Finite Group Databasebeta

← #22621941

Subgroups — #22621941

Order 9344.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989284C211yesmaximal, characteristic, complemented
2#17989256C211yesmaximal, characteristic, complemented
3#17988950C211yesmaximal, characteristic, complemented
4#17988912C211yesmaximal, characteristic, complemented
5#17988899C211yesmaximal, characteristic, complemented
6#17988892C211yesmaximal, characteristic, complemented
7#17988837C211yesmaximal, characteristic, complemented
8#17988821C211yesmaximal, characteristic, complemented
9#17988780C211yesmaximal, characteristic, complemented
10#17988731C211yesmaximal, characteristic, complemented
11#17988688C211yesmaximal, characteristic, complemented
12#17988655C211yesmaximal, characteristic, complemented
13#17988587C211yesmaximal, characteristic, complemented
14#17988583C211yesmaximal, characteristic, complemented
15#449×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic
17C2×#11924013C2211yescharacteristic
18C2×#11924011C2211yescharacteristic
19C22×#10596831C2211yescharacteristic
20#14556587—21no—
21#14556587C2211yescharacteristic
22#14556584—21no—
23#14556582C2211yescharacteristic
24#14556572—21no—
25#14556565—21no—
26#14556565C2211yescharacteristic
27#14556562—21no—
28#14556562—21no—
29#14556562C2211yescharacteristic
30#14556562C2211yescharacteristic
31Q8×Dic73C2211yescharacteristic
32D4×Dic73C2211yescharacteristic
33C4×C22⋊D73—21no—
34C4×C22⋊D73C2211yescharacteristic
35#14556551—21no—
36#14556550C2211yescharacteristic
37C4⋊C4×D73C2211yescharacteristic
38#14556525C2211yescharacteristic
39#14556524C2211yescharacteristic
40#14556523C2211yescharacteristic
41#14556520C2211yescharacteristic
42#14556515C2211yescharacteristic
43#14556515C2211yescharacteristic
44#14556513C2211yescharacteristic
45#14556513C2211yescharacteristic
46#14556512C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556512C2211yescharacteristic
49#14556511C2211yescharacteristic
50#14556503C2211yescharacteristic
51#14556501C2211yescharacteristic
52C2×#41×C73C2211yescharacteristic
53C2×SD16×C73C2211yescharacteristic
54C2×D8×C73C2211yescharacteristic
55#121×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59#11924029—22no—
60#11924029—41no—
61C2×D292—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⋊D73D411yescharacteristic
69C22×Dic73—21no—
70C2×C4×D73—21no—
71C2×C4×D73—21no—
72C2×C4×D73C2311yescharacteristic
73#11924013—41no—
74#11924011—41no—
75C2×#10596831—41no—
76C2×#10596831C2311yescharacteristic
77C2×#10596831C2311yescharacteristic
78C4⋊Dic73—21no—
79C4⋊Dic73—21no—
80C4⋊Dic73C2311yescharacteristic
81C4⋊Dic73C2311yescharacteristic
82C4⋊Dic73C2311yescharacteristic
83#11924007—21no—
84#11924007—21no—
85#11924007D411yescharacteristic
86C22⋊Dic73—21no—
87C22⋊Dic73—21no—
88C22⋊Dic73—21no—
89C22⋊Dic73—21no—
90C22⋊Dic73D411yescharacteristic
91#11924005—21no—
92#11924005D411yescharacteristic
93C4×Dic73—21no—
