Finite Group Databasebeta

← #13267964

Subgroups — #13267964

Order 1792.

218 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 63 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#11729143C211yesmaximal, characteristic
2#11729114C211yesmaximal, characteristic
3#11727047C211yesmaximal, characteristic
4#11726311C211yesmaximal, characteristic
5C7×#1364C211yesmaximal, characteristic
6#11725360C211yesmaximal, characteristic
7#11725280C211yesmaximal, characteristic
8C7×#500C2211yescharacteristic
9#89853—21no—
10#89851—21no—
11C2×Dic56—21no—
12#89602—21no—
13#89471C2211yescharacteristic
14C4×Dic28C2211yescharacteristic
15C7×C4⋊C16C2211yescharacteristic
16C7×#335C2211yescharacteristic
17#89298—21no—
18#89287—21no—
19#89285—21no—
20#89279—21no—
21C4⋊(C7⋊C16)C2211yescharacteristic
22C8×C7⋊C8C2211yescharacteristic
23#12423—71nomaximal, Sylow
24C7×C4⋊Q8—21no—
25C2×Dic28—21no—
26C2×Dic28—21no—
27C2×Dic28D411yescharacteristic
28#6432—21no—
29C4×Dic14—21no—
30C2×C7×C16—21no—
31C7×#107—21no—
32C7×#107—21no—
33C7×C4⋊C8—21no—
34C4×C7×C8C2311yescharacteristic
35#6409—41no—
36#6409—41no—
37#6392D411yescharacteristic
38#6390—21no—
39Dic7⋊C8—41no—
40C8×Dic7—41no—
41C2×C7⋊C16—21no—
42#6382—42no—
43C4×C7⋊C8D411yescharacteristic
44C4×C7⋊C8D411yescharacteristic
45Dic56—42no—
46#2225—71no—
47#2209—71no—
48#1707—71no—
49C8×Q16—71no—
50#1367—71no—
51#1364D711yescharacteristic
52#1362—71no—
53C2×C7×Q8—41no—
54C2×Dic14—21no—
55C2×Dic14—41no—
56C2×C7×C8—41no—
57C2×C7×C8C2×D411yescharacteristic
58C2×C7×C8#4111yescharacteristic
59C7×C4⋊C4—41no—
60C7×C4⋊C4—41no—
61C42×C7C2×D411yescharacteristic
62C4⋊Dic7—21no—
63C4⋊Dic7—41no—
64C4⋊Dic7—41no—
65Dic7⋊C4—41no—
66C4×Dic7—41no—
67C2×C7⋊C8—21no—
68C2×C7⋊C8D811yescharacteristic
69C2×C7⋊C8D811yescharacteristic
70Dic28—21no—
71Dic28—41no—
72Dic28—41no—
73Dic28—81no—
74Dic28SD1612yes—
75C7×C16—41no—
76C7⋊C16—41no—
77C2×Q32—141no—
78#500C2×D711yescharacteristic
79#498—141no—
80#494—71no—
81#487—141no—
82C8×Q8—141no—
83C4×Q16—71no—
84#367—141no—
85C4⋊C16—71no—
86C4⋊C16C2×D711yescharacteristic
87#358—141no—
88#358—141no—
89#335C2×D711yescharacteristic
90Q8⋊C8—141no—
91C82—71no—
92C7×Q8—81no—
93C7×Q8—81no—
94C2×C4×C7—81no—
95C2×C4×C7#12111yescharacteristic
96C2×C4×C7C2×D811yescharacteristic
97C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
98C2×Dic7—41no—
99C2×Dic7—41no—
100C2×Dic7—81no—
101Dic14—22no—
102Dic14—41no—
103Dic14—81no—
104Dic14—81no—
105C7×C8—21no—
106C7×C8—81no—
107C7×C8C2×SD1611yescharacteristic
108C7×C8#13511yescharacteristic
109C7⋊C8—22no—
110C7⋊C8—21no—
111C7⋊C8—21no—
112C2×Q16—71no—
113C2×Q16—141no—
114C2×Q16—141no—
115C4⋊Q8—21no—
116C4⋊Q8—141no—
117C4×Q8—141no—
118Q32—282no—
119C2×C16—21no—
120C2×C16—141no—
121#107—21no—
122#107—21no—
123#107—71no—
124#106—282no—
125C4⋊C8—21no—
126C4⋊C8—281no—
127#103—141no—
128#103—281no—
129#103—281no—
130C4×C8—71no—
131C4×C8—71no—
132C4×C8—281no—
133C4×C8C22×D711yescharacteristic
134C22×C7#45911yescharacteristic
135C4×C7—21no—
136C4×C7—161no—
137C4×C7#46511yescharacteristic
138C4×C7#47111yescharacteristic
139C4×C7#50811yescharacteristic
140C4×C7#51011yescharacteristic
141Dic7—42no—
142Dic7—81no—
143Dic7—161no—
144C2×Q8—41no—
145C2×Q8—141no—
146C2×Q8—281no—
147Q16—72no—
148Q16—141no—
149Q16—281no—
150Q16—281no—
151Q16—561no—
152C2×C8—41no—
153C2×C8—71no—
154C2×C8—71no—
155C2×C8—141no—
156C2×C8#115711yescharacteristic
157C2×C8D4×D711yescharacteristic
158C4⋊C4—41no—
159C4⋊C4—41no—
160C4⋊C4—141no—
161C4⋊C4—281no—
162C4⋊C4—281no—
163C4⋊C4—281no—
164C42—281no—
165C42D4×D711yescharacteristic
166C16—41no—
167C16—281no—
168C2×C7#166511yescharacteristic
169C2×C7#221111yescharacteristic
170C2×C7#221411yescharacteristic
171Q8—81no—
172Q8—81no—
173Q8—142no—
174Q8—281no—
175Q8—561no—
176Q8—561no—
177C2×C4—81no—
178C2×C4—281no—
179C2×C4—281no—
180C2×C4—561no—
181C2×C4#644711yescharacteristic
182C2×C4D7×D811yescharacteristic
183C2×C4#647711yescharacteristic
184C8—21no—
185C8—81no—
186C8—142no—
187C8—141no—
188C8—141no—
189C8D7×SD1611yescharacteristic
190C8#648211yescharacteristic
191C7#1242311yescharacteristic, complemented, Sylow
192C22#8955811yescharacteristic
193C4—21no—
194C4—161no—
195C4—282no—
196C4—561no—
197C4—1121no—
198C4#8952611yescharacteristic
199C4#8957911yescharacteristic
200C4#8968411yescharacteristic
201C4#8968711yescharacteristic
202C2#1172619411yescharacteristic
203C2#1172695911yescharacteristic
204C2#1172702711yescharacteristic
subgroupG/H
centerC22#89558
commutator, cosocleC4×C7×C8C23
FrattiniC4×C8C22×D7
FittingC7×#1364C2
socle, prime radicalC22×C7#459
hypercenter#1364D7
hypocenterC7#12423
LCSG ▷ C4×C7×C8 ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1364

Complements

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

NH ≅ G/Ntype
191. C7#12423semidirect

Maximal subgroups

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

subgroupindex
#117291432
#117291142
#117270472
#117263112
C7×#13642
#117253602
#117252802
#124237