Finite Group Databasebeta

← #22619043

Subgroups — #22619043

Order 9344.

388 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#11924027C211yesmaximal, characteristic
2#17988716C211yesmaximal, characteristic, complemented
3#17988715C211yesmaximal, characteristic, complemented
4#17988663C211yesmaximal, characteristic, complemented
5#17988662C211yesmaximal, characteristic, complemented
6#17988659C211yesmaximal, characteristic, complemented
7#17988658C211yesmaximal, characteristic, complemented
8#17988655C211yesmaximal, characteristic, complemented
9#17988642C211yesmaximal, characteristic, complemented
10#17988641C211yesmaximal, characteristic, complemented
11#17988637C211yesmaximal, characteristic, complemented
12#17988610C211yesmaximal, characteristic, complemented
13#17988609C211yesmaximal, characteristic, complemented
14C2×#14556520C211yesmaximal, characteristic, complemented
15#435×C73C211yesmaximal, characteristic, complemented
16C2×#11924027C411yescharacteristic
17C2×#11924012C2211yescharacteristic
18C2×#11924011C2211yescharacteristic
19C2×#11924011C2211yescharacteristic
20C22×#10596831C2211yescharacteristic
21C4×Dic146C2211yescharacteristic
22#14556556C411yescharacteristic
23D4×Dic73C411yescharacteristic
24C4×C22⋊D73C2211yescharacteristic
25C4×C22⋊D73C2211yescharacteristic
26#14556551C411yescharacteristic
27#14556551C411yescharacteristic
28#14556549C411yescharacteristic
29#14556547C411yescharacteristic
30#14556547C411yescharacteristic
31C2×C4×Dic73C2211yescharacteristic
32C2×C4×Dic73C2211yescharacteristic
33C42×D73C2211yescharacteristic
34C4⋊#10596831C2211yescharacteristic
35#14556520C2211yescharacteristic
36#14556520C2211yescharacteristic
37#14556520C2211yescharacteristic
38#14556520C2211yescharacteristic
39#14556520C2211yescharacteristic
40#14556520C2211yescharacteristic
41#14556520C2211yescharacteristic
42#14556520C2211yescharacteristic
43C22⋊#10596831C2211yescharacteristic
44C22⋊#10596831C2211yescharacteristic
45#14556503C2211yescharacteristic
46#14556503C2211yescharacteristic
47#14556502C2211yescharacteristic
48#14556501C2211yescharacteristic
49#14556501C2211yescharacteristic
50C8×Dic73C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C2×M16×C73C2211yescharacteristic
53C22×C8×C73C2211yescharacteristic
54C4×D4×C73C2211yescharacteristic
55C4⋊C8×C73C2211yescharacteristic
56C22⋊C8×C73C2211yescharacteristic
57C22⋊C8×C73C2211yescharacteristic
58#97×C73C2211yescharacteristic
59#11924027—24no—
60C2×Dic146C2×C411yescharacteristic
61C2×C22⋊D73C2×C411yescharacteristic
62C2×C22⋊D73C2×C411yescharacteristic
63C22×Dic73C2×C411yescharacteristic
64C22×Dic73C2×C411yescharacteristic
65C22×Dic73C2×C411yescharacteristic
66C22×Dic73C2×C411yescharacteristic
67C2×C4×D73C2×C411yescharacteristic
68C2×C4×D73C2×C411yescharacteristic
69C2×C4×D73C2311yescharacteristic
70#11924012—41no—
71#11924011—41no—
72#11924011—41no—
73C2×#10596831—41no—
74C2×#10596831C2311yescharacteristic
75C2×#10596831C2311yescharacteristic
76C2×#10596831C2311yescharacteristic
77C2×#10596831C2311yescharacteristic
78C4⋊Dic73C2×C411yescharacteristic
79#11924007C2×C411yescharacteristic
80#11924007C2×C411yescharacteristic
81#11924007C2×C411yescharacteristic
82#11924007C2×C411yescharacteristic
