Finite Group Databasebeta

← #22621982

Subgroups — #22621982

Order 9344.

376 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989277C211yesmaximal, characteristic
2#17988955C211yesmaximal, characteristic, complemented
3#17988925C211yesmaximal, characteristic, complemented
4#17988915C211yesmaximal, characteristic, complemented
5#17988894C211yesmaximal, characteristic, complemented
6#17988843C211yesmaximal, characteristic, complemented
7#17988826C211yesmaximal, characteristic, complemented
8#17988794C211yesmaximal, characteristic, complemented
9#17988743C211yesmaximal, characteristic, complemented
10#17988743C211yesmaximal, characteristic, complemented
11#17988692C211yesmaximal, characteristic, complemented
12#17988659C211yesmaximal, characteristic
13#17988596C211yesmaximal, characteristic, complemented
14C2×#14556515C211yesmaximal, characteristic, complemented
15D4×Q8×C73C211yesmaximal, characteristic
16C2×#11924018C2211yescharacteristic
17C2×#11924018C2211yescharacteristic
18C2×#11924018C2211yescharacteristic
19C2×#11924012C2211yescharacteristic
20C22×#10596831C2211yescharacteristic
21#14556584—21no—
22#14556583C2211yescharacteristic
23#14556581—21no—
24#14556572—21no—
25#14556570C2211yescharacteristic
26#14556570C2211yescharacteristic
27C4×Dic146C2211yescharacteristic
28#14556550C2211yescharacteristic
29#14556547—21no—
30C2×C4⋊Dic73C2211yescharacteristic
31#14556524C2211yescharacteristic
32#14556522C2211yescharacteristic
33#14556522C2211yescharacteristic
34C4⋊#10596831C2211yescharacteristic
35#14556515C2211yescharacteristic
36#14556515C2211yescharacteristic
37#14556515C2211yescharacteristic
38#14556515C2211yescharacteristic
39#14556515C2211yescharacteristic
40#14556515C2211yescharacteristic
41#14556515C2211yescharacteristic
42#14556515C2211yescharacteristic
43#14556515C2211yescharacteristic
44#14556514C2211yescharacteristic
45C22⋊#10596831C2211yescharacteristic
46C22⋊#10596831C2211yescharacteristic
47#14556502C2211yescharacteristic
48C22×Q8×C73C2211yescharacteristic
49C22×Q8×C73C2211yescharacteristic
50C4⋊Q8×C73—21no—
51C4⋊Q8×C73C2211yescharacteristic
52C22⋊Q8×C73—21no—
53C22⋊Q8×C73—21no—
54C22⋊Q8×C73C2211yescharacteristic
55C22⋊Q8×C73C2211yescharacteristic
56C4×Q8×C73C2211yescharacteristic
57C4×D4×C73—21no—
58C4×D4×C73C2211yescharacteristic
59C2×Dic146C2311yescharacteristic
60C22×Dic73—21no—
61#11924018—22no—
62#11924018—41no—
63#11924018—41no—
64#11924012—41no—
65C2×#10596831—41no—
66C2×#10596831C2311yescharacteristic
67C2×#10596831C2311yescharacteristic
68C2×#10596831C2311yescharacteristic
69C2×#10596831C2311yescharacteristic
70C4⋊Dic73—21no—
71C4⋊Dic73C2311yescharacteristic
72C4⋊Dic73C2311yescharacteristic
73C4⋊Dic73C2311yescharacteristic
74#11924007—21no—
75#11924007—21no—
76#11924007—21no—
77#11924007—21no—
78#11924007—21no—
79C22⋊Dic73—21no—
80C22⋊Dic73—21no—
81C22⋊Dic73—21no—
82C4×Dic73—21no—
83C4×Dic73—21no—
84C2×Q8×C73—21no—
85C2×Q8×C73—21no—
86C2×Q8×C73—22no—
87C2×Q8×C73—22no—
88C2×Q8×C73—41no—
89C2×Q8×C73—41no—
90C2×Q8×C73C2311yescharacteristic
91C2×Q8×C73C2311yescharacteristic
92C2×Q8×C73C2311yescharacteristic
93C2×D4×C73D411yescharacteristic
94C22×C4×C73—21no—
95C22×C4×C73—21no—
96C22×C4×C73C2311yescharacteristic
97C22×C4×C73C2311yescharacteristic
98C4⋊C4×C73—21no—
99C4⋊C4×C73—21no—
100C4⋊C4×C73—21no—
101C4⋊C4×C73—21no—
102C4⋊C4×C73—21no—
103C4⋊C4×C73D411yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C22⋊C4×C73—21no—
106C22⋊C4×C73—21no—
107C22⋊C4×C73D411yescharacteristic
108C22⋊C4×C73D411yescharacteristic
109C42×C73—21no—
110C42×C73C2311yescharacteristic
111C23×C73C2×D411yescharacteristic
112C23×C73C2×D411yescharacteristic
113Q8×C73—21no—
114Q8×C73—21no—
115Q8×C73—21no—
116Q8×C73—21no—
117Q8×C73—21no—
118Q8×C73—42no—
119Q8×C73—42no—
120Q8×C73#4112yes—
121D4×C73—22no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—42no—
131C2×C4×C73—42no—
132C2×C4×C73C2×D411yescharacteristic
133C2×C4×C73C2×D411yescharacteristic
134C2×C4×C73C2×D411yescharacteristic
135C2×C4×C73C2×D411yescharacteristic
136C2×C4×C73C2411yescharacteristic
137C2×Dic73—21no—
138C2×Dic73—21no—
139C2×Dic73—21no—
140C2×Dic73—21no—
141C2×Dic73—42no—
142Dic146—21no—
143Dic146—21no—
144#10596831—21no—
145#10596831—21no—
146#10596831—21no—
