Finite Group Databasebeta

← C2×#11740733 #14223251

Subgroups — C2×#11740733 #14223251

Order 1792.

3262 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#532C211yesmaximal, characteristic
2C22×#6514C214yesmaximal, complemented
3C22×#6432C211yesmaximal, characteristic, complemented
4#11740733C2116yesmaximal, direct product factor
5C2×#89864C212yesmaximal, complemented
6C2×#89848C212yesmaximal, complemented
7C2×#89832C214yesmaximal, complemented
8C2×C4×#1136C211yesmaximal, characteristic, complemented
9C22×C7×#41C2212yes—
10C23×Dic14C2212yes—
11C7×#532—24no—
12C7×#532C2218yes—
13C2×C7×C4⋊Q8C2211yescharacteristic
14C2×C7×#127C2211yescharacteristic
15C2×C7×#124C2212yes—
16C2×C7×#121—22no—
17C2×C4×C7×D4—22no—
18C22×C42×C7C2211yescharacteristic
19C2×#6514—232no—
20C2×#6514C22132yescomplemented
21C22×#1144C2218yes—
22C22×#1142C2218yes—
23C22×C4⋊Dic7—22no—
24C22×#1136C2212yes—
25C2×#6432—24no—
26C2×#6432—22no—
27C2×#6432C2212yes—
28C2×#6432C2212yes—
29C2×#6432C2218yescomplemented
30#89864C22116yescomplemented
31#89848C22116yescomplemented
32#89832C22132yescomplemented
33C4×#1136C2218yescomplemented
34C2×#6377C2212yes—
35C2×C4×C7⋊C8C2212yes—
36C2×#3152—71nomaximal, Sylow
37C2×C7×#41—24no—
38C2×C7×#41—216no—
39C2×C7×#41C2318yes—
40C22×C7×Q8C2312yes—
41C22×C7×D4—22no—
42C22×C7×D4—22no—
43C22×C7×D4C2312yes—
44C23×C4×C7—22no—
45C23×C4×C7D412yes—
46C23×C4×C7C2311yescharacteristic
47C23×Dic7—22no—
48C22×Dic14—216no—
49C22×Dic14—22no—
50C22×Dic14—24no—
51C22×Dic14C2314yes—
52C22×Dic14C2318yes—
53C7×C4⋊Q8—22no—
54C7×C4⋊Q8C2314yes—
55C7×#127—22no—
56C7×#127C2314yes—
57C7×#124—24no—
58C7×#124C2318yes—
59C7×#121—216no—
60C4×C7×D4—216no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C22⋊C4—24no—
63C2×C42×C7D412yes—
64C2×C42×C7D414yes—
65C2×C42×C7C2311yescharacteristic
66C2×C42×C7C2311yescharacteristic
67C2×C42×C7C2314yes—
68#6514—2128no—
69C2×#1144—232no—
70C2×#1144C23132yes—
71C2×#1142—232no—
72C2×#1142C23132yes—
73C2×C4⋊Dic7—24no—
74C2×C4⋊Dic7—24no—
75C2×C4⋊Dic7—216no—
76C2×#1136D4116yescomplemented
77C2×#1136C2318yes—
78C22×C7⋊C8C2314yes—
79#6432—24no—
80#6432—24no—
81#6432—216no—
82#6432C2318yes—
83#6432C2318yes—
84#6377C2318yes—
85C4×C7⋊C8C2318yes—
86C22×#137—74no—
87C2×#532D711yescharacteristic
88C22×C4⋊Q8—71no—
89#3152—716no—
90C2×#497—74no—
91C2×#494—72no—
92C2×#492—72no—
93C2×C4×M16—71no—
94C24×C7—22no—
95C24×C7C2×D411yescharacteristic
96C7×#41—232no—
97C7×#41—416no—
98C2×C7×Q8—22no—
99C2×C7×Q8—28no—
100C2×C7×Q8C2414yes—
101C2×C7×D4—28no—
102C2×C7×D4—28no—
103C2×C7×D4—28no—
104C2×C7×D4—22no—
105C2×C7×D4—48no—
106C2×C7×D4—48no—
107C2×C7×D4C2414yes—
108C22×C4×C7—28no—
109C22×C4×C7—22no—
110C22×C4×C7—28no—
111C22×C4×C7—48no—
112C22×C4×C7C2×D412yes—
113C22×C4×C7C2×D418yes—
114C22×C4×C7C2×D411yescharacteristic
115C22×C4×C7C2×D412yes—
116C22×C4×C7C2×D418yes—
117C22×C4×C7C2×D412yes—
118C22×C4×C7C2411yescharacteristic
119C22×C4×C7C2412yes—
120C22×Dic7—28no—
121C22×Dic7—24no—
122C22×Dic7—48no—
123C2×Dic14—216no—
124C2×Dic14—232no—
