Finite Group Databasebeta

← #34000360

Subgroups — #34000360

Order 18688.

364 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C4×#14556651C211yesmaximal, characteristic
2#22625166C211yesmaximal, characteristic
3#22610223C211yesmaximal, characteristic
4C2×#14556651C412yes—
5#17989555—21no—
6C4×#11924037—21no—
7#17989467—21no—
8#17989433—21no—
9#17989430C412yes—
10C2×C4×C22⋊D73C2211yescharacteristic
11C2×C22⋊#10596831C411yescharacteristic
12C2×#14556503—21no—
13#17988341—21no—
14C23×C8×C73C411yescharacteristic
15C2×#11924037—22no—
16C2×#11924036—41no—
17#14556651—22no—
18#14556651C814yescomplemented
19#14556648—41no—
20C22⋊#10596833—22no—
21#14556646—41no—
22C4×#10596833—41no—
23C22×C22⋊D73C2×C411yescharacteristic
24C22×C4×D73D411yescharacteristic
25C22×#10596831—21no—
26C4×C22⋊D73—41no—
27C4×C22⋊D73—41no—
28C2×#11924007D411yescharacteristic
29C2×C22⋊Dic73C2×C411yescharacteristic
30C2×#11924005Q811yescharacteristic
31C2×C4×Dic73D411yescharacteristic
32C22⋊#10596831—41no—
33#14556503—42no—
34C23×C4×C73C2×C411yescharacteristic
35C22×C8×C73—21no—
36C22×C8×C73—42no—
37C22×C8×C73—41no—
38#11924037—24no—
39#11924037—42no—
40#11924036—81no—
41#11924036—81no—
42C2×#10596833—42no—
43C2×#10596833—42no—
44C23×D73C4⋊C411yescharacteristic
45C2×C22⋊D73—41no—
46C2×C22⋊D73—41no—
47C2×C22⋊D73C2×C812yes—
48C2×C22⋊D73M1612yes—
49C22×Dic73C22⋊C411yescharacteristic
50C22×Dic73C22⋊C411yescharacteristic
51C22×Dic73C4⋊C411yescharacteristic
52C2×C4×D73—21no—
53C2×C4×D73—21no—
54C2×C4×D73—41no—
55C2×C4×D73—41no—
56C2×#10596831—41no—
57C2×#10596831—41no—
58C2×#10596831—41no—
59#11924007—41no—
60C22⋊Dic73—41no—
61#11924005—41no—
62C4×Dic73—21no—
63C4×Dic73—21no—
64C24×C73C4211yescharacteristic
65C22×C4×C73—21no—
66C22×C4×C73—21no—
67C22×C4×C73—41no—
68C22×C4×C73—41no—
69C22×C4×C73C22⋊C411yescharacteristic
70C22×C4×C73C4⋊C411yescharacteristic
71C2×C8×C73—22no—
72C2×C8×C73—41no—
73C2×C8×C73—42no—
74C2×C8×C73—41no—
75C2×C8×C73—42no—
76C23×C73—21no—
77C23×C73—21no—
78C23×C73—41no—
79C23×C73—41no—
80C23×C73#9511yescharacteristic
81C23×C73C4×C811yescharacteristic
82C23×C73#9711yescharacteristic
83C22×D73—21no—
84C22×D73—21no—
85C22×D73—41no—
86C22×D73—41no—
87C22×D73C4⋊C812yes—
88C2×C4×C73—21no—
89C2×C4×C73—21no—
90C2×C4×C73—21no—
91C2×C4×C73—42no—
92C2×C4×C73—41no—
93C2×C4×C73—41no—
94C2×C4×C73—41no—
95C2×C4×C73#9911yescharacteristic
96C2×C4×C73#9911yescharacteristic
97C22⋊D73—42no—
98C22⋊D73—42no—
99C2×Dic73—21no—
100C2×Dic73—21no—
101C2×Dic73—21no—
102C2×Dic73—21no—
103C2×Dic73—41no—
104C2×Dic73—41no—
105C2×Dic73C22⋊C812yes—
106C4×D73—41no—
107C4×D73—41no—
108C4×D73—81no—
109#10596833—44no—
110#10596833—82no—
111C8×C73—42no—
112#10596831—81no—
113C22×C73—21no—
114C22×C73—21no—
115C22×C73—21no—
116C22×C73—21no—
117C22×C73—41no—
118C22×C73—41no—
119C22×C73—42no—
120C22×C73—41no—
121C22×C73—41no—
122C22×C73#33611yescharacteristic
123C22×C73#34211yescharacteristic
124C22×C73#34411yescharacteristic
125C2×D73—22no—
126C2×D73—41no—
127C2×D73—41no—
128C2×D73—42no—
129C2×D73—81no—
130C4×C73—21no—
131C4×C73—41no—
132C4×C73AΣL(1,𝔽16)11yescharacteristic
133C4×C73#35211yescharacteristic
134Dic73—22no—
135Dic73—41no—
136Dic73—41no—
137#7203—731nomaximal, Sylow
138C2×C73—21no—
139C2×C73—21no—
