Finite Group Databasebeta

← #22620780

Subgroups — #22620780

Order 9344.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989165C211yesmaximal, characteristic, complemented
2#17989153C211yesmaximal, characteristic, complemented
3#17988927C211yesmaximal, characteristic, complemented
4#17988909C211yesmaximal, characteristic, complemented
5#17988903C211yesmaximal, characteristic, complemented
6#17988901C211yesmaximal, characteristic, complemented
7#17988839C211yesmaximal, characteristic, complemented
8#17988830C211yesmaximal, characteristic, complemented
9#17988820C211yesmaximal, characteristic, complemented
10#17988819C211yesmaximal, characteristic, complemented
11#17988736C211yesmaximal, characteristic, complemented
12#17988732C211yesmaximal, characteristic, complemented
13#17988719C211yesmaximal, characteristic, complemented
14#17988552C211yesmaximal, characteristic, complemented
15#449×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×D4×D73C2211yescharacteristic
18C2×#11924015C2211yescharacteristic
19C2×#11924013C2211yescharacteristic
20C2×#11924011C2211yescharacteristic, complemented
21C2×C8×D73C2211yescharacteristic, complemented
22#14556587—21no—
23#14556577—21no—
24#14556570—21no—
25#14556567C2211yescharacteristic
26#14556567C2211yescharacteristic, complemented
27#14556566C2211yescharacteristic
28#14556565—21no—
29#14556565C2211yescharacteristic
30#14556563—21no—
31#14556563—21no—
32#14556562C2211yescharacteristic
33#14556562C2211yescharacteristic
34#14556562C2211yescharacteristic, complemented
35#14556561—21no—
36#14556559—21no—
37#14556549C2211yescharacteristic
38C2×C4⋊Dic73C2211yescharacteristic, complemented
39#14556525C2211yescharacteristic, complemented
40#14556525C2211yescharacteristic, complemented
41#14556522C2211yescharacteristic, complemented
42#14556522C2211yescharacteristic, complemented
43#14556515C2211yescharacteristic, complemented
44#14556513C2211yescharacteristic
45#14556513C2211yescharacteristic
46#14556512C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556512C2211yescharacteristic, complemented
49C22⋊#10596831C2211yescharacteristic, complemented
50#14556503C2211yescharacteristic
51#14556503C2211yescharacteristic
52C2×#41×C73C2211yescharacteristic, complemented
53C2×SD16×C73C2211yescharacteristic
54C2×D8×C73C2211yescharacteristic
55#121×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic, complemented
57#102×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⋊D73—21no—
70C2×C22⋊D73—21no—
71C2×C22⋊D73D411yescharacteristic
72C2×C22⋊D73D411yescharacteristic
73D4×D73—41no—
74D4×D73—41no—
75C22×Dic73—21no—
76C2×C4×D73C2311yescharacteristic
77C2×C4×D73C2311yescharacteristic
78#11924015—41no—
79#11924013—41no—
80#11924011—41no—
81C2×#10596831C2311yescharacteristic
82C2×#10596831C2311yescharacteristic
83C8×D73—41no—
84C4⋊Dic73—21no—
85C4⋊Dic73C2311yescharacteristic
86C4⋊Dic73C2311yescharacteristic
87C4⋊Dic73C2311yescharacteristic
88#11924007—21no—
89#11924007—21no—
90C22⋊Dic73—21no—
91C22⋊Dic73—21no—
92C22⋊Dic73—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005—21no—
96#11924005—21no—
97#11924005—21no—
98C4×Dic73—21no—
99#41×C73—41no—
100#41×C73—41no—
101C2×Q8×C73C2311yescharacteristic
102C2×D4×C73—21no—
103C2×D4×C73—21no—
