Finite Group Databasebeta

← #22621922

Subgroups — #22621922

Order 9344.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989241C211yesmaximal, characteristic, complemented
2#17988946C211yesmaximal, characteristic, complemented
3#17988920C211yesmaximal, characteristic, complemented
4#17988898C211yesmaximal, characteristic, complemented
5#17988882C211yesmaximal, characteristic, complemented
6#17988835C211yesmaximal, characteristic, complemented
7#17988821C211yesmaximal, characteristic, complemented
8#17988799C211yesmaximal, characteristic, complemented
9#17988732C211yesmaximal, characteristic, complemented
10#17988726C211yesmaximal, characteristic, complemented
11#17988685C211yesmaximal, characteristic, complemented
12#17988659C211yesmaximal, characteristic, complemented
13#17988588C211yesmaximal, characteristic, complemented
14C2×#14556515C211yesmaximal, characteristic, complemented
15#548×C73C211yesmaximal, characteristic, complemented
16C2×#11924027—21no—
17C2×#11924015C2211yescharacteristic
18C2×#11924015C2211yescharacteristic
19C2×#11924013C2211yescharacteristic
20C2×#11924012C2211yescharacteristic
21C22×#10596831C2211yescharacteristic
22#14556591C2211yescharacteristic
23#14556575—21no—
24#14556575—21no—
25#14556571—21no—
26#14556565C2211yescharacteristic
27#14556565C2211yescharacteristic
28C4×D292C2211yescharacteristic
29C2×C4⋊Dic73C2211yescharacteristic
30C2×C4⋊Dic73C2211yescharacteristic
31#14556524C2211yescharacteristic
32#14556524C2211yescharacteristic
33#14556524C2211yescharacteristic
34C4⋊#10596831C2211yescharacteristic
35#14556515C2211yescharacteristic
36#14556515C2211yescharacteristic
37#14556515C2211yescharacteristic
38#14556515C2211yescharacteristic
39#14556515C2211yescharacteristic
40#14556515C2211yescharacteristic
41#14556512C2211yescharacteristic
42#14556512C2211yescharacteristic
43#14556512C2211yescharacteristic
44#14556511C2211yescharacteristic
45C22⋊#10596831C2211yescharacteristic
46C22⋊#10596831C2211yescharacteristic
47#14556502C2211yescharacteristic
48C2×#41×C73C2211yescharacteristic
49C22×Q8×C73C2211yescharacteristic
50#124×C73—21no—
51#124×C73C2211yescharacteristic
52C22⋊Q8×C73—21no—
53C22⋊Q8×C73C2211yescharacteristic
54#121×C73—21no—
55#121×C73C2211yescharacteristic
56C4×Q8×C73C2211yescharacteristic
57C4×D4×C73—21no—
58C4×D4×C73C2211yescharacteristic
59#11924027—44no—
60C2×Dic146—21no—
61C2×D292C2311yescharacteristic
62C2×C22⋊D73—21no—
63C2×C22⋊D73—21no—
64C22×Dic73—21no—
65C22×Dic73—21no—
66C2×C4×D73—21no—
67#11924015—22no—
68#11924015—41no—
69#11924013—41no—
70#11924012—41no—
71C2×#10596831—41no—
72C2×#10596831C2311yescharacteristic
73C2×#10596831C2311yescharacteristic
74C2×#10596831C2311yescharacteristic
75C2×#10596831C2311yescharacteristic
76C4⋊Dic73—21no—
77C4⋊Dic73—21no—
78C4⋊Dic73—21no—
79C4⋊Dic73C2311yescharacteristic
80C4⋊Dic73C2311yescharacteristic
81C4⋊Dic73C2311yescharacteristic
82#11924005—21no—
83#11924005—21no—
84#11924005—21no—
85#41×C73—22no—
86#41×C73—41no—
87C2×Q8×C73—21no—
88C2×Q8×C73—22no—
89C2×Q8×C73—41no—
