Finite Group Databasebeta

← #22625895

Subgroups — #22625895

Order 9344.

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

normal subgroups only

This group has 298 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×#14556660C211yesmaximal, characteristic
3C2×#14556654C211yesmaximal, characteristic
4#17989538C211yesmaximal, characteristic
5#17989460C211yesmaximal, characteristic
6#17989452C211yesmaximal, characteristic
7#103×D73C211yesmaximal, characteristic
8C2×#11924036C2211yescharacteristic
9Q8×#64408—22no—
10Q8×#64408—22no—
11C2×C4⋊#64408—21no—
12C2×C4⋊#64408—21no—
13C2×C4⋊#64408C2211yescharacteristic
14C2×C4⋊#64408C2211yescharacteristic
15C2×C4×#64408—21no—
16C2×C4×#64408C2211yescharacteristic
17#14556660—22no—
18#14556654—22no—
19(C2×#64408)⋊C4—21no—
20C2×Q8×D73C2211yescharacteristic
21C2×C8×D73C2211yescharacteristic
22C4⋊C4×D73C2211yescharacteristic
23#14556516C411yescharacteristic, complemented
24#14556515C411yescharacteristic, complemented
25#14556514C411yescharacteristic, complemented
26#103×C73C411yescharacteristic, complemented
27C22×#64408—21no—
28C22×#64408—21no—
29C22×#64408D411yescharacteristic
30C22×#64408D411yescharacteristic
31#11924036—21no—
32#11924036—21no—
33C2×#10596833—21no—
34C4⋊#64408—24no—
35C4⋊#64408—21no—
36C4⋊#64408—21no—
37C4⋊#64408—21no—
38C4⋊#64408—42no—
39C4⋊#64408D412yes—
40C4×#64408—24no—
41C4×#64408—21no—
42C4×#64408—21no—
43C2×Dic146—21no—
44C2×Dic146C2×C411yescharacteristic
45Q8×D73—21no—
46Q8×D73—21no—
47Q8×D73D412yes—
48Q8×D73Q812yes—
49C2×C4×D73—21no—
50C2×C4×D73—21no—
51C2×C4×D73C2311yescharacteristic
52C2×#10596831C2×C411yescharacteristic
53C8×D73—21no—
54C8×D73—21no—
55C4⋊Dic73C2×C411yescharacteristic
56#11924007—21no—
57C2×Q8×C73C2×C411yescharacteristic
58C2×C8×C73C2×C411yescharacteristic
59C4⋊C4×C73C2×C411yescharacteristic
60C22×D73C2×D411yescharacteristic
61C2×#64408—21no—
62C2×#64408—21no—
63C2×#64408—21no—
64C2×#64408—22no—
65C2×#64408—21no—
66C2×#64408—21no—
67C2×#64408—41no—
68C2×#64408—41no—
69C2×#64408—41no—
70C2×#64408—41no—
71C2×#64408—41no—
72C2×#64408Q1612yes—
73Q8×C73—21no—
74Q8×C73C4⋊C412yescomplemented
75C2×C4×C73—21no—
76C2×C4×C73—21no—
77C2×C4×C73C22×C411yescharacteristic
78C2×Dic73—21no—
79C2×Dic73—21no—
80C2×Dic73#4111yescharacteristic
81C4×D73—22no—
82C4×D73—22no—
83C4×D73—41no—
84C4×D73—41no—
85C4×D73C2×D411yescharacteristic
86C4×D73C2×D411yescharacteristic
87C4×D73C2×Q811yescharacteristic
88C4×D73#4111yescharacteristic
89Dic146—21no—
90Dic146—22no—
91Dic146—22no—
92Dic146C4⋊C412yescomplemented
93#10596833—41no—
94C8×C73—21no—
95#10596831—21no—
96C22×C73C4×D411yescharacteristic
97C2×D73#12011yescharacteristic
98C2×D73C22⋊Q811yescharacteristic
99C2×D73C2×Q1611yescharacteristic
100C2×D73#13511yescharacteristic
101C2×D73AGL(1,ℤ/8)11yescharacteristic
102C2×D73#13711yescharacteristic
103#64408—22no—
104#64408—41no—
105#64408—42no—
106#64408—81no—
107C4×C73—22no—
108C4×C73—41no—
109C4×C73C2×C4⋊C411yescharacteristic
110C4×C73C4×D411yescharacteristic
111Dic73—22no—
