Finite Group Databasebeta

← #22620801

Subgroups — #22620801

Order 9344.

410 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989161C211yesmaximal, characteristic, complemented
2#17989153C211yesmaximal, characteristic
3#17988927C211yesmaximal, characteristic, complemented
4#17988926C211yesmaximal, characteristic, complemented
5#17988912C211yesmaximal, characteristic, complemented
6#17988908C211yesmaximal, characteristic, complemented
7#17988836C211yesmaximal, characteristic, complemented
8#17988830C211yesmaximal, characteristic, complemented
9#17988819C211yesmaximal, characteristic, complemented
10#17988813C211yesmaximal, characteristic, complemented
11#17988736C211yesmaximal, characteristic, complemented
12#17988736C211yesmaximal, characteristic, complemented
13#17988726C211yesmaximal, characteristic, complemented
14#17988552C211yesmaximal, characteristic, complemented
15#448×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×D4×D73C2211yescharacteristic
18C2×#11924015C2211yescharacteristic
19C2×#11924015C2211yescharacteristic
20C2×#11924011C2211yescharacteristic, complemented
21C2×C8×D73C2211yescharacteristic, complemented
22#14556589—21no—
23#14556587—21no—
24#14556580—21no—
25#14556577—21no—
26#14556574—21no—
27#14556574—21no—
28#14556567C2211yescharacteristic
29#14556567C2211yescharacteristic
30#14556567C2211yescharacteristic, complemented
31#14556567C2211yescharacteristic, complemented
32#14556566C2211yescharacteristic
33#14556565C2211yescharacteristic
34#14556562C2211yescharacteristic
35#14556561—21no—
36#14556559—21no—
37#14556550C2211yescharacteristic, complemented
38#14556549C2211yescharacteristic
39#14556525C2211yescharacteristic, complemented
40#14556524C2211yescharacteristic, complemented
41#14556523C2211yescharacteristic, complemented
42#14556522C2211yescharacteristic, complemented
43#14556515C2211yescharacteristic, complemented
44#14556515C2211yescharacteristic, complemented
45#14556513C2211yescharacteristic
46#14556513C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556512C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic, complemented
50#14556503C2211yescharacteristic
51#14556503C2211yescharacteristic
52C22×Q8×C73C2211yescharacteristic, complemented
53C2×SD16×C73C2211yescharacteristic
54C2×SD16×C73C2211yescharacteristic
55#121×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic, complemented
57#103×C73C2211yescharacteristic, complemented
58C22⋊C8×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60#11924028—41no—
61#11924028—41no—
62C2×Dic146D411yescharacteristic
63C2×D292—21no—
64C2×D292D411yescharacteristic
65C2×D292C2311yescharacteristic
66C2×C22⋊D73—21no—
67C2×C22⋊D73—21no—
68C2×C22⋊D73—21no—
69C2×C22⋊D73D411yescharacteristic
70C2×C22⋊D73D411yescharacteristic
71D4×D73—41no—
72D4×D73—41no—
73C2×C4×D73C2311yescharacteristic
74C2×C4×D73C2311yescharacteristic
75#11924015—41no—
76#11924015—41no—
77#11924011—41no—
78C2×#10596831C2311yescharacteristic
79C2×#10596831C2311yescharacteristic
80C8×D73—41no—
81C4⋊Dic73C2311yescharacteristic
82C4⋊Dic73C2311yescharacteristic
83C4⋊Dic73C2311yescharacteristic
84#11924007—21no—
85#11924007—21no—
86#11924007—21no—
87#11924007—21no—
88C22⋊Dic73—21no—
89C22⋊Dic73—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005—21no—
96#11924005—21no—
