Finite Group Databasebeta

← #13264725

Subgroups — #13264725

Order 1792.

368 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 79 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#11739706C211yesmaximal, characteristic
2C7×#1458C211yesmaximal, characteristic
3#11729343C211yesmaximal, characteristic
4#11725265C212yesmaximal, complemented
5#11725264C212yesmaximal, complemented
6C2×C7×#117C2211yescharacteristic
7C2×#6433C411yescharacteristic
8C7×#431—21no—
9#89982—21no—
10#89979—21no—
11#89758C2211yescharacteristic
12#89755C2211yescharacteristic
13#89744—21no—
14#89725C411yescharacteristic
15#89721C411yescharacteristic
16#89717—21no—
17#89705—21no—
18#89704C411yescharacteristic
19C7×#324C2212yes—
20C7×#323—21no—
21#89325—21no—
22#89325C2212yes—
23#11853—71nomaximal, Sylow
24C23×C4×C7D411yescharacteristic
25C7×#117—41no—
26C7×#117—41no—
27C2×C7×C4⋊C4D411yescharacteristic
28C2×C7×C4⋊C4C2311yescharacteristic
29C2×C7×C22⋊C4C2×C411yescharacteristic
30C2×C7×C22⋊C4D411yescharacteristic
31C2×C42×C7C2×C411yescharacteristic
32C2×C42×C7D411yescharacteristic
33C2×C22⋊Dic7—21no—
34C2×C22⋊Dic7—21no—
35C2×C4⋊Dic7C2×C411yescharacteristic
36C2×C4⋊Dic7C2×C411yescharacteristic
37C2×Dic7⋊C4—21no—
38C2×Dic7⋊C4—21no—
39C2×Dic7⋊C4—21no—
40C2×Dic7⋊C4—21no—
41C2×C4×Dic7—21no—
42C2×#1136—22no—
43#6433—41no—
44#6433—41no—
45C7×C4⋊C8—41no—
46C7×C22⋊C8—22no—
47C4×C7×C8—41no—
48C7⋊#95—21no—
49C7⋊#95—21no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95C2×C411yescharacteristic
54C7⋊#95C2×C411yescharacteristic
55C22⋊(C7⋊C8)—41no—
56C22⋊(C7⋊C8)—41no—
57#2611—71no—
58#1822—71no—
59#1458D711yescharacteristic
60#1353—72no—
61#1346—72no—
62C24×C7C22⋊C411yescharacteristic
63C22×C4×C7—21no—
64C22×C4×C7—21no—
65C22×C4×C7—22no—
66C22×C4×C7—41no—
67C22×C4×C7C22⋊C411yescharacteristic
68C22×C4×C7C22⋊C411yescharacteristic
69C22×C4×C7C22⋊C411yescharacteristic
70C22×C4×C7C22×C411yescharacteristic
71C22×C4×C7C2×D411yescharacteristic
72C22×C4×C7C2×D411yescharacteristic
73C22×Dic7—21no—
74C22×Dic7—21no—
75C22×Dic7—21no—
76C22×Dic7—21no—
77C2×C7×C8—42no—
78C7×C4⋊C4—41no—
79C7×C4⋊C4—41no—
80C7×C22⋊C4—41no—
81C7×C22⋊C4—41no—
82C42×C7—21no—
83C42×C7—21no—
84C42×C7—21no—
85C42×C7—21no—
86C22⋊Dic7—42no—
87C22⋊Dic7—42no—
88C4⋊Dic7—41no—
89C4⋊Dic7—41no—
90Dic7⋊C4—42no—
91Dic7⋊C4—42no—
92Dic7⋊C4—41no—
93Dic7⋊C4—41no—
94Dic7⋊C4—42no—
95C4×Dic7—42no—
96#1136—42no—
97#1136—42no—
98C2×C7⋊C8—42no—
99C2×#125—71no—
100C2×#117C2×D711yescharacteristic
101#431—21no—
102#407—141no—
103#400—71no—
104#399—71no—
105#398—71no—
106#397—71no—
107#389—141no—
108#388—141no—
109#387—141no—
110#385—141no—
111#376—71no—
112#343—72no—
113#343—141no—
114#324C2×D712yes—
115#323—21no—
116C23×C7—21no—
117C23×C7—21no—
118C23×C7—21no—
119C23×C7—41no—
120C23×C7—41no—
121C23×C7C2×C22⋊C411yescharacteristic
122C2×C4×C7—21no—
123C2×C4×C7—21no—
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—42no—
131C2×C4×C7—42no—
132C2×C4×C7—41no—
133C2×C4×C7—41no—
134C2×C4×C7—41no—
135C2×C4×C7—41no—
136C2×C4×C7#9911yescharacteristic
137C2×C4×C7#9911yescharacteristic
138C2×C4×C7#13512yes—
139C2×Dic7—22no—
140C2×Dic7—41no—
141C2×Dic7—41no—
142C2×Dic7—41no—
143C2×Dic7—41no—
144C2×Dic7—41no—
145C2×Dic7—41no—
146C2×Dic7—41no—
147C2×Dic7—41no—
148C2×Dic7—41no—
149C2×Dic7—41no—
