Finite Group Databasebeta

← #22615885

Subgroups — #22615885

Order 9344.

462 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73⋊#401C211yesmaximal, characteristic, complemented
2#17988528C211yesmaximal, characteristic, complemented
3#17988527C211yesmaximal, characteristic, complemented
4#17988516C211yesmaximal, characteristic, complemented
5#17988516C211yesmaximal, characteristic, complemented
6#17988513C211yesmaximal, characteristic, complemented
7#17988509C211yesmaximal, characteristic, complemented
8#17988465C211yesmaximal, characteristic
9#17988465C211yesmaximal, characteristic
10#17988465C211yesmaximal, characteristic
11#17988461C211yesmaximal, characteristic, complemented
12#17988458C211yesmaximal, characteristic, complemented
13#17988458C211yesmaximal, characteristic, complemented
14#95×D73C211yesmaximal, characteristic, complemented
15#400×C73C211yesmaximal, characteristic, complemented
16C22×D292C2211yescharacteristic
17C22×C4×D73C2211yescharacteristic
18C22×C4×D73C2211yescharacteristic
19C22×C4×D73C2211yescharacteristic
20C2×C4⋊Dic73C2211yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×#11924005C2211yescharacteristic
25C2×#11924005C2211yescharacteristic
26C2×#11924005C2211yescharacteristic
27C2×#11924005C2211yescharacteristic
28C2×#11924005C2211yescharacteristic
29C2×#11924005C2211yescharacteristic
30C2×#11924005C2211yescharacteristic
31C2×#11924005C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33#14556498C2211yescharacteristic
34#14556498C2211yescharacteristic
35#14556498C2211yescharacteristic
36#14556498C2211yescharacteristic
37#14556498C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44C2×C4⋊C4×C73C2211yescharacteristic
45C2×C4⋊C4×C73C2211yescharacteristic
46#95×C73C2211yescharacteristic
47#95×C73C2211yescharacteristic
48#95×C73C2211yescharacteristic
49#95×C73C2211yescharacteristic
50#95×C73C2211yescharacteristic
51C23×D73C2311yescharacteristic
52C23×D73C2311yescharacteristic
53C2×D292—22no—
54C2×D292—22no—
55C2×D292—22no—
56C22×Dic73C2311yescharacteristic
57C22×Dic73C2311yescharacteristic
58C22×Dic73C2311yescharacteristic
59C22×Dic73C2311yescharacteristic
60C22×Dic73C2311yescharacteristic
61C22×Dic73C2311yescharacteristic
62C2×C4×D73—22no—
63C2×C4×D73—22no—
64C2×C4×D73—22no—
65C2×C4×D73—41no—
66C2×C4×D73—41no—
67C2×C4×D73—41no—
68C2×C4×D73—41no—
69C2×C4×D73—41no—
70C2×C4×D73—41no—
71C4⋊Dic73—41no—
72#11924007—41no—
73#11924007—41no—
74#11924007—41no—
75#11924005—22no—
76#11924005—22no—
77#11924005—22no—
78#11924005—41no—
79#11924005—41no—
80#11924005—41no—
81#11924005—41no—
82#11924005—41no—
83#11924005—41no—
84C22×C4×C73C2311yescharacteristic
85C22×C4×C73C2311yescharacteristic
86C22×C4×C73C2311yescharacteristic
87C22×C4×C73C2311yescharacteristic
88C22×C4×C73C2311yescharacteristic
89C22×C4×C73C2311yescharacteristic
90C22×C4×C73C2311yescharacteristic
91C4⋊C4×C73—41no—
92C4⋊C4×C73—41no—
93C23×C73C2411yescharacteristic
94C22×D73—21no—
95C22×D73—21no—
96C22×D73—21no—
97C22×D73—21no—
98C22×D73—21no—
99C22×D73—21no—
100C22×D73—21no—
101C22×D73—21no—
102C22×D73—21no—
103C22×D73—21no—
104C22×D73—21no—
105C22×D73#4112yes—
106C22×D73#4112yes—
107C22×D73#4112yes—
108C2×C4×C73—21no—
109C2×C4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—21no—
138C2×Dic73—21no—
139C2×Dic73—21no—
140C2×Dic73—21no—
141C2×Dic73—21no—
142C2×Dic73—21no—
143C2×Dic73—21no—
144C2×Dic73—21no—
145C2×Dic73—21no—
146C2×Dic73—21no—
147D292—44no—
148C4×D73—44no—
149C4×D73—44no—
150C4×D73—44no—
151C22×C73C2×#4111yescharacteristic
152C22×C73C2×#4111yescharacteristic
153C22×C73C2×#4111yescharacteristic
154C22×C73H(5,𝔽2)11yescharacteristic
155C22×C73H(5,𝔽2)11yescharacteristic
156C22×C73H(5,𝔽2)11yescharacteristic
157C22×C732−1+411yescharacteristic
158C2×D73—22no—
159C2×D73—22no—
160C2×D73—22no—
161C2×D73—22no—
162C2×D73—22no—
163C2×D73—22no—
164C2×D73—41no—
165C2×D73—41no—
166C2×D73—41no—
167C2×D73—41no—
168C2×D73—41no—
169C2×D73—41no—
170C2×D73—41no—
171C2×D73#12614yes—
172C4×C73—41no—
173C4×C73—41no—
174C4×C73—41no—
175C4×C73—41no—
176C4×C73—41no—
177C4×C73—41no—
178C4×C73—41no—
179Dic73—41no—
180Dic73—41no—
181Dic73—41no—
182Dic73—41no—
183Dic73—41no—
184Dic73—41no—
