Finite Group Databasebeta

← #22622151

Subgroups — #22622151

Order 9344.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989271C211yesmaximal, characteristic, complemented
2#17989231C211yesmaximal, characteristic
3#17988940C211yesmaximal, characteristic, complemented
4#17988929C211yesmaximal, characteristic, complemented
5#17988904C211yesmaximal, characteristic, complemented
6#17988885C211yesmaximal, characteristic, complemented
7#17988843C211yesmaximal, characteristic, complemented
8#17988830C211yesmaximal, characteristic, complemented
9#17988807C211yesmaximal, characteristic, complemented
10#17988746C211yesmaximal, characteristic, complemented
11SD16×Dic73C211yesmaximal, characteristic, complemented
12#17988662C211yesmaximal, characteristic, complemented
13#17988592C211yesmaximal, characteristic, complemented
14#17988585C211yesmaximal, characteristic, complemented
15#450×C73C211yesmaximal, characteristic, complemented
16C2×#11924027C2211yescharacteristic
17C2×#11924018C2211yescharacteristic, complemented
18C2×#11924012C2211yescharacteristic
19C2×#11924011C2211yescharacteristic, complemented
20#14556584—21no—
21#14556582C2211yescharacteristic, complemented
22#14556581—21no—
23#14556578C2211yescharacteristic
24#14556573—21no—
25#14556572—21no—
26#14556570C2211yescharacteristic
27#14556567C2211yescharacteristic, complemented
28#14556563—21no—
29#14556562C2211yescharacteristic
30#14556560—21no—
31Q8×Dic73C2211yescharacteristic, complemented
32D4×Dic73C2211yescharacteristic
33C4×C22⋊D73C2211yescharacteristic
34#14556550C2211yescharacteristic
35#14556549—21no—
36C4⋊C4×D73C2211yescharacteristic, complemented
37C2×C22⋊Dic73—21no—
38#14556525C2211yescharacteristic, complemented
39#14556523C2211yescharacteristic, complemented
40#14556522C2211yescharacteristic, complemented
41#14556520C2211yescharacteristic, complemented
42#14556516C2211yescharacteristic, complemented
43#14556516C2211yescharacteristic, complemented
44#14556515C2211yescharacteristic, complemented
45#14556514C2211yescharacteristic, complemented
46#14556512C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556512C2211yescharacteristic
49#14556512C2211yescharacteristic
50#14556503C2211yescharacteristic, complemented
51C8×Dic73C2211yescharacteristic, complemented
52C22×D4×C73C2211yescharacteristic
53C2×SD16×C73C2211yescharacteristic
54C2×SD16×C73C2211yescharacteristic
55C22⋊Q8×C73C2211yescharacteristic
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59#11924027—22no—
60#11924027—41no—
61C2×Dic146C2311yescharacteristic
62C2×C22⋊D73—21no—
63C2×C22⋊D73—21no—
64C2×C22⋊D73D411yescharacteristic
65C22×Dic73—21no—
66C22×Dic73—21no—
67C2×C4×D73—21no—
68C2×C4×D73C2311yescharacteristic
69#11924018—41no—
70#11924012—41no—
71#11924011—41no—
72C2×#10596831C2311yescharacteristic
73C2×#10596831C2311yescharacteristic
74C4⋊Dic73—21no—
75C4⋊Dic73—21no—
76C4⋊Dic73C2311yescharacteristic
77C4⋊Dic73C2311yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83#11924007D411yescharacteristic
84C22⋊Dic73—21no—
85C22⋊Dic73—21no—
86C22⋊Dic73—21no—
87C22⋊Dic73—21no—
88C22⋊Dic73—21no—
89C22⋊Dic73—21no—
