Finite Group Databasebeta

← C2×#11740511 #13520586

Subgroups — C2×#11740511 #13520586

Order 1792.

2894 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#125C211yesmaximal, characteristic, complemented
2C22×C4×D28C211yesmaximal, characteristic
3#11740511C2116yesmaximal, direct product factor
4C2×#89764C212yesmaximal, complemented
5C2×#89765C212yesmaximal, complemented
6C2×#89763C212yesmaximal
7C2×#89761C214yesmaximal, complemented
8C2×#89755C212yesmaximal, complemented
9C2×#89709C211yesmaximal, characteristic, complemented
10C23×D28C2211yescharacteristic
11C23×C4×D7C2212yes—
12C2×C7×#125—28no—
13C2×C7×#125C2218yescomplemented
14C22×C7×C4⋊C4C2212yes—
15C22×C7×C4⋊C4C2212yes—
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C42×C7C2211yescharacteristic
19C22×(C2×D7)⋊C4C2212yes—
20C22×(C2×D7)⋊C4C2214yes—
21C22×(C2×D7)⋊C4C2214yes—
22C22×C4⋊Dic7C2211yescharacteristic
23C22×Dic7⋊C4C2214yes—
24C2×C4×D28—28no—
25C2×C4×D28C2218yes—
26C2×C7⋊#95C2212yes—
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2214yes—
30#89765C22116yescomplemented
31#89764C22116yescomplemented
32#89763C22116yes—
33#89761C22132yescomplemented
34#89755C22116yescomplemented
35#89709C2218yescomplemented
36C2×#2633—71nomaximal, Sylow
37C24×D7C2312yes—
38C23×C4×C7C2312yes—
39C23×C4×C7C2312yes—
40C23×C4×C7C2311yescharacteristic
41C23×C4×C7C2311yescharacteristic
42C23×C4×C7C2311yescharacteristic
43C23×Dic7C2312yes—
44C23×Dic7C2314yes—
45C22×D28—28no—
46C22×D28—24no—
47C22×D28C2314yes—
48C22×C4×D7—28no—
49C22×C4×D7—48no—
50C22×C4×D7C2318yes—
51C7×#125—232no—
52C2×C7×C4⋊C4—28no—
53C2×C7×C4⋊C4—24no—
54C2×C7×C4⋊C4—24no—
55C2×C7×C4⋊C4—28no—
56C2×C7×C4⋊C4C2318yes—
57C2×C7×C4⋊C4C2318yes—
58C2×C7×C4⋊C4C2314yes—
59C2×C7×C4⋊C4C2314yes—
60C2×C42×C7D418yes—
61C2×C42×C7C2314yes—
62C2×(C2×D7)⋊C4—216no—
63C2×(C2×D7)⋊C4—28no—
64C2×(C2×D7)⋊C4—48no—
65C2×(C2×D7)⋊C4C2318yes—
66C2×(C2×D7)⋊C4C23116yes—
67C2×(C2×D7)⋊C4C23116yes—
68C2×C4⋊Dic7—24no—
69C2×C4⋊Dic7C2314yes—
70C2×Dic7⋊C4—48no—
71C2×Dic7⋊C4C23116yes—
72C4×D28—232no—
73C7⋊#95C2318yes—
74C7⋊#95C2318yes—
75C7⋊#95C2318yes—
76C7⋊#95C23116yes—
77C22×#125D711yescharacteristic, complemented
78C22×C4×D4—71no—
79#2633—716no—
80C2×#399—72no—
81C2×#398—72no—
82C2×#397—72no—
83C2×#394—72no—
84C2×#385—74no—
85C2×#383—71no—
86C24×C7C2411yescharacteristic
87C23×D7—24no—
88C23×D7—24no—
89C23×D7—28no—
90C23×D7—28no—
91C23×D7#4118yes—
92C23×D7C2414yes—
93C22×C4×C7—24no—
94C22×C4×C7—24no—
95C22×C4×C7—24no—
96C22×C4×C7—24no—
97C22×C4×C7—24no—
98C22×C4×C7—28no—
99C22×C4×C7—24no—
100C22×C4×C7—24no—
101C22×C4×C7C2×D414yes—
102C22×C4×C7C2×D414yes—
103C22×C4×C7C2×D414yes—
104C22×C4×C7C2414yes—
105C22×C4×C7C2414yes—
106C22×C4×C7C2412yes—
107C22×C4×C7C2412yes—
108C22×C4×C7C2412yes—
109C22×Dic7—24no—
110C22×Dic7—28no—
111C22×Dic7—28no—
112C22×Dic7—28no—
113C22×Dic7—28no—
114C22×Dic7C2418yes—
115C22×Dic7C2414yes—
116C2×D28—232no—
117C2×D28—216no—
