Finite Group Databasebeta

← C2×#11741013 #14233360

Subgroups — C2×#11741013 #14233360

Order 1792.

2058 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×D4×Q8C211yesmaximal, characteristic
2C2×#90261C211yesmaximal, characteristic, complemented
3#11741013C2116yesmaximal, direct product factor
4C2×#89866C213yesmaximal, complemented
5C2×#89865C213yesmaximal, complemented
6C2×Q8×C7⋊C8C211yesmaximal, characteristic, complemented
7C2×#89791C213yesmaximal
8C2×C4×#1142C213yesmaximal
9C23×C7×Q8—21no—
10C7×D4×Q8—24no—
11C7×D4×Q8C2218yes—
12C2×C7×C4⋊Q8C2213yes—
13C2×C7×C22⋊Q8—23no—
14C2×C4×C7×Q8C2211yescharacteristic
15C2×C4×C7×D4C2213yes—
16C2×Q8×Dic7—21no—
17C22×#1142C2213yes—
18#90261—24no—
19#90261C2218yescomplemented
20C2×#6453—23no—
21C2×#6432C2213yes—
22C2×C4×Dic14C2213yes—
23C2×#6406C2211yescharacteristic
24#89866C22124yescomplemented
25#89865C22124yescomplemented
26Q8×C7⋊C8C2218yescomplemented
27#89791C22124yes—
28C4×#1142C22124yes—
29C2×#6384C2213yes—
30C2×#6384C2216yes—
31C2×#6382C2213yes—
32C2×C4⋊(C7⋊C8)C2213yes—
33C2×C4×C7⋊C8C2213yes—
34C2×#3359—71nomaximal, Sylow
35C22×C7×Q8—28no—
36C22×C7×Q8—23no—
37C22×C7×Q8—48no—
38C22×C7×Q8D411yescharacteristic
39C22×C7×D4C2311yescharacteristic
40C23×C4×C7—23no—
41C22×Dic14C2313yes—
42C7×C4⋊Q8—26no—
43C7×C4⋊Q8C23112yes—
44C7×C22⋊Q8—224no—
45C4×C7×Q8D414yes—
46C4×C7×Q8C2314yes—
47C4×C7×D4—26no—
48C4×C7×D4C23112yes—
49C2×C7×C4⋊C4—23no—
50C2×C7×C4⋊C4D413yes—
51C2×C7×C4⋊C4C2313yes—
52C2×C7×C22⋊C4—23no—
53C2×C42×C7C2313yes—
54Q8×Dic7—28no—
55C2×#1142—212no—
56C2×#1142C23112yes—
57C2×C4⋊Dic7—23no—
58C2×C4⋊Dic7—23no—
59C2×C4⋊Dic7C2311yescharacteristic
60C2×Dic7⋊C4—23no—
61C2×C4×Dic7—23no—
62C22×C7⋊C8C2311yescharacteristic
63C22×C7⋊C8C2313yes—
64#6453—224no—
65#6432—26no—
66#6432C23112yes—
67C4×Dic14—26no—
68C4×Dic14C23112yes—
69#6406C2314yes—
70#6384C23112yes—
71#6384C23124yes—
72#6382C23112yes—
73C4⋊(C7⋊C8)C23112yes—
74C4×C7⋊C8C23112yes—
75C2×#557—71no—
76C2×D4×Q8D711yescharacteristic
77#3359—716no—
78C2×#487—73no—
79C2×#475—73no—
80C2×#461—73no—
81C2×C8×Q8—71no—
82C2×C4×SD16—73no—
83C24×C7—21no—
84C2×C7×Q8—212no—
85C2×C7×Q8—432no—
86C2×C7×Q8—412no—
87C2×C7×Q8SD1618yescomplemented
88C2×C7×Q8C2×D414yes—
89C2×C7×D4—21no—
90C2×C7×D4—22no—
91C2×C7×D4#4114yes—
92C2×C7×D4C2412yes—
93C22×C4×C7—23no—
94C22×C4×C7—212no—
95C22×C4×C7—412no—
96C22×C4×C7C2×D413yes—
97C22×C4×C7C2×D413yes—
98C22×C4×C7C2411yescharacteristic
99C22×Dic7—21no—
100C22×Dic7—23no—
101C2×Dic14—26no—
102C2×Dic14—26no—
103C2×Dic14—23no—
104C2×Dic14C2416yes—
105C7×C4⋊C4—212no—
106C7×C4⋊C4—23no—
107C7×C4⋊C4C2×D4112yes—
