Finite Group Databasebeta

← #13264630

Subgroups — #13264630

Order 1792.

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

normal subgroups only

This group has 340 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#11739931C211yesmaximal, characteristic
2C7×#1801C211yesmaximal, characteristic
3#11729379C211yesmaximal, characteristic
4#11725302C212yesmaximal
5#11725301C212yesmaximal
6C2×C4×C7×Q8C2211yescharacteristic
7C2×#6433C411yescharacteristic
8C7×#423—21no—
9C2×C7×#101—21no—
10#90001—21no—
11#89758C411yescharacteristic
12#89758C2211yescharacteristic
13#89755C411yescharacteristic
14#89755C2211yescharacteristic
15#89754—21no—
16#89709C411yescharacteristic
17#89705—21no—
18#89705—21no—
19#89698—21no—
20C7×#343C2212yes—
21#89323—21no—
22#89323C2212yes—
23#11835—71nomaximal, Sylow
24C22×C7×Q8D411yescharacteristic
25C2×C7×M16—22no—
26C4×C7×Q8—41no—
27C4×C7×Q8—41no—
28C2×C7×C4⋊C4C2×C411yescharacteristic
29C2×C7×C4⋊C4D411yescharacteristic
30C2×C7×C4⋊C4C2311yescharacteristic
31C2×C42×C7C2×C411yescharacteristic
32C2×C42×C7D411yescharacteristic
33C2×C42×C7D411yescharacteristic
34C2×C4⋊Dic7C2×C411yescharacteristic
35C2×C4⋊Dic7C2×C411yescharacteristic
36C2×Dic7⋊C4—21no—
37C2×Dic7⋊C4—21no—
38C2×Dic7⋊C4—21no—
39C2×Dic7⋊C4—21no—
40#6433—41no—
41#6433—41no—
42C7×C4⋊C8—41no—
43C7×C4⋊C8—41no—
44C7×#101—42no—
45C7⋊#95—21no—
46C7⋊#95—21no—
47C7⋊#95—21no—
48C7⋊#95—21no—
49C7⋊#95—21no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95C2×C411yescharacteristic
54C7⋊#95C2×C411yescharacteristic
55C22⋊(C7⋊C8)—22no—
56C4⋊(C7⋊C8)—41no—
57#6377—41no—
58#2634—71no—
59#1801D711yescharacteristic
60#1467—71no—
61#1353—72no—
62#1346—72no—
63C2×C7×Q8—21no—
64C2×C7×Q8—21no—
65C2×C7×Q8—41no—
66C2×C7×Q8—41no—
67C22×C4×C7C22⋊C411yescharacteristic
68C22×C4×C7C22⋊C411yescharacteristic
69C22×C4×C7C22⋊C411yescharacteristic
70C22×C4×C7C22⋊C411yescharacteristic
71C22×C4×C7C22×C411yescharacteristic
72C22×C4×C7C2×D411yescharacteristic
73C22×C4×C7C2×D411yescharacteristic
74C22×Dic7—21no—
75C22×Dic7—21no—
76C22×Dic7—21no—
77C22×Dic7—21no—
78C7×M16—42no—
79C7×M16—42no—
80C2×C7×C8—42no—
81C7×C4⋊C4—41no—
82C7×C4⋊C4—41no—
83C7×C4⋊C4—41no—
84C42×C7—21no—
85C42×C7—21no—
86C42×C7—21no—
87C42×C7—21no—
88C42×C7—21no—
89C42×C7—21no—
90C4⋊Dic7—41no—
91C4⋊Dic7—41no—
92Dic7⋊C4—42no—
93Dic7⋊C4—42no—
94Dic7⋊C4—41no—
95Dic7⋊C4—41no—
96Dic7⋊C4—41no—
97Dic7⋊C4—41no—
98C2×C7⋊C8—42no—
99C2×#125—71no—
100C2×C4×Q8C2×D711yescharacteristic
101#432—141no—
102#423—21no—
103C2×#101—21no—
104#400—71no—
105#400—71no—
106#400—141no—
107#398—71no—
108#398—71no—
109#395—141no—
110#387—141no—
111#387—141no—
112#383—71no—
113#343C2×D712yes—
114#324—72no—
115#324—141no—
116C23×C7C2×C22⋊C411yescharacteristic
117C7×Q8—42no—
118C7×Q8—42no—
119C2×C4×C7—21no—
120C2×C4×C7—21no—
121C2×C4×C7—21no—
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—41no—
131C2×C4×C7—41no—
132C2×C4×C7—41no—
133C2×C4×C7—41no—
134C2×C4×C7#9911yescharacteristic
135C2×C4×C7#9911yescharacteristic
136C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C7#13711yescharacteristic
138C2×Dic7—41no—
139C2×Dic7—41no—
140C2×Dic7—41no—
141C2×Dic7—41no—
142C2×Dic7—42no—
143C2×Dic7—41no—
144C2×Dic7—41no—