125C2×Dic14—28no—
126C2×Dic14—24no—
127C2×Dic14—48no—
128C2×Dic14—416no—
129C2×Dic14C2418yes—
130C7×C4⋊C4—28no—
131C7×C22⋊C4—216no—
132C42×C7C2×D418yes—
133C42×C7C2×D412yes—
134C42×C7C2×D412yes—
135C42×C7C2412yes—
136C42×C7C2412yes—
137#1144—264no—
138#1142—264no—
139C4⋊Dic7—216no—
140C4⋊Dic7—216no—
141#1136C2×D4132yescomplemented
142C2×C7⋊C8C2×D4116yes—
143C2×C7⋊C8C2418yes—
144C22×#41C2×D712yes—
145C23×Q8—72no—
146C2×#137—732no—
147C2×#137—1432no—
148C22×Q16—78no—
149C22×SD16—78no—
150C22×M16—72no—
151#532—24no—
152#532C2×D718yes—
153C2×C4⋊Q8—72no—
154C2×C4⋊Q8—72no—
155C2×C4⋊Q8—78no—
156C2×C4⋊Q8—142no—
157C2×C4⋊Q8—144no—
158C2×C4⋊Q8C2×D711yescharacteristic
159C2×#127C2×D711yescharacteristic
160C2×#124C2×D712yes—
161C2×#121—22no—
162C2×C4×D4—22no—
163C22×C4⋊C4—142no—
164C22×C42C2×D711yescharacteristic
165#497—732no—
166#494—716no—
167#492—716no—
168C4×M16—78no—
169C2×#97—72no—
170C2×C4×C8—72no—
171C23×C7—24no—
172C23×C7—24no—
173C23×C7—44no—
174C23×C7—48no—
175C23×C7#12714yes—
176C23×C7C22×D412yes—
177C23×C7C22×D411yescharacteristic
178C7×Q8—28no—
179C7×Q8—44no—
180C7×D4—28no—
181C7×D4—416no—
182C7×D4—44no—
183C7×D4—416no—
184C2×C4×C7—24no—
185C2×C4×C7—216no—
186C2×C4×C7—24no—
187C2×C4×C7—44no—
188C2×C4×C7—416no—
189C2×C4×C7#12714yes—
190C2×C4×C7#12718yes—
191C2×C4×C7#13718yescomplemented
192C2×C4×C7C22×D414yes—
193C2×C4×C7C22×D418yes—
194C2×C4×C7C22×D414yes—
195C2×C4×C7C22×D412yes—
196C2×C4×C7C22×D411yescharacteristic
197C2×C4×C7C22×D414yes—
198C2×C4×C7C2511yescharacteristic
199C2×Dic7—28no—
200C2×Dic7—416no—
201C2×Dic7—48no—
202Dic14—216no—
203Dic14—416no—
204Dic14—48no—
205C7⋊C8C22×D4116yes—
206C2×#41—24no—
207C2×#41—216no—
208C2×#41C22×D718yes—
209C22×Q8—74no—
210C22×Q8—78no—
211C22×Q8—144no—
212C22×Q8—142no—
213C22×Q8—1416no—
214C22×Q8C22×D712yes—
215C22×D4—22no—
216C22×D4—22no—
217C22×D4C22×D712yes—
218C23×C4—22no—
219C23×C4—142no—
220C23×C4C22⋊D712yes—
221C23×C4C22×D711yescharacteristic
222#137—14128no—
223C2×Q16—732no—
224C2×Q16—1432no—
225C2×SD16—732no—
226C2×SD16—1432no—
227C2×M16—716no—
228C2×M16—78no—
229C22×C8—74no—
230C4⋊Q8—22no—
231C4⋊Q8—78no—
232C4⋊Q8—78no—
233C4⋊Q8—1416no—
234C4⋊Q8—144no—
235C4⋊Q8—144no—
236C4⋊Q8C22×D714yes—
237#127—22no—
238#127C22×D714yes—
239#124—24no—
240#124C22×D718yes—
241#121—216no—
242C4×D4—216no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—1416no—
245C2×C4⋊C4—144no—
246C2×C4⋊C4—144no—
247C2×C22⋊C4—24no—
248C2×C42C22⋊D712yes—
249C2×C42C22⋊D714yes—
250C2×C42C22×D711yescharacteristic
251C2×C42C22×D711yescharacteristic
252C2×C42C22×D714yes—
253#97—78no—
254C4×C8—78no—
255C22×C7—28no—
256C22×C7—24no—
257C22×C7—44no—
258C22×C7—48no—
259C22×C7—88no—
260C22×C7C2×#12714yes—
261C22×C7C2×#12712yes—
262C22×C7C2×#13714yes—
263C22×C7C23×D411yescharacteristic
264C4×C7—24no—
265C4×C7—44no—
266C4×C7C2×#12714yes—
267C4×C7C2×#12712yes—
268C4×C7C2×#13718yescomplemented
269C4×C7C23×D412yes—
270Dic7—48no—
271C24—22no—
272C24C2×C22⋊D711yescharacteristic
273#41—232no—
274#41—416no—
275C2×Q8—22no—
