Finite Group Databasebeta

← #13242140

Subgroups — #13242140

Order 1792.

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

normal subgroups only

This group has 370 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#11733638C211yesmaximal, characteristic
2#11726361C211yesmaximal, characteristic
3#11726350C211yesmaximal, characteristic
4C7×#1271C211yesmaximal, characteristic
5#11725444C211yesmaximal, characteristic
6#11725284C211yesmaximal, characteristic
7#11725283C211yesmaximal, characteristic
8C7×#389C2211yescharacteristic
9C2×C8×Dic7—21no—
10#89757C411yescharacteristic
11#89753—21no—
12#89750—21no—
13#89749C411yescharacteristic
14#89749C411yescharacteristic
15#89745C411yescharacteristic
16C42×Dic7C2211yescharacteristic
17#89700C2211yescharacteristic
18#89425—21no—
19#89424—21no—
20C7×#336C2211yescharacteristic
21C7×#336C2211yescharacteristic
22#89345—21no—
23#89345—21no—
24#89345—21no—
25#89319C2211yescharacteristic
26#89319C2211yescharacteristic
27#7657—71nomaximal, Sylow
28C22×C7×C8—21no—
29C22×C7×C8—21no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4C2×C411yescharacteristic
32C2×C7×C4⋊C4C2×C411yescharacteristic
33C2×C42×C7C2311yescharacteristic
34C2×C4⋊Dic7—21no—
35C2×C4⋊Dic7C2×C411yescharacteristic
36C2×C4⋊Dic7C2×C411yescharacteristic
37C2×Dic7⋊C4—21no—
38C2×Dic7⋊C4—21no—
39C2×C4×Dic7C2×C411yescharacteristic
40C2×C4×Dic7C2×C411yescharacteristic
41C2×C4×Dic7D411yescharacteristic
42C2×C4×Dic7D411yescharacteristic
43C2×C4×Dic7D411yescharacteristic
44C2×C4×Dic7D411yescharacteristic
45C22×C7⋊C8—21no—
46C22×C7⋊C8—21no—
47C7×#95—21no—
48C7⋊#95—21no—
49C7⋊#95—21no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C7⋊#95—21no—
55C8×Dic7—24no—
56#2864—71no—
57#1839—71no—
58#1744—71no—
59#1271—71no—
60#1271—71no—
61#1271—71no—
62#1271D711yescharacteristic
63C22×C4×C7—21no—
64C22×C4×C7—21no—
65C22×C4×C7C22×C411yescharacteristic
66C22×C4×C7C2×D411yescharacteristic
67C22×C4×C7C2×D411yescharacteristic
68C22×Dic7—21no—
69C22×Dic7—21no—
70C22×Dic7C22⋊C411yescharacteristic
71C22×Dic7C22⋊C411yescharacteristic
72C22×Dic7C22⋊C411yescharacteristic
73C22×Dic7C22⋊C411yescharacteristic
74C2×C7×C8—22no—
75C2×C7×C8—41no—
76C2×C7×C8—41no—
77C2×C7×C8—41no—
78C2×C7×C8—41no—
79C2×C7×C8—41no—
80C7×C4⋊C4—21no—
81C7×C4⋊C4—21no—
82C7×C4⋊C4—41no—
83C7×C4⋊C4—41no—
84C7×C4⋊C4—41no—
85C42×C7—41no—
86C4⋊Dic7—21no—
87C4⋊Dic7—21no—
88C4⋊Dic7—42no—
89C4⋊Dic7—41no—
90Dic7⋊C4—41no—
91Dic7⋊C4—41no—
92Dic7⋊C4—42no—
93C4×Dic7—21no—
94C4×Dic7—21no—
95C4×Dic7—21no—
96C4×Dic7—21no—
97C4×Dic7—21no—
98C4×Dic7—21no—
99C4×Dic7—22no—
100C4×Dic7—22no—
101C4×Dic7—41no—
102C2×C7⋊C8—22no—
103C2×C7⋊C8—41no—
104C2×C7⋊C8—41no—
105C2×C7⋊C8—41no—
106C2×C7⋊C8—41no—
107C2×C7⋊C8—41no—
108C2×C4×C8—141no—
109#389—71no—
110#389—71no—
111#389—71no—
112#389C2×D711yescharacteristic
113#387—141no—
114#387—141no—
115#387—141no—
116#387—141no—
117#382—71no—
118#382—71no—
119C43—71no—
120#336—71no—
121#336—71no—
122#336—141no—
123#336—141no—
124#336—141no—
125#336C2×D711yescharacteristic
126#336C2×D711yescharacteristic
127C23×C7C2×C22⋊C411yescharacteristic
128C2×C4×C7—21no—
129C2×C4×C7—21no—
130C2×C4×C7—21no—
131C2×C4×C7—21no—
132C2×C4×C7—21no—
133C2×C4×C7—21no—
134C2×C4×C7—41no—
135C2×C4×C7—41no—
136C2×C4×C7—41no—
137C2×C4×C7—41no—
138C2×C4×C7—41no—
139C2×C4×C7—41no—
140C2×C4×C7#13111yescharacteristic
141C2×C4×C7#13111yescharacteristic
142C2×C4×C7#13511yescharacteristic
143C2×C4×C7#13511yescharacteristic
144C2×C4×C7#13511yescharacteristic
145C2×C4×C7#13511yescharacteristic
146C2×Dic7—21no—
147C2×Dic7—21no—
148C2×Dic7—21no—
149C2×Dic7—21no—
150C2×Dic7—21no—
151C2×Dic7—21no—
152C2×Dic7—21no—
153C2×Dic7—21no—
154C2×Dic7—21no—
155C2×Dic7—21no—
156C2×Dic7—41no—
157C2×Dic7—41no—
