Finite Group Databasebeta

← #22622137

Subgroups — #22622137

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#17989287C211yesmaximal, characteristic, complemented
2#17989232C211yesmaximal, characteristic, complemented
3#17988942C211yesmaximal, characteristic, complemented
4#17988930C211yesmaximal, characteristic, complemented
5#17988902C211yesmaximal, characteristic, complemented
6#17988887C211yesmaximal, characteristic, complemented
7#17988839C211yesmaximal, characteristic, complemented
8#17988832C211yesmaximal, characteristic, complemented
9#17988802C211yesmaximal, characteristic, complemented
10#17988729C211yesmaximal, characteristic, complemented
11#17988719C211yesmaximal, characteristic, complemented
12#17988666C211yesmaximal, characteristic, complemented
13#17988590C211yesmaximal, characteristic, complemented
14#17988585C211yesmaximal, characteristic, complemented
15C4×D8×C73C211yesmaximal, characteristic, complemented
16C2×#11924027C2211yescharacteristic
17C2×D4×D73C2211yescharacteristic
18C2×#11924016C2211yescharacteristic, complemented
19C2×#11924013C2211yescharacteristic
20C2×#11924011C2211yescharacteristic
21C2×#11924011C2211yescharacteristic, complemented
22#14556584—21no—
23#14556583C2211yescharacteristic, complemented
24#14556579C2211yescharacteristic
25#14556575—21no—
26#14556574—21no—
27#14556571C2211yescharacteristic
28#14556566C2211yescharacteristic
29#14556565—21no—
30#14556564—21no—
31#14556562C2211yescharacteristic
32#14556562C2211yescharacteristic, complemented
33#14556561—21no—
34C4×D292C2211yescharacteristic
35C4×C22⋊D73—21no—
36#14556549C2211yescharacteristic
37C4⋊C4×D73C2211yescharacteristic, complemented
38C2×#11924005—21no—
39#14556524C2211yescharacteristic, complemented
40#14556522C2211yescharacteristic, complemented
41C4⋊#10596831C2211yescharacteristic, complemented
42#14556516C2211yescharacteristic, complemented
43#14556516C2211yescharacteristic, complemented
44#14556514C2211yescharacteristic, complemented
45#14556513C2211yescharacteristic
46#14556513C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556512C2211yescharacteristic
49#14556511C2211yescharacteristic
50#14556503C2211yescharacteristic
51#14556503C2211yescharacteristic, complemented
52C2×D8×C73C2211yescharacteristic
53C4×D4×C73C2211yescharacteristic
54C4×D4×C73C2211yescharacteristic, complemented
55#107×C73C2211yescharacteristic, complemented
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic, complemented
58C4×C8×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60#11924027—22no—
61#11924027—41no—
62C2×Dic146C2311yescharacteristic
63C2×D292—21no—
64C2×D292D411yescharacteristic
65C2×D292C2311yescharacteristic
66C2×C22⋊D73—21no—
67C2×C22⋊D73—21no—
68C2×C22⋊D73—21no—
69C2×C22⋊D73—21no—
70D4×D73—22no—
71D4×D73—41no—
72C22×Dic73—21no—
73C2×C4×D73—21no—
74C2×C4×D73C2311yescharacteristic
75C2×C4×D73C2311yescharacteristic
76#11924016—41no—
77#11924013—41no—
78#11924011—41no—
79#11924011—41no—
80C2×#10596831C2311yescharacteristic
81C2×#10596831C2311yescharacteristic
82C4⋊Dic73—21no—
83C4⋊Dic73D411yescharacteristic
