Finite Group Databasebeta

← C2×#11741519 #14217237

Subgroups — C2×#11741519 #14217237

Order 1792.

5150 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C7×#41C211yesmaximal, characteristic
2C23×#1136C212yesmaximal, complemented
3#11741519C2116yesmaximal, direct product factor
4C2×#90006C218yesmaximal, complemented
5C2×#89979C214yesmaximal, complemented
6C22×C7×#41—216no—
7C22×C7×#41C414yes—
8C22×C7×#41C418yes—
9C22×C7×#41C2214yes—
10C22×C7×#41C2218yes—
11C23×C7×Q8C411yescharacteristic
12C23×C7×D4C412yes—
13C23×C7×D4C411yescharacteristic
14C24×C4×C7C2212yes—
15C24×C4×C7C2211yescharacteristic
16C22×#1136—216no—
17C22×#1136C2214yes—
18C22×#1136C2214yescomplemented
19C22×#1136C22116yescomplemented
20C23×C7⋊C8C2214yescomplemented
21#90006C22164yescomplemented
22#89979C22132yescomplemented
23C2×C22⋊(C7⋊C8)C22116yescomplemented
24C2×#2879—71nomaximal, Sylow
25C25×C7C2×C412yes—
26C25×C7C2×C411yescharacteristic
27C2×C7×#41—232no—
28C2×C7×#41—264no—
29C2×C7×#41—216no—
30C2×C7×#41—216no—
31C2×C7×#41—264no—
32C2×C7×#41C2×C4116yes—
33C2×C7×#41C2×C4132yes—
34C2×C7×#41C23116yes—
35C22×C7×Q8—28no—
36C22×C7×Q8C2×C414yes—
37C22×C7×Q8C2×C418yes—
38C22×C7×D4—216no—
39C22×C7×D4—28no—
40C22×C7×D4C2×C418yes—
41C22×C7×D4C2×C4116yes—
42C22×C7×D4C2×C414yes—
43C22×C7×D4C2×C418yes—
44C23×C4×C7—216no—
45C23×C4×C7C2×C412yes—
46C23×C4×C7C2×C414yes—
47C23×C4×C7C2×C418yes—
48C23×C4×C7C2×C411yescharacteristic
49C23×C4×C7C2×C412yes—
50C23×C4×C7C2×C414yes—
51C23×C4×C7D4116yes—
52C23×C4×C7C2314yes—
53C23×C4×C7C2318yes—
54C23×C4×C7C2312yes—
55C23×C4×C7C2314yes—
56C23×C4×C7C2311yescharacteristic
57C2×#1136—216no—
58C2×#1136—216no—
59C2×#1136—264no—
60C2×#1136C23116yes—
61C2×#1136C23116yescomplemented
62C22×C7⋊C8—216no—
63C22×C7⋊C8C2318yes—
64C22×C7⋊C8C23116yescomplemented
65C22⋊(C7⋊C8)C23164yescomplemented
66C23×#41D711yescharacteristic
67C23×M16—72no—
68#2879—716no—
69C2×#408—78no—
70C2×#407—74no—
71C24×C7—28no—
72C24×C7—44no—
73C24×C7—48no—
74C24×C7C22⋊C418yes—
75C24×C7C22×C414yes—
76C24×C7C22×C411yescharacteristic
77C24×C7C22×C412yes—
78C24×C7C22×C418yes—
79C24×C7C22×C414yes—
80C7×#41—264no—
81C7×#41—2128no—
82C7×#41—232no—
83C7×#41—232no—
84C2×C7×Q8—232no—
85C2×C7×Q8—216no—
86C2×C7×Q8C22×C4116yes—
87C2×C7×D4—232no—
88C2×C7×D4—264no—
89C2×C7×D4—232no—
90C2×C7×D4—216no—
91C2×C7×D4C22×C4132yes—
92C2×C7×D4C22×C4116yes—
93C22×C4×C7—28no—
94C22×C4×C7—232no—
95C22×C4×C7—216no—
96C22×C4×C7—216no—
97C22×C4×C7—232no—
98C22×C4×C7C22⋊C418yes—
99C22×C4×C7C22⋊C4116yes—
100C22×C4×C7C22⋊C4132yes—
101C22×C4×C7C22×C418yes—
102C22×C4×C7C22×C414yes—
103C22×C4×C7C22×C418yes—
104C22×C4×C7C22×C4116yes—
105C22×C4×C7C22×C412yes—
106C22×C4×C7C22×C411yescharacteristic
107C22×C4×C7C22×C414yes—
108C22×C4×C7C22×C412yes—
109C22×C4×C7C22×C414yes—
110C22×C4×C7C22×C418yes—
111C22×C4×C7C2×D418yes—
112C22×C4×C7C2×D418yes—
113C22×C4×C7C2×D418yes—
114C22×C4×C7C2×D4132yes—
115C22×C4×C7C2418yes—
116C22×C4×C7C2414yes—
117C22×C4×C7C2412yes—
118C22×C4×C7C2411yescharacteristic
119#1136—232no—
120#1136—232no—
121C2×C7⋊C8—216no—
