Finite Group Databasebeta

← #13253899

Subgroups — #13253899

Order 1792.

388 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 115 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#11730755C211yesmaximal, characteristic
2C7×#1767C211yesmaximal, characteristic
3#11727143C211yesmaximal, characteristic
4#11725465C212yesmaximal
5#11725465C212yesmaximal
6C2×C7×C4⋊C8—21no—
7C2×C7×#97C2212yes—
8C43×C7C2211yescharacteristic
9#89708C2211yescharacteristic
10#89708C2211yescharacteristic
11#89705—21no—
12#89705—21no—
13#89705—21no—
14#89705—21no—
15#89700C411yescharacteristic
16#89700C411yescharacteristic
17#89700C411yescharacteristic
18#89700C411yescharacteristic
19C2×#6377C2212yes—
20C7×#336—21no—
21#89319—21no—
22#89319—21no—
23#9893—71nomaximal, Sylow
24C22×C7×C8—22no—
25C2×C42×C7C2×C411yescharacteristic
26C2×C42×C7C2×C411yescharacteristic
27C2×C42×C7D411yescharacteristic
28C2×C42×C7D411yescharacteristic
29C2×C42×C7D411yescharacteristic
30C2×C42×C7D411yescharacteristic
31C2×C42×C7C2311yescharacteristic
32C2×C4⋊Dic7C2×C411yescharacteristic
33C2×C4⋊Dic7C2×C411yescharacteristic
34C2×C4⋊Dic7C2×C411yescharacteristic
35C2×C4⋊Dic7C2×C411yescharacteristic
36C2×Dic7⋊C4—21no—
37C2×Dic7⋊C4—21no—
38C2×Dic7⋊C4—21no—
39C2×Dic7⋊C4—21no—
40C22×C7⋊C8—22no—
41C7×C4⋊C8—24no—
42C7×#97—24no—
43C7⋊#95—21no—
44C7⋊#95—21no—
45C7⋊#95—21no—
46C7⋊#95—21no—
47C7⋊#95—21no—
48C7⋊#95—21no—
49C7⋊#95—21no—
50C7⋊#95—21no—
51#6377—22no—
52#6377Q814yes—
53#2864—71no—
54#1767D711yescharacteristic
55#1745—71no—
56#1295—72no—
57#1295—72no—
58C22×C4×C7C22⋊C411yescharacteristic
59C22×C4×C7C22⋊C411yescharacteristic
60C22×C4×C7C22⋊C411yescharacteristic
61C22×C4×C7C22⋊C411yescharacteristic
62C22×C4×C7C22×C411yescharacteristic
63C22×C4×C7C2×D411yescharacteristic
64C22×C4×C7C2×D411yescharacteristic
65C22×Dic7—21no—
66C22×Dic7—21no—
67C22×Dic7—21no—
68C22×Dic7—21no—
69C2×C7×C8—24no—
70C2×C7×C8—42no—
71C2×C7×C8—42no—
72C42×C7—22no—
73C42×C7—41no—
74C42×C7—41no—
75C42×C7—41no—
76C42×C7—41no—
77C42×C7—41no—
78C42×C7C2×Q812yes—
79C42×C7#4112yes—
80C4⋊Dic7—41no—
81C4⋊Dic7—41no—
82C4⋊Dic7—41no—
83C4⋊Dic7—41no—
84Dic7⋊C4—42no—
85Dic7⋊C4—42no—
86Dic7⋊C4—42no—
87Dic7⋊C4—42no—
88C2×C7⋊C8—24no—
89C2×C7⋊C8—42no—
90C2×C7⋊C8—42no—
91C2×C4⋊C8—21no—
92C2×#97—72no—
93C2×#97C2×D712yes—
94#389—71no—
95#389—71no—
96#389—71no—
97#389—71no—
98#387—141no—
99#387—141no—
100#387—141no—
101#387—141no—
102#382—71no—
103#382—71no—
104C43C2×D711yescharacteristic
105#336—21no—
106#336—141no—
107#336—141no—
108C23×C7C2×C22⋊C411yescharacteristic
109C2×C4×C7—21no—
110C2×C4×C7—21no—
111C2×C4×C7—21no—
112C2×C4×C7—21no—
113C2×C4×C7—21no—
114C2×C4×C7—21no—
115C2×C4×C7—21no—
116C2×C4×C7—21no—
117C2×C4×C7—21no—
118C2×C4×C7—21no—
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#10412yes—
127C2×C4×C7C4×Q812yes—
128C2×C4×C7C22⋊Q812yes—
129C2×C4×C7#12411yescharacteristic
130C2×C4×C7C4⋊Q811yescharacteristic
131C2×Dic7—41no—
132C2×Dic7—41no—
133C2×Dic7—41no—
134C2×Dic7—41no—
135C2×Dic7—41no—
136C2×Dic7—41no—
137C2×Dic7—41no—
138C2×Dic7—41no—
139C2×Dic7—41no—
140C2×Dic7—41no—
141C2×Dic7—41no—
142C2×Dic7—41no—
143C7×C8—44no—
144C7⋊C8—44no—
145C22×C8—22no—
146C22×C8—142no—
147C2×C4⋊C4—71no—
148C2×C4⋊C4—71no—
149C2×C4⋊C4—71no—
150C2×C4⋊C4—71no—
