Finite Group Databasebeta

← #13246439

Subgroups — #13246439

Order 1792.

778 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 778 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C22×#6452C211yesmaximal, characteristic
2C7×#1463C211yesmaximal, characteristic
3#11729306C211yesmaximal, characteristic
4#11727727C212yesmaximal
5#11727725C212yesmaximal
6C22×C7×C4⋊C4C2211yescharacteristic
7C22×C4⋊Dic7C2211yescharacteristic
8C22×Dic7⋊C4C411yescharacteristic
9C22×Dic7⋊C4C411yescharacteristic
10C22×Dic7⋊C4C411yescharacteristic
11C22×Dic7⋊C4C2211yescharacteristic
12C22×C4×Dic7C411yescharacteristic
13C2×#6452—22no—
14C2×#6452—22no—
15C2×#6452—24no—
16C2×#6452—24no—
17C7×#407C2212yes—
18#89979C2212yes—
19C7×#324—22no—
20#89349—24no—
21#89323—22no—
22#89264—24no—
23#8554—71nomaximal, Sylow
24C23×C4×C7C2×C411yescharacteristic
25C23×C4×C7C2×C411yescharacteristic
26C23×C4×C7C2311yescharacteristic
27C23×Dic7C2×C411yescharacteristic
28C23×Dic7C2×C411yescharacteristic
29C23×Dic7C2×C411yescharacteristic
30C23×Dic7C2×C411yescharacteristic
31C2×C7×M16—22no—
32C2×C7×C4⋊C4—22no—
33C2×C7×C4⋊C4—22no—
34C2×C7×C4⋊C4D412yes—
35C2×C7×C4⋊C4D412yes—
36C2×C4⋊Dic7—21no—
37C2×C4⋊Dic7—22no—
38C2×C4⋊Dic7—21no—
39C2×C4⋊Dic7D414yes—
40C2×Dic7⋊C4—22no—
41C2×Dic7⋊C4—22no—
42C2×Dic7⋊C4—22no—
43C2×Dic7⋊C4—21no—
44C2×Dic7⋊C4—22no—
45C2×Dic7⋊C4—21no—
46C2×Dic7⋊C4—22no—
47C2×Dic7⋊C4—22no—
48C2×Dic7⋊C4—22no—
49C2×Dic7⋊C4—22no—
50C2×Dic7⋊C4—22no—
51C2×Dic7⋊C4—22no—
52C2×Dic7⋊C4D414yes—
53C2×C4×Dic7—22no—
54C2×C4×Dic7—22no—
55C2×C4×Dic7—22no—
56C2×#1136—22no—
57#6452—216no—
58#6452—216no—
59C7×C22⋊C8—22no—
60C7×C22⋊C8—22no—
61C22⋊(C7⋊C8)—22no—
62C22⋊(C7⋊C8)—22no—
63C22×#125—71no—
64#1821—72no—
65#1463—72no—
66#1463—71no—
67#1463D711yescharacteristic
68C24×C7C22×C411yescharacteristic
69C22×C4×C7—21no—
70C22×C4×C7—21no—
71C22×C4×C7—21no—
72C22×C4×C7—21no—
73C22×C4×C7—42no—
74C22×C4×C7—42no—
75C22×C4×C7—42no—
76C22×C4×C7C22⋊C412yes—
77C22×C4×C7C22⋊C412yes—
78C22×C4×C7C2×D412yes—
79C22×C4×C7C2×D411yescharacteristic
80C22×C4×C7C2×D412yes—
81C22×C4×C7C2×D411yescharacteristic
82C22×Dic7—21no—
83C22×Dic7—21no—
84C22×Dic7—24no—
85C22×Dic7—21no—
86C22×Dic7—21no—
87C22×Dic7—21no—
88C22×Dic7—21no—
89C22×Dic7—21no—
90C22×Dic7—21no—
91C22×Dic7—42no—
92C22×Dic7—42no—
93C22×Dic7—42no—
94C22×Dic7C22⋊C412yes—
95C22×Dic7C22⋊C412yes—
96C22×Dic7C22⋊C412yes—
