Finite Group Databasebeta

← #22621937

Subgroups — #22621937

Order 9344.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989283C211yesmaximal, characteristic, complemented
2#17988951C211yesmaximal, characteristic, complemented
3#17988908C211yesmaximal, characteristic, complemented
4#17988898C211yesmaximal, characteristic, complemented
5#17988894C211yesmaximal, characteristic, complemented
6#17988838C211yesmaximal, characteristic, complemented
7#17988821C211yesmaximal, characteristic, complemented
8#17988779C211yesmaximal, characteristic, complemented
9#17988732C211yesmaximal, characteristic, complemented
10#17988732C211yesmaximal, characteristic, complemented
11#17988685C211yesmaximal, characteristic, complemented
12#17988659C211yesmaximal, characteristic, complemented
13#17988588C211yesmaximal, characteristic, complemented
14#17988583C211yesmaximal, characteristic, complemented
15#550×C73C211yesmaximal, characteristic, complemented
16C2×#11924015C2211yescharacteristic
17C2×#11924013C2211yescharacteristic
18C2×#11924013C2211yescharacteristic
19C2×#11924012C2211yescharacteristic
20C22×#10596831C2211yescharacteristic
21#14556586—21no—
22#14556583C2211yescharacteristic
23#14556573—21no—
24#14556565C2211yescharacteristic
25#14556565C2211yescharacteristic
26#14556563—21no—
27C4×D292C2211yescharacteristic
28#14556551—21no—
29#14556550C2211yescharacteristic
30C2×C4⋊Dic73C2211yescharacteristic
31#14556524C2211yescharacteristic
32#14556524C2211yescharacteristic
33#14556522C2211yescharacteristic
34C4⋊#10596831C2211yescharacteristic
35#14556515C2211yescharacteristic
36#14556515C2211yescharacteristic
37#14556515C2211yescharacteristic
38#14556512C2211yescharacteristic
39#14556512C2211yescharacteristic
40#14556512C2211yescharacteristic
41#14556512C2211yescharacteristic
42#14556512C2211yescharacteristic
43#14556512C2211yescharacteristic
44#14556511C2211yescharacteristic
45C22⋊#10596831C2211yescharacteristic
46C22⋊#10596831C2211yescharacteristic
47#14556502C2211yescharacteristic
48C2×#41×C73C2211yescharacteristic
49C2×#41×C73C2211yescharacteristic
50#127×C73—21no—
51#127×C73C2211yescharacteristic
52#121×C73—21no—
53#121×C73—21no—
54#121×C73C2211yescharacteristic
55#121×C73C2211yescharacteristic
56C4×Q8×C73C2211yescharacteristic
57C4×D4×C73—21no—
58C4×D4×C73C2211yescharacteristic
59C2×D292C2311yescharacteristic
60C2×C22⋊D73—21no—
61C2×C22⋊D73—21no—
62C22×Dic73—21no—
63C2×C4×D73—21no—
64#11924015—22no—
65#11924013—41no—
66#11924013—41no—
67#11924012—41no—
68C2×#10596831—41no—
69C2×#10596831C2311yescharacteristic
70C2×#10596831C2311yescharacteristic
71C2×#10596831C2311yescharacteristic
72C2×#10596831C2311yescharacteristic
73C4⋊Dic73—21no—
74C4⋊Dic73C2311yescharacteristic
75C4⋊Dic73C2311yescharacteristic
76C4⋊Dic73C2311yescharacteristic
77#11924007—21no—
78#11924007—21no—
79C22⋊Dic73—21no—
80#11924005—21no—
81#11924005—21no—
82#11924005—21no—
83C4×Dic73—21no—
84#41×C73—22no—
85#41×C73—22no—
86#41×C73—41no—
87#41×C73—41no—
88C2×Q8×C73C2311yescharacteristic
89C2×D4×C73—21no—
90C2×D4×C73—21no—
91C2×D4×C73—21no—
92C2×D4×C73—21no—
93C2×D4×C73—21no—
94C2×D4×C73—21no—
95C2×D4×C73D411yescharacteristic
96C2×D4×C73C2311yescharacteristic
97C2×D4×C73C2311yescharacteristic
98C22×C4×C73—21no—
99C22×C4×C73—21no—
100C22×C4×C73C2311yescharacteristic
101C22×C4×C73C2311yescharacteristic
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×C73—21no—
112C23×C73—21no—
113C23×C73C2×D411yescharacteristic
114C23×C73C2×D411yescharacteristic
115C22×D73—21no—
116Q8×C73—21no—
117Q8×C73#4112yes—
118D4×C73—21no—
119D4×C73—21no—
120D4×C73—21no—
121D4×C73—21no—
122D4×C73—41no—
123D4×C73—42no—
124D4×C73—42no—
125D4×C73—42no—
126D4×C73—81no—
127D4×C73—81no—
128D4×C73—81no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—42no—
136C2×C4×C73—42no—
137C2×C4×C73C2×D411yescharacteristic
138C2×C4×C73C2×D411yescharacteristic
139C2×C4×C73C2×D411yescharacteristic
140C2×C4×C73C2×D411yescharacteristic
141C2×C4×C73C2411yescharacteristic
142C22⋊D73—42no—
143C22⋊D73—81no—
144C2×Dic73—21no—
145C2×Dic73—21no—
146C2×Dic73—21no—
147C2×Dic73—81no—
148D292—21no—
149D292—21no—
150C4×D73—81no—
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—21no—
161C22×C73—41no—
162C22×C73—41no—
163C22×C73—41no—
164C22×C73—41no—
165C22×C73—41no—
166C22×C73—41no—
167C22×C73C22×D411yescharacteristic