112Dic73—41no—
113Dic73C22⋊Q811yescharacteristic
114Dic73#12311yescharacteristic
115C2×C73#38511yescharacteristic
116C2×C73C4×Q1611yescharacteristic
117C2×C73#44011yescharacteristic
118D73#44911yescharacteristic
119D73#45111yescharacteristic
120D73#47711yescharacteristic
121D73#47911yescharacteristic
122#1863—731nomaximal, Sylow
123C73#186311yescharacteristic, complemented, Sylow
124C2×C4×Q8—731no—
125C2×#107—731no—
126C2×#103—731no—
127C2×#103—731no—
128#389—731no—
129#340—731no—
130#336—731no—
131C22×Q8—731no—
132C22×C8—731no—
133C22×C8—731no—
134C4×Q8—1462no—
135C4×Q8—1462no—
136C2×C4⋊C4—731no—
137C2×C4⋊C4—731no—
138C2×C4⋊C4—731no—
139C2×C4⋊C4—1461no—
140C2×C4⋊C4—1461no—
141C2×C42—731no—
142C2×C42—1461no—
143#107—1462no—
144#103—731no—
145#103—731no—
146#103—731no—
147#103—1462no—
148#103#6440811yescharacteristic, complemented
149#95—1461no—
150C2×Q8—732no—
151C2×Q8—732no—
152C2×Q8—731no—
153C2×Q8—1461no—
154C2×Q8—1461no—
155C2×Q8—1461no—
156C2×Q8C2×#6440811yescharacteristic
157C22×C4—731no—
158C22×C4—731no—
159C22×C4—731no—
160C22×C4—1461no—
161C22×C4—1461no—
162C22×C4—1461no—
163C22×C4—1461no—
164C2×C8—731no—
165C2×C8—1461no—
166C2×C8—1461no—
167C2×C8—1461no—
168C2×C8—1461no—
169C2×C8—1461no—
170C2×C8C2×#6440811yescharacteristic
171C4⋊C4—2922no—
172C4⋊C4—732no—
173C4⋊C4—731no—
174C4⋊C4—1461no—
175C4⋊C4—1461no—
176C4⋊C4—1461no—
177C4⋊C4—1461no—
178C4⋊C4—1464no—
179C4⋊C4C2×#6440811yescharacteristic
180C42—1461no—
181C42—1461no—
182C42—1464no—
183C23—731no—
184Q8—21no—
185Q8—732no—
186Q8—1462no—
187Q8—1462no—
188Q8—1461no—
189Q8C4⋊#6440812yescomplemented
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—2921no—
193C2×C4—2921no—
194C2×C4—2921no—
195C2×C4—2921no—
196C2×C4—2921no—
197C2×C4—2921no—
198C2×C4—2921no—
199C2×C4—731no—
200C2×C4—731no—
201C2×C4—731no—
202C2×C4—731no—
203C2×C4—731no—
204C2×C4—732no—
205C2×C4—1462no—
206C2×C4—1462no—
207C2×C4—1462no—
208C2×C4—1461no—
209C2×C4—1461no—
210C2×C4—1461no—
211C2×C4—1461no—
212C2×C4—1461no—
213C2×C4—1461no—
214C2×C4—1461no—
215C2×C4C22×#6440811yescharacteristic
216C8—21no—
217C8—2921no—
218C8—1461no—
219C22—731no—
220C22—731no—
221C22—731no—
222C22—731no—
223C22—731no—
224C22—731no—
225C22D4×#6440811yescharacteristic
226C4—22no—
227C4—41no—
228C4—2922no—
229C4—2921no—
230C4—2921no—
231C4—5841no—
232C4—731no—
233C4—731no—
234C4—1462no—
235C4—1462no—
236C4C2×C4⋊#6440811yescharacteristic
237C4D4×#6440811yescharacteristic
238C2—731no—
239C2—731no—
240C2—731no—
241C2—731no—
242C2#1798953411yescharacteristic
243C2Q16×#6440811yescharacteristic
244C2#1798962611yescharacteristic
subgroupG/H
centerC22D4×#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#103×C73C4
socleC22×C73C4×D4
hypercenter#103#64408
hypocenterC73#1863
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
23. #14556516C4semidirect
24. #14556515C4semidirect
25. #14556514C4semidirect
26. #103×C73C4semidirect
74. Q8×C73C4⋊C4semidirect
92. Dic146C4⋊C4semidirect
123. C73#1863semidirect
148. #103#64408semidirect
189. Q8C4⋊#64408semidirect