Finite Group Databasebeta

← #13265105

Subgroups — #13265105

Order 1792.

316 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 83 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#11739352C211yesmaximal, characteristic
2#11727028C211yesmaximal, characteristic, complemented
3D7×#334C211yesmaximal, characteristic, complemented
4C7×#1363C211yesmaximal, characteristic, complemented
5#11725605C211yesmaximal, characteristic, complemented
6#11725368C211yesmaximal, characteristic, complemented
7#11725273C211yesmaximal, characteristic, complemented
8#90382—21no—
9C7×#499C2211yescharacteristic
10#89840—21no—
11#89659C411yescharacteristic
12#89655C411yescharacteristic
13#89645C411yescharacteristic
14#89644C411yescharacteristic
15#89636—21no—
16#89624—21no—
17D7×C4⋊C8—21no—
18#89468C2211yescharacteristic
19C4×C8×D7C2211yescharacteristic
20C7×C4⋊C16C2211yescharacteristic
21C7×#334C2211yescharacteristic
22(C2×D7)⋊C16—21no—
23C16×Dic7—21no—
24#89275—21no—
25C4⋊(C7⋊C16)C2211yescharacteristic
26#89252C2211yescharacteristic
27#11944—71nomaximal, Sylow
28C7×#125—21no—
29C2×Dic28C2×C411yescharacteristic
30C2×D56C2×C411yescharacteristic
31C2×#1132—21no—
32C2×C8×D7—41no—
33C2×C8×D7C2×C411yescharacteristic
34C2×C8×D7D411yescharacteristic
35#6461—41no—
36#6460—21no—
37#6458—21no—
38#6457—41no—
39#6456—21no—
40#6456—41no—
41#6455—41no—
42#6450—21no—
43#6438—21no—
44C42×D7D411yescharacteristic
45C2×C7×C16—21no—
46C7×#107C2×C411yescharacteristic
47C7×#107C2×C411yescharacteristic
48C7×#106—21no—
49C7×C4⋊C8—21no—
50C4×C7×C8C2311yescharacteristic
51Dic7⋊C8—41no—
52C8×Dic7C2×C411yescharacteristic
53C8×Dic7D411yescharacteristic
54C2×C7⋊C16—21no—
55#6384—21no—
56#6384—21no—
57#6383—21no—
58#6383—21no—
59C4⋊(C7⋊C8)—21no—
60C4×C7⋊C8D411yescharacteristic
61#3168—71no—
62#2162—71no—
63C2×#334—71no—
64#1363—71no—
65#1363D711yescharacteristic, complemented
66#1360—71no—
67#1360—71no—
68C2×D28—21no—
69C2×D28—41no—
70C2×C4×D7—41no—
71C2×C4×D7C22⋊C411yescharacteristic
72C2×C4×D7D811yescharacteristic
73C2×C4×D7SD1611yescharacteristic
74C2×Dic14—21no—
75C2×C7×C8—41no—
76C2×C7×C8C22×C411yescharacteristic
77C2×C7×C8C2×D411yescharacteristic
78C7×C4⋊C4—21no—
79C7×C4⋊C4—21no—
80C7×C4⋊C4—41no—
81C7×C4⋊C4—41no—
82C42×C7C2×D411yescharacteristic
83(C2×D7)⋊C4—41no—
84(C2×D7)⋊C4—41no—
85(C2×D7)⋊C4—41no—
86(C2×D7)⋊C4—41no—
87(C2×D7)⋊C4—41no—
88C4⋊Dic7—41no—
89Dic7⋊C4—41no—
90C4×Dic7—41no—
91C4×Dic7C22⋊C411yescharacteristic
92C4×Dic7D811yescharacteristic
93C4×Dic7SD1611yescharacteristic
94C2×C7⋊C8—41no—
95C2×C7⋊C8C22⋊C411yescharacteristic
96C2×C7⋊C8C22⋊C411yescharacteristic
97Dic28—41no—
98D56—41no—
99#1132—41no—
100#1132—41no—
101C8×D7—21no—
102C8×D7—21no—
103C8×D7—41no—
104C8×D7—82no—
105C7×C16—41no—
106C7⋊C16—41no—
107#529—141no—
108#499C2×D711yescharacteristic
109#495—71no—
110#488—141no—
111#467—71no—
112#466—71no—
113#465—141no—
114C4×Q16—71no—
115C4×SD16—141no—
116C4×D8—71no—
117C2×C4⋊C8—141no—
118C2×C4×C8—71no—
119C4⋊C16—71no—
120C4⋊C16C2×D711yescharacteristic
121C22⋊C16—141no—
122C4×C16—141no—
123#334—71no—
124#334—141no—
125#334C2×D711yescharacteristic
126C22×D7—41no—
127C22×D7#10211yescharacteristic
128C2×C4×C7—41no—
129C2×C4×C7—41no—
130C2×C4×C7C2×C22⋊C411yescharacteristic
131C2×C4×C7C2×D811yescharacteristic
132C2×C4×C7C2×SD1611yescharacteristic
133C2×Dic7—41no—
134C2×Dic7#10211yescharacteristic
135C2×Dic7#10211yescharacteristic
136C2×Dic7#10211yescharacteristic
137D28—41no—
138D28—41no—
139D28—82no—
140C4×D7—22no—
141C4×D7—21no—
142C4×D7—21no—
143C4×D7—22no—
144C4×D7—82no—