84C4⋊Dic73C2311yescharacteristic
85C4⋊Dic73C2311yescharacteristic
86#11924007—21no—
87#11924007—21no—
88#11924007—21no—
89C22⋊Dic73—21no—
90C22⋊Dic73—21no—
91#11924005—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005—21no—
96#11924005D411yescharacteristic
97#11924005D411yescharacteristic
98C4×Dic73—21no—
99C2×D4×C73C2311yescharacteristic
100C2×D4×C73C2311yescharacteristic
101C22×C4×C73—21no—
102C22×C4×C73—21no—
103D8×C73—22no—
104C2×C8×C73C2311yescharacteristic
105C2×C8×C73C2311yescharacteristic
106C4⋊C4×C73C2311yescharacteristic
107C4⋊C4×C73C2311yescharacteristic
108C22⋊C4×C73—21no—
109C22⋊C4×C73—21no—
110C42×C73C2311yescharacteristic
111C23×C73—21no—
112C23×C73—21no—
113C22×D73—21no—
114C22×D73—42no—
115C22×D73—42no—
116C22×D73—81no—
117C22×D73C2×D411yescharacteristic
118C22×D73C2×D411yescharacteristic
119D4×C73—21no—
120D4×C73—21no—
121D4×C73—21no—
122D4×C73#4112yes—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—81no—
126C2×C4×C73—81no—
127C2×C4×C73C2×D411yescharacteristic
128C2×C4×C73C2×D411yescharacteristic
129C2×C4×C73C2411yescharacteristic
130C22⋊D73—42no—
131C22⋊D73—42no—
132C22⋊D73—42no—
133C22⋊D73—81no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—42no—
138C2×Dic73C2×D411yescharacteristic
139C2×Dic73C2×D411yescharacteristic
140D292—21no—
141D292—21no—
142D292—41no—
143D292—81no—
144C4×D73—21no—
145C4×D73—21no—
146C4×D73—21no—
147C4×D73—21no—
148C4×D73—81no—
149Dic146—21no—
150Dic146—21no—
151C8×C73—21no—
152C8×C73—21no—
153#10596831—21no—
154#10596831—21no—
155C22×C73—22no—
156C22×C73—41no—
157C22×C73—41no—
158C22×C73—41no—
159C22×C73—41no—
160C22×C73—41no—
161C22×C73C22×D411yescharacteristic
162C2×D73—21no—
163C2×D73—21no—
164C2×D73—21no—
165C2×D73—21no—
166C2×D73—21no—
167C2×D73—21no—
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×C73C2×#4111yescharacteristic
177C4×C73H(5,𝔽2)11yescharacteristic
178Dic73—21no—
179Dic73—21no—
180Dic73—41no—
181Dic73—41no—
182Dic73—41no—
183C2×C73—42no—
184C2×C73—81no—
185C2×C73#54611yescharacteristic
186C2×C73#57511yescharacteristic
187C2×C73#57611yescharacteristic
188D73—41no—
189D73—41no—
190D73—81no—
191#3322—731nomaximal, Sylow
192C73#332211yescharacteristic, complemented, Sylow
193#553—731no—
194#546—731no—
195#488—731no—
196#485—731no—
197#480—731no—
198#478—731no—
199#469—731no—
200#468—731no—
201#463—731no—
202#449—731no—
203#447—731no—
204C4×D8D7311yescharacteristic, complemented
205#436—731no—
206#418—731no—
207#417—731no—
208C2×#41—731no—
209C22×D4—731no—
210C2×SD16—731no—
211C2×D8—731no—
212C2×D8C2×D7311yescharacteristic
213C2×M16—731no—
214C2×M16—731no—
215#126—1461no—
216#125—731no—
217#124—731no—
218#123—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—1461no—
229C4×D4C2×D7311yescharacteristic
230C4×D4C2×D7311yescharacteristic, complemented
231#117—731no—
232C2×C4⋊C4—731no—
233C2×C22⋊C4—1461no—
234#107—731no—
235#107C2×D7311yescharacteristic, complemented
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#102—731no—
245#102—731no—
246#102C2×D7311yescharacteristic
247#102C2×D7311yescharacteristic, complemented
248C22⋊C8—731no—
249C22⋊C8—731no—
