Finite Group Databasebeta

← #22622042

Subgroups — #22622042

Order 9344.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989294C211yesmaximal, characteristic, complemented
2#17988946C211yesmaximal, characteristic, complemented
3#17988915C211yesmaximal, characteristic, complemented
4#17988903C211yesmaximal, characteristic, complemented
5#17988872C211yesmaximal, characteristic, complemented
6#17988843C211yesmaximal, characteristic, complemented
7#17988814C211yesmaximal, characteristic, complemented
8#17988806C211yesmaximal, characteristic, complemented
9#17988749C211yesmaximal, characteristic, complemented
10#17988743C211yesmaximal, characteristic, complemented
11#17988692C211yesmaximal, characteristic, complemented
12#17988659C211yesmaximal, characteristic, complemented
13#17988588C211yesmaximal, characteristic, complemented
14C2×#14556515C211yesmaximal, characteristic, complemented
15#548×C73C211yesmaximal, characteristic
16C2×#11924018C2211yescharacteristic
17C2×#11924018C2211yescharacteristic
18C2×#11924016C2211yescharacteristic
19C2×#11924012C2211yescharacteristic
20C22×#10596831C2211yescharacteristic
21#14556591C2211yescharacteristic
22#14556582—21no—
23#14556570C2211yescharacteristic
24#14556570C2211yescharacteristic
25#14556568—21no—
26#14556568—21no—
27C4×Dic146C2211yescharacteristic
28D4×Dic73—21no—
29C2×C4⋊Dic73C2211yescharacteristic
30C2×C4⋊Dic73C2211yescharacteristic
31#14556522C2211yescharacteristic
32#14556522C2211yescharacteristic
33#14556522C2211yescharacteristic
34C4⋊#10596831C2211yescharacteristic
35#14556515C2211yescharacteristic
36#14556515C2211yescharacteristic
37#14556515C2211yescharacteristic
38#14556515C2211yescharacteristic
39#14556515C2211yescharacteristic
40#14556515C2211yescharacteristic
41#14556514C2211yescharacteristic
42#14556512C2211yescharacteristic
43#14556512C2211yescharacteristic
44#14556512C2211yescharacteristic
45C22⋊#10596831C2211yescharacteristic
46C22⋊#10596831C2211yescharacteristic
47#14556502C2211yescharacteristic
48C2×#41×C73C2211yescharacteristic
49C22×Q8×C73C2211yescharacteristic
50#124×C73—21no—
51#124×C73C2211yescharacteristic
52C22⋊Q8×C73—21no—
53C22⋊Q8×C73C2211yescharacteristic
54#121×C73—21no—
55#121×C73C2211yescharacteristic
56C4×Q8×C73C2211yescharacteristic
57C4×D4×C73—21no—
58C4×D4×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146C2311yescharacteristic
61C22×Dic73—21no—
62C22×Dic73—21no—
63#11924018—22no—
64#11924018—41no—
65#11924016—41no—
66#11924012—41no—
67C2×#10596831—41no—
68C2×#10596831C2311yescharacteristic
69C2×#10596831C2311yescharacteristic
70C2×#10596831C2311yescharacteristic
71C2×#10596831C2311yescharacteristic
72C4⋊Dic73—21no—
73C4⋊Dic73—21no—
74C4⋊Dic73—21no—
75C4⋊Dic73C2311yescharacteristic
76C4⋊Dic73C2311yescharacteristic
77C4⋊Dic73C2311yescharacteristic
78#11924007—21no—
79#11924007—21no—
80#11924007—21no—
81C22⋊Dic73—21no—
82C22⋊Dic73—21no—
83C4×Dic73—21no—
