Finite Group Databasebeta

← #22620216

Subgroups — #22620216

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#17989065C211yesmaximal, characteristic, complemented
3#17988912C211yesmaximal, characteristic, complemented
4#17988908C211yesmaximal, characteristic, complemented
5#17988896C211yesmaximal, characteristic, complemented
6#17988892C211yesmaximal, characteristic, complemented
7#17988785C211yesmaximal, characteristic, complemented
8#17988785C211yesmaximal, characteristic, complemented
9#17988726C211yesmaximal, characteristic, complemented
10#17988690C211yesmaximal, characteristic, complemented
11#17988688C211yesmaximal, characteristic, complemented
12SD16×Dic73C211yesmaximal, characteristic, complemented
13#17988672C211yesmaximal, characteristic, complemented
14#17988645C211yesmaximal, characteristic, complemented
15#448×C73C211yesmaximal, characteristic, complemented
16C2×#11924015C2211yescharacteristic
17C2×#11924015C2211yescharacteristic
18#14556587C2211yescharacteristic
19#14556582C2211yescharacteristic
20#14556575—21no—
21#14556573—21no—
22#14556565C2211yescharacteristic
23#14556563—21no—
24#14556562—21no—
25Q8×Dic73—21no—
26Q8×Dic73—21no—
27Q8×Dic73C2211yescharacteristic
28Q8×Dic73C2211yescharacteristic
29Q8×Dic73C2211yescharacteristic
30Q8×Dic73C2211yescharacteristic
31D4×Dic73C2211yescharacteristic
32#14556553C2211yescharacteristic
33#14556550—21no—
34#14556550—21no—
35#14556550C2211yescharacteristic
36#14556550C2211yescharacteristic
37#14556525C2211yescharacteristic
38#14556524C2211yescharacteristic
39#14556523C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556520C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556515C2211yescharacteristic
44#14556515C2211yescharacteristic
45#14556513C2211yescharacteristic
46#14556513C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556512C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556501C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C22×Q8×C73C2211yescharacteristic
53C2×SD16×C73C2211yescharacteristic
54C2×SD16×C73C2211yescharacteristic
55#121×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59C2×D292C2311yescharacteristic
60C2×C22⋊D73—21no—
61C2×C22⋊D73—21no—
62C2×C22⋊D73—21no—
63C22×Dic73—21no—
64C2×C4×D73—21no—
65#11924015—22no—
66#11924015—22no—
67C2×#10596831C2311yescharacteristic
68C2×#10596831C2311yescharacteristic
69C4⋊Dic73—21no—
70C4⋊Dic73—21no—
71C4⋊Dic73—21no—
72C4⋊Dic73—21no—
73C4⋊Dic73—21no—
74C4⋊Dic73D411yescharacteristic
75C4⋊Dic73D411yescharacteristic
76C4⋊Dic73C2311yescharacteristic
77C4⋊Dic73C2311yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79#11924007—21no—
80C22⋊Dic73—21no—
81C22⋊Dic73—21no—
82C22⋊Dic73D411yescharacteristic
83C22⋊Dic73D411yescharacteristic
84#11924005—21no—
85#11924005—21no—
86C4×Dic73—21no—
87C4×Dic73—21no—
88C4×Dic73—21no—
89C4×Dic73—21no—
90C4×Dic73—21no—
91C4×Dic73C2311yescharacteristic
92C4×Dic73C2311yescharacteristic
93C2×Q8×C73—22no—
94C2×Q8×C73—22no—
95C2×Q8×C73—21no—
96C2×Q8×C73C2311yescharacteristic
97C2×Q8×C73C2311yescharacteristic
98C2×D4×C73—21no—
99C2×D4×C73C2311yescharacteristic
100C22×C4×C73—21no—
101C22×C4×C73C2311yescharacteristic
102SD16×C73—22no—
103SD16×C73—22no—
104C2×C8×C73C2311yescharacteristic
105C2×C8×C73C2311yescharacteristic
106C4⋊C4×C73C2311yescharacteristic
107C22⋊C4×C73—21no—
108C23×C73—21no—
109C23×C73C2×D411yescharacteristic
110C22×D73—21no—
111Q8×C73—24no—
112Q8×C73—21no—
113Q8×C73—21no—
114Q8×C73#4112yes—
115Q8×C73#4112yes—
116D4×C73—21no—
117D4×C73—21no—
118D4×C73—81no—
119C2×C4×C73—24no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73C2×D411yescharacteristic
