Finite Group Databasebeta

← #22625893

Subgroups — #22625893

Order 9344.

262 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 66 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#17989666C211yesmaximal, characteristic
2#17989602C211yesmaximal, characteristic, complemented
3#17989592C211yesmaximal, characteristic, complemented
4#17989584C211yesmaximal, characteristic
5#17989470C211yesmaximal, characteristic, complemented
6#17989458C211yesmaximal, characteristic, complemented
7#104×D73C211yesmaximal, characteristic
8#14556679—21no—
9#14556678—22no—
10#14556678—21no—
11C2×#11924038—21no—
12C2×#11924038C2211yescharacteristic
13C2×#11924038C2211yescharacteristic
14D73⋊M16—21no—
15D73⋊M16C2211yescharacteristic
16#14556670C2211yescharacteristic
17#14556662—21no—
18#14556661—21no—
19#14556658—22no—
20#14556656—21no—
21#14556655—21no—
22#41×D73C2211yescharacteristic
23M16×D73C2211yescharacteristic
24C42×D73C2211yescharacteristic
25#14556519C411yescharacteristic, complemented
26#14556518C411yescharacteristic, complemented
27#14556517C411yescharacteristic, complemented
28#104×C73C411yescharacteristic, complemented
29#11924038—22no—
30#11924038—21no—
31#11924038—21no—
32#11924038—21no—
33#11924038—21no—
34#11924038D411yescharacteristic
35#11924038D411yescharacteristic
36#11924037—22no—
37#11924037—21no—
38#11924036—22no—
39#11924036—21no—
40C2×#10596833—22no—
41C2×#10596833—21no—
42C2×#10596833D412yes—
43C4⋊#64408—21no—
44C22⋊#64408—21no—
45C4×#64408—21no—
46#11924029D411yescharacteristic
47#11924028—21no—
48#11924028C2×C411yescharacteristic
49#11924027—21no—
50#11924027D411yescharacteristic
51Q8×D73Q811yescharacteristic
52D4×D73—21no—
53D4×D73Q811yescharacteristic
54C2×C4×D73—21no—
55C2×C4×D73—21no—
56C2×C4×D73C2311yescharacteristic
57#11924012C2×C411yescharacteristic
58#11924011—21no—
59C8×D73—21no—
60C4×Dic73—21no—
61C4×Dic73C2×C411yescharacteristic
62#41×C73C2×C411yescharacteristic
63M16×C73C2×C411yescharacteristic
64C42×C73C2×C411yescharacteristic
65C22×D73—21no—
66C22×D73#4111yescharacteristic
67C2×#64408—41no—
68Q8×C73C4⋊C411yescharacteristic
69D4×C73—21no—
70D4×C73C4⋊C411yescharacteristic
71C2×C4×C73—21no—
72C2×C4×C73—21no—
73C2×C4×C73C22×C411yescharacteristic
74C22⋊D73—21no—
75C22⋊D73—21no—
76C22⋊D73—21no—
77C2×Dic73—21no—
78C2×Dic73—21no—
79C2×Dic73C2×D411yescharacteristic
80D292—21no—
81D292C4⋊C411yescharacteristic
82C4×D73—21no—
83C4×D73—21no—
84C4×D73—21no—
85C4×D73—42no—
86C4×D73C2×D411yescharacteristic
87C4×D73C2×D411yescharacteristic
88C4×D73C2×Q811yescharacteristic
89C4×D73#4111yescharacteristic
90Dic146—21no—
91Dic146C4⋊C411yescharacteristic
92#10596833—21no—
93#10596833—22no—
94#10596833—21no—
95#10596833—41no—
96C8×C73—21no—
97#10596831—21no—
98C22×C73—21no—
99C22×C73C4×D411yescharacteristic
100C2×D73—21no—
101C2×D73—41no—
102C2×D73—81no—
103C2×D73C22⋊Q811yescharacteristic
104C2×D73#12311yescharacteristic
105#64408—81no—
