Finite Group Databasebeta

← #22622096

Subgroups — #22622096

Order 9344.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×Dic146C211yesmaximal, characteristic, complemented
2#17988957C211yesmaximal, characteristic, complemented
3#17988928C211yesmaximal, characteristic, complemented
4#17988922C211yesmaximal, characteristic, complemented
5#17988891C211yesmaximal, characteristic, complemented
6#17988831C211yesmaximal, characteristic, complemented
7#17988814C211yesmaximal, characteristic, complemented
8#17988792C211yesmaximal, characteristic, complemented
9#17988725C211yesmaximal, characteristic, complemented
10#17988725C211yesmaximal, characteristic, complemented
11#17988687C211yesmaximal, characteristic, complemented
12#17988659C211yesmaximal, characteristic, complemented
13#17988595C211yesmaximal, characteristic, complemented
14C2×#14556514C211yesmaximal, characteristic, complemented
15#553×C73C211yesmaximal, characteristic
16C22×Dic146C2211yescharacteristic
17C22×Dic146C2211yescharacteristic
18C2×#11924016C2211yescharacteristic
19C2×#11924016C2211yescharacteristic
20C2×#11924016C2211yescharacteristic
21C2×#11924012C2211yescharacteristic
22C22×#10596831C2211yescharacteristic
23#14556591C2211yescharacteristic
24#14556590—21no—
25#14556570C2211yescharacteristic
26#14556570C2211yescharacteristic
27#14556568—21no—
28#14556568—21no—
29C4×Dic146C2211yescharacteristic
30D4×Dic73—21no—
31#14556524C2211yescharacteristic
32#14556524C2211yescharacteristic
33#14556522C2211yescharacteristic
34C4⋊#10596831C2211yescharacteristic
35#14556514C2211yescharacteristic
36#14556514C2211yescharacteristic
37#14556514C2211yescharacteristic
38#14556514C2211yescharacteristic
39#14556514C2211yescharacteristic
40#14556514C2211yescharacteristic
41#14556514C2211yescharacteristic
42#14556514C2211yescharacteristic
43#14556514C2211yescharacteristic
44#14556512C2211yescharacteristic
45C22⋊#10596831C2211yescharacteristic
46C22⋊#10596831C2211yescharacteristic
47#14556502C2211yescharacteristic
48#126×C73—21no—
49#125×C73C2211yescharacteristic
50#123×C73—21no—
51#121×C73—21no—
52#121×C73C2211yescharacteristic
53#121×C73C2211yescharacteristic
54C4×D4×C73—21no—
55C4×D4×C73C2211yescharacteristic
56C4×D4×C73C2211yescharacteristic
57#117×C73C2211yescharacteristic
58C2×C4⋊C4×C73C2211yescharacteristic
59C2×Dic146—22no—
60C2×Dic146—22no—
61C2×Dic146—21no—
62C2×Dic146—21no—
63C2×Dic146—41no—
64C2×Dic146—41no—
65C2×Dic146C2311yescharacteristic
66C2×Dic146C2311yescharacteristic
67C2×Dic146C2311yescharacteristic
68C22×Dic73—21no—
69C22×Dic73—21no—
70#11924016—22no—
71#11924016—41no—
72#11924016—41no—
73#11924012—41no—
74C2×#10596831—41no—
75C2×#10596831C2311yescharacteristic
76C2×#10596831C2311yescharacteristic
77C2×#10596831C2311yescharacteristic
78C2×#10596831C2311yescharacteristic
79C4⋊Dic73—21no—
80C4⋊Dic73—21no—
81C4⋊Dic73C2311yescharacteristic
