Finite Group Databasebeta

← #22620016

Subgroups — #22620016

Order 9344.

390 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#17989122C211yesmaximal, characteristic
2C4×Q8×D73C211yesmaximal, characteristic, complemented
3#17988919C211yesmaximal, characteristic, complemented
4#17988902C211yesmaximal, characteristic
5#17988891C211yesmaximal, characteristic, complemented
6#17988810C211yesmaximal, characteristic, complemented
7#17988809C211yesmaximal, characteristic, complemented
8#17988744C211yesmaximal, characteristic, complemented
9#17988727C211yesmaximal, characteristic
10#17988681C211yesmaximal, characteristic, complemented
11#17988679C211yesmaximal, characteristic, complemented
12#17988674C211yesmaximal, characteristic, complemented
13#17988672C211yesmaximal, characteristic, complemented
14#17988639C211yesmaximal, characteristic, complemented
15#479×C73C211yesmaximal, characteristic, complemented
16C2×Q8×D73C2211yescharacteristic
17C2×Dic292C2211yescharacteristic
18C2×#11924018C2211yescharacteristic
19C2×#11924017C2211yescharacteristic
20C2×#11924015C2211yescharacteristic
21#14556586—21no—
22#14556579C2211yescharacteristic
23#14556576—21no—
24#14556571C2211yescharacteristic
25#14556566C2211yescharacteristic
26Q8×Dic73C2211yescharacteristic
27C4×Dic146—21no—
28C4×Dic146C2211yescharacteristic
29#14556556—21no—
30#14556556C2211yescharacteristic
31#14556556C2211yescharacteristic
32#14556553—21no—
33#14556553C2211yescharacteristic
34#14556549—21no—
35C4⋊C4×D73—21no—
36C4⋊C4×D73C2211yescharacteristic
37C42×D73—21no—
38C42×D73C2211yescharacteristic
39#14556524C2211yescharacteristic
40#14556522C2211yescharacteristic
41C4⋊#10596831C2211yescharacteristic
42#14556516C2211yescharacteristic
43#14556514C2211yescharacteristic
44#14556514C2211yescharacteristic
45#14556514C2211yescharacteristic
46#14556513C2211yescharacteristic
47#14556511C2211yescharacteristic
48#14556503C2211yescharacteristic
49#14556503C2211yescharacteristic
50C8×Dic73C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52#125×C73C2211yescharacteristic
53C4×Q8×C73C2211yescharacteristic
54#107×C73C2211yescharacteristic
55#106×C73C2211yescharacteristic
56C4⋊C8×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58#103×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146C2311yescharacteristic
61C2×Dic146C2311yescharacteristic
62Q8×D73—22no—
63Q8×D73—22no—
64C2×D292—21no—
65C2×D292C2311yescharacteristic
66C2×C4×D73—21no—
67C2×C4×D73—21no—
68C2×C4×D73—21no—
69C2×C4×D73D411yescharacteristic
70C2×C4×D73D411yescharacteristic
71C2×C4×D73C2311yescharacteristic
72Dic292—22no—
73#11924018—22no—
74#11924017—22no—
75#11924015—22no—
76C2×#10596831C2311yescharacteristic
77C2×#10596831C2311yescharacteristic
78C4⋊Dic73—21no—
79C4⋊Dic73—21no—
80C4⋊Dic73C2311yescharacteristic
81#11924007—21no—
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924005—21no—
86#11924005—21no—
87#11924005—21no—
88#11924005—21no—
89#11924005—21no—
90C4×Dic73—21no—
91C4×Dic73—21no—
92C4×Dic73—21no—
93C4×Dic73—21no—
94C4×Dic73D411yescharacteristic
95C4×Dic73D411yescharacteristic
96C4×Dic73C2311yescharacteristic
97C2×Q8×C73C2311yescharacteristic
98C2×C8×C73C2311yescharacteristic
99C2×C8×C73C2311yescharacteristic
100C4⋊C4×C73—21no—
101C4⋊C4×C73—21no—
102C4⋊C4×C73—21no—
103C4⋊C4×C73C2311yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C4⋊C4×C73C2311yescharacteristic
106C42×C73—21no—
107C42×C73C2311yescharacteristic
108C22×D73—21no—
109C22×D73C2×D411yescharacteristic
110Q8×C73—21no—
111Q8×C73#4112yes—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73C2×D411yescharacteristic
117C2×C4×C73C2×D411yescharacteristic
118C2×C4×C73C2411yescharacteristic
119C2×Dic73—21no—
120C2×Dic73—21no—
121C2×Dic73—21no—
122C2×Dic73C2×D411yescharacteristic
123C2×Dic73C2×D411yescharacteristic
124C2×Dic73C2×D411yescharacteristic
125D292—21no—
126D292—21no—