90C22⋊Dic73D411yescharacteristic
91#11924005—21no—
92#11924005D411yescharacteristic
93C4×Dic73—21no—
94C4×Dic73—21no—
95C4×Dic73C2311yescharacteristic
96C24×C73—21no—
97C2×Q8×C73C2311yescharacteristic
98C2×D4×C73—22no—
99C2×D4×C73—21no—
100C2×D4×C73—41no—
101C2×D4×C73C2311yescharacteristic
102C2×D4×C73C2311yescharacteristic
103C22×C4×C73C2311yescharacteristic
104SD16×C73—22no—
105SD16×C73—41no—
106C2×C8×C73C2311yescharacteristic
107C2×C8×C73C2311yescharacteristic
108C4⋊C4×C73—21no—
109C4⋊C4×C73C2311yescharacteristic
110C22⋊C4×C73—21no—
111C23×C73—21no—
112C23×C73—21no—
113C23×C73—42no—
114C23×C73—42no—
115C23×C73—81no—
116C23×C73C2×D411yescharacteristic
117C22×D73C2×D411yescharacteristic
118Q8×C73—21no—
119Q8×C73—21no—
120D4×C73—21no—
121D4×C73—21no—
122D4×C73—21no—
123D4×C73—42no—
124D4×C73#4112yes—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73C2×D411yescharacteristic
130C2×C4×C73C2411yescharacteristic
131C22⋊D73—41no—
132C22⋊D73—42no—
133C22⋊D73—81no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—21no—
138C2×Dic73—42no—
139C2×Dic73—81no—
140C2×Dic73C2×D411yescharacteristic
141C2×Dic73C2×D411yescharacteristic
142C2×Dic73C2×D411yescharacteristic
143C4×D73—21no—
144C4×D73—21no—
145C4×D73—42no—
146Dic146—21no—
147Dic146—21no—
148C8×C73—21no—
149C8×C73—21no—
150#10596831—21no—
151#10596831—21no—
152C22×C73—22no—
153C22×C73—21no—
154C22×C73—21no—
155C22×C73—21no—
156C22×C73—41no—
157C22×C73—41no—
158C22×C73—41no—
159C22×C73—41no—
160C22×C73—41no—
161C22×C73—84no—
162C22×C73C22×D411yescharacteristic
163C2×D73—21no—
164C2×D73—21no—
165C2×D73—21no—
166C4×C73—21no—
167C4×C73—41no—
168C4×C73—41no—
169C4×C73C2×#4111yescharacteristic
170C4×C73H(5,𝔽2)11yescharacteristic
171Dic73—21no—
172Dic73—21no—
173Dic73—21no—
174Dic73—41no—
175Dic73—41no—
176Dic73—41no—
177Dic73—41no—
178C2×C73—41no—
179C2×C73—42no—
180C2×C73—81no—
181C2×C73#54611yescharacteristic
182C2×C73#57511yescharacteristic
183C2×C73#57711yescharacteristic
184D73—41no—
185#3323—731nomaximal, Sylow
186C73#332311yescharacteristic, complemented, Sylow
187#552—731no—
188#546—731no—
189#488—731no—
190#485—731no—
191#481—731no—
192#478—731no—
193#470—731no—
194#468—731no—
195#464—731no—
196#452—731no—
197#450D7311yescharacteristic, complemented
198C4×SD16—731no—
199#436—731no—
200#418—731no—
201#417—731no—
202C2×#41—731no—
203C22×D4C2×D7311yescharacteristic
204C2×Q16—731no—
205C2×SD16C2×D7311yescharacteristic
206C2×SD16C2×D7311yescharacteristic
207C2×M16—731no—
208C2×M16—731no—
209#126—1461no—
210#125—731no—
211#125—1461no—
212#124—731no—
213#123—1461no—
214#123—1461no—
215C22⋊Q8—731no—
216C22⋊Q8—731no—
217C22⋊Q8C2×D7311yescharacteristic
218#121—731no—
219#121—1461no—
220#120—1461no—
221C4×Q8—731no—
222C4×D4—731no—
223C4×D4—731no—
224#117—731no—
225#117—1461no—
226C2×C4⋊C4—731no—
227C2×C22⋊C4—1461no—
228#107—731no—
229#106—731no—
230#106—731no—
231C4⋊C8—731no—
232#103—731no—
233#103—731no—
234#103—731no—
235#103—731no—
236#102—731no—
237#102—731no—
238#102—731no—
239#102—731no—
240#102C2×D7311yescharacteristic
241#102C2×D7311yescharacteristic
242C22⋊C8—731no—
243C22⋊C8C2×D7311yescharacteristic
244C4×C8—731no—
