Finite Group Databasebeta

← #22622639

Subgroups — #22622639

Order 9344.

396 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989296C211yesmaximal, characteristic, complemented
2#17989258C211yesmaximal, characteristic, complemented
3#17988952C211yesmaximal, characteristic, complemented
4#17988950C211yesmaximal, characteristic, complemented
5#17988932C211yesmaximal, characteristic, complemented
6#17988887C211yesmaximal, characteristic, complemented
7#17988886C211yesmaximal, characteristic, complemented
8#17988876C211yesmaximal, characteristic, complemented
9#17988782C211yesmaximal, characteristic, complemented
10#17988780C211yesmaximal, characteristic, complemented
11#17988780C211yesmaximal, characteristic, complemented
12#17988715C211yesmaximal, characteristic, complemented
13#17988696C211yesmaximal, characteristic, complemented
14#17988667C211yesmaximal, characteristic, complemented
15#442×C73C211yesmaximal, characteristic, complemented
16C2×#11924028—21no—
17C2×#11924013C2211yescharacteristic
18C2×#11924013C2211yescharacteristic
19#14556590C2211yescharacteristic
20#14556588C2211yescharacteristic
21#14556587C2211yescharacteristic
22#14556587C2211yescharacteristic
23#14556583C2211yescharacteristic
24#14556582C2211yescharacteristic
25#14556570—21no—
26#14556568—21no—
27#14556568—21no—
28#14556565—21no—
29#14556564—21no—
30#14556564—21no—
31C4×Dic146C2211yescharacteristic
32D4×Dic73C2211yescharacteristic
33D4×Dic73C2211yescharacteristic
34#14556553C2211yescharacteristic
35#14556553C2211yescharacteristic
36C2×#11924007—21no—
37#14556524C2211yescharacteristic
38#14556522C2211yescharacteristic
39C4⋊#10596831C2211yescharacteristic
40#14556520C2211yescharacteristic
41#14556520C2211yescharacteristic
42#14556513C2211yescharacteristic
43#14556513C2211yescharacteristic
44#14556513C2211yescharacteristic
45#14556513C2211yescharacteristic
46#14556512C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556511C2211yescharacteristic
49#14556511C2211yescharacteristic
50#14556501C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C2×D8×C73C2211yescharacteristic
53C4×D4×C73C2211yescharacteristic
54C4×D4×C73C2211yescharacteristic
55#106×C73C2211yescharacteristic
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58#97×C73C2211yescharacteristic
59#11924028—44no—
60C2×Dic146—21no—
61C2×Dic146D411yescharacteristic
62C2×D292—21no—
63C2×D292—21no—
64C2×D292C2311yescharacteristic
65C2×D292C2311yescharacteristic
66C2×C22⋊D73—21no—
67C2×C22⋊D73—21no—
68C2×C22⋊D73—21no—
69C2×C22⋊D73—21no—
70C22×Dic73—21no—
71C22×Dic73—21no—
72C2×C4×D73—21no—
73C2×C4×D73—21no—
74#11924013—22no—
75#11924013—22no—
76C2×#10596831C2311yescharacteristic
77C2×#10596831C2311yescharacteristic
78C4⋊Dic73—21no—
79C4⋊Dic73D411yescharacteristic
80C4⋊Dic73C2311yescharacteristic
81C4⋊Dic73C2311yescharacteristic
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86#11924007D411yescharacteristic
87#11924007D411yescharacteristic
