Finite Group Databasebeta

← #22620101

Subgroups — #22620101

Order 9344.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989116C211yesmaximal, characteristic
2C4×Q8×D73C211yesmaximal, characteristic, complemented
3#17988921C211yesmaximal, characteristic, complemented
4#17988904C211yesmaximal, characteristic
5#17988895C211yesmaximal, characteristic, complemented
6#17988894C211yesmaximal, characteristic, complemented
7#17988806C211yesmaximal, characteristic, complemented
8#17988741C211yesmaximal, characteristic, complemented
9#17988724C211yesmaximal, characteristic
10#17988694C211yesmaximal, characteristic, complemented
11#17988691C211yesmaximal, characteristic, complemented
12#17988688C211yesmaximal, characteristic, complemented
13#17988684C211yesmaximal, characteristic, complemented
14#17988643C211yesmaximal, characteristic, complemented
15#464×C73C211yesmaximal, characteristic, complemented
16C2×Q8×D73C2211yescharacteristic
17C2×#11924018C2211yescharacteristic
18C2×#11924016C2211yescharacteristic
19#14556584—21no—
20#14556583C2211yescharacteristic
21#14556573—21no—
22#14556567C2211yescharacteristic
23#14556562C2211yescharacteristic
24Q8×Dic73C2211yescharacteristic
25Q8×Dic73C2211yescharacteristic
26C4×Dic146—21no—
27C4×Dic146C2211yescharacteristic
28#14556556—21no—
29#14556556C2211yescharacteristic
30D4×Dic73C2211yescharacteristic
31#14556551—21no—
32#14556547—21no—
33C4⋊C4×D73—21no—
34C4⋊C4×D73C2211yescharacteristic
35C42×D73—21no—
36C42×D73C2211yescharacteristic
37#14556525C2211yescharacteristic
38#14556524C2211yescharacteristic
39#14556523C2211yescharacteristic
40#14556522C2211yescharacteristic
41C4⋊#10596831C2211yescharacteristic
42#14556516C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556515C2211yescharacteristic
45#14556515C2211yescharacteristic
46#14556515C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556503C2211yescharacteristic
49#14556503C2211yescharacteristic
50#14556501C2211yescharacteristic
51#14556501C2211yescharacteristic
52C2×Q16×C73C2211yescharacteristic
53C2×SD16×C73C2211yescharacteristic
54#124×C73C2211yescharacteristic
55C4×Q8×C73C2211yescharacteristic
56C4⋊C8×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146C2311yescharacteristic
61Q8×D73—22no—
62Q8×D73—22no—
63C2×C22⋊D73—21no—
64C22×Dic73—21no—
65C2×C4×D73—21no—
66C2×C4×D73—21no—
67C2×C4×D73D411yescharacteristic
68C2×C4×D73D411yescharacteristic
69C2×C4×D73C2311yescharacteristic
70#11924018—22no—
71#11924016—22no—
72C2×#10596831C2311yescharacteristic
73C2×#10596831C2311yescharacteristic
74C4⋊Dic73—21no—
75C4⋊Dic73—21no—
76C4⋊Dic73C2311yescharacteristic
77C4⋊Dic73C2311yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85C22⋊Dic73—21no—
86C22⋊Dic73—21no—
87#11924005—21no—
88C4×Dic73—21no—
89C4×Dic73—21no—
90C4×Dic73—21no—
91C4×Dic73—21no—
92C4×Dic73D411yescharacteristic
93C4×Dic73D411yescharacteristic
94C4×Dic73C2311yescharacteristic
95C2×Q8×C73C2311yescharacteristic
96C2×Q8×C73C2311yescharacteristic
97C2×D4×C73C2311yescharacteristic
98Q16×C73—22no—
99SD16×C73—22no—
100C2×C8×C73C2311yescharacteristic
101C2×C8×C73C2311yescharacteristic
102C4⋊C4×C73—21no—
103C4⋊C4×C73C2311yescharacteristic
104C22⋊C4×C73—21no—
105C22⋊C4×C73—21no—
106C42×C73—21no—
107C42×C73C2311yescharacteristic
108C23×C73—21no—
109C22×D73C2×D411yescharacteristic
110Q8×C73—21no—
111Q8×C73—21no—
112Q8×C73—21no—
113Q8×C73#4112yes—
114D4×C73—21no—
115D4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73C2×D411yescharacteristic
120C2×C4×C73C2×D411yescharacteristic
121C2×C4×C73C2411yescharacteristic
122C22⋊D73—42no—
123C2×Dic73—21no—
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—42no—
128C2×Dic73C2×D411yescharacteristic
129C2×Dic73C2×D411yescharacteristic
130C2×Dic73C2×D411yescharacteristic
131C4×D73—24no—
132C4×D73—22no—
133C4×D73—21no—
134C4×D73—21no—
135C4×D73—41no—
136C4×D73—42no—
137Dic146—24no—
138Dic146—21no—
139Dic146#4112yes—
140C8×C73—21no—
141C8×C73—21no—
142#10596831—21no—
143#10596831—21no—
144C22×C73—41no—
145C22×C73—41no—
146C22×C73—41no—
147C22×C73C22×D411yescharacteristic
148C2×D73—21no—
149C2×D73—21no—