97C4×Dic73—21no—
98C4×Dic73—21no—
99C2×Q8×C73—21no—
100C2×Q8×C73—41no—
101C2×Q8×C73—41no—
102C2×Q8×C73C2311yescharacteristic
103C2×Q8×C73C2311yescharacteristic
104C2×D4×C73—21no—
105C2×D4×C73C2311yescharacteristic
106C22×C4×C73—21no—
107C22×C4×C73C2311yescharacteristic
108SD16×C73—41no—
109SD16×C73—41no—
110C2×C8×C73C2311yescharacteristic
111C2×C8×C73C2311yescharacteristic
112C4⋊C4×C73C2311yescharacteristic
113C22⋊C4×C73—21no—
114C23×C73—21no—
115C23×C73C2×D411yescharacteristic
116C22×D73—21no—
117C22×D73—42no—
118C22×D73—81no—
119C22×D73—81no—
120C22×D73C2×D411yescharacteristic
121C22×D73C2×D411yescharacteristic
122Q8×C73—21no—
123Q8×C73—21no—
124Q8×C73—21no—
125Q8×C73—21no—
126Q8×C73—42no—
127D4×C73—21no—
128D4×C73—21no—
129D4×C73—81no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—42no—
136C2×C4×C73C2×D411yescharacteristic
137C2×C4×C73C2411yescharacteristic
138C22⋊D73—41no—
139C22⋊D73—41no—
140C22⋊D73—42no—
141C22⋊D73—81no—
142C22⋊D73—81no—
143C2×Dic73—21no—
144C2×Dic73—21no—
145C2×Dic73—21no—
146C2×Dic73C2×D411yescharacteristic
147C2×Dic73C2×D411yescharacteristic
148D292—21no—
149D292—21no—
150D292—41no—
151D292—81no—
152C4×D73—21no—
153C4×D73—21no—
154C4×D73—21no—
155C4×D73—21no—
156Dic146—41no—
157C8×C73—21no—
158C8×C73—21no—
159#10596831—21no—
160#10596831—21no—
161C22×C73—21no—
162C22×C73—21no—
163C22×C73—21no—
164C22×C73—41no—
165C22×C73—41no—
166C22×C73—41no—
167C22×C73C22×D411yescharacteristic
168C2×D73—21no—
169C2×D73—21no—
170C2×D73—21no—
171C2×D73—21no—
172C2×D73—21no—
173C2×D73—21no—
174C2×D73—41no—
175C2×D73—41no—
176C2×D73—41no—
177C2×D73—84no—
178C4×C73—21no—
179C4×C73—41no—
180C4×C73—41no—
181C4×C73—41no—
182C4×C73H(5,𝔽2)11yescharacteristic
183C4×C73H(5,𝔽2)11yescharacteristic
184Dic73—21no—
185Dic73—21no—
186Dic73—41no—
187Dic73—41no—
188Dic73—41no—
189C2×C73—41no—
190C2×C73—81no—
191C2×C73#53411yescharacteristic
192C2×C73#57711yescharacteristic
193C2×C73#57711yescharacteristic
194D73—41no—
195D73—41no—
196D73—81no—
197#3200—731nomaximal, Sylow
198C73#320011yescharacteristic, complemented, Sylow
199#536—731no—
200#535—731no—
201#485—731no—
202#485—731no—
203#482—731no—
204#482—731no—
205#468—731no—
206#468—731no—
207#465—731no—
208#465—731no—
209#450—731no—
210#450—731no—
211#448—731no—
212#448D7311yescharacteristic, complemented
213#408—731no—
214C2×#41—731no—
215C22×Q8C2×D7311yescharacteristic, complemented
216C22×D4—731no—
217C2×SD16—731no—
218C2×SD16—731no—
219C2×SD16C2×D7311yescharacteristic
220C2×SD16C2×D7311yescharacteristic
221C2×M16—731no—
222C22×C8—731no—
223C4⋊Q8—1461no—
224#127—1461no—
225#124—1461no—
226#124—1461no—
227#123—1461no—
228#123—1461no—
229C22⋊Q8—731no—
230C22⋊Q8—731no—
231C22⋊Q8—731no—
232C22⋊Q8—731no—
233#121—731no—
234#121—731no—
235#121—731no—
236#121C2×D7311yescharacteristic
237#120—1461no—
238#120—1461no—
239#117—731no—
240#117—731no—
241#107—731no—
242#107—731no—
243#106—731no—
244#106—731no—
245#103—731no—
246#103—731no—
247#103C2×D7311yescharacteristic, complemented
248#103C2×D7311yescharacteristic, complemented
249#102—731no—
250#102—731no—
251#102—731no—
252#102—731no—
253C22⋊C8—731no—
254C22⋊C8—731no—
255C22⋊C8—731no—
256C22⋊C8C2×D7311yescharacteristic, complemented
257C24—1461no—
258#41—2921no—
259#41—2921no—
260C2×Q8—21no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×Q8—731no—
