Finite Group Databasebeta

← #13245264

Subgroups — #13245264

Order 1792.

826 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 826 conjugacy classes of subgroups — too many to draw. Only its 135 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
1C2×D7×#125C211yesmaximal, characteristic
2C2×C7×#330C211yesmaximal, characteristic, complemented
3C2×#89338C211yesmaximal, characteristic, complemented
4#11727561C212yesmaximal
5C2×#89260C212yesmaximal, complemented
6C2×C7×#125C2211yescharacteristic
7D7×#125—22no—
8D7×#125—22no—
9D7×#125—24no—
10C2×D7×C4⋊C4—22no—
11C2×D7×C4⋊C4C412yes—
12C2×#6453C412yes—
13C2×#6452—22no—
14C2×C42×D7C2211yescharacteristic
15C2×#6433C2211yescharacteristic
16C2×C7×#97C2212yes—
17C2×(C2×D7)⋊C8—22no—
18C2×#6377C2212yes—
19C7×#330—22no—
20#89345—22no—
21#89338—22no—
22#89260—24no—
23#8335—71nomaximal, Sylow
24C22×C4×D7—22no—
25C22×C4×D7C2×C411yescharacteristic
26C22×C4×D7D412yes—
27C22×C7×C8—22no—
28C7×#125—22no—
29C7×#125D412yes—
30C7×#125D412yes—
31C2×C7×C4⋊C4—22no—
32C2×C7×C4⋊C4C2×C412yes—
33C2×C42×C7C2311yescharacteristic
34C2×C4⋊Dic7—22no—
35C2×C4⋊Dic7C2×C412yes—
36C2×Dic7⋊C4—22no—
37C2×Dic7⋊C4—22no—
38C2×Dic7⋊C4—22no—
39C2×C4×Dic7C2×C411yescharacteristic
40C2×C4×Dic7D412yes—
41C22×C7⋊C8—22no—
42D7×C4⋊C4—28no—
43D7×C4⋊C4—28no—
44D7×C4⋊C4—24no—
45D7×C4⋊C4—24no—
46#6453—24no—
47#6453—24no—
48#6452—28no—
49#6452—28no—
50C42×D7—21no—
51C42×D7—22no—
52C42×D7—21no—
53#6433—21no—
54#6433—21no—
55#6433D414yes—
56C7×#97—22no—
57C7×#97—22no—
58(C2×D7)⋊C8—28no—
59#6377—22no—
60#6377—22no—
61C22×#125—71no—
62#1749—72no—
63C2×#330—72no—
64C2×#330—71no—
65C2×#330D711yescharacteristic, complemented
66C23×D7C22⋊C411yescharacteristic
67C22×C4×C7—22no—
68C22×C4×C7C22×C411yescharacteristic
69C22×C4×C7C2×D412yes—
70C22×Dic7—22no—
71C22×Dic7C22⋊C412yes—
72C22×Dic7C22⋊C411yescharacteristic
73C2×C4×D7—22no—
74C2×C4×D7—21no—
75C2×C4×D7—21no—
76C2×C4×D7—22no—
77C2×C4×D7—28no—
78C2×C4×D7—24no—
79C2×C4×D7—22no—
80C2×C4×D7—22no—
81C2×C4×D7—42no—
82C2×C4×D7—44no—
83C2×C4×D7—44no—
84C2×C7×C8—24no—
85C2×C7×C8—42no—
86C2×C7×C8—42no—
87C7×C4⋊C4—22no—
88C7×C4⋊C4—24no—
89C7×C4⋊C4—24no—
90C7×C4⋊C4C22⋊C414yes—
91C42×C7C2×D411yescharacteristic
92C42×C7C2×D412yes—
93C42×C7C2×D411yescharacteristic
94C4⋊Dic7—28no—
95C4⋊Dic7—22no—
96C4⋊Dic7C22⋊C414yes—
97Dic7⋊C4—28no—
98Dic7⋊C4—28no—
99Dic7⋊C4—24no—
100Dic7⋊C4—24no—
101C4×Dic7—21no—
102C4×Dic7—21no—
103C4×Dic7—22no—
104C4×Dic7—22no—
105C2×C7⋊C8—24no—
106C2×C7⋊C8—42no—
107C2×C7⋊C8—42no—
108C2×#125—72no—
109C2×#125—71no—
110C2×#125—142no—
111C2×#125—144no—
112C2×#125—142no—
113C2×#125—142no—
114C2×#125C2×D711yescharacteristic
115C22×C4⋊C4—72no—
116C22×C4⋊C4—142no—
117C22×C42—71no—
118C2×C22⋊C8—142no—
119C2×#97—72no—
120C2×#97C2×D712yes—
121#336—142no—
122#330—22no—
123#330—144no—
124#330—142no—
125C23×C7C2×C22⋊C411yescharacteristic
126C22×D7—21no—
127C22×D7—21no—
128C22×D7—22no—
129C22×D7#10112yes—
130C22×D7#10414yes—
131C2×C4×C7—21no—
132C2×C4×C7—21no—
133C2×C4×C7—22no—
134C2×C4×C7—22no—
135C2×C4×C7—24no—
136C2×C4×C7—42no—
137C2×C4×C7—42no—
138C2×C4×C7C2×C22⋊C411yescharacteristic
139C2×C4×C7C2×C22⋊C411yescharacteristic
140C2×C4×C7#12012yes—
141C2×C4×C7#12012yes—
142C2×Dic7—21no—
143C2×Dic7—21no—
144C2×Dic7—22no—
145C2×Dic7—24no—
146C2×Dic7—22no—
147C2×Dic7—22no—
148C2×Dic7—42no—
149C2×Dic7—42no—
150C2×Dic7#10112yes—
151C4×D7—24no—
152C4×D7—24no—
153C4×D7—44no—
154C4×D7—44no—
155C4×D7—416no—
156C7×C8—44no—
157C7⋊C8—44no—
158C23×C4—71no—
159C23×C4—72no—
160C23×C4—142no—
161C22×C8—22no—
