Finite Group Databasebeta

← #22622086

Subgroups — #22622086

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#17989303C211yesmaximal, characteristic, complemented
2#17989230C211yesmaximal, characteristic, complemented
3#17988926C211yesmaximal, characteristic, complemented
4#17988910C211yesmaximal, characteristic, complemented
5#17988864C211yesmaximal, characteristic, complemented
6#17988836C211yesmaximal, characteristic, complemented
7#17988822C211yesmaximal, characteristic, complemented
8#17988799C211yesmaximal, characteristic, complemented
9#17988735C211yesmaximal, characteristic, complemented
10#17988722C211yesmaximal, characteristic, complemented
11#17988700C211yesmaximal, characteristic, complemented
12#17988660C211yesmaximal, characteristic, complemented
13#17988590C211yesmaximal, characteristic, complemented
14#17988582C211yesmaximal, characteristic, complemented
15#489×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic
17C2×D4×D73C2211yescharacteristic
18C2×#11924015C2211yescharacteristic, complemented
19C2×D584C2211yescharacteristic
20C2×#11924013C2211yescharacteristic
21C2×#11924011C2211yescharacteristic
22C2×C8×D73C2211yescharacteristic, complemented
23#14556580—21no—
24#14556580—21no—
25#14556573—21no—
26#14556567C2211yescharacteristic
27#14556566—21no—
28#14556566C2211yescharacteristic
29#14556566C2211yescharacteristic, complemented
30#14556564—21no—
31#14556562C2211yescharacteristic
32#14556561—21no—
33C4×D292C2211yescharacteristic
34C4×D292C2211yescharacteristic
35C4×D292C2211yescharacteristic, complemented
36#14556549—21no—
37#14556549C2211yescharacteristic
38#14556549C2211yescharacteristic, complemented
39C22⋊C4×D73—21no—
40#14556524C2211yescharacteristic, complemented
41#14556524C2211yescharacteristic, complemented
42#14556523C2211yescharacteristic, complemented
43C4⋊#10596831C2211yescharacteristic, complemented
44#14556515C2211yescharacteristic, complemented
45#14556513C2211yescharacteristic
46#14556513C2211yescharacteristic, complemented
47#14556512C2211yescharacteristic
48#14556511C2211yescharacteristic
49#14556511C2211yescharacteristic
50#14556503C2211yescharacteristic
51#14556503C2211yescharacteristic, complemented
52C4⋊Q8×C73C2211yescharacteristic, complemented
53#124×C73C2211yescharacteristic
54#103×C73C2211yescharacteristic, complemented
55#103×C73C2211yescharacteristic, complemented
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58#97×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60#11924029—22no—
61#11924029—41no—
62C2×D292—21no—
63C2×D292—21no—
64C2×D292—21no—
65C2×D292D411yescharacteristic
66C2×D292C2311yescharacteristic
67C2×D292C2311yescharacteristic
68C2×C22⋊D73—21no—
69C2×C22⋊D73—21no—
70D4×D73—22no—
71D4×D73—41no—
72C2×C4×D73—21no—
73C2×C4×D73—21no—
74C2×C4×D73—21no—
75C2×C4×D73C2311yescharacteristic
76C2×C4×D73C2311yescharacteristic
77#11924015—41no—
78D584—22no—
79#11924013—41no—
80#11924011—41no—
81C2×#10596831C2311yescharacteristic
82C2×#10596831C2311yescharacteristic
83C8×D73—41no—
84C4⋊Dic73D411yescharacteristic
85C4⋊Dic73C2311yescharacteristic
86C4⋊Dic73C2311yescharacteristic
87#11924007—21no—