104C2×D4×C73C2311yescharacteristic
105C2×D4×C73C2311yescharacteristic
106C22×C4×C73—21no—
107C22×C4×C73C2311yescharacteristic
108SD16×C73—41no—
109D8×C73—41no—
110C2×C8×C73C2311yescharacteristic
111C2×C8×C73C2311yescharacteristic
112C4⋊C4×C73C2311yescharacteristic
113C22⋊C4×C73—21no—
114C23×C73—21no—
115C23×C73—21no—
116C23×C73C2×D411yescharacteristic
117C22×D73—21no—
118C22×D73—42no—
119C22×D73—81no—
120C22×D73—81no—
121C22×D73C2×D411yescharacteristic
122C22×D73C2×D411yescharacteristic
123Q8×C73—21no—
124Q8×C73—21no—
125D4×C73—21no—
126D4×C73—21no—
127D4×C73—21no—
128D4×C73—21no—
129D4×C73—42no—
130D4×C73—81no—
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—
143C22⋊D73—81no—
144C22⋊D73—81no—
145C2×Dic73—21no—
146C2×Dic73—21no—
147C2×Dic73—21no—
148C2×Dic73—81no—
149C2×Dic73C2×D411yescharacteristic
150C2×Dic73C2×D411yescharacteristic
151D292—21no—
152D292—21no—
153D292—41no—
154D292—81no—
155C4×D73—21no—
156C4×D73—21no—
157C4×D73—21no—
158C4×D73—21no—
159Dic146—41no—
160C8×C73—21no—
161C8×C73—21no—
162#10596831—21no—
163#10596831—21no—
164C22×C73—21no—
165C22×C73—21no—
166C22×C73—21no—
167C22×C73—41no—
168C22×C73—41no—
169C22×C73—41no—
170C22×C73—41no—
171C22×C73—41no—
172C22×C73—41no—
173C22×C73C22×D411yescharacteristic
174C2×D73—21no—
175C2×D73—21no—
176C2×D73—21no—
177C2×D73—21no—
178C2×D73—21no—
179C2×D73—21no—
180C2×D73—41no—
181C2×D73—41no—
182C2×D73—41no—
183C2×D73—84no—
184C4×C73—21no—
185C4×C73—41no—
186C4×C73—41no—
187C4×C73H(5,𝔽2)11yescharacteristic
188C4×C73H(5,𝔽2)11yescharacteristic
189Dic73—21no—
190Dic73—21no—
191Dic73—41no—
192Dic73—41no—
193Dic73—41no—
194C2×C73—41no—
195C2×C73—81no—
196C2×C73—81no—
197C2×C73#53411yescharacteristic
198C2×C73#57611yescharacteristic
199C2×C73#57711yescharacteristic
200D73—41no—
201D73—41no—
202D73—81no—
203#3198—731nomaximal, Sylow
204C73#319811yescharacteristic, complemented, Sylow
205#537—731no—
206#535—731no—
207#485—731no—
208#482—731no—
209#481—731no—
210#480—731no—
211#469—731no—
212#468—731no—
213#466—731no—
214#465—731no—
215#450—731no—
216#449—731no—
217#449D7311yescharacteristic, complemented
218#447—731no—
219#408—731no—
220C2×#41—731no—
221C2×#41C2×D7311yescharacteristic, complemented
222C22×D4—731no—
223C2×SD16—731no—
224C2×SD16C2×D7311yescharacteristic
225C2×D8—731no—
226C2×D8C2×D7311yescharacteristic
227C2×M16—731no—
228C22×C8—731no—
229#127—1461no—
230#124—1461no—
231C22⋊Q8—731no—
232C22⋊Q8—731no—
233C22⋊Q8—1461no—
234#121—731no—
235#121—731no—
236#121—731no—
237#121—731no—
238#121—731no—
239#121—1461no—
240#121—1461no—
241#121—1461no—
242#121C2×D7311yescharacteristic
243#120—1461no—
244#120—1461no—
245#117—731no—
246C2×C4⋊C4—731no—
247#107—731no—
248#107—731no—
249#106—731no—
250#106—731no—
251#103—731no—
252#103C2×D7311yescharacteristic, complemented
253#102—731no—
254#102—731no—
255#102—731no—
256#102—731no—
257#102—731no—
258#102C2×D7311yescharacteristic, complemented
259C22⋊C8—731no—
260C22⋊C8—731no—
261C22⋊C8—731no—
262C22⋊C8C2×D7311yescharacteristic, complemented
263C24—1461no—
264#41—41no—
265#41—41no—
266#41—2921no—
267#41—2921no—
268C2×Q8—731no—
269C2×Q8C22×D7311yescharacteristic
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—2921no—
273C2×D4—2921no—
274C2×D4—731no—
275C2×D4—731no—
276C2×D4—731no—