127D292—42no—
128C4×D73—24no—
129C4×D73—22no—
130C4×D73—21no—
131C4×D73—21no—
132C4×D73—22no—
133C4×D73—42no—
134C4×D73—42no—
135Dic146—24no—
136Dic146—21no—
137Dic146—21no—
138Dic146—21no—
139Dic146#4112yes—
140C8×C73—21no—
141C8×C73—21no—
142#10596831—21no—
143#10596831—21no—
144C22×C73C22×D411yescharacteristic
145C2×D73—21no—
146C2×D73—21no—
147C2×D73—41no—
148C2×D73—41no—
149C2×D73—41no—
150C2×D73#13512yes—
151C4×C73—22no—
152C4×C73—21no—
153C4×C73—21no—
154C4×C73—41no—
155C4×C73—41no—
156C4×C73—41no—
157C4×C73C2×#4111yescharacteristic
158C4×C73C2×#4111yescharacteristic
159Dic73—21no—
160Dic73—22no—
161Dic73—21no—
162Dic73—41no—
163Dic73—41no—
164Dic73#13712yes—
165C2×C73#52511yescharacteristic
166C2×C73C2×#13511yescharacteristic
167C2×C73C2×#13711yescharacteristic
168D73—22no—
169D73—81no—
170#3108—731nomaximal, Sylow
171C73#310811yescharacteristic, complemented, Sylow
172#529—731no—
173C2×C4×Q8—731no—
174#483—731no—
175#480—731no—
176#479—731no—
177#479D7311yescharacteristic, complemented
178#464—731no—
179#464—731no—
180#451—731no—
181#448—731no—
182C4×Q16—731no—
183C4×Q16—731no—
184C4×SD16—731no—
185C4×SD16—731no—
186#431—731no—
187C22×Q8—731no—
188C2×Q16—731no—
189C2×Q16—731no—
190C2×SD16—731no—
191C2×SD16—731no—
192#126—1461no—
193#125C2×D7311yescharacteristic
194#124—731no—
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#107C2×D7311yescharacteristic
214#106—731no—
215#106C2×D7311yescharacteristic
216C4⋊C8—731no—
217C4⋊C8C2×D7311yescharacteristic
218#103—731no—
219#103—731no—
220#103—731no—
221#103—731no—
222#103C2×D7311yescharacteristic
223#103C2×D7311yescharacteristic
224#102—731no—
225#102—731no—
226C22⋊C8—731no—
227C22⋊C8—731no—
228C4×C8—731no—
229C4×C8—731no—
230C2×Q8—731no—
231C2×Q8—731no—
232C2×Q8—1461no—
233C2×Q8—1462no—
234C2×Q8—1462no—
235C2×Q8C22×D7311yescharacteristic
236C2×D4—731no—
237C2×D4—1461no—
238C22×C4—731no—
239C22×C4—731no—
240C22×C4—731no—
241C22×C4—1461no—
242C22×C4—1461no—
243C22×C4—1461no—
244Q16—1462no—
245Q16—1462no—
246SD16—1462no—
247SD16—1462no—
248C2×C8—731no—
249C2×C8—731no—
250C2×C8C22×D7311yescharacteristic
251C2×C8C22×D7311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—731no—
256C4⋊C4—1461no—
257C4⋊C4—1461no—
258C4⋊C4—1461no—
259C4⋊C4—1461no—
260C4⋊C4—1461no—
261C4⋊C4—1461no—
262C4⋊C4C22×D7311yescharacteristic
263C4⋊C4C22×D7311yescharacteristic
264C4⋊C4C22×D7311yescharacteristic
265C22⋊C4—1461no—
266C22⋊C4—1461no—
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—731no—
280C23—1461no—
281Q8—21no—
282Q8—732no—
283Q8—1464no—
284Q8—1461no—
285Q8—1461no—
286Q8—1461no—
287Q8#1192402912yes—
288D4—2922no—
289D4—1461no—
290D4—1461no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—2922no—
296C2×C4—2922no—
297C2×C4—731no—
298C2×C4—731no—
299C2×C4—731no—
300C2×C4—1462no—
301C2×C4—1462no—
302C2×C4—1464no—
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—2921no—
316C22—2921no—
317C22—2921no—
318C22—732no—
319C22—1461no—
320C22—1461no—
321C22C2×D4×D7311yescharacteristic
322C4—21no—
323C4—22no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—2921no—
329C4—2921no—
330C4—732no—
331C4—1461no—
332C4—1462no—
333C4—1461no—
334C4#41×D7311yescharacteristic
335C4C2×#1192402911yescharacteristic
336C2—5841no—
337C2—1462no—
338C2#1798910011yescharacteristic
339C2#135×D7311yescharacteristic
340C2#137×D7311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#479×C73C2
socleC22×C73C22×D4
hypercenter#479D73
hypocenterC73#3108
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D73C2semidirect
3. #17988919C2semidirect
5. #17988891C2semidirect
6. #17988810C2semidirect
7. #17988809C2semidirect
8. #17988744C2semidirect
10. #17988681C2semidirect
11. #17988679C2semidirect
12. #17988674C2semidirect
13. #17988672C2semidirect
14. #17988639C2semidirect
15. #479×C73C2semidirect
171. C73#3108semidirect
177. #479D73semidirect