97C22×Dic7C22⋊C412yes—
98C7×M16—44no—
99C2×C7×C8—42no—
100C7×C4⋊C4—24no—
101C7×C4⋊C4—24no—
102C4⋊Dic7—24no—
103C4⋊Dic7—24no—
104Dic7⋊C4—28no—
105Dic7⋊C4—28no—
106Dic7⋊C4—28no—
107Dic7⋊C4—24no—
108Dic7⋊C4—24no—
109C4×Dic7—28no—
110#1136—44no—
111C2×C7⋊C8—42no—
112C2×#125—144no—
113C2×#125—144no—
114C2×#125—142no—
115C2×#125—142no—
116C22×C4⋊C4—71no—
117C22×C4⋊C4—71no—
118C22×C4⋊C4—71no—
119C22×C4⋊C4—71no—
120C22×C4⋊C4—71no—
121C22×C4⋊C4C2×D711yescharacteristic
122C22×C42—71no—
123#407—72no—
124#407C2×D712yes—
125#343—144no—
126#324—22no—
127#324—144no—
128#324—142no—
129C23×C7—22no—
130C23×C7—22no—
131C23×C7—22no—
132C23×C7C2×C22⋊C411yescharacteristic
133C23×C7C2×C22⋊C411yescharacteristic
134C23×C7C2×C22⋊C411yescharacteristic
135C2×C4×C7—24no—
136C2×C4×C7—22no—
137C2×C4×C7—22no—
138C2×C4×C7—24no—
139C2×C4×C7—41no—
140C2×C4×C7—42no—
141C2×C4×C7—41no—
142C2×C4×C7—42no—
143C2×C4×C7—42no—
144C2×C4×C7—42no—
145C2×C4×C7—42no—
146C2×C4×C7—42no—
147C2×C4×C7#12012yes—
148C2×C4×C7#12012yes—
149C2×Dic7—24no—
150C2×Dic7—24no—
151C2×Dic7—22no—
152C2×Dic7—22no—
153C2×Dic7—22no—
154C2×Dic7—22no—
155C2×Dic7—22no—
156C2×Dic7—42no—
157C2×Dic7—42no—
158C2×Dic7—42no—
159C2×Dic7—42no—
160C2×Dic7—42no—
161C2×Dic7—42no—
162C2×Dic7—42no—
163C2×Dic7—42no—
164C2×Dic7—42no—
165C2×Dic7#10114yes—
166C7×C8—82no—
167C7⋊C8—82no—
168C23×C4—71no—
169C23×C4—71no—
170C23×C4—71no—
171C23×C4—71no—
172C23×C4C4×D711yescharacteristic
173C23×C4C4×D711yescharacteristic
174C23×C4C22×D711yescharacteristic
175C2×M16—22no—
176C2×M16—142no—
177#125—1416no—
178#125—1416no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—74no—
182C2×C4⋊C4—74no—
183C2×C4⋊C4—142no—
184C2×C4⋊C4—142no—
185C2×C4⋊C4—142no—
186C2×C4⋊C4—142no—
187C2×C4⋊C4—142no—
188C2×C4⋊C4—142no—
189C2×C4⋊C4—142no—
190C2×C4⋊C4—142no—
191C2×C4⋊C4—142no—
192C2×C4⋊C4—141no—
193C2×C4⋊C4—141no—
194C2×C4⋊C4—142no—
195C2×C4⋊C4—142no—
196C2×C4⋊C4—141no—
197C2×C4⋊C4—141no—
198C2×C4⋊C4D2812yes—
199C2×C4⋊C4C22⋊D712yes—
200C2×C42—142no—
201C2×C42—142no—
202C2×C42—142no—
203C22⋊C8—22no—
204C22⋊C8—22no—
205C22⋊C8—142no—
206C22⋊C8—142no—
207C22×C7—28no—
208C22×C7—21no—
209C22×C7—21no—
210C22×C7—21no—
211C22×C7—21no—
212C22×C7—21no—
213C22×C7—21no—
214C22×C7#37911yescharacteristic
215C22×C7#41012yes—
216C22×C7C2×#10112yes—
217C22×C7#41312yes—
218C4×C7—22no—
219C4×C7—22no—
220C4×C7—42no—
221C4×C7—42no—
