Finite Group Databasebeta

← #22621931

Subgroups — #22621931

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#17989258C211yesmaximal, characteristic, complemented
2#17988953C211yesmaximal, characteristic, complemented
3#17988911C211yesmaximal, characteristic, complemented
4#17988900C211yesmaximal, characteristic, complemented
5#17988891C211yesmaximal, characteristic, complemented
6#17988838C211yesmaximal, characteristic, complemented
7#17988821C211yesmaximal, characteristic, complemented
8#17988782C211yesmaximal, characteristic, complemented
9#17988730C211yesmaximal, characteristic, complemented
10#17988730C211yesmaximal, characteristic, complemented
11#17988687C211yesmaximal, characteristic, complemented
12#17988659C211yesmaximal, characteristic, complemented
13#17988586C211yesmaximal, characteristic, complemented
14#17988581C211yesmaximal, characteristic, complemented
15#553×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×#11924028C2211yescharacteristic
18C2×#11924016C2211yescharacteristic
19C2×#11924013C2211yescharacteristic
20C2×#11924013C2211yescharacteristic
21C2×#11924012C2211yescharacteristic
22C22×#10596831C2211yescharacteristic
23#14556588C2211yescharacteristic
24#14556587—21no—
25#14556565C2211yescharacteristic
26#14556565C2211yescharacteristic
27#14556564—21no—
28#14556564—21no—
29C4×Dic146C2211yescharacteristic
30#14556553—21no—
31#14556524C2211yescharacteristic
32#14556524C2211yescharacteristic
33#14556522C2211yescharacteristic
34C4⋊#10596831C2211yescharacteristic
35#14556514C2211yescharacteristic
36#14556514C2211yescharacteristic
37#14556514C2211yescharacteristic
38#14556512C2211yescharacteristic
39#14556511C2211yescharacteristic
40#14556511C2211yescharacteristic
41#14556511C2211yescharacteristic
42#14556511C2211yescharacteristic
43#14556511C2211yescharacteristic
44#14556511C2211yescharacteristic
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
59#11924028—22no—
60#11924028—22no—
61#11924028—41no—
62#11924028—41no—
63C2×Dic146C2311yescharacteristic
64C2×D292—21no—
65C2×D292—21no—
66C2×D292C2311yescharacteristic
67C2×D292C2311yescharacteristic
68C2×C22⋊D73—21no—
69C2×C22⋊D73—21no—
70C2×C22⋊D73—21no—
71C2×C22⋊D73—21no—
72C2×C4×D73—21no—
73C2×C4×D73—21no—
74#11924016—22no—
75#11924013—41no—
76#11924013—41no—
77#11924012—41no—
78C2×#10596831—41no—
79C2×#10596831C2311yescharacteristic
80C2×#10596831C2311yescharacteristic
81C2×#10596831C2311yescharacteristic
82C2×#10596831C2311yescharacteristic
83C4⋊Dic73C2311yescharacteristic
84#11924007—21no—
85#11924005—21no—
86#11924005—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
114C22×D73—21no—
115C22×D73—21no—
116D4×C73—21no—
117D4×C73—21no—
118D4×C73—41no—
119D4×C73—42no—
120D4×C73—81no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—81no—
129C2×C4×C73—81no—
130C2×C4×C73C2×D411yescharacteristic
131C2×C4×C73C2×D411yescharacteristic
132C2×C4×C73C2×D411yescharacteristic
133C2×C4×C73C2×D411yescharacteristic
134C2×C4×C73C2411yescharacteristic
135C22⋊D73—42no—
136C22⋊D73—42no—
137C22⋊D73—81no—
138C22⋊D73—81no—
139C2×Dic73—21no—
140C2×Dic73—21no—
141D292—21no—
142D292—21no—
143D292—21no—
144D292—21no—
145D292—42no—
146D292—81no—
147C4×D73—42no—
148C4×D73—42no—
149Dic146—21no—
150Dic146#4112yes—
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×C73C22×D411yescharacteristic
165C2×D73—41no—
166C2×D73—41no—
167C2×D73—41no—
