Finite Group Databasebeta

← #13249792

Subgroups — #13249792

Order 1792.

436 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 99 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#11739931C211yesmaximal, characteristic
2#11739881C211yesmaximal, characteristic
3C4×C7×#101C211yesmaximal, characteristic
4#11727617C212yesmaximal
5#11725472C212yesmaximal
6C2×C4×C7×Q8C2211yescharacteristic
7C2×#6433C2211yescharacteristic
8C2×C7×#101—21no—
9C4×C7×M16C2212yes—
10#90001—21no—
11#89796—24no—
12#89758C411yescharacteristic
13#89758C411yescharacteristic
14#89755C411yescharacteristic
15#89755C411yescharacteristic
16#89754—21no—
17#89709C2211yescharacteristic
18#89705—21no—
19#89705—21no—
20#89698—21no—
21#89698C2212yes—
22#89697—21no—
23C7×#343—21no—
24#89260—24no—
25#9190—71nomaximal, Sylow
26C22×C7×Q8D411yescharacteristic
27C2×C7×M16—22no—
28C4×C7×Q8—22no—
29C4×C7×Q8—22no—
30C2×C7×C4⋊C4C2×C411yescharacteristic
31C2×C7×C4⋊C4C2×C411yescharacteristic
32C2×C7×C4⋊C4D411yescharacteristic
33C2×C42×C7D411yescharacteristic
34C2×C42×C7D411yescharacteristic
35C2×C42×C7C2311yescharacteristic
36C2×C4⋊Dic7C2×C411yescharacteristic
37C2×C4⋊Dic7C2×C411yescharacteristic
38C2×Dic7⋊C4—21no—
39C2×Dic7⋊C4—21no—
40C2×Dic7⋊C4—21no—
41C2×Dic7⋊C4—21no—
42#6433—22no—
43#6433—22no—
44C7×#101—24no—
45C7×#97—22no—
46C4×C7×C8—22no—
47C7⋊#95—21no—
48C7⋊#95—21no—
49C7⋊#95—21no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C7⋊#95—21no—
55C7⋊#95C2×C411yescharacteristic
56C7⋊#95C2×C411yescharacteristic
57C22⋊(C7⋊C8)—22no—
58C4⋊(C7⋊C8)—22no—
59C4⋊(C7⋊C8)—22no—
60C4⋊(C7⋊C8)—22no—
61#6377—22no—
62#6377D414yes—
63C4×C7⋊C8—22no—
64#2983—71no—
65#2634—71no—
66C4×#101D711yescharacteristic
67#1528—72no—
68#1288—72no—
69C2×C7×Q8—22no—
70C2×C7×Q8—22no—
71C2×C7×Q8—41no—
72C22×C4×C7C22⋊C411yescharacteristic
73C22×C4×C7C22⋊C411yescharacteristic
74C22×C4×C7C22⋊C411yescharacteristic
75C22×C4×C7C22⋊C411yescharacteristic
76C22×C4×C7C22×C411yescharacteristic
77C22×C4×C7C2×D411yescharacteristic
78C22×C4×C7C2×D411yescharacteristic
79C22×Dic7—21no—
80C22×Dic7—21no—
81C22×Dic7—21no—
82C22×Dic7—21no—
83C7×M16—24no—
84C7×M16—42no—
85C2×C7×C8—42no—
86C7×C4⋊C4—22no—
87C7×C4⋊C4—22no—
88C7×C4⋊C4—22no—
89C42×C7—21no—
90C42×C7—21no—
91C42×C7—21no—
92C42×C7—21no—
93C42×C7C2×D412yes—
94C42×C7#4112yes—
95C4⋊Dic7—22no—
96C4⋊Dic7—22no—
97Dic7⋊C4—42no—
98Dic7⋊C4—42no—
99Dic7⋊C4—41no—
100Dic7⋊C4—42no—
101Dic7⋊C4—41no—
102C2×C7⋊C8—24no—
103C2×#125—71no—
104C2×C4×Q8C2×D711yescharacteristic
105#446—144no—
106#432—72no—
107#432—141no—
108#431—141no—
109C2×#101—21no—
110C4×M16C2×D712yes—
111#400—71no—
112#400—71no—
113#400—141no—
114#398—71no—
115#398—71no—
116#395—141no—
117#387—141no—
118#387—141no—
119#383—71no—
120#343—21no—
121#330—144no—
122C23×C7C2×C22⋊C411yescharacteristic
123C7×Q8—44no—
124C2×C4×C7—21no—
125C2×C4×C7—21no—
126C2×C4×C7—21no—
127C2×C4×C7—21no—
128C2×C4×C7—21no—
129C2×C4×C7—21no—
130C2×C4×C7—21no—
131C2×C4×C7—21no—
132C2×C4×C7—21no—
133C2×C4×C7—41no—
134C2×C4×C7—41no—
135C2×C4×C7—41no—
136C2×C4×C7—41no—
137C2×C4×C7#10412yes—
138C2×C4×C7C4×D412yes—
139C2×C4×C7#12011yescharacteristic
140C2×C4×C7#12112yes—
141C2×C4×C7#12311yescharacteristic
142C2×Dic7—41no—
143C2×Dic7—41no—
144C2×Dic7—41no—
145C2×Dic7—41no—
146C2×Dic7—42no—
147C2×Dic7—41no—