140C2×C73—41no—
141C2×C73—41no—
142C2×C73#128211yescharacteristic
143C2×C73#139011yescharacteristic
144C2×C73#139211yescharacteristic
145D73—42no—
146#1869—731no—
147C4×#100—731no—
148#1459—731no—
149C73#720311yescharacteristic, complemented, Sylow
150C23×C8#6440811yescharacteristic
151C2×C4×D4—731no—
152C2×#100—732no—
153C2×C22⋊C8—731no—
154C2×C22⋊C8—1461no—
155C2×C22⋊C8—1461no—
156C4×M16—1461no—
157#343—1461no—
158#336—1461no—
159#324—1461no—
160#323—732no—
161C22×D4—731no—
162C23×C4—731no—
163C23×C4C2×#6440811yescharacteristic
164C2×M16—1462no—
165C22×C8—21no—
166C22×C8—42no—
167C22×C8—41no—
168C22×C8—2921no—
169C22×C8—1461no—
170C4×D4—2921no—
171C4×D4—2921no—
172C2×C4⋊C4—731no—
173C2×C22⋊C4—731no—
174C2×C22⋊C4—731no—
175C2×C42—731no—
176#100—734no—
177#100—1462no—
178C22⋊C8—2922no—
179C22⋊C8—2921no—
180C22⋊C8—2921no—
181C22⋊C8—1462no—
182#97—2921no—
183C4×C8—2921no—
184C24—731no—
185C24C4×#6440811yescharacteristic
186C2×D4—2921no—
187C2×D4—2921no—
188C2×D4—732no—
189C2×D4—732no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—2921no—
195C22×C4—2921no—
196C22×C4—731no—
197C22×C4—731no—
198C22×C4—731no—
199C22×C4—1461no—
200C22×C4—1461no—
201C22×C4C22⋊#6440811yescharacteristic
202C22×C4C4⋊#6440811yescharacteristic
203M16—2922no—
204M16—1464no—
205C2×C8—22no—
206C2×C8—41no—
207C2×C8—42no—
208C2×C8—41no—
209C2×C8—42no—
210C2×C8—2922no—
211C2×C8—2921no—
212C2×C8—2921no—
213C2×C8—2922no—
214C2×C8—2921no—
215C2×C8—5841no—
216C2×C8—5841no—
217C4⋊C4—2921no—
218C22⋊C4—2921no—
219C22⋊C4—2921no—
220C42—1461no—
221C42—1461no—
222C23—21no—
223C23—21no—
224C23—41no—
225C23—41no—
226C23—2921no—
227C23—2921no—
228C23—732no—
229C23—1461no—
230C23—1461no—
231C23(C2×#64408)⋊C411yescharacteristic
232C23C8×#6440811yescharacteristic
233C23#1455664511yescharacteristic
234D4—2922no—
235D4—2922no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—2921no—
244C2×C4—2921no—
245C2×C4—2921no—
246C2×C4—2921no—
247C2×C4—5841no—
248C2×C4—732no—
249C2×C4—1461no—
250C2×C4—1461no—
251C2×C4—1461no—
252C2×C4—1461no—
253C2×C4#1455664911yescharacteristic
254C2×C4#1455665011yescharacteristic
255C8—42no—
256C8—2924no—
257C8—5841no—
258C8—5842no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—41no—
264C22—41no—
265C22—42no—
266C22—41no—
267C22—41no—
268C22—2922no—
269C22—2921no—
270C22—2921no—
271C22—5841no—
272C22—1462no—
273C22#1798945211yescharacteristic
274C22#1798946511yescharacteristic
275C22#1798946911yescharacteristic
276C4—21no—
277C4—41no—
278C4—2921no—
279C4—2921no—
280C4—1462no—
281C4#1798948711yescharacteristic
282C4#1798948911yescharacteristic
283C2—21no—
284C2—21no—
285C2—41no—
286C2—41no—
287C2—2922no—
288C2#2262477311yescharacteristic
289C2#2262501511yescharacteristic
290C2#2262502211yescharacteristic
subgroupG/H
centerC2×C4#14556649
commutatorC23×C73C4×C8
FrattiniC23×C4C2×#64408
FittingC23×C8×C73C4
socleC22×C73#342
prime radicalC22×C22⋊D73C2×C4
cosocleC2×C4×C22⋊D73C22
hypercenterC23×C8#64408
hypocenterC73#7203
LCSG ▷ C23×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
18. #14556651C8semidirect
149. C73#7203semidirect

Maximal subgroups

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

subgroupindex
C4×#145566512
#226251662
#226102232
#720373