Finite Group Databasebeta

← #22622044

Subgroups — #22622044

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
1#17989294C211yesmaximal, characteristic, complemented
2#17989246C211yesmaximal, characteristic
3#17988947C211yesmaximal, characteristic, complemented
4#17988918C211yesmaximal, characteristic, complemented
5#17988906C211yesmaximal, characteristic, complemented
6#17988873C211yesmaximal, characteristic, complemented
7#17988845C211yesmaximal, characteristic, complemented
8#17988816C211yesmaximal, characteristic, complemented
9#17988810C211yesmaximal, characteristic, complemented
10#17988751C211yesmaximal, characteristic, complemented
11#17988745C211yesmaximal, characteristic, complemented
12#17988695C211yesmaximal, characteristic, complemented
13#17988589C211yesmaximal, characteristic, complemented
14C2×#14556516C211yesmaximal, characteristic, complemented
15#435×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C22×Dic146C2211yescharacteristic
18C2×Dic292C2211yescharacteristic
19C2×Dic292C2211yescharacteristic
20C2×#11924017C2211yescharacteristic
21#14556591C2211yescharacteristic
22#14556582—21no—
23#14556579C2211yescharacteristic
24#14556577—21no—
25#14556570C2211yescharacteristic
26#14556570C2211yescharacteristic
27#14556570C2211yescharacteristic
28#14556569—21no—
29#14556568—21no—
30#14556568—21no—
31#14556565C2211yescharacteristic
32#14556563—21no—
33C4×Dic146C2211yescharacteristic
34C4×Dic146C2211yescharacteristic
35D4×Dic73—21no—
36#14556551—21no—
37C2×C4⋊Dic73C2211yescharacteristic
38C2×C4⋊Dic73C2211yescharacteristic
39#14556523C2211yescharacteristic
40#14556523C2211yescharacteristic
41#14556523C2211yescharacteristic
42#14556516C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556516C2211yescharacteristic
45#14556516C2211yescharacteristic
46#14556516C2211yescharacteristic
47#14556516C2211yescharacteristic
48#14556516C2211yescharacteristic
49#14556513C2211yescharacteristic
50#14556513C2211yescharacteristic
51#14556513C2211yescharacteristic
52C2×M16×C73C2211yescharacteristic
53C22×C8×C73C2211yescharacteristic
54C4×D4×C73C2211yescharacteristic
55C4⋊C8×C73C2211yescharacteristic
56C22⋊C8×C73C2211yescharacteristic
57C22⋊C8×C73C2211yescharacteristic
58#97×C73C2211yescharacteristic
59#11924028—22no—
60#11924028—41no—
61C2×Dic146—22no—
62C2×Dic146—21no—
63C2×Dic146—21no—
64C2×Dic146—41no—
65C2×Dic146C2311yescharacteristic
66C2×Dic146C2311yescharacteristic
67C2×Dic146C2311yescharacteristic
68C2×D292C2311yescharacteristic
69C2×C22⋊D73—21no—
70C2×C22⋊D73—21no—
71C22×Dic73—21no—
72C22×Dic73—21no—
73C22×Dic73—21no—
74C2×C4×D73—21no—
75Dic292—22no—
76Dic292—41no—
77#11924017—41no—
78C4⋊Dic73—21no—
79C4⋊Dic73—21no—
80C4⋊Dic73—21no—
81C4⋊Dic73C2311yescharacteristic
82C4⋊Dic73C2311yescharacteristic
83C4⋊Dic73C2311yescharacteristic
84C4⋊Dic73C2311yescharacteristic
85#11924007—21no—
86#11924007—21no—
87#11924007—21no—
88#11924007—21no—
89#11924007—21no—