108C7×C4⋊C4C2416yes—
109C7×C22⋊C4—212no—
110C42×C7C2×D416yes—
111C42×C7C2416yes—
112#1142—224no—
113C4⋊Dic7—21no—
114C4⋊Dic7—212no—
115C4⋊Dic7—212no—
116C4⋊Dic7C2412yes—
117Dic7⋊C4—212no—
118C4×Dic7—212no—
119C2×C7⋊C8—26no—
120C2×C7⋊C8—22no—
121C2×C7⋊C8C2412yes—
122C2×C7⋊C8C2416yes—
123C23×Q8—21no—
124C22×SD16—73no—
125#557—78no—
126#557—144no—
127D4×Q8—24no—
128D4×Q8C2×D718yes—
129C2×C4⋊Q8—73no—
130C2×C4⋊Q8C2×D713yes—
131C2×#125—143no—
132C2×C22⋊Q8—23no—
133C2×C4×Q8—73no—
134C2×C4×Q8—141no—
135C2×C4×Q8C2×D711yescharacteristic
136C2×C4×D4C2×D713yes—
137#487—724no—
138#475—724no—
139#461—724no—
140C8×Q8—78no—
141C4×SD16—724no—
142C2×#106—73no—
143C2×C4⋊C8—73no—
144C2×#103—76no—
145C2×#103—73no—
146C2×#102—71no—
147C2×C4×C8—73no—
148C23×C7—24no—
149C23×C7—22no—
150C23×C7—42no—
151C23×C7—42no—
152C23×C7C22×D411yescharacteristic
153C7×Q8—424no—
154C7×Q8C2×SD16116yescomplemented
155C7×D4—24no—
156C7×D4—22no—
157C7×D4C2×#4114yes—
158C2×C4×C7—26no—
159C2×C4×C7—26no—
160C2×C4×C7—46no—
161C2×C4×C7—424no—
162C2×C4×C7C2×SD16112yes—
163C2×C4×C7C22×D416yes—
164C2×C4×C7C22×D411yescharacteristic
165C2×C4×C7C22×D416yes—
166C2×C4×C7C2×#4112yes—
167C2×C4×C72−1+412yes—
168C2×C4×C7C2511yescharacteristic
169C2×Dic7—22no—
170C2×Dic7—26no—
171C2×Dic7—46no—
172C2×Dic7—42no—
173Dic14—26no—
174Dic14—26no—
175Dic14—46no—
176C7⋊C8—26no—
177C7⋊C8—22no—
178C22×Q8—28no—
179C22×Q8—23no—
180C22×Q8—48no—
181C22×Q8—73no—
182C22×Q8C22⋊D711yescharacteristic
183C22×D4C22×D711yescharacteristic
184C23×C4—23no—
185C2×SD16—712no—
186C2×SD16—1412no—
187C22×C8—73no—
188C22×C8—71no—
189C4⋊Q8—26no—
190C4⋊Q8—712no—
191C4⋊Q8—146no—
192C4⋊Q8C22×D7112yes—
193#125—1424no—
194C22⋊Q8—224no—
195C4×Q8—712no—
196C4×Q8—148no—
197C4×Q8—146no—
198C4×Q8C22⋊D714yes—
199C4×Q8C22×D714yes—
200C4×D4—26no—
201C4×D4C22×D7112yes—
202C2×C4⋊C4—23no—
203C2×C4⋊C4—71no—
204C2×C4⋊C4—143no—
205C2×C4⋊C4—143no—
206C2×C4⋊C4—143no—
207C2×C4⋊C4C22⋊D713yes—
208C2×C4⋊C4C22×D713yes—
209C2×C22⋊C4—23no—
210C2×C42—143no—
211C2×C42C22×D713yes—
212#106—712no—
213C4⋊C8—712no—
214#103—712no—
215#103—724no—
216#102—74no—
217C4×C8—712no—
218C22×C7—24no—
219C22×C7—48no—
220C22×C7—42no—
221C22×C7—42no—
222C22×C7#54812yes—
223C22×C7C22×SD1612yes—
224C22×C7#57812yes—
225C22×C7C23×D411yescharacteristic
226C4×C7—26no—
227C4×C7—46no—
228C4×C7#54812yes—
229C4×C7C22×SD16112yes—
230C4×C7C22×#4111yescharacteristic
231C4×C7C2×2−1+411yescharacteristic
232Dic7—46no—
233Dic7—42no—
234C24—21no—
235C2×Q8—212no—
236C2×Q8—432no—
237C2×Q8—412no—
238C2×Q8—76no—
239C2×Q8—143no—
240C2×Q8—146no—
241C2×Q8—146no—