264C2×Q8C22×D7311yescharacteristic
265C2×Q8C22×D7311yescharacteristic
266C2×D4—21no—
267C2×D4—2921no—
268C2×D4—2921no—
269C2×D4—731no—
270C2×D4—731no—
271C2×D4—731no—
272C2×D4—731no—
273C2×D4—1461no—
274C2×D4—1461no—
275C2×D4—1461no—
276C2×D4—1461no—
277C2×D4C22×D7311yescharacteristic
278C22×C4—21no—
279C22×C4—731no—
280C22×C4—731no—
281C22×C4C22×D7311yescharacteristic
282SD16—41no—
283SD16—41no—
284SD16—2921no—
285SD16—2921no—
286M16—2921no—
287C2×C8—2921no—
288C2×C8—731no—
289C2×C8—731no—
290C2×C8C22×D7311yescharacteristic
291C2×C8C22×D7311yescharacteristic
292C4⋊C4—731no—
293C4⋊C4—731no—
294C4⋊C4—731no—
295C4⋊C4—1461no—
296C4⋊C4—1461no—
297C4⋊C4—1461no—
298C4⋊C4—1461no—
299C4⋊C4C22×D7311yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—1461no—
302C22⋊C4—1461no—
303C22⋊C4—1461no—
304C22⋊C4—1461no—
305C22⋊C4—1461no—
306C22⋊C4—1461no—
307C22⋊C4—1461no—
308C22⋊C4—1461no—
309C22⋊C4—1461no—
310C42—1461no—
311C42—1461no—
312C23—21no—
313C23—2922no—
314C23—5841no—
315C23—5841no—
316C23—731no—
317C23—731no—
318C23—1461no—
319C23D4×D7311yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—42no—
325Q8—2921no—
326D4—21no—
327D4—21no—
328D4—81no—
329D4—2921no—
330D4—2921no—
331D4—2921no—
332D4—2922no—
333D4—5841no—
334D4—5841no—
335D4—5841no—
336D4—1461no—
337D4—1461no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—731no—
345C2×C4—731no—
346C2×C4—1461no—
347C2×C4—1461no—
348C2×C4—1461no—
349C2×C4—1461no—
350C2×C4—1461no—
351C2×C4—1461no—
352C2×C4—1461no—
353C2×C4D4×D7311yescharacteristic
354C2×C4C23×D7311yescharacteristic
355C8—21no—
356C8—21no—
357C8—1461no—
358C8—1461no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—2921no—
366C22—2921no—
367C22—2921no—
368C22—5844no—
369C22—1461no—
370C22—1461no—
371C22—1461no—
372C22—1461no—
373C22—1461no—
374C22—1461no—
375C22C2×D4×D7311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—2921no—
381C4—2921no—
382C4—2921no—
383C4—1461no—
384C4—1461no—
385C4#1455663611yescharacteristic
386C4#1455663611yescharacteristic
387C2—41no—
388C2—81no—
389C2—2921no—
390C2—2921no—
391C2—5841no—
392C2#1798914711yescharacteristic
393C2#1798939311yescharacteristic
394C2#1798939611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#448×C73C2
socleC22×C73C22×D4
hypercenter#448D73
hypocenterC73#3200
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. #17989161C2semidirect
3. #17988927C2semidirect
4. #17988926C2semidirect
5. #17988912C2semidirect
6. #17988908C2semidirect
7. #17988836C2semidirect
8. #17988830C2semidirect
9. #17988819C2semidirect
10. #17988813C2semidirect
11. #17988736C2semidirect
12. #17988736C2semidirect
13. #17988726C2semidirect
14. #17988552C2semidirect
15. #448×C73C2semidirect
20. C2×#11924011C22semidirect
21. C2×C8×D73C22semidirect
30. #14556567C22semidirect
31. #14556567C22semidirect
37. #14556550C22semidirect
39. #14556525C22semidirect
40. #14556524C22semidirect
41. #14556523C22semidirect
42. #14556522C22semidirect
43. #14556515C22semidirect
44. #14556515C22semidirect
49. C22⋊#10596831C22semidirect
52. C22×Q8×C73C22semidirect
56. #103×C73C22semidirect
57. #103×C73C22semidirect
58. C22⋊C8×C73C22semidirect
198. C73#3200semidirect
212. #448D73semidirect
215. C22×Q8C2×D73semidirect
247. #103C2×D73semidirect
248. #103C2×D73semidirect
256. C22⋊C8C2×D73semidirect