Finite Group Databasebeta

← #22620000

Subgroups — #22620000

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#17989141C211yesmaximal, characteristic, complemented
2C4×#11924029C211yesmaximal, characteristic
3#17988930C211yesmaximal, characteristic, complemented
4#17988926C211yesmaximal, characteristic, complemented
5#17988870C211yesmaximal, characteristic, complemented
6#17988866C211yesmaximal, characteristic, complemented
7#17988795C211yesmaximal, characteristic, complemented
8#17988791C211yesmaximal, characteristic, complemented
9#17988752C211yesmaximal, characteristic
10#17988748C211yesmaximal, characteristic
11C4×#11924018C211yesmaximal, characteristic, complemented
12C4×#11924017C211yesmaximal, characteristic, complemented
13C4×#11924015C211yesmaximal, characteristic, complemented
14#17988638C211yesmaximal, characteristic, complemented
15C4×Q16×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic
17C2×#11924018C2211yescharacteristic
18C2×#11924017C2211yescharacteristic
19C2×#11924015C2211yescharacteristic
20#14556590C2211yescharacteristic
21#14556589C2211yescharacteristic
22#14556581—21no—
23#14556571C2211yescharacteristic
24#14556569—21no—
25#14556567C2211yescharacteristic
26Q8×Dic73C2211yescharacteristic
27C4×Dic146—21no—
28C4×Dic146C2211yescharacteristic
29C4×D292—21no—
30C4×D292C2211yescharacteristic
31#14556553—21no—
32#14556553C2211yescharacteristic
33#14556549—21no—
34#14556549C2211yescharacteristic
35#14556548—21no—
36C42×D73—21no—
37C42×D73C2211yescharacteristic
38#14556524C2211yescharacteristic
39#14556523C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556520C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556515C2211yescharacteristic
45#14556515C2211yescharacteristic
46#14556514C2211yescharacteristic
47#14556513C2211yescharacteristic
48#14556511C2211yescharacteristic
49#14556503C2211yescharacteristic
50#14556503C2211yescharacteristic
51C4×#10596831C2211yescharacteristic
52C2×Q16×C73C2211yescharacteristic
53C4×Q8×C73C2211yescharacteristic
54C4×Q8×C73C2211yescharacteristic
55#107×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58C4×C8×C73C2211yescharacteristic
59#11924029—22no—
60#11924029—22no—
61C2×Dic146—21no—
62C2×Dic146C2311yescharacteristic
63C2×D292—21no—
64C2×D292C2311yescharacteristic
65C2×C4×D73—21no—
66C2×C4×D73—21no—
67C2×C4×D73—21no—
68C2×C4×D73D411yescharacteristic
69C2×C4×D73D411yescharacteristic
70C2×C4×D73C2311yescharacteristic
71#11924018—22no—
72#11924017—22no—
73#11924015—22no—
74C2×#10596831C2311yescharacteristic
75C2×#10596831C2311yescharacteristic
76C4⋊Dic73—21no—
77C4⋊Dic73—21no—
78C4⋊Dic73C2311yescharacteristic
79C4⋊Dic73C2311yescharacteristic
80#11924007—21no—
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×Dic73D411yescharacteristic
94C4×Dic73D411yescharacteristic
95C4×Dic73C2311yescharacteristic
96C2×Q8×C73C2311yescharacteristic
97C2×Q8×C73C2311yescharacteristic
98Q16×C73—22no—
99C2×C8×C73C2311yescharacteristic
100C2×C8×C73C2311yescharacteristic
101C4⋊C4×C73—21no—
102C4⋊C4×C73—21no—
103C4⋊C4×C73C2311yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C42×C73—21no—
106C42×C73—21no—
107C42×C73C2311yescharacteristic
108C22×D73—21no—
109C22×D73C2×D411yescharacteristic
110Q8×C73—21no—
111Q8×C73—21no—
112Q8×C73—21no—
113Q8×C73#4112yes—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73C2×D411yescharacteristic
119C2×C4×C73C2×D411yescharacteristic
120C2×C4×C73C2411yescharacteristic
121C2×Dic73—21no—
122C2×Dic73—21no—
123C2×Dic73—21no—
124C2×Dic73C2×D411yescharacteristic
125C2×Dic73C2×D411yescharacteristic
126C2×Dic73C2×D411yescharacteristic
127D292—24no—
128D292—21no—
129D292#4112yes—
130C4×D73—24no—
131C4×D73—22no—
