Finite Group Databasebeta

← #32995419

Subgroups — #32995419

Order 18688.

284 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 69 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#22618568C211yesmaximal, characteristic
2#22611740C212yesmaximal, complemented
3#22607882C211yesmaximal, characteristic, complemented
4#22607866C212yesmaximal
5C73×#1327C211yesmaximal, characteristic, complemented
6C2×#14556548C411yescharacteristic
7#17988647—22no—
8#17988647—22no—
9#17988611C411yescharacteristic
10#17988550C411yescharacteristic
11#17988550C2211yescharacteristic
12M16×Dic73C411yescharacteristic
13M16×Dic73C2211yescharacteristic
14#17988407—22no—
15#17988369C2212yes—
16#17988364—22no—
17#423×C73C2211yescharacteristic
18#349×C73C2212yes—
19C22×C4×D73C2×C411yescharacteristic
20C2×#11924012C2×C411yescharacteristic
21C2×#11924012C2×C411yescharacteristic
22#14556548—21no—
23#14556548—21no—
24#14556548—22no—
25C2×#11924007—21no—
26C2×#11924005—21no—
27C2×C4×Dic73C2×C411yescharacteristic
28#14556531—22no—
29C4⋊#10596831—22no—
30#14556503—22no—
31#14556503—22no—
32#14556501—21no—
33#14556501D412yes—
34C8×Dic73—21no—
35C8×Dic73D412yes—
36C2×M16×C73C2×C411yescharacteristic
37C2×M16×C73C2311yescharacteristic
38C2×C42×C73C2×C411yescharacteristic
39M32×C73—22no—
40C4⋊C8×C73—22no—
41C23×D73M1611yescharacteristic
42C22×Dic73—21no—
43C22×Dic73M1611yescharacteristic
44C2×C4×D73—21no—
45C2×C4×D73—21no—
46C2×C4×D73—41no—
47C2×C4×D73—41no—
48#11924012—41no—
49#11924012—41no—
50C2×#10596831—21no—
51C2×#10596831C22⋊C412yes—
52#11924007—22no—
53#11924007—22no—
54#11924005—22no—
55#11924005—22no—
56C4×Dic73—21no—
57C4×Dic73C22⋊C411yescharacteristic
58C4×Dic73C22⋊C411yescharacteristic
59#11924003—42no—
60C22×C4×C73—21no—
61C22×C4×C73C22×C411yescharacteristic
62M16×C73—41no—
63M16×C73—41no—
64C2×C8×C73—21no—
65C2×C8×C73C2×D412yes—
66C42×C73—21no—
67C42×C73M1612yes—
68C16×C73—42no—
69C23×C73C2×M1611yescharacteristic
70C22×D73—21no—
71C22×D73—41no—
72C22×D73—81no—
73C2×C4×C73—21no—
74C2×C4×C73—21no—
75C2×C4×C73—22no—
76C2×C4×C73—81no—
77C2×C4×C73C2×C22⋊C411yescharacteristic
78C2×C4×C73C2×M1611yescharacteristic
79C2×Dic73—21no—
80C2×Dic73—21no—
81C2×Dic73—21no—
82C2×Dic73—41no—
83C2×Dic73—81no—
84C4×D73—42no—
85C4×D73—41no—
86C4×D73—41no—
87C8×C73—22no—
88C8×C73—41no—
89#10596831—22no—
90#10596831—41no—
91C22×C73—21no—
92C22×C73—41no—
93C22×C73#40711yescharacteristic
94C2×D73—42no—
95C2×D73—41no—
96C2×D73—82no—
97C4×C73—21no—
98C4×C73—42no—
99C4×C73#41011yescharacteristic
100C4×C73#41311yescharacteristic
101Dic73—41no—
102Dic73—41no—
103Dic73—41no—
104#11522—731nomaximal, Sylow
105C2×C73—21no—
106C2×C73—41no—
107C2×C73#146411yescharacteristic
108D73—81no—
109#2921—731no—
110#2165—732no—
111#1327—731no—
112#1327D7311yescharacteristic, complemented
113#1320—732no—
114C73#1152211yescharacteristic, complemented, Sylow
115C2×#117—731no—
116#433—1462no—
117#433—1462no—
118#423—731no—
119#423C2×D7311yescharacteristic
120#407—731no—
121#407—731no—
122C4×M16—731no—
123C4×M16—731no—
124#364—1462no—
125#349—732no—
126#349C2×D7312yes—
127#347—1462no—
128C23×C4—731no—
129C2×M16—731no—
130C2×M16—731no—
131C2×M16C4×D7311yescharacteristic
132C2×M16C22×D7311yescharacteristic
133#117—1461no—
134#117—1461no—
135#117—1462no—
136C2×C4⋊C4—1461no—
137C2×C22⋊C4—1461no—
138C2×C42—731no—
139C2×C42C4×D7311yescharacteristic
140M32—22no—
141M32—1462no—
142C4⋊C8—22no—
143C4⋊C8—1462no—
144C22⋊C8—1462no—
145C22⋊C8—1462no—
146#97—732no—
147#97—1461no—
148C4×C8—732no—
149C4×C8—1461no—
150C24—731no—
151C22×C4—21no—
152C22×C4—2921no—
153C22×C4—2921no—
154C22×C4—731no—
155C22×C4—1461no—
156C22×C4—1461no—
157C22×C4—1461no—
158C22×C4C2×C4×D7311yescharacteristic
159M16—41no—
160M16—41no—
161M16—2921no—
162M16—2921no—
163C2×C8—21no—
164C2×C8—732no—
165C2×C8—1461no—
166C2×C8D4×D7312yes—
167C4⋊C4—1462no—
168C4⋊C4—1462no—
169C22⋊C4—1462no—
170C22⋊C4—1462no—
171C42—21no—
172C42—731no—
173C42—731no—
174C42—1461no—
175C42#1192401112yes—
176C16—42no—
177C16—2922no—
178C23—2921no—
179C23—5841no—
180C23—1461no—
181C23M16×D7311yescharacteristic
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—81no—
186C2×C4—2922no—
187C2×C4—2921no—
188C2×C4—2921no—
189C2×C4—2921no—
190C2×C4—5841no—
191C2×C4—1461no—
192C2×C4—1461no—
193C2×C4—1461no—
194C2×C4C22⋊C4×D7311yescharacteristic
195C2×C4C2×#1192401111yescharacteristic
196C8—22no—
197C8—41no—
198C8—2921no—
199C8—1462no—
200C22—21no—
201C22—41no—
202C22—2922no—
203C22—2921no—
204C22—5842no—
205C22#1798854911yescharacteristic
206C4—21no—
207C4—42no—
208C4—2921no—
209C4—2921no—
210C4—2921no—
211C4#1798855911yescharacteristic
212C4#1798857011yescharacteristic
213C2—21no—
214C2—41no—
215C2—5841no—
216C2#2260826411yescharacteristic
subgroupG/H
centerC4#17988559
commutatorC22×C4×C73C22×C4
FrattiniC2×M16C22×D73
FittingC73×#1327C2
socleC2×C73#1464
prime radicalC23×D73M16
cosocleC2×M16×C73C23
hypercenter#1327D73
hypocenterC73#11522
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1327

Complements

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

NH ≅ G/Ntype
2. #22611740C2semidirect
3. #22607882C2semidirect
5. C73×#1327C2semidirect
112. #1327D73semidirect
114. C73#11522semidirect

Maximal subgroups

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

subgroupindex
#226185682
#226117402
#226078822
#226078662
C73×#13272
#1152273