Finite Group Databasebeta

← #22625925

Subgroups — #22625925

Order 9344.

338 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 80 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×Q8×#64408C211yesmaximal, characteristic
2C2×#14556654C211yesmaximal, characteristic
3C2×#14556654C211yesmaximal, characteristic
4(C2×#64408)⋊Q8C211yesmaximal, characteristic
5#17989461C211yesmaximal, characteristic
6#17989452C211yesmaximal, characteristic
7C2×Q16×D73C211yesmaximal, characteristic
8C2×#11924036C2211yescharacteristic
9Q8×#64408—22no—
10Q8×#64408—22no—
11C2×C4⋊#64408—21no—
12C2×C4⋊#64408C2211yescharacteristic
13C2×C4⋊#64408C2211yescharacteristic
14C2×C4×#64408—21no—
15C2×C4×#64408C2211yescharacteristic
16#14556654—22no—
17#14556654—22no—
18(C2×#64408)⋊C4—21no—
19(C2×#64408)⋊C4—21no—
20C2×Q8×D73C2211yescharacteristic
21C2×Q8×D73C2211yescharacteristic
22C2×Dic292C411yescharacteristic, complemented
23C2×#11924018C411yescharacteristic, complemented
24C2×#11924018C411yescharacteristic, complemented
25Q16×D73—22no—
26Q16×D73—22no—
27C2×C8×D73C2211yescharacteristic
28C2×Q16×C73C411yescharacteristic, complemented
29C22×#64408—21no—
30C22×#64408—21no—
31C22×#64408D411yescharacteristic
32C22×#64408D411yescharacteristic
33#11924036—21no—
34#11924036—21no—
35C2×#10596833—21no—
36C4⋊#64408—24no—
37C4⋊#64408—21no—
38C4⋊#64408—21no—
39C4⋊#64408—21no—
40C4⋊#64408D412yes—
41C4×#64408—24no—
42C4×#64408—21no—
43C4×#64408—21no—
44C2×Dic146—21no—
45C2×Dic146—21no—
46C2×Dic146C2×C411yescharacteristic
47C2×Dic146C2×C411yescharacteristic
48Q8×D73—21no—
49Q8×D73—21no—
50Q8×D73—21no—
51Q8×D73—21no—
52Q8×D73—21no—
53Q8×D73—21no—
54Q8×D73D412yes—
55Q8×D73D412yes—
56C2×C4×D73—21no—
57C2×C4×D73—21no—
58C2×C4×D73C2311yescharacteristic
59Dic292—22no—
60#11924018—22no—
61#11924018—22no—
62C2×#10596831C2×C411yescharacteristic
63C8×D73—21no—
64C8×D73—21no—
65C2×Q8×C73C2×C411yescharacteristic
66C2×Q8×C73C2×C411yescharacteristic
67Q16×C73—22no—
68C2×C8×C73C2×C411yescharacteristic
69C22×D73C2×D411yescharacteristic
70C2×#64408—21no—
71C2×#64408—21no—
72C2×#64408—21no—
73C2×#64408—22no—
74C2×#64408—21no—
75C2×#64408—21no—
76C2×#64408—41no—
77C2×#64408—41no—
78C2×#64408—41no—
79C2×#64408—41no—
80C2×#64408—41no—
81C2×#64408Q1612yescomplemented
82Q8×C73—21no—
83Q8×C73—21no—
84Q8×C73—21no—
85Q8×C73C22⋊C412yes—
86C2×C4×C73—21no—
87C2×C4×C73—21no—
88C2×C4×C73C22×C411yescharacteristic
89C2×Dic73—21no—
90C2×Dic73—21no—
91C2×Dic73#4111yescharacteristic
92C4×D73—22no—
93C4×D73—22no—
94C4×D73—41no—
95C4×D73—41no—
96C4×D73C2×D411yescharacteristic
97C4×D73C2×D411yescharacteristic
98C4×D73C2×D411yescharacteristic
99C4×D73#4111yescharacteristic
100Dic146—21no—
101Dic146—22no—
102Dic146—22no—
103Dic146—21no—
104Dic146—21no—
105Dic146—41no—
106Dic146—41no—
107Dic146C22⋊C412yes—
108#10596833—41no—
109C8×C73—21no—
110#10596831—21no—
111C22×C73C4×D411yescharacteristic
112C2×D73#12011yescharacteristic
113C2×D73#12111yescharacteristic
114C2×D73C2×Q1611yescharacteristic
115C2×D73#13511yescharacteristic
116C2×D73#13711yescharacteristic
117C2×D73#13711yescharacteristic
118#64408—22no—
119#64408—41no—
120#64408—42no—
121#64408—81no—
122C4×C73—22no—
123C4×C73—41no—
124C4×C73C2×C22⋊C411yescharacteristic