88C22⋊Dic73—21no—
89C22⋊Dic73—21no—
90#11924005—21no—
91#11924005—21no—
92C4×Dic73C2311yescharacteristic
93C4×Dic73C2311yescharacteristic
94C2×D4×C73C2311yescharacteristic
95C2×D4×C73C2311yescharacteristic
96C22×C4×C73—21no—
97C22×C4×C73—21no—
98D8×C73—22no—
99C2×C8×C73C2311yescharacteristic
100C2×C8×C73C2311yescharacteristic
101C4⋊C4×C73C2311yescharacteristic
102C4⋊C4×C73C2311yescharacteristic
103C22⋊C4×C73—21no—
104C22⋊C4×C73—21no—
105C42×C73C2311yescharacteristic
106C23×C73—21no—
107C23×C73—21no—
108C22×D73—21no—
109C22×D73—21no—
110D4×C73—21no—
111D4×C73—21no—
112D4×C73—21no—
113D4×C73#4112yescomplemented
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—42no—
117C2×C4×C73—81no—
118C2×C4×C73C2×D411yescharacteristic
119C2×C4×C73C2×D411yescharacteristic
120C2×C4×C73C2411yescharacteristic
121C22⋊D73—42no—
122C22⋊D73—42no—
123C22⋊D73—81no—
124C22⋊D73—81no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—42no—
128C2×Dic73—81no—
129C2×Dic73C2×D411yescharacteristic
130C2×Dic73C2×D411yescharacteristic
131C2×Dic73C2×D411yescharacteristic
132C2×Dic73C2×D411yescharacteristic
133D292—21no—
134D292—21no—
135D292—21no—
136D292—21no—
137D292—42no—
138D292—81no—
139C4×D73—42no—
140C4×D73—42no—
141Dic146—22no—
142Dic146—81no—
143C8×C73—21no—
144C8×C73—21no—
145#10596831—21no—
146#10596831—21no—
147C22×C73—22no—
148C22×C73—41no—
149C22×C73—41no—
150C22×C73—41no—
151C22×C73—41no—
152C22×C73—41no—
153C22×C73C22×D411yescharacteristic
154C2×D73—41no—
155C2×D73—41no—
156C2×D73—41no—
157C2×D73—41no—
158C2×D73—41no—
159C2×D73—41no—
160C4×C73—21no—
161C4×C73—21no—
162C4×C73—41no—
163C4×C73—41no—
164C4×C73C2×#4111yescharacteristic
165C4×C732−1+411yescharacteristic
166Dic73—21no—
167Dic73—21no—
168Dic73—21no—
169Dic73—41no—
170Dic73—41no—
171Dic73AGL(1,ℤ/8)12yes—
172C2×C73—42no—
173C2×C73—81no—
174C2×C73#54811yescharacteristic
175C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
176C2×C73#57611yescharacteristic
177D73—81no—
178D73—81no—
179#3366—731nomaximal, Sylow
180C73#336611yescharacteristic, complemented, Sylow
181#554—731no—
182#550—731no—
183#490—731no—
184#490—731no—
185#486—731no—
186#478—731no—
187#478—731no—
188#476—731no—
189#459—731no—
190#459—731no—
191#459—731no—
192#446—731no—
193#442—731no—
194#442D7311yescharacteristic, complemented
195C4×D8—731no—
196C2×#41—1461no—
197C2×D8—731no—
198C2×D8—731no—
199C2×D8C2×D7311yescharacteristic
200C4⋊Q8—731no—
201#127—731no—
202#127—731no—
203#127—731no—
204#125—731no—
205#125—731no—
206C22⋊Q8—1461no—
207C22⋊Q8—1461no—
208C22⋊Q8—1461no—
209#121—1461no—
210#121—1461no—
211#121—1461no—
212C4×Q8—731no—
213C4×D4—731no—
214C4×D4—731no—
215C4×D4—731no—
216C4×D4—731no—
217C4×D4C2×D7311yescharacteristic
218C4×D4C2×D7311yescharacteristic
219C2×C4⋊C4—1461no—
220#107—731no—
221#106—731no—
222#106C2×D7311yescharacteristic
223C4⋊C8—731no—
224C4⋊C8—731no—
225C4⋊C8—731no—
226#102—731no—
227#102—731no—
228#102—731no—
