Finite Group Databasebeta

← C2×#11743338 #14261633

Subgroups — C2×#11743338 #14261633

Order 1792.

6338 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#533C211yesmaximal, characteristic
2#11743338C2132yesmaximal, direct product factor
3C2×#90412C214yesmaximal, complemented
4C2×C7⋊#564C214yesmaximal, complemented
5C2×#90316C218yesmaximal
6C2×#90258C214yesmaximal, complemented
7C2×#90261C214yesmaximal, complemented
8C2×#90209C214yesmaximal
9C2×#90161C212yesmaximal
10C7×#533C22116yes—
11C2×C7×C4⋊Q8C2212yes—
12C2×C7×#125C2212yes—
13C2×C7×C22⋊Q8C2214yes—
14C2×C4×C7×Q8C2214yes—
15C2×C7×#117C2212yes—
16C22×C42×C7C2211yescharacteristic
17C2×Q8×Dic7C2218yes—
18C2×#6507C2218yes—
19C2×#6489C2214yes—
20C2×#6487C2214yes—
21C2×#6487C2214yes—
22#90412C22164yescomplemented
23C7⋊#564C22164yescomplemented
24#90316C221128yes—
25#90261C22164yescomplemented
26#90258C22164yescomplemented
27#90209C22164yes—
28C2×#6453C2218yes—
29C2×#6453C22116yes—
30C2×#6452C22116yes—
31C2×#6452C22116yes—
32C2×#6450C2218yes—
33C2×#6442C22116yes—
34#90161C22132yes—
35C2×#6433C2214yes—
36C2×#6433C2214yes—
37C2×#6432C2212yes—
38C2×#6432C2212yes—
39C2×#6432C2214yes—
40C2×C4×Dic14C2214yes—
41C2×C4×Dic14C2214yes—
42C2×C4×Dic14C2218yes—
43C2×#3556—71nomaximal, Sylow
44C22×C7×Q8C2314yes—
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2312yes—
47C22×Dic14C2314yes—
48C22×Dic14C2314yes—
49C7×C4⋊Q8C23116yes—
50C7×#125C23116yes—
51C7×C22⋊Q8C23132yes—
52C4×C7×Q8C23132yes—
53C7×#117C23116yes—
54C2×C7×C4⋊C4C2314yes—
55C2×C7×C4⋊C4C2314yes—
56C2×C7×C4⋊C4C2318yes—
57C2×C7×C22⋊C4C2314yes—
58C2×C42×C7C2311yescharacteristic
59C2×C42×C7C2312yes—
60C2×C42×C7C2314yes—
61C2×C42×C7C2311yescharacteristic
62C2×C42×C7C2318yes—
63C2×C22⋊Dic7C2318yes—
64Q8×Dic7C23164yes—
65#6507C23164yes—
66#6489C23132yes—
67C2×C4⋊Dic7C2314yes—
68C2×C4⋊Dic7C2314yes—
69C2×C4⋊Dic7C2314yes—
70C2×C4⋊Dic7C2314yes—
71C2×C4⋊Dic7C23116yes—
72#6487C23132yes—
73#6487C23132yes—
74C2×Dic7⋊C4C2318yes—
75C2×Dic7⋊C4C2318yes—
76C2×Dic7⋊C4C23116yes—
77C2×Dic7⋊C4C23116yes—
78C2×C4×Dic7C2318yes—
79C2×C4×Dic7C23116yes—
80#6453C231128yes—
81#6453C23164yes—
82#6452C231128yes—
83#6452C231128yes—
84#6450C23164yes—
85#6442C231128yes—
86#6433C23132yes—
87#6433C23132yes—
88#6432C23116yes—
89#6432C23116yes—
90#6432C23132yes—
91C4×Dic14C23132yes—
92C4×Dic14C23132yes—
93C4×Dic14C23164yes—
94#3556—732no—
95C2×#564—74no—
96C2×#557—74no—
97C2×#557—74no—
98C2×#557—74no—
99C2×#541—78no—
100C2×#541—74no—
101C2×#533—72no—
102C2×#533D711yescharacteristic
103C24×C7C2411yescharacteristic
104C2×C7×Q8—216no—
105C2×C7×Q8C24116yes—
106C22×C4×C7—24no—
107C22×C4×C7—28no—
108C22×C4×C7C2418yes—