88C22⋊Dic73—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005—21no—
96#11924005D411yescharacteristic
97#11924005D411yescharacteristic
98C4×Dic73—21no—
99C4×Dic73—21no—
100C2×Q8×C73—21no—
101C2×Q8×C73C2311yescharacteristic
102C2×D4×C73C2311yescharacteristic
103C2×C8×C73C2311yescharacteristic
104C2×C8×C73C2311yescharacteristic
105C4⋊C4×C73—21no—
106C4⋊C4×C73C2311yescharacteristic
107C4⋊C4×C73C2311yescharacteristic
108C22⋊C4×C73—21no—
109C22⋊C4×C73—21no—
110C42×C73C2311yescharacteristic
111C23×C73—21no—
112C22×D73—21no—
113C22×D73—21no—
114C22×D73—42no—
115C22×D73—42no—
116C22×D73—81no—
117C22×D73C2×D411yescharacteristic
118C22×D73C2×D411yescharacteristic
119Q8×C73—21no—
120Q8×C73—21no—
121Q8×C73—81no—
122D4×C73—21no—
123D4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73C2×D411yescharacteristic
128C2×C4×C73C2×D411yescharacteristic
129C2×C4×C73C2411yescharacteristic
130C22⋊D73—42no—
131C22⋊D73—81no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73C2×D411yescharacteristic
135C2×Dic73C2×D411yescharacteristic
136D292—21no—
137D292—21no—
138D292—21no—
139D292—41no—
140D292—42no—
141D292—81no—
142D292—81no—
143D292#4112yes—
144C4×D73—21no—
145C4×D73—21no—
146C4×D73—21no—
147C4×D73—21no—
148C4×D73—42no—
149C4×D73—42no—
150C4×D73—81no—
151C8×C73—21no—
152C8×C73—21no—
153#10596831—21no—
154#10596831—21no—
155C22×C73—41no—
156C22×C73—41no—
157C22×C73—41no—
158C22×C73C22×D411yescharacteristic
159C2×D73—21no—
160C2×D73—21no—
161C2×D73—22no—
162C2×D73—21no—
163C2×D73—21no—
164C2×D73—21no—
165C2×D73—21no—
166C2×D73—41no—
167C2×D73—41no—
168C2×D73—41no—
169C2×D73—41no—
170C2×D73—41no—
171C2×D73—84no—
172C4×C73—21no—
173C4×C73—21no—
174C4×C73—41no—
175C4×C73—41no—
176C4×C73—41no—
177C4×C73C2×#4111yescharacteristic
178C4×C73H(5,𝔽2)11yescharacteristic
179Dic73—21no—
180Dic73—21no—
181Dic73—41no—
182Dic73—41no—
183C2×C73—81no—
184C2×C73#54611yescharacteristic
185C2×C73#57511yescharacteristic
186C2×C73#57611yescharacteristic
187D73—41no—
188D73—41no—
189D73—42no—
190D73—81no—
191#3319—731nomaximal, Sylow
192C73#331911yescharacteristic, complemented, Sylow
193#555—731no—
194#546—731no—
195#489D7311yescharacteristic, complemented
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#418—731no—
207#416—731no—
208C2×#41—731no—
209C22×D4—731no—
210C2×SD16—731no—
211C2×D8—731no—
212C2×D8—731no—
213C2×M16—731no—
214C22×C8—731no—
215C4⋊Q8C2×D7311yescharacteristic, complemented
216#124—1461no—
217#124—1461no—
218#124C2×D7311yescharacteristic
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—731no—
232#117—1461no—
233C2×C22⋊C4—1461no—
234#107—731no—
235#107—731no—
236#106—731no—
237C4⋊C8—731no—
238#103—731no—
239#103C2×D7311yescharacteristic, complemented
240#103C2×D7311yescharacteristic, complemented
241#102—731no—
242#102—731no—
243#102—731no—
244#102—731no—
245#102—731no—
246#102C2×D7311yescharacteristic
247#102C2×D7311yescharacteristic
248C22⋊C8—731no—
249C22⋊C8—731no—
250#97C2×D7311yescharacteristic, complemented
251C24—1461no—
252#41—2921no—
253#41—1462no—
254C2×Q8—21no—
255C2×Q8C22×D7311yescharacteristic
256C2×D4—2921no—
257C2×D4—731no—
258C2×D4—731no—
259C2×D4—731no—
260C2×D4—1461no—