250C4×C8C2×D7311yescharacteristic, complemented
251C24—1461no—
252#41—2921no—
253#41—1462no—
254C2×Q8—731no—
255C2×D4—2921no—
256C2×D4—731no—
257C2×D4—731no—
258C2×D4—1461no—
259C2×D4—1461no—
260C2×D4—1461no—
261C2×D4—1461no—
262C2×D4—1462no—
263C2×D4—1461no—
264C2×D4C22×D7311yescharacteristic
265C2×D4C22×D7311yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—731no—
269C22×C4—731no—
270C22×C4—1461no—
271C22×C4—1461no—
272SD16—2921no—
273D8—22no—
274D8—2921no—
275M16—2921no—
276M16—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⋊C4—1461no—
287C4⋊C4—1461no—
288C4⋊C4C22×D7311yescharacteristic
289C4⋊C4C22×D7311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—731no—
293C22⋊C4—731no—
294C22⋊C4—1461no—
295C22⋊C4—1461no—
296C22⋊C4—1461no—
297C22⋊C4—1461no—
298C22⋊C4—1461no—
299C22⋊C4—1461no—
300C22⋊C4—1461no—
301C42—1461no—
302C42C22×D7311yescharacteristic
303C23—21no—
304C23—21no—
305C23—2922no—
306C23—2922no—
307C23—5841no—
308C23—731no—
309C23—731no—
310C23—1461no—
311Q8—1461no—
312Q8—1461no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—2921no—
317D4—2922no—
318D4—2922no—
319D4—2922no—
320D4—5841no—
321D4—5841no—
322D4—1461no—
323D4—1461no—
324D4#1192402812yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—2922no—
330C2×C4—5841no—
331C2×C4—731no—
332C2×C4—731no—
333C2×C4—1461no—
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—22no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—2921no—
354C22—2921no—
355C22—2921no—
356C22—5844no—
357C22—1461no—
358C22—1461no—
359C22—1461no—
360C22—1461no—
361C22—1461no—
362C22—1461no—
363C22C2×D4×D7311yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—2921no—
369C4—2921no—
370C4—2921no—
371C4—1461no—
372C4—1461no—
373C4C2×#1192402811yescharacteristic
374C4#1455663711yescharacteristic
375C2—42no—
376C2—81no—
377C2—2921no—
378C2—2921no—
379C2—5841no—
380C2#1798923311yescharacteristic
381C2#1798938411yescharacteristic
382C2#1798938811yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC4×D8×C73C2
socleC22×C73C22×D4
hypercenterC4×D8D73
hypocenterC73#3322
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #17989287C2semidirect
2. #17989232C2semidirect
3. #17988942C2semidirect
4. #17988930C2semidirect
5. #17988902C2semidirect
6. #17988887C2semidirect
7. #17988839C2semidirect
8. #17988832C2semidirect
9. #17988802C2semidirect
10. #17988729C2semidirect
11. #17988719C2semidirect
12. #17988666C2semidirect
13. #17988590C2semidirect
14. #17988585C2semidirect
15. C4×D8×C73C2semidirect
18. C2×#11924016C22semidirect
21. C2×#11924011C22semidirect
23. #14556583C22semidirect
32. #14556562C22semidirect
37. C4⋊C4×D73C22semidirect
39. #14556524C22semidirect
40. #14556522C22semidirect
41. C4⋊#10596831C22semidirect
42. #14556516C22semidirect
43. #14556516C22semidirect
44. #14556514C22semidirect
51. #14556503C22semidirect
54. C4×D4×C73C22semidirect
55. #107×C73C22semidirect
57. #102×C73C22semidirect
58. C4×C8×C73C22semidirect
192. C73#3322semidirect
204. C4×D8D73semidirect
230. C4×D4C2×D73semidirect
235. #107C2×D73semidirect
247. #102C2×D73semidirect
250. C4×C8C2×D73semidirect