150C2×D73#13712yes—
151C4×C73—22no—
152C4×C73—21no—
153C4×C73—21no—
154C4×C73—41no—
155C4×C73—41no—
156C4×C73C2×#4111yescharacteristic
157C4×C73C2×#4111yescharacteristic
158Dic73—21no—
159Dic73—22no—
160Dic73—21no—
161Dic73—21no—
162Dic73—41no—
163Dic73—41no—
164Dic73—41no—
165C2×C73—81no—
166C2×C73#52511yescharacteristic
167C2×C73C2×#13711yescharacteristic
168C2×C73#57511yescharacteristic
169D73—22no—
170#3117—731nomaximal, Sylow
171C73#311711yescharacteristic, complemented, Sylow
172#529—731no—
173C2×C4×Q8—731no—
174#484—731no—
175#481—731no—
176#479—731no—
177#479—731no—
178#464—731no—
179#464D7311yescharacteristic, complemented
180#451—731no—
181#448—731no—
182#441—731no—
183#441—731no—
184#440—731no—
185#440—731no—
186#432—731no—
187C22×Q8—731no—
188C2×Q16—731no—
189C2×Q16C2×D7311yescharacteristic
190C2×SD16—731no—
191C2×SD16C2×D7311yescharacteristic
192#126—1461no—
193#125—731no—
194#124C2×D7311yescharacteristic
195#123—1461no—
196C22⋊Q8—731no—
197#121—731no—
198C4×Q8—731no—
199C4×Q8—731no—
200C4×Q8—731no—
201C4×Q8—731no—
202C4×Q8—1461no—
203C4×Q8—1461no—
204C4×Q8C2×D7311yescharacteristic
205C4×D4—731no—
206C4×D4—1461no—
207#117—1461no—
208C2×C4⋊C4—731no—
209C2×C4⋊C4—1461no—
210C2×C42—731no—
211C2×C42—1461no—
212#107—731no—
213#107—731no—
214#106—731no—
215#106—731no—
216C4⋊C8—731no—
217C4⋊C8C2×D7311yescharacteristic
218#103—731no—
219#103—731no—
220#103—731no—
221#103—731no—
222#103—731no—
223#103C2×D7311yescharacteristic
224#102—731no—
225#102C2×D7311yescharacteristic
226C22⋊C8—731no—
227C22⋊C8—731no—
228#97—731no—
229#97—731no—
230C2×Q8—731no—
231C2×Q8—1461no—
232C2×Q8—1462no—
233C2×Q8—1462no—
234C2×Q8C22×D7311yescharacteristic
235C2×Q8C22×D7311yescharacteristic
236C2×D4—1461no—
237C2×D4C22×D7311yescharacteristic
238C22×C4—731no—
239C22×C4—731no—
240C22×C4—731no—
241C22×C4—1461no—
242C22×C4—1461no—
243C22×C4—1461no—
244Q16—22no—
245Q16—1462no—
246SD16—22no—
247SD16—1462no—
248C2×C8—731no—
249C2×C8—731no—
250C2×C8C22×D7311yescharacteristic
251C2×C8C22×D7311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—731no—
254C4⋊C4—731no—
255C4⋊C4—731no—
256C4⋊C4—1461no—
257C4⋊C4—1461no—
258C4⋊C4—1461no—
259C4⋊C4—1461no—
260C4⋊C4—1461no—
261C4⋊C4—1461no—
262C4⋊C4—1461no—
263C4⋊C4—1461no—
264C4⋊C4C22×D7311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—1461no—
268C22⋊C4—1461no—
269C22⋊C4—1461no—
270C42—21no—
271C42—731no—
272C42—731no—
273C42—731no—
274C42—1461no—
275C42—1461no—
276C42—1461no—
277C42—1461no—
278C42C22×D7311yescharacteristic
279C23—21no—
280C23—731no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—732no—
285Q8—1464no—
286Q8—1461no—
287Q8#1192402712yes—
288D4—21no—
289D4—21no—
290D4—2922no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—2921no—
295C2×C4—2922no—
296C2×C4—2922no—
297C2×C4—731no—
298C2×C4—731no—
299C2×C4—731no—
300C2×C4—1462no—
301C2×C4—1464no—
302C2×C4—1461no—
303C2×C4—1461no—
304C2×C4—1461no—
305C2×C4—1461no—
306C2×C4—1461no—
307C2×C4—1461no—
308C2×C4D4×D7311yescharacteristic
309C2×C4D4×D7311yescharacteristic
310C2×C4C23×D7311yescharacteristic
311C8—21no—
312C8—21no—
313C8—1461no—
314C8—1461no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—732no—
319C22—1461no—
320C22—1461no—
321C22C2×D4×D7311yescharacteristic
322C4—21no—
323C4—21no—
324C4—22no—
325C4—41no—
326C4—41no—
327C4—2921no—
328C4—2921no—
329C4—2921no—
330C4—1461no—
331C4—1461no—
332C4—1461no—
333C4—1462no—
334C4#41×D7311yescharacteristic
335C4C2×#1192402711yescharacteristic
336C2—81no—
337C2—1462no—
338C2#1798909711yescharacteristic
339C2#137×D7311yescharacteristic
340C2#1798938411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#464×C73C2
socleC22×C73C22×D4
hypercenter#464D73
hypocenterC73#3117
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D73C2semidirect
3. #17988921C2semidirect
5. #17988895C2semidirect
6. #17988894C2semidirect
7. #17988806C2semidirect
8. #17988741C2semidirect
10. #17988694C2semidirect
11. #17988691C2semidirect
12. #17988688C2semidirect
13. #17988684C2semidirect
14. #17988643C2semidirect
15. #464×C73C2semidirect
171. C73#3117semidirect
179. #464D73semidirect