245C24—21no—
246#41—2921no—
247#41—1462no—
248C2×Q8—731no—
249C2×Q8C22×D7311yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—731no—
254C2×D4—1461no—
255C2×D4—1461no—
256C2×D4C22×D7311yescharacteristic
257C2×D4C22×D7311yescharacteristic
258C22×C4—731no—
259C22×C4—1461no—
260C22×C4—1461no—
261C22×C4—1461no—
262C22×C4C22×D7311yescharacteristic
263Q16—2921no—
264SD16—22no—
265SD16—41no—
266M16—2921no—
267M16—2921no—
268C2×C8—731no—
269C2×C8—731no—
270C2×C8C22×D7311yescharacteristic
271C2×C8C22×D7311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—731no—
274C4⋊C4—731no—
275C4⋊C4—731no—
276C4⋊C4—731no—
277C4⋊C4—1461no—
278C4⋊C4—1461no—
279C4⋊C4—1461no—
280C4⋊C4—1461no—
281C4⋊C4—1461no—
282C4⋊C4—1461no—
283C4⋊C4C22×D7311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—731no—
286C22⋊C4—731no—
287C22⋊C4—1461no—
288C22⋊C4—1461no—
289C22⋊C4—1461no—
290C22⋊C4—1461no—
291C22⋊C4—1461no—
292C22⋊C4—1461no—
293C22⋊C4—1461no—
294C42—731no—
295C42—1461no—
296C42—1461no—
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23—731no—
303C23D4×D7311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—1461no—
307Q8—1461no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—42no—
312D4—2922no—
313D4—2921no—
314D4—5841no—
315D4#1192402712yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—2922no—
321C2×C4—2922no—
322C2×C4—5841no—
323C2×C4—731no—
324C2×C4—731no—
325C2×C4—731no—
326C2×C4—1461no—
327C2×C4—1461no—
328C2×C4—1461no—
329C2×C4—1461no—
330C2×C4—1461no—
331C2×C4—1461no—
332C2×C4D4×D7311yescharacteristic
333C2×C4C23×D7311yescharacteristic
334C8—21no—
335C8—21no—
336C8—1461no—
337C8—1461no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—84no—
348C22—1461no—
349C22—1461no—
350C22—1461no—
351C22C2×D4×D7311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—2921no—
356C4—2921no—
357C4—2921no—
358C4—2921no—
359C4—1461no—
360C4—1461no—
361C4—1461no—
362C4C2×#1192402711yescharacteristic
363C4#1455663611yescharacteristic
364C2—41no—
365C2—42no—
366C2—81no—
367C2—2921no—
368C2#1798922411yescharacteristic
369C2#1798938311yescharacteristic
370C2#1798939311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#450×C73C2
socleC22×C73C22×D4
hypercenter#450D73
hypocenterC73#3323
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #17989271C2semidirect
3. #17988940C2semidirect
4. #17988929C2semidirect
5. #17988904C2semidirect
6. #17988885C2semidirect
7. #17988843C2semidirect
8. #17988830C2semidirect
9. #17988807C2semidirect
10. #17988746C2semidirect
11. SD16×Dic73C2semidirect
12. #17988662C2semidirect
13. #17988592C2semidirect
14. #17988585C2semidirect
15. #450×C73C2semidirect
17. C2×#11924018C22semidirect
19. C2×#11924011C22semidirect
21. #14556582C22semidirect
27. #14556567C22semidirect
31. Q8×Dic73C22semidirect
36. C4⋊C4×D73C22semidirect
38. #14556525C22semidirect
39. #14556523C22semidirect
40. #14556522C22semidirect
41. #14556520C22semidirect
42. #14556516C22semidirect
43. #14556516C22semidirect
44. #14556515C22semidirect
45. #14556514C22semidirect
50. #14556503C22semidirect
51. C8×Dic73C22semidirect
186. C73#3323semidirect
197. #450D73semidirect