168C2×D73—41no—
169C2×D73—41no—
170C2×D73—41no—
171C4×C73—21no—
172C4×C73—21no—
173C4×C73—22no—
174C4×C73—21no—
175C4×C73—21no—
176C4×C73—41no—
177C4×C73C2×#4111yescharacteristic
178C4×C73H(5,𝔽2)11yescharacteristic
179Dic73—41no—
180Dic73—41no—
181Dic73—41no—
182C2×C73—41no—
183C2×C73—41no—
184C2×C73—81no—
185C2×C73—81no—
186C2×C73#54611yescharacteristic
187C2×C73#57511yescharacteristic
188C2×C73#57611yescharacteristic
189D73—81no—
190#3309—731nomaximal, Sylow
191C73#330911yescharacteristic, complemented, Sylow
192#553—731no—
193#550D7311yescharacteristic, complemented
194#490—731no—
195#482—731no—
196#480—731no—
197#479—731no—
198#469—731no—
199#466—731no—
200#459—731no—
201#449—731no—
202#449—731no—
203#440—731no—
204#435—731no—
205#417—731no—
206#416—731no—
207C2×#41C2×D7311yescharacteristic
208C2×#41C2×D7311yescharacteristic
209C2×SD16—731no—
210C2×D8—731no—
211C2×D8—731no—
212C2×M16—731no—
213C22×C8—731no—
214#127—21no—
215#127C2×D7311yescharacteristic
216#126—1461no—
217#125—731no—
218#123—1461no—
219#121—21no—
220#121—21no—
221#121—731no—
222#121—731no—
223#121—1461no—
224#121C2×D7311yescharacteristic
225#121C2×D7311yescharacteristic
226C4×Q8C2×D7311yescharacteristic
227C4×D4—21no—
228C4×D4—731no—
229C4×D4—1461no—
230C4×D4C2×D7311yescharacteristic
231#117—731no—
232C2×C4⋊C4—731no—
233#107—731no—
234#107—731no—
235#106—731no—
236C4⋊C8—731no—
237#103—731no—
238#103—731no—
239#103—731no—
240#102—731no—
241#102—731no—
242#102—731no—
243#102—731no—
244#102—731no—
245#102—731no—
246#102—731no—
247C22⋊C8—731no—
248C22⋊C8—731no—
249#97—731no—
250#41—22no—
251#41—22no—
252#41—41no—
253#41—41no—
254C2×Q8C22×D7311yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—731no—
262C2×D4—1461no—
263C2×D4—1461no—
264C2×D4C22⋊D7311yescharacteristic
265C2×D4C22×D7311yescharacteristic
266C2×D4C22×D7311yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—1461no—
270C22×C4—1461no—
271C22×C4C22×D7311yescharacteristic
272C22×C4C22×D7311yescharacteristic
273SD16—1462no—
274D8—2921no—
275D8—2921no—
276M16—2921no—
277C2×C8—2921no—
278C2×C8—731no—
279C2×C8—731no—
280C2×C8—731no—
281C2×C8—731no—
282C4⋊C4—21no—
283C4⋊C4—731no—
284C4⋊C4—731no—
285C4⋊C4—731no—
286C4⋊C4—1461no—
287C4⋊C4—1461no—
288C4⋊C4—1461no—
289C4⋊C4C22⋊D7311yescharacteristic
290C4⋊C4C22×D7311yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—1461no—
294C22⋊C4—1461no—
295C22⋊C4—1461no—
296C22⋊C4—1461no—
297C22⋊C4C22⋊D7311yescharacteristic
298C22⋊C4C22⋊D7311yescharacteristic
299C42—21no—
300C42—1461no—
301C42C22×D7311yescharacteristic
302C23—21no—
303C23—21no—
304C23—1461no—
305C23C2×C22⋊D7311yescharacteristic
306C23C2×C22⋊D7311yescharacteristic
307Q8—21no—
308Q8#1192402712yes—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—41no—
314D4—42no—
315D4—42no—
316D4—42no—
317D4—81no—
318D4—81no—
319D4—81no—
320D4—2922no—
321D4—5841no—
322D4—1461no—
323D4—1461no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—5841no—
333C2×C4—5841no—
334C2×C4—1461no—
335C2×C4—1461no—
336C2×C4—1461no—
337C2×C4C2×C22⋊D7311yescharacteristic
338C2×C4C2×C22⋊D7311yescharacteristic
339C2×C4C2×C22⋊D7311yescharacteristic
340C2×C4C2×C22⋊D7311yescharacteristic
341C2×C4C23×D7311yescharacteristic
342C8—1461no—
343C8—1461no—
344C8—1461no—
345C8—1461no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—2921no—
359C22—2921no—
360C22—2921no—
361C22C22×C22⋊D7311yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—22no—
367C4—41no—
368C4—2921no—
369C4—2921no—
370C4—2921no—
371C4C2×#1192402711yescharacteristic
372C4#1455663611yescharacteristic
373C2—41no—
374C2—41no—
375C2—81no—
376C2—81no—
377C2—5841no—
378C2#1798923111yescharacteristic
379C2#1798938511yescharacteristic
380C2#1798939011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#550×C73C2
socleC22×C73C22×D4
hypercenter#550D73
hypocenterC73#3309
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #17989283C2semidirect
2. #17988951C2semidirect
3. #17988908C2semidirect
4. #17988898C2semidirect
5. #17988894C2semidirect
6. #17988838C2semidirect
7. #17988821C2semidirect
8. #17988779C2semidirect
9. #17988732C2semidirect
10. #17988732C2semidirect
11. #17988685C2semidirect
12. #17988659C2semidirect
13. #17988588C2semidirect
14. #17988583C2semidirect
15. #550×C73C2semidirect
191. C73#3309semidirect
193. #550D73semidirect