Finite Group Databasebeta

← #13245155

Subgroups — #13245155

Order 1792.

1174 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 1174 conjugacy classes of subgroups — too many to draw. Only its 155 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×#6487C211yesmaximal, characteristic
2C7×#1779C211yesmaximal, characteristic
3#11729880C211yesmaximal, characteristic
4C2×#89264C214yesmaximal, complemented
5C24×C4×C7C2211yescharacteristic
6C23×Dic14C411yescharacteristic
7C22×C22⋊Dic7C412yes—
8C22×C4⋊Dic7C411yescharacteristic
9C2×#6487—22no—
10C2×#6487—22no—
11C2×#6487—28no—
12C22×Dic7⋊C4C2212yes—
13C2×C7×C22⋊C8—22no—
14C2×C7×C22⋊C8C2212yes—
15C2×C22⋊(C7⋊C8)—22no—
16C2×C22⋊(C7⋊C8)C2212yes—
17#89264—28no—
18#8308—71nomaximal, Sylow
19C25×C7C2×C411yescharacteristic
20C23×C4×C7—24no—
21C23×C4×C7—44no—
22C23×C4×C7C2×C411yescharacteristic
23C23×C4×C7D412yes—
24C23×C4×C7D412yes—
25C23×C4×C7C2311yescharacteristic
26C23×Dic7C2×C412yes—
27C23×Dic7C2×C412yes—
28C22×Dic14—22no—
29C22×Dic14—24no—
30C22×Dic14—44no—
31C22×C7×C8—22no—
32C2×C22⋊Dic7—24no—
33C2×C22⋊Dic7—24no—
34C2×C22⋊Dic7—24no—
35C2×C4⋊Dic7—22no—
36C2×C4⋊Dic7—24no—
37#6487—216no—
38#6487—216no—
39C2×Dic7⋊C4—22no—
40C2×Dic7⋊C4—24no—
41C2×Dic7⋊C4—22no—
42C2×Dic7⋊C4D418yes—
43C22×C7⋊C8—22no—
44C7×C22⋊C8—24no—
45C7×C22⋊C8—44no—
46C22⋊(C7⋊C8)—24no—
47C22⋊(C7⋊C8)—44no—
48C22×C22⋊Q8—71no—
49#1779—71no—
50#1779D711yescharacteristic
51C2×#324—74no—
52C24×C7—24no—
53C24×C7—22no—
54C24×C7—22no—
55C24×C7—22no—
56C24×C7—42no—
57C24×C7C22⋊C412yes—
58C24×C7C22×C411yescharacteristic
59C22×C4×C7—22no—
60C22×C4×C7—24no—
61C22×C4×C7—24no—
62C22×C4×C7—24no—
63C22×C4×C7—24no—
64C22×C4×C7—24no—
65C22×C4×C7—42no—
66C22×C4×C7—42no—
67C22×C4×C7—42no—
68C22×C4×C7—416no—
69C22×C4×C7C22⋊C412yes—
70C22×C4×C7C2×D411yescharacteristic
71C22×C4×C7C2×D411yescharacteristic
72C22×C4×C7C2×D414yes—
73C22×Dic7—22no—
74C22×Dic7—22no—
75C22×Dic7—22no—
76C22×Dic7—22no—
77C22×Dic7—24no—
78C22×Dic7—24no—
79C22×Dic7—44no—
80C22×Dic7C22⋊C414yes—
81C22×Dic7C22⋊C414yes—
82C2×Dic14—28no—
83C2×Dic14—416no—
84C2×Dic14—44no—
85C2×Dic14—44no—
86C2×C7×C8—44no—
87C2×C7×C8—42no—
88C22⋊Dic7—216no—
89C4⋊Dic7—28no—
90Dic7⋊C4—28no—
91Dic7⋊C4—28no—
92C2×C7⋊C8—44no—
93C2×C7⋊C8—42no—
94C23×Q8—71no—
95C24×C4C2×D711yescharacteristic
96C2×C22⋊Q8—148no—
97C2×C22⋊Q8—142no—
98C2×C22⋊Q8—142no—
99C22×C4⋊C4—72no—
100C22×C4⋊C4—71no—
101C22×C22⋊C4—72no—
102C2×C22⋊C8—22no—
103C2×C22⋊C8—72no—
104C2×C22⋊C8—142no—
105C2×C22⋊C8C2×D712yes—
106#324—148no—
107C23×C7—22no—
108C23×C7—22no—
109C23×C7—28no—
110C23×C7—22no—
111C23×C7—22no—
112C23×C7—22no—
113C23×C7—22no—
114C23×C7—22no—
115C23×C7—22no—
116C23×C7—48no—
117C23×C7—48no—
118C23×C7—44no—
119C23×C7—44no—
120C23×C7#10114yes—
121C23×C7C2×C22⋊C412yes—
122C23×C7C2×C22⋊C411yescharacteristic
123C23×C7#13112yes—
124C23×C7#13112yes—
125C2×C4×C7—28no—
126C2×C4×C7—22no—
127C2×C4×C7—22no—
128C2×C4×C7—22no—
129C2×C4×C7—22no—
130C2×C4×C7—44no—
131C2×C4×C7—48no—
132C2×C4×C7—48no—
133C2×C4×C7#9914yes—
134C2×C4×C7#12012yes—
135C2×C4×C7#12012yes—
136C2×Dic7—24no—
137C2×Dic7—24no—
138C2×Dic7—28no—
139C2×Dic7—44no—
140C2×Dic7—42no—
141C2×Dic7—42no—
142C2×Dic7—44no—
143C2×Dic7—44no—
144C2×Dic7—44no—
145Dic14—416no—
146C7×C8—82no—
147C7⋊C8—82no—
148C25C4×D711yescharacteristic
149C22×Q8—144no—
150C22×Q8—142no—
151C22×Q8—284no—
152C23×C4—24no—
153C23×C4—44no—
154C23×C4—72no—
155C23×C4—72no—
156C23×C4C4×D711yescharacteristic
