Finite Group Databasebeta

← #34011029

Subgroups — #34011029

Order 18688.

414 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 74 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×#14556652C211yesmaximal, characteristic
2#22625193C211yesmaximal, characteristic
3#22624915C214yesmaximal
4#22614920C211yesmaximal, characteristic
5#17989608—21no—
6C2×#14556652—21no—
7C4×#11924037—21no—
8#17989467C2212yes—
9#17989433C2212yes—
10#17989432—21no—
11C2×#14556589—21no—
12C2×C4×Dic146C2211yescharacteristic
13#17988518C412yes—
14#17988518C2212yes—
15#17988494—21no—
16#17988483—21no—
17#17988483—21no—
18C4×C4⋊Dic73C411yescharacteristic
19C2×C4⋊Q8×C73C411yescharacteristic
20C2×#11924037—22no—
21C4⋊#10596833—41no—
22#14556652—24no—
23C22⋊#10596833—22no—
24#14556646—41no—
25#14556646—41no—
26C4×#10596833—41no—
27C22×Dic146D411yescharacteristic
28#14556589—44no—
29C4×Dic146—41no—
30C4×Dic146—41no—
31C2×C4⋊Dic73—21no—
32C2×C4⋊Dic73D411yescharacteristic
33C2×#11924007—22no—
34C2×#11924007—22no—
35C2×#11924007C2×C411yescharacteristic
36C2×#11924007C2311yescharacteristic
37C2×C4×Dic73—21no—
38C2×C4×Dic73D411yescharacteristic
39C2×C4×Dic73D411yescharacteristic
40#14556498—22no—
41#14556498—22no—
42#14556498C2×C412yes—
43C22×Q8×C73—21no—
44C4⋊Q8×C73—41no—
45C4⋊Q8×C73—41no—
46C2×C4⋊C4×C73—21no—
47C2×C4⋊C4×C73C2×C412yes—
48C2×C42×C73C2×C411yescharacteristic
49#11924037—24no—
50#11924037—42no—
51C2×#10596833—42no—
52C2×#10596833—42no—
53C2×Dic146—22no—
54C2×Dic146—22no—
55C2×Dic146—41no—
56C22×Dic73—22no—
57C22×Dic73C22⋊C411yescharacteristic
58C22×Dic73C22⋊C411yescharacteristic
59C22×Dic73C2×D411yescharacteristic
60C22×Dic73C2×D411yescharacteristic
61C4⋊Dic73—24no—
62C4⋊Dic73—41no—
63#11924007—41no—
64#11924007—41no—
65#11924007—44no—
66#11924007—44no—
67C4×Dic73—21no—
68C4×Dic73—21no—
69C4×Dic73—21no—
70C4×Dic73—21no—
71C4×Dic73—42no—
72C2×Q8×C73—42no—
73C2×Q8×C73—42no—
74C2×Q8×C73—42no—
75C22×C4×C73—22no—
76C22×C4×C73C22⋊C411yescharacteristic
77C22×C4×C73C22⋊C411yescharacteristic
78C22×C4×C73C22×C411yescharacteristic
79C4⋊C4×C73—42no—
80C4⋊C4×C73—41no—
81C4⋊C4×C73—41no—
82C42×C73—21no—
83C42×C73—21no—
84C23×C73C2×C22⋊C411yescharacteristic
85Q8×C73—84no—
86C2×C4×C73—21no—
87C2×C4×C73—21no—
88C2×C4×C73—22no—
89C2×C4×C73—21no—
90C2×C4×C73—41no—
91C2×C4×C73—42no—
92C2×C4×C73—42no—
93C2×C4×C73—42no—
94C2×C4×C73#9911yescharacteristic
95C2×C4×C73#9911yescharacteristic
96C2×C4×C73#10412yes—
97C2×Dic73—21no—
98C2×Dic73—21no—
99C2×Dic73—24no—
100C2×Dic73—21no—
101C2×Dic73—21no—
102C2×Dic73—21no—
103C2×Dic73—21no—
104C2×Dic73—21no—
105C2×Dic73—42no—
106C2×Dic73—42no—
107C2×Dic73—41no—
108C2×Dic73—41no—
109C2×Dic73AGL(1,ℤ/8)12yes—
110Dic146—44no—
111#10596833—44no—
112#10596833—82no—
113C22×C73—21no—
114C22×C73—21no—
115C22×C73C2×#9911yescharacteristic
116C22×C73#41811yescharacteristic
117C22×C73C2×#10411yescharacteristic
118C4×C73—21no—
119C4×C73—22no—
120C4×C73—41no—
121C4×C73—82no—
122C4×C73#35612yes—
123Dic73—22no—
124Dic73—44no—
125Dic73—41no—
126Dic73—41no—
127Dic73—41no—
128#11782—731nomaximal, Sylow
129C2×C73—21no—
130C2×C73—21no—
