Finite Group Databasebeta

← #34033695

Subgroups — #34033695

Order 18688.

292 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 81 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#22627134C211yesmaximal, characteristic
2#22627130C211yesmaximal, characteristic
3#22626966C214yesmaximal
4#22626720C211yesmaximal, characteristic
5#17989690—21no—
6C4⋊#11924040—21no—
7#17989684C2212yes—
8#17989684C2212yes—
9#17989681—21no—
10C4×#11924040—21no—
11#17989638—21no—
12#17989637—21no—
13#17989636—21no—
14Q8×#10596833—21no—
15#17989594C2212yes—
16#17989591C411yescharacteristic
17#17989552C412yes—
18C4×#11924036C2211yescharacteristic
19#17989142C411yescharacteristic
20C2×#11924040—22no—
21C2×#11924040—22no—
22C2×#11924038C2×C412yes—
23C2×#11924036C2×C411yescharacteristic
24C2×#11924036C2311yescharacteristic
25#14556658—22no—
26C4⋊#10596833—22no—
27C4⋊#10596833—21no—
28C4⋊#10596833—21no—
29#14556646—22no—
30C4×#10596833—22no—
31C4×#10596833D411yescharacteristic
32C4×#10596833D411yescharacteristic
33C4×#10596833D411yescharacteristic
34C4×#10596833D411yescharacteristic
35#14556591C811yescharacteristic
36#14556582C812yes—
37#14556571—21no—
38#14556567—21no—
39Q8×Dic73—21no—
40#14556556—21no—
41#14556549C2×C412yes—
42C42×D73C2×C411yescharacteristic
43C4⋊Q8×C73C811yescharacteristic
44#11924040—42no—
45#11924040—42no—
46#11924038—42no—
47#11924036—22no—
48#11924036—41no—
49C2×#10596833—22no—
50C2×#10596833C22⋊C411yescharacteristic
51C2×#10596833C22⋊C411yescharacteristic
52C2×#10596833C2×D411yescharacteristic
53C2×#10596833C2×D411yescharacteristic
54C2×Dic146—21no—
55C2×C4×D73M1611yescharacteristic
56C2×C4×D73M1611yescharacteristic
57C2×C4×D73C22×C411yescharacteristic
58C4⋊Dic73—21no—
59C4⋊Dic73—22no—
60C4⋊Dic73C2×C812yes—
61#11924007—22no—
62#11924005—22no—
63C4×Dic73—22no—
64C4×Dic73C22⋊C411yescharacteristic
65C4×Dic73C22⋊C411yescharacteristic
66C4×Dic73C2×C811yescharacteristic
67C2×Q8×C73—21no—
68C4⋊C4×C73—21no—
69C4⋊C4×C73C2×C812yes—
70C42×C73C2×C811yescharacteristic
71C22×D73C2×M1611yescharacteristic
72Q8×C73—42no—
73C2×C4×C73—22no—
74C2×C4×C73C22⋊C811yescharacteristic
75C2×C4×C73C22⋊C811yescharacteristic
76C2×C4×C73C22×C811yescharacteristic
77C2×Dic73—22no—
78C2×Dic73C22⋊C811yescharacteristic
79C2×Dic73C22⋊C811yescharacteristic
80C2×Dic73C2×C22⋊C411yescharacteristic
81C4×D73—22no—
82C4×D73—21no—
83C4×D73—21no—
84C4×D73—41no—
85Dic146—42no—
86#10596833—21no—
87#10596833—21no—
88#10596833—21no—
89#10596833—42no—
90#10596833#10112yes—
91C22×C73C2×C22⋊C811yescharacteristic
92C2×D73—21no—
93C2×D73—21no—
94C2×D73—21no—
95C4×C73—21no—
96C4×C73—21no—
97C4×C73—42no—
98C4×C73#35012yes—
99Dic73—21no—
100Dic73—21no—