132C4×D73—21no—
133C4×D73—21no—
134C4×D73—22no—
135C4×D73—42no—
136C4×D73—42no—
137Dic146—21no—
138Dic146—21no—
139Dic146—42no—
140C8×C73—21no—
141C8×C73—21no—
142#10596831—21no—
143#10596831—21no—
144C22×C73C22×D411yescharacteristic
145C2×D73—21no—
146C2×D73—22no—
147C2×D73—21no—
148C2×D73—21no—
149C2×D73—41no—
150C2×D73—41no—
151C4×C73—22no—
152C4×C73—21no—
153C4×C73—41no—
154C4×C73—41no—
155C4×C73—41no—
156C4×C73#13712yes—
157C4×C73C2×#4111yescharacteristic
158C4×C73C2×#4111yescharacteristic
159Dic73—21no—
160Dic73—21no—
161Dic73—41no—
162Dic73—41no—
163Dic73—41no—
164Dic73#13512yes—
165C2×C73#52511yescharacteristic
166C2×C73C2×#13511yescharacteristic
167C2×C73C2×#13711yescharacteristic
168D73—41no—
169D73—42no—
170#3107—731nomaximal, Sylow
171C73#310711yescharacteristic, complemented, Sylow
172#533—731no—
173C4×#41—731no—
174#485—731no—
175#485—731no—
176#475—731no—
177#474—731no—
178#462—731no—
179#461—731no—
180#452—731no—
181#452—731no—
182C4×Q16—731no—
183C4×Q16D7311yescharacteristic, complemented
184C4×SD16—731no—
185C4×SD16—731no—
186#431—731no—
187C2×#41—731no—
188C2×Q16—731no—
189C2×Q16C2×D7311yescharacteristic
190C2×SD16—731no—
191C2×SD16—731no—
192C4⋊Q8—731no—
193C4⋊Q8—731no—
194#125—1461no—
195C22⋊Q8—731no—
196C22⋊Q8—731no—
197C22⋊Q8—1461no—
198C4×Q8—731no—
199C4×Q8—731no—
200C4×Q8—1461no—
201C4×Q8C2×D7311yescharacteristic
202C4×Q8C2×D7311yescharacteristic
203C4×D4—731no—
204C4×D4—731no—
205C4×D4—1461no—
206C4×D4—1461no—
207#117—731no—
208#117—1461no—
209#117—1461no—
210C2×C42—731no—
211C2×C42—1461no—
212#107—731no—
213#107C2×D7311yescharacteristic
214#106—731no—
215#106—731no—
216C4⋊C8—731no—
217C4⋊C8—731no—
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×C8C2×D7311yescharacteristic
230#41—1462no—
231#41—1462no—
232C2×Q8—731no—
233C2×Q8—1461no—
234C2×Q8C22×D7311yescharacteristic
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—22no—
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—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⋊C4C22×D7311yescharacteristic
264C4⋊C4C22×D7311yescharacteristic
265C22⋊C4—1461no—
266C22⋊C4—1461no—
267C22⋊C4—1461no—
268C22⋊C4—1461no—
269C22⋊C4—1461no—
270C42—21no—
271C42—21no—
272C42—731no—
273C42—731no—
274C42—731no—
275C42—1461no—
276C42—1461no—
277C42—1461no—
278C42C22×D7311yescharacteristic
279C23—731no—
280C23—1461no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—2922no—
285Q8—1461no—
286Q8—1461no—
287Q8#1192402812yes—
288D4—732no—
289D4—1464no—
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—1464no—
302C2×C4—1461no—
303C2×C4—1461no—
304C2×C4—1461no—
305C2×C4—1462no—
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—1461no—
318C22—1462no—
319C22—1461no—
320C22—1461no—
321C22C2×D4×D7311yescharacteristic
322C4—22no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—2921no—
328C4—2921no—
329C4—2921no—
330C4—732no—
331C4—1461no—
332C4—1461no—
333C4#1455662312yes—
334C4#41×D7311yescharacteristic
335C4C2×#1192402811yescharacteristic
336C2—2922no—
337C2—2921no—
338C2#1798909611yescharacteristic
339C2#135×D7311yescharacteristic
340C2C2×#1455662311yescharacteristic
subgroupG/H
centerC2×C4D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC4×Q16×C73C2
socleC22×C73C22×D4
hypercenterC4×Q16D73
hypocenterC73#3107
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
1. #17989141C2semidirect
3. #17988930C2semidirect
4. #17988926C2semidirect
5. #17988870C2semidirect
6. #17988866C2semidirect
7. #17988795C2semidirect
8. #17988791C2semidirect
11. C4×#11924018C2semidirect
12. C4×#11924017C2semidirect
13. C4×#11924015C2semidirect
14. #17988638C2semidirect
15. C4×Q16×C73C2semidirect
171. C73#3107semidirect
183. C4×Q16D73semidirect