Finite Group Databasebeta

← #22620162

Subgroups — #22620162

Order 9344.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989208C211yesmaximal, characteristic
2#17989064C211yesmaximal, characteristic, complemented
3#17988929C211yesmaximal, characteristic, complemented
4#17988912C211yesmaximal, characteristic
5#17988883C211yesmaximal, characteristic, complemented
6#17988873C211yesmaximal, characteristic, complemented
7#17988810C211yesmaximal, characteristic, complemented
8#17988810C211yesmaximal, characteristic, complemented
9#17988745C211yesmaximal, characteristic, complemented
10#17988728C211yesmaximal, characteristic
11#17988695C211yesmaximal, characteristic, complemented
12#17988689C211yesmaximal, characteristic, complemented
13C4×Dic292C211yesmaximal, characteristic, complemented
14C4×#11924017C211yesmaximal, characteristic, complemented
15#433×C73C211yesmaximal, characteristic, complemented
16C22×Dic146C2211yescharacteristic
17C2×Dic292C2211yescharacteristic
18C2×Dic292C2211yescharacteristic
19C2×#11924017C2211yescharacteristic
20C2×#11924017C2211yescharacteristic
21#14556591C2211yescharacteristic
22#14556586—21no—
23#14556579C2211yescharacteristic
24#14556577—21no—
25#14556573—21no—
26#14556570C2211yescharacteristic
27#14556569—21no—
28#14556565C2211yescharacteristic
29C4×Dic146C2211yescharacteristic
30C4×Dic146C2211yescharacteristic
31C4×Dic146C2211yescharacteristic
32C4×Dic146C2211yescharacteristic
33C4×Dic146C2211yescharacteristic
34#14556556—21no—
35#14556556—21no—
36C4×D292C2211yescharacteristic
37#14556550C2211yescharacteristic
38#14556547—21no—
39#14556547—21no—
40#14556525C2211yescharacteristic
41#14556525C2211yescharacteristic
42#14556523C2211yescharacteristic
43#14556523C2211yescharacteristic
44#14556516C2211yescharacteristic
45#14556516C2211yescharacteristic
46#14556516C2211yescharacteristic
47#14556516C2211yescharacteristic
48#14556516C2211yescharacteristic
49#14556516C2211yescharacteristic
50#14556513C2211yescharacteristic
51#14556513C2211yescharacteristic
52#117×C73C2211yescharacteristic
53C4⋊C8×C73C2211yescharacteristic
54C4⋊C8×C73C2211yescharacteristic
55C22⋊C8×C73C2211yescharacteristic
56C22⋊C8×C73C2211yescharacteristic
57#97×C73C2211yescharacteristic
58C4×C8×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146—22no—
61C2×Dic146—22no—
62C2×Dic146—21no—
63C2×Dic146C2311yescharacteristic
64C2×Dic146C2311yescharacteristic
65C2×Dic146C2311yescharacteristic
66C2×D292C2311yescharacteristic
67C2×C22⋊D73—21no—
68C22×Dic73—21no—
69C2×C4×D73—21no—
70Dic292—22no—
71Dic292—22no—
72#11924017—22no—
73#11924017—22no—
74C4⋊Dic73—21no—
75C4⋊Dic73C2311yescharacteristic
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—
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91C4×Dic73—21no—
92C4×Dic73—21no—
93C4×Dic73—21no—
94C4×Dic73—21no—
95C4×Dic73—21no—
96C4×Dic73—21no—
97C22×C4×C73C2311yescharacteristic
98C2×C8×C73C2311yescharacteristic
99C2×C8×C73C2311yescharacteristic
100C2×C8×C73C2311yescharacteristic
101C2×C8×C73C2311yescharacteristic
102C4⋊C4×C73D411yescharacteristic
103C4⋊C4×C73D411yescharacteristic
104C22⋊C4×C73D411yescharacteristic
105C22⋊C4×C73D411yescharacteristic
106C42×C73C2311yescharacteristic
107C42×C73C2311yescharacteristic
108C23×C73C2×D411yescharacteristic
109C22×D73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73C2×D411yescharacteristic
113C2×C4×C73C2×D411yescharacteristic
114C2×C4×C73C2×D411yescharacteristic
115C2×C4×C73C2×D411yescharacteristic
116C2×C4×C73C2×D411yescharacteristic
117C2×C4×C73C2411yescharacteristic
118C22⋊D73—81no—
119C2×Dic73—24no—
120C2×Dic73—21no—
121C2×Dic73—21no—
122C2×Dic73—21no—
123C2×Dic73—21no—
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127D292—21no—
128D292—21no—
129C4×D73—81no—
130Dic146—24no—
131Dic146—21no—
132Dic146—21no—
133Dic146—21no—
134Dic146—21no—
135Dic146—81no—
136Dic146#4112yes—
137Dic146#4112yes—
138C8×C73—21no—
139C8×C73—21no—
140C8×C73—21no—
141C8×C73—21no—
142C22×C73—21no—
143C22×C73—21no—
144C22×C73—21no—
145C22×C73C22×D411yescharacteristic
146C2×D73—41no—
147C2×D73—41no—
148C2×D73—41no—
149C4×C73—21no—
150C4×C73—21no—
