Finite Group Databasebeta

← C2×#11740783 #14223080

Subgroups — C2×#11740783 #14223080

Order 1792.

2246 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#533C211yesmaximal, characteristic, complemented
2C22×#6438C211yesmaximal, characteristic
3#11740783C2116yesmaximal, direct product factor
4C2×#89861C214yesmaximal, complemented
5C2×#89840C214yesmaximal, complemented
6C2×#89776C212yesmaximal, complemented
7C2×#89773C212yesmaximal
8C2×C4×#1136C211yesmaximal, characteristic, complemented
9C23×D28C2211yescharacteristic
10C23×Dic14C2211yescharacteristic
11C7×#533—24no—
12C7×#533C2218yescomplemented
13C2×C7×C4⋊Q8C2212yescomplemented
14C2×C7×#125C2212yescomplemented
15C2×C7×C22⋊Q8—22no—
16C2×C4×C7×Q8—22no—
17C2×C7×#117C2212yes—
18C22×C42×C7C2211yescharacteristic
19C22×(C2×D7)⋊C4—22no—
20C22×#1136C2212yes—
21C2×#6438—22no—
22C2×#6438—24no—
23C2×#6438C2212yes—
24C2×#6438C2218yes—
25C2×#6438C2212yes—
26#89861C22132yescomplemented
27#89840C22132yescomplemented
28#89776C22116yescomplemented
29#89773C22116yes—
30C2×#6384C2218yescomplemented
31C2×#6383C2218yes—
32C4×#1136C2218yescomplemented
33C2×#6377C2212yescomplemented
34C2×C4×C7⋊C8C2212yescomplemented
35C2×#3140—71nomaximal, Sylow
36C24×D7—21no—
37C22×C7×Q8—22no—
38C23×C4×C7D412yes—
39C23×C4×C7C2311yescharacteristic
40C23×Dic7—21no—
41C22×D28—28no—
42C22×D28—21no—
43C22×D28—22no—
44C22×D28C2312yes—
45C22×D28C2314yes—
46C22×Dic14—28no—
47C22×Dic14—21no—
48C22×Dic14—22no—
49C22×Dic14C2312yes—
50C22×Dic14C2314yes—
51C7×C4⋊Q8—24no—
52C7×C4⋊Q8C2318yescomplemented
53C7×#125—24no—
54C7×#125C2318yescomplemented
55C7×C22⋊Q8—216no—
56C4×C7×Q8—216no—
57C7×#117—24no—
58C7×#117C2318yes—
59C2×C7×C4⋊C4—24no—
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4C2314yes—
62C2×C7×C22⋊C4—22no—
63C2×C42×C7—22no—
64C2×C42×C7D412yes—
65C2×C42×C7D414yes—
66C2×C42×C7C2311yescharacteristic
67C2×C42×C7C2311yescharacteristic
68C2×C42×C7C2314yes—
69C2×(C2×D7)⋊C4—24no—
70C2×(C2×D7)⋊C4—24no—
71C2×(C2×D7)⋊C4—216no—
72C2×#1136—28no—
73C2×#1136C2318yes—
74C22×C7⋊C8C2314yes—
75#6438—216no—
76#6438—24no—
77#6438—24no—
78#6438C2318yes—
79#6438C2318yes—
80#6384C23132yescomplemented
81#6383C23132yes—
82#6377C2318yescomplemented
83C4×C7⋊C8C2318yescomplemented
84C2×#533D711yescharacteristic, complemented
85C22×#124—71no—
86#3140—716no—
87C2×#489—74no—
88C2×#488—74no—
89C2×#419—72no—
90C2×#418—72no—
91C2×C4×M16—71no—
92C24×C7C2×D411yescharacteristic
93C23×D7—24no—
94C23×D7—22no—
95C23×D7—48no—
96C23×D7—44no—
97C2×C7×Q8—28no—
98C2×C7×Q8—48no—
99C22×C4×C7—24no—
100C22×C4×C7—44no—
101C22×C4×C7C2×D412yes—
102C22×C4×C7C2×D412yes—
103C22×C4×C7C2×D418yes—
104C22×C4×C7C2×D411yescharacteristic
105C22×C4×C7C2×D412yes—
106C22×C4×C7#4118yes—
107C22×C4×C7C2411yescharacteristic
108C22×C4×C7C2412yes—
109C22×Dic7—24no—
110C22×Dic7—22no—
111C22×Dic7—44no—
112C2×D28—28no—
113C2×D28—216no—
114C2×D28—24no—
115C2×D28—22no—
116C2×D28—48no—
117C2×D28—44no—
118C2×D28C2414yes—
119C2×Dic14—28no—
120C2×Dic14—216no—
121C2×Dic14—24no—
122C2×Dic14—22no—
123C2×Dic14—48no—
124C2×Dic14—44no—