229#102—731no—
230#102—731no—
231#102—731no—
232#102—731no—
233#102—731no—
234#102C2×D7311yescharacteristic
235#102C2×D7311yescharacteristic
236#97—731no—
237#97C2×D7311yescharacteristic
238C4×C8—731no—
239#41—2924no—
240C2×Q8—731no—
241C2×Q8—1461no—
242C2×D4—731no—
243C2×D4—731no—
244C2×D4—1461no—
245C2×D4—1461no—
246C2×D4—1461no—
247C2×D4—1461no—
248C2×D4—1461no—
249C2×D4—1461no—
250C2×D4C22×D7311yescharacteristic
251C2×D4C22×D7311yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—1461no—
255C22×C4—1461no—
256C22×C4—1461no—
257C22×C4—1461no—
258D8—22no—
259D8—1462no—
260D8—1462no—
261C2×C8—731no—
262C2×C8—731no—
263C2×C8C22×D7311yescharacteristic
264C2×C8C22×D7311yescharacteristic
265C4⋊C4—731no—
266C4⋊C4—731no—
267C4⋊C4—731no—
268C4⋊C4—731no—
269C4⋊C4—731no—
270C4⋊C4—1461no—
271C4⋊C4—1461no—
272C4⋊C4—1461no—
273C4⋊C4—1461no—
274C4⋊C4—1461no—
275C4⋊C4C22×D7311yescharacteristic
276C4⋊C4C22×D7311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—1461no—
280C22⋊C4—1461no—
281C22⋊C4—1461no—
282C22⋊C4—1461no—
283C42—731no—
284C42—731no—
285C42C22×D7311yescharacteristic
286C23—21no—
287C23—21no—
288C23—1461no—
289C23—1461no—
290Q8—5841no—
291Q8—1462no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—2922no—
296D4—2922no—
297D4—2922no—
298D4—5841no—
299D4—5841no—
300D4—5841no—
301D4—1461no—
302D4—1461no—
303D4—1461no—
304D4—1461no—
305D4#1192402812yescomplemented
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—81no—
310C2×C4—2922no—
311C2×C4—2922no—
312C2×C4—2922no—
313C2×C4—5841no—
314C2×C4—731no—
315C2×C4—731no—
316C2×C4—731no—
317C2×C4—731no—
318C2×C4—1461no—
319C2×C4—1461no—
320C2×C4D4×D7311yescharacteristic
321C2×C4D4×D7311yescharacteristic
322C2×C4C23×D7311yescharacteristic
323C8—21no—
324C8—21no—
325C8—1461no—
326C8—1461no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—2921no—
334C22—2921no—
335C22—2921no—
336C22—2921no—
337C22—2921no—
338C22—2921no—
339C22C2×D4×D7311yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—2921no—
345C4—2921no—
346C4—732no—
347C4—1461no—
348C4—1461no—
349C4—1461no—
350C4C2×#1192402811yescharacteristic
351C4#1455663811yescharacteristic
352C2—42no—
353C2—81no—
354C2—5841no—
355C2—5841no—
356C2#1798924611yescharacteristic
357C2AGL(1,ℤ/8)×D7311yescharacteristic
358C2#1798939111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#442×C73C2
socleC22×C73C22×D4
hypercenter#442D73
hypocenterC73#3366
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #17989296C2semidirect
2. #17989258C2semidirect
3. #17988952C2semidirect
4. #17988950C2semidirect
5. #17988932C2semidirect
6. #17988887C2semidirect
7. #17988886C2semidirect
8. #17988876C2semidirect
9. #17988782C2semidirect
10. #17988780C2semidirect
11. #17988780C2semidirect
12. #17988715C2semidirect
13. #17988696C2semidirect
14. #17988667C2semidirect
15. #442×C73C2semidirect
113. D4×C73#41semidirect
180. C73#3366semidirect
194. #442D73semidirect
305. D4#11924028semidirect