Finite Group Databasebeta

← C2×#11741133 #14233356

Subgroups — C2×#11741133 #14233356

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×#557C211yesmaximal, characteristic, complemented
2C2×Q8×D28C211yesmaximal, characteristic
3#11741133C2116yesmaximal, direct product factor
4C2×#89855C213yesmaximal
5C2×#89853C213yesmaximal, complemented
6C2×Q8×C7⋊C8C211yesmaximal, characteristic, complemented
7C2×#89792C213yesmaximal, complemented
8C2×C4×#1143C213yesmaximal
9C22×Q8×D7—21no—
10C7×#557—24no—
11C7×#557C2218yescomplemented
12C2×C7×C4⋊Q8C2213yes—
13C2×C7×#125—23no—
14C2×C4×C7×Q8—21no—
15C2×C4×C7×Q8C2213yes—
16C2×C4×C7×Q8C2211yescharacteristic
17C22×#1143C2213yes—
18Q8×D28—24no—
19Q8×D28C2218yes—
20C2×#6460—23no—
21C2×C4×D28C2213yes—
22C2×#6432C2213yes—
23C2×#6409C2213yes—
24C2×#6409C2216yes—
25#89855C22124yes—
26#89853C22124yescomplemented
27C4×#1143C22124yes—
28Q8×C7⋊C8C2218yescomplemented
29#89792C22124yescomplemented
30C2×#6383C2211yescharacteristic
31C2×#6382C2213yes—
32C2×C4⋊(C7⋊C8)C2213yes—
33C2×C4×C7⋊C8C2213yes—
34C2×#3359—71nomaximal, Sylow
35C22×C7×Q8D411yescharacteristic
36C22×C7×Q8C2313yes—
37C2×Q8×D7—28no—
38C2×Q8×D7—48no—
39C22×D28C2311yescharacteristic
40C22×C4×D7—23no—
41C22×Dic14—23no—
42C7×C4⋊Q8—26no—
43C7×C4⋊Q8C23112yes—
44C7×#125—224no—
45C4×C7×Q8—28no—
46C4×C7×Q8—26no—
47C4×C7×Q8D414yes—
48C4×C7×Q8C23112yes—
49C4×C7×Q8C2314yes—
50C2×C7×C4⋊C4—23no—
51C2×C7×C4⋊C4—23no—
52C2×C7×C4⋊C4—23no—
53C2×C7×C4⋊C4D413yes—
54C2×C7×C4⋊C4C2311yescharacteristic
55C2×C42×C7—23no—
56C2×C42×C7C2313yes—
57C2×#1143—212no—
58C2×#1143C23112yes—
59C2×(C2×D7)⋊C4—23no—
60C2×C4⋊Dic7—23no—
61C2×C4⋊Dic7C2313yes—
62C22×C7⋊C8C2311yescharacteristic
63C22×C7⋊C8C2313yes—
64#6460—224no—
65C4×D28—26no—
66C4×D28C23112yes—
67#6432—26no—
68#6432C23112yes—
69#6409C23124yes—
70#6409C23112yes—
71#6383C2314yes—
72#6382C23112yes—
73C4⋊(C7⋊C8)C23112yes—
74C4×C7⋊C8C23112yes—
75C2×#557D711yescharacteristic, complemented
76C2×D4×Q8—71no—
77#3359—716no—
78C2×#487—73no—
79C2×#475—73no—
80C2×#461—73no—
81C2×C8×Q8—71no—
82C2×C4×SD16—73no—
83C23×D7—21no—
84C2×C7×Q8—23no—
85C2×C7×Q8—26no—
86C2×C7×Q8—26no—
87C2×C7×Q8SD1618yescomplemented
88C2×C7×Q8C2×D414yes—
89C2×C7×Q8C2416yes—
90C22×C4×C7—21no—
91C22×C4×C7—23no—
92C22×C4×C7C2×D413yes—
93C22×C4×C7C2×D413yes—
94C22×C4×C7C2411yescharacteristic
95C22×Dic7—23no—
96Q8×D7—432no—
97C2×D28—21no—
98C2×D28—22no—
99C2×D28#4114yes—
100C2×D28C2412yes—