90C22⋊Dic73—21no—
91C22⋊Dic73—21no—
92C22⋊Dic73—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005—21no—
96C4×Dic73—21no—
97C4×Dic73—21no—
98C2×D4×C73D411yescharacteristic
99C22×C4×C73C2311yescharacteristic
100C22×C4×C73C2311yescharacteristic
101M16×C73—41no—
102C2×C8×C73—41no—
103C2×C8×C73C2311yescharacteristic
104C2×C8×C73C2311yescharacteristic
105C2×C8×C73C2311yescharacteristic
106C2×C8×C73C2311yescharacteristic
107C4⋊C4×C73D411yescharacteristic
108C22⋊C4×C73D411yescharacteristic
109C22⋊C4×C73D411yescharacteristic
110C42×C73C2311yescharacteristic
111C23×C73C2×D411yescharacteristic
112C23×C73C2×D411yescharacteristic
113C22×D73—21no—
114D4×C73—22no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73C2×D411yescharacteristic
120C2×C4×C73C2×D411yescharacteristic
121C2×C4×C73C2×D411yescharacteristic
122C2×C4×C73C2×D411yescharacteristic
123C2×C4×C73C2411yescharacteristic
124C22⋊D73—42no—
125C22⋊D73—42no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—42no—
134C2×Dic73—81no—
135C2×Dic73—81no—
136D292—21no—
137D292—21no—
138C4×D73—42no—
139Dic146—21no—
140Dic146—21no—
141Dic146—21no—
142Dic146—21no—
143Dic146—21no—
144Dic146—42no—
145Dic146—81no—
146Dic146#4112yes—
147C8×C73—21no—
148C8×C73—21no—
149C8×C73—21no—
150C8×C73—21no—
151C22×C73—21no—
152C22×C73—21no—
153C22×C73—21no—
154C22×C73—21no—
155C22×C73—21no—
156C22×C73#13712yes—
157C22×C73C22×D411yescharacteristic
158C2×D73—41no—
159C2×D73—41no—
160C2×D73—41no—
161C4×C73—21no—
162C4×C73—21no—
163C4×C73—21no—
164C4×C73—21no—
165C4×C73C2×#4111yescharacteristic
166C4×C73H(5,𝔽2)11yescharacteristic
167Dic73—22no—
168Dic73—41no—
169Dic73—41no—
170Dic73—41no—
171Dic73—41no—
172Dic73—41no—
173Dic73—41no—
174C2×C73—22no—
175C2×C73—41no—
176C2×C73#54611yescharacteristic
177C2×C73C2×#13711yescharacteristic
178C2×C73#57711yescharacteristic
179D73—81no—
180#3316—731nomaximal, Sylow
181C73#331611yescharacteristic, complemented, Sylow
182#554—731no—
183#548—731no—
184#489—731no—
185#483—731no—
186#481—731no—
187#475—731no—
188#470—731no—
189#465—731no—
190#464—731no—
191#452—731no—
192#451—731no—
193#441—731no—
194#435D7311yescharacteristic, complemented
195#417—731no—
196C2×#103—731no—
197C2×#41—731no—
198C22×Q8—731no—
199C2×Q16—731no—
200C2×Q16—731no—
201C2×SD16—731no—
202C2×M16C2×D7311yescharacteristic
203C22×C8C2×D7311yescharacteristic
204C4⋊Q8—731no—
205#125—1461no—
206#124—731no—
207#124—1461no—
208C22⋊Q8—731no—
209C22⋊Q8—731no—
210C22⋊Q8—731no—
211C22⋊Q8—1461no—
212C22⋊Q8—1461no—
213C22⋊Q8—1461no—
214#121—731no—
215#121—1461no—
216C4×Q8—731no—
217C4×Q8—731no—
218C4×D4—1461no—
219C4×D4—1461no—
220C4×D4C2×D7311yescharacteristic
221C2×C4⋊C4—731no—
222C2×C4⋊C4—731no—
223#106—731no—
224#106—731no—
225#106—731no—
226C4⋊C8C2×D7311yescharacteristic
227#103—731no—
228#103—731no—
229#103—731no—
230#103—731no—
231#103—731no—
232#103—731no—
233#103—731no—
234#102—731no—
235#102—731no—
236#102—731no—