150C2×Dic7—41no—
151C7×C8—82no—
152C7⋊C8—82no—
153C23×C4D2811yescharacteristic
154C2×M16—142no—
155#125—281no—
156#125—281no—
157#117—41no—
158#117—41no—
159C2×C4⋊C4—71no—
160C2×C4⋊C4—71no—
161C2×C4⋊C4—141no—
162C2×C4⋊C4—141no—
163C2×C4⋊C4—141no—
164C2×C4⋊C4—141no—
165C2×C4⋊C4D2811yescharacteristic
166C2×C4⋊C4C22×D711yescharacteristic
167C2×C22⋊C4—141no—
168C2×C22⋊C4—141no—
169C2×C22⋊C4C4×D711yescharacteristic
170C2×C22⋊C4C22⋊D711yescharacteristic
171C2×C42—141no—
172C2×C42C4×D711yescharacteristic
173C2×C42C22⋊D711yescharacteristic
174C4⋊C8—41no—
175C22⋊C8—22no—
176C22⋊C8—281no—
177C22⋊C8—281no—
178C4×C8—41no—
179#95—71no—
180#95—71no—
181#95—141no—
182#95—141no—
183#95—141no—
184#95—141no—
185#95—141no—
186C22×C7—21no—
187C22×C7—21no—
188C22×C7—42no—
189C22×C7—41no—
190C22×C7—41no—
191C22×C7—41no—
192C22×C7—81no—
193C22×C7C2×#9911yescharacteristic
194C22×C7#41611yescharacteristic
195C22×C7#42111yescharacteristic
196C4×C7—22no—
197C4×C7—21no—
198C4×C7—21no—
199C4×C7—41no—
200C4×C7—41no—
201C4×C7—41no—
202C4×C7—41no—
203Dic7—42no—
204Dic7—81no—
205Dic7—81no—
206Dic7—81no—
207C24(C2×D7)⋊C411yescharacteristic
208C22×C4—22no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—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×C4C2×C4×D711yescharacteristic
220C22×C4C2×D2811yescharacteristic
221C22×C4C2×C22⋊D711yescharacteristic
222M16—282no—
223M16—282no—
224C2×C8—42no—
225C2×C8—282no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—281no—
229C4⋊C4—281no—
230C4⋊C4—282no—
231C4⋊C4—282no—
232C4⋊C4—282no—
233C4⋊C4—281no—
234C4⋊C4—281no—
235C22⋊C4—41no—
236C22⋊C4—41no—
237C22⋊C4—282no—
238C22⋊C4—282no—
239C42—21no—
240C42—21no—
241C42—21no—
242C42—21no—
243C42—282no—
244C2×C7—21no—
245C2×C7—21no—
246C2×C7—81no—
247C2×C7#151611yescharacteristic
248C2×C7#212311yescharacteristic
249C2×C7#213211yescharacteristic
250C23—21no—
251C23—21no—
252C23—21no—
253C23—41no—
254C23—41no—
255C23C2×(C2×D7)⋊C411yescharacteristic
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—142no—
271C2×C4—281no—
272C2×C4—281no—
273C2×C4—281no—
274C2×C4—281no—
275C2×C4—281no—
276C2×C4—281no—
277C2×C4—281no—
278C2×C4—281no—
279C2×C4—281no—
280C2×C4—281no—
281C2×C4—281no—
282C2×C4#638011yescharacteristic
283C2×C4#638011yescharacteristic
284C2×C4#646712yes—
285C8—82no—
286C8—562no—
287C7#1185311yescharacteristic, complemented, Sylow
288C22—21no—
289C22—21no—
290C22—42no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—81no—
295C22C2×#638011yescharacteristic
296C22#8988511yescharacteristic
297C22#8991111yescharacteristic
298C4—22no—
299C4—21no—
300C4—21no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—282no—
306C4—561no—
307C4—561no—
308C4—561no—
309C2—21no—
310C2—21no—
311C2—81no—
312C2#1172769711yescharacteristic
313C2#1172781211yescharacteristic
314C2#1172790211yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1458C2
socleC22×C7C2×#99
prime radicalC24×C7C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1458D7
hypocenterC7#11853
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
4. #11725265C2semidirect
5. #11725264C2semidirect
287. C7#11853semidirect

Maximal subgroups

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

subgroupindex
#117397062
C7×#14582
#117293432
#117252652
#117252642
#118537