151C4×C73—21no—
152C4×C73—21no—
153C4×C73—21no—
154C4×C73C2×#4111yescharacteristic
155C4×C73C2×#4111yescharacteristic
156Dic73—22no—
157Dic73—22no—
158Dic73—41no—
159Dic73—41no—
160Dic73—41no—
161Dic73—41no—
162Dic73—41no—
163C2×C73—41no—
164C2×C73#52511yescharacteristic
165C2×C73#57711yescharacteristic
166C2×C73#57811yescharacteristic
167D73—81no—
168#3121—731nomaximal, Sylow
169C73#312111yescharacteristic, complemented, Sylow
170#542—731no—
171#519—731no—
172#485—731no—
173#482—731no—
174#477—731no—
175#475—731no—
176#464—731no—
177#464—731no—
178#451—731no—
179#448—731no—
180#441—731no—
181#440—731no—
182C4×Q16—731no—
183C4×SD16—731no—
184#433D7311yescharacteristic, complemented
185C22×Q8—731no—
186C2×Q16—731no—
187C2×Q16—731no—
188C2×SD16—731no—
189C2×SD16—731no—
190C4⋊Q8—731no—
191#126—1461no—
192#124—731no—
193#124—1461no—
194#123—1461no—
195C22⋊Q8—731no—
196C22⋊Q8—1461no—
197#121—731no—
198C4×Q8—731no—
199C4×Q8—731no—
200C4×Q8—731no—
201C4×Q8—731no—
202C4×Q8—731no—
203C4×Q8—1461no—
204C4×Q8—1461no—
205C4×D4—731no—
206#117—731no—
207#117—1461no—
208#117—1461no—
209#117C2×D7311yescharacteristic
210#107—731no—
211#107—731no—
212#106—731no—
213#106—731no—
214C4⋊C8C2×D7311yescharacteristic
215C4⋊C8C2×D7311yescharacteristic
216#103—731no—
217#103—731no—
218#103—731no—
219#103—731no—
220#103—731no—
221#103—731no—
222#102—731no—
223#102—731no—
224C22⋊C8C2×D7311yescharacteristic
225C22⋊C8C2×D7311yescharacteristic
226#97C2×D7311yescharacteristic
227C4×C8C2×D7311yescharacteristic
228C2×Q8—731no—
229C2×Q8—731no—
230C2×Q8—731no—
231C2×Q8—1462no—
232C2×Q8—1462no—
233C2×Q8—1461no—
234C2×Q8—1461no—
235C2×D4—731no—
236C2×D4—1461no—
237C22×C4—1461no—
238C22×C4—1461no—
239C22×C4C22×D7311yescharacteristic
240Q16—1462no—
241Q16—1462no—
242SD16—1462no—
243SD16—1462no—
244C2×C8C22×D7311yescharacteristic
245C2×C8C22×D7311yescharacteristic
246C2×C8C22×D7311yescharacteristic
247C2×C8C22×D7311yescharacteristic
248C4⋊C4—731no—
249C4⋊C4—731no—
250C4⋊C4—731no—
251C4⋊C4—731no—
252C4⋊C4—1461no—
253C4⋊C4—1461no—
254C4⋊C4—1461no—
255C4⋊C4—1461no—
256C4⋊C4—1461no—
257C4⋊C4—1461no—
258C4⋊C4—1461no—
259C4⋊C4D29211yescharacteristic
260C4⋊C4D29211yescharacteristic
261C22⋊C4—1461no—
262C22⋊C4—1461no—
263C22⋊C4—1461no—
264C22⋊C4—1461no—
265C22⋊C4—1461no—
266C22⋊C4—1461no—
267C22⋊C4D29211yescharacteristic
268C22⋊C4D29211yescharacteristic
269C42—1461no—
270C42—1461no—
271C42—1461no—
272C42—1461no—
273C42—1461no—
274C42—1461no—
275C42C22×D7311yescharacteristic
276C42C22×D7311yescharacteristic
277C23—1461no—
278C23C2×D29211yescharacteristic
279Q8—5841no—
280Q8—732no—
281Q8—732no—
282Q8—1464no—
283Q8—1461no—
284Q8—1461no—
285Q8—1461no—
286Q8—1461no—
287D4—5841no—
288D4—1461no—
289D4—1461no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—5841no—
293C2×C4—1461no—
294C2×C4—1461no—
295C2×C4—1461no—
296C2×C4—1461no—
297C2×C4—1461no—
298C2×C4—1464no—
299C2×C4—1461no—
300C2×C4—1461no—
301C2×C4C2×D29211yescharacteristic
302C2×C4C2×D29211yescharacteristic
303C2×C4C2×D29211yescharacteristic
304C2×C4C2×D29211yescharacteristic
305C2×C4C2×D29211yescharacteristic
306C2×C4C23×D7311yescharacteristic
307C8—21no—
308C8—21no—
309C8—21no—
310C8—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—2921no—
315C22—2921no—
316C22—2921no—
317C22C22×D29211yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—2921no—
324C4—2921no—
325C4—2921no—
326C4—2921no—
327C4—2921no—
328C4—1462no—
329C4—1462no—
330C4#41×D7311yescharacteristic
331C4#41×D7311yescharacteristic
332C2—41no—
333C2—5841no—
334C2#1798909911yescharacteristic
335C2#1798939911yescharacteristic
336C2#1798940411yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#433×C73C2
socleC22×C73C22×D4
hypercenter#433D73
hypocenterC73#3121
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #17989064C2semidirect
3. #17988929C2semidirect
5. #17988883C2semidirect
6. #17988873C2semidirect
7. #17988810C2semidirect
8. #17988810C2semidirect
9. #17988745C2semidirect
11. #17988695C2semidirect
12. #17988689C2semidirect
13. C4×Dic292C2semidirect
14. C4×#11924017C2semidirect
15. #433×C73C2semidirect
169. C73#3121semidirect
184. #433D73semidirect