C2C2×#1174530111yescharacteristic
360C2C2×#1174524611yescharacteristic
361C2C2×#1174524711yescharacteristic
362C2C2×#1174530211yescharacteristic
subgroupG/H
centerC24C22×D29
commutatorC22×C29C23×C4
FrattiniC23C23×D29
FittingC22×C22⋊C4×C29C2
socleC24×C29C23
prime radicalC23×C22⋊D29C2
cosocleC23×C29C24
hypercenterC22×C22⋊C4D29
hypocenterC29C2×#390
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C24 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#90779C2semidirect
3. C22×C22⋊Dic29C2semidirect
4. C22×#90781C2semidirect
5. C22×#90781C2semidirect
6. C22×C4×Dic29C2semidirect
7. #14271063C2direct (N × H)
8. C22×C22⋊C4×C29C2semidirect
15. C22×C22⋊D29C4semidirect
21. C2×C22⋊C4×C29C22semidirect
23. C2×C22⋊Dic29C22semidirect
26. C2×#90781C22semidirect
27. C2×#90781C22semidirect
29. C2×#90779C22semidirect
31. C2×C4×Dic29C22semidirect
54. C22×C4×C29D4semidirect
60. C2×C22⋊D29C2×C4semidirect
69. C22×Dic29D4semidirect
122. C2×C4×C29C2×D4semidirect
131. C2×Dic29C22⋊C4semidirect
135. C2×Dic29C2×D4semidirect
171. Dic29C2×C22⋊C4semidirect
177. C22×C22⋊C4D29semidirect
181. C2×C29#390semidirect
210. C2×C22⋊C4C2×D29semidirect
213. C29C2×#390semidirect
252. C22×C4C22⋊D29semidirect
317. C2×C4C2×C22⋊D29semidirect
355. C2#14271063direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊D292
C22×#907792
C22×C22⋊Dic292
C22×#907812
C22×C4×Dic292
#142710632
C22×C22⋊C4×C292
C2×#39029