Finite Group Databasebeta

← #22622374

Subgroups — #22622374

Order 9344.

376 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989271C211yesmaximal, characteristic, complemented
2#17989238C211yesmaximal, characteristic
3#17988995C211yesmaximal, characteristic, complemented
4#17988916C211yesmaximal, characteristic, complemented
5#17988912C211yesmaximal, characteristic, complemented
6#17988902C211yesmaximal, characteristic, complemented
7#17988890C211yesmaximal, characteristic, complemented
8#17988880C211yesmaximal, characteristic, complemented
9#17988835C211yesmaximal, characteristic, complemented
10#17988819C211yesmaximal, characteristic, complemented
11#17988690C211yesmaximal, characteristic, complemented
12#17988661C211yesmaximal, characteristic, complemented
13#17988627C211yesmaximal, characteristic, complemented
14#107×D73C211yesmaximal, characteristic, complemented
15#484×C73C211yesmaximal, characteristic, complemented
16C2×#11924028—21no—
17C2×#11924015C2211yescharacteristic
18C2×#11924012C2211yescharacteristic
19C2×C8×D73C2211yescharacteristic
20#14556590C2211yescharacteristic
21#14556584—21no—
22#14556582C2211yescharacteristic
23#14556581—21no—
24#14556576—21no—
25#14556574—21no—
26#14556573—21no—
27#14556569—21no—
28#14556567C2211yescharacteristic
29#14556566C2211yescharacteristic
30#14556565C2211yescharacteristic
31Q8×Dic73C2211yescharacteristic
32#14556553C2211yescharacteristic
33C4×C22⋊D73C2211yescharacteristic
34#14556550C2211yescharacteristic
35#14556549—21no—
36C4⋊C4×D73C2211yescharacteristic
37C4⋊C4×D73C2211yescharacteristic
38#14556525C2211yescharacteristic
39#14556524C2211yescharacteristic
40#14556524C2211yescharacteristic
41#14556524C2211yescharacteristic
42#14556523C2211yescharacteristic
43#14556522C2211yescharacteristic
44#14556522C2211yescharacteristic
45#14556520C2211yescharacteristic
46#14556515C2211yescharacteristic
47#14556513C2211yescharacteristic
48#14556513C2211yescharacteristic
49#14556511C2211yescharacteristic
50#14556503C2211yescharacteristic
51#14556501C2211yescharacteristic
52C22⋊Q8×C73C2211yescharacteristic
53C2×C4⋊C4×C73C2211yescharacteristic
54#107×C73C2211yescharacteristic
55#107×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59#11924028—44no—
60C2×Dic146—21no—
61C2×D292—21no—
62C2×D292C2311yescharacteristic
63C2×C22⋊D73—21no—
64C2×C22⋊D73D411yescharacteristic
65C2×C4×D73—21no—
66C2×C4×D73—21no—
67C2×C4×D73—21no—
68C2×C4×D73C2311yescharacteristic
69#11924015—22no—
70#11924012—22no—
71C2×#10596831C2311yescharacteristic
72C2×#10596831C2311yescharacteristic
73C8×D73—22no—
74C4⋊Dic73—21no—
75C4⋊Dic73—21no—
76C4⋊Dic73C2311yescharacteristic
77C4⋊Dic73C2311yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83#11924007—21no—
84#11924007D411yescharacteristic
85C22⋊Dic73—21no—
86C22⋊Dic73D411yescharacteristic
87#11924005—21no—
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005D411yescharacteristic
92C4×Dic73—21no—
93C4×Dic73—21no—
94C4×Dic73C2311yescharacteristic
95C2×Q8×C73C2311yescharacteristic
96C22×C4×C73—21no—
97C22×C4×C73C2311yescharacteristic
98C2×C8×C73C2311yescharacteristic
99C2×C8×C73C2311yescharacteristic
100C4⋊C4×C73—21no—
101C4⋊C4×C73—21no—
102C4⋊C4×C73C2311yescharacteristic
103C4⋊C4×C73C2311yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C22⋊C4×C73—21no—
106C23×C73C2×D411yescharacteristic
107C22×D73—21no—
108C22×D73C2×D411yescharacteristic
109Q8×C73—21no—
110Q8×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—42no—
118C2×C4×C73C2×D411yescharacteristic
119C2×C4×C73C2411yescharacteristic
120C22⋊D73—22no—
121C22⋊D73—42no—
122C2×Dic73—21no—
123C2×Dic73—21no—
124C2×Dic73—21no—
125C2×Dic73C2×D411yescharacteristic
126C2×Dic73C2×D411yescharacteristic
127C2×Dic73C2×D411yescharacteristic
128D292—21no—
129D292—21no—
130D292—42no—
131C4×D73—21no—
132C4×D73—21no—
133C4×D73—42no—
134C4×D73—42no—
135C4×D73—42no—
136Dic146—42no—
137C8×C73—21no—
138C8×C73—21no—
139#10596831—21no—
140#10596831#4112yescomplemented
141C22×C73—21no—
142C22×C73—21no—
143C22×C73—21no—
144C22×C73C22×D411yescharacteristic
145C2×D73—21no—
146C2×D73—21no—
147C2×D73—41no—
148C2×D73—41no—
149C2×D73—41no—
