Finite Group Databasebeta

← #22613449

Subgroups — #22613449

Order 9344.

500 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556568C211yesmaximal, characteristic
2C2×#14556556C211yesmaximal, characteristic, complemented
3#17988523C211yesmaximal, characteristic
4#17988520C211yesmaximal, characteristic, complemented
5#17988518C211yesmaximal, characteristic, complemented
6#17988491C211yesmaximal, characteristic, complemented
7#17988482C211yesmaximal, characteristic, complemented
8#17988481C211yesmaximal, characteristic
9#17988475C211yesmaximal, characteristic
10#17988473C211yesmaximal, characteristic, complemented
11#17988472C211yesmaximal, characteristic, complemented
12#17988456C211yesmaximal, characteristic, complemented
13#17988445C211yesmaximal, characteristic
14C22⋊C4×Dic73C211yesmaximal, characteristic
15#399×C73C211yesmaximal, characteristic
16C22×Dic146C2211yescharacteristic
17C23×Dic73C2211yescharacteristic
18#14556568—24no—
19#14556556—24no—
20C2×C4⋊Dic73C2211yescharacteristic
21C2×C4⋊Dic73C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×#11924007C2211yescharacteristic
28C2×#11924007C2211yescharacteristic
29C2×#11924007C2211yescharacteristic
30C2×C22⋊Dic73C2211yescharacteristic
31C2×C22⋊Dic73C2211yescharacteristic
32C2×C22⋊Dic73C2211yescharacteristic
33C2×C4×Dic73C2211yescharacteristic
34C2×C4×Dic73C2211yescharacteristic
35C2×C4×Dic73C2211yescharacteristic
36C2×C4×Dic73C2211yescharacteristic
37#14556498C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46C2×C4⋊C4×C73C2211yescharacteristic
47C2×C4⋊C4×C73C2211yescharacteristic
48C2×C4⋊C4×C73C2211yescharacteristic
49C2×C22⋊C4×C73C2211yescharacteristic
50C2×C22⋊C4×C73C2211yescharacteristic
51C2×C22⋊C4×C73C2211yescharacteristic
52#95×C73C2211yescharacteristic
53C2×Dic146—22no—
54C2×Dic146—22no—
55C2×Dic146D414yes—
56C22×Dic73—22no—
57C22×Dic73—22no—
58C22×Dic73—22no—
59C22×Dic73C2311yescharacteristic
60C22×Dic73C2311yescharacteristic
61C22×Dic73C2311yescharacteristic
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C22×Dic73C2311yescharacteristic
65C22×Dic73C2311yescharacteristic
66C22×Dic73C2311yescharacteristic
67C4⋊Dic73—22no—
68C4⋊Dic73—22no—
69#11924007—22no—
70#11924007—22no—
71#11924007—22no—
72#11924007—22no—
73#11924007—22no—
74#11924007—41no—
75#11924007—41no—
76#11924007—41no—
77C22⋊Dic73—22no—
78C22⋊Dic73—41no—
79C22⋊Dic73Q814yescomplemented
80C4×Dic73—22no—
81C4×Dic73—22no—
82C4×Dic73—22no—
83C4×Dic73—22no—
84C24×C73C2311yescharacteristic
85C22×C4×C73C2311yescharacteristic
86C22×C4×C73C2311yescharacteristic
87C22×C4×C73C2311yescharacteristic
88C22×C4×C73C2311yescharacteristic
89C22×C4×C73C2311yescharacteristic
90C22×C4×C73C2311yescharacteristic
91C4⋊C4×C73—22no—
92C4⋊C4×C73—22no—
93C4⋊C4×C73—41no—
94C22⋊C4×C73—22no—
95C22⋊C4×C73—22no—
96C22⋊C4×C73—41no—
97C23×C73—21no—
98C23×C73—21no—
99C23×C73—21no—
100C23×C73—21no—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73C2×Q812yes—
104C23×C73C2411yescharacteristic
105C2×C4×C73—21no—
106C2×C4×C73—21no—
107C2×C4×C73—21no—
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×C73C2×D412yes—
122C2×C4×C73#4112yes—
123C2×Dic73—21no—
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—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—44no—
142C2×Dic73C2×D412yes—
143C2×Dic73C2×D412yes—
144C2×Dic73C2×Q812yes—
145C2×Dic73C2×Q812yes—
146C2×Dic73#4112yes—
147C2×Dic73#4112yes—
148Dic146—28no—
149C22×C73—22no—
150C22×C73—22no—
151C22×C73—22no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73—41no—
155C22×C73—41no—
156C22×C73C22×D411yescharacteristic
157C22×C73C22×Q811yescharacteristic
158C22×C73C2×#4111yescharacteristic
159C22×C73C2×#4111yescharacteristic
160C22×C73C2×#4111yescharacteristic
161C22×C73H(5,𝔽2)11yescharacteristic
162C22×C732−1+411yescharacteristic
163C4×C73—22no—
164C4×C73—22no—
165C4×C73—41no—
166C4×C73—41no—
167C4×C73—41no—
168C4×C73—41no—
169Dic73—22no—
170Dic73—22no—
171Dic73—22no—
172Dic73—41no—