148C2×Dic7—41no—
149C2×Dic7—41no—
150C2×Dic7—41no—
151C2×Dic7—41no—
152C2×Dic7—41no—
153C7×C8—44no—
154C7⋊C8—44no—
155C22×Q8C22⋊D711yescharacteristic
156C2×M16—22no—
157#125—142no—
158#125—142no—
159C4×Q8—22no—
160C4×Q8—22no—
161C2×C4⋊C4—71no—
162C2×C4⋊C4—71no—
163C2×C4⋊C4—141no—
164C2×C4⋊C4—141no—
165C2×C4⋊C4—141no—
166C2×C4⋊C4—141no—
167C2×C4⋊C4C4×D711yescharacteristic
168C2×C4⋊C4C4×D711yescharacteristic
169C2×C4⋊C4C22⋊D711yescharacteristic
170C2×C42D2811yescharacteristic
171C2×C42D2811yescharacteristic
172C2×C42C22×D711yescharacteristic
173C4⋊C8—142no—
174C4⋊C8—142no—
175C4⋊C8—142no—
176#101—24no—
177C22⋊C8—142no—
178#97—22no—
179#97—74no—
180#97—142no—
181C4×C8—22no—
182C4×C8—142no—
183#95—71no—
184#95—71no—
185#95—141no—
186#95—141no—
187#95—141no—
188#95—141no—
189#95—141no—
190#95—141no—
191#95—141no—
192#95—141no—
193C22×C7—21no—
194C22×C7—21no—
195C22×C7#38611yescharacteristic
196C22×C7C2×#10411yescharacteristic
197C22×C7#42111yescharacteristic
198C4×C7—22no—
199C4×C7—22no—
200C4×C7—21no—
201C4×C7—21no—
202C4×C7—22no—
203C4×C7—41no—
204C4×C7—41no—
205C4×C7—41no—
206Dic7—81no—
207Dic7—81no—
208Dic7—81no—
209Dic7—81no—
210C2×Q8—22no—
211C2×Q8—22no—
212C2×Q8—41no—
213C22×C4—141no—
214C22×C4—141no—
215C22×C4—141no—
216C22×C4—141no—
217C22×C4(C2×D7)⋊C411yescharacteristic
218C22×C4(C2×D7)⋊C411yescharacteristic
219C22×C4(C2×D7)⋊C411yescharacteristic
220C22×C4(C2×D7)⋊C411yescharacteristic
221C22×C4C2×C4×D711yescharacteristic
222C22×C4C2×D2811yescharacteristic
223C22×C4C2×C22⋊D711yescharacteristic
224M16—24no—
225M16—42no—
226C2×C8—42no—
227C2×C8—144no—
228C4⋊C4—22no—
229C4⋊C4—22no—
230C4⋊C4—22no—
231C4⋊C4—142no—
232C4⋊C4—142no—
233C4⋊C4—282no—
234C4⋊C4—281no—
235C4⋊C4—281no—
236C4⋊C4—282no—
237C4⋊C4—282no—
238C42—21no—
239C42—21no—
240C42—21no—
241C42—21no—
242C42D4×D712yes—
243C42#115912yes—
244C2×C7—21no—
245C2×C7—21no—
246C2×C7#187111yescharacteristic
247C2×C7#191211yescharacteristic
248C2×C7#191511yescharacteristic
249C23C2×(C2×D7)⋊C411yescharacteristic
250Q8—44no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—281no—
265C2×C4—281no—
266C2×C4—281no—
267C2×C4—281no—
268C2×C4—282no—
269C2×C4—281no—
270C2×C4—281no—
271C2×C4—281no—
272C2×C4—281no—
273C2×C4—281no—
274C2×C4—281no—
275C2×C4#637912yes—
276C2×C4(C22⋊D7)⋊C412yes—
277C2×C4#644511yescharacteristic
278C2×C4#644911yescharacteristic
279C2×C4#650212yes—
280C8—44no—
281C8—284no—
282C7#919011yescharacteristic, complemented, Sylow
283C22—21no—
284C22—21no—
285C22C2×#637911yescharacteristic
286C22#8973011yescharacteristic
287C22#8977711yescharacteristic
288C4—22no—
289C4—22no—
290C4—22no—
291C4—21no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—561no—
297C4—561no—
298C4—561no—
299C4—561no—
300C2—21no—
301C2—21no—
302C2#1172720711yescharacteristic
303C2#1172785911yescharacteristic
304C2#1172789211yescharacteristic
subgroupG/H
centerC22#89730
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC4×C7×#101C2
socleC22×C7#386
prime radicalC23×C7C2×C22⋊C4
cosocleC2×C42×C7C23
hypercenterC4×#101D7
hypocenterC7#9190
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
282. C7#9190semidirect

Maximal subgroups

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

subgroupindex
#117399312
#117398812
C4×C7×#1012
#117276172
#117254722
#91907