276C2×Q8—28no—
277C2×Q8—78no—
278C2×Q8—148no—
279C2×Q8—144no—
280C2×Q8—1416no—
281C2×Q8—1432no—
282C2×Q8—288no—
283C2×Q8—2816no—
284C2×Q8C23×D714yes—
285C2×D4—28no—
286C2×D4—28no—
287C2×D4—28no—
288C2×D4—22no—
289C2×D4—48no—
290C2×D4—48no—
291C2×D4C23×D714yes—
292C22×C4—28no—
293C22×C4—22no—
294C22×C4—28no—
295C22×C4—48no—
296C22×C4—148no—
297C22×C4—144no—
298C22×C4—288no—
299C22×C4D4×D718yes—
300C22×C4C2×C22⋊D718yes—
301C22×C4C2×C22⋊D712yes—
302C22×C4C2×C22⋊D712yes—
303C22×C4C2×C22⋊D711yescharacteristic
304C22×C4C2×C22⋊D712yes—
305C22×C4C23×D712yes—
306C22×C4C23×D711yescharacteristic
307Q16—1464no—
308SD16—1464no—
309M16—732no—
310C2×C8—716no—
311C2×C8—78no—
312C4⋊C4—28no—
313C4⋊C4—1416no—
314C4⋊C4—1416no—
315C22⋊C4—216no—
316C42C2×C22⋊D718yes—
317C42C2×C22⋊D712yes—
318C42C2×C22⋊D712yes—
319C42C23×D712yes—
320C42C23×D712yes—
321C2×C7—24no—
322C2×C7—84no—
323C2×C7#315214yescomplemented
324C2×C7C22×#12711yescharacteristic
325C2×C7C22×#13712yes—
326C23—24no—
327C23—24no—
328C23—44no—
329C23—48no—
330C23#650314yes—
331C23C22×C22⋊D712yes—
332C23C22×C22⋊D711yescharacteristic
333Q8—28no—
334Q8—44no—
335Q8—1416no—
336Q8—2816no—
337Q8—288no—
338D4—28no—
339D4—416no—
340D4—44no—
341D4—416no—
342C2×C4—24no—
343C2×C4—216no—
344C2×C4—24no—
345C2×C4—44no—
346C2×C4—416no—
347C2×C4—148no—
348C2×C4—2816no—
349C2×C4—288no—
350C2×C4#650314yes—
351C2×C4#650318yes—
352C2×C4#651418yescomplemented
353C2×C4C2×D4×D714yes—
354C2×C4C2×D4×D718yes—
355C2×C4C22×C22⋊D714yes—
356C2×C4C22×C22⋊D712yes—
357C2×C4C22×C22⋊D711yescharacteristic
358C2×C4C22×C22⋊D714yes—
359C2×C4C24×D711yescharacteristic
360C8—716no—
361C7C2×#315211yescharacteristic, complemented, Sylow
362C22—28no—
363C22—24no—
364C22—44no—
365C22—48no—
366C22—88no—
367C22C2×#650314yes—
368C22C2×#650312yes—
369C22C2×#651414yes—
370C22C23×C22⋊D711yescharacteristic
371C4—24no—
372C4—44no—
373C4—288no—
374C4C2×#650314yes—
375C4C2×#650312yes—
376C4C2×#651418yescomplemented
377C4C22×D4×D712yes—
378C2—24no—
379C2—84no—
380C2#1174073314yesdirect product factor
381C2C22×#650311yescharacteristic
382C2C22×#651412yes—
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
Fitting, prime radicalC2×C7×#532C2
socleC23×C7C22×D4
hypercenterC2×#532D7
hypocenterC7C2×#3152
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
2. C22×#6514C2semidirect
3. C22×#6432C2semidirect
4. #11740733C2direct (N × H)
5. C2×#89864C2semidirect
6. C2×#89848C2semidirect
7. C2×#89832C2semidirect
8. C2×C4×#1136C2semidirect
20. C2×#6514C22semidirect
29. C2×#6432C22semidirect
30. #89864C22semidirect
31. #89848C22semidirect
32. #89832C22semidirect
33. C4×#1136C22semidirect
76. C2×#1136D4semidirect
141. #1136C2×D4semidirect
191. C2×C4×C7#137semidirect
268. C4×C7C2×#137semidirect
323. C2×C7#3152semidirect
352. C2×C4#6514semidirect
361. C7C2×#3152semidirect
376. C4C2×#6514semidirect
380. C2#11740733direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5322
C22×#65142
C22×#64322
#117407332
C2×#898642
C2×#898482
C2×#898322
C2×C4×#11362
C2×#31527