277C2×D4—731no—
278C2×D4—1461no—
279C2×D4—1461no—
280C2×D4—1461no—
281C2×D4—1461no—
282C2×D4—1461no—
283C2×D4—1461no—
284C2×D4C22×D7311yescharacteristic
285C2×D4C22×D7311yescharacteristic
286C22×C4—21no—
287C22×C4—731no—
288C22×C4—731no—
289C22×C4—1461no—
290C22×C4C22×D7311yescharacteristic
291SD16—41no—
292SD16—2921no—
293D8—41no—
294D8—2921no—
295M16—2921no—
296C2×C8—2921no—
297C2×C8—731no—
298C2×C8—731no—
299C2×C8C22×D7311yescharacteristic
300C2×C8C22×D7311yescharacteristic
301C4⋊C4—731no—
302C4⋊C4—731no—
303C4⋊C4—731no—
304C4⋊C4—1461no—
305C4⋊C4—1461no—
306C4⋊C4—1461no—
307C4⋊C4C22×D7311yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—1461no—
310C22⋊C4—1461no—
311C22⋊C4—1461no—
312C22⋊C4—1461no—
313C22⋊C4—1461no—
314C22⋊C4—1461no—
315C22⋊C4—1461no—
316C22⋊C4—1461no—
317C42—1461no—
318C23—21no—
319C23—21no—
320C23—2922no—
321C23—5841no—
322C23—5841no—
323C23—731no—
324C23—731no—
325C23—1461no—
326C23D4×D7311yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—2921no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—81no—
336D4—2921no—
337D4—2921no—
338D4—2921no—
339D4—2922no—
340D4—5841no—
341D4—5841no—
342D4—5841no—
343D4—5841no—
344D4—5841no—
345D4—1461no—
346D4—1461no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—5841no—
353C2×C4—731no—
354C2×C4—731no—
355C2×C4—1461no—
356C2×C4—1461no—
357C2×C4—1461no—
358C2×C4—1461no—
359C2×C4—1461no—
360C2×C4—1461no—
361C2×C4—1461no—
362C2×C4D4×D7311yescharacteristic
363C2×C4C23×D7311yescharacteristic
364C8—21no—
365C8—21no—
366C8—1461no—
367C8—1461no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—2921no—
378C22—2921no—
379C22—2921no—
380C22—5844no—
381C22—1461no—
382C22—1461no—
383C22—1461no—
384C22—1461no—
385C22—1461no—
386C22—1461no—
387C22C2×D4×D7311yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—2921no—
392C4—2921no—
393C4—2921no—
394C4—1461no—
395C4—1461no—
396C4#1455663611yescharacteristic
397C4#1455663611yescharacteristic
398C2—41no—
399C2—81no—
400C2—81no—
401C2—2921no—
402C2—2921no—
403C2—5841no—
404C2#1798914711yescharacteristic
405C2#1798938911yescharacteristic
406C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#449×C73C2
socleC22×C73C22×D4
hypercenter#449D73
hypocenterC73#3198
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #17989165C2semidirect
2. #17989153C2semidirect
3. #17988927C2semidirect
4. #17988909C2semidirect
5. #17988903C2semidirect
6. #17988901C2semidirect
7. #17988839C2semidirect
8. #17988830C2semidirect
9. #17988820C2semidirect
10. #17988819C2semidirect
11. #17988736C2semidirect
12. #17988732C2semidirect
13. #17988719C2semidirect
14. #17988552C2semidirect
15. #449×C73C2semidirect
20. C2×#11924011C22semidirect
21. C2×C8×D73C22semidirect
26. #14556567C22semidirect
34. #14556562C22semidirect
38. C2×C4⋊Dic73C22semidirect
39. #14556525C22semidirect
40. #14556525C22semidirect
41. #14556522C22semidirect
42. #14556522C22semidirect
43. #14556515C22semidirect
48. #14556512C22semidirect
49. C22⋊#10596831C22semidirect
52. C2×#41×C73C22semidirect
56. #103×C73C22semidirect
57. #102×C73C22semidirect
58. C22⋊C8×C73C22semidirect
204. C73#3198semidirect
217. #449D73semidirect
221. C2×#41C2×D73semidirect
252. #103C2×D73semidirect
258. #102C2×D73semidirect
262. C22⋊C8C2×D73semidirect