147#10596831—21no—
148C22×C73—21no—
149C22×C73—21no—
150C22×C73—21no—
151C22×C73—21no—
152C22×C73—21no—
153C22×C73#13712yes—
154C22×C73C22×D411yescharacteristic
155C4×C73—21no—
156C4×C73—21no—
157C4×C73—22no—
158C4×C73—21no—
159C4×C73—21no—
160C4×C73—41no—
161C4×C73—41no—
162C4×C73—41no—
163C4×C73C2×#4111yescharacteristic
164C4×C73H(5,𝔽2)11yescharacteristic
165Dic73—41no—
166Dic73—41no—
167Dic73—41no—
168Dic73—41no—
169C2×C73—22no—
170C2×C73—41no—
171C2×C73#54611yescharacteristic
172C2×C73C2×#13711yescharacteristic
173C2×C73#57811yescharacteristic
174#3312—731nomaximal, Sylow
175C73#331211yescharacteristic, complemented, Sylow
176#552—731no—
177D4×Q8D7311yescharacteristic
178#491—731no—
179#485—731no—
180#483—731no—
181#479—731no—
182#470—731no—
183#467—731no—
184#462—731no—
185#451—731no—
186#451—731no—
187#441—731no—
188#435—731no—
189#419—731no—
190C2×#103—731no—
191C22×Q8C2×D7311yescharacteristic
192C22×Q8C2×D7311yescharacteristic
193C2×Q16—731no—
194C2×Q16—731no—
195C2×Q16—731no—
196C2×M16—731no—
197C22×C8—731no—
198C4⋊Q8—21no—
199C4⋊Q8C2×D7311yescharacteristic
200#126—1461no—
201#125—731no—
202#125—1461no—
203#123—1461no—
204C22⋊Q8—21no—
205C22⋊Q8—21no—
206C22⋊Q8—731no—
207C22⋊Q8—731no—
208C22⋊Q8C2×D7311yescharacteristic
209C22⋊Q8C2×D7311yescharacteristic
210C4×Q8—731no—
211C4×Q8C2×D7311yescharacteristic
212C4×D4—21no—
213C4×D4C2×D7311yescharacteristic
214#117—731no—
215#117—1461no—
216C2×C4⋊C4—731no—
217#107—731no—
218#106—731no—
219#106—731no—
220C4⋊C8—731no—
221#103—731no—
222#103—731no—
223#103—731no—
224#103—731no—
225#103—731no—
226#103—731no—
227#103—731no—
228#103—731no—
229#103—731no—
230#103—731no—
231C22⋊C8—731no—
232C22⋊C8—731no—
233#97—731no—
234C2×Q8—21no—
235C2×Q8—21no—
236C2×Q8—22no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8—731no—
241C2×Q8C22×D7311yescharacteristic
242C2×Q8C22×D7311yescharacteristic
243C2×Q8C22×D7311yescharacteristic
244C2×D4C22⋊D7311yescharacteristic
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—1461no—
248C22×C4C22×D7311yescharacteristic
249C22×C4C22×D7311yescharacteristic
250Q16—2921no—
251Q16—2921no—
252Q16—1462no—
253M16—2921no—
254C2×C8—2921no—
255C2×C8—731no—
256C2×C8—731no—
257C2×C8—731no—
258C2×C8—731no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—731no—
265C4⋊C4—731no—
266C4⋊C4—731no—
267C4⋊C4—1461no—
268C4⋊C4—1461no—
269C4⋊C4—1461no—
270C4⋊C4—1461no—
271C4⋊C4—1461no—
272C4⋊C4—1461no—
273C4⋊C4C22⋊D7311yescharacteristic
274C4⋊C4C22×D7311yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—1461no—
278C22⋊C4—1461no—
279C22⋊C4—1461no—
280C22⋊C4C22⋊D7311yescharacteristic
281C22⋊C4C22⋊D7311yescharacteristic
282C42—21no—
283C42—1461no—
284C42—1461no—
285C42C22×D7311yescharacteristic
286C23C2×C22⋊D7311yescharacteristic
287C23C2×C22⋊D7311yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—42no—
294Q8—42no—
295Q8—1461no—
296Q8—1461no—
297Q8#1192402712yes—
298D4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—2922no—
310C2×C4—1461no—
311C2×C4—1461no—
312C2×C4—1461no—
313C2×C4—1461no—
314C2×C4C2×C22⋊D7311yescharacteristic
315C2×C4C2×C22⋊D7311yescharacteristic
316C2×C4C2×C22⋊D7311yescharacteristic
317C2×C4C2×C22⋊D7311yescharacteristic
318C2×C4C23×D7311yescharacteristic
319C8—1461no—
320C8—1461no—
321C8—1461no—
322C8—1461no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22#1455662212yes—
329C22C22×C22⋊D7311yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—22no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—2921no—
339C4—2921no—
340C4—2921no—
341C4—2921no—
342C4C2×#1192402711yescharacteristic
343C4#1455663611yescharacteristic
344C2—22no—
345C2—41no—
346C2#1798923111yescharacteristic
347C2C2×#1455662211yescharacteristic
348C2#1798940211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingD4×Q8×C73C2
socleC22×C73C22×D4
hypercenterD4×Q8D73
hypocenterC73#3312
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
2. #17988955C2semidirect
3. #17988925C2semidirect
4. #17988915C2semidirect
5. #17988894C2semidirect
6. #17988843C2semidirect
7. #17988826C2semidirect
8. #17988794C2semidirect
9. #17988743C2semidirect
10. #17988743C2semidirect
11. #17988692C2semidirect
13. #17988596C2semidirect
14. C2×#14556515C2semidirect
175. C73#3312semidirect