Finite Group Databasebeta

← #13251470

Subgroups — #13251470

Order 1792.

424 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C7×#2983C211yesmaximal, characteristic
2#11739922C211yesmaximal, characteristic
3#11729379C211yesmaximal, characteristic
4#11728568C212yesmaximal
5#11725555C212yesmaximal
6C2×C4×C7×Q8C2211yescharacteristic
7C2×#6433C2211yescharacteristic
8C7×#446—24no—
9C7×#432—21no—
10C7×#432C2212yes—
11C7×#431—21no—
12#90002C411yescharacteristic
13#90002C411yescharacteristic
14#89756—21no—
15#89756—21no—
16#89749C411yescharacteristic
17#89748C411yescharacteristic
18C4×C4⋊Dic7C2211yescharacteristic
19#89705—21no—
20#89705—21no—
21#89698C2212yes—
22#89323—21no—
23#89323—21no—
24#89260—24no—
25#9450—71nomaximal, Sylow
26C22×C7×Q8C2×C411yescharacteristic
27C4×C7×Q8—22no—
28C4×C7×Q8—22no—
29C2×C7×C4⋊C4C2×C411yescharacteristic
30C2×C7×C4⋊C4D411yescharacteristic
31C2×C7×C4⋊C4D411yescharacteristic
32C2×C42×C7D411yescharacteristic
33C2×C42×C7D411yescharacteristic
34C2×C42×C7C2311yescharacteristic
35C2×C4⋊Dic7—21no—
36C2×C4⋊Dic7C2×C411yescharacteristic
37C2×C4⋊Dic7C2×C411yescharacteristic
38C2×Dic7⋊C4—21no—
39C2×Dic7⋊C4—21no—
40C2×Dic7⋊C4—21no—
41C2×Dic7⋊C4—21no—
42C2×C4×Dic7C2×C411yescharacteristic
43C2×C4×Dic7C2×C411yescharacteristic
44#6433—22no—
45#6433—22no—
46C7×C4⋊C8—22no—
47C7×C4⋊C8—22no—
48C7×C4⋊C8—22no—
49C7×C22⋊C8—22no—
50C7×#97—22no—
51C7×#97D414yes—
52C4×C7×C8—22no—
53C7⋊#95—21no—
54C7⋊#95—21no—
55C7⋊#95—21no—
56C7⋊#95—21no—
57C7⋊#95—21no—
58C7⋊#95—21no—
59C7⋊#95—21no—
60C22⋊(C7⋊C8)—22no—
61C4⋊(C7⋊C8)—22no—
62#6377—22no—
63#2983D711yescharacteristic
64#2565—71no—
65#1534—72no—
66#1467—71no—
67#1285—72no—
68C2×C7×Q8—22no—
69C2×C7×Q8—22no—
70C2×C7×Q8—41no—
71C22×C4×C7C22⋊C411yescharacteristic
72C22×C4×C7C22⋊C411yescharacteristic
73C22×C4×C7C22⋊C411yescharacteristic
74C22×C4×C7C22⋊C411yescharacteristic
75C22×C4×C7C22×C411yescharacteristic
76C22×C4×C7C2×D411yescharacteristic
77C22×C4×C7C2×D411yescharacteristic
78C22×Dic7—21no—
79C22×Dic7—21no—
80C22×Dic7—21no—
81C22×Dic7—21no—
82C2×C7×C8—24no—
83C7×C4⋊C4—22no—
84C7×C4⋊C4—22no—
85C7×C4⋊C4—22no—
86C42×C7—21no—
87C42×C7—21no—
88C42×C7—21no—
89C42×C7—21no—
90C42×C7C2×D412yes—
91C42×C7#4112yes—
92C4⋊Dic7—22no—
93C4⋊Dic7—22no—
94C4⋊Dic7—42no—
95Dic7⋊C4—42no—
96Dic7⋊C4—42no—
97Dic7⋊C4—41no—
98Dic7⋊C4—42no—
99Dic7⋊C4—41no—
100C4×Dic7—41no—
101C4×Dic7—41no—
102C2×C7⋊C8—42no—
103C2×#125—71no—
104C2×C4×Q8C2×D711yescharacteristic
105#446—24no—
106#432—21no—
107#432—72no—
108#432C2×D712yes—
109#431—21no—
110#398—141no—
111#398—141no—
112#391—71no—
113#391—71no—
114#387—141no—
115#387—141no—
116#384—71no—
117#382—71no—
118C4×C4⋊C4—71no—
119#330—144no—
120#324—141no—
121#324—141no—
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#10112yes—
138C2×C4×C7C4×D412yes—
139C2×C4×C7#12011yescharacteristic
140C2×C4×C7#12112yes—
141C2×C4×C7#12311yescharacteristic
142C2×Dic7—22no—
143C2×Dic7—41no—
144C2×Dic7—41no—
145C2×Dic7—41no—
146C2×Dic7—41no—
147C2×Dic7—41no—
148C2×Dic7—41no—
149C2×Dic7—42no—
150C2×Dic7—41no—
151C2×Dic7—41no—
152C2×Dic7—41no—
153C7×C8—44no—
154C7⋊C8—82no—
