Finite Group Databasebeta

← #22622088

Subgroups — #22622088

Order 9344.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989300C211yesmaximal, characteristic, complemented
2#17989231C211yesmaximal, characteristic, complemented
3#17988945C211yesmaximal, characteristic, complemented
4#17988928C211yesmaximal, characteristic, complemented
5#17988909C211yesmaximal, characteristic, complemented
6#17988865C211yesmaximal, characteristic, complemented
7#17988833C211yesmaximal, characteristic, complemented
8#17988822C211yesmaximal, characteristic, complemented
9#17988801C211yesmaximal, characteristic, complemented
10#17988733C211yesmaximal, characteristic, complemented
11#17988721C211yesmaximal, characteristic, complemented
12#17988696C211yesmaximal, characteristic, complemented
13#17988656C211yesmaximal, characteristic, complemented
14#17988580C211yesmaximal, characteristic, complemented
15#418×C73C211yesmaximal, characteristic, complemented
16C2×#11924027C2211yescharacteristic
17C2×#11924017C2211yescharacteristic, complemented
18C2×#11924013C2211yescharacteristic
19C2×#11924013C2211yescharacteristic
20C2×C8×D73C2211yescharacteristic, complemented
21#14556590C2211yescharacteristic, complemented
22#14556579—21no—
23#14556578C2211yescharacteristic
24#14556577—21no—
25#14556572—21no—
26#14556570C2211yescharacteristic
27#14556566C2211yescharacteristic, complemented
28#14556565C2211yescharacteristic
29#14556564—21no—
30#14556563—21no—
31#14556562C2211yescharacteristic
32#14556560—21no—
33D4×Dic73C2211yescharacteristic
34#14556553C2211yescharacteristic, complemented
35C4×C22⋊D73C2211yescharacteristic
36#14556549C2211yescharacteristic, complemented
37#14556548—21no—
38C2×C22⋊Dic73—21no—
39#14556525C2211yescharacteristic, complemented
40#14556524C2211yescharacteristic, complemented
41#14556522C2211yescharacteristic, complemented
42#14556520C2211yescharacteristic, complemented
43#14556516C2211yescharacteristic, complemented
44#14556514C2211yescharacteristic, complemented
45#14556514C2211yescharacteristic, complemented
46#14556513C2211yescharacteristic, complemented
47#14556512C2211yescharacteristic
48#14556512C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic, complemented
51#14556501C2211yescharacteristic, complemented
52C22×D4×C73C2211yescharacteristic
53C2×M16×C73C2211yescharacteristic
54#117×C73C2211yescharacteristic
55#102×C73C2211yescharacteristic
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59#11924027—22no—
60#11924027—41no—
61C2×Dic146—21no—
62C2×Dic146C2311yescharacteristic
63C2×D292—21no—
64C2×D292C2311yescharacteristic
65C2×C22⋊D73—21no—
66C2×C22⋊D73—21no—
67C2×C22⋊D73—21no—
68C2×C22⋊D73D411yescharacteristic
69C22×Dic73—21no—
70C22×Dic73—21no—
71C2×C4×D73—21no—
72C2×C4×D73C2311yescharacteristic
73#11924017—41no—
74#11924013—22no—
75#11924013—41no—
76C2×#10596831C2311yescharacteristic
77C2×#10596831C2311yescharacteristic
78C8×D73—41no—
79C4⋊Dic73C2311yescharacteristic
80C4⋊Dic73C2311yescharacteristic
81#11924007—21no—
82#11924007—21no—
83#11924007D411yescharacteristic
84C22⋊Dic73—21no—
85C22⋊Dic73—21no—
86C22⋊Dic73—21no—
87C22⋊Dic73—21no—
88C22⋊Dic73—21no—
89C22⋊Dic73D411yescharacteristic
90#11924005—21no—