94C4×Dic73—21no—
95C4×Dic73C2311yescharacteristic
96#41×C73—22no—
97#41×C73—41no—
98C2×Q8×C73C2311yescharacteristic
99C2×D4×C73—21no—
100C2×D4×C73—21no—
101C2×D4×C73C2311yescharacteristic
102C2×D4×C73C2311yescharacteristic
103C22×C4×C73—21no—
104C22×C4×C73C2311yescharacteristic
105SD16×C73—22no—
106D8×C73—41no—
107C2×C8×C73C2311yescharacteristic
108C2×C8×C73C2311yescharacteristic
109C4⋊C4×C73C2311yescharacteristic
110C22⋊C4×C73—21no—
111C23×C73—21no—
112C23×C73—21no—
113C23×C73C2×D411yescharacteristic
114C22×D73—21no—
115C22×D73C2×D411yescharacteristic
116Q8×C73—21no—
117Q8×C73#4112yes—
118D4×C73—21no—
119D4×C73—21no—
120D4×C73—21no—
121D4×C73—21no—
122D4×C73—42no—
123D4×C73—81no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—42no—
129C2×C4×C73C2×D411yescharacteristic
130C2×C4×C73C2411yescharacteristic
131C22⋊D73—41no—
132C22⋊D73—42no—
133C22⋊D73—42no—
134C22⋊D73—81no—
135C22⋊D73—81no—
136C22⋊D73—81no—
137C2×Dic73—21no—
138C2×Dic73—21no—
139C2×Dic73—21no—
140C2×Dic73—81no—
141C2×Dic73C2×D411yescharacteristic
142C2×Dic73C2×D411yescharacteristic
143C2×Dic73C2×D411yescharacteristic
144D292—21no—
145D292—21no—
146D292—42no—
147C4×D73—21no—
148C4×D73—21no—
149C4×D73—42no—
150C4×D73—81no—
151C8×C73—21no—
152C8×C73—21no—
153#10596831—21no—
154#10596831—21no—
155C22×C73—21no—
156C22×C73—21no—
157C22×C73—21no—
158C22×C73—41no—
159C22×C73—41no—
160C22×C73—41no—
161C22×C73—41no—
162C22×C73—41no—
163C22×C73—41no—
164C22×C73C22×D411yescharacteristic
165C2×D73—21no—
166C2×D73—21no—
167C2×D73—21no—
168C2×D73—41no—
169C2×D73—41no—
170C2×D73—41no—
171C4×C73—22no—
172C4×C73—21no—
173C4×C73—41no—
174C4×C73C2×#4111yescharacteristic
175C4×C73H(5,𝔽2)11yescharacteristic
176Dic73—21no—
177Dic73—21no—
178Dic73—21no—
179Dic73—41no—
180Dic73—41no—
181Dic73—41no—
182C2×C73—41no—
183C2×C73—81no—
184C2×C73—81no—
185C2×C73#54611yescharacteristic
186C2×C73#57511yescharacteristic
187C2×C73#57611yescharacteristic
188D73—41no—
189D73—81no—
190#3309—731nomaximal, Sylow
191C73#330911yescharacteristic, complemented, Sylow
192#553—731no—
193#550—731no—
194#490—731no—
195#482—731no—
196#480—731no—
197#479—731no—
198#469—731no—
199#466—731no—
200#459—731no—
201#449—731no—
202#449D7311yescharacteristic, complemented
203#440—731no—
204#435—731no—
205#417—731no—
206#416—731no—
207C2×#41—731no—
208C2×#41C2×D7311yescharacteristic
209C2×SD16C2×D7311yescharacteristic
210C2×D8—731no—
211C2×D8C2×D7311yescharacteristic
212C2×M16—731no—
213C22×C8—731no—
214#127—731no—
215#127—1461no—
216#126—1461no—
217#125—731no—
218#123—1461no—
219#121—731no—
220#121—731no—
221#121—731no—
222#121—1461no—
223#121—1461no—
224#121—1461no—
225#121C2×D7311yescharacteristic
226C4×Q8—731no—
227C4×D4—731no—
228C4×D4—731no—
229C4×D4—1461no—
230C4×D4—1461no—
231#117—731no—
232C2×C4⋊C4—731no—
233#107—731no—
234#107—731no—
235#106—731no—
236C4⋊C8—731no—
237#103—731no—
238#103—731no—
239#103C2×D7311yescharacteristic
240#102—731no—
