Finite Group Databasebeta

← #13263472

Subgroups — #13263472

Order 1792.

426 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11739819C211yesmaximal, characteristic
2C7×#1459C211yesmaximal, characteristic
3#11729357C211yesmaximal, characteristic
4#11725253C214yesmaximal, complemented
5C2×C4×C7×D4C2211yescharacteristic
6C22×C4⋊Dic7C411yescharacteristic
7C2×C7×C22⋊C8—21no—
8#89992C412yes—
9#89984—21no—
10#89984C411yescharacteristic
11#89758—21no—
12#89721—21no—
13#89718C2212yes—
14#89700—21no—
15#89698—21no—
16C7×#324—21no—
17C7×#323C2212yes—
18#89320—21no—
19#89320C2212yes—
20#11576—71nomaximal, Sylow
21C22×C7×D4C2×C411yescharacteristic
22C23×C4×C7C2×C411yescharacteristic
23C23×C4×C7D411yescharacteristic
24C23×Dic7C2×C412yes—
25C22×C7×C8—41no—
26C4×C7×D4—41no—
27C4×C7×D4—41no—
28C2×C7×C4⋊C4D411yescharacteristic
29C2×C7×C22⋊C4D411yescharacteristic
30C2×C7×C22⋊C4C2311yescharacteristic
31C2×C42×C7D411yescharacteristic
32C2×C22⋊Dic7—22no—
33C2×C22⋊Dic7C2×C412yes—
34C2×C4⋊Dic7—21no—
35C2×C4⋊Dic7—21no—
36C2×C4⋊Dic7—21no—
37C2×C4⋊Dic7—41no—
38C2×C4⋊Dic7—41no—
39C2×Dic7⋊C4—22no—
40C7×C22⋊C8—22no—
41C7×C22⋊C8—41no—
42C7⋊#95—22no—
43C7⋊#95—21no—
44C7⋊#95—22no—
45C22⋊(C7⋊C8)—22no—
46C4⋊(C7⋊C8)—41no—
47#6377—41no—
48#2487—71no—
49#1466—71no—
50#1459D711yescharacteristic
51#1326—74no—
52C24×C7C22⋊C411yescharacteristic
53C24×C7C22×C411yescharacteristic
54C2×C7×D4—22no—
55C2×C7×D4—22no—
56C2×C7×D4—41no—
57C22×C4×C7—21no—
58C22×C4×C7—21no—
59C22×C4×C7—21no—
60C22×C4×C7—21no—
61C22×C4×C7—42no—
62C22×C4×C7—42no—
63C22×C4×C7C22⋊C411yescharacteristic
64C22×C4×C7C22⋊C411yescharacteristic
65C22×C4×C7C22⋊C411yescharacteristic
66C22×C4×C7C2×D411yescharacteristic
67C22×C4×C7C2×D411yescharacteristic
68C22×Dic7—22no—
69C22×Dic7—22no—
70C22×Dic7—42no—
71C22×Dic7—82no—
72C2×C7×C8—42no—
73C2×C7×C8—82no—
74C7×C4⋊C4—41no—
75C7×C22⋊C4—41no—
76C7×C22⋊C4—41no—
77C42×C7—21no—
78C42×C7—21no—
79C22⋊Dic7—24no—
80C22⋊Dic7—82no—
81C4⋊Dic7—42no—
82C4⋊Dic7—42no—
83C4⋊Dic7—41no—
84C4⋊Dic7—41no—
85Dic7⋊C4—82no—
86C2×C7⋊C8—42no—
87C2×C4×D4C2×D711yescharacteristic
88C22×C4⋊C4—71no—
89#432—141no—
90C2×C22⋊C8—21no—
91#400—141no—
92#399—141no—
93#389—141no—
94#386—72no—
95#385—72no—
96#380—71no—
97#380—141no—
98#324—21no—
99#323—72no—
100#323—141no—
101#323C2×D712yes—
102C23×C7—21no—
103C23×C7—21no—
104C23×C7—21no—
105C23×C7—21no—
106C23×C7—41no—
107C23×C7—41no—
108C23×C7—41no—
109C23×C7—41no—
110C23×C7#10112yes—
111C23×C7C2×C22⋊C411yescharacteristic
112C23×C7#13112yes—
113C7×D4—44no—
114C2×C4×C7—22no—
115C2×C4×C7—21no—
116C2×C4×C7—21no—
117C2×C4×C7—21no—
118C2×C4×C7—21no—
119C2×C4×C7—21no—
120C2×C4×C7—21no—
121C2×C4×C7—42no—
122C2×C4×C7—42no—
123C2×C4×C7—42no—
124C2×C4×C7—41no—
125C2×C4×C7—41no—
126C2×C4×C7—41no—
127C2×C4×C7—81no—
128C2×C4×C7#9911yescharacteristic
129C2×C4×C7#9911yescharacteristic
130C2×Dic7—42no—
131C2×Dic7—42no—
132C2×Dic7—42no—
133C2×Dic7—42no—
134C2×Dic7—42no—
135C2×Dic7—42no—
136C2×Dic7—84no—
137C7×C8—82no—
138C7⋊C8—82no—
139C22×D4C4×D711yescharacteristic
140C23×C4—72no—
141C23×C4C4×D711yescharacteristic
142C23×C4C22⋊D711yescharacteristic
143C22×C8—41no—
144C4×D4—41no—