83C22⋊Dic73C2×C411yescharacteristic
84C22⋊Dic73C2×C411yescharacteristic
85#11924005C2×C411yescharacteristic
86#11924005C2×C411yescharacteristic
87C4×Dic73C2×C411yescharacteristic
88C4×Dic73C2×C411yescharacteristic
89C4×Dic73C2×C411yescharacteristic
90C4×Dic73C2×C411yescharacteristic
91C4×Dic73C2×C411yescharacteristic
92C4×Dic73C2×C411yescharacteristic
93C4×Dic73C2311yescharacteristic
94C4×Dic73C2311yescharacteristic
95C4×Dic73C2311yescharacteristic
96C2×D4×C73C2×C411yescharacteristic
97C22×C4×C73C2311yescharacteristic
98C22×C4×C73C2311yescharacteristic
99M16×C73—41no—
100C2×C8×C73—41no—
101C2×C8×C73C2311yescharacteristic
102C2×C8×C73C2311yescharacteristic
103C2×C8×C73C2311yescharacteristic
104C2×C8×C73C2311yescharacteristic
105C4⋊C4×C73C2×C411yescharacteristic
106C22⋊C4×C73C2×C411yescharacteristic
107C22⋊C4×C73C2×C411yescharacteristic
108C42×C73C2311yescharacteristic
109C23×C73C22×C411yescharacteristic
110C23×C73C22×C411yescharacteristic
111C22×D73C22×C411yescharacteristic
112D4×C73—22no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73C22×C411yescharacteristic
118C2×C4×C73C22×C411yescharacteristic
119C2×C4×C73C22×C411yescharacteristic
120C2×C4×C73C22×C411yescharacteristic
121C2×C4×C73C2411yescharacteristic
122C22⋊D73—22no—
123C22⋊D73—22no—
124C2×Dic73—22no—
125C2×Dic73—41no—
126C2×Dic73—41no—
127C2×Dic73M1614yescomplemented
128C2×Dic73C22×C411yescharacteristic
129C2×Dic73C22×C411yescharacteristic
130C2×Dic73C22×C411yescharacteristic
131C2×Dic73C22×C411yescharacteristic
132C2×Dic73C22×C411yescharacteristic
133C2×Dic73C22×C411yescharacteristic
134C2×Dic73C22×C411yescharacteristic
135C4×D73—21no—
136C4×D73—21no—
137C4×D73—22no—
138C4×D73—41no—
139Dic146—22no—
140C8×C73—21no—
141C8×C73—21no—
142C8×C73—21no—
143C8×C73—21no—
144#10596831—21no—
145#10596831—21no—
146#10596831—21no—
147#10596831—21no—
148C22×C73—21no—
149C22×C73—21no—
150C22×C73—21no—
151C22×C73—21no—
152C22×C73—21no—
153C22×C73C2×M1612yes—
154C22×C73C23×C411yescharacteristic
155C2×D73—21no—
156C2×D73—21no—
157C2×D73—21no—
158C4×C73—21no—
159C4×C73—21no—
160C4×C73—21no—
161C4×C73—21no—
162C4×C73H(5,𝔽2)11yescharacteristic
163C4×C732−1+411yescharacteristic
164Dic73—21no—
165Dic73—21no—
166Dic73—21no—
167Dic73—21no—
168Dic73—21no—
169Dic73C2×M1612yes—
170Dic73C2×M1612yes—
171C2×C73—22no—
172C2×C73—41no—
173C2×C73#52011yescharacteristic
174C2×C73C22×M1611yescharacteristic
175C2×C73#56811yescharacteristic
176D73—41no—
177#2989—731nomaximal, Sylow
178C73#298911yescharacteristic, complemented, Sylow
179C4×#41—731no—
180#446—731no—
181#446—731no—
182#436—731no—
183#436—731no—
184#435—731no—
185#435—731no—
186#435—731no—
187#435D7311yescharacteristic, complemented
188#432—731no—
189#432—731no—
190#431—731no—
191#423—731no—
192#423—731no—
193C2×C4⋊C8—731no—
194C2×#41—731no—
195C2×M16—731no—
196C2×M16—731no—
197C2×M16—731no—
198C2×M16C2×D7311yescharacteristic
199C22×C8—731no—
200C22×C8C2×D7311yescharacteristic
201C4×Q8—731no—
202C4×Q8—731no—
203C4×D4—731no—
204C4×D4—731no—
205C4×D4—731no—
206C4×D4—731no—
207C4×D4—731no—
208C4×D4C2×D7311yescharacteristic
209#117—731no—
210#117—731no—
211#117—731no—
212C2×C42—731no—
213C2×C42—731no—
214C2×C42—731no—
215C4⋊C8—731no—