162C22×C8—142no—
163#125—22no—
164#125—74no—
165#125—144no—
166#125—148no—
167#125—148no—
168#125—144no—
169#125—141no—
170#125—141no—
171#125D2812yes—
172#125C22⋊D712yes—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—72no—
175C2×C4⋊C4—144no—
176C2×C4⋊C4—148no—
177C2×C4⋊C4—148no—
178C2×C4⋊C4—142no—
179C2×C4⋊C4—142no—
180C2×C4⋊C4—142no—
181C2×C4⋊C4—142no—
182C2×C4⋊C4—144no—
183C2×C4⋊C4C4×D712yes—
184C2×C42—71no—
185C2×C42—72no—
186C2×C42—141no—
187C2×C42—142no—
188C2×C42—141no—
189C2×C42C22×D711yescharacteristic
190C22⋊C8—148no—
191#97—22no—
192#97—22no—
193#97—142no—
194#97—142no—
195C22×C7#37911yescharacteristic
196C22×C7C2×#10111yescharacteristic
197C22×C7C2×#10111yescharacteristic
198C22×C7C2×#10412yes—
199C22×C7#42112yes—
200C2×D7—24no—
201C2×D7—22no—
202C2×D7—24no—
203C2×D7—22no—
204C2×D7#33014yescomplemented
205C4×C7—21no—
206C4×C7—21no—
207C4×C7—22no—
208C4×C7—22no—
209C4×C7—44no—
210Dic7—22no—
211Dic7—42no—
212Dic7—44no—
213C24—71no—
214C22×C4—22no—
215C22×C4—71no—
216C22×C4—72no—
217C22×C4—142no—
218C22×C4—142no—
219C22×C4—144no—
220C22×C4—148no—
221C22×C4—141no—
222C22×C4—141no—
223C22×C4—142no—
224C22×C4—142no—
225C22×C4—142no—
226C22×C4—282no—
227C22×C4—284no—
228C22×C4—284no—
229C22×C4C2×C4×D711yescharacteristic
230C22×C4D4×D712yes—
231C2×C8—24no—
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—144no—
235C2×C8—282no—
236C2×C8—282no—
237C4⋊C4—22no—
238C4⋊C4—24no—
239C4⋊C4—24no—
240C4⋊C4—74no—
241C4⋊C4—148no—
242C4⋊C4—148no—
243C4⋊C4—148no—
244C4⋊C4—144no—
245C4⋊C4—142no—
246C4⋊C4—144no—
247C4⋊C4(C2×D7)⋊C414yes—
248C42—141no—
249C42—142no—
250C42—141no—
251C42—142no—
252C42C2×D2811yescharacteristic
253C42D4×D712yes—
254C42C2×C22⋊D711yescharacteristic
255C2×C7C2×#33011yescharacteristic
256C2×C7#152812yes—
257C2×C7#153411yescharacteristic
258C2×C7#178411yescharacteristic
259C2×C7#178912yes—
260D7—24no—
261C23—72no—
262C23—74no—
263C23—141no—
264C23—141no—
265C23—142no—
266C23D7×C22⋊C411yescharacteristic
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—24no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—72no—
275C2×C4—144no—
276C2×C4—144no—
277C2×C4—141no—
278C2×C4—141no—
279C2×C4—142no—
280C2×C4—144no—
281C2×C4—142no—
282C2×C4—142no—
283C2×C4—284no—
284C2×C4—284no—
285C2×C4—2816no—
286C2×C4—282no—
287C2×C4—282no—
288C2×C4D7×C22⋊C411yescharacteristic
289C2×C4#644512yes—
290C2×C4C2×(C2×D7)⋊C411yescharacteristic
291C2×C4#650012yes—
292C8—44no—
293C8—284no—
294C7#833511yescharacteristic, complemented, Sylow
295C22—74no—
296C22—144no—
297C22—144no—
298C22—142no—
299C22—142no—
300C22D7×#10111yescharacteristic
301C22D7×#10111yescharacteristic
302C22D7×#10412yes—
303C22#8959312yes—
304C22#8972711yescharacteristic
305C4—22no—
306C4—22no—
307C4—21no—
308C4—21no—
309C4—44no—
310C4—142no—
311C4—282no—
312C4—284no—
313C2—144no—
314C2D7×#33011yescharacteristic
315C2#1172611712yes—
316C2#1172612111yescharacteristic
317C2#1172786711yescharacteristic
318C2#1172813412yes—
subgroupG/H
centerC23D7×C22⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC2×C7×#330C2
socleC23×C7C2×C22⋊C4
prime radicalC23×D7C22⋊C4
cosocleC2×C42×C7C23
hypercenterC2×#330D7
hypocenterC7#8335
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
2. C2×C7×#330C2semidirect
3. C2×#89338C2semidirect
5. C2×#89260C2semidirect
65. C2×#330D7semidirect
204. C2×D7#330semidirect
294. C7#8335semidirect

Maximal subgroups

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

subgroupindex
C2×D7×#1252
C2×C7×#3302
C2×#893382
#117275612
C2×#892602
#83357