Finite Group Databasebeta

← #22620783

Subgroups — #22620783

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#17988928C211yesmaximal, characteristic, complemented
3#17988911C211yesmaximal, characteristic, complemented
4#17988903C211yesmaximal, characteristic, complemented
5#17988898C211yesmaximal, characteristic, complemented
6#17988838C211yesmaximal, characteristic, complemented
7#17988831C211yesmaximal, characteristic, complemented
8#17988821C211yesmaximal, characteristic, complemented
9#17988814C211yesmaximal, characteristic, complemented
10#17988738C211yesmaximal, characteristic, complemented
11#17988730C211yesmaximal, characteristic, complemented
12#17988730C211yesmaximal, characteristic, complemented
13#17988721C211yesmaximal, characteristic, complemented
14#17988554C211yesmaximal, characteristic, complemented
15#535×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic, complemented
17C2×#11924016C2211yescharacteristic
18C2×#11924016C2211yescharacteristic
19C2×#11924013C2211yescharacteristic
20C2×#11924013C2211yescharacteristic
21C2×#11924012C2211yescharacteristic, complemented
22C22×#10596831C2211yescharacteristic, complemented
23#14556570C2211yescharacteristic
24#14556570C2211yescharacteristic, complemented
25#14556567—21no—
26#14556565C2211yescharacteristic
27#14556565C2211yescharacteristic, complemented
28#14556563—21no—
29#14556563—21no—
30#14556562—21no—
31C2×C4⋊Dic73C2211yescharacteristic, complemented
32#14556524C2211yescharacteristic, complemented
33#14556524C2211yescharacteristic, complemented
34#14556522C2211yescharacteristic, complemented
35#14556522C2211yescharacteristic, complemented
36#14556514C2211yescharacteristic, complemented
37#14556514C2211yescharacteristic, complemented
38#14556512C2211yescharacteristic
39#14556512C2211yescharacteristic
40#14556512C2211yescharacteristic
41#14556512C2211yescharacteristic
42#14556511C2211yescharacteristic, complemented
43#14556511C2211yescharacteristic, complemented
44C22⋊#10596831C2211yescharacteristic
45C22⋊#10596831C2211yescharacteristic
46C22⋊#10596831C2211yescharacteristic, complemented
47C22⋊#10596831C2211yescharacteristic, complemented
48C2×#41×C73C2211yescharacteristic
49C22×D4×C73C2211yescharacteristic
50#127×C73—21no—
51#124×C73—21no—
52#121×C73C2211yescharacteristic
53#121×C73C2211yescharacteristic
54#121×C73C2211yescharacteristic
55#121×C73C2211yescharacteristic
56#120×C73—21no—
57#120×C73—21no—
58#117×C73C2211yescharacteristic
59#11924028—41no—
60#11924028—41no—
61C2×Dic146C2311yescharacteristic
62C2×D292C2311yescharacteristic
63C2×C22⋊D73—21no—
64C2×C22⋊D73—21no—
65C2×C22⋊D73—21no—
66C22×Dic73—21no—
67C2×C4×D73—21no—
68#11924016—41no—
69#11924016—41no—
70#11924013—41no—
71#11924013—41no—
72#11924012—41no—
73C2×#10596831—41no—
74C2×#10596831C2311yescharacteristic
75C2×#10596831C2311yescharacteristic
76C2×#10596831C2311yescharacteristic
77C2×#10596831C2311yescharacteristic
78C4⋊Dic73—21no—
79C4⋊Dic73C2311yescharacteristic
80C4⋊Dic73C2311yescharacteristic
81#11924007—21no—
82#11924007—21no—
83C22⋊Dic73—21no—
84C22⋊Dic73—21no—
85#11924005—21no—
86#11924005—21no—
87C24×C73—21no—
88#41×C73—41no—
89#41×C73—41no—
90C2×Q8×C73D411yescharacteristic
91C2×D4×C73—21no—
92C2×D4×C73—21no—