237C22⋊C8C2×D7311yescharacteristic
238C22⋊C8C2×D7311yescharacteristic
239#97C2×D7311yescharacteristic
240#41—2921no—
241#41—1462no—
242C2×Q8—2921no—
243C2×Q8—731no—
244C2×Q8—731no—
245C2×Q8—731no—
246C2×Q8—1462no—
247C2×Q8—1461no—
248C2×Q8—1461no—
249C2×D4—731no—
250C2×D4—1461no—
251C2×D4—1461no—
252C2×D4D29211yescharacteristic
253C22×C4—1461no—
254C22×C4—1461no—
255C22×C4—1461no—
256C22×C4—1461no—
257C22×C4C22×D7311yescharacteristic
258C22×C4C22×D7311yescharacteristic
259Q16—2921no—
260Q16—1462no—
261SD16—2921no—
262M16—41no—
263C2×C8—41no—
264C2×C8C22×D7311yescharacteristic
265C2×C8C22×D7311yescharacteristic
266C2×C8C22×D7311yescharacteristic
267C2×C8C22×D7311yescharacteristic
268C4⋊C4—731no—
269C4⋊C4—731no—
270C4⋊C4—731no—
271C4⋊C4—731no—
272C4⋊C4—1461no—
273C4⋊C4—1461no—
274C4⋊C4—1461no—
275C4⋊C4—1461no—
276C4⋊C4—1461no—
277C4⋊C4—1461no—
278C4⋊C4—1461no—
279C4⋊C4—1461no—
280C4⋊C4D29211yescharacteristic
281C22⋊C4—1461no—
282C22⋊C4—1461no—
283C22⋊C4—1461no—
284C22⋊C4—1461no—
285C22⋊C4—1461no—
286C22⋊C4—1461no—
287C22⋊C4D29211yescharacteristic
288C22⋊C4D29211yescharacteristic
289C42—1461no—
290C42—1461no—
291C42C22×D7311yescharacteristic
292C23—1461no—
293C23C2×D29211yescharacteristic
294C23C2×D29211yescharacteristic
295Q8—2922no—
296Q8—5841no—
297Q8—732no—
298Q8—1461no—
299Q8—1461no—
300Q8—1461no—
301Q8—1461no—
302Q8—1461no—
303D4—22no—
304D4—2922no—
305D4—2922no—
306D4—1461no—
307D4—1461no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—2922no—
313C2×C4—2922no—
314C2×C4—5841no—
315C2×C4—5841no—
316C2×C4—1461no—
317C2×C4—1461no—
318C2×C4—1461no—
319C2×C4—1461no—
320C2×C4—1461no—
321C2×C4—1461no—
322C2×C4—1461no—
323C2×C4C2×D29211yescharacteristic
324C2×C4C2×D29211yescharacteristic
325C2×C4C2×D29211yescharacteristic
326C2×C4C2×D29211yescharacteristic
327C2×C4C23×D7311yescharacteristic
328C8—21no—
329C8—21no—
330C8—21no—
331C8—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—2921no—
338C22—2921no—
339C22—2921no—
340C22#1455662412yes—
341C22C22×D29211yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—2921no—
347C4—2921no—
348C4—2921no—
349C4—2921no—
350C4—2921no—
351C4—2921no—
352C4—1462no—
353C4#41×D7311yescharacteristic
354C4#1455663611yescharacteristic
355C2—22no—
356C2—41no—
357C2—5841no—
358C2#1798923211yescharacteristic
359C2C2×#1455662411yescharacteristic
360C2#1798939911yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#435×C73C2
socleC22×C73C22×D4
hypercenter#435D73
hypocenterC73#3316
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #17989294C2semidirect
3. #17988947C2semidirect
4. #17988918C2semidirect
5. #17988906C2semidirect
6. #17988873C2semidirect
7. #17988845C2semidirect
8. #17988816C2semidirect
9. #17988810C2semidirect
10. #17988751C2semidirect
11. #17988745C2semidirect
12. #17988695C2semidirect
13. #17988589C2semidirect
14. C2×#14556516C2semidirect
15. #435×C73C2semidirect
181. C73#3316semidirect
194. #435D73semidirect