Finite Group Databasebeta

← #22620218

Subgroups — #22620218

Order 9344.

382 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989190C211yesmaximal, characteristic
2#17989064C211yesmaximal, characteristic, complemented
3#17988911C211yesmaximal, characteristic, complemented
4#17988897C211yesmaximal, characteristic, complemented
5#17988893C211yesmaximal, characteristic, complemented
6#17988786C211yesmaximal, characteristic, complemented
7#17988786C211yesmaximal, characteristic, complemented
8#17988728C211yesmaximal, characteristic, complemented
9#17988725C211yesmaximal, characteristic, complemented
10#17988686C211yesmaximal, characteristic, complemented
11#17988684C211yesmaximal, characteristic, complemented
12#17988678C211yesmaximal, characteristic, complemented
13#17988674C211yesmaximal, characteristic, complemented
14#17988645C211yesmaximal, characteristic, complemented
15#482×C73C211yesmaximal, characteristic, complemented
16C22×Dic146C2211yescharacteristic
17C2×#11924017C2211yescharacteristic
18C2×#11924017C2211yescharacteristic
19C2×#11924016C2211yescharacteristic
20C2×#11924016C2211yescharacteristic
21#14556587C2211yescharacteristic
22#14556582C2211yescharacteristic
23#14556575—21no—
24#14556573—21no—
25#14556565C2211yescharacteristic
26#14556563—21no—
27#14556562—21no—
28C4×Dic146—21no—
29C4×Dic146—21no—
30#14556556C2211yescharacteristic
31#14556556C2211yescharacteristic
32#14556556C2211yescharacteristic
33#14556556C2211yescharacteristic
34D4×Dic73C2211yescharacteristic
35#14556553C2211yescharacteristic
36#14556550C2211yescharacteristic
37#14556547—21no—
38#14556547—21no—
39#14556524C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556520C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556516C2211yescharacteristic
45#14556514C2211yescharacteristic
46#14556514C2211yescharacteristic
47#14556511C2211yescharacteristic
48#14556511C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556501C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52#121×C73C2211yescharacteristic
53#117×C73C2211yescharacteristic
54#107×C73C2211yescharacteristic
55#106×C73C2211yescharacteristic
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146—22no—
61C2×Dic146—22no—
62C2×Dic146C2311yescharacteristic
63C2×Dic146C2311yescharacteristic
64C2×D292C2311yescharacteristic
65C2×C22⋊D73—21no—
66C2×C22⋊D73—21no—
67C2×C22⋊D73—21no—
68C22×Dic73—21no—
69C22×Dic73—21no—
70C2×C4×D73—21no—
71#11924017—22no—
72#11924017—22no—
73#11924016—22no—
74#11924016—22no—
75C2×#10596831C2311yescharacteristic
76C2×#10596831C2311yescharacteristic
77C4⋊Dic73—21no—
78C4⋊Dic73D411yescharacteristic
79C4⋊Dic73D411yescharacteristic
80C4⋊Dic73C2311yescharacteristic
81#11924007—21no—
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86C22⋊Dic73—21no—
87C22⋊Dic73D411yescharacteristic
88C22⋊Dic73D411yescharacteristic
89#11924005—21no—
90#11924005—21no—
91C4×Dic73—21no—
92C4×Dic73—21no—
93C4×Dic73—21no—
94C4×Dic73—21no—
95C4×Dic73C2311yescharacteristic
96C4×Dic73C2311yescharacteristic
97C2×D4×C73—21no—
98C2×D4×C73C2311yescharacteristic
99C22×C4×C73C2311yescharacteristic
100C2×C8×C73C2311yescharacteristic
101C2×C8×C73C2311yescharacteristic
102C4⋊C4×C73C2311yescharacteristic
103C4⋊C4×C73C2311yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C22⋊C4×C73—21no—
106C22⋊C4×C73—21no—
107C42×C73—21no—
108C23×C73—21no—
109C23×C73C2×D411yescharacteristic
110C22×D73—21no—
111D4×C73—21no—
112D4×C73—21no—
113D4×C73—81no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73C2×D411yescharacteristic
120C2×C4×C73C2411yescharacteristic
121C22⋊D73—81no—
122C22⋊D73—81no—
123C22⋊D73—81no—
124C2×Dic73—24no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—81no—
129C2×Dic73C2×D411yescharacteristic
130C2×Dic73C2×D411yescharacteristic
131C2×Dic73C2×D411yescharacteristic
132C2×Dic73C2×D411yescharacteristic
133D292—21no—
134D292—21no—
135C4×D73—81no—
136Dic146—24no—
137Dic146—21no—
138Dic146—21no—
139Dic146#4112yes—
140Dic146#4112yes—
141C8×C73—21no—
142C8×C73—21no—
143#10596831—21no—
144#10596831—21no—
145C22×C73—21no—
146C22×C73—21no—
147C22×C73—21no—
148C22×C73—41no—
149C22×C73—41no—
150C22×C73—41no—