84#41×C73—22no—
85#41×C73—41no—
86C2×Q8×C73—21no—
87C2×Q8×C73—22no—
88C2×Q8×C73—41no—
89C2×Q8×C73C2311yescharacteristic
90C2×Q8×C73C2311yescharacteristic
91C2×D4×C73—21no—
92C2×D4×C73—21no—
93C2×D4×C73D411yescharacteristic
94C2×D4×C73C2311yescharacteristic
95C22×C4×C73—21no—
96C22×C4×C73—21no—
97C22×C4×C73C2311yescharacteristic
98C22×C4×C73C2311yescharacteristic
99C4⋊C4×C73—21no—
100C4⋊C4×C73—21no—
101C4⋊C4×C73D411yescharacteristic
102C4⋊C4×C73C2311yescharacteristic
103C22⋊C4×C73—21no—
104C22⋊C4×C73—21no—
105C22⋊C4×C73—21no—
106C22⋊C4×C73—21no—
107C22⋊C4×C73D411yescharacteristic
108C22⋊C4×C73D411yescharacteristic
109C42×C73—21no—
110C42×C73C2311yescharacteristic
111C23×C73—21no—
112C23×C73C2×D411yescharacteristic
113C23×C73C2×D411yescharacteristic
114Q8×C73—21no—
115Q8×C73—21no—
116Q8×C73—21no—
117Q8×C73—42no—
118Q8×C73#4112yes—
119D4×C73—22no—
120D4×C73—21no—
121D4×C73—21no—
122D4×C73—42no—
123D4×C73—42no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73—42no—
132C2×C4×C73—42no—
133C2×C4×C73C2×D411yescharacteristic
134C2×C4×C73C2×D411yescharacteristic
135C2×C4×C73C2×D411yescharacteristic
136C2×C4×C73C2×D411yescharacteristic
137C2×C4×C73C2411yescharacteristic
138C2×Dic73—21no—
139C2×Dic73—21no—
140C2×Dic73—21no—
141C2×Dic73—21no—
142C2×Dic73—81no—
143C2×Dic73—81no—
144Dic146—21no—
145Dic146—21no—
146Dic146—81no—
147#10596831—21no—
148#10596831—21no—
149#10596831—21no—
150#10596831—21no—
151C22×C73—21no—
152C22×C73—21no—
153C22×C73—21no—
154C22×C73—21no—
155C22×C73—21no—
156C22×C73—41no—
157C22×C73—41no—
158C22×C73—41no—
159C22×C73#13712yes—
160C22×C73C22×D411yescharacteristic
161C4×C73—21no—
162C4×C73—21no—
163C4×C73—22no—
164C4×C73—21no—
165C4×C73—21no—
166C4×C73—41no—
167C4×C73—41no—
168C4×C73C2×#4111yescharacteristic
169C4×C73H(5,𝔽2)11yescharacteristic
170Dic73—41no—
171Dic73—41no—
172Dic73—41no—
173Dic73—41no—
174C2×C73—22no—
175C2×C73—41no—
176C2×C73—81no—
177C2×C73#54611yescharacteristic
178C2×C73C2×#13711yescharacteristic
179C2×C73#57711yescharacteristic
180#3316—731nomaximal, Sylow
181C73#331611yescharacteristic, complemented, Sylow
182#554—731no—
183#548D7311yescharacteristic
184#489—731no—
185#483—731no—
186#481—731no—
187#475—731no—
188#470—731no—
189#465—731no—
190#464—731no—
191#452—731no—
192#451—731no—
193#441—731no—
194#435—731no—
195#417—731no—
196C2×#103—731no—
197C2×#41C2×D7311yescharacteristic
198C22×Q8C2×D7311yescharacteristic
199C2×Q16—731no—
200C2×Q16—731no—
201C2×SD16—731no—
202C2×M16—731no—
203C22×C8—731no—
204C4⋊Q8—731no—
205#125—1461no—
206#124—21no—
207#124C2×D7311yescharacteristic
208C22⋊Q8—21no—
209C22⋊Q8—731no—
210C22⋊Q8—731no—
211C22⋊Q8—1461no—
212C22⋊Q8—1461no—
213C22⋊Q8C2×D7311yescharacteristic
214#121—21no—
215#121C2×D7311yescharacteristic
216C4×Q8—731no—
217C4×Q8C2×D7311yescharacteristic
218C4×D4—21no—
219C4×D4—1461no—
220C4×D4C2×D7311yescharacteristic
221C2×C4⋊C4—731no—
222C2×C4⋊C4—731no—