145Dic14—41no—
146Dic14—41no—
147C7×C8—21no—
148C7×C8—81no—
149C7×C8#13511yescharacteristic
150C7×C8#13511yescharacteristic
151C7⋊C8—21no—
152C7⋊C8—21no—
153C7⋊C8—81no—
154C2×Q16—71no—
155C2×SD16—141no—
156C2×D8—71no—
157C22×C8—71no—
158C22×C8—71no—
159C22×C8—281no—
160#126—281no—
161#125—21no—
162#124—141no—
163#123—281no—
164C22⋊Q8—141no—
165#121—141no—
166C4×Q8—141no—
167C4×D4—141no—
168C4×D4—281no—
169#117—281no—
170C2×C42—71no—
171C2×C16—21no—
172C2×C16—141no—
173#107C4×D711yescharacteristic
174#107C4×D711yescharacteristic
175#106—21no—
176C4⋊C8—21no—
177C4⋊C8—141no—
178C4⋊C8—281no—
179#103—141no—
180#103—141no—
181#102—141no—
182#102—141no—
183C4×C8—71no—
184C4×C8—71no—
185C4×C8—71no—
186C4×C8C22×D711yescharacteristic
187C22×C7C2×#10211yescharacteristic
188C2×D7—21no—
189C2×D7—21no—
190C2×D7—81no—
191C2×D7—81no—
192C2×D7—81no—
193C2×D7#35912yes—
194C4×C7—21no—
195C4×C7—21no—
196C4×C7—81no—
197C4×C7—81no—
198C4×C7#41311yescharacteristic
199C4×C7#41611yescharacteristic
200Dic7—21no—
201Dic7—21no—
202Dic7—81no—
203Dic7#36012yes—
204C2×Q8—141no—
205C2×D4—141no—
206C2×D4—281no—
207C22×C4—71no—
208C22×C4—71no—
209C22×C4—71no—
210C22×C4—281no—
211Q16—281no—
212SD16—281no—
213SD16—281no—
214D8—281no—
215C2×C8—41no—
216C2×C8—71no—
217C2×C8—71no—
218C2×C8—141no—
219C2×C8—141no—
220C2×C8—281no—
221C2×C8—281no—
222C2×C8—562no—
223C2×C8C2×C4×D711yescharacteristic
224C2×C8D4×D711yescharacteristic
225C4⋊C4—21no—
226C4⋊C4—21no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—281no—
230C4⋊C4—281no—
231C22⋊C4—281no—
232C22⋊C4—281no—
233C22⋊C4—281no—
234C22⋊C4—281no—
235C22⋊C4—281no—
236C42—71no—
237C42—71no—
238C42—71no—
239C42—281no—
240C42D4×D711yescharacteristic
241C16—41no—
242C16—281no—
243C2×C7#154011yescharacteristic
244C2×C7C2×#35911yescharacteristic
245C2×C7C2×#36011yescharacteristic
246D7—22no—
247D7—161no—
248C23—71no—
249C23—281no—
250Q8—281no—
251Q8—281no—
252D4—281no—
253D4—281no—
254D4—562no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—71no—
258C2×C4—71no—
259C2×C4—71no—
260C2×C4—142no—
261C2×C4—142no—
262C2×C4—141no—
263C2×C4—141no—
264C2×C4—281no—
265C2×C4—562no—
266C2×C4D7×C22⋊C411yescharacteristic
267C2×C4D7×D811yescharacteristic
268C2×C4D7×SD1611yescharacteristic
269C8—21no—
270C8—81no—
271C8—141no—
272C8—141no—
273C8—561no—
274C8#647911yescharacteristic
275C8#648211yescharacteristic
276C7#1194411yescharacteristic, complemented, Sylow
277C22—72no—
278C22—141no—
279C22—141no—
280C22—561no—
281C22—561no—
282C22—561no—
283C22D7×#10211yescharacteristic
284C4—21no—
285C4—21no—
286C4—72no—
287C4—81no—
288C4—81no—
289C4—141no—
290C4—141no—
291C4—561no—
292C4#8952311yescharacteristic
293C4#8957611yescharacteristic
294C2—142no—
295C2—1121no—
296C2#1172617111yescharacteristic
297C2D7×#35911yescharacteristic
298C2D7×#36011yescharacteristic
subgroupG/H
centerC22D7×#102
commutatorC2×C7×C8C22×C4
FrattiniC4×C8C22×D7
FittingC7×#1363C2
socleC22×C7C2×#102
prime radical#89655C4
cosocleC4×C7×C8C23
hypercenter#1363D7
hypocenterC7#11944
LCSG ▷ C2×C7×C8 ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1363

Complements

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

NH ≅ G/Ntype
2. #11727028C2semidirect
3. D7×#334C2semidirect
4. C7×#1363C2semidirect
5. #11725605C2semidirect
6. #11725368C2semidirect
7. #11725273C2semidirect
65. #1363D7semidirect
276. C7#11944semidirect

Maximal subgroups

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

subgroupindex
#117393522
#117270282
D7×#3342
C7×#13632
#117256052
#117253682
#117252732
#119447