Finite Group Databasebeta

← #22622220

Subgroups — #22622220

Order 9344.

386 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989301C211yesmaximal, characteristic
2#17989250C211yesmaximal, characteristic, complemented
3#17988936C211yesmaximal, characteristic, complemented
4#17988930C211yesmaximal, characteristic, complemented
5#17988925C211yesmaximal, characteristic, complemented
6#17988881C211yesmaximal, characteristic, complemented
7#17988832C211yesmaximal, characteristic, complemented
8#17988790C211yesmaximal, characteristic, complemented
9#17988725C211yesmaximal, characteristic, complemented
10#17988724C211yesmaximal, characteristic, complemented
11#17988678C211yesmaximal, characteristic, complemented
12#17988663C211yesmaximal, characteristic, complemented
13#17988597C211yesmaximal, characteristic, complemented
14#17988594C211yesmaximal, characteristic, complemented
15#468×C73C211yesmaximal, characteristic, complemented
16C22×Dic146C2211yescharacteristic
17C2×Q8×D73C2211yescharacteristic
18C2×#11924016C2211yescharacteristic
19C2×#11924016C2211yescharacteristic
20C2×#11924011C2211yescharacteristic
21#14556590—21no—
22#14556590C2211yescharacteristic
23#14556589C2211yescharacteristic
24#14556578—21no—
25#14556577—21no—
26#14556571C2211yescharacteristic
27#14556569—21no—
28#14556568—21no—
29#14556563—21no—
30#14556562C2211yescharacteristic
31#14556556C2211yescharacteristic
32D4×Dic73C2211yescharacteristic
33C4×C22⋊D73C2211yescharacteristic
34#14556551—21no—
35#14556550C2211yescharacteristic
36#14556549C2211yescharacteristic
37#14556547—21no—
38#14556524C2211yescharacteristic
39#14556522C2211yescharacteristic
40#14556520C2211yescharacteristic
41#14556516C2211yescharacteristic
42#14556516C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556516C2211yescharacteristic
45#14556515C2211yescharacteristic
46#14556515C2211yescharacteristic
47#14556514C2211yescharacteristic
48#14556514C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C2×SD16×C73C2211yescharacteristic
53C2×M16×C73C2211yescharacteristic
54C22⋊Q8×C73C2211yescharacteristic
55#121×C73C2211yescharacteristic
56#107×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59C2×Dic146—22no—
60C2×Dic146—21no—
61C2×Dic146—21no—
62C2×Dic146—21no—
63C2×Dic146—41no—
64C2×Dic146C2311yescharacteristic
65C2×Dic146C2311yescharacteristic
66Q8×D73—22no—
67Q8×D73—41no—
68C2×C22⋊D73—21no—
69C2×C22⋊D73D411yescharacteristic
70C22×Dic73—21no—
71C22×Dic73—21no—
72C2×C4×D73—21no—
73C2×C4×D73C2311yescharacteristic
74#11924016—22no—
75#11924016—41no—
76#11924011—41no—
77C2×#10596831C2311yescharacteristic
78C2×#10596831C2311yescharacteristic
79C4⋊Dic73—21no—
80C4⋊Dic73C2311yescharacteristic
81C4⋊Dic73C2311yescharacteristic
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86#11924007D411yescharacteristic
87C22⋊Dic73—21no—
88C22⋊Dic73—21no—
89C22⋊Dic73—21no—
90C22⋊Dic73D411yescharacteristic
91#11924005—21no—
92#11924005—21no—
93#11924005D411yescharacteristic
94C4×Dic73—21no—
95C4×Dic73—21no—
96C4×Dic73—21no—
97C4×Dic73C2311yescharacteristic
98C2×Q8×C73C2311yescharacteristic
99C2×D4×C73—21no—
100C2×D4×C73C2311yescharacteristic
101C22×C4×C73C2311yescharacteristic
102SD16×C73—41no—
103M16×C73—41no—
104C2×C8×C73C2311yescharacteristic
105C2×C8×C73C2311yescharacteristic
106C4⋊C4×C73—21no—
107C4⋊C4×C73C2311yescharacteristic
108C4⋊C4×C73C2311yescharacteristic
109C22⋊C4×C73—21no—
110C22⋊C4×C73—21no—
111C23×C73—21no—
112C23×C73C2×D411yescharacteristic
113C22×D73C2×D411yescharacteristic
114Q8×C73—21no—
115Q8×C73—21no—
116D4×C73—21no—
117D4×C73—21no—
118D4×C73—81no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73C2×D411yescharacteristic
125C2×C4×C73C2411yescharacteristic
126C22⋊D73—22no—
127C22⋊D73—81no—
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—42no—
133C2×Dic73—42no—
134C2×Dic73C2×D411yescharacteristic
135C2×Dic73C2×D411yescharacteristic
136C2×Dic73C2×D411yescharacteristic
137C4×D73—21no—
138C4×D73—21no—
139C4×D73—42no—
140Dic146—21no—
141Dic146—21no—
142Dic146—21no—
143Dic146—42no—
144Dic146—42no—
145Dic146—81no—
146Dic146#4112yes—
147C8×C73—21no—
148C8×C73—21no—
149#10596831—21no—
150#10596831—21no—
151C22×C73—21no—
152C22×C73—21no—
153C22×C73—21no—
154C22×C73—41no—
155C22×C73—41no—
156C22×C73—41no—