150C2×D73AGL(1,ℤ/8)12yes—
151C4×C73—21no—
152C4×C73—41no—
153C4×C73—41no—
154C4×C73—41no—
155C4×C73—41no—
156C4×C73C2×#4111yescharacteristic
157C4×C732−1+411yescharacteristic
158Dic73—21no—
159Dic73—21no—
160Dic73—21no—
161Dic73—41no—
162Dic73—41no—
163Dic73—41no—
164C2×C73—41no—
165C2×C73#54711yescharacteristic
166C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
167C2×C73#57811yescharacteristic
168D73—22no—
169D73—81no—
170#3343—731nomaximal, Sylow
171C73#334311yescharacteristic, complemented, Sylow
172#552—731no—
173#547—731no—
174#501—731no—
175#484D7311yescharacteristic, complemented
176#483—731no—
177#482—731no—
178#480—731no—
179#478—731no—
180#477—731no—
181#468—731no—
182#465—731no—
183#440—731no—
184#435—731no—
185#428—731no—
186C2×#107—731no—
187C2×#41—1461no—
188C2×SD16—731no—
189C2×M16—731no—
190C22×C8—731no—
191C4⋊Q8—731no—
192#126—1461no—
193#125—731no—
194#125—1461no—
195#123—1461no—
196#123—1461no—
197#123—1461no—
198C22⋊Q8—731no—
199C22⋊Q8—1461no—
200C22⋊Q8C2×D7311yescharacteristic
201#121—731no—
202#121—731no—
203C4×Q8—731no—
204C4×D4—731no—
205C4×D4—731no—
206#117—731no—
207#117—1461no—
208C2×C4⋊C4—731no—
209C2×C4⋊C4—731no—
210C2×C4⋊C4C2×D7311yescharacteristic
211#107—731no—
212#107—731no—
213#107—731no—
214#107—731no—
215#107C2×D7311yescharacteristic
216#107C2×D7311yescharacteristic
217#106—731no—
218#106—731no—
219#106—731no—
220C4⋊C8—731no—
221#103—731no—
222#103C2×D7311yescharacteristic
223#103C2×D7311yescharacteristic
224#102—731no—
225#102—731no—
226#102—731no—
227C22⋊C8—731no—
228C22⋊C8C2×D7311yescharacteristic
229#97—731no—
230#41—2924no—
231C2×Q8—1461no—
232C2×Q8C22×D7311yescharacteristic
233C2×D4—731no—
234C2×D4—731no—
235C2×D4—1461no—
236C2×D4—1461no—
237C22×C4—21no—
238C22×C4—731no—
239C22×C4—1461no—
240C22×C4—1461no—
241C22×C4—1461no—
242C22×C4C22×D7311yescharacteristic
243SD16—1462no—
244M16—1462no—
245C2×C8—731no—
246C2×C8—731no—
247C2×C8—1462no—
248C2×C8C22×D7311yescharacteristic
249C2×C8C22×D7311yescharacteristic
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—731no—
253C4⋊C4—731no—
254C4⋊C4—731no—
255C4⋊C4—731no—
256C4⋊C4—1461no—
257C4⋊C4—1461no—
258C4⋊C4—1461no—
259C4⋊C4—1461no—
260C4⋊C4—1461no—
261C4⋊C4—1461no—
262C4⋊C4—1461no—
263C4⋊C4C22×D7311yescharacteristic
264C4⋊C4C22×D7311yescharacteristic
265C4⋊C4C22×D7311yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—731no—
268C22⋊C4—731no—
269C22⋊C4—1461no—
270C22⋊C4—1461no—
271C22⋊C4—1461no—
272C22⋊C4—1461no—
273C22⋊C4—1461no—
274C42—731no—
275C42—1461no—
276C42—1461no—
277C23—731no—
278C23—1461no—
279C23D4×D7311yescharacteristic
280Q8—21no—
281Q8—21no—
282Q8—2922no—
283D4—2922no—
284D4—2922no—
285D4—1462no—
286D4—1461no—
287D4—1461no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—2922no—
296C2×C4—2922no—
297C2×C4—2922no—
298C2×C4—731no—
299C2×C4—731no—
300C2×C4—731no—
301C2×C4—1461no—
302C2×C4—1461no—
303C2×C4—1461no—
304C2×C4—1461no—
305C2×C4—1461no—
306C2×C4D4×D7311yescharacteristic
307C2×C4C23×D7311yescharacteristic
308C8—21no—
309C8—21no—
310C8—732no—
311C8—1461no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—2921no—
316C22—2921no—
317C22—2921no—
318C22—732no—
319C22—1461no—
320C22—1461no—
321C22C2×D4×D7311yescharacteristic
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—2921no—
328C4—2921no—
329C4—2921no—
330C4—1461no—
331C4—1461no—
332C4—1461no—
333C4#41×D7311yescharacteristic
334C4#1455663811yescharacteristic
335C2—41no—
336C2—5841no—
337C2—1462no—
338C2#1798923511yescharacteristic
339C2AGL(1,ℤ/8)×D7311yescharacteristic
340C2#1798940011yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#484×C73C2
socleC22×C73C22×D4
hypercenter#484D73
hypocenterC73#3343
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #17989271C2semidirect
3. #17988995C2semidirect
4. #17988916C2semidirect
5. #17988912C2semidirect
6. #17988902C2semidirect
7. #17988890C2semidirect
8. #17988880C2semidirect
9. #17988835C2semidirect
10. #17988819C2semidirect
11. #17988690C2semidirect
12. #17988661C2semidirect
13. #17988627C2semidirect
14. #107×D73C2semidirect
15. #484×C73C2semidirect
140. #10596831#41semidirect
171. C73#3343semidirect
175. #484D73semidirect