93C2×D4×C73—21no—
94C2×D4×C73—21no—
95C2×D4×C73—21no—
96C2×D4×C73—41no—
97C2×D4×C73—41no—
98C2×D4×C73D411yescharacteristic
99C2×D4×C73D411yescharacteristic
100C2×D4×C73D411yescharacteristic
101C2×D4×C73C2311yescharacteristic
102C2×D4×C73C2311yescharacteristic
103C22×C4×C73C2311yescharacteristic
104C22×C4×C73C2311yescharacteristic
105C22×C4×C73C2311yescharacteristic
106C4⋊C4×C73C2311yescharacteristic
107C4⋊C4×C73C2311yescharacteristic
108C22⋊C4×C73—21no—
109C22⋊C4×C73—21no—
110C22⋊C4×C73—21no—
111C22⋊C4×C73—21no—
112C22⋊C4×C73—21no—
113C42×C73—21no—
114C23×C73—21no—
115C23×C73—21no—
116C23×C73—42no—
117C23×C73—81no—
118C23×C73—81no—
119C23×C73C2×D411yescharacteristic
120C23×C73C2×D411yescharacteristic
121C23×C73C2×D411yescharacteristic
122C22×D73—21no—
123Q8×C73—41no—
124D4×C73—21no—
125D4×C73—21no—
126D4×C73—21no—
127D4×C73—21no—
128D4×C73—41no—
129D4×C73—41no—
130D4×C73—41no—
131D4×C73—42no—
132D4×C73—81no—
133D4×C73—81no—
134D4×C73—81no—
135D4×C73—81no—
136C2×C4×C73—21no—
137C2×C4×C73—21no—
138C2×C4×C73—21no—
139C2×C4×C73—21no—
140C2×C4×C73—21no—
141C2×C4×C73—21no—
142C2×C4×C73—21no—
143C2×C4×C73—21no—
144C2×C4×C73C2×D411yescharacteristic
145C2×C4×C73C2×D411yescharacteristic
146C2×C4×C73C2×D411yescharacteristic
147C2×C4×C73C2411yescharacteristic
148C22⋊D73—42no—
149C22⋊D73—81no—
150C22⋊D73—81no—
151C2×Dic73—21no—
152C2×Dic73—21no—
153C2×Dic73—21no—
154C2×Dic73—81no—
155D292—21no—
156D292—21no—
157C4×D73—42no—
158Dic146—21no—
159Dic146—21no—
160#10596831—21no—
161#10596831—21no—
162#10596831—21no—
163#10596831—21no—
164C22×C73—21no—
165C22×C73—21no—
166C22×C73—21no—
167C22×C73—21no—
168C22×C73—21no—
169C22×C73—21no—
170C22×C73—21no—
171C22×C73—21no—
172C22×C73—21no—
173C22×C73—41no—
174C22×C73—41no—
175C22×C73—41no—
176C22×C73—41no—
177C22×C73—41no—
178C22×C73—41no—
179C22×C73—84no—
180C22×C73C22×D411yescharacteristic
181C2×D73—41no—
182C2×D73—41no—
183C2×D73—41no—
184C4×C73—21no—
185C4×C73—21no—
186C4×C73—21no—
187C4×C73—41no—
188C4×C73—41no—
189C4×C73H(5,𝔽2)11yescharacteristic
190C4×C73H(5,𝔽2)11yescharacteristic
191Dic73—41no—
192Dic73—41no—
193Dic73—41no—
194C2×C73—41no—
195C2×C73—41no—
196C2×C73—41no—
197C2×C73—81no—
198C2×C73—81no—
199C2×C73#53411yescharacteristic
200C2×C73#57611yescharacteristic
201C2×C73#57711yescharacteristic
202D73—81no—
203#3198—731nomaximal, Sylow
204C73#319811yescharacteristic, complemented, Sylow
205#537—731no—
206#535D7311yescharacteristic, complemented
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#447—731no—
219#408—731no—
220C2×#41—731no—
221C2×#41C2×D7311yescharacteristic
222C22×D4C2×D7311yescharacteristic
223C2×SD16—731no—
224C2×SD16—731no—
225C2×D8—731no—
226C2×D8—731no—
227C2×M16—731no—
228C22×C8—731no—
229#127—21no—
230#124—21no—
231C22⋊Q8—731no—
232C22⋊Q8—731no—
233C22⋊Q8—1461no—
234#121—731no—
235#121—731no—
236#121—1461no—
237#121—1461no—
238#121—1461no—
239#121C2×D7311yescharacteristic
240#121C2×D7311yescharacteristic
241#121C2×D7311yescharacteristic
242#121C2×D7311yescharacteristic
243#120—21no—
244#120—21no—
245#117C2×D7311yescharacteristic
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#102—731no—
258#102—731no—
259C22⋊C8—731no—
260C22⋊C8—731no—
261C22⋊C8—731no—
262C22⋊C8—731no—