151C2×C4⋊C4—141no—
152C2×C4⋊C4—141no—
153C2×C4⋊C4—141no—
154C2×C4⋊C4—141no—
155C2×C42C4×D711yescharacteristic
156C2×C42C4×D711yescharacteristic
157C2×C42D2811yescharacteristic
158C2×C42D2811yescharacteristic
159C2×C42C22⋊D711yescharacteristic
160C2×C42C22⋊D711yescharacteristic
161C2×C42C22×D711yescharacteristic
162C4⋊C8—24no—
163#97—24no—
164#97—74no—
165#97—142no—
166#95—141no—
167#95—141no—
168#95—141no—
169#95—141no—
170#95—141no—
171#95—141no—
172#95—141no—
173#95—141no—
174C22×C7#39111yescharacteristic
175C22×C7#41311yescharacteristic
176C22×C7#41311yescharacteristic
177C22×C7C2×#10411yescharacteristic
178C22×C7#42111yescharacteristic
179C22×C7#42111yescharacteristic
180C22×C7#42111yescharacteristic
181C4×C7—21no—
182C4×C7—21no—
183C4×C7—22no—
184C4×C7—22no—
185C4×C7—22no—
186C4×C7—41no—
187C4×C7—41no—
188C4×C7—41no—
189Dic7—81no—
190Dic7—81no—
191Dic7—81no—
192Dic7—81no—
193C22×C4—141no—
194C22×C4—141no—
195C22×C4—141no—
196C22×C4—141no—
197C22×C4(C2×D7)⋊C411yescharacteristic
198C22×C4(C2×D7)⋊C411yescharacteristic
199C22×C4(C2×D7)⋊C411yescharacteristic
200C22×C4(C2×D7)⋊C411yescharacteristic
201C22×C4C2×C4×D711yescharacteristic
202C22×C4C2×D2811yescharacteristic
203C22×C4C2×C22⋊D711yescharacteristic
204C2×C8—24no—
205C2×C8—42no—
206C2×C8—42no—
207C2×C8—144no—
208C2×C8—282no—
209C2×C8—282no—
210C4⋊C4—281no—
211C4⋊C4—281no—
212C4⋊C4—281no—
213C4⋊C4—281no—
214C4⋊C4—282no—
215C4⋊C4—282no—
216C4⋊C4—282no—
217C4⋊C4—282no—
218C42—22no—
219C42—41no—
220C42—41no—
221C42—41no—
222C42—41no—
223C42—41no—
224C42#115912yes—
225C42Q8×D712yes—
226C2×C7#152911yescharacteristic
227C2×C7#153211yescharacteristic
228C2×C7#153511yescharacteristic
229C2×C7#153511yescharacteristic
230C2×C7#198611yescharacteristic
231C2×C7#199511yescharacteristic
232C2×C7#199811yescharacteristic
233C23C2×(C2×D7)⋊C411yescharacteristic
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—281no—
252C2×C4—281no—
253C2×C4—281no—
254C2×C4—281no—
255C2×C4—281no—
256C2×C4—281no—
257C2×C4—281no—
258C2×C4—281no—
259C2×C4—281no—
260C2×C4—281no—
261C2×C4—281no—
262C2×C4—281no—
263C2×C4#637912yes—
264C2×C4#645012yes—
265C2×C4#646012yes—
266C2×C4#649911yescharacteristic
267C2×C4#650711yescharacteristic
268C8—44no—
269C8—284no—
270C7#989311yescharacteristic, complemented, Sylow
271C22C2×#637911yescharacteristic
272C22#8974611yescharacteristic
273C22#8977711yescharacteristic
274C22#8990411yescharacteristic
275C22#8990411yescharacteristic
276C22#8991111yescharacteristic
277C22#8991111yescharacteristic
278C4—22no—
279C4—21no—
280C4—21no—
281C4—22no—
282C4—22no—
283C4—41no—
284C4—41no—
285C4—41no—
286C4—561no—
287C4—561no—
288C4—561no—
289C4—561no—
290C2#1172724711yescharacteristic
291C2#1172755311yescharacteristic
292C2#1172761511yescharacteristic
293C2#1172826911yescharacteristic
294C2#1172827911yescharacteristic
295C2#1172856311yescharacteristic
296C2#1172856411yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#1767C2
socle, prime radicalC23×C7C2×C22⋊C4
cosocleC2×C42×C7C23
hypercenter#1767D7
hypocenterC7#9893
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
270. C7#9893semidirect

Maximal subgroups

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

subgroupindex
#117307552
C7×#17672
#117271432
#117254652
#98937