223#106—731no—
224#106—731no—
225#106—731no—
226C4⋊C8—731no—
227#103—731no—
228#103—731no—
229#103—731no—
230#103—731no—
231#103—731no—
232#103—731no—
233#103—731no—
234#102—731no—
235#102—731no—
236#102—731no—
237C22⋊C8—731no—
238C22⋊C8—731no—
239#97—731no—
240#41—22no—
241#41—41no—
242C2×Q8—21no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—731no—
246C2×Q8—1461no—
247C2×Q8C22×D7311yescharacteristic
248C2×Q8C22×D7311yescharacteristic
249C2×D4—21no—
250C2×D4—21no—
251C2×D4C22⋊D7311yescharacteristic
252C2×D4C22×D7311yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—1461no—
256C22×C4—1461no—
257C22×C4C22×D7311yescharacteristic
258C22×C4C22×D7311yescharacteristic
259Q16—2921no—
260Q16—1462no—
261SD16—2921no—
262M16—2921no—
263C2×C8—2921no—
264C2×C8—731no—
265C2×C8—731no—
266C2×C8—731no—
267C2×C8—731no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—731no—
271C4⋊C4—731no—
272C4⋊C4—731no—
273C4⋊C4—1461no—
274C4⋊C4—1461no—
275C4⋊C4—1461no—
276C4⋊C4—1461no—
277C4⋊C4—1461no—
278C4⋊C4—1461no—
279C4⋊C4C22⋊D7311yescharacteristic
280C4⋊C4C22×D7311yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—1461no—
286C22⋊C4—1461no—
287C22⋊C4C22⋊D7311yescharacteristic
288C22⋊C4C22⋊D7311yescharacteristic
289C42—21no—
290C42—1461no—
291C42C22×D7311yescharacteristic
292C23—21no—
293C23C2×C22⋊D7311yescharacteristic
294C23C2×C22⋊D7311yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—42no—
299Q8—5841no—
300Q8—1461no—
301Q8—1461no—
302Q8#1192402712yes—
303D4—22no—
304D4—21no—
305D4—21no—
306D4—42no—
307D4—42no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—5841no—
318C2×C4—5841no—
319C2×C4—1461no—
320C2×C4—1461no—
321C2×C4—1461no—
322C2×C4—1461no—
323C2×C4C2×C22⋊D7311yescharacteristic
324C2×C4C2×C22⋊D7311yescharacteristic
325C2×C4C2×C22⋊D7311yescharacteristic
326C2×C4C2×C22⋊D7311yescharacteristic
327C2×C4C23×D7311yescharacteristic
328C8—1461no—
329C8—1461no—
330C8—1461no—
331C8—1461no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22#1455662112yes—
341C22C22×C22⋊D7311yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—22no—
347C4—41no—
348C4—41no—
349C4—2921no—
350C4—2921no—
351C4—2921no—
352C4—2921no—
353C4C2×#1192402711yescharacteristic
354C4#1455663611yescharacteristic
355C2—22no—
356C2—41no—
357C2—81no—
358C2#1798923111yescharacteristic
359C2C2×#1455662111yescharacteristic
360C2#1798939511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#548×C73C2
socleC22×C73C22×D4
hypercenter#548D73
hypocenterC73#3316
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #17989294C2semidirect
2. #17988946C2semidirect
3. #17988915C2semidirect
4. #17988903C2semidirect
5. #17988872C2semidirect
6. #17988843C2semidirect
7. #17988814C2semidirect
8. #17988806C2semidirect
9. #17988749C2semidirect
10. #17988743C2semidirect
11. #17988692C2semidirect
12. #17988659C2semidirect
13. #17988588C2semidirect
14. C2×#14556515C2semidirect
181. C73#3316semidirect