Finite Group Databasebeta

← #13520667

Subgroups — #13520667

Order 1792.

1698 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×C4⋊C4C211yesmaximal, characteristic
2#11739628C214yesmaximal
3C4×#6487C214yesmaximal
4#11739505C212yesmaximal
5#11731193C218yesmaximal, complemented
6#11731116C214yesmaximal, complemented
7#11731114C214yesmaximal, complemented
8#11730806C212yesmaximal
9#11730805C212yesmaximal
10C22×C7×C4⋊C4C2212yes—
11C22×C42×C7C2212yes—
12C22×C42×C7C2211yescharacteristic
13C2×#6487C2214yes—
14C2×C4×Dic14C2214yes—
15C4×C7×C4⋊C4C2214yes—
16C4×C7×C4⋊C4C2214yes—
17C2×C7×#95C2211yescharacteristic
18C2×C7×#95C2211yescharacteristic
19#89984C2214yes—
20#89984C2214yes—
21#89983C2214yes—
22#89982C2218yes—
23C4×C22⋊Dic7C2214yes—
24#89758C2218yes—
25#89756C2218yes—
26#89756C2218yes—
27#89751C2218yes—
28#89709C2214yes—
29#89708C2214yes—
30C4×C4⋊Dic7C2212yes—
31C4×C4⋊Dic7C2212yes—
32C4×C4⋊Dic7C2214yes—
33#89705C2218yes—
34#89704C2214yes—
35C4×Dic7⋊C4C2218yes—
36#89701C2214yes—
37#89700C2214yes—
38#89433C2218yes—
39#89432C2218yes—
40#89429C2218yes—
41#89428C2218yes—
42#34595—71nomaximal, Sylow
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2311yescharacteristic
45C23×C4×C7C2312yes—
46C23×C4×C7C2311yescharacteristic
47C23×C4×C7C2312yes—
48C22×Dic14C2314yes—
49C2×C7×C4⋊C4—28no—
50C2×C7×C4⋊C4C2318yes—
51C2×C42×C7—44no—
52C2×C42×C7Q818yescomplemented
53C2×C42×C7C2314yes—
54C2×C42×C7C2314yes—
55C2×C42×C7C2312yes—
56C2×C42×C7C2312yes—
57C2×C22⋊Dic7C2318yes—
58C2×C4⋊Dic7C2314yes—
59C2×C4⋊Dic7C2314yes—
60C2×C4⋊Dic7C2314yes—
61C2×C4⋊Dic7C2314yes—
62C2×C4⋊Dic7C2314yes—
63#6487—216no—
64C2×Dic7⋊C4C2318yes—
65C2×Dic7⋊C4C2318yes—
66C2×Dic7⋊C4C2318yes—
67C2×C4×Dic7C2314yes—
68C2×C4×Dic7C2314yes—
69C4×Dic14—48no—
70C7×#95C2314yes—
71C7×#95C2314yes—
72C7⋊#95C2318yes—
73C7⋊#95C2318yes—
74C7⋊#95C2318yes—
75C7⋊#95C2318yes—
76C7⋊#95C2318yes—
77C7⋊#95C2318yes—
78C7⋊#95C2314yes—
79C7⋊#95C2314yes—
80#2666—78no—
81#2659—72no—
82#2646—72no—
83#2627—74no—
84#2402—74no—
85#2399—74no—
86C4×C22⋊Q8—74no—
87#2283—72no—
88C2×C4×C4⋊C4D711yescharacteristic
89C24×C7C2411yescharacteristic
90C22×C4×C7—24no—
91C22×C4×C7—22no—
92C22×C4×C7—22no—
93C22×C4×C7—24no—
94C22×C4×C7—42no—
95C22×C4×C7—42no—
96C22×C4×C7—42no—
97C22×C4×C7—42no—
98C22×C4×C7—42no—
99C22×C4×C7C2×Q814yes—
100C22×C4×C7C2×Q814yes—
101C22×C4×C7C2×Q814yes—
102C22×C4×C7#4118yes—
103C22×C4×C7C2414yes—
104C22×C4×C7C2411yescharacteristic
105C22×C4×C7C2412yes—
106C22×C4×C7C2412yes—
107C22×C4×C7C2414yes—
108C22×C4×C7C2411yescharacteristic
109C22×Dic7C2418yes—
110C22×Dic7C2418yes—
111C2×Dic14—28no—
112C2×Dic14—44no—