118C2×D28—28no—
119C2×C4×D7—216no—
120C2×C4×D7—416no—
121C2×C4×D7—432no—
122C7×C4⋊C4—216no—
123C7×C4⋊C4—28no—
124C7×C4⋊C4—28no—
125C7×C4⋊C4—216no—
126C42×C7C2×D4116yes—
127(C2×D7)⋊C4—232no—
128(C2×D7)⋊C4—216no—
129(C2×D7)⋊C4—416no—
130C4⋊Dic7—28no—
131Dic7⋊C4—416no—
132C23×D4—71no—
133C24×C4—72no—
134C2×#125—28no—
135C2×#125C2×D718yescomplemented
136C2×C4×D4—78no—
137C2×C4×D4—148no—
138C22×C4⋊C4—71no—
139C22×C4⋊C4—74no—
140C22×C4⋊C4C2×D712yes—
141C22×C4⋊C4C2×D711yescharacteristic
142C22×C4⋊C4C2×D711yescharacteristic
143C22×C4⋊C4C2×D712yes—
144C22×C22⋊C4—74no—
145C22×C22⋊C4—72no—
146C22×C22⋊C4—74no—
147C22×C42C2×D711yescharacteristic
148#399—716no—
149#398—716no—
150#397—716no—
151#394—716no—
152#385—732no—
153#383—78no—
154C2×#95—72no—
155C2×#95—74no—
156C2×#95—72no—
157C2×#95—72no—
158C23×C7C22×D412yes—
159C23×C7C2×#4114yes—
160C23×C7H(5,𝔽2)14yes—
161C23×C72−1+414yes—
162C23×C7C2511yescharacteristic
163C22×D7—216no—
164C22×D7—232no—
165C22×D7—24no—
166C22×D7—24no—
167C22×D7—28no—
168C22×D7—28no—
169C22×D7—48no—
170C22×D7—48no—
171C22×D7—416no—
172C22×D7C2×#4118yes—
173C2×C4×C7—28no—
174C2×C4×C7—28no—
175C2×C4×C7—28no—
176C2×C4×C7—24no—
177C2×C4×C7—24no—
178C2×C4×C7—24no—
179C2×C4×C7—24no—
180C2×C4×C7—24no—
181C2×C4×C7—28no—
182C2×C4×C7—24no—
183C2×C4×C7—24no—
184C2×C4×C7—48no—
185C2×C4×C7—48no—
186C2×C4×C7C22×D414yes—
187C2×C4×C7C22×D414yes—
188C2×C4×C7C22×D414yes—
189C2×Dic7—24no—
190C2×Dic7—28no—
191C2×Dic7—28no—
192C2×Dic7—28no—
193C2×Dic7—28no—
194C2×Dic7—48no—
195C2×Dic7—416no—
196D28—232no—
197C4×D7—432no—
198C25—72no—
199C22×D4—74no—
200C22×D4—148no—
201C22×D4—144no—
202C23×C4—74no—
203C23×C4—72no—
204C23×C4—78no—
205C23×C4—148no—
206C23×C4—288no—
207C23×C4C22×D712yes—
208C23×C4C22×D712yes—
209C23×C4C22×D711yescharacteristic
210C23×C4C22×D711yescharacteristic
211C23×C4C22×D711yescharacteristic
212#125—232no—
213C4×D4—1432no—
214C2×C4⋊C4—24no—
215C2×C4⋊C4—24no—
216C2×C4⋊C4—28no—
217C2×C4⋊C4—28no—
218C2×C4⋊C4—74no—
219C2×C4⋊C4—716no—
220C2×C4⋊C4—144no—
221C2×C4⋊C4—288no—
222C2×C4⋊C4C22×D718yes—
223C2×C4⋊C4C22×D718yes—
224C2×C4⋊C4C22×D714yes—
225C2×C4⋊C4C22×D714yes—
226C2×C22⋊C4—78no—
227C2×C22⋊C4—716no—
228C2×C22⋊C4—716no—
229C2×C22⋊C4—1416no—
230C2×C22⋊C4—148no—
231C2×C22⋊C4—288no—
232C2×C42C22⋊D718yes—
233C2×C42C22×D714yes—
234#95—78no—
235#95—78no—
236#95—78no—
237#95—716no—
238C22×C7#52514yes—
239C22×C7#53514yes—
240C22×C7#53614yes—
241C22×C7#539116yes—
242C22×C7C23×D411yescharacteristic
243C22×C7C22×#4112yes—
244C22×C7C2×H(5,𝔽2)12yes—
245C22×C7C2×2−1+412yes—
246C2×D7—28no—
247C2×D7—216no—
248C2×D7—432no—
249C2×D7—44no—
250C2×D7—44no—
251C2×D7—48no—
252C4×C7—24no—
253C4×C7—24no—
254C4×C7—24no—
255C4×C7—44no—
256C4×C7—44no—
257Dic7—44no—
258Dic7—48no—
259C24—78no—
260C24—74no—
261C24—148no—
262C24—144no—
263C24—148no—
264C24—144no—
265C24C23×D711yescharacteristic
266C2×D4—1416no—
267C2×D4—1432no—
268C2×D4—148no—