109C22×C4×C7C2411yescharacteristic
110C22×C4×C7C2412yes—
111C22×C4×C7C2414yes—
112C22×C4×C7C2418yes—
113C22×C4×C7C2412yes—
114C22×C4×C7C2411yescharacteristic
115C22×Dic7C2418yes—
116C22×Dic7C2418yes—
117C2×Dic14—216no—
118C2×Dic14—216no—
119C2×Dic14C24116yes—
120C2×Dic14C24116yes—
121C7×C4⋊C4C24116yes—
122C7×C4⋊C4C24116yes—
123C7×C4⋊C4C24132yes—
124C7×C22⋊C4C24116yes—
125C42×C7C2414yes—
126C42×C7C2418yes—
127C42×C7C24116yes—
128C42×C7C2414yes—
129C22⋊Dic7C24132yes—
130C4⋊Dic7C24116yes—
131C4⋊Dic7C24116yes—
132C4⋊Dic7C24116yes—
133C4⋊Dic7C24116yes—
134C4⋊Dic7C24164yes—
135Dic7⋊C4C24132yes—
136Dic7⋊C4C24132yes—
137Dic7⋊C4C24164yes—
138Dic7⋊C4C24164yes—
139C4×Dic7C24132yes—
140C4×Dic7C24164yes—
141#564—764no—
142#557—764no—
143#557—764no—
144#557—764no—
145#541—7128no—
146#541—764no—
147#533—732no—
148#533C2×D7116yes—
149C2×C4⋊Q8—78no—
150C2×C4⋊Q8—72no—
151C2×C4⋊Q8—72no—
152C2×C4⋊Q8—74no—
153C2×C4⋊Q8C2×D712yes—
154C2×#126—716no—
155C2×#125—716no—
156C2×#125—716no—
157C2×#125—78no—
158C2×#125—716no—
159C2×#125—74no—
160C2×#125—74no—
161C2×#125C2×D712yes—
162C2×C22⋊Q8—74no—
163C2×C22⋊Q8—74no—
164C2×C22⋊Q8C2×D714yes—
165C2×C4×Q8—78no—
166C2×C4×Q8—78no—
167C2×C4×Q8—74no—
168C2×C4×Q8—74no—
169C2×C4×Q8—78no—
170C2×C4×Q8C2×D714yes—
171C2×#117—74no—
172C2×#117C2×D712yes—
173C22×C42C2×D711yescharacteristic
174C23×C7—22no—
175C23×C7—24no—
176C23×C7C2512yes—
177C23×C7C2511yescharacteristic
178C7×Q8—232no—
179C2×C4×C7—22no—
180C2×C4×C7—24no—
181C2×C4×C7—216no—
182C2×C4×C7—28no—
183C2×C4×C7—216no—
184C2×C4×C72−1+414yes—
185C2×C4×C72−1+418yes—
186C2×C4×C7C25116yes—
187C2×C4×C7C2512yes—
188C2×C4×C7C2514yes—
189C2×C4×C7C2514yes—
190C2×C4×C7C2512yes—
191C2×Dic7—216no—
192C2×Dic7—216no—
193C2×Dic7C25116yes—
194C2×Dic7C25116yes—
195Dic14—232no—
196Dic14—232no—
197C22×Q8—74no—
198C22×Q8—74no—
199C22×Q8C22×D714yes—
200C23×C4C22×D712yes—
201C23×C4C22×D711yescharacteristic
202C4⋊Q8—764no—
203C4⋊Q8—716no—
204C4⋊Q8—716no—
205C4⋊Q8—732no—
206C4⋊Q8C22×D7116yes—
207#126—7128no—
208#125—764no—
209#125—7128no—
210#125—7128no—
211#125—7128no—
212#125—732no—
213#125—732no—
214#125C22×D7116yes—
215C22⋊Q8—732no—
216C22⋊Q8—732no—
217C22⋊Q8C22×D7132yes—
218C4×Q8—764no—
219C4×Q8—764no—
220C4×Q8—732no—
221C4×Q8—732no—
222C4×Q8—764no—
223C4×Q8C22×D7132yes—
224#117—732no—
225#117C22×D7116yes—
226C2×C4⋊C4—74no—
227C2×C4⋊C4—74no—
228C2×C4⋊C4—74no—
229C2×C4⋊C4—74no—
230C2×C4⋊C4—78no—
231C2×C4⋊C4—78no—
232C2×C4⋊C4—716no—
233C2×C4⋊C4—716no—
234C2×C4⋊C4—716no—
235C2×C4⋊C4C22×D714yes—
236C2×C4⋊C4C22×D714yes—
237C2×C4⋊C4C22×D718yes—
238C2×C22⋊C4—78no—
239C2×C22⋊C4C22×D714yes—
240C2×C42—78no—
241C2×C42—716no—
242C2×C42C22×D714yes—