155C22×Q8C4×D711yescharacteristic
156#125—142no—
157#125—142no—
158C4×Q8—22no—
159C4×Q8—22no—
160C2×C4⋊C4—71no—
161C2×C4⋊C4—71no—
162C2×C4⋊C4—141no—
163C2×C4⋊C4—141no—
164C2×C4⋊C4—141no—
165C2×C4⋊C4—141no—
166C2×C4⋊C4—141no—
167C2×C4⋊C4C4×D711yescharacteristic
168C2×C4⋊C4D2811yescharacteristic
169C2×C4⋊C4D2811yescharacteristic
170C2×C42—71no—
171C2×C42—71no—
172C2×C42C22⋊D711yescharacteristic
173C2×C42C22⋊D711yescharacteristic
174C2×C42C22×D711yescharacteristic
175C4⋊C8—22no—
176C4⋊C8—22no—
177C4⋊C8—22no—
178C4⋊C8—142no—
179C22⋊C8—22no—
180C22⋊C8—142no—
181#97—22no—
182#97—142no—
183#97C22⋊D714yes—
184C4×C8—22no—
185#95—141no—
186#95—141no—
187#95—141no—
188#95—141no—
189#95—141no—
190#95—141no—
191#95—141no—
192C22×C7—21no—
193C22×C7—21no—
194C22×C7#38611yescharacteristic
195C22×C7C2×#10111yescharacteristic
196C22×C7#41311yescharacteristic
197C4×C7—22no—
198C4×C7—22no—
199C4×C7—22no—
200C4×C7—21no—
201C4×C7—21no—
202C4×C7—41no—
203C4×C7—41no—
204C4×C7—41no—
205Dic7—42no—
206Dic7—81no—
207Dic7—81no—
208Dic7—81no—
209C2×Q8—22no—
210C2×Q8—22no—
211C2×Q8—41no—
212C22×C4—141no—
213C22×C4—141no—
214C22×C4—141no—
215C22×C4—141no—
216C22×C4(C2×D7)⋊C411yescharacteristic
217C22×C4(C2×D7)⋊C411yescharacteristic
218C22×C4(C2×D7)⋊C411yescharacteristic
219C22×C4(C2×D7)⋊C411yescharacteristic
220C22×C4C2×C4×D711yescharacteristic
221C22×C4C2×D2811yescharacteristic
222C22×C4C2×C22⋊D711yescharacteristic
223C2×C8—24no—
224C2×C8—282no—
225C4⋊C4—22no—
226C4⋊C4—22no—
227C4⋊C4—22no—
228C4⋊C4—142no—
229C4⋊C4—142no—
230C4⋊C4—282no—
231C4⋊C4—282no—
232C4⋊C4—282no—
233C4⋊C4—281no—
234C4⋊C4—282no—
235C4⋊C4—281no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—281no—
241C42—281no—
242C42#115712yes—
243C42C2×C22⋊D712yes—
244C2×C7—21no—
245C2×C7—21no—
246C2×C7#188411yescharacteristic
247C2×C7#190111yescharacteristic
248C2×C7#191211yescharacteristic
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—142no—
265C2×C4—281no—
266C2×C4—281no—
267C2×C4—281no—
268C2×C4—281no—
269C2×C4—281no—
270C2×C4—281no—
271C2×C4—282no—
272C2×C4—281no—
273C2×C4—281no—
274C2×C4—281no—
275C2×C4#639812yes—
276C2×C4C4×C22⋊D712yes—
277C2×C4#649211yescharacteristic
278C2×C4#649312yes—
279C2×C4#651611yescharacteristic
280C8—44no—
281C8—562no—
282C7#945011yescharacteristic, complemented, Sylow
283C22—21no—
284C22—21no—
285C22#8990411yescharacteristic
286C22C2×#639811yescharacteristic
287C22#8998511yescharacteristic
288C4—21no—
289C4—21no—
290C4—22no—
291C4—22no—
292C4—22no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—282no—
297C4—561no—
298C4—561no—
299C4—561no—
300C2—21no—
301C2—21no—
302C2#1172941711yescharacteristic
303C2#1172975711yescharacteristic
304C2#1172977511yescharacteristic
subgroupG/H
centerC22#89985
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#2983C2
socleC22×C7#386
prime radicalC23×C7C2×C22⋊C4
cosocleC2×C42×C7C23
hypercenter#2983D7
hypocenterC7#9450
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
282. C7#9450semidirect

Maximal subgroups

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

subgroupindex
C7×#29832
#117399222
#117293792
#117285682
#117255552
#94507