151C22×C73C22×D411yescharacteristic
152C2×D73—41no—
153C2×D73—41no—
154C2×D73—41no—
155C4×C73—21no—
156C4×C73—41no—
157C4×C73—41no—
158C4×C73—41no—
159C4×C73C2×#4111yescharacteristic
160C4×C73C2×#4111yescharacteristic
161Dic73—22no—
162Dic73—22no—
163Dic73—21no—
164Dic73—21no—
165Dic73—21no—
166Dic73—21no—
167Dic73—41no—
168C2×C73—41no—
169C2×C73—81no—
170C2×C73#52511yescharacteristic
171C2×C73#57711yescharacteristic
172C2×C73#57711yescharacteristic
173D73—81no—
174#3126—731nomaximal, Sylow
175C73#312611yescharacteristic, complemented, Sylow
176#540—731no—
177#519—731no—
178#482—731no—
179#482D7311yescharacteristic, complemented
180#479—731no—
181#479—731no—
182#460—731no—
183#460—731no—
184#448—731no—
185#448—731no—
186#440—731no—
187#440—731no—
188C4×SD16—731no—
189C4×SD16—731no—
190#433—731no—
191C22×Q8—731no—
192C2×SD16—731no—
193C2×SD16—731no—
194C2×SD16—731no—
195C2×SD16—731no—
196#127—731no—
197#125—731no—
198#123—1461no—
199#123—1461no—
200#121—731no—
201#121—1461no—
202#121—1461no—
203#121C2×D7311yescharacteristic
204C4×Q8—731no—
205C4×Q8—731no—
206C4×Q8—731no—
207C4×Q8—731no—
208C4×Q8—1461no—
209C4×Q8—1461no—
210C4×D4—731no—
211C4×D4—731no—
212#117—731no—
213#117—1461no—
214#117—1461no—
215#117C2×D7311yescharacteristic
216#107—731no—
217#107C2×D7311yescharacteristic
218#106—731no—
219#106C2×D7311yescharacteristic
220C4⋊C8—731no—
221C4⋊C8—731no—
222#103—731no—
223#103—731no—
224#103—731no—
225#103—731no—
226#102—731no—
227#102—731no—
228#102C2×D7311yescharacteristic
229#102C2×D7311yescharacteristic
230C22⋊C8—731no—
231C22⋊C8C2×D7311yescharacteristic
232#97—731no—
233C4×C8—731no—
234C2×Q8—731no—
235C2×Q8—731no—
236C2×Q8—1462no—
237C2×Q8—1462no—
238C2×Q8—1461no—
239C2×D4—21no—
240C2×D4—731no—
241C2×D4—1461no—
242C2×D4—1461no—
243C2×D4—1461no—
244C2×D4C22×D7311yescharacteristic
245C22×C4—1461no—
246C22×C4—1461no—
247C22×C4—1461no—
248C22×C4C22×D7311yescharacteristic
249SD16—1462no—
250SD16—1462no—
251SD16—1462no—
252SD16—1462no—
253C2×C8—731no—
254C2×C8—731no—
255C2×C8C22×D7311yescharacteristic
256C2×C8C22×D7311yescharacteristic
257C4⋊C4—731no—
258C4⋊C4—731no—
259C4⋊C4—731no—
260C4⋊C4—1461no—
261C4⋊C4—1461no—
262C4⋊C4—1461no—
263C4⋊C4—1461no—
264C4⋊C4—1461no—
265C4⋊C4—1461no—
266C4⋊C4C22×D7311yescharacteristic
267C4⋊C4C22×D7311yescharacteristic
268C4⋊C4C22×D7311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—731no—
272C22⋊C4—731no—
273C22⋊C4—1461no—
274C22⋊C4—1461no—
275C22⋊C4—1461no—
276C42—21no—
277C42—731no—
278C42—731no—
279C42—1461no—
280C42—1461no—
281C42—1461no—
282C42—1461no—
283C23—21no—
284C23—1461no—
285C23D4×D7311yescharacteristic
286Q8—732no—
287Q8—732no—
288Q8—1464no—
289Q8—1461no—
290Q8—1461no—
291D4—21no—
292D4—21no—
293D4—81no—
294D4—5841no—
295D4—5841no—
296D4—5841no—
297D4—1461no—
298D4—1461no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—5841no—
305C2×C4—5841no—
306C2×C4—731no—
307C2×C4—731no—
308C2×C4—731no—
309C2×C4—731no—
310C2×C4—1461no—
311C2×C4—1464no—
312C2×C4—1461no—
313C2×C4—1461no—
314C2×C4D4×D7311yescharacteristic
315C2×C4C23×D7311yescharacteristic
316C8—21no—
317C8—21no—
318C8—1461no—
319C8—1461no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—2921no—
327C22—2921no—
328C22—2921no—
329C22C2×D4×D7311yescharacteristic
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—2921no—
335C4—1461no—
336C4—1461no—
337C4—1461no—
338C4—1461no—
339C4—1462no—
340C4—1462no—
341C4#41×D7311yescharacteristic
342C4#41×D7311yescharacteristic
343C2—41no—
344C2—81no—
345C2—5841no—
346C2#1798909511yescharacteristic
347C2#1798939411yescharacteristic
348C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#482×C73C2
socleC22×C73C22×D4
hypercenter#482D73
hypocenterC73#3126
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #17989064C2semidirect
3. #17988911C2semidirect
4. #17988897C2semidirect
5. #17988893C2semidirect
6. #17988786C2semidirect
7. #17988786C2semidirect
8. #17988728C2semidirect
9. #17988725C2semidirect
10. #17988686C2semidirect
11. #17988684C2semidirect
12. #17988678C2semidirect
13. #17988674C2semidirect
14. #17988645C2semidirect
15. #482×C73C2semidirect
175. C73#3126semidirect
179. #482D73semidirect