101C2×C4×D7—212no—
102C2×C4×D7—412no—
103C2×Dic14—212no—
104C2×Dic14—412no—
105C7×C4⋊C4—212no—
106C7×C4⋊C4—212no—
107C7×C4⋊C4—212no—
108C7×C4⋊C4—21no—
109C7×C4⋊C4C2×D4112yes—
110C7×C4⋊C4C2412yes—
111C42×C7—212no—
112C42×C7C2×D416yes—
113C42×C7C2416yes—
114#1143—224no—
115(C2×D7)⋊C4—212no—
116C4⋊Dic7—23no—
117C4⋊Dic7—212no—
118C4⋊Dic7C2416yes—
119C2×C7⋊C8—26no—
120C2×C7⋊C8—22no—
121C2×C7⋊C8C2412yes—
122C2×C7⋊C8C2416yes—
123C23×Q8—141no—
124C22×SD16—73no—
125#557—24no—
126#557C2×D718yescomplemented
127D4×Q8—78no—
128D4×Q8—144no—
129C2×C4⋊Q8—73no—
130C2×C4⋊Q8C2×D713yes—
131C2×#125—23no—
132C2×C22⋊Q8—143no—
133C2×C4×Q8—21no—
134C2×C4×Q8C2×D713yes—
135C2×C4×Q8C2×D711yescharacteristic
136C2×C4×D4—73no—
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×C7C22×D411yescharacteristic
149C22×D7—24no—
150C22×D7—22no—
151C22×D7—42no—
152C22×D7—42no—
153C7×Q8—26no—
154C7×Q8—26no—
155C7×Q8—46no—
156C7×Q8C2×SD16116yescomplemented
157C2×C4×C7—26no—
158C2×C4×C7—22no—
159C2×C4×C7—26no—
160C2×C4×C7—46no—
161C2×C4×C7—42no—
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—26no—
170C2×Dic7—46no—
171D28—24no—
172D28—22no—
173D28C2×#4114yes—
174C4×D7—424no—
175Dic14—424no—
176C7⋊C8—26no—
177C7⋊C8—22no—
178C22×Q8—148no—
179C22×Q8—143no—
180C22×Q8—288no—
181C22×Q8C22⋊D711yescharacteristic
182C22×Q8C22×D713yes—
183C22×D4—71no—
184C23×C4—143no—
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—224no—
194C22⋊Q8—1424no—
195C4×Q8—28no—
196C4×Q8—26no—
197C4×Q8C22⋊D714yes—
198C4×Q8C22×D7112yes—
199C4×Q8C22×D714yes—
200C4×D4—712no—
201C4×D4—146no—
202C2×C4⋊C4—23no—
203C2×C4⋊C4—23no—
204C2×C4⋊C4—23no—
205C2×C4⋊C4—73no—
206C2×C4⋊C4—143no—
207C2×C4⋊C4C22⋊D713yes—
208C2×C4⋊C4C22×D711yescharacteristic
209C2×C22⋊C4—143no—
210C2×C42—23no—
211C2×C42C22×D713yes—
212#106—712no—
213C4⋊C8—712no—
214#103—712no—
215#103—724no—
216#102—74no—
217C4×C8—712no—
218C22×C7#54812yes—
219C22×C7C22×SD1612yes—
220C22×C7#57812yes—
221C22×C7C23×D411yescharacteristic
222C2×D7—24no—
223C2×D7—48no—
224C2×D7—42no—
225C2×D7—42no—
226C4×C7—26no—
227C4×C7—46no—
228C4×C7—42no—
229C4×C7#54812yes—
230C4×C7C22×SD16112yes—
231C4×C7C22×#4111yescharacteristic
232C4×C7C2×2−1+411yescharacteristic
233Dic7—46no—
234C24—141no—
235C2×Q8—23no—
236C2×Q8—26no—
237C2×Q8—26no—
238C2×Q8—1412no—
239C2×Q8—2832no—
240C2×Q8—2812no—
241C2×Q8#114318yescomplemented
242C2×Q8C2×C22⋊D714yes—
243C2×Q8C23×D716yes—
244C2×D4—74no—