157C22×C73C22×D411yescharacteristic
158C2×D73—21no—
159C2×D73—21no—
160C2×D73—21no—
161C4×C73—21no—
162C4×C73—41no—
163C4×C73—41no—
164C4×C73—41no—
165C4×C73C2×#4111yescharacteristic
166C4×C73H(5,𝔽2)11yescharacteristic
167Dic73—22no—
168Dic73—21no—
169Dic73—21no—
170Dic73—41no—
171Dic73—41no—
172Dic73—41no—
173Dic73#13712yes—
174C2×C73—41no—
175C2×C73—81no—
176C2×C73#54611yescharacteristic
177C2×C73C2×#13711yescharacteristic
178C2×C73#57711yescharacteristic
179D73—41no—
180#3329—731nomaximal, Sylow
181C73#332911yescharacteristic, complemented, Sylow
182#555—731no—
183D4×Q8—731no—
184#487—731no—
185#485—731no—
186#485—731no—
187#477—731no—
188#468—731no—
189#468D7311yescharacteristic, complemented
190#461—731no—
191#448—731no—
192#448—731no—
193C4×SD16—731no—
194#436—731no—
195#419—731no—
196#419—731no—
197C22×Q8—731no—
198C22×Q8—731no—
199C2×SD16—731no—
200C2×SD16—731no—
201C2×SD16C2×D7311yescharacteristic
202C2×M16—731no—
203C2×M16C2×D7311yescharacteristic
204C4⋊Q8—731no—
205C4⋊Q8—731no—
206C4⋊Q8—1461no—
207#124—1461no—
208#124—1461no—
209C22⋊Q8—731no—
210C22⋊Q8—1461no—
211C22⋊Q8—1461no—
212C22⋊Q8C2×D7311yescharacteristic
213#121—731no—
214#121—1461no—
215#121C2×D7311yescharacteristic
216C4×Q8—731no—
217C4×D4—731no—
218C4×D4—731no—
219C4×D4—1461no—
220#117—731no—
221#117—731no—
222#117—1461no—
223#107—731no—
224#107C2×D7311yescharacteristic
225#106—731no—
226C4⋊C8—731no—
227#103—731no—
228#103—731no—
229#103—731no—
230#103—731no—
231#103—731no—
232#103—731no—
233#103—731no—
234#103—731no—
235#103C2×D7311yescharacteristic
236#102C2×D7311yescharacteristic
237C22⋊C8—731no—
238C22⋊C8—731no—
239C4×C8—731no—
240C2×Q8—2921no—
241C2×Q8—2921no—
242C2×Q8—731no—
243C2×Q8—731no—
244C2×Q8—1462no—
245C2×Q8—1461no—
246C2×Q8—1461no—
247C2×Q8—1462no—
248C2×Q8—1461no—
249C2×Q8C22×D7311yescharacteristic
250C2×D4—21no—
251C2×D4—731no—
252C2×D4—1461no—
253C2×D4C22×D7311yescharacteristic
254C22×C4—731no—
255C22×C4—1461no—
256C22×C4—1461no—
257C22×C4—1461no—
258C22×C4C22×D7311yescharacteristic
259SD16—41no—
260SD16—2921no—
261SD16—1462no—
262M16—41no—
263M16—2921no—
264C2×C8—731no—
265C2×C8—731no—
266C2×C8C22×D7311yescharacteristic
267C2×C8C22×D7311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—731no—
270C4⋊C4—731no—
271C4⋊C4—731no—
272C4⋊C4—1461no—
273C4⋊C4—1461no—
274C4⋊C4—1461no—
275C4⋊C4—1461no—
276C4⋊C4—1461no—
277C4⋊C4C22×D7311yescharacteristic
278C4⋊C4C22×D7311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—731no—
282C22⋊C4—731no—
283C22⋊C4—1461no—
284C22⋊C4—1461no—
285C22⋊C4—1461no—
286C22⋊C4—1461no—
287C22⋊C4—1461no—
288C42—731no—
289C42—1461no—
290C42—1461no—
291C42—1461no—
292C23—21no—
293C23—731no—
294C23D4×D7311yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—2922no—
298Q8—2922no—
299Q8—5841no—
300Q8—732no—
301Q8—1461no—
302Q8—1461no—
303Q8—1461no—
304D4—21no—
305D4—21no—
306D4—81no—
307D4—5841no—
308D4—1462no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—2922no—
315C2×C4—2922no—
316C2×C4—2922no—
317C2×C4—731no—
318C2×C4—731no—
319C2×C4—731no—
320C2×C4—1461no—
321C2×C4—1461no—
322C2×C4—1461no—
323C2×C4—1461no—
324C2×C4—1461no—
325C2×C4—1461no—
326C2×C4D4×D7311yescharacteristic
327C2×C4C23×D7311yescharacteristic
328C8—21no—
329C8—21no—
330C8—1461no—
331C8—1461no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—1461no—
339C22—1461no—
340C22—1461no—
341C22C2×D4×D7311yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—2921no—
347C4—2921no—
348C4—2921no—
349C4—732no—
350C4—1461no—
351C4—1462no—
352C4—1461no—
353C4#41×D7311yescharacteristic
354C4#1455663611yescharacteristic
355C2—41no—
356C2—81no—
357C2—2921no—
358C2#1798922611yescharacteristic
359C2#137×D7311yescharacteristic
360C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#468×C73C2
socleC22×C73C22×D4
hypercenter#468D73
hypocenterC73#3329
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
2. #17989250C2semidirect
3. #17988936C2semidirect
4. #17988930C2semidirect
5. #17988925C2semidirect
6. #17988881C2semidirect
7. #17988832C2semidirect
8. #17988790C2semidirect
9. #17988725C2semidirect
10. #17988724C2semidirect
11. #17988678C2semidirect
12. #17988663C2semidirect
13. #17988597C2semidirect
14. #17988594C2semidirect
15. #468×C73C2semidirect
181. C73#3329semidirect
189. #468D73semidirect