Finite Group Databasebeta

← #22620616

Subgroups — #22620616

Order 9344.

374 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989208C211yesmaximal, characteristic, complemented
2#17988997C211yesmaximal, characteristic, complemented
3#17988974C211yesmaximal, characteristic, complemented
4#17988944C211yesmaximal, characteristic, complemented
5#17988933C211yesmaximal, characteristic, complemented
6#17988838C211yesmaximal, characteristic, complemented
7#17988831C211yesmaximal, characteristic, complemented
8#17988821C211yesmaximal, characteristic, complemented
9#17988814C211yesmaximal, characteristic, complemented
10#17988697C211yesmaximal, characteristic, complemented
11#17988687C211yesmaximal, characteristic, complemented
12C4×#11924016C211yesmaximal, characteristic, complemented
13C4×#11924013C211yesmaximal, characteristic, complemented
14#17988543C211yesmaximal, characteristic, complemented
15#540×C73C211yesmaximal, characteristic, complemented
16C2×#11924016C2211yescharacteristic
17C2×#11924016C2211yescharacteristic
18C2×#11924013C2211yescharacteristic
19C2×#11924013C2211yescharacteristic
20C2×#11924012C2211yescharacteristic
21C22×#10596831C2211yescharacteristic
22#14556591C2211yescharacteristic
23#14556586—21no—
24#14556579C2211yescharacteristic
25#14556577—21no—
26#14556573—21no—
27#14556570C2211yescharacteristic
28#14556569—21no—
29#14556565C2211yescharacteristic
30C4×Dic146C2211yescharacteristic
31C4×D292C2211yescharacteristic
32#14556524C2211yescharacteristic
33#14556524C2211yescharacteristic
34#14556522C2211yescharacteristic
35#14556522C2211yescharacteristic
36#14556514C2211yescharacteristic
37#14556514C2211yescharacteristic
38#14556512C2211yescharacteristic
39#14556512C2211yescharacteristic
40#14556512C2211yescharacteristic
41#14556512C2211yescharacteristic
42#14556511C2211yescharacteristic
43#14556511C2211yescharacteristic
44#14556502C2211yescharacteristic
45#14556502C2211yescharacteristic
46C4×#10596831C2211yescharacteristic
47C4×#10596831C2211yescharacteristic
48#127×C73C2211yescharacteristic
49#125×C73C2211yescharacteristic
50#123×C73—21no—
51#123×C73—21no—
52#121×C73—21no—
53#121×C73—21no—
54#121×C73C2211yescharacteristic
55#121×C73C2211yescharacteristic
56C4×D4×C73C2211yescharacteristic
57C4×D4×C73C2211yescharacteristic
58#117×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146C2311yescharacteristic
61C2×D292C2311yescharacteristic
62C2×C22⋊D73—21no—
63C2×C4×D73—21no—
64#11924016—22no—
65#11924016—22no—
66#11924013—22no—
67#11924013—22no—
68#11924012—22no—
69C2×#10596831—22no—
70C2×#10596831C2311yescharacteristic
71C2×#10596831C2311yescharacteristic
72C2×#10596831C2311yescharacteristic
73C2×#10596831C2311yescharacteristic
74C4⋊Dic73—21no—
75C4⋊Dic73C2311yescharacteristic
76C4⋊Dic73C2311yescharacteristic
77#11924007—21no—
78#11924007—21no—
79C22⋊Dic73—21no—
80#11924005—21no—
81#11924005—21no—
82#11924005—21no—
83#11924005—21no—
84C4×Dic73—21no—
85C2×D4×C73—21no—
86C2×D4×C73—21no—
87C2×D4×C73—21no—
88C2×D4×C73—21no—
89C2×D4×C73C2311yescharacteristic
90C2×D4×C73C2311yescharacteristic
91C22×C4×C73—21no—
92C22×C4×C73—21no—
93C22×C4×C73C2311yescharacteristic
94C4⋊C4×C73—21no—
95C4⋊C4×C73—21no—
96C4⋊C4×C73D411yescharacteristic
97C4⋊C4×C73D411yescharacteristic
98C4⋊C4×C73C2311yescharacteristic
99C4⋊C4×C73C2311yescharacteristic
100C22⋊C4×C73—21no—
101C22⋊C4×C73—21no—
102C22⋊C4×C73—21no—
103C22⋊C4×C73—21no—
104C22⋊C4×C73D411yescharacteristic
105C22⋊C4×C73D411yescharacteristic
106C42×C73C2311yescharacteristic
107C42×C73C2311yescharacteristic
108C23×C73—21no—
109C23×C73—21no—
110C23×C73C2×D411yescharacteristic
111C22×D73—21no—
112D4×C73—21no—
113D4×C73—21no—
114D4×C73—21no—
115D4×C73—21no—
116D4×C73—81no—
117D4×C73—81no—
118D4×C73—81no—
119D4×C73—81no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—81no—
125C2×C4×C73—81no—
126C2×C4×C73C2×D411yescharacteristic
127C2×C4×C73C2×D411yescharacteristic
128C2×C4×C73C2×D411yescharacteristic
129C2×C4×C73C2×D411yescharacteristic
130C2×C4×C73C2×D411yescharacteristic
131C2×C4×C73C2411yescharacteristic
132C22⋊D73—81no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136D292—21no—
137D292—21no—
138C4×D73—81no—
139Dic146—21no—
140Dic146—21no—
141Dic146—81no—
142#10596831—21no—
143#10596831—21no—
144#10596831#4112yes—
145#10596831#4112yes—
146C22×C73—21no—
147C22×C73—21no—
148C22×C73—21no—