245C2×D4—72no—
246C2×D4—142no—
247C2×D4—141no—
248C22×C4—21no—
249C22×C4—23no—
250C22×C4—143no—
251C22×C4—1412no—
252C22×C4—2812no—
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—212no—
263C4⋊C4—212no—
264C4⋊C4—21no—
265C4⋊C4—76no—
266C4⋊C4—143no—
267C4⋊C4—1412no—
268C4⋊C4C2×C22⋊D7112yes—
269C4⋊C4C23×D712yes—
270C22⋊C4—1412no—
271C42—212no—
272C42C2×C22⋊D716yes—
273C42C23×D716yes—
274C2×C7#335914yescomplemented
275C2×C7C2×#54811yescharacteristic
276C2×C7C23×SD1611yescharacteristic
277C2×C7C2×#57811yescharacteristic
278D7—44no—
279C23—144no—
280C23—142no—
281C23—282no—
282C23—282no—
283C23C22×C22⋊D711yescharacteristic
284Q8—26no—
285Q8—26no—
286Q8—46no—
287Q8—2824no—
288Q8C2×#1143116yescomplemented
289D4—74no—
290D4—144no—
291D4—142no—
292C2×C4—26no—
293C2×C4—22no—
294C2×C4—26no—
295C2×C4—46no—
296C2×C4—42no—
297C2×C4—146no—
298C2×C4—286no—
299C2×C4—2824no—
300C2×C4C2×#1143112yes—
301C2×C4D7×#4112yes—
302C2×C4#655412yes—
303C2×C4C22×C22⋊D716yes—
304C2×C4C22×C22⋊D716yes—
305C2×C4C22×C22⋊D711yescharacteristic
306C2×C4C24×D711yescharacteristic
307C8—146no—
308C8—142no—
309C7C2×#335911yescharacteristic, complemented, Sylow
310C22—144no—
311C22—282no—
312C22—282no—
313C22—288no—
314C22C22×#114312yes—
315C22#9052212yes—
316C22#9052912yes—
317C22C23×C22⋊D711yescharacteristic
318C4—26no—
319C4—46no—
320C4—42no—
321C4—286no—
322C4C22×#1143112yes—
323C4#9052212yes—
324C4C2×D7×#4111yescharacteristic
325C4C2×#655411yescharacteristic
326C2—284no—
327C2#1174113314yesdirect product factor
328C2C23×#114311yescharacteristic
329C2C2×#9052211yescharacteristic
330C2C2×#9052911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#557C2
socleC23×C7C22×D4
prime radicalC22×D28C23
hypercenterC2×#557D7
hypocenterC7C2×#3359
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. C2×C7×#557C2semidirect
3. #11741133C2direct (N × H)
5. C2×#89853C2semidirect
6. C2×Q8×C7⋊C8C2semidirect
7. C2×#89792C2semidirect
11. C7×#557C22semidirect
26. #89853C22semidirect
28. Q8×C7⋊C8C22semidirect
29. #89792C22semidirect
75. C2×#557D7semidirect
87. C2×C7×Q8SD16semidirect
126. #557C2×D7semidirect
156. C7×Q8C2×SD16semidirect
241. C2×Q8#1143semidirect
274. C2×C7#3359semidirect
288. Q8C2×#1143semidirect
309. C7C2×#3359semidirect
327. C2#11741133direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5572
C2×Q8×D282
#117411332
C2×#898552
C2×#898532
C2×Q8×C7⋊C82
C2×#897922
C2×C4×#11432
C2×#33597