145C4×D4—41no—
146C2×C4⋊C4—141no—
147C2×C4⋊C4—141no—
148C2×C4⋊C4—141no—
149C2×C4⋊C4—142no—
150C2×C4⋊C4—281no—
151C2×C4⋊C4—281no—
152C2×C4⋊C4C22⋊D711yescharacteristic
153C2×C22⋊C4—72no—
154C2×C22⋊C4—142no—
155C2×C22⋊C4D2811yescharacteristic
156C2×C22⋊C4C22×D711yescharacteristic
157C2×C42D2811yescharacteristic
158C4⋊C8—281no—
159C22⋊C8—22no—
160C22⋊C8—41no—
161C22⋊C8—142no—
162#97—281no—
163#95—141no—
164#95—142no—
165#95—142no—
166C22×C7—21no—
167C22×C7—21no—
168C22×C7—22no—
169C22×C7—22no—
170C22×C7—42no—
171C22×C7—42no—
172C22×C7—42no—
173C22×C7—41no—
174C22×C7—41no—
175C22×C7—41no—
176C22×C7—41no—
177C22×C7—81no—
178C22×C7#40811yescharacteristic
179C22×C7C2×#9911yescharacteristic
180C22×C7C2×#10111yescharacteristic
181C4×C7—21no—
182C4×C7—41no—
183C4×C7—41no—
184C4×C7—41no—
185C4×C7—41no—
186C4×C7#35212yes—
187Dic7—82no—
188Dic7—82no—
189C24(C2×D7)⋊C411yescharacteristic
190C24C2×C4×D711yescharacteristic
191C2×D4—22no—
192C2×D4—22no—
193C2×D4—41no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—42no—
199C22×C4—42no—
200C22×C4—142no—
201C22×C4—142no—
202C22×C4—282no—
203C22×C4—562no—
204C22×C4(C2×D7)⋊C411yescharacteristic
205C22×C4(C2×D7)⋊C411yescharacteristic
206C22×C4(C2×D7)⋊C411yescharacteristic
207C22×C4C2×D2811yescharacteristic
208C22×C4C2×C22⋊D711yescharacteristic
209C2×C8—42no—
210C2×C8—82no—
211C2×C8—282no—
212C4⋊C4—41no—
213C4⋊C4—282no—
214C4⋊C4—282no—
215C4⋊C4—281no—
216C4⋊C4—281no—
217C4⋊C4—562no—
218C22⋊C4—41no—
219C22⋊C4—41no—
220C22⋊C4—144no—
221C22⋊C4—562no—
222C42—21no—
223C42—21no—
224C2×C7—21no—
225C2×C7—21no—
226C2×C7—42no—
227C2×C7—42no—
228C2×C7#147211yescharacteristic
229C2×C7C2×#35211yescharacteristic
230C2×C7#212211yescharacteristic
231C23—21no—
232C23—21no—
233C23—21no—
234C23—21no—
235C23—41no—
236C23—41no—
237C23—41no—
238C23—41no—
239C23#639812yes—
240C23#646412yes—
241C23C2×(C2×D7)⋊C411yescharacteristic
242D4—44no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—81no—
257C2×C4—282no—
258C2×C4—282no—
259C2×C4—282no—
260C2×C4—282no—
261C2×C4—282no—
262C2×C4—282no—
263C2×C4—564no—
264C2×C4#638011yescharacteristic
265C2×C4#638011yescharacteristic
266C8—82no—
267C8—562no—
268C7#1157611yescharacteristic, complemented, Sylow
269C22—21no—
270C22—21no—
271C22—22no—
272C22—22no—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—81no—
281C22C2×#638011yescharacteristic
282C22#8988211yescharacteristic
283C22C2×#639811yescharacteristic
284C4—21no—
285C4—41no—
286C4—41no—
287C4—41no—
288C4—41no—
289C4—562no—
290C4—562no—
291C4#8926712yes—
292C2—21no—
293C2—21no—
294C2—42no—
295C2—42no—
296C2#1172767711yescharacteristic
297C2C2×#8926711yescharacteristic
298C2#1172790011yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC24×C7C22×C4
FrattiniC2×C22⋊C4C22×D7
FittingC7×#1459C2
socleC22×C7C2×#99
prime radicalC22×C7×D4C2×C4
cosocleC2×C7×C22⋊C4C23
hypercenter#1459D7
hypocenterC7#11576
LCSG ▷ C24×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
4. #11725253C2semidirect
268. C7#11576semidirect

Maximal subgroups

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

subgroupindex
#117398192
C7×#14592
#117293572
#117252532
#115767