113C2×Dic14—44no—
114C7×C4⋊C4—216no—
115C42×C7—28no—
116C42×C7—44no—
117C42×C7C2×Q818yes—
118C42×C7C2×Q818yes—
119C22⋊Dic7—216no—
120C4⋊Dic7—28no—
121C4⋊Dic7—44no—
122C4⋊Dic7—44no—
123C4⋊Dic7—44no—
124C4⋊Dic7—44no—
125Dic7⋊C4—216no—
126Dic7⋊C4—48no—
127Dic7⋊C4—48no—
128C4×Dic7—28no—
129C4×Dic7—28no—
130C2×C22⋊Q8—74no—
131C2×C4×Q8—74no—
132C22×C4⋊C4C2×D712yes—
133C22×C42C2×D712yes—
134C22×C42C2×D711yescharacteristic
135#400—78no—
136#400—78no—
137#398—78no—
138#398—78no—
139#398—78no—
140#398—78no—
141#395—78no—
142#395—78no—
143#391—74no—
144#389—74no—
145#387—78no—
146#385—78no—
147#383—74no—
148#382—74no—
149#381—74no—
150#380—74no—
151#380—74no—
152C4×C4⋊C4—72no—
153C4×C4⋊C4—78no—
154C4×C4⋊C4—72no—
155C4×C4⋊C4—74no—
156C4×C4⋊C4C2×D714yes—
157C4×C4⋊C4C2×D714yes—
158C4×C22⋊C4—74no—
159#376—74no—
160C2×#95C2×D711yescharacteristic
161C2×#95C2×D711yescharacteristic
162C23×C7—21no—
163C23×C7—21no—
164C23×C7—22no—
165C23×C7C22×Q812yes—
166C23×C7C2×#4114yes—
167C23×C7C2511yescharacteristic
168C2×C4×C7—28no—
169C2×C4×C7—24no—
170C2×C4×C7—24no—
171C2×C4×C7—21no—
172C2×C4×C7—21no—
173C2×C4×C7—24no—
174C2×C4×C7—24no—
175C2×C4×C7—28no—
176C2×C4×C7—24no—
177C2×C4×C7—24no—
178C2×C4×C7—24no—
179C2×C4×C7—44no—
180C2×C4×C7—48no—
181C2×C4×C7—48no—
182C2×C4×C7C22×Q814yes—
183C2×C4×C7C22×Q812yes—
184C2×C4×C7C22×Q814yes—
185C2×C4×C7C22×Q812yes—
186C2×C4×C7C2×#4118yes—
187C2×C4×C7H(5,𝔽2)12yes—
188C2×C4×C72−1+412yes—
189C2×Dic7—28no—
190C2×Dic7—28no—
191C2×Dic7—28no—
192C2×Dic7—28no—
193C2×Dic7—28no—
194C2×Dic7—28no—
195Dic14—416no—
196C22×Q8—74no—
197C23×C4C22×D711yescharacteristic
198C23×C4C22×D711yescharacteristic
199C23×C4C22×D712yes—
200C23×C4C22×D711yescharacteristic
201C23×C4C22×D712yes—
202C22⋊Q8—1416no—
203C4×Q8—288no—
204C2×C4⋊C4—28no—
205C2×C4⋊C4—78no—
206C2×C4⋊C4—74no—
207C2×C4⋊C4—78no—
208C2×C4⋊C4—74no—
209C2×C4⋊C4—78no—
210C2×C4⋊C4—74no—
211C2×C4⋊C4—74no—
212C2×C4⋊C4—74no—
213C2×C4⋊C4C22×D718yes—
214C2×C22⋊C4—78no—
215C2×C42—44no—
216C2×C42—74no—
217C2×C42—74no—
218C2×C42Dic1418yescomplemented
219C2×C42C22×D714yes—
220C2×C42C22×D714yes—
221C2×C42C22×D712yes—
222C2×C42C22×D712yes—
223#95—78no—
224#95—78no—
225#95—78no—
226#95—78no—
227#95—74no—
228#95—74no—
229#95—78no—
230#95—78no—
231#95C22×D714yes—
232#95C22×D714yes—
233C22×C7—22no—
234C22×C7—22no—
235C22×C7—24no—
236C22×C7—24no—
237C22×C7#53314yes—
238C22×C7C23×Q811yescharacteristic
239C22×C7C22×#4112yes—
240C22×C7C2×H(5,𝔽2)11yescharacteristic
241C22×C7C2×2−1+411yescharacteristic
242C22×C7#58512yes—
243C4×C7—24no—
244C4×C7—22no—
245C4×C7—24no—
246C4×C7—28no—
247C4×C7—44no—
248C4×C7#54414yes—
249Dic7—48no—