90C2×Q8×C73C2311yescharacteristic
91C2×Q8×C73C2311yescharacteristic
92C2×D4×C73—21no—
93C2×D4×C73—21no—
94C2×D4×C73D411yescharacteristic
95C2×D4×C73C2311yescharacteristic
96C22×C4×C73—21no—
97C22×C4×C73—21no—
98C22×C4×C73C2311yescharacteristic
99C22×C4×C73C2311yescharacteristic
100C4⋊C4×C73—21no—
101C4⋊C4×C73—21no—
102C4⋊C4×C73D411yescharacteristic
103C4⋊C4×C73C2311yescharacteristic
104C22⋊C4×C73—21no—
105C22⋊C4×C73—21no—
106C22⋊C4×C73—21no—
107C22⋊C4×C73—21no—
108C22⋊C4×C73D411yescharacteristic
109C22⋊C4×C73D411yescharacteristic
110C42×C73—21no—
111C42×C73C2311yescharacteristic
112C23×C73—21no—
113C23×C73C2×D411yescharacteristic
114C23×C73C2×D411yescharacteristic
115C22×D73—21no—
116Q8×C73—21no—
117Q8×C73—21no—
118Q8×C73—21no—
119Q8×C73—42no—
120Q8×C73#4112yescomplemented
121D4×C73—22no—
122D4×C73—21no—
123D4×C73—21no—
124D4×C73—42no—
125D4×C73—42no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—42no—
134C2×C4×C73—42no—
135C2×C4×C73C2×D411yescharacteristic
136C2×C4×C73C2×D411yescharacteristic
137C2×C4×C73C2×D411yescharacteristic
138C2×C4×C73C2×D411yescharacteristic
139C2×C4×C73C2411yescharacteristic
140C22⋊D73—42no—
141C22⋊D73—42no—
142C2×Dic73—21no—
143C2×Dic73—21no—
144C2×Dic73—21no—
145C2×Dic73—42no—
146C2×Dic73—42no—
147D292—21no—
148D292—21no—
149C4×D73—42no—
150Dic146—42no—
151#10596831—21no—
152#10596831—21no—
153#10596831—21no—
154#10596831—21no—
155C22×C73—21no—
156C22×C73—21no—
157C22×C73—21no—
158C22×C73—21no—
159C22×C73—21no—
160C22×C73—41no—
161C22×C73—41no—
162C22×C73—41no—
163C22×C73AGL(1,ℤ/8)12yes—
164C22×C73C22×D411yescharacteristic
165C2×D73—41no—
166C2×D73—41no—
167C2×D73—41no—
168C4×C73—21no—
169C4×C73—21no—
170C4×C73—22no—
171C4×C73—21no—
172C4×C73—21no—
173C4×C73—41no—
174C4×C73—41no—
175C4×C73C2×#4111yescharacteristic
176C4×C73H(5,𝔽2)11yescharacteristic
177Dic73—41no—
178Dic73—41no—
179Dic73—41no—
180C2×C73—22no—
181C2×C73—41no—
182C2×C73—81no—
183C2×C73#54611yescharacteristic
184C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
185C2×C73#57811yescharacteristic
186D73—81no—
187#3308—731nomaximal, Sylow
188C73#330811yescharacteristic, complemented, Sylow
189#548D7311yescharacteristic, complemented
190#547—731no—
191#489—731no—
192#484—731no—
193#480—731no—
194#477—731no—
195#468—731no—
196#466—731no—
197#463—731no—
198#449—731no—
199#448—731no—
200#440—731no—
201#435—731no—
202#417—731no—
203C2×#103—731no—
204C2×#41—1461no—
205C2×#41C2×D7311yescharacteristic
206C22×Q8C2×D7311yescharacteristic
207C2×SD16—731no—
208C2×SD16—731no—
209C2×D8—731no—
210C2×M16—731no—
211C22×C8—731no—
212C4⋊Q8—731no—
213#124—21no—
214#124C2×D7311yescharacteristic
215#123—1461no—
216#123—1461no—
217C22⋊Q8—21no—
218C22⋊Q8—1461no—
219C22⋊Q8C2×D7311yescharacteristic
220#121—21no—
221#121—731no—
222#121—731no—
223#121C2×D7311yescharacteristic
224C4×Q8C2×D7311yescharacteristic
225C4×D4—21no—
226C4×D4—731no—
227C4×D4C2×D7311yescharacteristic
228C2×C4⋊C4—731no—
229C2×C4⋊C4—731no—
230#107—731no—
231#107—731no—
232#107—731no—
233C4⋊C8—731no—
234#103—731no—
235#103—731no—
