Finite Group Databasebeta

← #34034112

Subgroups — #34034112

Order 18688.

410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×#17989709C211yesmaximal, characteristic
2#22627109C211yesmaximal, characteristic
3#22627094C212yesmaximal, complemented
4#22627010C212yesmaximal, complemented
5#22625690C211yesmaximal, characteristic
6#17989709—22no—
7#17989709—22no—
8C2×#14556688C412yescomplemented
9C2×#14556688C2211yescharacteristic
10#17989706C2212yes—
11C2×#14556686C412yescomplemented
12C2×#14556686C2211yescharacteristic
13#17989686C414yescomplemented
14#17989682—22no—
15#64408⋊C16—22no—
16C2×#14556679C2211yescharacteristic
17#17989568C411yescharacteristic
18#17989553C2212yes—
19#17989470C412yes—
20#17988570C411yescharacteristic
21#14556688—24no—
22#14556688—22no—
23#14556688—22no—
24#14556687C2×C414yes—
25#14556686—22no—
26#14556686—22no—
27#14556686—22no—
28#14556686D412yes—
29#14556686D412yes—
30C2×#11924040C2×C412yes—
31C2×#11924040C2×C411yescharacteristic
32C2×#11924040C2×C411yescharacteristic
33#14556679—22no—
34#14556679—22no—
35C2×#11924038C2×C412yes—
36C2×#11924038C2×C411yescharacteristic
37C2×#11924036C2×C412yes—
38C2×#11924036C2311yescharacteristic
39#14556670C2×C412yes—
40#14556650C814yes—
41#14556645—22no—
42C8×#64408—22no—
43C2×#11924029C2×C411yescharacteristic
44M16×D73C2×C412yes—
45#14556510C811yescharacteristic
46#14556507C812yes—
47#101×C73C811yescharacteristic
48#11924040—22no—
49#11924040—24no—
50#11924040C22⋊C411yescharacteristic
51#11924040C22⋊C411yescharacteristic
52#11924040C22⋊C412yes—
53#11924038—22no—
54#11924038—24no—
55#11924036—22no—
56#11924036—22no—
57#11924036C2×D412yes—
58#11924036#4112yes—
59C2×#10596833C4212yes—
60C2×#10596833C22×C411yescharacteristic
61C2×#10596833C22×C411yescharacteristic
62C4⋊#64408—22no—
63C22⋊#64408C2×C814yes—
64C4×#64408—22no—
65#11924029—22no—
66#11924029—22no—
67C2×D292C2×C812yes—
68C2×D292C2×C811yescharacteristic
69C2×C4×D73C4212yes—
70C2×C4×D73C22×C411yescharacteristic
71#11924012C2×C812yes—
72#11924011—22no—
73C8×D73—22no—
74C2×Q8×C73C2×C811yescharacteristic
75M16×C73C2×C812yes—
76C22×D73C4×C812yes—
77C22×D73C22×C811yescharacteristic
78C2×#64408—24no—
79Q8×C73—22no—
80C2×C4×C73C4×C812yes—
81C2×C4×C73C22×C811yescharacteristic
82C2×Dic73C2×C4211yescharacteristic
83D292—24no—
84D292—22no—
85C4×D73—22no—
86C4×D73—22no—
87C4×D73C4×D412yes—
88C4×D73#13112yes—
89#10596833—22no—
90#10596833C2×C22⋊C411yescharacteristic
91#10596833#11711yescharacteristic
92#10596833C4×D412yes—
93C8×C73—22no—
94#10596831—22no—
95C22×C73C2×C4×C811yescharacteristic
96C2×D73—22no—
97C2×D73—41no—
98C2×D73—42no—
99C2×D73C8×D412yes—
100#64408—44no—
101C4×C73—22no—
102C4×C73C8×D412yes—
103Dic73C4×C22⋊C411yescharacteristic
104Dic73#40511yescharacteristic
105#12613—731nomaximal, Sylow
106C2×C73—21no—
107C2×C73C8×C22⋊C411yescharacteristic
108D73—22no—
109D73—42no—
110C2×#504—731no—
111#2115—731no—
112#2108—732no—
113#1757—731no—
114#1378—732no—
115C73#1261311yescharacteristic, complemented, Sylow
116C2×#131—731no—
117#504—1462no—
118#504—1462no—
119C2×M32—732no—
120C2×M32—731no—
121C2×M32—732no—
122C22×C16—731no—
123C22×C16—732no—
124#413—731no—
125#410—731no—
126#405—732no—
127#349—734no—
128#346—1462no—
129C4×C16—1462no—
130#344—732no—
131C2×#41—731no—
132#131—1462no—
133#131—1462no—
134C2×M16—731no—
135C2×M16—732no—
136C2×M16—732no—
137C22×C8—731no—
138C22×C8—732no—
139#117—732no—
140M32—734no—
141M32—1464no—
142M32—1462no—
143M32—1462no—
144C2×C16—731no—
145C2×C16—731no—
146C2×C16—732no—
147C2×C16—732no—
148C2×C16—732no—
149C2×C16—1462no—
150C2×C16—1462no—
151C2×C16—1462no—
152#101—731no—
153#101#1059684211yescharacteristic
154#100—732no—
155#99—734no—
156#97—1462no—
157C4×C8—1462no—
158#41—1462no—
159#41—1462no—
160C2×Q8C2×#1059684211yescharacteristic
161C2×D4—732no—
162C2×D4—731no—
163C22×C4—731no—
164C22×C4—732no—
165M16—732no—
166M16—1462no—
167M16—1464no—
168M16—1462no—
169M16C2×#1059684212yes—
170C2×C8—731no—
171C2×C8—731no—
172C2×C8—732no—
173C2×C8—732no—
174C2×C8—732no—
175C2×C8—1462no—
176C2×C8—1462no—
177C2×C8—1462no—
178C4⋊C4—1462no—
179C22⋊C4—734no—
180C42—1462no—
181C16—731no—
182C16—731no—
183C16—732no—
184C16—1462no—
185C16—1464no—
186C23—731no—
187C23—732no—
188Q8—22no—
189D4—1464no—
190D4—1462no—
191C2×C4—731no—
192C2×C4—732no—
193C2×C4—732no—
194C2×C4—1462no—
195C2×C4—1462no—
196C2×C4—1464no—
197C2×C4C4×#1059684212yes—
198C2×C4C22×#1059684211yescharacteristic
199C8—22no—
200C8—731no—
201C8—732no—
202C8—731no—
203C8—1462no—
204C8—1462no—
205C22—2922no—
206C22—2921no—
207C22—732no—
208C22—1462no—
209C22C2×C4×#1059684211yescharacteristic
210C4—22no—
211C4—2924no—
212C4—731no—
213C4—731no—
214C4D4×#1059684212yes—
215C2—21no—
216C2—2922no—
217C2—1462no—
218C2C22⋊C4×#1059684211yescharacteristic
subgroupG/H
centerC2C22⋊C4×#10596842
commutatorC22×C73C2×C4×C8
FrattiniC2×C4C22×#10596842
Fitting#101×C73C8
socleC2×C73C8×C22⋊C4
prime radicalC2×#11924029C2×C4
cosocleC2×#11924036C23
hypercenter#101#10596842
hypocenterC73#12613
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

Complements

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

NH ≅ G/Ntype
3. #22627094C2semidirect
4. #22627010C2semidirect
8. C2×#14556688C4semidirect
11. C2×#14556686C4semidirect
13. #17989686C4semidirect
115. C73#12613semidirect

Maximal subgroups

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

subgroupindex
C2×#179897092
#226271092
#226270942
#226270102
#226256902
#1261373