Finite Group Databasebeta

← #34014376

Subgroups — #34014376

Order 18688.

312 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 60 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×#17989498C212yesmaximal
2#22625074C212yesmaximal, complemented
3#22625073C212yesmaximal, complemented
4#22620313C211yesmaximal, characteristic
5C2×#14556652—22no—
6#17989498—22no—
7#17989498C2214yes—
8C2×#14556591C2211yescharacteristic
9#17988957C411yescharacteristic
10#17988957C411yescharacteristic
11#17988957C2211yescharacteristic
12#17988957C2211yescharacteristic
13#17988939—22no—
14#17988595—22no—
15C4×#11924012C411yescharacteristic
16#533×C73C411yescharacteristic
17C2×#11924037—42no—
18#14556652—24no—
19#14556652—42no—
20C22×Dic146D412yes—
21C2×#11924012—21no—
22#14556591—41no—
23#14556591C2×C411yescharacteristic
24#14556591D412yes—
25#14556591C2311yescharacteristic
26C2×C4⋊Dic73—41no—
27#14556514—22no—
28#14556514—22no—
29#14556514—22no—
30#14556514—22no—
31#14556502C2×C411yescharacteristic
32#14556502C2×C411yescharacteristic
33C4×#10596831—21no—
34C4⋊Q8×C73—21no—
35#125×C73C2×C411yescharacteristic
36#125×C73C2×C411yescharacteristic
37C22⋊Q8×C73—41no—
38C4×Q8×C73—41no—
39#117×C73—21no—
40C2×C42×C73C2×C411yescharacteristic
41#11924037—44no—
42#11924037—82no—
43C2×#10596833—82no—
44C2×Dic146—22no—
45C2×Dic146—42no—
46C2×Dic146—42no—
47C2×Dic146C22⋊C412yes—
48C2×Dic146C2×D412yes—
49C22×Dic73—22no—
50#11924012—42no—
51C2×#10596831—21no—
52C2×#10596831—21no—
53C4⋊Dic73—41no—
54C4⋊Dic73—42no—
55C4⋊Dic73—41no—
56C2×Q8×C73—41no—
57C22×C4×C73—21no—
58C22×C4×C73C22⋊C411yescharacteristic
59C4⋊C4×C73—21no—
60C4⋊C4×C73—21no—
61C4⋊C4×C73—41no—
62C4⋊C4×C73—41no—
63C4⋊C4×C73—41no—
64C22⋊C4×C73—41no—
65C42×C73—21no—
66C42×C73—41no—
67C42×C73C22⋊C411yescharacteristic
68C42×C73C22×C411yescharacteristic
69C23×C73#9911yescharacteristic
70Q8×C73—82no—
71C2×C4×C73—22no—
72C2×C4×C73—21no—
73C2×C4×C73—21no—
74C2×C4×C73—42no—
75C2×C4×C73—41no—
76C2×C4×C73—41no—
77C2×C4×C73#9911yescharacteristic
78C2×C4×C73C2×C22⋊C411yescharacteristic
79C2×Dic73—22no—
80C2×Dic73—22no—
81C2×Dic73—42no—
82C2×Dic73—42no—
83Dic146—42no—
84Dic146—42no—
85Dic146—82no—
86#10596833—84no—
87#10596831—41no—
88#10596831—41no—
89C22×C73—41no—
90C22×C73#35412yes—
91C22×C73C2×#9911yescharacteristic
92C4×C73—22no—
93C4×C73—21no—
94C4×C73—21no—
95C4×C73—41no—
96C4×C73—81no—
97C4×C73—81no—
98Dic73—42no—
99Dic73—42no—
100#13599—731nomaximal, Sylow
101C2×C73—21no—
102C2×C73—22no—
103C2×C73C2×#35411yescharacteristic
104#3139—731no—
105C2×#356—732no—
106#1413—732no—
107#1413—732no—
108C73#1359911yescharacteristic, complemented, Sylow
109#533#6440811yescharacteristic
110C2×C4⋊Q8—731no—
111#491—731no—
112#491—731no—
113#491—731no—
114#491—731no—
115#487—1462no—
116#419—1462no—
117C2×#101—1462no—
118C4×M16—731no—
119#356—734no—
120#356—1462no—
121C22×Q8—732no—
122C2×M16—2922no—
123C2×M16—1461no—
124C4⋊Q8—21no—
125C4⋊Q8—2921no—
126C4⋊Q8—732no—
127C4⋊Q8—731no—
128C4⋊Q8—731no—
129#125C2×#6440811yescharacteristic
130#125C2×#6440811yescharacteristic
131C22⋊Q8—41no—
132C4×Q8—41no—
133#117—21no—
134C2×C4⋊C4—2921no—
135C2×C42C2×#6440811yescharacteristic
136#103—1462no—
137#103—1462no—
138#103—1462no—
139#103—1462no—
140#101—2922no—
141#101—1464no—
142#97—731no—
143#97—731no—
144C4×C8—1461no—
145C2×Q8—41no—
146C2×Q8—2922no—
147C2×Q8—2922no—
148C2×Q8—732no—
149C2×Q8—732no—
150C2×Q8—1462no—
151C22×C4—21no—
152C22×C4—1462no—
153C22×C4C22⋊#6440811yescharacteristic
154M16—2922no—
155M16—2924no—
156M16—5842no—
157C2×C8—5842no—
158C2×C8—1461no—
159C2×C8—1461no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—41no—
165C4⋊C4—2922no—
166C4⋊C4—2921no—
167C4⋊C4—2921no—
168C22⋊C4—41no—
169C42—21no—
170C42—41no—
171C42C22⋊#6440811yescharacteristic
172C42C22×#6440811yescharacteristic
173C23#1455664911yescharacteristic
174Q8—82no—
175Q8—2922no—
176Q8—2922no—
177Q8—5842no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—42no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—2922no—
185C2×C4—2922no—
186C2×C4—1462no—
187C2×C4—1462no—
188C2×C4#1455664911yescharacteristic
189C2×C4C2×C22⋊#6440811yescharacteristic
190C8—2921no—
191C8—2921no—
192C8—5844no—
193C22—41no—
194C22#1798949312yes—
195C22C2×#1455664911yescharacteristic
196C4—22no—
197C4—21no—
198C4—21no—
199C4—41no—
200C4—81no—
201C4—81no—
202C4—2922no—
203C4—2922no—
204C2—21no—
205C2—22no—
206C2C2×#1798949311yescharacteristic
subgroupG/H
centerC2C2×#17989493
commutatorC42×C73C22×C4
FrattiniC42C22×#64408
Fitting#533×C73C4
socleC2×C73C2×#354
prime radicalC23×C73#99
cosocle#14556591C23
hypercenter#533#64408
hypocenterC73#13599
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #22625074C2semidirect
3. #22625073C2semidirect
108. C73#13599semidirect

Maximal subgroups

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

subgroupindex
C2×#179894982
#226250742
#226250732
#226203132
#1359973