Finite Group Databasebeta

← #22615233

Subgroups — #22615233

Order 9344.

468 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73⋊#401C211yesmaximal, characteristic, complemented
2#17988514C211yesmaximal, characteristic, complemented
3#17988509C211yesmaximal, characteristic, complemented
4#17988504C211yesmaximal, characteristic
5#17988478C211yesmaximal, characteristic, complemented
6#17988476C211yesmaximal, characteristic, complemented
7#17988474C211yesmaximal, characteristic, complemented
8#17988468C211yesmaximal, characteristic, complemented
9#17988465C211yesmaximal, characteristic
10#17988465C211yesmaximal, characteristic
11#17988458C211yesmaximal, characteristic, complemented
12#17988449C211yesmaximal, characteristic, complemented
13C4×#11924005C211yesmaximal, characteristic, complemented
14#17988434C211yesmaximal, characteristic, complemented
15#382×C73C211yesmaximal, characteristic, complemented
16C22×D292C2211yescharacteristic
17C22×C4×D73C2211yescharacteristic
18C22×C4×D73C2211yescharacteristic
19C2×C4⋊Dic73C2211yescharacteristic
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×#11924005C2211yescharacteristic
23C2×#11924005C2211yescharacteristic
24C2×#11924005C2211yescharacteristic
25C2×#11924005C2211yescharacteristic
26C2×#11924005C2211yescharacteristic
27C2×#11924005C2211yescharacteristic
28C2×#11924005C2211yescharacteristic
29C2×#11924005C2211yescharacteristic
30C2×#11924005C2211yescharacteristic
31C2×#11924005C2211yescharacteristic
32C2×C4×Dic73C2211yescharacteristic
33C2×C4×Dic73C2211yescharacteristic
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
46C2×C42×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—41no—
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—
68C4⋊Dic73—41no—
69#11924007—22no—
70#11924007—22no—
71#11924005—22no—
72#11924005—22no—
73#11924005—22no—
74#11924005—22no—
75#11924005—22no—
76#11924005—22no—
77#11924005—22no—
78#11924005—41no—
79#11924005—41no—
80#11924005—41no—
81C4×Dic73—41no—
82C4×Dic73—41no—
83C22×C4×C73C2311yescharacteristic
84C22×C4×C73C2311yescharacteristic
85C22×C4×C73C2311yescharacteristic
86C22×C4×C73C2311yescharacteristic
87C22×C4×C73C2311yescharacteristic
88C22×C4×C73C2311yescharacteristic
89C22×C4×C73C2311yescharacteristic
90C4⋊C4×C73—41no—
91C4⋊C4×C73—41no—
92C42×C73—22no—
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—21no—
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#4112yes—
128C2×C4×C73#4112yes—
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#4112yes—
147D292—44no—
148C4×D73—44no—
149C4×D73—44no—
150C22×C73C2×#4111yescharacteristic
151C22×C73C2×#4111yescharacteristic
152C22×C73C2×#4111yescharacteristic
153C22×C73C2×#4111yescharacteristic
154C22×C73C2×#4111yescharacteristic
155C22×C73H(5,𝔽2)11yescharacteristic
156C22×C73H(5,𝔽2)11yescharacteristic
157C2×D73—22no—
158C2×D73—22no—
159C2×D73—22no—
160C2×D73—22no—
161C2×D73—22no—
162C2×D73—22no—
163C2×D73—41no—
164C2×D73—41no—
165C2×D73—41no—
166C2×D73—41no—
167C2×D73—41no—
168C2×D73—41no—
169C2×D73—41no—
170C2×D73—41no—
171C4×C73—22no—
172C4×C73—22no—
173C4×C73—41no—
174C4×C73—41no—
175C4×C73—41no—
176C4×C73—41no—
177C4×C73—41no—
178Dic73—22no—
179Dic73—41no—
180Dic73—41no—
181Dic73—41no—
182Dic73—41no—
183Dic73—41no—
184C2×C73#52911yescharacteristic
185C2×C73#52911yescharacteristic
186C2×C73#53811yescharacteristic
187C2×C73#55111yescharacteristic
188C2×C73#55111yescharacteristic
189C2×C73#55311yescharacteristic
190C2×C73#55311yescharacteristic
191D73—42no—
192D73—42no—