122C2×C7⋊C8—232no—
123C2×C7⋊C8C24116yes—
124C22×#41—216no—
125C22×#41Dic714yes—
126C22×#41Dic718yes—
127C22×#41C2×D714yes—
128C22×#41C2×D718yes—
129C23×Q8Dic711yescharacteristic
130C23×D4Dic712yes—
131C23×D4Dic711yescharacteristic
132C24×C4C2×D712yes—
133C24×C4C2×D711yescharacteristic
134C22×M16—74no—
135C22×M16—74no—
136C22×M16—716no—
137C22×M16—1416no—
138C23×C8—74no—
139#408—764no—
140#407—732no—
141C2×C22⋊C8—716no—
142C23×C7—24no—
143C23×C7—28no—
144C23×C7—216no—
145C23×C7—28no—
146C23×C7—216no—
147C23×C7—416no—
148C23×C7—48no—
149C23×C7—416no—
150C23×C7—432no—
151C23×C7C2×C22⋊C414yes—
152C23×C7C2×C22⋊C418yes—
153C23×C7C2×C22⋊C4116yes—
154C23×C7C23×C418yes—
155C23×C7C23×C412yes—
156C23×C7C23×C414yes—
157C23×C7C23×C411yescharacteristic
158C7×Q8—232no—
159C7×D4—264no—
160C7×D4—232no—
161C2×C4×C7—216no—
162C2×C4×C7—28no—
163C2×C4×C7—216no—
164C2×C4×C7—232no—
165C2×C4×C7—216no—
166C2×C4×C7C2×C22⋊C418yes—
167C2×C4×C7C2×C22⋊C414yes—
168C2×C4×C7C2×C22⋊C4116yes—
169C2×C4×C7C2×C22⋊C418yes—
170C2×C4×C7C2×C22⋊C4116yes—
171C2×C4×C7C2×C22⋊C4132yes—
172C2×C4×C7C23×C418yes—
173C2×C4×C7C23×C412yes—
174C2×C4×C7C23×C411yescharacteristic
175C2×C4×C7C23×C414yes—
176C2×C4×C7C22×D414yes—
177C2×C4×C7C22×D418yes—
178C2×C4×C7C22×D418yes—
179C2×C4×C7C22×D418yes—
180C2×C4×C7C2511yescharacteristic
181C7⋊C8—216no—
182C25C2×Dic712yes—
183C25C2×Dic711yescharacteristic
184C2×#41—232no—
185C2×#41—264no—
186C2×#41—216no—
187C2×#41—216no—
188C2×#41—264no—
189C2×#41C2×Dic7116yes—
190C2×#41C2×Dic7132yes—
191C2×#41C22×D7116yes—
192C22×Q8—28no—
193C22×Q8C2×Dic714yes—
194C22×Q8C2×Dic718yes—
195C22×D4—216no—
196C22×D4—28no—
197C22×D4C2×Dic718yes—
198C22×D4C2×Dic7116yes—
199C22×D4C2×Dic714yes—
200C22×D4C2×Dic718yes—
201C23×C4—216no—
202C23×C4C2×Dic712yes—
203C23×C4C2×Dic714yes—
204C23×C4C2×Dic718yes—
205C23×C4C2×Dic711yescharacteristic
206C23×C4C2×Dic712yes—
207C23×C4C2×Dic714yes—
208C23×C4C22⋊D7116yes—
209C23×C4C22×D718yes—
210C23×C4C22×D714yes—
211C23×C4C22×D714yes—
212C23×C4C22×D712yes—
213C23×C4C22×D711yescharacteristic
214C2×M16—716no—
215C2×M16—716no—
216C2×M16—1416no—
217C2×M16—1416no—
218C2×M16—1464no—
219C22×C8—716no—
220C22×C8—78no—
221C22×C8—1416no—
222C22⋊C8—764no—
223C22×C7—28no—
224C22×C7—216no—
225C22×C7—24no—
226C22×C7—28no—
227C22×C7—28no—
228C22×C7—216no—
229C22×C7—416no—
230C22×C7—432no—
231C22×C7—416no—
232C22×C7C22×C22⋊C414yes—
233C22×C7C22×C22⋊C418yes—
234C22×C7C22×C22⋊C412yes—
235C22×C7#56814yes—
236C22×C7C24×C411yescharacteristic
237C4×C7—28no—
238C4×C7C22×C22⋊C412yes—
239C4×C7C22×C22⋊C414yes—
240C4×C7C22×C22⋊C418yes—
241C4×C7C23×D412yes—
242C24—28no—
243C24—44no—
244C24—48no—
245C24C22⋊Dic718yes—
246C24C22×Dic714yes—
247C24C22×Dic711yescharacteristic
248C24C22×Dic712yes—
249C24C22×Dic718yes—
250C24C22×Dic714yes—
251#41—264no—
252#41—2128no—
253#41—232no—
254#41—232no—
255C2×Q8—232no—
256C2×Q8—216no—
257C2×Q8C22×Dic7116yes—
258C2×D4—232no—
259C2×D4—264no—
260C2×D4—232no—
261C2×D4—216no—
262C2×D4C22×Dic7132yes—
263C2×D4C22×Dic7116yes—
264C22×C4—28no—
265C22×C4—232no—
266C22×C4—216no—
