Finite Group Databasebeta

← #22620779

Subgroups — #22620779

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#17989166C211yesmaximal, characteristic, complemented
2#17989154C211yesmaximal, characteristic, complemented
3#17988929C211yesmaximal, characteristic, complemented
4#17988908C211yesmaximal, characteristic, complemented
5#17988904C211yesmaximal, characteristic, complemented
6#17988899C211yesmaximal, characteristic, complemented
7#17988837C211yesmaximal, characteristic, complemented
8#17988832C211yesmaximal, characteristic, complemented
9#17988820C211yesmaximal, characteristic, complemented
10#17988815C211yesmaximal, characteristic, complemented
11#17988738C211yesmaximal, characteristic, complemented
12#17988729C211yesmaximal, characteristic, complemented
13#17988729C211yesmaximal, characteristic, complemented
14#17988552C211yesmaximal, characteristic, complemented
15#447×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×#11924027C2211yescharacteristic, complemented
18C2×#11924016C2211yescharacteristic
19C2×#11924016C2211yescharacteristic
20C2×#11924011C2211yescharacteristic, complemented
21C2×C8×D73C2211yescharacteristic, complemented
22#14556587—21no—
23#14556578—21no—
24#14556571C2211yescharacteristic, complemented
25#14556570C2211yescharacteristic
26#14556568—21no—
27#14556564—21no—
28#14556563—21no—
29#14556562—21no—
30#14556562C2211yescharacteristic
31#14556562C2211yescharacteristic
32#14556562C2211yescharacteristic
33#14556562C2211yescharacteristic
34#14556562C2211yescharacteristic, complemented
35#14556560—21no—
36#14556560—21no—
37#14556550C2211yescharacteristic
38C4⋊C4×D73C2211yescharacteristic, complemented
39#14556525C2211yescharacteristic, complemented
40#14556524C2211yescharacteristic, complemented
41#14556523C2211yescharacteristic, complemented
42#14556522C2211yescharacteristic, complemented
43#14556516C2211yescharacteristic, complemented
44#14556516C2211yescharacteristic, complemented
45#14556512C2211yescharacteristic
46#14556512C2211yescharacteristic
47#14556512C2211yescharacteristic, complemented
48#14556512C2211yescharacteristic, complemented
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic, complemented
51#14556503C2211yescharacteristic, complemented
52C22×D4×C73C2211yescharacteristic
53C2×D8×C73C2211yescharacteristic
54C2×D8×C73C2211yescharacteristic
55#121×C73C2211yescharacteristic
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59#11924028—41no—
60#11924028—41no—
61#11924027—41no—
62#11924027—41no—
63C2×Dic146D411yescharacteristic
64C2×Dic146C2311yescharacteristic
65C2×D292D411yescharacteristic
66C2×C22⋊D73—21no—
67C2×C22⋊D73—21no—
68C2×C22⋊D73—21no—
69C2×C22⋊D73—21no—
70C2×C22⋊D73—21no—
71C2×C22⋊D73—21no—
72C2×C22⋊D73D411yescharacteristic
73C2×C22⋊D73D411yescharacteristic
74C22×Dic73—21no—
75C2×C4×D73—21no—
76C2×C4×D73C2311yescharacteristic
77C2×C4×D73C2311yescharacteristic
78#11924016—41no—
79#11924016—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—
93C22⋊Dic73—21no—
94C22⋊Dic73—21no—
95C22⋊Dic73—21no—
96C22⋊Dic73—21no—
97#11924005—21no—
98C4×Dic73—21no—
99C24×C73—21no—
100C2×D4×C73—21no—
101C2×D4×C73—21no—
102C2×D4×C73—41no—
103C2×D4×C73—41no—
104C2×D4×C73C2311yescharacteristic
105C2×D4×C73C2311yescharacteristic
106C2×D4×C73C2311yescharacteristic
107C22×C4×C73C2311yescharacteristic
108D8×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×C73—21no—
117C23×C73—42no—
118C23×C73—81no—
119C23×C73—81no—
120C23×C73C2×D411yescharacteristic
121C22×D73C2×D411yescharacteristic
122C22×D73C2×D411yescharacteristic
123D4×C73—21no—
124D4×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×C73C2×D411yescharacteristic
135C2×C4×C73C2411yescharacteristic
136C22⋊D73—41no—
137C22⋊D73—41no—
138C22⋊D73—42no—
139C22⋊D73—81no—
140C22⋊D73—81no—
141C22⋊D73—81no—
142C22⋊D73—81no—
143C22⋊D73—81no—
144C2×Dic73—21no—
145C2×Dic73—21no—
146C2×Dic73—21no—
147C2×Dic73—21no—
148C2×Dic73—42no—
149C2×Dic73C2×D411yescharacteristic
150C2×Dic73C2×D411yescharacteristic