242C2×Q8#114218yescomplemented
243C2×Q8C2×C22⋊D714yes—
244C2×D4—22no—
245C2×D4—21no—
246C2×D4#116114yes—
247C2×D4C23×D712yes—
248C22×C4—23no—
249C22×C4—212no—
250C22×C4—412no—
251C22×C4—141no—
252C22×C4—143no—
253C22×C4C2×C22⋊D713yes—
254C22×C4C2×C22⋊D713yes—
255C22×C4C23×D711yescharacteristic
256SD16—1424no—
257C2×C8—72no—
258C2×C8—76no—
259C2×C8—146no—
260C2×C8—142no—
261C4⋊C4—212no—
262C4⋊C4—23no—
263C4⋊C4—72no—
264C4⋊C4—1412no—
265C4⋊C4—141no—
266C4⋊C4—1412no—
267C4⋊C4—1412no—
268C4⋊C4C2×C22⋊D7112yes—
269C4⋊C4C23×D716yes—
270C22⋊C4—212no—
271C42—1412no—
272C42C2×C22⋊D716yes—
273C42C23×D716yes—
274C2×C7—44no—
275C2×C7#335914yescomplemented
276C2×C7C2×#54811yescharacteristic
277C2×C7C23×SD1611yescharacteristic
278C2×C7C2×#57811yescharacteristic
279C23—24no—
280C23—22no—
281C23—42no—
282C23—42no—
283C23C22×C22⋊D711yescharacteristic
284Q8—424no—
285Q8—146no—
286Q8—146no—
287Q8—286no—
288Q8C2×#1142116yescomplemented
289D4—24no—
290D4—22no—
291D4C2×#116114yes—
292C2×C4—26no—
293C2×C4—26no—
294C2×C4—46no—
295C2×C4—424no—
296C2×C4—142no—
297C2×C4—146no—
298C2×C4—286no—
299C2×C4—282no—
300C2×C4C2×#1142112yes—
301C2×C4C2×#116112yes—
302C2×C4#655112yes—
303C2×C4C22×C22⋊D716yes—
304C2×C4C22×C22⋊D716yes—
305C2×C4C22×C22⋊D711yescharacteristic
306C2×C4C24×D711yescharacteristic
307C8—146no—
308C8—142no—
309C7C2×#335911yescharacteristic, complemented, Sylow
310C22—24no—
311C22—42no—
312C22—48no—
313C22—42no—
314C22C22×#114212yes—
315C22#9050812yes—
316C22#9052912yes—
317C22C23×C22⋊D711yescharacteristic
318C4—26no—
319C4—46no—
320C4—286no—
321C4—282no—
322C4C22×#1142112yes—
323C4#9050812yes—
324C4C22×#116111yescharacteristic
325C4C2×#655111yescharacteristic
326C2—44no—
327C2#1174101314yesdirect product factor
328C2C23×#114211yescharacteristic
329C2C2×#9050811yescharacteristic
330C2C2×#9052911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×D4×Q8C2
socleC23×C7C22×D4
prime radicalC22×C7×D4C23
hypercenterC2×D4×Q8D7
hypocenterC7C2×#3359
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#90261C2semidirect
3. #11741013C2direct (N × H)
4. C2×#89866C2semidirect
5. C2×#89865C2semidirect
6. C2×Q8×C7⋊C8C2semidirect
19. #90261C22semidirect
24. #89866C22semidirect
25. #89865C22semidirect
26. Q8×C7⋊C8C22semidirect
87. C2×C7×Q8SD16semidirect
154. C7×Q8C2×SD16semidirect
242. C2×Q8#1142semidirect
275. C2×C7#3359semidirect
288. Q8C2×#1142semidirect
309. C7C2×#3359semidirect
327. C2#11741013direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×D4×Q82
C2×#902612
#117410132
C2×#898662
C2×#898652
C2×Q8×C7⋊C82
C2×#897912
C2×C4×#11422
C2×#33597