236#103—731no—
237#103—731no—
238#103—731no—
239#103—731no—
240#102—731no—
241#102—731no—
242#102—731no—
243#102—731no—
244C22⋊C8—731no—
245C22⋊C8—731no—
246#97—731no—
247#41—22no—
248#41—41no—
249#41—2924no—
250C2×Q8—21no—
251C2×Q8—22no—
252C2×Q8—41no—
253C2×Q8—1461no—
254C2×Q8C22×D7311yescharacteristic
255C2×Q8C22×D7311yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—731no—
259C2×D4—1461no—
260C2×D4—1461no—
261C2×D4C22⋊D7311yescharacteristic
262C2×D4C22×D7311yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—1461no—
266C22×C4—1461no—
267C22×C4—1461no—
268C22×C4C22×D7311yescharacteristic
269C22×C4C22×D7311yescharacteristic
270SD16—2921no—
271SD16—1462no—
272D8—2921no—
273M16—2921no—
274C2×C8—2921no—
275C2×C8—731no—
276C2×C8—731no—
277C2×C8—731no—
278C2×C8—731no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—731no—
282C4⋊C4—731no—
283C4⋊C4—731no—
284C4⋊C4—1461no—
285C4⋊C4—1461no—
286C4⋊C4—1461no—
287C4⋊C4C22⋊D7311yescharacteristic
288C4⋊C4C22×D7311yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—1461no—
294C22⋊C4—1461no—
295C22⋊C4—1461no—
296C22⋊C4C22⋊D7311yescharacteristic
297C22⋊C4C22⋊D7311yescharacteristic
298C42—21no—
299C42C22×D7311yescharacteristic
300C23—21no—
301C23—1461no—
302C23C2×C22⋊D7311yescharacteristic
303C23C2×C22⋊D7311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—2922no—
309Q8#1192402712yescomplemented
310D4—22no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—42no—
315D4—2922no—
316D4—2922no—
317D4—1461no—
318D4—1461no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—2922no—
329C2×C4—2922no—
330C2×C4—2922no—
331C2×C4—1461no—
332C2×C4—1461no—
333C2×C4—1461no—
334C2×C4C2×C22⋊D7311yescharacteristic
335C2×C4C2×C22⋊D7311yescharacteristic
336C2×C4C2×C22⋊D7311yescharacteristic
337C2×C4C2×C22⋊D7311yescharacteristic
338C2×C4C23×D7311yescharacteristic
339C8—1461no—
340C8—1461no—
341C8—1461no—
342C8—1461no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—2921no—
352C22—2921no—
353C22—2921no—
354C22#1455661612yes—
355C22C22×C22⋊D7311yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—22no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—2921no—
364C4—2921no—
365C4—2921no—
366C4C2×#1192402711yescharacteristic
367C4#1455663611yescharacteristic
368C2—22no—
369C2—41no—
370C2—81no—
371C2—5841no—
372C2#1798923111yescharacteristic
373C2C2×#1455661611yescharacteristic
374C2#1798940211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#548×C73C2
socleC22×C73C22×D4
hypercenter#548D73
hypocenterC73#3308
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #17989241C2semidirect
2. #17988946C2semidirect
3. #17988920C2semidirect
4. #17988898C2semidirect
5. #17988882C2semidirect
6. #17988835C2semidirect
7. #17988821C2semidirect
8. #17988799C2semidirect
9. #17988732C2semidirect
10. #17988726C2semidirect
11. #17988685C2semidirect
12. #17988659C2semidirect
13. #17988588C2semidirect
14. C2×#14556515C2semidirect
15. #548×C73C2semidirect
120. Q8×C73#41semidirect
188. C73#3308semidirect
189. #548D73semidirect
309. Q8#11924027semidirect