269C22×C4—24no—
270C22×C4—24no—
271C22×C4—24no—
272C22×C4—28no—
273C22×C4—24no—
274C22×C4—24no—
275C22×C4—24no—
276C22×C4—24no—
277C22×C4—78no—
278C22×C4—74no—
279C22×C4—148no—
280C22×C4—148no—
281C22×C4—148no—
282C22×C4—148no—
283C22×C4—144no—
284C22×C4—1416no—
285C22×C4—2816no—
286C22×C4—2832no—
287C22×C4C2×C22⋊D714yes—
288C22×C4C2×C22⋊D714yes—
289C22×C4C2×C22⋊D714yes—
290C22×C4C23×D714yes—
291C22×C4C23×D714yes—
292C22×C4C23×D712yes—
293C22×C4C23×D712yes—
294C22×C4C23×D712yes—
295C4⋊C4—28no—
296C4⋊C4—28no—
297C4⋊C4—216no—
298C4⋊C4—216no—
299C4⋊C4—148no—
300C4⋊C4—2816no—
301C22⋊C4—1432no—
302C22⋊C4—1416no—
303C22⋊C4—2816no—
304C42C2×C22⋊D7116yes—
305C2×C7#263318yescomplemented
306C2×C7C2×#52511yescharacteristic
307C2×C7C2×#53511yescharacteristic
308C2×C7C2×#53611yescharacteristic
309C2×C7C2×#53914yes—
310D7—48no—
311C23—78no—
312C23—1432no—
313C23—1416no—
314C23—148no—
315C23—144no—
316C23—148no—
317C23—144no—
318C23—2816no—
319C23—288no—
320C23—288no—
321C23#655114yes—
322C23D7×#4114yes—
323C23#655314yes—
324C23C22×C22⋊D712yes—
325C23C24×D711yescharacteristic
326D4—1432no—
327C2×C4—28no—
328C2×C4—28no—
329C2×C4—28no—
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—28no—
334C2×C4—24no—
335C2×C4—24no—
336C2×C4—24no—
337C2×C4—24no—
338C2×C4—48no—
339C2×C4—48no—
340C2×C4—148no—
341C2×C4—148no—
342C2×C4—148no—
343C2×C4—148no—
344C2×C4—144no—
345C2×C4—2832no—
346C2×C4—2816no—
347C2×C4—288no—
348C2×C4C22×C22⋊D714yes—
349C2×C4C22×C22⋊D714yes—
350C2×C4C22×C22⋊D714yes—
351C7C2×#263311yescharacteristic, complemented, Sylow
352C22—148no—
353C22—1416no—
354C22—284no—
355C22—284no—
356C22—2832no—
357C22—288no—
358C22#90383116yes—
359C22#9050714yes—
360C22#9051914yes—
361C22#9052114yes—
362C22C2×#655112yes—
363C22C2×D7×#4112yes—
364C22C2×#655312yes—
365C22C23×C22⋊D711yescharacteristic
366C4—24no—
367C4—24no—
368C4—24no—
369C4—44no—
370C4—44no—
371C4—284no—
372C4—288no—
373C2—288no—
374C2#1174051118yesdirect product factor
375C2C2×#9038314yes—
376C2C2×#9050711yescharacteristic
377C2C2×#9051911yescharacteristic
378C2C2×#9052111yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC22×C7×#125C2
socleC24×C7C24
prime radicalC23×D28C22
hypercenterC22×#125D7
hypocenterC7C2×#2633
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
1. C22×C7×#125C2semidirect
3. #11740511C2direct (N × H)
4. C2×#89764C2semidirect
5. C2×#89765C2semidirect
7. C2×#89761C2semidirect
8. C2×#89755C2semidirect
9. C2×#89709C2semidirect
13. C2×C7×#125C22semidirect
30. #89765C22semidirect
31. #89764C22semidirect
33. #89761C22semidirect
34. #89755C22semidirect
35. #89709C22semidirect
77. C22×#125D7semidirect
135. C2×#125C2×D7semidirect
305. C2×C7#2633semidirect
351. C7C2×#2633semidirect
374. C2#11740511direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1252
C22×C4×D282
#117405112
C2×#897642
C2×#897652
C2×#897632
C2×#897612
C2×#897552
C2×#897092
C2×#26337