Finite Group Databasebeta

← #22621737

Subgroups — #22621737

Order 9344.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989237C211yesmaximal, characteristic, complemented
2D4×C22⋊D73C211yesmaximal, characteristic, complemented
3#17988932C211yesmaximal, characteristic, complemented
4#17988901C211yesmaximal, characteristic, complemented
5#17988899C211yesmaximal, characteristic, complemented
6#17988865C211yesmaximal, characteristic, complemented
7#17988821C211yesmaximal, characteristic, complemented
8#17988820C211yesmaximal, characteristic, complemented
9#17988780C211yesmaximal, characteristic, complemented
10#17988719C211yesmaximal, characteristic, complemented
11D8×Dic73C211yesmaximal, characteristic, complemented
12#17988650C211yesmaximal, characteristic, complemented
13C2×#14556512C211yesmaximal, characteristic, complemented
14#102×D73C211yesmaximal, characteristic, complemented
15#447×C73C211yesmaximal, characteristic, complemented
16C2×#11924027—21no—
17C22×C22⋊D73—21no—
18C2×D4×D73C2211yescharacteristic
19C2×#11924013C2211yescharacteristic, complemented
20C22×#10596831C2211yescharacteristic, complemented
21C2×C8×D73C2211yescharacteristic, complemented
22#14556590C2211yescharacteristic, complemented
23#14556587C2211yescharacteristic
24#14556573—21no—
25#14556572—21no—
26#14556568—21no—
27#14556565C2211yescharacteristic
28#14556563—21no—
29#14556562C2211yescharacteristic
30#14556562C2211yescharacteristic, complemented
31#14556560—21no—
32#14556559—21no—
33D4×Dic73C2211yescharacteristic
34D4×Dic73C2211yescharacteristic, complemented
35C4×C22⋊D73C2211yescharacteristic
36C2×C4⋊Dic73C2211yescharacteristic, complemented
37C4⋊C4×D73C2211yescharacteristic, complemented
38#14556525C2211yescharacteristic, complemented
39#14556525C2211yescharacteristic, complemented
40#14556524C2211yescharacteristic, complemented
41#14556520C2211yescharacteristic, complemented
42#14556513C2211yescharacteristic, complemented
43#14556513C2211yescharacteristic, complemented
44#14556512C2211yescharacteristic
45#14556512C2211yescharacteristic
46#14556512C2211yescharacteristic, complemented
47#14556512C2211yescharacteristic, complemented
48#14556512C2211yescharacteristic, complemented
49#14556511C2211yescharacteristic, complemented
50#14556503C2211yescharacteristic, complemented
51C8×Dic73C2211yescharacteristic, complemented
52C22×D4×C73C2211yescharacteristic
53C2×D8×C73C2211yescharacteristic
54C2×D8×C73C2211yescharacteristic, complemented
55#121×C73C2211yescharacteristic, complemented
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic, complemented
58C22⋊C8×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60#11924027—44no—
61C2×Dic146—21no—
62C2×D292C2311yescharacteristic
63C2×C22⋊D73—21no—
64C2×C22⋊D73—21no—
65C2×C22⋊D73—21no—
66C2×C22⋊D73—21no—
67C2×C22⋊D73—21no—
68C2×C22⋊D73—21no—
69C2×C22⋊D73—44no—
70C2×C22⋊D73D411yescharacteristic
71D4×D73—22no—
72D4×D73—41no—
73C22×Dic73—21no—
74C22×Dic73—21no—
75C22×Dic73—21no—
76C2×C4×D73—21no—
77C2×C4×D73C2311yescharacteristic
78#11924013—41no—
79C2×#10596831—41no—
80C2×#10596831C2311yescharacteristic
81C2×#10596831C2311yescharacteristic
82C8×D73—41no—
83C4⋊Dic73—21no—
84C4⋊Dic73C2311yescharacteristic
85C4⋊Dic73C2311yescharacteristic
86C4⋊Dic73C2311yescharacteristic
87#11924007—21no—
88#11924007—21no—
89#11924007D411yescharacteristic
90C22⋊Dic73—21no—
91C22⋊Dic73—21no—
92C22⋊Dic73—21no—
93C22⋊Dic73—21no—
94C22⋊Dic73D411yescharacteristic
95#11924005—21no—
96#11924005D411yescharacteristic
97C4×Dic73C2311yescharacteristic