125C2×Dic14C2414yes—
126C7×C4⋊C4—216no—
127C7×C4⋊C4—28no—
128C7×C4⋊C4—24no—
129C7×C4⋊C4C2418yes—
130C7×C22⋊C4—28no—
131C42×C7—28no—
132C42×C7C2×D418yes—
133C42×C7C2×D412yes—
134C42×C7C2×D412yes—
135C42×C7C2412yes—
136C42×C7C2412yes—
137(C2×D7)⋊C4—216no—
138(C2×D7)⋊C4—216no—
139#1136—216no—
140C2×C7⋊C8—28no—
141C2×C7⋊C8C2418yes—
142C23×Q8—71no—
143C23×D4—71no—
144C22×M16—72no—
145#533—24no—
146#533C2×D718yescomplemented
147C2×C4⋊Q8C2×D712yescomplemented
148C2×#125C2×D712yescomplemented
149C2×#124—72no—
150C2×#124—72no—
151C2×#124—78no—
152C2×#124—142no—
153C2×#124—144no—
154C2×C22⋊Q8—22no—
155C2×C4×Q8—22no—
156C2×#117C2×D712yes—
157C22×C22⋊C4—142no—
158C22×C42C2×D711yescharacteristic
159#489—732no—
160#488—732no—
161#419—716no—
162#418—716no—
163C2×#103—78no—
164C2×#102—78no—
165C4×M16—78no—
166C2×#97—72no—
167C2×C4×C8—72no—
168C23×C7—24no—
169C23×C7#12414yes—
170C23×C7C22×D412yes—
171C23×C7C22×D411yescharacteristic
172C22×D7—24no—
173C22×D7—416no—
174C22×D7—48no—
175C22×D7—44no—
176C22×D7—48no—
177C22×D7—816no—
178C7×Q8—416no—
179C2×C4×C7—24no—
180C2×C4×C7—24no—
181C2×C4×C7—28no—
182C2×C4×C7—48no—
183C2×C4×C7—48no—
184C2×C4×C7#12418yes—
185C2×C4×C7#12414yes—
186C2×C4×C7C22×D414yes—
187C2×C4×C7C22×D414yes—
188C2×C4×C7C22×D412yes—
189C2×C4×C7C22×D411yescharacteristic
190C2×C4×C7C2×#4114yes—
191C2×C4×C7C2×#4118yes—
192C2×C4×C7C2511yescharacteristic
193C2×Dic7—24no—
194C2×Dic7—48no—
195C2×Dic7—44no—
196D28—28no—
197D28—48no—
198D28—44no—
199Dic14—28no—
200Dic14—48no—
201Dic14—44no—
202C7⋊C8—28no—
203C25—141no—
204C22×Q8—22no—
205C22×Q8—72no—
206C22×Q8—74no—
207C22×Q8—142no—
208C22×Q8—141no—
209C22×Q8—148no—
210C22×D4—72no—
211C22×D4—74no—
212C22×D4—148no—
213C22×D4—142no—
214C22×D4—141no—
215C23×C4—141no—
216C23×C4C22⋊D712yes—
217C23×C4C22×D711yescharacteristic
218C2×M16—78no—
219C2×M16—148no—
220C22×C8—74no—
221C4⋊Q8—24no—
222C4⋊Q8C22×D718yescomplemented
223#125—24no—
224#125C22×D718yescomplemented
225#124—78no—
226#124—78no—
227#124—1416no—
228#124—144no—
229#124—144no—
230C22⋊Q8—216no—
231C4×Q8—216no—
232#117—24no—
233#117C22×D718yes—
234C2×C4⋊C4—24no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4C22×D714yes—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—1416no—
239C2×C22⋊C4—144no—
240C2×C22⋊C4—144no—
241C2×C42—22no—
242C2×C42C22⋊D712yes—
243C2×C42C22⋊D714yes—
244C2×C42C22×D711yescharacteristic
245C2×C42C22×D711yescharacteristic
246C2×C42C22×D714yes—
247#103—732no—
248#102—732no—
249#97—78no—
250C4×C8—78no—
251C22×C7—28no—
252C22×C7—24no—
253C22×C7C2×#12414yes—
254C22×C7C2×#12412yes—
255C22×C7#57514yes—
256C22×C7C23×D411yescharacteristic
257C2×D7—44no—
258C2×D7—48no—
259C2×D7—816no—
260C2×D7—88no—
261C4×C7—24no—
262C4×C7—24no—
263C4×C7—48no—
264C4×C7C2×#12414yes—
265C4×C7C2×#12412yes—
266C4×C7C22×#4112yes—
267Dic7—44no—
268C24—144no—
269C24—142no—
270C24—288no—
271C24—284no—
272C24C2×C22⋊D711yescharacteristic
273C2×Q8—28no—
274C2×Q8—48no—
275C2×Q8—74no—
276C2×Q8—144no—
277C2×Q8—142no—
278C2×Q8—148no—
279C2×Q8—1416no—
280C2×Q8—288no—
281C2×Q8—284no—
282C2×D4—74no—