261C2×D4—1461no—
262C2×D4—1461no—
263C2×D4—1461no—
264C2×D4—1462no—
265C2×D4—1461no—
266C2×D4C22×D7311yescharacteristic
267C22×C4—731no—
268C22×C4—731no—
269C22×C4—1461no—
270C22×C4—1461no—
271C22×C4—1461no—
272SD16—2921no—
273D8—2921no—
274D8—1462no—
275M16—2921no—
276C2×C8—2921no—
277C2×C8—731no—
278C2×C8—731no—
279C2×C8C22×D7311yescharacteristic
280C2×C8C22×D7311yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—731no—
283C4⋊C4—731no—
284C4⋊C4—731no—
285C4⋊C4—1461no—
286C4⋊C4C22×D7311yescharacteristic
287C4⋊C4C22×D7311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—731no—
291C22⋊C4—731no—
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—1461no—
301C42—1461no—
302C42C22×D7311yescharacteristic
303C23—21no—
304C23—2922no—
305C23—2922no—
306C23—5841no—
307C23—731no—
308C23—731no—
309C23—1461no—
310C23—1461no—
311Q8—21no—
312Q8—21no—
313Q8—81no—
314D4—21no—
315D4—21no—
316D4—2921no—
317D4—2922no—
318D4—2922no—
319D4—5841no—
320D4—5841no—
321D4—5841no—
322D4—732no—
323D4—1461no—
324D4—1461no—
325D4—1461no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—2922no—
330C2×C4—2922no—
331C2×C4—5841no—
332C2×C4—731no—
333C2×C4—731no—
334C2×C4—1461no—
335C2×C4—1461no—
336C2×C4—1461no—
337C2×C4—1461no—
338C2×C4—1461no—
339C2×C4—1461no—
340C2×C4D4×D7311yescharacteristic
341C2×C4D4×D7311yescharacteristic
342C2×C4C23×D7311yescharacteristic
343C8—21no—
344C8—21no—
345C8—1461no—
346C8—1461no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—2921no—
351C22—2921no—
352C22—2921no—
353C22—2921no—
354C22—2921no—
355C22—5844no—
356C22—1461no—
357C22—1461no—
358C22—1461no—
359C22—1461no—
360C22—1462no—
361C22—1461no—
362C22—1461no—
363C22C2×D4×D7311yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—2921no—
370C4—2921no—
371C4—1461no—
372C4—1461no—
373C4#41×D7311yescharacteristic
374C4#1455663711yescharacteristic
375C2—81no—
376C2—2922no—
377C2—2921no—
378C2—2921no—
379C2—5841no—
380C2#1798923011yescharacteristic
381C2#1798938611yescharacteristic
382C2#1798939111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#489×C73C2
socleC22×C73C22×D4
hypercenter#489D73
hypocenterC73#3319
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #17989303C2semidirect
2. #17989230C2semidirect
3. #17988926C2semidirect
4. #17988910C2semidirect
5. #17988864C2semidirect
6. #17988836C2semidirect
7. #17988822C2semidirect
8. #17988799C2semidirect
9. #17988735C2semidirect
10. #17988722C2semidirect
11. #17988700C2semidirect
12. #17988660C2semidirect
13. #17988590C2semidirect
14. #17988582C2semidirect
15. #489×C73C2semidirect
18. C2×#11924015C22semidirect
22. C2×C8×D73C22semidirect
29. #14556566C22semidirect
35. C4×D292C22semidirect
38. #14556549C22semidirect
40. #14556524C22semidirect
41. #14556524C22semidirect
42. #14556523C22semidirect
43. C4⋊#10596831C22semidirect
44. #14556515C22semidirect
46. #14556513C22semidirect
51. #14556503C22semidirect
52. C4⋊Q8×C73C22semidirect
54. #103×C73C22semidirect
55. #103×C73C22semidirect
58. #97×C73C22semidirect
192. C73#3319semidirect
195. #489D73semidirect
215. C4⋊Q8C2×D73semidirect
239. #103C2×D73semidirect
240. #103C2×D73semidirect
250. #97C2×D73semidirect