Finite Group Databasebeta

← #13264948

Subgroups — #13264948

Order 1792.

372 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 95 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#11739926C211yesmaximal, characteristic
2C7×#1801C211yesmaximal, characteristic
3#11729378C211yesmaximal, characteristic
4#11725302C212yesmaximal
5#11725300C212yesmaximal
6C2×C4×C7×Q8C2211yescharacteristic
7C2×C4×Dic14C411yescharacteristic
8C7×#423—21no—
9C2×C7×#101—21no—
10#90002—21no—
11#89758C411yescharacteristic
12#89758C2211yescharacteristic
13#89751C411yescharacteristic
14#89751C2211yescharacteristic
15#89745—21no—
16#89708C411yescharacteristic
17#89705—21no—
18#89705—21no—
19#89697—21no—
20C7×#343C2212yes—
21#89323—21no—
22#89323C2212yes—
23#11905—71nomaximal, Sylow
24C22×C7×Q8D411yescharacteristic
25C22×Dic14C2×C411yescharacteristic
26C2×C7×M16—22no—
27C4×C7×Q8—41no—
28C4×C7×Q8—41no—
29C2×C7×C4⋊C4C2×C411yescharacteristic
30C2×C7×C4⋊C4D411yescharacteristic
31C2×C7×C4⋊C4C2311yescharacteristic
32C2×C42×C7C2×C411yescharacteristic
33C2×C42×C7D411yescharacteristic
34C2×C42×C7D411yescharacteristic
35C2×C4⋊Dic7—21no—
36C2×C4⋊Dic7C2×C411yescharacteristic
37C2×Dic7⋊C4—21no—
38C2×Dic7⋊C4—21no—
39C2×Dic7⋊C4—21no—
40C2×C4×Dic7—21no—
41C4×Dic14—41no—
42C4×Dic14—41no—
43C7×C4⋊C8—41no—
44C7×C4⋊C8—41no—
45C7×#101—42no—
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—
57C4×C7⋊C8—41no—
58#2581—71no—
59#1801D711yescharacteristic
60#1461—71no—
61#1354—72no—
62#1353—72no—
63C2×C7×Q8—41no—
64C2×C7×Q8—41no—
65C2×C7×Q8SD1612yes—
66C2×C7×Q8Q1612yes—
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—
78C2×Dic14—41no—
79C2×Dic14—42no—
80C7×M16—42no—
81C7×M16—42no—
82C2×C7×C8—42no—
83C7×C4⋊C4—41no—
84C7×C4⋊C4—41no—
85C7×C4⋊C4—41no—
86C42×C7—21no—
87C42×C7—21no—
88C42×C7—21no—
89C42×C7—21no—
90C42×C7—21no—
91C42×C7—21no—
92C4⋊Dic7—42no—
93C4⋊Dic7—41no—
94Dic7⋊C4—42no—
95Dic7⋊C4—42no—
96Dic7⋊C4—41no—
97Dic7⋊C4—41no—
98C4×Dic7—42no—
99C2×C7⋊C8—42no—
100C2×C4×Q8—71no—
101C2×C4×Q8C2×D711yescharacteristic
102#431—141no—
103#423—21no—
104C2×#101—21no—
105#400—71no—
106#400—71no—
107#395—71no—
108#395—71no—
109#391—141no—
110#389—141no—
111#387—141no—
112#387—141no—
113#382—71no—
114#343C2×D712yes—
115#324—72no—
116#324—141no—
117C23×C7C2×C22⋊C411yescharacteristic
118C7×Q8—42no—
119C7×Q8—42no—
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—41no—
130C2×C4×C7—41no—
131C2×C4×C7—41no—
132C2×C4×C7—41no—
133C2×C4×C7#9911yescharacteristic
134C2×C4×C7#9911yescharacteristic
135C2×C4×C7#10312yes—
136C2×C4×C7#10312yes—
137C2×C4×C7C2×SD1611yescharacteristic
138C2×C4×C7C2×Q1611yescharacteristic
139C2×Dic7—22no—
140C2×Dic7—41no—
141C2×Dic7—41no—
142C2×Dic7—41no—
143C2×Dic7—41no—
144C2×Dic7—41no—
145C2×Dic7—41no—
146C2×Dic7—42no—
147C2×Dic7—41no—
148C2×Dic7—41no—
149C2×Dic7—41no—
150Dic14—42no—
151Dic14—42no—
152C7×C8—82no—
153C7⋊C8—82no—
154C22×Q8—71no—
155C22×Q8C22⋊D711yescharacteristic
156C2×M16—22no—
