Finite Group Databasebeta

← #13254728

Subgroups — #13254728

Order 1792.

564 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 83 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#11739755C212yesmaximal, complemented
2#11736471C211yesmaximal, characteristic, complemented
3C7×#1955C211yesmaximal, characteristic, complemented
4#11727552C212yesmaximal, complemented
5#11725514C211yesmaximal, characteristic, complemented
6C2×C4×C7×D4C2211yescharacteristic
7#90168C2212yes—
8C2×C7×C4⋊C8C2211yescharacteristic
9C2×C7×C22⋊C8—22no—
10C2×C7×#97C2211yescharacteristic
11#89989—22no—
12#89887—22no—
13#89787—22no—
14#89786—24no—
15#89780—22no—
16#89740—22no—
17#89698C2212yes—
18#89618—22no—
19#89615—22no—
20#89259—24no—
21#10026—71nomaximal, Sylow
22C22×C7×D4D411yescharacteristic
23C23×C4×C7—21no—
24C2×#1157—22no—
25C22×C7×C8—21no—
26C22×C7×C8D412yes—
27C4×C7×D4—22no—
28C4×C7×D4—22no—
29C2×C7×C4⋊C4D411yescharacteristic
30C2×C7×C22⋊C4—21no—
31C2×C42×C7C2311yescharacteristic
32C2×#1141—24no—
33#6493—22no—
34#6493—22no—
35C2×D56—22no—
36#6438—22no—
37#6437D412yes—
38C4×D28—22no—
39C4×D28—22no—
40#6432D412yes—
41C7×C4⋊C8—22no—
42C7×C22⋊C8—44no—
43C7×#97—22no—
44#6406—24no—
45C22⋊(C7⋊C8)—22no—
46#6395—24no—
47#6392—22no—
48#6383—24no—
49#6382—24no—
50C4⋊(C7⋊C8)—22no—
51#6377D414yes—
52#3245—71no—
53#3109—72no—
54#1955D711yescharacteristic, complemented
55#1530—72no—
56#1290—71no—
57C24×C7—21no—
58C2×C7×D4—22no—
59C2×C7×D4—42no—
60C22×C4×C7—21no—
61C22×C4×C7—42no—
62C22×C4×C7—42no—
63C22×C4×C7—41no—
64C22×C4×C7—41no—
65C22×C4×C7C2×D411yescharacteristic
66C22×C4×C7C2×D411yescharacteristic
67C22×C4×C7#4111yescharacteristic
68C2×C22⋊D7—42no—
69#1157—84no—
70C2×D28—22no—
71C2×D28—22no—
72C2×D28—22no—
73C2×C4×D7—42no—
74C2×Dic14—22no—
75C2×C7×C8—22no—
76C2×C7×C8—22no—
77C2×C7×C8—41no—
78C2×C7×C8—41no—
79C2×C7×C8—42no—
80C7×C4⋊C4—22no—
81C7×C22⋊C4—42no—
82C42×C7C2×D412yes—
83C42×C7C2×D412yes—
84#1141—48no—
85(C2×D7)⋊C4—42no—
86(C2×D7)⋊C4—42no—
87C4⋊Dic7—22no—
88C4⋊Dic7—22no—
89C2×C7⋊C8—24no—
90D56—82no—
91#532—72no—
92C2×C4×D4C2×D711yescharacteristic
93#481—142no—
94#476—142no—
95#474—142no—
96#466—142no—
97#459—142no—
98#459—142no—
99#447—142no—
100#442—144no—
101#432—72no—
102C2×C4⋊C8C2×D711yescharacteristic
103C2×C22⋊C8—22no—
104C2×#97C2×D711yescharacteristic
105#329—144no—
106C23×C7—22no—
107C23×C7—42no—
108C23×C7—41no—
109C23×C7—41no—
110C23×C7—42no—
111C23×C7#12111yescharacteristic
112C22×D7—42no—
113C7×D4—24no—
114C7×D4—42no—
115C2×C4×C7—22no—
116C2×C4×C7—21no—
117C2×C4×C7—21no—
118C2×C4×C7—41no—
119C2×C4×C7—42no—
120C2×C4×C7—41no—
121C2×C4×C7—82no—
122C2×C4×C7—81no—
123C2×C4×C7—81no—
124C2×C4×C7#12012yes—
125C2×C4×C7#12011yescharacteristic
126C2×C4×C7#12112yes—
127C2×C4×C7#12711yescharacteristic
128C22⋊D7—84no—
129C2×Dic7—42no—
130D28—44no—
131D28—42no—
132D28—42no—
133D28—82no—
134C4×D7—84no—
135Dic14—82no—
136C7×C8—42no—
137C7×C8—42no—
138C7⋊C8—44no—
139C2×#41—142no—
140C22×D4D2811yescharacteristic
141C23×C4—21no—
142C2×D8—142no—
143C2×D8—144no—
144C22×C8—21no—
145C22×C8C22⋊D712yes—
146C4⋊Q8—72no—