193#2576—731nomaximal, Sylow
194C73#257611yescharacteristic, complemented, Sylow
195#401—731no—
196#397—731no—
197#396—731no—
198#394—731no—
199#388—731no—
200#388—731no—
201#387—731no—
202#387—731no—
203#386—731no—
204#386—731no—
205#385—731no—
206#382D7311yescharacteristic, complemented
207#381—731no—
208C4×C22⋊C4—731no—
209C4×C22⋊C4—731no—
210C22×D4—731no—
211C23×C4—731no—
212C23×C4—731no—
213C2×C4⋊C4—731no—
214C2×C4⋊C4—731no—
215C2×C4⋊C4—731no—
216C2×C4⋊C4C2×D7311yescharacteristic
217C2×C4⋊C4C2×D7311yescharacteristic
218C2×C22⋊C4—731no—
219C2×C22⋊C4—731no—
220C2×C22⋊C4—731no—
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×C42—731no—
229C2×C42—731no—
230C2×C42C2×D7311yescharacteristic
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
245C24—731no—
246C24—731no—
247C2×D4—2921no—
248C2×D4—1462no—
249C2×D4—1462no—
250C22×C4—2921no—
251C22×C4—2921no—
252C22×C4—2921no—
253C22×C4—731no—
254C22×C4—731no—
255C22×C4—731no—
256C22×C4—731no—
257C22×C4—731no—
258C22×C4—731no—
259C22×C4—1462no—
260C22×C4—1462no—
261C22×C4—1462no—
262C22×C4C22×D7311yescharacteristic
263C22×C4C22×D7311yescharacteristic
264C22×C4C22×D7311yescharacteristic
265C22×C4C22×D7311yescharacteristic
266C22×C4C22×D7311yescharacteristic
267C22×C4C22×D7311yescharacteristic
268C22×C4C22×D7311yescharacteristic
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—2921no—
272C4⋊C4—1462no—
273C4⋊C4—1462no—
274C22⋊C4—2921no—
275C22⋊C4—2921no—
276C22⋊C4—2921no—
277C22⋊C4—1462no—
278C22⋊C4—1462no—
279C22⋊C4—1462no—
280C22⋊C4—1462no—
281C22⋊C4—1462no—
282C22⋊C4—1462no—
283C22⋊C4—1462no—
284C42—22no—
285C42—2921no—
286C42—2921no—
287C23—732no—
288C23—732no—
289C23—1461no—
290C23—1461no—
291C23—1461no—
292C23—1461no—
293C23—1461no—
294C23—1461no—
295C23—1461no—
296C23—1461no—
297C23—1461no—
298C23—1461no—
299C23—1461no—
300C23—1461no—
301C23C23×D7311yescharacteristic
302D4—2924no—
303C2×C4—21no—
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—2924no—
323C2×C4—2924no—
324C2×C4—732no—
325C2×C4—1461no—
326C2×C4—1461no—
327C2×C4—1461no—
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#1192402812yes—
343C2×C4#1192402912yes—
344C22—2921no—
345C22—2921no—
346C22—2921no—
347C22—2921no—
348C22—2921no—
349C22—2921no—
350C22—2921no—
351C22—2921no—
352C22—1462no—
353C22—1462no—
354C22—1462no—
355C22—1462no—
356C22—1462no—
357C22—1462no—
358C22#41×D7311yescharacteristic
359C22#41×D7311yescharacteristic
360C22#41×D7311yescharacteristic
361C22C2×#1192402811yescharacteristic
362C22C2×#1192402911yescharacteristic
363C22#1455663611yescharacteristic
364C22#1455663711yescharacteristic
365C4—22no—
366C4—22no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—2921no—
373C4—2921no—
374C4—2921no—
375C4—2921no—
376C4—2921no—
377C4—1462no—
378C2—2922no—
379C2—2922no—
380C2#1798911511yescharacteristic
381C2#1798912211yescharacteristic
382C2#1798917111yescharacteristic
383C2#1798926111yescharacteristic
384C2#1798926711yescharacteristic
385C2#1798928511yescharacteristic
386C2#1798929011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#382×C73C2
hypercenter#382D73
hypocenterC73#2576
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. C73⋊#401C2semidirect
2. #17988514C2semidirect
3. #17988509C2semidirect
5. #17988478C2semidirect
6. #17988476C2semidirect
7. #17988474C2semidirect
8. #17988468C2semidirect
11. #17988458C2semidirect
12. #17988449C2semidirect
13. C4×#11924005C2semidirect
14. #17988434C2semidirect
15. #382×C73C2semidirect
194. C73#2576semidirect
206. #382D73semidirect