91#11924005—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005D411yescharacteristic
95C4×Dic73—21no—
96C4×Dic73C2311yescharacteristic
97C24×C73—21no—
98C2×D4×C73—22no—
99C2×D4×C73—21no—
100C2×D4×C73—41no—
101C2×D4×C73C2311yescharacteristic
102C2×D4×C73C2311yescharacteristic
103C22×C4×C73C2311yescharacteristic
104M16×C73—41no—
105C2×C8×C73C2311yescharacteristic
106C2×C8×C73C2311yescharacteristic
107C4⋊C4×C73C2311yescharacteristic
108C4⋊C4×C73C2311yescharacteristic
109C22⋊C4×C73—21no—
110C42×C73—21no—
111C23×C73—21no—
112C23×C73—21no—
113C23×C73—42no—
114C23×C73—42no—
115C23×C73—81no—
116C23×C73C2×D411yescharacteristic
117C22×D73—21no—
118C22×D73C2×D411yescharacteristic
119D4×C73—21no—
120D4×C73—21no—
121D4×C73—21no—
122D4×C73—42no—
123D4×C73#4112yes—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73C2×D411yescharacteristic
129C2×C4×C73C2411yescharacteristic
130C22⋊D73—41no—
131C22⋊D73—42no—
132C22⋊D73—81no—
133C22⋊D73—81no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—42no—
138C2×Dic73—81no—
139C2×Dic73C2×D411yescharacteristic
140C2×Dic73C2×D411yescharacteristic
141C2×Dic73C2×D411yescharacteristic
142D292—21no—
143D292—21no—
144D292—81no—
145C4×D73—21no—
146C4×D73—21no—
147C4×D73—42no—
148Dic146—21no—
149Dic146—21no—
150Dic146—81no—
151C8×C73—21no—
152C8×C73—21no—
153#10596831—21no—
154#10596831—21no—
155C22×C73—22no—
156C22×C73—21no—
157C22×C73—21no—
158C22×C73—21no—
159C22×C73—41no—
160C22×C73—41no—
161C22×C73—41no—
162C22×C73—41no—
163C22×C73—41no—
164C22×C73—84no—
165C22×C73C22×D411yescharacteristic
166C2×D73—21no—
167C2×D73—21no—
168C2×D73—21no—
169C2×D73—41no—
170C2×D73—41no—
171C2×D73—41no—
172C4×C73—21no—
173C4×C73—41no—
174C4×C73—41no—
175C4×C73C2×#4111yescharacteristic
176C4×C73H(5,𝔽2)11yescharacteristic
177Dic73—21no—
178Dic73—21no—
179Dic73—21no—
180Dic73—41no—
181Dic73—41no—
182Dic73—41no—
183C2×C73—41no—
184C2×C73—42no—
185C2×C73—81no—
186C2×C73#54611yescharacteristic
187C2×C73#57511yescharacteristic
188C2×C73#57611yescharacteristic
189D73—41no—
190D73—81no—
191#3319—731nomaximal, Sylow
192C73#331911yescharacteristic, complemented, Sylow
193#555—731no—
194#546—731no—
195#489—731no—
196#485—731no—
197#482—731no—
198#474—731no—
199#468—731no—
200#466—731no—
201#463—731no—
202#449—731no—
203#447—731no—
204#442—731no—
205#435—731no—
206#418D7311yescharacteristic, complemented
207#416—731no—
208C2×#41—731no—
209C22×D4C2×D7311yescharacteristic
210C2×SD16—731no—
211C2×D8—731no—
212C2×D8—731no—
213C2×M16C2×D7311yescharacteristic
214C22×C8—731no—
215C4⋊Q8—731no—
216#124—731no—
217#124—1461no—
218#124—1461no—
219#123—1461no—
220C22⋊Q8—731no—
221#121—731no—
222#121—731no—
223#121—731no—
224#121—1461no—
225#121—1461no—
226#120—1461no—
227C4×D4—731no—
228C4×D4—731no—
229C4×D4—731no—
230#117—731no—
231#117—1461no—
232#117C2×D7311yescharacteristic
233C2×C22⋊C4—1461no—
234#107—731no—
235#107—731no—
236#106—731no—
237C4⋊C8—731no—
238#103—731no—
239#103—731no—
240#103—731no—
241#102—731no—
242#102—731no—
243#102—731no—
244#102C2×D7311yescharacteristic
245#102C2×D7311yescharacteristic
246#102C2×D7311yescharacteristic
247#102C2×D7311yescharacteristic
248C22⋊C8—731no—
249C22⋊C8—731no—
250#97—731no—
251C24—21no—
252#41—2921no—