147#127—72no—
148#124—142no—
149#121—142no—
150#121—142no—
151C4×D4—22no—
152C4×D4—22no—
153C4×D4—142no—
154C4×D4—142no—
155C2×C4⋊C4D2811yescharacteristic
156C2×C22⋊C4—21no—
157C2×C42C22×D711yescharacteristic
158#107—142no—
159#106—144no—
160C4⋊C8—22no—
161C4⋊C8—142no—
162#102—144no—
163#102—144no—
164#102—144no—
165C22⋊C8—44no—
166C22⋊C8—142no—
167#97—22no—
168#97—74no—
169C22×C7—21no—
170C22×C7—21no—
171C22×C7—44no—
172C22×C7—42no—
173C22×C7—82no—
174C22×C7—81no—
175C22×C7—81no—
176C22×C7#39211yescharacteristic
177C22×C7#47212yes—
178C2×D7—82no—
179C2×D7—82no—
180C2×D7—82no—
181C4×C7—21no—
182C4×C7—22no—
183C4×C7—22no—
184C4×C7—81no—
185C4×C7#45311yescharacteristic
186C4×C7#45411yescharacteristic
187Dic7—82no—
188C24—21no—
189#41—564no—
190C2×Q8—142no—
191C2×D4—22no—
192C2×D4—42no—
193C2×D4—142no—
194C2×D4—142no—
195C2×D4—142no—
196C2×D4—282no—
197C22×C4—21no—
198C22×C4—42no—
199C22×C4—42no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—282no—
203C22×C4C2×D2811yescharacteristic
204C22×C4#115711yescharacteristic
205C22×C4C2×C22⋊D711yescharacteristic
206D8—288no—
207D8—562no—
208C2×C8—22no—
209C2×C8—22no—
210C2×C8—41no—
211C2×C8—41no—
212C2×C8—42no—
213C2×C8—144no—
214C4⋊C4—22no—
215C4⋊C4—142no—
216C4⋊C4—142no—
217C22⋊C4—42no—
218C22⋊C4—282no—
219C22⋊C4—282no—
220C42D4×D712yes—
221C42D4×D712yes—
222C2×C7—22no—
223C2×C7—82no—
224C2×C7#200611yescharacteristic
225C2×C7#201011yescharacteristic
226C2×C7#201811yescharacteristic
227D7—162no—
228C23—22no—
229C23—42no—
230C23—41no—
231C23—42no—
232C23—41no—
233C23—282no—
234C23#649311yescharacteristic
235Q8—562no—
236D4—24no—
237D4—42no—
238D4—284no—
239D4—282no—
240D4—282no—
241D4—562no—
242D4—564no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—82no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4—282no—
253C2×C4—564no—
254C2×C4#644512yes—
255C2×C4#644712yes—
256C2×C4#650011yescharacteristic
257C2×C4#650311yescharacteristic
258C8—42no—
259C8—42no—
260C8—284no—
261C7#1002611yescharacteristic, complemented, Sylow
262C22—21no—
263C22—21no—
264C22—44no—
265C22—42no—
266C22—82no—
267C22—81no—
268C22—81no—
269C22—562no—
270C22—562no—
271C22—562no—
272C22#8973211yescharacteristic
273C22#8991412yes—
274C4—21no—
275C4—22no—
276C4—22no—
277C4—81no—
278C4—562no—
279C4#8983411yescharacteristic
280C4#8984911yescharacteristic
281C2—22no—
282C2—82no—
283C2—1122no—
284C2#1172741811yescharacteristic
285C2#1172774711yescharacteristic
286C2#1172776011yescharacteristic
subgroupG/H
centerC22#89732
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1955C2
socleC22×C7#392
hypercenter#1955D7
hypocenterC7#10026
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1955

Complements

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

NH ≅ G/Ntype
1. #11739755C2semidirect
2. #11736471C2semidirect
3. C7×#1955C2semidirect
4. #11727552C2semidirect
5. #11725514C2semidirect
54. #1955D7semidirect
261. C7#10026semidirect

Maximal subgroups

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

subgroupindex
#117397552
#117364712
C7×#19552
#117275522
#117255142
#100267