267C22×C4—216no—
268C22×C4—232no—
269C22×C4C22⋊Dic718yes—
270C22×C4C22⋊Dic7116yes—
271C22×C4C22⋊Dic7132yes—
272C22×C4C22×Dic718yes—
273C22×C4C22×Dic714yes—
274C22×C4C22×Dic7116yes—
275C22×C4C22×Dic718yes—
276C22×C4C22×Dic711yescharacteristic
277C22×C4C22×Dic712yes—
278C22×C4C22×Dic714yes—
279C22×C4C22×Dic712yes—
280C22×C4C22×Dic718yes—
281C22×C4C22×Dic714yes—
282C22×C4C2×C22⋊D718yes—
283C22×C4C2×C22⋊D718yes—
284C22×C4C2×C22⋊D718yes—
285C22×C4C2×C22⋊D7132yes—
286C22×C4C23×D718yes—
287C22×C4C23×D714yes—
288C22×C4C23×D712yes—
289C22×C4C23×D711yescharacteristic
290M16—1432no—
291M16—1432no—
292C2×C8—716no—
293C2×C8—1416no—
294C2×C8—1432no—
295C2×C7—24no—
296C2×C7—28no—
297C2×C7—48no—
298C2×C7#287914yescomplemented
299C2×C7C23×C22⋊C411yescharacteristic
300C2×C7C2×#56812yes—
301C23—24no—
302C23—28no—
303C23—216no—
304C23—216no—
305C23—28no—
306C23—416no—
307C23—48no—
308C23—416no—
309C23—432no—
310C23C2×C22⋊Dic714yes—
311C23C2×C22⋊Dic718yes—
312C23C2×C22⋊Dic7116yes—
313C23C23×Dic718yes—
314C23C23×Dic712yes—
315C23C23×Dic714yes—
316C23C23×Dic711yescharacteristic
317Q8—232no—
318D4—264no—
319D4—232no—
320C2×C4—216no—
321C2×C4—28no—
322C2×C4—232no—
323C2×C4—216no—
324C2×C4—216no—
325C2×C4C2×C22⋊Dic718yes—
326C2×C4C2×C22⋊Dic714yes—
327C2×C4C2×C22⋊Dic7116yes—
328C2×C4C2×C22⋊Dic718yes—
329C2×C4C2×C22⋊Dic7116yes—
330C2×C4C2×C22⋊Dic7132yes—
331C2×C4C23×Dic718yes—
332C2×C4C23×Dic712yes—
333C2×C4C23×Dic711yescharacteristic
334C2×C4C23×Dic714yes—
335C2×C4C22×C22⋊D714yes—
336C2×C4C22×C22⋊D718yes—
337C2×C4C22×C22⋊D718yes—
338C2×C4C22×C22⋊D718yes—
339C2×C4C24×D711yescharacteristic
340C8—1416no—
341C7C2×#287911yescharacteristic, complemented, Sylow
342C22—24no—
343C22—28no—
344C22—28no—
345C22—216no—
346C22—216no—
347C22—28no—
348C22—416no—
349C22—432no—
350C22—416no—
351C22#9051014yes—
352C22C22×C22⋊Dic714yes—
353C22C22×C22⋊Dic718yes—
354C22C22×C22⋊Dic712yes—
355C22C24×Dic711yescharacteristic
356C4—28no—
357C4C22×C22⋊Dic714yes—
358C4C22×C22⋊Dic712yes—
359C4C22×C22⋊Dic718yes—
360C4C23×C22⋊D712yes—
361C2—24no—
362C2—28no—
363C2—48no—
364C2#1174151914yesdirect product factor
365C2C2×#9051012yes—
366C2C23×C22⋊Dic711yescharacteristic
subgroupG/H
centerC22×C4C23×D7
commutatorC22×C7C24×C4
FrattiniC2×C4C24×D7
Fitting, prime radicalC23×C7×#41C2
socleC23×C7C23×C4
cosocleC2×C4×C7C25
hypercenterC23×#41D7
hypocenterC7C2×#2879
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C23×#41

Complements

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

NH ≅ G/Ntype
2. C23×#1136C2semidirect
3. #11741519C2direct (N × H)
4. C2×#90006C2semidirect
5. C2×#89979C2semidirect
18. C22×#1136C22semidirect
19. C22×#1136C22semidirect
20. C23×C7⋊C8C22semidirect
21. #90006C22semidirect
22. #89979C22semidirect
23. C2×C22⋊(C7⋊C8)C22semidirect
61. C2×#1136C23semidirect
64. C22×C7⋊C8C23semidirect
65. C22⋊(C7⋊C8)C23semidirect
298. C2×C7#2879semidirect
341. C7C2×#2879semidirect
364. C2#11741519direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C7×#412
C23×#11362
#117415192
C2×#900062
C2×#899792
C2×#28797