Finite Group Databasebeta

← #22616501

Subgroups — #22616501

Order 9344.

456 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556584C211yesmaximal, characteristic
2#17988526C211yesmaximal, characteristic, complemented
3#17988520C211yesmaximal, characteristic, complemented
4#17988518C211yesmaximal, characteristic, complemented
5#17988515C211yesmaximal, characteristic
6#17988515C211yesmaximal, characteristic
7#17988506C211yesmaximal, characteristic, complemented
8#17988494C211yesmaximal, characteristic, complemented
9#17988482C211yesmaximal, characteristic, complemented
10#17988480C211yesmaximal, characteristic
11#17988468C211yesmaximal, characteristic, complemented
12#17988460C211yesmaximal, characteristic
13#17988452C211yesmaximal, characteristic, complemented
14#17988450C211yesmaximal, characteristic
15C2×C22⋊Q8×C73C211yesmaximal, characteristic
16#14556584—24no—
17C2×C4⋊Dic73C2211yescharacteristic
18C2×C4⋊Dic73C2211yescharacteristic
19C2×#11924007C2211yescharacteristic
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×C22⋊Dic73C2211yescharacteristic
26C2×C22⋊Dic73C2211yescharacteristic
27C2×C22⋊Dic73C2211yescharacteristic
28C2×C22⋊Dic73C2211yescharacteristic
29C2×C4×Dic73C2211yescharacteristic
30C2×C4×Dic73C2211yescharacteristic
31#14556498C2211yescharacteristic
32#14556498C2211yescharacteristic
33#14556498C2211yescharacteristic
34#14556498C2211yescharacteristic
35#14556498C2211yescharacteristic
36#14556498C2211yescharacteristic
37#14556498C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45C22×Q8×C73C2211yescharacteristic
46C23×C4×C73C2211yescharacteristic
47C22⋊Q8×C73—24no—
48C2×C4⋊C4×C73C2211yescharacteristic
49C2×C4⋊C4×C73C2211yescharacteristic
50C2×C4⋊C4×C73C2211yescharacteristic
51C2×C22⋊C4×C73C2211yescharacteristic
52C2×C22⋊C4×C73C2211yescharacteristic
53C22×Dic73C2311yescharacteristic
54C22×Dic73C2311yescharacteristic
55C22×Dic73C2311yescharacteristic
56C22×Dic73C2311yescharacteristic
57C22×Dic73C2311yescharacteristic
58C22×Dic73C2311yescharacteristic
59C22×Dic73C2311yescharacteristic
60C22×Dic73C2311yescharacteristic
61C4⋊Dic73—22no—
62C4⋊Dic73—41no—
63#11924007—22no—
64#11924007—22no—
65#11924007—22no—
66#11924007—22no—
67#11924007—41no—
68#11924007—41no—
69C22⋊Dic73—22no—
70C22⋊Dic73—22no—
71C22⋊Dic73—22no—
72C22⋊Dic73—41no—
73C4×Dic73—22no—
74C4×Dic73—22no—
75C24×C73C2311yescharacteristic
76C2×Q8×C73—22no—
77C2×Q8×C73—22no—
78C2×Q8×C73—41no—
79C22×C4×C73—22no—
80C22×C4×C73—22no—
81C22×C4×C73—41no—
82C22×C4×C73C2311yescharacteristic
83C22×C4×C73C2311yescharacteristic
84C22×C4×C73C2311yescharacteristic
85C22×C4×C73C2311yescharacteristic
86C22×C4×C73C2311yescharacteristic
87C22×C4×C73C2311yescharacteristic
88C4⋊C4×C73—22no—
89C4⋊C4×C73—22no—
90C4⋊C4×C73—22no—
91C22⋊C4×C73—22no—
92C22⋊C4×C73D414yes—
93C23×C73—21no—
94C23×C73—21no—
95C23×C73—21no—
96C23×C73—21no—
97C23×C73—21no—
98C23×C73—21no—
99C23×C73C2×D412yes—
100C23×C73C2411yescharacteristic
101Q8×C73—44no—
102C2×C4×C73—21no—
103C2×C4×C73—21no—
104C2×C4×C73—21no—
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—44no—
118C2×C4×C73C2×D412yes—
119C2×C4×C73C2×D412yes—
120C2×C4×C73#4112yes—
121C2×Dic73—21no—
122C2×Dic73—21no—
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—21no—
142C2×Dic73—21no—
143C2×Dic73—21no—
144C2×Dic73#4112yes—
145C22×C73—22no—
146C22×C73—22no—
147C22×C73—22no—
148C22×C73—41no—
149C22×C73—41no—
150C22×C73—41no—
151C22×C73—41no—
152C22×C73C22×D411yescharacteristic
153C22×C73C2×#4111yescharacteristic
154C22×C73C2×#4111yescharacteristic
155C22×C73H(5,𝔽2)11yescharacteristic
156C22×C732−1+411yescharacteristic
157C22×C732−1+411yescharacteristic
158C22×C732−1+411yescharacteristic
159C4×C73—22no—
160C4×C73—22no—
161C4×C73—22no—
162C4×C73—41no—
163C4×C73—41no—
164C4×C73—41no—
165Dic73—22no—
166Dic73—41no—
167Dic73—41no—