243C2×C42C22×D711yescharacteristic
244C2×C42C22×D712yes—
245C2×C42C22×D711yescharacteristic
246C2×C42C22×D718yes—
247C22×C7—22no—
248C22×C7—24no—
249C22×C7—44no—
250C22×C7C2×2−1+412yes—
251C22×C7C2×2−1+414yes—
252C22×C7C2611yescharacteristic
253C4×C7—22no—
254C4×C7—24no—
255C4×C7—216no—
256C4×C7C2×2−1+414yes—
257C4×C7C2×2−1+418yes—
258Dic7—216no—
259Dic7—216no—
260C24C23×D711yescharacteristic
261C2×Q8—216no—
262C2×Q8—716no—
263C2×Q8—716no—
264C2×Q8—1416no—
265C2×Q8—1416no—
266C2×Q8C23×D7116yes—
267C22×C4—24no—
268C22×C4—28no—
269C22×C4—78no—
270C22×C4—78no—
271C22×C4C23×D718yes—
272C22×C4C23×D714yes—
273C22×C4C23×D718yes—
274C22×C4C23×D711yescharacteristic
275C22×C4C23×D712yes—
276C22×C4C23×D711yescharacteristic
277C22×C4C23×D712yes—
278C4⋊C4—732no—
279C4⋊C4—732no—
280C4⋊C4—764no—
281C4⋊C4—764no—
282C4⋊C4—716no—
283C4⋊C4—716no—
284C4⋊C4—716no—
285C4⋊C4—716no—
286C4⋊C4—764no—
287C4⋊C4C23×D7116yes—
288C4⋊C4C23×D7116yes—
289C4⋊C4C23×D7132yes—
290C22⋊C4—732no—
291C22⋊C4C23×D7116yes—
292C42—732no—
293C42—764no—
294C42C23×D714yes—
295C42C23×D718yes—
296C42C23×D714yes—
297C42C23×D7116yes—
298C2×C7—42no—
299C2×C7#355614yescomplemented
300C2×C7C22×2−1+411yescharacteristic
301C2×C7C22×2−1+412yes—
302C23—22no—
303C23—24no—
304C23C24×D712yes—
305C23C24×D711yescharacteristic
306Q8—232no—
307Q8—1432no—
308Q8—1432no—
309C2×C4—22no—
310C2×C4—24no—
311C2×C4—216no—
312C2×C4—28no—
313C2×C4—216no—
314C2×C4—716no—
315C2×C4—716no—
316C2×C4—1416no—
317C2×C4—1416no—
318C2×C4#655114yes—
319C2×C4#655418yes—
320C2×C4C24×D7116yes—
321C2×C4C24×D712yes—
322C2×C4C24×D714yes—
323C2×C4C24×D712yes—
324C2×C4C24×D714yes—
325C7C2×#355611yescharacteristic, complemented, Sylow
326C22—22no—
327C22—24no—
328C22—44no—
329C22C2×#655112yes—
330C22C2×#655414yes—
331C22C25×D711yescharacteristic
332C4—22no—
333C4—24no—
334C4—216no—
335C4—1416no—
336C4—1416no—
337C4C2×#655114yes—
338C4C2×#655418yes—
339C2—42no—
340C2#1174333814yesdirect product factor
341C2C22×#655111yescharacteristic
342C2C22×#655412yes—
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC2×C7×#533C2
socleC23×C7C25
prime radicalC24×C7C24
hypercenterC2×#533D7
hypocenterC7C2×#3556
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
2. #11743338C2direct (N × H)
3. C2×#90412C2semidirect
4. C2×C7⋊#564C2semidirect
6. C2×#90258C2semidirect
7. C2×#90261C2semidirect
22. #90412C22semidirect
23. C7⋊#564C22semidirect
25. #90261C22semidirect
26. #90258C22semidirect
299. C2×C7#3556semidirect
325. C7C2×#3556semidirect
340. C2#11743338direct (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
#117433382
C2×#904122
C2×C7⋊#5642
C2×#903162
C2×#902582
C2×#902612
C2×#902092
C2×#901612
C2×#35567