98C24×C73—21no—
99C2×D4×C73—22no—
100C2×D4×C73—21no—
101C2×D4×C73—21no—
102C2×D4×C73—41no—
103C2×D4×C73C2311yescharacteristic
104C2×D4×C73C2311yescharacteristic
105C2×D4×C73C2311yescharacteristic
106C22×C4×C73C2311yescharacteristic
107D8×C73—22no—
108D8×C73—41no—
109C2×C8×C73C2311yescharacteristic
110C2×C8×C73C2311yescharacteristic
111C4⋊C4×C73C2311yescharacteristic
112C22⋊C4×C73—21no—
113C23×C73—21no—
114C23×C73—21no—
115C23×C73—21no—
116C23×C73—42no—
117C23×C73—42no—
118C23×C73—81no—
119C23×C73C2×D411yescharacteristic
120C22×D73—21no—
121C22×D73—42no—
122C22×D73—42no—
123C22×D73—81no—
124C22×D73C2×D411yescharacteristic
125D4×C73—21no—
126D4×C73—21no—
127D4×C73—21no—
128D4×C73—21no—
129D4×C73—21no—
130D4×C73—42no—
131D4×C73—42no—
132D4×C73#4112yescomplemented
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—21no—
136C2×C4×C73C2×D411yescharacteristic
137C2×C4×C73C2411yescharacteristic
138C22⋊D73—42no—
139C22⋊D73—42no—
140C22⋊D73—42no—
141C22⋊D73—42no—
142C22⋊D73—42no—
143C22⋊D73—81no—
144C22⋊D73D814yescomplemented
145C2×Dic73—21no—
146C2×Dic73—21no—
147C2×Dic73—21no—
148C2×Dic73—42no—
149C2×Dic73—42no—
150C2×Dic73—42no—
151C2×Dic73C2×D411yescharacteristic
152C2×Dic73C2×D411yescharacteristic
153C2×Dic73C2×D411yescharacteristic
154D292—21no—
155D292—21no—
156C4×D73—21no—
157C4×D73—21no—
158C4×D73—42no—
159Dic146—42no—
160C8×C73—21no—
161C8×C73—21no—
162#10596831—21no—
163#10596831—21no—
164C22×C73—21no—
165C22×C73—21no—
166C22×C73—22no—
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—84no—
176C22×C73C2×D812yes—
177C22×C73C22×D411yescharacteristic
178C2×D73—21no—
179C2×D73—21no—
180C2×D73—41no—
181C2×D73—41no—
182C2×D73—41no—
183C2×D73—84no—
184C2×D73C2×D812yes—
185C4×C73—21no—
186C4×C73—41no—
187C4×C73C2×#4111yescharacteristic
188C4×C73H(5,𝔽2)11yescharacteristic
189Dic73—21no—
190Dic73—21no—
191Dic73—41no—
192Dic73—41no—
193Dic73—41no—
194Dic73C2×D812yes—
195C2×C73—22no—
196C2×C73—42no—
197C2×C73—81no—
198C2×C73—81no—
199C2×C73#54611yescharacteristic
200C2×C73C22×D811yescharacteristic
201C2×C73#57711yescharacteristic
202D73—22no—
203D73—81no—
204#3294—731nomaximal, Sylow
205C73#329411yescharacteristic, complemented, Sylow
206#547—731no—
207D42—731no—
208#486—731no—
209#480—731no—
210#480—731no—
211#474—731no—
212#466—731no—
213#466—731no—
214#459—731no—
215#447—731no—
216#447D7311yescharacteristic, complemented
217C4×D8—731no—
218C8×D4—731no—
219C2×#102—731no—
220C2×#102—731no—
221C2×#41—1461no—
222C22×D4—731no—
223C22×D4—1461no—
224C22×D4C2×D7311yescharacteristic
225C2×D8—731no—
226C2×D8C2×D7311yescharacteristic
227C2×D8C2×D7311yescharacteristic, complemented
228C22×C8—731no—
229C22×C8—731no—
230C4⋊Q8—731no—
231#127—731no—
232#123—1461no—
233#123—1461no—
234C22⋊Q8—1461no—
235#121—731no—
236#121—731no—
237#121—731no—
238#121—1461no—
239#121C2×D7311yescharacteristic, complemented
240#120—1461no—
241#120—1461no—
242C4×D4—731no—
243C4×D4—731no—
244C4×D4—731no—
245C2×C4⋊C4—731no—
246C2×C4⋊C4—731no—
247#107—731no—
248#107—731no—
249#107—731no—
250C4⋊C8—731no—
251#102—731no—
252#102—731no—
253#102—731no—
254#102—731no—
255#102—731no—
256#102—731no—
257#102—731no—
258#102—731no—
259#102C2×D7311yescharacteristic
260#102C2×D7311yescharacteristic, complemented
261C22⋊C8—731no—
262C22⋊C8C2×D7311yescharacteristic, complemented
263C4×C8—731no—
264C24—21no—
265C24—1461no—
266#41—2924no—
267C2×Q8—1461no—
268C2×D4—22no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—2924no—
273C2×D4—2921no—
274C2×D4—731no—
275C2×D4—731no—
276C2×D4—1461no—