157C23×C4D2812yes—
158C23×C4C22⋊D712yes—
159C23×C4C22×D711yescharacteristic
160C22×C8—22no—
161C22×C8—142no—
162C22⋊Q8—1416no—
163C22⋊Q8—1416no—
164C2×C4⋊C4—78no—
165C2×C4⋊C4—144no—
166C2×C4⋊C4—142no—
167C2×C4⋊C4—142no—
168C2×C4⋊C4—144no—
169C2×C4⋊C4—142no—
170C2×C22⋊C4—144no—
171C2×C22⋊C4—144no—
172C2×C22⋊C4—144no—
173C22⋊C8—24no—
174C22⋊C8—44no—
175C22⋊C8—144no—
176C22⋊C8—284no—
177C22×C7—24no—
178C22×C7—24no—
179C22×C7—22no—
180C22×C7—22no—
181C22×C7—24no—
182C22×C7—24no—
183C22×C7—24no—
184C22×C7—416no—
185C22×C7—42no—
186C22×C7—42no—
187C22×C7—42no—
188C22×C7—42no—
189C22×C7#37911yescharacteristic
190C22×C7#40811yescharacteristic
191C22×C7#40811yescharacteristic
192C22×C7#40814yes—
193C22×C7C2×#9912yes—
194C22×C7C2×#10112yes—
195C4×C7—22no—
196C4×C7—22no—
197C4×C7—24no—
198Dic7—44no—
199Dic7—44no—
200C24—22no—
201C24—24no—
202C24—22no—
203C24—22no—
204C24—42no—
205C24(C2×D7)⋊C412yes—
206C24C2×C4×D711yescharacteristic
207C2×Q8—148no—
208C2×Q8—2816no—
209C2×Q8—284no—
210C2×Q8—284no—
211C22×C4—22no—
212C22×C4—24no—
213C22×C4—24no—
214C22×C4—24no—
215C22×C4—24no—
216C22×C4—24no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—416no—
221C22×C4—74no—
222C22×C4—74no—
223C22×C4—142no—
224C22×C4—142no—
225C22×C4—144no—
226C22×C4—144no—
227C22×C4—142no—
228C22×C4—142no—
229C22×C4—284no—
230C22×C4(C2×D7)⋊C412yes—
231C22×C4C2×D2811yescharacteristic
232C22×C4D4×D714yes—
233C22×C4C2×C22⋊D711yescharacteristic
234C2×C8—44no—
235C2×C8—42no—
236C2×C8—284no—
237C2×C8—282no—
238C4⋊C4—148no—
239C4⋊C4—148no—
240C4⋊C4—148no—
241C22⋊C4—1416no—
242C2×C7—24no—
243C2×C7—44no—
244C2×C7#147212yes—
245C2×C7#147212yes—
246C2×C7#178011yescharacteristic
247C2×C7#178111yescharacteristic
248C2×C7#178411yescharacteristic
249C23—22no—
250C23—22no—
251C23—28no—
252C23—22no—
253C23—22no—
254C23—22no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23—48no—
259C23—48no—
260C23—44no—
261C23—44no—
262C23#639814yes—
263C23D7×C22⋊C412yes—
264C23#646412yes—
265C23#647012yes—
266C23C2×(C2×D7)⋊C411yescharacteristic
267Q8—2816no—
268C2×C4—28no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—44no—
274C2×C4—48no—
275C2×C4—48no—
276C2×C4—144no—
277C2×C4—144no—
278C2×C4—148no—
279C2×C4—284no—
280C2×C4—282no—
281C2×C4—282no—
282C2×C4—284no—
283C2×C4—284no—
284C2×C4—284no—
285C2×C4#638014yes—
286C2×C4#644512yes—
287C2×C4#650012yes—
288C8—82no—
289C8—562no—
290C7#830811yescharacteristic, complemented, Sylow
291C22—24no—
292C22—24no—
293C22—22no—
294C22—22no—
295C22—24no—
296C22—24no—
297C22—24no—
298C22—416no—
299C22—42no—
300C22—42no—
301C22—42no—
302C22—42no—
303C22#8949914yes—
304C22C2×#638012yes—
305C22#8972711yescharacteristic
306C22#8988211yescharacteristic
307C22#8990111yescharacteristic
308C22C2×#639812yes—
309C4—22no—
310C4—22no—
311C4—24no—
312C4—284no—
313C4—284no—
314C2—24no—
315C2—44no—
316C2#1172725211yescharacteristic
317C2#1172767712yes—
318C2#1172771011yescharacteristic
319C2#1172772612yes—
320C2#1172774411yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC24×C7C22×C4
FrattiniC23×C4C22×D7
FittingC7×#1779C2
socleC23×C7C2×C22⋊C4
prime radicalC25×C7C2×C4
cosocleC23×C4×C7C23
hypercenter#1779D7
hypocenterC7#8308
LCSG ▷ C24×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
4. C2×#89264C2semidirect
290. C7#8308semidirect

Maximal subgroups

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

subgroupindex
C22×#64872
C7×#17792
#117298802
C2×#892642
#83087