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85C22⋊Dic73—21no—
86C22⋊Dic73—21no—
87C4×Dic73—21no—
88C2×D4×C73—21no—
89C2×D4×C73—21no—
90C2×D4×C73D411yescharacteristic
91C2×D4×C73C2311yescharacteristic
92C22×C4×C73—21no—
93C22×C4×C73—21no—
94C22×C4×C73C2311yescharacteristic
95C22×C4×C73C2311yescharacteristic
96C4⋊C4×C73—21no—
97C4⋊C4×C73—21no—
98C4⋊C4×C73—21no—
99C4⋊C4×C73D411yescharacteristic
100C4⋊C4×C73C2311yescharacteristic
101C4⋊C4×C73C2311yescharacteristic
102C4⋊C4×C73C2311yescharacteristic
103C22⋊C4×C73—21no—
104C22⋊C4×C73—21no—
105C22⋊C4×C73—21no—
106C22⋊C4×C73—21no—
107C22⋊C4×C73D411yescharacteristic
108C22⋊C4×C73D411yescharacteristic
109C42×C73—21no—
110C42×C73C2311yescharacteristic
111C23×C73—21no—
112C23×C73C2×D411yescharacteristic
113C23×C73C2×D411yescharacteristic
114D4×C73—22no—
115D4×C73—21no—
116D4×C73—21no—
117D4×C73—42no—
118D4×C73—81no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—81no—
127C2×C4×C73—81no—
128C2×C4×C73C2×D411yescharacteristic
129C2×C4×C73C2×D411yescharacteristic
130C2×C4×C73C2×D411yescharacteristic
131C2×C4×C73C2×D411yescharacteristic
132C2×C4×C73C2411yescharacteristic
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—42no—
138C2×Dic73—42no—
139Dic146—21no—
140Dic146—21no—
141Dic146—21no—
142Dic146—21no—
143Dic146—21no—
144Dic146—42no—
145Dic146—42no—
146Dic146#4112yes—
147#10596831—21no—
148#10596831—21no—
149#10596831—21no—
150#10596831—21no—
151C22×C73—21no—
152C22×C73—21no—
153C22×C73—21no—
154C22×C73—21no—
155C22×C73—21no—
156C22×C73—41no—
157C22×C73—41no—
158C22×C73—41no—
159C22×C73#13712yes—
160C22×C73C22×D411yescharacteristic
161C4×C73—21no—
162C4×C73—21no—
163C4×C73—21no—
164C4×C73—21no—
165C4×C73—41no—
166C4×C73—41no—
167C4×C73—41no—
168C4×C73C2×#4111yescharacteristic
169C4×C73H(5,𝔽2)11yescharacteristic
170Dic73—22no—
171Dic73—41no—
172Dic73—41no—
173Dic73—41no—
174C2×C73—22no—
175C2×C73—41no—
176C2×C73—81no—
177C2×C73#54611yescharacteristic
178C2×C73C2×#13711yescharacteristic
179C2×C73#57711yescharacteristic
180#3320—731nomaximal, Sylow
181C73#332011yescharacteristic, complemented, Sylow
182#553D7311yescharacteristic
183D4×Q8—731no—
184#491—731no—
185#485—731no—
186#484—731no—
187#479—731no—
188#468—731no—
189#465—731no—
190#461—731no—
191#448—731no—
192#448—731no—
193#440—731no—
194#435—731no—
195#419—731no—
196C2×#103—731no—
197C22×Q8—731no—
198C22×Q8—731no—
199C2×SD16—731no—
200C2×SD16—731no—
201C2×SD16—731no—
202C2×M16—731no—
203C22×C8—731no—
204C4⋊Q8—731no—
205C4⋊Q8—1461no—
206#126—21no—
207#125C2×D7311yescharacteristic
208#123—21no—
209C22⋊Q8—731no—
210C22⋊Q8—731no—
211C22⋊Q8—1461no—
212C22⋊Q8—1461no—
213#121—21no—
214#121C2×D7311yescharacteristic
215#121C2×D7311yescharacteristic
216C4×Q8—731no—
217C4×D4—21no—
218C4×D4—1461no—
219C4×D4C2×D7311yescharacteristic
220C4×D4C2×D7311yescharacteristic
221#117C2×D7311yescharacteristic
222C2×C4⋊C4C2×D7311yescharacteristic
