Finite Group Databasebeta

← #22622000

Subgroups — #22622000

Order 9344.

380 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989305C211yesmaximal, characteristic, complemented
2#17989243C211yesmaximal, characteristic
3#17988945C211yesmaximal, characteristic, complemented
4#17988931C211yesmaximal, characteristic, complemented
5#17988881C211yesmaximal, characteristic, complemented
6#17988831C211yesmaximal, characteristic, complemented
7#17988829C211yesmaximal, characteristic, complemented
8#17988808C211yesmaximal, characteristic, complemented
9#17988750C211yesmaximal, characteristic, complemented
10#17988745C211yesmaximal, characteristic, complemented
11#17988693C211yesmaximal, characteristic, complemented
12#17988661C211yesmaximal, characteristic, complemented
13#17988595C211yesmaximal, characteristic, complemented
14#17988580C211yesmaximal, characteristic, complemented
15#482×C73C211yesmaximal, characteristic, complemented
16C2×#11924027C2211yescharacteristic
17C22×Dic146C2211yescharacteristic
18C2×Dic292C2211yescharacteristic
19C2×Dic292C2211yescharacteristic
20C2×#11924016C2211yescharacteristic
21C2×#11924012C2211yescharacteristic
22C2×C8×D73C2211yescharacteristic
23#14556590C2211yescharacteristic
24#14556585—21no—
25#14556584—21no—
26#14556578C2211yescharacteristic
27#14556577—21no—
28#14556577—21no—
29#14556571C2211yescharacteristic
30#14556571C2211yescharacteristic
31#14556570C2211yescharacteristic
32#14556568—21no—
33#14556563—21no—
34C4×Dic146—21no—
35#14556556C2211yescharacteristic
36#14556556C2211yescharacteristic
37D4×Dic73—21no—
38C4×C22⋊D73C2211yescharacteristic
39#14556549C2211yescharacteristic
40#14556524C2211yescharacteristic
41#14556520C2211yescharacteristic
42#14556516C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556514C2211yescharacteristic
45#14556514C2211yescharacteristic
46#14556514C2211yescharacteristic
47#14556514C2211yescharacteristic
48#14556514C2211yescharacteristic
49#14556512C2211yescharacteristic
50#14556503C2211yescharacteristic
51#14556501C2211yescharacteristic
52#121×C73C2211yescharacteristic
53#117×C73C2211yescharacteristic
54#107×C73C2211yescharacteristic
55#106×C73C2211yescharacteristic
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59#11924027—22no—
60#11924027—41no—
61C2×Dic146—22no—
62C2×Dic146—21no—
63C2×Dic146—21no—
64C2×Dic146—41no—
65C2×Dic146C2311yescharacteristic
66C2×Dic146C2311yescharacteristic
67C2×Dic146C2311yescharacteristic
68C2×C22⋊D73—21no—
69C2×C22⋊D73D411yescharacteristic
70C22×Dic73—21no—
71C22×Dic73—21no—
72C2×C4×D73C2311yescharacteristic
73Dic292—22no—
74Dic292—41no—
75#11924016—41no—
76#11924012—41no—
77C2×#10596831C2311yescharacteristic
78C2×#10596831C2311yescharacteristic
79C8×D73—41no—
80C4⋊Dic73—21no—
81C4⋊Dic73—21no—
82C4⋊Dic73C2311yescharacteristic
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86#11924007—21no—
87#11924007D411yescharacteristic
88C22⋊Dic73—21no—
89C22⋊Dic73—21no—
90C22⋊Dic73—21no—
91C22⋊Dic73D411yescharacteristic
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005D411yescharacteristic
96C4×Dic73—21no—
97C4×Dic73—21no—
98C4×Dic73—21no—
99C4×Dic73C2311yescharacteristic
100C2×D4×C73—21no—
101C2×D4×C73C2311yescharacteristic
102C22×C4×C73C2311yescharacteristic
103C2×C8×C73C2311yescharacteristic
104C2×C8×C73C2311yescharacteristic
105C4⋊C4×C73C2311yescharacteristic
106C4⋊C4×C73C2311yescharacteristic
107C4⋊C4×C73C2311yescharacteristic
108C22⋊C4×C73—21no—
109C22⋊C4×C73—21no—
110C42×C73—21no—
111C23×C73—21no—
112C23×C73C2×D411yescharacteristic
113C22×D73C2×D411yescharacteristic
114D4×C73—21no—
115D4×C73—21no—
116D4×C73—42no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73C2×D411yescharacteristic
123C2×C4×C73C2411yescharacteristic
124C22⋊D73—41no—
125C22⋊D73—42no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73—42no—
131C2×Dic73—42no—
132C2×Dic73C2×D411yescharacteristic
133C2×Dic73C2×D411yescharacteristic
134C2×Dic73C2×D411yescharacteristic
135C4×D73—21no—
136C4×D73—21no—
137Dic146—21no—
138Dic146—21no—
139Dic146—21no—
140Dic146—21no—
141Dic146—21no—
142Dic146—42no—
143Dic146—42no—
144Dic146#4112yes—
145C8×C73—21no—
146C8×C73—21no—
147#10596831—21no—
148#10596831—21no—
149C22×C73—21no—
150C22×C73—21no—