151D292—41no—
152C4×D73—21no—
153C4×D73—21no—
154C4×D73—21no—
155C4×D73—21no—
156C4×D73—81no—
157Dic146—21no—
158Dic146—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×C73—41no—
174C22×C73—41no—
175C22×C73—41no—
176C22×C73—84no—
177C22×C73C22×D411yescharacteristic
178C2×D73—21no—
179C2×D73—21no—
180C2×D73—21no—
181C2×D73—21no—
182C2×D73—21no—
183C2×D73—21no—
184C4×C73—21no—
185C4×C73—41no—
186C4×C73H(5,𝔽2)11yescharacteristic
187C4×C73H(5,𝔽2)11yescharacteristic
188Dic73—21no—
189Dic73—21no—
190Dic73—41no—
191Dic73—41no—
192Dic73—41no—
193Dic73—41no—
194C2×C73—41no—
195C2×C73—81no—
196C2×C73—81no—
197C2×C73—81no—
198C2×C73#53411yescharacteristic
199C2×C73#57611yescharacteristic
200C2×C73#57711yescharacteristic
201D73—41no—
202D73—41no—
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#449—731no—
218#447D7311yescharacteristic, complemented
219#408—731no—
220C2×#41—731no—
221C2×#41—731no—
222C22×D4C2×D7311yescharacteristic
223C2×SD16—731no—
224C2×SD16—731no—
225C2×D8C2×D7311yescharacteristic
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#103—731no—
253#102—731no—
254#102—731no—
255#102—731no—
256#102—731no—
257#102C2×D7311yescharacteristic
258#102C2×D7311yescharacteristic
259C22⋊C8—731no—
260C22⋊C8—731no—
261C22⋊C8—731no—
262C22⋊C8C2×D7311yescharacteristic
263C24—21no—
264#41—2921no—
265#41—2921no—
266#41—2921no—
267#41—2921no—
268C2×Q8—731no—
269C2×Q8—731no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—731no—
275C2×D4—731no—
276C2×D4—731no—
277C2×D4—1461no—
278C2×D4—1461no—
279C2×D4—1461no—
280C2×D4—1461no—
281C2×D4—1461no—
282C2×D4—1461no—
283C2×D4C22×D7311yescharacteristic
284C2×D4C22×D7311yescharacteristic
285C2×D4C22×D7311yescharacteristic
286C22×C4—731no—
287C22×C4—731no—
288C22×C4—1461no—
289C22×C4—1461no—
290C22×C4C22×D7311yescharacteristic
291SD16—2921no—
292SD16—2921no—
293D8—41no—
294D8—41no—
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—21no—
321C23—42no—
322C23—81no—
323C23—81no—
324C23—731no—
325C23—731no—
326C23D4×D7311yescharacteristic
327Q8—2921no—
328Q8—1461no—
329Q8—1461no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—42no—
337D4—81no—
338D4—2921no—
339D4—2922no—
340D4—2921no—
341D4—2921no—
342D4—5841no—
343D4—5841no—
344D4—5841no—
345D4—5841no—
346D4—5841no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—2922no—
351C2×C4—5841no—
352C2×C4—731no—
353C2×C4—731no—
354C2×C4—1461no—
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—41no—
378C22—41no—
379C22—41no—
380C22—84no—
381C22—1461no—
382C22—1461no—
383C22—1461no—
384C22—1461no—
385C22—1461no—
386C22—1461no—
387C22C2×D4×D7311yescharacteristic
388C4—21no—
389C4—41no—
390C4—2921no—
391C4—2921no—
392C4—2921no—
393C4—2921no—
394C4—1461no—
395C4—1461no—
396C4#1455663611yescharacteristic
397C4#1455663611yescharacteristic
398C2—41no—
399C2—81no—
400C2—81no—
401C2—81no—
402C2—2921no—
403C2—2921no—
404C2#1798914711yescharacteristic
405C2#1798938811yescharacteristic
406C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#447×C73C2
socleC22×C73C22×D4
hypercenter#447D73
hypocenterC73#3198
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #17989166C2semidirect
2. #17989154C2semidirect
3. #17988929C2semidirect
4. #17988908C2semidirect
5. #17988904C2semidirect
6. #17988899C2semidirect
7. #17988837C2semidirect
8. #17988832C2semidirect
9. #17988820C2semidirect
10. #17988815C2semidirect
11. #17988738C2semidirect
12. #17988729C2semidirect
13. #17988729C2semidirect
14. #17988552C2semidirect
15. #447×C73C2semidirect
17. C2×#11924027C22semidirect
20. C2×#11924011C22semidirect
21. C2×C8×D73C22semidirect
24. #14556571C22semidirect
34. #14556562C22semidirect
38. C4⋊C4×D73C22semidirect
39. #14556525C22semidirect
40. #14556524C22semidirect
41. #14556523C22semidirect
42. #14556522C22semidirect
43. #14556516C22semidirect
44. #14556516C22semidirect
47. #14556512C22semidirect
48. #14556512C22semidirect
50. #14556503C22semidirect
51. #14556503C22semidirect
204. C73#3198semidirect
218. #447D73semidirect