149C22×C73—41no—
150C22×C73—41no—
151C22×C73—41no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73—41no—
155C22×C73C22×D411yescharacteristic
156C2×D73—41no—
157C2×D73—41no—
158C2×D73—41no—
159C4×C73—21no—
160C4×C73—21no—
161C4×C73—21no—
162C4×C73—21no—
163C4×C73—21no—
164C4×C73—41no—
165C4×C73—41no—
166C4×C73C2×#4111yescharacteristic
167C4×C73C2×#4111yescharacteristic
168Dic73—41no—
169Dic73—41no—
170Dic73—41no—
171C2×C73—41no—
172C2×C73—81no—
173C2×C73—81no—
174C2×C73#53211yescharacteristic
175C2×C73#57611yescharacteristic
176C2×C73#57711yescharacteristic
177D73—81no—
178#3179—731nomaximal, Sylow
179C73#317911yescharacteristic, complemented, Sylow
180#542—731no—
181#540D7311yescharacteristic, complemented
182#501—731no—
183#496—731no—
184#488—731no—
185#486—731no—
186#469—731no—
187#468—731no—
188#466—731no—
189#465—731no—
190#442—731no—
191#440—731no—
192C4×SD16—731no—
193C4×D8—731no—
194#405—731no—
195C2×SD16—731no—
196C2×SD16—731no—
197C2×D8—731no—
198C2×D8—731no—
199C2×M16—731no—
200C22×C8—731no—
201C4⋊Q8—731no—
202#127C2×D7311yescharacteristic
203#126—1461no—
204#125C2×D7311yescharacteristic
205#124—731no—
206#124—1461no—
207#123—21no—
208#123—21no—
209#123—1461no—
210C22⋊Q8—731no—
211C22⋊Q8—1461no—
212#121—21no—
213#121—21no—
214#121—731no—
215#121C2×D7311yescharacteristic
216#121C2×D7311yescharacteristic
217C4×Q8—731no—
218C4×D4—731no—
219C4×D4C2×D7311yescharacteristic
220C4×D4C2×D7311yescharacteristic
221#117C2×D7311yescharacteristic
222#107—731no—
223#107—731no—
224#106—731no—
225#106—731no—
226#103—731no—
227#103—731no—
228#102—731no—
229#102—731no—
230#102—731no—
231#102—731no—
232#102—731no—
233#102—731no—
234#97—731no—
235#97—731no—
236C4×C8—731no—
237C4×C8—731no—
238C2×Q8—731no—
239C2×Q8—1461no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—731no—
245C2×D4—1461no—
246C2×D4C22×D7311yescharacteristic
247C2×D4C22×D7311yescharacteristic
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—1461no—
251C22×C4C22×D7311yescharacteristic
252SD16—1462no—
253SD16—1462no—
254D8—1462no—
255D8—1462no—
256M16—1462no—
257C2×C8—731no—
258C2×C8—731no—
259C2×C8—731no—
260C2×C8—731no—
261C2×C8—1462no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—731no—
265C4⋊C4—731no—
266C4⋊C4—1461no—
267C4⋊C4—1461no—
268C4⋊C4—1461no—
269C4⋊C4C22⋊D7311yescharacteristic
270C4⋊C4C22⋊D7311yescharacteristic
271C4⋊C4C22×D7311yescharacteristic
272C4⋊C4C22×D7311yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—1461no—
278C22⋊C4—1461no—
279C22⋊C4—1461no—
280C22⋊C4—1461no—
281C22⋊C4—1461no—
282C22⋊C4C22⋊D7311yescharacteristic
283C22⋊C4C22⋊D7311yescharacteristic
284C42—1461no—
285C42C22×D7311yescharacteristic
286C42C22×D7311yescharacteristic
287C23—21no—
288C23—21no—
289C23—1461no—
290C23C2×C22⋊D7311yescharacteristic
291Q8—5841no—
292Q8—1461no—
293Q8—1461no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—81no—
299D4—81no—
300D4—81no—
301D4—81no—
302D4—5841no—
303D4—1461no—
304D4—1461no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—5841no—
312C2×C4—1461no—
313C2×C4—1461no—
314C2×C4—1461no—
315C2×C4C2×C22⋊D7311yescharacteristic
316C2×C4C2×C22⋊D7311yescharacteristic
317C2×C4C2×C22⋊D7311yescharacteristic
318C2×C4C2×C22⋊D7311yescharacteristic
319C2×C4C2×C22⋊D7311yescharacteristic
320C2×C4C23×D7311yescharacteristic
321C8—732no—
322C8—732no—
323C8—1461no—
324C8—1461no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—2921no—
335C22—2921no—
336C22—2921no—
337C22C22×C22⋊D7311yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—2921no—
346C4—2921no—
347C4—2921no—
348C4#41×D7311yescharacteristic
349C4#41×D7311yescharacteristic
350C2—41no—
351C2—81no—
352C2—81no—
353C2—5841no—
354C2#1798913311yescharacteristic
355C2#1798939011yescharacteristic
356C2#1798939811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#540×C73C2
socleC22×C73C22×D4
hypercenter#540D73
hypocenterC73#3179
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #17989208C2semidirect
2. #17988997C2semidirect
3. #17988974C2semidirect
4. #17988944C2semidirect
5. #17988933C2semidirect
6. #17988838C2semidirect
7. #17988831C2semidirect
8. #17988821C2semidirect
9. #17988814C2semidirect
10. #17988697C2semidirect
11. #17988687C2semidirect
12. C4×#11924016C2semidirect
13. C4×#11924013C2semidirect
14. #17988543C2semidirect
15. #540×C73C2semidirect
179. C73#3179semidirect
181. #540D73semidirect