Finite Group Databasebeta

← #13247204

Subgroups — #13247204

Order 1792.

526 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 123 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#11739507C211yesmaximal, characteristic
2C7×#1749C211yesmaximal, characteristic
3#11729283C211yesmaximal, characteristic
4#11725465C214yesmaximal, complemented
5C22×C42×C7C2211yescharacteristic
6C2×#6489C412yes—
7C2×C7×C22⋊C8—21no—
8C2×C7×#97C2212yes—
9#89984—21no—
10#89984—21no—
11C2×C22⋊(C7⋊C8)—21no—
12#89708C2212yes—
13#89707C411yescharacteristic
14#89707C411yescharacteristic
15C4×C4⋊Dic7—21no—
16C4×C4⋊Dic7—21no—
17C2×#6377C2212yes—
18C7×#336—21no—
19#89319—21no—
20#8721—71nomaximal, Sylow
21C23×C4×C7C2×C411yescharacteristic
22C23×C4×C7D411yescharacteristic
23C23×C4×C7D411yescharacteristic
24C22×C7×C8—22no—
25C2×C42×C7—24no—
26C2×C42×C7C2×C411yescharacteristic
27C2×C42×C7D411yescharacteristic
28C2×C42×C7D411yescharacteristic
29C2×C42×C7C2311yescharacteristic
30C2×C22⋊Dic7—22no—
31#6489—44no—
32C2×C4⋊Dic7—21no—
33C2×C4⋊Dic7—21no—
34C2×C4⋊Dic7—21no—
35C2×C4⋊Dic7—21no—
36C2×C4⋊Dic7C2×C412yes—
37C2×C4⋊Dic7C2×C412yes—
38C2×C4×Dic7—22no—
39C22×C7⋊C8—22no—
40C7×C22⋊C8—24no—
41C7×#97—24no—
42C7⋊#95—22no—
43C7⋊#95—22no—
44C22⋊(C7⋊C8)—24no—
45#6377—24no—
46#2285—71no—
47#1749—71no—
48#1749D711yescharacteristic
49#1295—74no—
50C24×C7C22⋊C411yescharacteristic
51C22×C4×C7—22no—
52C22×C4×C7—22no—
53C22×C4×C7—22no—
54C22×C4×C7—22no—
55C22×C4×C7—22no—
56C22×C4×C7—22no—
57C22×C4×C7—22no—
58C22×C4×C7—41no—
59C22×C4×C7—41no—
60C22×C4×C7C22⋊C411yescharacteristic
61C22×C4×C7C22⋊C411yescharacteristic
62C22×C4×C7C22⋊C411yescharacteristic
63C22×C4×C7C22×C411yescharacteristic
64C22×C4×C7C2×D411yescharacteristic
65C22×C4×C7C2×D411yescharacteristic
66C22×Dic7—22no—
67C22×Dic7—22no—
68C2×C7×C8—24no—
69C2×C7×C8—42no—
70C2×C7×C8—42no—
71C42×C7—22no—
72C42×C7—22no—
73C42×C7—22no—
74C42×C7#4114yes—
75C22⋊Dic7—44no—
76C4⋊Dic7—42no—
77C4⋊Dic7—42no—
78C4⋊Dic7—42no—
79C4⋊Dic7—42no—
80C4⋊Dic7—42no—
81C4⋊Dic7—42no—
82C4×Dic7—44no—
83C2×C7⋊C8—24no—
84C2×C7⋊C8—42no—
85C2×C7⋊C8—42no—
86C2×#117—72no—
87C22×C42C2×D711yescharacteristic
88C2×C22⋊C8—21no—
89C2×C22⋊C8—141no—
90C2×#97—72no—
91C2×#97C2×D712yes—
92#384—71no—
93#384—71no—
94#382—72no—
95#380—141no—
96#380—141no—
97C4×C4⋊C4—141no—
98C4×C4⋊C4—141no—
99#336—21no—
100#336—141no—
101C23×C7—21no—
102C23×C7—21no—
103C23×C7—21no—
104C23×C7—21no—
105C23×C7—21no—
106C23×C7—21no—
107C23×C7#10112yes—
108C23×C7C2×C22⋊C411yescharacteristic
109C2×C4×C7—28no—
110C2×C4×C7—21no—
111C2×C4×C7—21no—
112C2×C4×C7—21no—
113C2×C4×C7—21no—
114C2×C4×C7—21no—
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—21no—
122C2×C4×C7—44no—
123C2×C4×C7—44no—
124C2×C4×C7#10012yes—
125C2×C4×C7#10412yes—
126C2×C4×C7#10412yes—
127C2×C4×C7#11712yes—
128C2×C4×C7#12312yes—
129C2×C4×C7#12312yes—
130C2×Dic7—42no—
131C2×Dic7—42no—
132C2×Dic7—42no—
133C2×Dic7—42no—
134C2×Dic7—42no—
135C2×Dic7—42no—
136C7×C8—44no—
137C7⋊C8—44no—
138C23×C4C4×D711yescharacteristic
139C23×C4D2811yescharacteristic
140C23×C4C22⋊D711yescharacteristic
141C22×C8—22no—
142C22×C8—142no—
143#117—284no—
144C2×C4⋊C4—72no—
145C2×C4⋊C4—72no—
146C2×C4⋊C4—141no—
147C2×C4⋊C4—141no—
148C2×C4⋊C4—141no—
149C2×C4⋊C4—141no—