216C4⋊C8—731no—
217C4⋊C8—731no—
218C4⋊C8—731no—
219C4⋊C8—731no—
220C4⋊C8—731no—
221C4⋊C8—731no—
222C4⋊C8—731no—
223C4⋊C8—731no—
224C4⋊C8C2×D7311yescharacteristic
225C22⋊C8—731no—
226C22⋊C8—731no—
227C22⋊C8—731no—
228C22⋊C8—731no—
229C22⋊C8C2×D7311yescharacteristic
230C22⋊C8C2×D7311yescharacteristic
231#97—731no—
232#97—731no—
233#97—731no—
234#97C2×D7311yescharacteristic
235C4×C8—731no—
236C4×C8—731no—
237#41—1464no—
238C2×Q8—731no—
239C2×D4—731no—
240C2×D4—731no—
241C2×D4C4×D7311yescharacteristic
242C22×C4—731no—
243C22×C4—731no—
244C22×C4—731no—
245C22×C4—731no—
246C22×C4—731no—
247C22×C4—731no—
248C22×C4—731no—
249C22×C4C22×D7311yescharacteristic
250C22×C4C22×D7311yescharacteristic
251M16—41no—
252M16—2921no—
253M16—2921no—
254M16—2921no—
255C2×C8—41no—
256C2×C8—2921no—
257C2×C8—731no—
258C2×C8—731no—
259C2×C8—731no—
260C2×C8—731no—
261C2×C8C22×D7311yescharacteristic
262C2×C8C22×D7311yescharacteristic
263C2×C8C22×D7311yescharacteristic
264C2×C8C22×D7311yescharacteristic
265C4⋊C4—731no—
266C4⋊C4—731no—
267C4⋊C4—731no—
268C4⋊C4—731no—
269C4⋊C4—731no—
270C4⋊C4C4×D7311yescharacteristic
271C22⋊C4—731no—
272C22⋊C4—731no—
273C22⋊C4—731no—
274C22⋊C4—731no—
275C22⋊C4C4×D7311yescharacteristic
276C22⋊C4C4×D7311yescharacteristic
277C42—731no—
278C42—731no—
279C42—731no—
280C42—731no—
281C42—731no—
282C42—731no—
283C42—731no—
284C42—731no—
285C42—731no—
286C42C22×D7311yescharacteristic
287C23—731no—
288C23C2×C4×D7311yescharacteristic
289C23C2×C4×D7311yescharacteristic
290Q8—1462no—
291D4—22no—
292D4—1462no—
293D4—1462no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—2921no—
299C2×C4—2921no—
300C2×C4—2921no—
301C2×C4—734no—
302C2×C4—731no—
303C2×C4—731no—
304C2×C4—731no—
305C2×C4—731no—
306C2×C4—731no—
307C2×C4—731no—
308C2×C4—731no—
309C2×C4—1462no—
310C2×C4—1462no—
311C2×C4—1461no—
312C2×C4—1461no—
313C2×C4C2×C4×D7311yescharacteristic
314C2×C4C2×C4×D7311yescharacteristic
315C2×C4C2×C4×D7311yescharacteristic
316C2×C4C2×C4×D7311yescharacteristic
317C2×C4C23×D7311yescharacteristic
318C8—21no—
319C8—21no—
320C8—21no—
321C8—21no—
322C8—1461no—
323C8—1461no—
324C8—1461no—
325C8—1461no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—1461no—
332C22—1461no—
333C22—1461no—
334C22M16×D7312yes—
335C22C22×C4×D7311yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—732no—
341C4—732no—
342C4—1461no—
343C4—1461no—
344C4—1461no—
345C4—1461no—
346C4—1461no—
347C4#1455663611yescharacteristic
348C4#1455663811yescharacteristic
349C2—22no—
350C2—41no—
351C2—2921no—
352C2#1798906611yescharacteristic
353C2C2×M16×D7311yescharacteristic
354C2#1798935211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D73
commutator, socleC22×C73C23×C4
Fitting#435×C73C2
hypercenter#435D73
hypocenterC73#2989
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #17988716C2semidirect
3. #17988715C2semidirect
4. #17988663C2semidirect
5. #17988662C2semidirect
6. #17988659C2semidirect
7. #17988658C2semidirect
8. #17988655C2semidirect
9. #17988642C2semidirect
10. #17988641C2semidirect
11. #17988637C2semidirect
12. #17988610C2semidirect
13. #17988609C2semidirect
14. C2×#14556520C2semidirect
15. #435×C73C2semidirect
127. C2×Dic73M16semidirect
178. C73#2989semidirect
187. #435D73semidirect