126C2×C4×C73C2411yescharacteristic
127C22⋊D73—81no—
128C22⋊D73—81no—
129C22⋊D73—81no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—81no—
134C2×Dic73C2×D411yescharacteristic
135C2×Dic73C2×D411yescharacteristic
136C2×Dic73C2×D411yescharacteristic
137C2×Dic73C2×D411yescharacteristic
138D292—21no—
139D292—21no—
140C4×D73—81no—
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—22no—
156C4×C73—22no—
157C4×C73—21no—
158C4×C73—41no—
159C4×C73C2×#4111yescharacteristic
160C4×C73C2×#4111yescharacteristic
161Dic73—21no—
162Dic73—21no—
163Dic73—21no—
164Dic73—21no—
165Dic73—41no—
166Dic73—41no—
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#482—731no—
180#479—731no—
181#479—731no—
182#460—731no—
183#460—731no—
184#448—731no—
185#448D7311yescharacteristic, complemented
186#440—731no—
187#440—731no—
188C4×SD16—731no—
189C4×SD16—731no—
190#433—731no—
191C22×Q8C2×D7311yescharacteristic
192C2×SD16—731no—
193C2×SD16—731no—
194C2×SD16C2×D7311yescharacteristic
195C2×SD16C2×D7311yescharacteristic
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—731no—
214#117—1461no—
215#117—1461no—
216#107—731no—
217#107—731no—
218#106—731no—
219#106—731no—
220C4⋊C8—731no—
221C4⋊C8—731no—
222#103—731no—
223#103—731no—
224#103C2×D7311yescharacteristic
225#103C2×D7311yescharacteristic
226#102—731no—
227#102—731no—
228#102—731no—
229#102—731no—
230C22⋊C8—731no—
231C22⋊C8C2×D7311yescharacteristic
232#97—731no—
233C4×C8—731no—
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8—21no—
237C2×Q8C22×D7311yescharacteristic
238C2×Q8C22×D7311yescharacteristic
239C2×D4—21no—
240C2×D4—731no—
241C2×D4—1461no—
242C2×D4—1461no—
243C2×D4—1461no—
244C2×D4C22×D7311yescharacteristic
245C22×C4—21no—
246C22×C4—1461no—
247C22×C4—1461no—
248C22×C4C22×D7311yescharacteristic
249SD16—22no—
250SD16—22no—
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—731no—
261C4⋊C4—731no—
262C4⋊C4—1461no—
263C4⋊C4—1461no—
264C4⋊C4—1461no—
265C4⋊C4—1461no—
266C4⋊C4—1461no—
267C4⋊C4—1461no—
268C4⋊C4C22×D7311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—731no—
271C22⋊C4—731no—
272C22⋊C4—1461no—
273C22⋊C4—1461no—
274C22⋊C4—1461no—
275C22⋊C4—1461no—
276C42—731no—
277C42—731no—
278C42—1461no—
279C42—1461no—
280C42—1461no—
281C42—1461no—
282C42—1461no—
283C23—21no—
284C23—1461no—
285C23D4×D7311yescharacteristic
286Q8—24no—
287Q8—21no—
288Q8—21no—
289Q8#1192402712yes—
290Q8#1192402712yes—
291D4—21no—
292D4—21no—
293D4—81no—
294D4—5841no—
295D4—5841no—
296D4—5841no—
297D4—1461no—
298D4—1461no—
299C2×C4—24no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—5841no—
306C2×C4—5841no—
307C2×C4—731no—
308C2×C4—731no—
309C2×C4—731no—
310C2×C4—731no—
311C2×C4—1461no—
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—22no—
331C4—22no—
332C4—21no—
333C4—41no—
334C4—2921no—
335C4—2921no—
336C4—2921no—
337C4—1461no—
338C4—1461no—
339C4—1461no—
340C4—1461no—
341C4C2×#1192402711yescharacteristic
342C4C2×#1192402711yescharacteristic
343C2—41no—
344C2—81no—
345C2—5841no—
346C2#1798909311yescharacteristic
347C2#1798939311yescharacteristic
348C2#1798939611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#448×C73C2
socleC22×C73C22×D4
hypercenter#448D73
hypocenterC73#3126
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
2. #17989065C2semidirect
3. #17988912C2semidirect
4. #17988908C2semidirect
5. #17988896C2semidirect
6. #17988892C2semidirect
7. #17988785C2semidirect
8. #17988785C2semidirect
9. #17988726C2semidirect
10. #17988690C2semidirect
11. #17988688C2semidirect
12. SD16×Dic73C2semidirect
13. #17988672C2semidirect
14. #17988645C2semidirect
15. #448×C73C2semidirect
175. C73#3126semidirect
185. #448D73semidirect