173Dic73—41no—
174Dic73—41no—
175Dic73—41no—
176Dic73#12314yes—
177C2×C73—42no—
178C2×C73C2×#12311yescharacteristic
179C2×C73#53311yescharacteristic
180C2×C73#54211yescharacteristic
181C2×C73D4×Q811yescharacteristic
182C2×C73#55011yescharacteristic
183C2×C73#55211yescharacteristic
184C2×C73#55411yescharacteristic
185#2423—731nomaximal, Sylow
186C73#242311yescharacteristic, complemented, Sylow
187C2×C22⋊Q8—731no—
188C2×C4×Q8—731no—
189#399—731no—
190#399D7311yescharacteristic
191#398—731no—
192#398—731no—
193#391—731no—
194#389—731no—
195#388—731no—
196#388—731no—
197#387—731no—
198#387—731no—
199#384—731no—
200#380—731no—
201C4×C22⋊C4—731no—
202C22×Q8—731no—
203C23×C4—731no—
204C22⋊Q8—1464no—
205C4×Q8—1464no—
206C2×C4⋊C4—731no—
207C2×C4⋊C4—731no—
208C2×C4⋊C4—731no—
209C2×C4⋊C4—731no—
210C2×C4⋊C4—731no—
211C2×C4⋊C4—731no—
212C2×C4⋊C4—731no—
213C2×C4⋊C4—731no—
214C2×C4⋊C4—731no—
215C2×C4⋊C4—731no—
216C2×C4⋊C4C2×D7311yescharacteristic
217C2×C4⋊C4C2×D7311yescharacteristic
218C2×C4⋊C4C2×D7311yescharacteristic
219C2×C22⋊C4—731no—
220C2×C22⋊C4—731no—
221C2×C22⋊C4—731no—
222C2×C22⋊C4C2×D7311yescharacteristic
223C2×C22⋊C4C2×D7311yescharacteristic
224C2×C22⋊C4C2×D7311yescharacteristic
225C2×C42—731no—
226C2×C42—731no—
227C2×C42—731no—
228C2×C42—731no—
229#95—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#95C2×D7311yescharacteristic
239C24C22×D7311yescharacteristic
240C2×Q8—734no—
241C2×Q8—1462no—
242C2×Q8—1462no—
243C22×C4—731no—
244C22×C4—731no—
245C22×C4—731no—
246C22×C4—731no—
247C22×C4—731no—
248C22×C4—731no—
249C22×C4—731no—
250C22×C4—731no—
251C22×C4—1462no—
252C22×C4—1462no—
253C22×C4—1462no—
254C22×C4C22×D7311yescharacteristic
255C22×C4C22×D7311yescharacteristic
256C22×C4C22×D7311yescharacteristic
257C22×C4C22×D7311yescharacteristic
258C22×C4C22×D7311yescharacteristic
259C22×C4C22×D7311yescharacteristic
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—41no—
263C4⋊C4—2921no—
264C4⋊C4—2921no—
265C4⋊C4—2921no—
266C4⋊C4—1462no—
267C4⋊C4—1462no—
268C4⋊C4—1462no—
269C4⋊C4—1462no—
270C4⋊C4—1462no—
271C4⋊C4—1462no—
272C4⋊C4—1462no—
273C22⋊C4—22no—
274C22⋊C4—22no—
275C22⋊C4—41no—
276C22⋊C4—2921no—
277C22⋊C4—734no—
278C22⋊C4—1462no—
279C42—1462no—
280C42—1462no—
281C42—1462no—
282C42—1462no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23Q8×D7312yes—
290C23C23×D7311yescharacteristic
291Q8—1468no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—2924no—
309C2×C4—732no—
310C2×C4—732no—
311C2×C4—732no—
312C2×C4—732no—
313C2×C4—732no—
314C2×C4—732no—
315C2×C4—1461no—
316C2×C4—1461no—
317C2×C4—1461no—
318C2×C4—1461no—
319C2×C4—1461no—
320C2×C4—1461no—
321C2×C4—1461no—
322C2×C4—1461no—
323C2×C4—1461no—
324C2×C4—1461no—
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×C4D4×D7312yes—
334C2×C4#1192402712yes—
335C22—22no—
336C22—22no—
337C22—22no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22C2×D4×D7311yescharacteristic
343C22C2×Q8×D7311yescharacteristic
344C22#41×D7311yescharacteristic
345C22#41×D7311yescharacteristic
346C22C2×#1192402711yescharacteristic
347C22#1455663611yescharacteristic
348C22#1455663811yescharacteristic
349C4—22no—
350C4—22no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—2921no—
356C4—2921no—
357C4—2921no—
358C4—2921no—
359C4—734no—
360C4—1462no—
361C4—1462no—
362C4—1462no—
363C2—42no—
364C2#123×D7311yescharacteristic
365C2#1798913911yescharacteristic
366C2#1798920511yescharacteristic
367C2#1798925011yescharacteristic
368C2#1798925711yescharacteristic
369C2#1798927411yescharacteristic
370C2#1798929111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#399×C73C2
hypercenter#399D73
hypocenterC73#2423
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
2. C2×#14556556C2semidirect
4. #17988520C2semidirect
5. #17988518C2semidirect
6. #17988491C2semidirect
7. #17988482C2semidirect
10. #17988473C2semidirect
11. #17988472C2semidirect
12. #17988456C2semidirect
79. C22⋊Dic73Q8semidirect
186. C73#2423semidirect