222Dic7—24no—
223Dic7—42no—
224Dic7—42no—
225Dic7—42no—
226C24C2×C4×D711yescharacteristic
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—72no—
235C22×C4—72no—
236C22×C4—72no—
237C22×C4—72no—
238C22×C4—144no—
239C22×C4—141no—
240C22×C4—141no—
241C22×C4—141no—
242C22×C4—141no—
243C22×C4—141no—
244C22×C4—141no—
245C22×C4—141no—
246C22×C4—141no—
247C22×C4—282no—
248C22×C4—282no—
249C22×C4—282no—
250C22×C4(C2×D7)⋊C412yes—
251C22×C4(C2×D7)⋊C412yes—
252C22×C4C2×D2811yescharacteristic
253C22×C4D4×D712yes—
254C22×C4D4×D712yes—
255C22×C4C2×C22⋊D711yescharacteristic
256M16—44no—
257M16—284no—
258C2×C8—42no—
259C2×C8—282no—
260C4⋊C4—24no—
261C4⋊C4—24no—
262C4⋊C4—148no—
263C4⋊C4—148no—
264C4⋊C4—148no—
265C4⋊C4—144no—
266C4⋊C4—144no—
267C4⋊C4—144no—
268C4⋊C4—144no—
269C42—148no—
270C2×C7—22no—
271C2×C7—22no—
272C2×C7—22no—
273C2×C7#178211yescharacteristic
274C2×C7#178411yescharacteristic
275C2×C7#178511yescharacteristic
276C23—22no—
277C23—22no—
278C23—22no—
279C23D7×C22⋊C411yescharacteristic
280C23D7×C22⋊C411yescharacteristic
281C23C2×(C2×D7)⋊C411yescharacteristic
282C2×C4—24no—
283C2×C4—24no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—74no—
295C2×C4—144no—
296C2×C4—144no—
297C2×C4—142no—
298C2×C4—142no—
299C2×C4—142no—
300C2×C4—142no—
301C2×C4—142no—
302C2×C4—282no—
303C2×C4—282no—
304C2×C4—282no—
305C2×C4—282no—
306C2×C4—282no—
307C2×C4—282no—
308C2×C4—282no—
309C2×C4—282no—
310C2×C4—282no—
311C2×C4#644512yes—
312C2×C4#650012yes—
313C8—82no—
314C8—562no—
315C7#855411yescharacteristic, complemented, Sylow
316C22—28no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22#8951212yes—
324C22D7×#10112yes—
325C22#8972711yescharacteristic
326C22#8990412yes—
327C4—22no—
328C4—22no—
329C4—42no—
330C4—42no—
331C4—144no—
332C4—282no—
333C4—282no—
334C4—282no—
335C2—22no—
336C2—22no—
337C2—22no—
338C2#1172774311yescharacteristic
339C2#1172778111yescharacteristic
340C2#1172786711yescharacteristic
subgroupG/H
centerC22#89727
commutator, prime radicalC24×C7C22×C4
FrattiniC23×C4C22×D7
FittingC7×#1463C2
socleC22×C7#379
cosocleC23×C4×C7C23
hypercenter#1463D7
hypocenterC7#8554
LCSG ▷ C24×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
315. C7#8554semidirect

Maximal subgroups

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

subgroupindex
C22×#64522
C7×#14632
#117293062
#117277272
#117277252
#85547