145C2×Dic7—41no—
146C2×Dic7—41no—
147C2×Dic7—41no—
148C2×Dic7—41no—
149C7×C8—82no—
150C7⋊C8—82no—
151C22×Q8C22⋊D711yescharacteristic
152C2×M16—22no—
153#125—281no—
154#125—281no—
155C4×Q8—41no—
156C4×Q8—41no—
157C2×C4⋊C4—71no—
158C2×C4⋊C4—71no—
159C2×C4⋊C4—141no—
160C2×C4⋊C4—141no—
161C2×C4⋊C4—141no—
162C2×C4⋊C4—141no—
163C2×C4⋊C4C4×D711yescharacteristic
164C2×C4⋊C4D2811yescharacteristic
165C2×C4⋊C4C22×D711yescharacteristic
166C2×C42C4×D711yescharacteristic
167C2×C42D2811yescharacteristic
168C2×C42C22⋊D711yescharacteristic
169C4⋊C8—41no—
170C4⋊C8—41no—
171C4⋊C8—281no—
172#101—42no—
173C22⋊C8—142no—
174#97—281no—
175#95—71no—
176#95—71no—
177#95—141no—
178#95—141no—
179#95—141no—
180#95—141no—
181#95—141no—
182#95—141no—
183#95—141no—
184#95—141no—
185C22×C7—21no—
186C22×C7—21no—
187C22×C7C2×#9911yescharacteristic
188C22×C7#41711yescharacteristic
189C22×C7#42111yescharacteristic
190C4×C7—21no—
191C4×C7—21no—
192C4×C7—21no—
193C4×C7—21no—
194C4×C7—41no—
195C4×C7—41no—
196C4×C7—41no—
197C4×C7—41no—
198C4×C7—41no—
199Dic7—81no—
200Dic7—81no—
201Dic7—81no—
202Dic7—81no—
203C2×Q8—21no—
204C2×Q8—21no—
205C2×Q8—41no—
206C2×Q8—41no—
207C22×C4—141no—
208C22×C4—141no—
209C22×C4—141no—
210C22×C4—141no—
211C22×C4(C2×D7)⋊C411yescharacteristic
212C22×C4(C2×D7)⋊C411yescharacteristic
213C22×C4(C2×D7)⋊C411yescharacteristic
214C22×C4(C2×D7)⋊C411yescharacteristic
215C22×C4C2×C4×D711yescharacteristic
216C22×C4C2×D2811yescharacteristic
217C22×C4C2×C22⋊D711yescharacteristic
218M16—42no—
219M16—42no—
220C2×C8—42no—
221C2×C8—282no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—281no—
226C4⋊C4—281no—
227C4⋊C4—282no—
228C4⋊C4—282no—
229C4⋊C4—281no—
230C4⋊C4—281no—
231C4⋊C4—281no—
232C4⋊C4—281no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—21no—
237C42—21no—
238C42—21no—
239C2×C7—21no—
240C2×C7—21no—
241C2×C7#151311yescharacteristic
242C2×C7#212311yescharacteristic
243C2×C7#213311yescharacteristic
244C23C2×(C2×D7)⋊C411yescharacteristic
245Q8—42no—
246Q8—42no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—281no—
263C2×C4—281no—
264C2×C4—281no—
265C2×C4—281no—
266C2×C4—282no—
267C2×C4—281no—
268C2×C4—281no—
269C2×C4—281no—
270C2×C4—281no—
271C2×C4—281no—
272C2×C4—281no—
273C2×C4#638011yescharacteristic
274C2×C4#638011yescharacteristic
275C2×C4#649511yescharacteristic
276C2×C4#650511yescharacteristic
277C8—82no—
278C8—562no—
279C7#1183511yescharacteristic, complemented, Sylow
280C22—21no—
281C22—21no—
282C22C2×#638011yescharacteristic
283C22#8973811yescharacteristic
284C22#8977711yescharacteristic
285C4—21no—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—41no—
294C4—561no—
295C4—561no—
296C4—561no—
297C4—561no—
298C2—21no—
299C2—21no—
300C2#1172726211yescharacteristic
301C2#1172788211yescharacteristic
302C2#1172790111yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1801C2
socleC22×C7C2×#99
prime radicalC23×C7C2×C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1801D7
hypocenterC7#11835
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
279. C7#11835semidirect

Maximal subgroups

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

subgroupindex
#117399312
C7×#18012
#117293792
#117253022
#117253012
#118357