168C2×D73—41no—
169C2×D73—41no—
170C2×D73—41no—
171C4×C73—21no—
172C4×C73—21no—
173C4×C73—21no—
174C4×C73—21no—
175C4×C73—41no—
176C4×C73—41no—
177C4×C73—41no—
178C4×C73C2×#4111yescharacteristic
179C4×C73H(5,𝔽2)11yescharacteristic
180Dic73—22no—
181Dic73—41no—
182C2×C73—41no—
183C2×C73—41no—
184C2×C73—81no—
185C2×C73#54611yescharacteristic
186C2×C73#57511yescharacteristic
187C2×C73#57611yescharacteristic
188D73—81no—
189D73—81no—
190#3309—731nomaximal, Sylow
191C73#330911yescharacteristic, complemented, Sylow
192#553D7311yescharacteristic, complemented
193#550—731no—
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×#41—731no—
208C2×#41—731no—
209C2×SD16—731no—
210C2×D8—731no—
211C2×D8—731no—
212C2×M16—731no—
213C22×C8—731no—
214#127—731no—
215#127—1461no—
216#126—21no—
217#125C2×D7311yescharacteristic
218#123—21no—
219#121—21no—
220#121—731no—
221#121—731no—
222#121—1461no—
223#121—1461no—
224#121C2×D7311yescharacteristic
225#121C2×D7311yescharacteristic
226C4×Q8—731no—
227C4×D4—21no—
228C4×D4—1461no—
229C4×D4C2×D7311yescharacteristic
230C4×D4C2×D7311yescharacteristic
231#117C2×D7311yescharacteristic
232C2×C4⋊C4C2×D7311yescharacteristic
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—2921no—
251#41—2921no—
252#41—1462no—
253#41—1462no—
254C2×Q8—731no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—731no—
258C2×D4—731no—
259C2×D4—1461no—
260C2×D4—1461no—
261C2×D4—1461no—
262C2×D4—1461no—
263C2×D4—1461no—
264C2×D4—1461no—
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—21no—
284C4⋊C4—21no—
285C4⋊C4—731no—
286C4⋊C4—1461no—
287C4⋊C4C22⋊D7311yescharacteristic
288C4⋊C4C22×D7311yescharacteristic
289C4⋊C4C22×D7311yescharacteristic
290C4⋊C4C22×D7311yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—1461no—
296C22⋊C4—1461no—
297C22⋊C4C22⋊D7311yescharacteristic
298C22⋊C4C22⋊D7311yescharacteristic
299C42—21no—
300C42—1461no—
301C42C22×D7311yescharacteristic
302C23—21no—
303C23—1461no—
304C23—1461no—
305C23C2×C22⋊D7311yescharacteristic
306C23C2×C22⋊D7311yescharacteristic
307Q8—732no—
308Q8—1461no—
309D4—21no—
310D4—21no—
311D4—41no—
312D4—42no—
313D4—81no—
314D4—2922no—
315D4—2922no—
316D4—2922no—
317D4—5841no—
318D4—5841no—
319D4—5841no—
320D4—1461no—
321D4—1461no—
322D4—1461no—
323D4—1461no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—2922no—
334C2×C4—2922no—
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—2921no—
356C22—2921no—
357C22—2921no—
358C22—2921no—
359C22—2921no—
360C22—2921no—
361C22C22×C22⋊D7311yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—2921no—
370C4—1462no—
371C4#41×D7311yescharacteristic
372C4#1455663711yescharacteristic
373C2—41no—
374C2—41no—
375C2—81no—
376C2—5841no—
377C2—5841no—
378C2#1798922511yescharacteristic
379C2#1798938511yescharacteristic
380C2#1798939011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#553×C73C2
socleC22×C73C22×D4
hypercenter#553D73
hypocenterC73#3309
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. #17989258C2semidirect
2. #17988953C2semidirect
3. #17988911C2semidirect
4. #17988900C2semidirect
5. #17988891C2semidirect
6. #17988838C2semidirect
7. #17988821C2semidirect
8. #17988782C2semidirect
9. #17988730C2semidirect
10. #17988730C2semidirect
11. #17988687C2semidirect
12. #17988659C2semidirect
13. #17988586C2semidirect
14. #17988581C2semidirect
15. #553×C73C2semidirect
191. C73#3309semidirect
192. #553D73semidirect