241#102—731no—
242#102—731no—
243#102—731no—
244#102—731no—
245#102—731no—
246#102C2×D7311yescharacteristic
247C22⋊C8—731no—
248C22⋊C8C2×D7311yescharacteristic
249#97—731no—
250#41—22no—
251#41—41no—
252#41—2921no—
253#41—1462no—
254C2×Q8C22×D7311yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—731no—
258C2×D4—731no—
259C2×D4—1461no—
260C2×D4—1461no—
261C2×D4—1461no—
262C2×D4—1461no—
263C2×D4—1461no—
264C2×D4—1461no—
265C2×D4C22×D7311yescharacteristic
266C2×D4C22×D7311yescharacteristic
267C22×C4—21no—
268C22×C4—731no—
269C22×C4—1461no—
270C22×C4—1461no—
271C22×C4—1461no—
272C22×C4C22×D7311yescharacteristic
273SD16—22no—
274D8—41no—
275D8—2921no—
276M16—2921no—
277C2×C8—2921no—
278C2×C8—731no—
279C2×C8—731no—
280C2×C8C22×D7311yescharacteristic
281C2×C8C22×D7311yescharacteristic
282C4⋊C4—731no—
283C4⋊C4—731no—
284C4⋊C4—731no—
285C4⋊C4—731no—
286C4⋊C4—1461no—
287C4⋊C4—1461no—
288C4⋊C4—1461no—
289C4⋊C4—1461no—
290C4⋊C4C22×D7311yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—731no—
293C22⋊C4—731no—
294C22⋊C4—1461no—
295C22⋊C4—1461no—
296C22⋊C4—1461no—
297C22⋊C4—1461no—
298C22⋊C4—1461no—
299C42—731no—
300C42—1461no—
301C42—1461no—
302C23—21no—
303C23—21no—
304C23—731no—
305C23—1461no—
306C23D4×D7311yescharacteristic
307Q8—21no—
308Q8#1192402712yes—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—81no—
315D4—2922no—
316D4—2922no—
317D4—2921no—
318D4—2922no—
319D4—5841no—
320D4—5841no—
321D4—5841no—
322D4—1461no—
323D4—1461no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—2922no—
330C2×C4—5841no—
331C2×C4—5841no—
332C2×C4—731no—
333C2×C4—731no—
334C2×C4—731no—
335C2×C4—1461no—
336C2×C4—1461no—
337C2×C4—1461no—
338C2×C4—1461no—
339C2×C4—1461no—
340C2×C4D4×D7311yescharacteristic
341C2×C4C23×D7311yescharacteristic
342C8—21no—
343C8—21no—
344C8—1461no—
345C8—1461no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—2921no—
356C22—2921no—
357C22—2921no—
358C22—1461no—
359C22—1461no—
360C22—1461no—
361C22C2×D4×D7311yescharacteristic
362C4—21no—
363C4—22no—
364C4—41no—
365C4—2921no—
366C4—2921no—
367C4—2921no—
368C4—1461no—
369C4—1461no—
370C4—1461no—
371C4C2×#1192402711yescharacteristic
372C4#1455663611yescharacteristic
373C2—41no—
374C2—81no—
375C2—81no—
376C2—2921no—
377C2—5841no—
378C2#1798922411yescharacteristic
379C2#1798938411yescharacteristic
380C2#1798939111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#449×C73C2
socleC22×C73C22×D4
hypercenter#449D73
hypocenterC73#3309
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. #17989284C2semidirect
2. #17989256C2semidirect
3. #17988950C2semidirect
4. #17988912C2semidirect
5. #17988899C2semidirect
6. #17988892C2semidirect
7. #17988837C2semidirect
8. #17988821C2semidirect
9. #17988780C2semidirect
10. #17988731C2semidirect
11. #17988688C2semidirect
12. #17988655C2semidirect
13. #17988587C2semidirect
14. #17988583C2semidirect
15. #449×C73C2semidirect
191. C73#3309semidirect
202. #449D73semidirect