250Dic7—48no—
251C24C23×D711yescharacteristic
252C2×Q8—148no—
253C2×Q8—284no—
254C2×Q8—284no—
255C22×C4—24no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—24no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—78no—
265C22×C4—78no—
266C22×C4C2×Dic1414yes—
267C22×C4C2×Dic1414yes—
268C22×C4C2×Dic1414yes—
269C22×C4#115718yes—
270C22×C4C23×D714yes—
271C22×C4C23×D711yescharacteristic
272C22×C4C23×D712yes—
273C22×C4C23×D712yes—
274C22×C4C23×D714yes—
275C22×C4C23×D711yescharacteristic
276C4⋊C4—216no—
277C4⋊C4—1416no—
278C4⋊C4—148no—
279C4⋊C4—288no—
280C4⋊C4—288no—
281C4⋊C4—284no—
282C4⋊C4—284no—
283C4⋊C4—284no—
284C4⋊C4—284no—
285C22⋊C4—1416no—
286C42—28no—
287C42—44no—
288C42—148no—
289C42—148no—
290C42C2×Dic1418yes—
291C42C2×Dic1418yes—
292C2×C7—24no—
293C2×C7C2×#53311yescharacteristic
294C2×C7C2×#54411yescharacteristic
295C2×C7#345811yescharacteristic
296C2×C7#345912yes—
297C2×C7#346112yes—
298C23—21no—
299C23—21no—
300C23—22no—
301C23C22×Dic1412yes—
302C23C2×#115714yes—
303C23C24×D711yescharacteristic
304Q8—2816no—
305C2×C4—28no—
306C2×C4—24no—
307C2×C4—24no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—24no—
311C2×C4—24no—
312C2×C4—28no—
313C2×C4—24no—
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—44no—
317C2×C4—48no—
318C2×C4—48no—
319C2×C4—148no—
320C2×C4—148no—
321C2×C4—148no—
322C2×C4—148no—
323C2×C4—148no—
324C2×C4—148no—
325C2×C4C22×Dic1414yes—
326C2×C4C22×Dic1412yes—
327C2×C4C22×Dic1414yes—
328C2×C4C22×Dic1412yes—
329C2×C4C2×#115718yes—
330C2×C4#654812yes—
331C2×C4#655112yes—
332C7#3459511yescharacteristic, complemented, Sylow
333C22—22no—
334C22—22no—
335C22—24no—
336C22—24no—
337C22#9016114yes—
338C22C23×Dic1411yescharacteristic
339C22C22×#115712yes—
340C22C2×#654811yescharacteristic
341C22C2×#655111yescharacteristic
342C22#9061612yes—
343C4—24no—
344C4—22no—
345C4—24no—
346C4—28no—
347C4—44no—
348C4—288no—
349C4—288no—
350C4#9019114yes—
351C2—24no—
352C2C2×#9016111yescharacteristic
353C2C2×#9019111yescharacteristic
354C2#1174279311yescharacteristic
355C2#1174284412yes—
356C2#1174287912yes—
subgroupG/H
centerC22×C4C23×D7
commutator, socle, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C4×C7×C4⋊C4C2
prime radicalC24×C7C24
hypercenterC2×C4×C4⋊C4D7
hypocenterC7#34595
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
5. #11731193C2semidirect
6. #11731116C2semidirect
7. #11731114C2semidirect
52. C2×C42×C7Q8semidirect
218. C2×C42Dic14semidirect
332. C7#34595semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C7×C4⋊C42
#117396282
C4×#64872
#117395052
#117311932
#117311162
#117311142
#117308062
#117308052
#345957