101Dic73—42no—
102Dic73#41011yescharacteristic
103Dic73C2×#10111yescharacteristic
104#11498—731nomaximal, Sylow
105C2×C73#146111yescharacteristic
106C2×C73C2×#35011yescharacteristic
107C2×C73#211711yescharacteristic
108D73—41no—
109#2960—731no—
110#2163—731no—
111#2162—731no—
112#1323—734no—
113C73#1149811yescharacteristic, complemented, Sylow
114#533—731no—
115#446—1461no—
116#446—1461no—
117C8×Q8—1461no—
118C8×Q8—1461no—
119#424—732no—
120#423—731no—
121#405—732no—
122C2×C4×C8—731no—
123C4⋊C16—1461no—
124C4⋊C16—1461no—
125C22⋊C16—732no—
126C22⋊C16—732no—
127#346—1461no—
128C4×C16—1461no—
129C2×M16—732no—
130C22×C8—731no—
131C22×C8—731no—
132C4⋊Q8—731no—
133C4⋊Q8#1059684211yescharacteristic
134#125—732no—
135C22⋊Q8—1461no—
136C22⋊Q8—1461no—
137C4×Q8—1461no—
138C4×Q8—1461no—
139#117—732no—
140C2×C42—731no—
141C2×C16—1462no—
142C2×C16—1462no—
143C4⋊C8—1461no—
144C4⋊C8—1461no—
145C4⋊C8—1462no—
146C4⋊C8—1462no—
147#97—1462no—
148C4×C8—731no—
149C4×C8—731no—
150C4×C8—731no—
151C4×C8—731no—
152C4×C8—1462no—
153C2×Q8—21no—
154C2×Q8—1461no—
155C22×C4—731no—
156C22×C4—731no—
157C22×C4—731no—
158M16—2922no—
159C2×C8—2921no—
160C2×C8—731no—
161C2×C8—731no—
162C2×C8—731no—
163C2×C8—731no—
164C2×C8—1462no—
165C2×C8—1462no—
166C4⋊C4—21no—
167C4⋊C4—732no—
168C4⋊C4—1462no—
169C4⋊C4—1462no—
170C4⋊C4—1461no—
171C4⋊C4C2×#1059684212yes—
172C22⋊C4—1462no—
173C42—731no—
174C42—731no—
175C42—731no—
176C42—1462no—
177C42C2×#1059684211yescharacteristic
178C16—2922no—
179C16—2922no—
180C23—731no—
181Q8—42no—
182Q8—2922no—
183C2×C4—22no—
184C2×C4—2921no—
185C2×C4—731no—
186C2×C4—731no—
187C2×C4—731no—
188C2×C4—1461no—
189C2×C4—1461no—
190C2×C4—1462no—
191C2×C4—1462no—
192C2×C4C22⋊#1059684211yescharacteristic
193C2×C4C22⋊#1059684211yescharacteristic
194C2×C4C22×#1059684211yescharacteristic
195C8—2922no—
196C8—732no—
197C8—1461no—
198C8—1461no—
199C8—1461no—
200C22—1461no—
201C22—1461no—
202C22—1461no—
203C22C2×C22⋊#1059684211yescharacteristic
204C4—21no—
205C4—21no—
206C4—42no—
207C4—2922no—
208C4—731no—
209C4—731no—
210C4—1461no—
211C4—1461no—
212C4#1798968812yes—
213C2—2921no—
214C2#2262704611yescharacteristic
215C2C2×#1798968811yescharacteristic
216C2#2262711311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10596842
commutatorC2×C4×C73C22×C8
FrattiniC2×C4C22×#10596842
FittingC4⋊Q8×C73C8
socleC22×C73C2×C22⋊C8
prime radicalC22×D73C2×M16
cosocleC2×#11924036C23
hypercenterC4⋊Q8#10596842
hypocenterC73#11498
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
113. C73#11498semidirect

Maximal subgroups

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

subgroupindex
#226271342
#226271302
#226269662
#226267202
#1149873