106C4×C73—21no—
107C4×C73—41no—
108C4×C73C2×C4⋊C411yescharacteristic
109C4×C73C4×D411yescharacteristic
110Dic73—22no—
111Dic73—21no—
112Dic73#12011yescharacteristic
113Dic73C22⋊Q811yescharacteristic
114C2×C73—21no—
115C2×C73—41no—
116C2×C73#38511yescharacteristic
117D73—21no—
118D73—21no—
119D73—41no—
120#1861—731nomaximal, Sylow
121C73#186111yescharacteristic, complemented, Sylow
122#568—731no—
123#430—731no—
124#423—731no—
125#421—731no—
126C2×#104—731no—
127#344—731no—
128#339—731no—
129C2×#41—731no—
130#131—1462no—
131#131—1461no—
132#131—1461no—
133C2×M16—731no—
134C2×M16—731no—
135C2×M16—731no—
136C2×M16—731no—
137C2×M16—1461no—
138C2×M16—1461no—
139#117—731no—
140C2×C42—731no—
141#108—1461no—
142#108—1461no—
143C4⋊C8—1462no—
144#104—731no—
145#104—731no—
146#104—731no—
147#104—1461no—
148#104—1461no—
149#104#6440811yescharacteristic, complemented
150#41—731no—
151#41—731no—
152#41—731no—
153#41—1461no—
154#41—1461no—
155#41C2×#6440811yescharacteristic
156C2×Q8—731no—
157C2×D4—731no—
158C2×D4—1461no—
159C22×C4—731no—
160C22×C4—1461no—
161C22×C4—1461no—
162M16—731no—
163M16—731no—
164M16—731no—
165M16—1461no—
166M16—1461no—
167M16—1461no—
168M16—1461no—
169M16—1461no—
170M16—1461no—
171M16—1462no—
172M16—1462no—
173M16C2×#6440811yescharacteristic
174C2×C8—732no—
175C2×C8—1461no—
176C2×C8—1461no—
177C2×C8—1461no—
178C2×C8—1462no—
179C2×C8—1462no—
180C4⋊C4—1461no—
181C22⋊C4—1461no—
182C42—731no—
183C42—1461no—
184C42—1461no—
185C42C2×#6440811yescharacteristic
186C23—731no—
187C23—1461no—
188Q8—731no—
189Q8—1461no—
190Q8C4⋊#6440811yescharacteristic
191D4—21no—
192D4—731no—
193D4—1461no—
194D4—1461no—
195D4—1461no—
196D4—1461no—
197D4C4⋊#6440811yescharacteristic
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—2922no—
201C2×C4—2921no—
202C2×C4—731no—
203C2×C4—731no—
204C2×C4—731no—
205C2×C4—731no—
206C2×C4—731no—
207C2×C4—1461no—
208C2×C4—1461no—
209C2×C4—1461no—
210C2×C4—1461no—
211C2×C4—1461no—
212C2×C4C22×#6440811yescharacteristic
213C8—21no—
214C8—2921no—
215C8—1462no—
216C8—1461no—
217C8—1461no—
218C8—1461no—
219C22—21no—
220C22—2921no—
221C22—5841no—
222C22—731no—
223C22—731no—
224C22—1461no—
225C22D4×#6440811yescharacteristic
226C4—21no—
227C4—41no—
228C4—5841no—
229C4—731no—
230C4—731no—
231C4—1462no—
232C4—1461no—
233C4C2×C4⋊#6440811yescharacteristic
234C4D4×#6440811yescharacteristic
235C2—21no—
236C2—41no—
237C2—2921no—
238C2—1461no—
239C2—1461no—
240C2#1798953411yescharacteristic
subgroupG/H
centerC2#17989534
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#104×C73C4
socleC2×C73#385
hypercenter#104#64408
hypocenterC73#1861
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #17989602C2semidirect
3. #17989592C2semidirect
5. #17989470C2semidirect
6. #17989458C2semidirect
25. #14556519C4semidirect
26. #14556518C4semidirect
27. #14556517C4semidirect
28. #104×C73C4semidirect
121. C73#1861semidirect
149. #104#64408semidirect