185C2×C73C2×#12611yescharacteristic
186C2×C73#53811yescharacteristic
187C2×C73#53811yescharacteristic
188C2×C73#53811yescharacteristic
189C2×C73#53911yescharacteristic
190C2×C73#53911yescharacteristic
191C2×C73#53911yescharacteristic
192D73—24no—
193D73—81no—
194#2643—731nomaximal, Sylow
195C73#264311yescharacteristic, complemented, Sylow
196#401—731no—
197#400—731no—
198#400—731no—
199#400D7311yescharacteristic, complemented
200#397—731no—
201#397—731no—
202#397—731no—
203#396—731no—
204#386—731no—
205#386—731no—
206#386—731no—
207#385—731no—
208#385—731no—
209#385—731no—
210C2×#95—731no—
211C22×D4—731no—
212C23×C4—731no—
213C23×C4—731no—
214C23×C4—731no—
215C2×C4⋊C4—731no—
216C2×C4⋊C4—731no—
217C2×C4⋊C4—731no—
218C2×C4⋊C4—731no—
219C2×C4⋊C4C2×D7311yescharacteristic
220C2×C4⋊C4C2×D7311yescharacteristic
221C2×C22⋊C4—731no—
222C2×C22⋊C4—731no—
223C2×C22⋊C4—731no—
224C2×C22⋊C4—731no—
225C2×C22⋊C4—731no—
226C2×C22⋊C4—731no—
227C2×C22⋊C4—731no—
228C2×C22⋊C4—731no—
229C2×C22⋊C4—731no—
230#95—731no—
231#95—731no—
232#95—731no—
233#95—731no—
234#95—731no—
235#95—731no—
236#95—731no—
237#95—731no—
238#95—731no—
239#95—731no—
240#95—731no—
241#95C2×D7311yescharacteristic
242#95C2×D7311yescharacteristic
243#95C2×D7311yescharacteristic
244#95C2×D7311yescharacteristic
245#95C2×D7311yescharacteristic
246C24—731no—
247C24—731no—
248C2×D4—1462no—
249C2×D4—1462no—
250C2×D4—1462no—
251C22×C4—2921no—
252C22×C4—2921no—
253C22×C4—2921no—
254C22×C4—2921no—
255C22×C4—2921no—
256C22×C4—2921no—
257C22×C4—731no—
258C22×C4—731no—
259C22×C4—731no—
260C22×C4—731no—
261C22×C4—731no—
262C22×C4—731no—
263C22×C4—1462no—
264C22×C4—1462no—
265C22×C4—1462no—
266C22×C4C22×D7311yescharacteristic
267C22×C4C22×D7311yescharacteristic
268C22×C4C22×D7311yescharacteristic
269C22×C4C22×D7311yescharacteristic
270C22×C4C22×D7311yescharacteristic
271C22×C4C22×D7311yescharacteristic
272C22×C4C22×D7311yescharacteristic
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—2921no—
276C4⋊C4—2921no—
277C4⋊C4—2921no—
278C4⋊C4—2921no—
279C22⋊C4—2921no—
280C22⋊C4—2921no—
281C22⋊C4—2921no—
282C22⋊C4—2921no—
283C22⋊C4—2921no—
284C22⋊C4—2921no—
285C22⋊C4—1462no—
286C22⋊C4—1462no—
287C22⋊C4—1462no—
288C23—732no—
289C23—732no—
290C23—732no—
291C23—1461no—
292C23—1461no—
293C23—1461no—
294C23—1461no—
295C23—1461no—
296C23—1461no—
297C23—1461no—
298C23—1461no—
299C23—1461no—
300C23—1461no—
301C23—1461no—
302C23C23×D7311yescharacteristic
303D4—2924no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—2924no—
326C2×C4—2924no—
327C2×C4—2924no—
328C2×C4—1461no—
329C2×C4—1461no—
330C2×C4—1461no—
331C2×C4—1461no—
332C2×C4—1461no—
333C2×C4—1461no—
334C2×C4—1461no—
335C2×C4—1461no—
336C2×C4—1461no—
337C2×C4—1461no—
338C2×C4—1461no—
339C2×C4—1461no—
340C2×C4—1461no—
341C2×C4—1461no—
342C2×C4—1461no—
343C2×C4—1461no—
344C2×C4—1461no—
345C2×C4—1461no—
346C22—2921no—
347C22—2921no—
348C22—2921no—
349C22—2921no—
350C22—2921no—
351C22—2921no—
352C22—2921no—
353C22—734no—
354C22—1462no—
355C22—1462no—
356C22—1462no—
357C22—1462no—
358C22—1462no—
359C22—1462no—
360C22#41×D7311yescharacteristic
361C22#41×D7311yescharacteristic
362C22#41×D7311yescharacteristic
363C22#1455663611yescharacteristic
364C22#1455663711yescharacteristic
365C22#1455663711yescharacteristic
366C22#1455663911yescharacteristic
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—2921no—
375C4—2921no—
376C4—2921no—
377C4—2921no—
378C4—2921no—
379C4—2921no—
380C2—5841no—
381C2—1464no—
382C2#126×D7311yescharacteristic
383C2#1798917111yescharacteristic
384C2#1798917311yescharacteristic
385C2#1798917611yescharacteristic
386C2#1798918311yescharacteristic
387C2#1798918511yescharacteristic
388C2#1798918511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#400×C73C2
hypercenter#400D73
hypocenterC73#2643
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C73⋊#401C2semidirect
2. #17988528C2semidirect
3. #17988527C2semidirect
4. #17988516C2semidirect
5. #17988516C2semidirect
6. #17988513C2semidirect
7. #17988509C2semidirect
11. #17988461C2semidirect
12. #17988458C2semidirect
13. #17988458C2semidirect
14. #95×D73C2semidirect
15. #400×C73C2semidirect
195. C73#2643semidirect
199. #400D73semidirect