151C22×C73—21no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73—41no—
155C22×C73C22×D411yescharacteristic
156C2×D73—21no—
157C2×D73—21no—
158C2×D73—21no—
159C4×C73—21no—
160C4×C73—41no—
161C4×C73—41no—
162C4×C73—41no—
163C4×C73C2×#4111yescharacteristic
164C4×C73H(5,𝔽2)11yescharacteristic
165Dic73—22no—
166Dic73—21no—
167Dic73—21no—
168Dic73—21no—
169Dic73—41no—
170Dic73—41no—
171Dic73—41no—
172C2×C73—41no—
173C2×C73—81no—
174C2×C73#54611yescharacteristic
175C2×C73#57511yescharacteristic
176C2×C73#57811yescharacteristic
177D73—41no—
178#3313—731nomaximal, Sylow
179C73#331311yescharacteristic, complemented, Sylow
180#556—731no—
181#548—731no—
182#489—731no—
183#485—731no—
184#482D7311yescharacteristic, complemented
185#477—731no—
186#468—731no—
187#467—731no—
188#464—731no—
189#452—731no—
190#451—731no—
191#441—731no—
192#435—731no—
193#419—731no—
194#416—731no—
195C2×#41—731no—
196C22×Q8—731no—
197C2×Q16—731no—
198C2×Q16—731no—
199C2×SD16—731no—
200C2×M16—731no—
201C22×C8—731no—
202C4⋊Q8—731no—
203#126—1461no—
204#126—1461no—
205#124—731no—
206#124—1461no—
207#124—1461no—
208C22⋊Q8—731no—
209C22⋊Q8—731no—
210C22⋊Q8—731no—
211C22⋊Q8—1461no—
212#121—1461no—
213#121C2×D7311yescharacteristic
214C4×Q8—731no—
215C4×Q8—731no—
216C4×Q8—1461no—
217C4×D4—731no—
218C4×D4—1461no—
219#117—731no—
220#117C2×D7311yescharacteristic
221#107—731no—
222#107C2×D7311yescharacteristic
223#106C2×D7311yescharacteristic
224C4⋊C8—731no—
225#103—731no—
226#103—731no—
227#103—731no—
228#103—731no—
229#103—731no—
230#103—731no—
231#103—731no—
232#102—731no—
233#102C2×D7311yescharacteristic
234#102C2×D7311yescharacteristic
235C22⋊C8—731no—
236C22⋊C8C2×D7311yescharacteristic
237#97—731no—
238#41—2921no—
239#41—1462no—
240C2×Q8—2921no—
241C2×Q8—731no—
242C2×Q8—731no—
243C2×Q8—731no—
244C2×Q8—1462no—
245C2×Q8—1461no—
246C2×Q8—1461no—
247C2×D4—21no—
248C2×D4—731no—
249C2×D4—1461no—
250C2×D4C22×D7311yescharacteristic
251C22×C4—731no—
252C22×C4—1461no—
253C22×C4—1461no—
254C22×C4C22×D7311yescharacteristic
255Q16—2921no—
256Q16—1462no—
257SD16—2921no—
258M16—2921no—
259C2×C8—2921no—
260C2×C8—731no—
261C2×C8—731no—
262C2×C8C22×D7311yescharacteristic
263C2×C8C22×D7311yescharacteristic
264C4⋊C4—731no—
265C4⋊C4—731no—
266C4⋊C4—1461no—
267C4⋊C4—1461no—
268C4⋊C4—1461no—
269C4⋊C4—1461no—
270C4⋊C4—1461no—
271C4⋊C4—1461no—
272C4⋊C4C22×D7311yescharacteristic
273C4⋊C4C22×D7311yescharacteristic
274C4⋊C4C22×D7311yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—731no—
278C22⋊C4—731no—
279C22⋊C4—1461no—
280C22⋊C4—1461no—
281C22⋊C4—1461no—
282C22⋊C4—1461no—
283C22⋊C4—1461no—
284C22⋊C4—1461no—
285C42—21no—
286C42—731no—
287C42—1461no—
288C42—1461no—
289C42—1461no—
290C23—21no—
291C23—731no—
292C23D4×D7311yescharacteristic
293Q8—2922no—
294Q8—2922no—
295Q8—732no—
296Q8—1461no—
297Q8—1461no—
298Q8—1461no—
299Q8—1461no—
300Q8—1461no—
301D4—21no—
302D4—21no—
303D4—42no—
304D4—2921no—
305D4—2922no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—2922no—
312C2×C4—2922no—
313C2×C4—731no—
314C2×C4—731no—
315C2×C4—731no—
316C2×C4—1461no—
317C2×C4—1461no—
318C2×C4—1461no—
319C2×C4—1461no—
320C2×C4—1461no—
321C2×C4—1461no—
322C2×C4D4×D7311yescharacteristic
323C2×C4C23×D7311yescharacteristic
324C8—21no—
325C8—21no—
326C8—1461no—
327C8—1461no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—1461no—
335C22—1461no—
336C22—1461no—
337C22C2×D4×D7311yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—2921no—
343C4—2921no—
344C4—2921no—
345C4—1461no—
346C4—1461no—
347C4—1461no—
348C4—1462no—
349C4#41×D7311yescharacteristic
350C4#1455663711yescharacteristic
351C2—41no—
352C2—81no—
353C2—2921no—
354C2#1798922911yescharacteristic
355C2#1798938311yescharacteristic
356C2#1798940111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#482×C73C2
socleC22×C73C22×D4
hypercenter#482D73
hypocenterC73#3313
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #17989305C2semidirect
3. #17988945C2semidirect
4. #17988931C2semidirect
5. #17988881C2semidirect
6. #17988831C2semidirect
7. #17988829C2semidirect
8. #17988808C2semidirect
9. #17988750C2semidirect
10. #17988745C2semidirect
11. #17988693C2semidirect
12. #17988661C2semidirect
13. #17988595C2semidirect
14. #17988580C2semidirect
15. #482×C73C2semidirect
179. C73#3313semidirect
184. #482D73semidirect