263C24—21no—
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—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—731no—
278C2×D4—1461no—
279C2×D4—1461no—
280C2×D4—1461no—
281C2×D4C22⋊D7311yescharacteristic
282C2×D4C22⋊D7311yescharacteristic
283C2×D4C22⋊D7311yescharacteristic
284C2×D4C22×D7311yescharacteristic
285C2×D4C22×D7311yescharacteristic
286C22×C4—1461no—
287C22×C4—1461no—
288C22×C4C22×D7311yescharacteristic
289C22×C4C22×D7311yescharacteristic
290C22×C4C22×D7311yescharacteristic
291SD16—2921no—
292SD16—2921no—
293D8—2921no—
294D8—2921no—
295M16—2921no—
296C2×C8—2921no—
297C2×C8—731no—
298C2×C8—731no—
299C2×C8—731no—
300C2×C8—731no—
301C4⋊C4—731no—
302C4⋊C4—731no—
303C4⋊C4—1461no—
304C4⋊C4—1461no—
305C4⋊C4—1461no—
306C4⋊C4C22×D7311yescharacteristic
307C4⋊C4C22×D7311yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—1461no—
314C22⋊C4—1461no—
315C22⋊C4—1461no—
316C22⋊C4—1461no—
317C42—21no—
318C23—21no—
319C23—21no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—1461no—
324C23C2×C22⋊D7311yescharacteristic
325C23C2×C22⋊D7311yescharacteristic
326C23C2×C22⋊D7311yescharacteristic
327Q8—41no—
328Q8—1461no—
329Q8—1461no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—41no—
335D4—41no—
336D4—41no—
337D4—42no—
338D4—81no—
339D4—81no—
340D4—81no—
341D4—81no—
342D4—2922no—
343D4—5841no—
344D4—5841no—
345D4—1461no—
346D4—1461no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—2922no—
356C2×C4—5841no—
357C2×C4—1461no—
358C2×C4—1461no—
359C2×C4—1461no—
360C2×C4C2×C22⋊D7311yescharacteristic
361C2×C4C2×C22⋊D7311yescharacteristic
362C2×C4C2×C22⋊D7311yescharacteristic
363C2×C4C23×D7311yescharacteristic
364C8—1461no—
365C8—1461no—
366C8—1461no—
367C8—1461no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—84no—
384C22—2921no—
385C22—2921no—
386C22—2921no—
387C22C22×C22⋊D7311yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—41no—
392C4—41no—
393C4—2921no—
394C4—2921no—
395C4—2921no—
396C4#1455663611yescharacteristic
397C4#1455663611yescharacteristic
398C2—41no—
399C2—41no—
400C2—41no—
401C2—81no—
402C2—81no—
403C2—5841no—
404C2#1798914611yescharacteristic
405C2#1798939011yescharacteristic
406C2#1798939811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#535×C73C2
socleC22×C73C22×D4
hypercenter#535D73
hypocenterC73#3198
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #17989165C2semidirect
2. #17988928C2semidirect
3. #17988911C2semidirect
4. #17988903C2semidirect
5. #17988898C2semidirect
6. #17988838C2semidirect
7. #17988831C2semidirect
8. #17988821C2semidirect
9. #17988814C2semidirect
10. #17988738C2semidirect
11. #17988730C2semidirect
12. #17988730C2semidirect
13. #17988721C2semidirect
14. #17988554C2semidirect
15. #535×C73C2semidirect
16. C2×#11924028C22semidirect
21. C2×#11924012C22semidirect
22. C22×#10596831C22semidirect
24. #14556570C22semidirect
27. #14556565C22semidirect
31. C2×C4⋊Dic73C22semidirect
32. #14556524C22semidirect
33. #14556524C22semidirect
34. #14556522C22semidirect
35. #14556522C22semidirect
36. #14556514C22semidirect
37. #14556514C22semidirect
42. #14556511C22semidirect
43. #14556511C22semidirect
46. C22⋊#10596831C22semidirect
47. C22⋊#10596831C22semidirect
204. C73#3198semidirect
206. #535D73semidirect