168Dic73—41no—
169Dic73—41no—
170Dic73—41no—
171Dic73—41no—
172Dic73—41no—
173C2×C73—42no—
174C2×C73#53611yescharacteristic
175C2×C73#54111yescharacteristic
176C2×C73#54211yescharacteristic
177C2×C73#54611yescharacteristic
178C2×C73#54711yescharacteristic
179C2×C73#55211yescharacteristic
180C2×C73#56311yescharacteristic
181#2698—731nomaximal, Sylow
182C73#269811yescharacteristic, complemented, Sylow
183C2×#126—731no—
184C2×C22⋊Q8D7311yescharacteristic
185#400—731no—
186#398—731no—
187#398—731no—
188#397—731no—
189#397—731no—
190#395—731no—
191#391—731no—
192#389—731no—
193#388—731no—
194#387—731no—
195#385—731no—
196#382—731no—
197#381—731no—
198C22×Q8C2×D7311yescharacteristic
199C23×C4C2×D7311yescharacteristic
200#126—1464no—
201C22⋊Q8—24no—
202C2×C4⋊C4—731no—
203C2×C4⋊C4—731no—
204C2×C4⋊C4—731no—
205C2×C4⋊C4—731no—
206C2×C4⋊C4—731no—
207C2×C4⋊C4—731no—
208C2×C4⋊C4—731no—
209C2×C4⋊C4—731no—
210C2×C4⋊C4C2×D7311yescharacteristic
211C2×C4⋊C4C2×D7311yescharacteristic
212C2×C4⋊C4C2×D7311yescharacteristic
213C2×C22⋊C4—731no—
214C2×C22⋊C4—731no—
215C2×C22⋊C4—731no—
216C2×C22⋊C4—731no—
217C2×C22⋊C4C2×D7311yescharacteristic
218C2×C22⋊C4C2×D7311yescharacteristic
219C2×C42—731no—
220C2×C42—731no—
221#95—731no—
222#95—731no—
223#95—731no—
224#95—731no—
225#95—731no—
226#95—731no—
227#95—731no—
228#95—731no—
229#95—731no—
230#95—731no—
231#95—731no—
232#95—731no—
233#95—731no—
234#95—731no—
235C24C22×D7311yescharacteristic
236C2×Q8—22no—
237C2×Q8—22no—
238C2×Q8—41no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—41no—
242C22×C4—731no—
243C22×C4—731no—
244C22×C4—731no—
245C22×C4—731no—
246C22×C4—731no—
247C22×C4—731no—
248C22×C4—731no—
249C22×C4—731no—
250C22×C4C22×D7311yescharacteristic
251C22×C4C22×D7311yescharacteristic
252C22×C4C22×D7311yescharacteristic
253C22×C4C22×D7311yescharacteristic
254C22×C4C22×D7311yescharacteristic
255C22×C4C22×D7311yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—2921no—
260C4⋊C4—2921no—
261C4⋊C4—2921no—
262C4⋊C4—1462no—
263C4⋊C4—1462no—
264C4⋊C4—1462no—
265C4⋊C4—1462no—
266C4⋊C4—1462no—
267C22⋊C4—22no—
268C22⋊C4—2921no—
269C22⋊C4—1462no—
270C22⋊C4—1462no—
271C22⋊C4—1462no—
272C22⋊C4C22⋊D7314yes—
273C42—1462no—
274C42—1462no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23C2×C22⋊D7312yes—
282C23C23×D7311yescharacteristic
283Q8—44no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—44no—
300C2×C4—732no—
301C2×C4—1461no—
302C2×C4—1461no—
303C2×C4—1461no—
304C2×C4—1461no—
305C2×C4—1461no—
306C2×C4—1461no—
307C2×C4—1461no—
308C2×C4—1461no—
309C2×C4—1461no—
310C2×C4—1461no—
311C2×C4—1461no—
312C2×C4—1461no—
313C2×C4—1461no—
314C2×C4—1461no—
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×C4C2×C22⋊D7312yes—
325C2×C4C2×C22⋊D7312yes—
326C2×C4#1192402712yes—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22C22×C22⋊D7311yescharacteristic
335C22#41×D7311yescharacteristic
336C22C2×#1192402711yescharacteristic
337C22#1455663611yescharacteristic
338C22#1455663811yescharacteristic
339C22#1455663911yescharacteristic
340C22#1455663911yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—2921no—
348C4—2921no—
349C4—2921no—
350C4—2921no—
351C4—2921no—
352C4—2921no—
353C4—2921no—
354C4—1462no—
355C2—42no—
356C2#1798916111yescharacteristic
357C2#1798919711yescharacteristic
358C2#1798920711yescharacteristic
359C2#1798923111yescharacteristic
360C2#1798923611yescharacteristic
361C2#1798927111yescharacteristic
362C2#1798933811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×C22⋊Q8×C73C2
hypercenterC2×C22⋊Q8D73
hypocenterC73#2698
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #17988526C2semidirect
3. #17988520C2semidirect
4. #17988518C2semidirect
7. #17988506C2semidirect
8. #17988494C2semidirect
9. #17988482C2semidirect
11. #17988468C2semidirect
13. #17988452C2semidirect
182. C73#2698semidirect