223#107—731no—
224#107—731no—
225#106—731no—
226C4⋊C8—731no—
227#103—731no—
228#103—731no—
229#103—731no—
230#103—731no—
231#103—731no—
232#103—731no—
233#103—731no—
234#103—731no—
235#103—731no—
236#102—731no—
237C22⋊C8—731no—
238C22⋊C8—731no—
239#97—731no—
240C2×Q8—2921no—
241C2×Q8—2921no—
242C2×Q8—731no—
243C2×Q8—731no—
244C2×Q8—731no—
245C2×Q8—1462no—
246C2×Q8—1462no—
247C2×Q8—1461no—
248C2×Q8—1461no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4C22⋊D7311yescharacteristic
252C2×D4C22×D7311yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—1461no—
256C22×C4—1461no—
257C22×C4C22×D7311yescharacteristic
258C22×C4C22×D7311yescharacteristic
259SD16—2921no—
260SD16—2921no—
261SD16—1462no—
262M16—2921no—
263C2×C8—2921no—
264C2×C8—731no—
265C2×C8—731no—
266C2×C8—731no—
267C2×C8—731no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—731no—
272C4⋊C4—1461no—
273C4⋊C4—1461no—
274C4⋊C4—1461no—
275C4⋊C4—1461no—
276C4⋊C4—1461no—
277C4⋊C4C22⋊D7311yescharacteristic
278C4⋊C4C22×D7311yescharacteristic
279C4⋊C4C22×D7311yescharacteristic
280C4⋊C4C22×D7311yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—1461no—
286C22⋊C4—1461no—
287C22⋊C4C22⋊D7311yescharacteristic
288C22⋊C4C22⋊D7311yescharacteristic
289C42—21no—
290C42—1461no—
291C42C22×D7311yescharacteristic
292C23—21no—
293C23C2×C22⋊D7311yescharacteristic
294C23C2×C22⋊D7311yescharacteristic
295Q8—2922no—
296Q8—2922no—
297Q8—732no—
298Q8—1461no—
299Q8—1461no—
300Q8—1461no—
301Q8—1461no—
302Q8—1461no—
303D4—22no—
304D4—21no—
305D4—21no—
306D4—42no—
307D4—81no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—2922no—
318C2×C4—2922no—
319C2×C4—1461no—
320C2×C4—1461no—
321C2×C4—1461no—
322C2×C4—1461no—
323C2×C4C2×C22⋊D7311yescharacteristic
324C2×C4C2×C22⋊D7311yescharacteristic
325C2×C4C2×C22⋊D7311yescharacteristic
326C2×C4C2×C22⋊D7311yescharacteristic
327C2×C4C23×D7311yescharacteristic
328C8—1461no—
329C8—1461no—
330C8—1461no—
331C8—1461no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22#1455662112yes—
341C22C22×C22⋊D7311yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—2921no—
350C4—2921no—
351C4—2921no—
352C4—1462no—
353C4#41×D7311yescharacteristic
354C4#1455663711yescharacteristic
355C2—22no—
356C2—41no—
357C2—81no—
358C2#1798922511yescharacteristic
359C2C2×#1455662111yescharacteristic
360C2#1798939811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#553×C73C2
socleC22×C73C22×D4
hypercenter#553D73
hypocenterC73#3320
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. D4×Dic146C2semidirect
2. #17988957C2semidirect
3. #17988928C2semidirect
4. #17988922C2semidirect
5. #17988891C2semidirect
6. #17988831C2semidirect
7. #17988814C2semidirect
8. #17988792C2semidirect
9. #17988725C2semidirect
10. #17988725C2semidirect
11. #17988687C2semidirect
12. #17988659C2semidirect
13. #17988595C2semidirect
14. C2×#14556514C2semidirect
181. C73#3320semidirect