131C2×C73#150711yescharacteristic
132C2×C73#212311yescharacteristic
133C2×C73C2×#35611yescharacteristic
134#2546—731no—
135C4×#101—731no—
136#1467—731no—
137#1346—734no—
138C73#1178211yescharacteristic, complemented, Sylow
139C2×C4⋊Q8—1461no—
140C2×C4⋊Q8#6440811yescharacteristic
141C2×C4×Q8—731no—
142#432—1461no—
143C2×#101—1461no—
144C4×M16—1461no—
145#398—732no—
146#398—732no—
147#391—1461no—
148#389—1461no—
149#389—1461no—
150C4×C4⋊C4—731no—
151#343—732no—
152#324—732no—
153#324—1461no—
154C22×Q8—21no—
155C22×Q8—731no—
156C2×M16—1462no—
157C4⋊Q8—41no—
158C4⋊Q8—41no—
159C4⋊Q8—2924no—
160C4×Q8—2921no—
161C4×Q8—2921no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—731no—
164C2×C4⋊C4—731no—
165C2×C4⋊C4—731no—
166C2×C4⋊C4—1462no—
167C2×C4⋊C4—1462no—
168C2×C4⋊C4—1461no—
169C2×C4⋊C4C2×#6440812yes—
170C2×C42—731no—
171C2×C42—731no—
172C2×C42—1461no—
173C2×C42C2×#6440811yescharacteristic
174C4⋊C8—2921no—
175#101—1464no—
176C22⋊C8—1462no—
177#97—2921no—
178#97—2921no—
179C4×C8—2921no—
180#95—732no—
181#95—1462no—
182#95—1462no—
183C2×Q8—42no—
184C2×Q8—42no—
185C2×Q8—42no—
186C2×Q8—2921no—
187C2×Q8—1462no—
188C2×Q8—1462no—
189C22×C4—22no—
190C22×C4—731no—
191C22×C4—731no—
192C22×C4—731no—
193C22×C4—731no—
194C22×C4—1462no—
195C22×C4C22⋊#6440811yescharacteristic
196C22×C4C22⋊#6440811yescharacteristic
197C22×C4C22×#6440811yescharacteristic
198M16—2922no—
199M16—1464no—
200C2×C8—2922no—
201C2×C8—2922no—
202C4⋊C4—42no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—2921no—
206C4⋊C4—2921no—
207C4⋊C4—2921no—
208C4⋊C4—2924no—
209C4⋊C4—2924no—
210C4⋊C4—1464no—
211C42—21no—
212C42—21no—
213C42—2922no—
214C42—1461no—
215C42—1461no—
216C42—1461no—
217C42—1461no—
218C23C2×C22⋊#6440811yescharacteristic
219Q8—84no—
220Q8—2924no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—41no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—2922no—
230C2×C4—2922no—
231C2×C4—2921no—
232C2×C4—2921no—
233C2×C4—732no—
234C2×C4—1464no—
235C2×C4—1461no—
236C2×C4—1461no—
237C2×C4—1461no—
238C2×C4—1461no—
239C2×C4—1461no—
240C2×C4—1461no—
241C2×C4—1461no—
242C2×C4#1455664911yescharacteristic
243C2×C4#1455664911yescharacteristic
244C2×C4#1455665512yes—
245C8—2924no—
246C8—5842no—
247C22—21no—
248C22—21no—
249C22C2×#1455664911yescharacteristic
250C22#1798957911yescharacteristic
251C22C2×#1455665511yescharacteristic
252C4—22no—
253C4—21no—
254C4—41no—
255C4—82no—
256C4—2924no—
257C4—2921no—
258C4—2921no—
259C4—2921no—
260C4—1462no—
261C4#1798949712yes—
262C2—21no—
263C2—21no—
264C2#2262532711yescharacteristic
265C2#2262619311yescharacteristic
266C2C2×#1798949711yescharacteristic
subgroupG/H
centerC22C2×#14556649
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
FittingC2×C4⋊Q8×C73C4
socleC22×C73C2×#99
prime radicalC23×C73C2×C22⋊C4
cosocleC2×#11924007C23
hypercenterC2×C4⋊Q8#64408
hypocenterC73#11782
LCSG ▷ C22×C4×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
138. C73#11782semidirect

Maximal subgroups

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

subgroupindex
C4×#145566522
#226251932
#226249152
#226149202
#1178273