277C2×D4—1461no—
278C2×D4—1461no—
279C2×D4—1461no—
280C2×D4—1461no—
281C2×D4—1461no—
282C2×D4—1462no—
283C2×D4C22×D7311yescharacteristic
284C2×D4C22×D7311yescharacteristic
285C2×D4C22×D7311yescharacteristic
286C22×C4—731no—
287C22×C4—1461no—
288C22×C4—1461no—
289C22×C4—1461no—
290C22×C4—1461no—
291C22×C4C22×D7311yescharacteristic
292D8—22no—
293D8—41no—
294D8—2921no—
295C2×C8—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—731no—
305C4⋊C4—1461no—
306C4⋊C4—1461no—
307C4⋊C4—1461no—
308C4⋊C4C22×D7311yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—731no—
311C22⋊C4—731no—
312C22⋊C4—1461no—
313C22⋊C4—1461no—
314C22⋊C4—1461no—
315C22⋊C4—1461no—
316C22⋊C4—1461no—
317C42—731no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—42no—
322C23—42no—
323C23—81no—
324C23—2922no—
325C23—2922no—
326C23—5841no—
327C23—731no—
328C23—1461no—
329C23D4×D7311yescharacteristic
330Q8—2922no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—42no—
337D4—42no—
338D4—2922no—
339D4—2922no—
340D4—2922no—
341D4—2922no—
342D4—2922no—
343D4—5841no—
344D4—734no—
345D4—1461no—
346D4—1461no—
347D4#1192402712yescomplemented
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—2922no—
352C2×C4—2922no—
353C2×C4—2922no—
354C2×C4—2922no—
355C2×C4—731no—
356C2×C4—731no—
357C2×C4—731no—
358C2×C4—1461no—
359C2×C4—1461no—
360C2×C4—1461no—
361C2×C4—1461no—
362C2×C4—1461no—
363C2×C4D4×D7311yescharacteristic
364C2×C4C23×D7311yescharacteristic
365C8—21no—
366C8—21no—
367C8—1461no—
368C8—1461no—
369C22—21no—
370C22—21no—
371C22—22no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—84no—
381C22—2921no—
382C22—2921no—
383C22—2921no—
384C22—5844no—
385C22—732no—
386C22—1461no—
387C22—1461no—
388C22D8×D7312yes—
389C22C2×D4×D7311yescharacteristic
390C4—21no—
391C4—41no—
392C4—2921no—
393C4—2921no—
394C4—2921no—
395C4—732no—
396C4—1461no—
397C4—1461no—
398C4C2×#1192402711yescharacteristic
399C4#1455663611yescharacteristic
400C2—22no—
401C2—42no—
402C2—81no—
403C2—81no—
404C2—5841no—
405C2—1462no—
406C2#1798922411yescharacteristic
407C2C2×D8×D7311yescharacteristic
408C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#447×C73C2
socleC22×C73C22×D4
hypercenter#447D73
hypocenterC73#3294
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. #17989237C2semidirect
2. D4×C22⋊D73C2semidirect
3. #17988932C2semidirect
4. #17988901C2semidirect
5. #17988899C2semidirect
6. #17988865C2semidirect
7. #17988821C2semidirect
8. #17988820C2semidirect
9. #17988780C2semidirect
10. #17988719C2semidirect
11. D8×Dic73C2semidirect
12. #17988650C2semidirect
13. C2×#14556512C2semidirect
14. #102×D73C2semidirect
15. #447×C73C2semidirect
19. C2×#11924013C22semidirect
20. C22×#10596831C22semidirect
21. C2×C8×D73C22semidirect
22. #14556590C22semidirect
30. #14556562C22semidirect
34. D4×Dic73C22semidirect
36. C2×C4⋊Dic73C22semidirect
37. C4⋊C4×D73C22semidirect
38. #14556525C22semidirect
39. #14556525C22semidirect
40. #14556524C22semidirect
41. #14556520C22semidirect
42. #14556513C22semidirect
43. #14556513C22semidirect
46. #14556512C22semidirect
47. #14556512C22semidirect
48. #14556512C22semidirect
49. #14556511C22semidirect
50. #14556503C22semidirect
51. C8×Dic73C22semidirect
54. C2×D8×C73C22semidirect
55. #121×C73C22semidirect
57. #102×C73C22semidirect
58. C22⋊C8×C73C22semidirect
132. D4×C73#41semidirect
144. C22⋊D73D8semidirect
205. C73#3294semidirect
216. #447D73semidirect
227. C2×D8C2×D73semidirect
239. #121C2×D73semidirect
260. #102C2×D73semidirect
262. C22⋊C8C2×D73semidirect
347. D4#11924027semidirect