150C2×C22⋊C4—142no—
151C2×C42—24no—
152C2×C42—142no—
153C2×C42C4×D711yescharacteristic
154C2×C42D2811yescharacteristic
155C2×C42C22⋊D711yescharacteristic
156C2×C42C22×D711yescharacteristic
157C22⋊C8—24no—
158C22⋊C8—144no—
159#97—24no—
160#97—144no—
161#95—142no—
162#95—142no—
163C22×C7—22no—
164C22×C7—22no—
165C22×C7—22no—
166C22×C7—41no—
167C22×C7—41no—
168C22×C7—41no—
169C22×C7—41no—
170C22×C7#38111yescharacteristic
171C22×C7C2×#10011yescharacteristic
172C22×C7C2×#10111yescharacteristic
173C22×C7C2×#10411yescharacteristic
174C22×C7C2×#10411yescharacteristic
175C22×C7#42111yescharacteristic
176C22×C7#42111yescharacteristic
177C4×C7—22no—
178C4×C7—22no—
179C4×C7—22no—
180C4×C7—22no—
181C4×C7—22no—
182C4×C7—22no—
183Dic7—82no—
184Dic7—82no—
185C24(C2×D7)⋊C411yescharacteristic
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—142no—
196C22×C4—142no—
197C22×C4(C2×D7)⋊C411yescharacteristic
198C22×C4(C2×D7)⋊C411yescharacteristic
199C22×C4(C2×D7)⋊C411yescharacteristic
200C22×C4C2×C4×D711yescharacteristic
201C22×C4C2×D2811yescharacteristic
202C22×C4C2×C22⋊D711yescharacteristic
203C2×C8—24no—
204C2×C8—42no—
205C2×C8—42no—
206C2×C8—144no—
207C2×C8—282no—
208C2×C8—282no—
209C4⋊C4—282no—
210C4⋊C4—282no—
211C4⋊C4—282no—
212C4⋊C4—282no—
213C4⋊C4—282no—
214C4⋊C4—282no—
215C22⋊C4—284no—
216C42—22no—
217C42—22no—
218C42—22no—
219C42—284no—
220C42#115914yes—
221C2×C7—42no—
222C2×C7#152511yescharacteristic
223C2×C7#153111yescharacteristic
224C2×C7#153111yescharacteristic
225C2×C7#153611yescharacteristic
226C2×C7#182111yescharacteristic
227C2×C7#182611yescharacteristic
228C2×C7#182611yescharacteristic
229C23—21no—
230C23—21no—
231C23—21no—
232C23—21no—
233C23—21no—
234C23—21no—
235C23#639812yes—
236C23C2×(C2×D7)⋊C411yescharacteristic
237C2×C4—28no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—44no—
251C2×C4—44no—
252C2×C4—282no—
253C2×C4—282no—
254C2×C4—282no—
255C2×C4—282no—
256C2×C4—282no—
257C2×C4—282no—
258C2×C4#637912yes—
259C2×C4#639712yes—
260C2×C4#639912yes—
261C2×C4#644012yes—
262C2×C4#644912yes—
263C2×C4#649812yes—
264C8—44no—
265C8—284no—
266C7#872111yescharacteristic, complemented, Sylow
267C22—22no—
268C22—22no—
269C22—22no—
270C22—41no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22C2×#637911yescharacteristic
275C22#8971511yescharacteristic
276C22#8977711yescharacteristic
277C22C2×#639711yescharacteristic
278C22C2×#639811yescharacteristic
279C22C2×#639911yescharacteristic
280C22#8991111yescharacteristic
281C4—22no—
282C4—22no—
283C4—22no—
284C4—22no—
285C4—22no—
286C4—22no—
287C4—562no—
288C4—562no—
289C2—42no—
290C2#1172719611yescharacteristic
291C2#1172755511yescharacteristic
292C2#1172761311yescharacteristic
293C2#1172772711yescharacteristic
294C2#1172772911yescharacteristic
295C2#1172856511yescharacteristic
296C2#1172856711yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#1749C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C22⋊C4
cosocleC2×C42×C7C23
hypercenter#1749D7
hypocenterC7#8721
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
4. #11725465C2semidirect
266. C7#8721semidirect

Maximal subgroups

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

subgroupindex
#117395072
C7×#17492
#117292832
#117254652
#87217