158C2×Dic7—41no—
159C2×Dic7—41no—
160C2×Dic7—41no—
161C2×Dic7—41no—
162C2×Dic7#10112yes—
163C2×Dic7#10412yes—
164C7×C8—42no—
165C7×C8—81no—
166C7⋊C8—42no—
167C7⋊C8—81no—
168C22×C8—21no—
169C22×C8—21no—
170C22×C8—141no—
171C22×C8—141no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—71no—
174C2×C4⋊C4—71no—
175C2×C4⋊C4—141no—
176C2×C4⋊C4—141no—
177C2×C4⋊C4—141no—
178C2×C4⋊C4C4×D711yescharacteristic
179C2×C4⋊C4C4×D711yescharacteristic
180C2×C42—71no—
181C2×C42—71no—
182C2×C42—71no—
183C2×C42—71no—
184C2×C42—71no—
185C2×C42—71no—
186C2×C42C22×D711yescharacteristic
187C4×C8—144no—
188#95—21no—
189#95—141no—
190#95—141no—
191#95—141no—
192#95—141no—
193#95—141no—
194#95—141no—
195#95—141no—
196C22×C7#40811yescharacteristic
197C22×C7#41011yescharacteristic
198C22×C7C2×#10111yescharacteristic
199C22×C7#41611yescharacteristic
200C22×C7#41611yescharacteristic
201C22×C7C2×#10411yescharacteristic
202C22×C7#42111yescharacteristic
203C4×C7—21no—
204C4×C7—21no—
205C4×C7—21no—
206C4×C7—21no—
207C4×C7—21no—
208C4×C7—21no—
209C4×C7—81no—
210C4×C7—81no—
211Dic7—22no—
212Dic7—22no—
213Dic7—41no—
214Dic7—41no—
215Dic7—81no—
216Dic7—81no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—71no—
220C22×C4—71no—
221C22×C4—71no—
222C22×C4—71no—
223C22×C4—141no—
224C22×C4—141no—
225C22×C4C2×C4×D711yescharacteristic
226C22×C4D4×D711yescharacteristic
227C22×C4D4×D711yescharacteristic
228C2×C8—22no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—142no—
235C2×C8—281no—
236C2×C8—281no—
237C2×C8—281no—
238C2×C8—281no—
239C2×C8—281no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—141no—
246C4⋊C4—141no—
247C4⋊C4—281no—
248C4⋊C4—282no—
249C4⋊C4—282no—
250C4⋊C4—281no—
251C4⋊C4—281no—
252C42—41no—
253C42—142no—
254C42—142no—
255C42—141no—
256C42—141no—
257C42—141no—
258C42—141no—
259C42—141no—
260C42—141no—
261C42—281no—
262C2×C7#147011yescharacteristic
263C2×C7#148211yescharacteristic
264C2×C7#149411yescharacteristic
265C2×C7#150011yescharacteristic
266C2×C7#152111yescharacteristic
267C2×C7#153111yescharacteristic
268C2×C7#154411yescharacteristic
269C23D7×C22⋊C411yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—72no—
283C2×C4—72no—
284C2×C4—141no—
285C2×C4—141no—
286C2×C4—141no—
287C2×C4—141no—
288C2×C4—141no—
289C2×C4—141no—
290C2×C4—141no—
291C2×C4—141no—
292C2×C4—141no—
293C2×C4—141no—
294C2×C4—281no—
295C2×C4—281no—
296C2×C4—281no—
297C2×C4—281no—
298C2×C4—281no—
299C2×C4—281no—
300C2×C4#646411yescharacteristic
301C2×C4#647011yescharacteristic
302C2×C4#647511yescharacteristic
303C2×C4#647911yescharacteristic
304C2×C4#647911yescharacteristic
305C2×C4#648211yescharacteristic
306C8—42no—
307C8—81no—
308C8—282no—
309C8—561no—
310C7#765711yescharacteristic, complemented, Sylow
311C22#8949911yescharacteristic
312C22#8951211yescharacteristic
313C22D7×#10111yescharacteristic
314C22#8954411yescharacteristic
315C22#8957611yescharacteristic
316C22D7×#10411yescharacteristic
317C22#8959311yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—81no—
325C4—81no—
326C4—142no—
327C4—142no—
328C4—281no—
329C4—281no—
330C4—561no—
331C4—561no—
332C2#1172588211yescharacteristic
333C2#1172593111yescharacteristic
334C2#1172598711yescharacteristic
335C2#1172603711yescharacteristic
336C2#1172606211yescharacteristic
337C2#1172611911yescharacteristic
338C2#1172617311yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#1271C2
socle, prime radicalC23×C7C2×C22⋊C4
cosocleC2×C42×C7C23
hypercenter#1271D7
hypocenterC7#7657
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
310. C7#7657semidirect

Maximal subgroups

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

subgroupindex
#117336382
#117263612
#117263502
C7×#12712
#117254442
#117252842
#117252832
#76577