125C4×C73C4×D411yescharacteristic
126Dic73—22no—
127Dic73—41no—
128Dic73#12111yescharacteristic
129Dic73#12311yescharacteristic
130C2×C73#38611yescharacteristic
131C2×C73C4×Q1611yescharacteristic
132C2×C73#44111yescharacteristic
133D73#45111yescharacteristic
134D73#45211yescharacteristic
135D73#46211yescharacteristic
136D73#46411yescharacteristic
137#1878—731nomaximal, Sylow
138C73#187811yescharacteristic, complemented, Sylow
139C22×Q16—731no—
140C2×C4×Q8—731no—
141C2×#103—731no—
142C2×#103—731no—
143#391—731no—
144#340—731no—
145#336—731no—
146C22×Q8—731no—
147C22×Q8—731no—
148C2×Q16—731no—
149C2×Q16—731no—
150C2×Q16—731no—
151C2×Q16—1462no—
152C2×Q16—1462no—
153C2×Q16#6440811yescharacteristic, complemented
154C22×C8—731no—
155C22×C8—731no—
156C4×Q8—1462no—
157C4×Q8—1462no—
158C2×C4⋊C4—731no—
159C2×C4⋊C4—731no—
160C2×C4⋊C4—1461no—
161C2×C42—731no—
162C2×C42—1461no—
163#103—1462no—
164#103—1462no—
165#95—1461no—
166#95—1461no—
167C2×Q8—732no—
168C2×Q8—732no—
169C2×Q8—731no—
170C2×Q8—731no—
171C2×Q8—1461no—
172C2×Q8—1461no—
173C2×Q8—1461no—
174C2×Q8—1461no—
175C2×Q8—1461no—
176C2×Q8—1461no—
177C2×Q8—1461no—
178C2×Q8—1461no—
179C2×Q8C2×#6440811yescharacteristic
180C2×Q8C2×#6440811yescharacteristic
181C22×C4—731no—
182C22×C4—731no—
183C22×C4—731no—
184C22×C4—1461no—
185C22×C4—1461no—
186C22×C4—1461no—
187C22×C4—1461no—
188Q16—22no—
189Q16—1462no—
190Q16—1462no—
191Q16—1462no—
192C2×C8—731no—
193C2×C8—1461no—
194C2×C8—1461no—
195C2×C8—1461no—
196C2×C8—1461no—
197C2×C8—1461no—
198C2×C8C2×#6440811yescharacteristic
199C4⋊C4—732no—
200C4⋊C4—1461no—
201C4⋊C4—1461no—
202C4⋊C4—1461no—
203C4⋊C4—1464no—
204C42—1461no—
205C42—1461no—
206C42—1464no—
207C23—731no—
208Q8—21no—
209Q8—21no—
210Q8—21no—
211Q8—2921no—
212Q8—2921no—
213Q8—732no—
214Q8—1462no—
215Q8—1462no—
216Q8—1461no—
217Q8—1461no—
218Q8—1461no—
219Q8C22⋊#6440812yes—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—2921no—
223C2×C4—2921no—
224C2×C4—2921no—
225C2×C4—2921no—
226C2×C4—2921no—
227C2×C4—2921no—
228C2×C4—2921no—
229C2×C4—731no—
230C2×C4—731no—
231C2×C4—731no—
232C2×C4—731no—
233C2×C4—731no—
234C2×C4—732no—
235C2×C4—1462no—
236C2×C4—1462no—
237C2×C4—1462no—
238C2×C4—1461no—
239C2×C4—1461no—
240C2×C4—1461no—
241C2×C4—1461no—
242C2×C4—1461no—
243C2×C4—1461no—
244C2×C4—1461no—
245C2×C4C22×#6440811yescharacteristic
246C8—21no—
247C8—2921no—
248C8—1461no—
249C22—731no—
250C22—731no—
251C22—731no—
252C22—731no—
253C22—731no—
254C22—731no—
255C22D4×#6440811yescharacteristic
256C4—22no—
257C4—41no—
258C4—2922no—
259C4—2921no—
260C4—2921no—
261C4—5841no—
262C4—731no—
263C4—731no—
264C4—1462no—
265C4—1462no—
266C4C2×C22⋊#6440811yescharacteristic
267C4D4×#6440811yescharacteristic
268C2—731no—
269C2—731no—
270C2—731no—
271C2—731no—
272C2#1798953511yescharacteristic
273C2Q16×#6440811yescharacteristic
274C2#1798962711yescharacteristic
subgroupG/H
centerC22D4×#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC2×Q16×C73C4
socleC22×C73C4×D4
hypercenterC2×Q16#64408
hypocenterC73#1878
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
22. C2×Dic292C4semidirect
23. C2×#11924018C4semidirect
24. C2×#11924018C4semidirect
28. C2×Q16×C73C4semidirect
81. C2×#64408Q16semidirect
138. C73#1878semidirect
153. C2×Q16#64408semidirect