157C4×Q8—41no—
158C4×Q8—41no—
159C4×Q8—281no—
160C4×Q8—281no—
161C2×C4⋊C4—71no—
162C2×C4⋊C4—141no—
163C2×C4⋊C4—141no—
164C2×C4⋊C4—141no—
165C2×C4⋊C4—141no—
166C2×C4⋊C4C4×D711yescharacteristic
167C2×C4⋊C4D2811yescharacteristic
168C2×C4⋊C4C22×D711yescharacteristic
169C2×C42—141no—
170C2×C42C4×D711yescharacteristic
171C2×C42D2811yescharacteristic
172C2×C42C22⋊D711yescharacteristic
173C4⋊C8—41no—
174C4⋊C8—41no—
175C4⋊C8—281no—
176#101—42no—
177C22⋊C8—142no—
178C4×C8—281no—
179#95—71no—
180#95—71no—
181#95—141no—
182#95—141no—
183#95—141no—
184#95—141no—
185#95—141no—
186#95—141no—
187#95—141no—
188C22×C7—21no—
189C22×C7—21no—
190C22×C7C2×#9911yescharacteristic
191C22×C7C2×#10311yescharacteristic
192C22×C7#42111yescharacteristic
193C4×C7—21no—
194C4×C7—21no—
195C4×C7—21no—
196C4×C7—22no—
197C4×C7—22no—
198C4×C7—21no—
199C4×C7—41no—
200C4×C7—41no—
201C4×C7—41no—
202Dic7—42no—
203Dic7—81no—
204Dic7—81no—
205Dic7—81no—
206C2×Q8—41no—
207C2×Q8—41no—
208C2×Q8—281no—
209C2×Q8—282no—
210C2×Q8#114212yes—
211C2×Q8#114412yes—
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×C4(C2×D7)⋊C411yescharacteristic
220C22×C4C2×C4×D711yescharacteristic
221C22×C4C2×D2811yescharacteristic
222C22×C4C2×C22⋊D711yescharacteristic
223M16—42no—
224M16—42no—
225C2×C8—42no—
226C2×C8—282no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—281no—
231C4⋊C4—282no—
232C4⋊C4—282no—
233C4⋊C4—282no—
234C4⋊C4—281no—
235C4⋊C4—281no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—21no—
241C42—21no—
242C42—282no—
243C2×C7—21no—
244C2×C7—21no—
245C2×C7#152011yescharacteristic
246C2×C7#212011yescharacteristic
247C2×C7#213311yescharacteristic
248C23C2×(C2×D7)⋊C411yescharacteristic
249Q8—42no—
250Q8—42no—
251Q8—282no—
252Q8—282no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—142no—
267C2×C4—281no—
268C2×C4—281no—
269C2×C4—281no—
270C2×C4—281no—
271C2×C4—281no—
272C2×C4—281no—
273C2×C4—282no—
274C2×C4—281no—
275C2×C4—281no—
276C2×C4—281no—
277C2×C4#638011yescharacteristic
278C2×C4#638011yescharacteristic
279C2×C4#638412yes—
280C2×C4#638412yes—
281C2×C4C2×#114211yescharacteristic
282C2×C4C2×#114411yescharacteristic
283C8—82no—
284C8—562no—
285C7#1190511yescharacteristic, complemented, Sylow
286C22—21no—
287C22—21no—
288C22C2×#638011yescharacteristic
289C22C2×#638411yescharacteristic
290C22#8977711yescharacteristic
291C4—21no—
292C4—21no—
293C4—21no—
294C4—21no—
295C4—22no—
296C4—22no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—282no—
301C4—561no—
302C4—561no—
303C4—561no—
304C2—21no—
305C2—21no—
306C2#1172726411yescharacteristic
307C2#1172788211yescharacteristic
308C2#1172789911yescharacteristic
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#11905
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
285. C7#11905semidirect

Maximal subgroups

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

subgroupindex
#117399262
C7×#18012
#117293782
#117253022
#117253002
#119057