283C2×D4—148no—
284C2×D4—1416no—
285C2×D4—144no—
286C2×D4—142no—
287C2×D4—288no—
288C2×D4—284no—
289C22×C4—24no—
290C22×C4—44no—
291C22×C4—144no—
292C22×C4—142no—
293C22×C4—284no—
294C22×C4#116118yes—
295C22×C4C2×C22⋊D712yes—
296C22×C4C2×C22⋊D712yes—
297C22×C4C2×C22⋊D718yes—
298C22×C4C2×C22⋊D712yes—
299C22×C4C2×C22⋊D711yescharacteristic
300C22×C4C23×D712yes—
301C22×C4C23×D711yescharacteristic
302M16—1416no—
303C2×C8—78no—
304C2×C8—148no—
305C4⋊C4—216no—
306C4⋊C4—28no—
307C4⋊C4—24no—
308C4⋊C4C23×D718yes—
309C22⋊C4—28no—
310C22⋊C4—1416no—
311C22⋊C4—1416no—
312C42—28no—
313C42C2×C22⋊D718yes—
314C42C2×C22⋊D712yes—
315C42C2×C22⋊D712yes—
316C42C23×D712yes—
317C42C23×D712yes—
318C2×C7—24no—
319C2×C7#314014yescomplemented
320C2×C7C22×#12411yescharacteristic
321C2×C7C2×#57512yes—
322D7—84no—
323C23—24no—
324C23—144no—
325C23—2816no—
326C23—288no—
327C23—284no—
328C23—288no—
329C23—5616no—
330C23#651014yes—
331C23C22×C22⋊D712yes—
332C23C22×C22⋊D711yescharacteristic
333Q8—416no—
334Q8—148no—
335Q8—284no—
336Q8—288no—
337D4—148no—
338D4—284no—
339D4—288no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—28no—
343C2×C4—48no—
344C2×C4—48no—
345C2×C4—144no—
346C2×C4—288no—
347C2×C4—284no—
348C2×C4#651018yes—
349C2×C4#651014yes—
350C2×C4C2×#116114yes—
351C2×C4C2×#116118yes—
352C2×C4C22×C22⋊D714yes—
353C2×C4C22×C22⋊D714yes—
354C2×C4C22×C22⋊D712yes—
355C2×C4C22×C22⋊D711yescharacteristic
356C2×C4C24×D711yescharacteristic
357C8—148no—
358C7C2×#314011yescharacteristic, complemented, Sylow
359C22—24no—
360C22—28no—
361C22—284no—
362C22—288no—
363C22—5616no—
364C22—568no—
365C22C2×#651014yes—
366C22C2×#651012yes—
367C22#9051314yes—
368C22C23×C22⋊D711yescharacteristic
369C4—24no—
370C4—24no—
371C4—48no—
372C4—284no—
373C4C2×#651012yes—
374C4C2×#651014yes—
375C4C22×#116112yes—
376C2—24no—
377C2—564no—
378C2#1174078314yesdirect product factor
379C2C22×#651011yescharacteristic
380C2C2×#9051312yes—
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#533C2
socleC23×C7C22×D4
prime radicalC23×D28C22
hypercenterC2×#533D7
hypocenterC7C2×#3140
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. C2×C7×#533C2semidirect
3. #11740783C2direct (N × H)
4. C2×#89861C2semidirect
5. C2×#89840C2semidirect
6. C2×#89776C2semidirect
8. C2×C4×#1136C2semidirect
12. C7×#533C22semidirect
13. C2×C7×C4⋊Q8C22semidirect
14. C2×C7×#125C22semidirect
26. #89861C22semidirect
27. #89840C22semidirect
28. #89776C22semidirect
30. C2×#6384C22semidirect
32. C4×#1136C22semidirect
33. C2×#6377C22semidirect
34. C2×C4×C7⋊C8C22semidirect
52. C7×C4⋊Q8C23semidirect
54. C7×#125C23semidirect
80. #6384C23semidirect
82. #6377C23semidirect
83. C4×C7⋊C8C23semidirect
84. C2×#533D7semidirect
146. #533C2×D7semidirect
147. C2×C4⋊Q8C2×D7semidirect
148. C2×#125C2×D7semidirect
222. C4⋊Q8C22×D7semidirect
224. #125C22×D7semidirect
319. C2×C7#3140semidirect
358. C7C2×#3140semidirect
378. C2#11740783direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5332
C22×#64382
#117407832
C2×#898612
C2×#898402
C2×#897762
C2×#897732
C2×C4×#11362
C2×#31407