253#41—1462no—
254C2×Q8—731no—
255C2×Q8—1461no—
256C2×D4—22no—
257C2×D4—21no—
258C2×D4—41no—
259C2×D4—731no—
260C2×D4—731no—
261C2×D4—1461no—
262C2×D4—1461no—
263C2×D4—1461no—
264C2×D4—1461no—
265C2×D4C22×D7311yescharacteristic
266C2×D4C22×D7311yescharacteristic
267C22×C4—731no—
268C22×C4—1461no—
269C22×C4—1461no—
270C22×C4—1461no—
271C22×C4C22×D7311yescharacteristic
272SD16—2921no—
273D8—2921no—
274D8—1462no—
275M16—41no—
276C2×C8—2921no—
277C2×C8—731no—
278C2×C8—731no—
279C2×C8C22×D7311yescharacteristic
280C2×C8C22×D7311yescharacteristic
281C4⋊C4—731no—
282C4⋊C4—731no—
283C4⋊C4—731no—
284C4⋊C4—1461no—
285C4⋊C4—1461no—
286C4⋊C4C22×D7311yescharacteristic
287C4⋊C4C22×D7311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—731no—
290C22⋊C4—731no—
291C22⋊C4—1461no—
292C22⋊C4—1461no—
293C22⋊C4—1461no—
294C22⋊C4—1461no—
295C22⋊C4—1461no—
296C22⋊C4—1461no—
297C22⋊C4—1461no—
298C22⋊C4—1461no—
299C22⋊C4—1461no—
300C42—21no—
301C42—731no—
302C42—1461no—
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—731no—
309C23—1461no—
310C23D4×D7311yescharacteristic
311Q8—5841no—
312Q8—1461no—
313Q8—1461no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—42no—
318D4—2922no—
319D4—2921no—
320D4—5841no—
321D4—5841no—
322D4—5841no—
323D4—1461no—
324D4—1461no—
325D4#1192402812yes—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—2922no—
331C2×C4—2922no—
332C2×C4—5841no—
333C2×C4—731no—
334C2×C4—731no—
335C2×C4—731no—
336C2×C4—1461no—
337C2×C4—1461no—
338C2×C4—1461no—
339C2×C4—1461no—
340C2×C4—1461no—
341C2×C4D4×D7311yescharacteristic
342C2×C4C23×D7311yescharacteristic
343C8—21no—
344C8—21no—
345C8—1461no—
346C8—1461no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—84no—
357C22—2921no—
358C22—2921no—
359C22—2921no—
360C22—1461no—
361C22—1461no—
362C22—1461no—
363C22C2×D4×D7311yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—2921no—
368C4—2921no—
369C4—2921no—
370C4—1461no—
371C4—1461no—
372C4—1461no—
373C4C2×#1192402811yescharacteristic
374C4#1455663611yescharacteristic
375C2—41no—
376C2—42no—
377C2—81no—
378C2—2921no—
379C2—5841no—
380C2#1798922711yescharacteristic
381C2#1798938311yescharacteristic
382C2#1798939111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#418×C73C2
socleC22×C73C22×D4
hypercenter#418D73
hypocenterC73#3319
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #17989300C2semidirect
2. #17989231C2semidirect
3. #17988945C2semidirect
4. #17988928C2semidirect
5. #17988909C2semidirect
6. #17988865C2semidirect
7. #17988833C2semidirect
8. #17988822C2semidirect
9. #17988801C2semidirect
10. #17988733C2semidirect
11. #17988721C2semidirect
12. #17988696C2semidirect
13. #17988656C2semidirect
14. #17988580C2semidirect
15. #418×C73C2semidirect
17. C2×#11924017C22semidirect
20. C2×C8×D73C22semidirect
21. #14556590C22semidirect
27. #14556566C22semidirect
34. #14556553C22semidirect
36. #14556549C22semidirect
39. #14556525C22semidirect
40. #14556524C22semidirect
41. #14556522C22semidirect
42. #14556520C22semidirect
43. #14556516C22semidirect
44. #14556514C22semidirect
45. #14556514C22semidirect
46. #14556513C22semidirect
50. #14556503C22semidirect
51. #14556501C22semidirect
192. C73#3319semidirect
206. #418D73semidirect