Finite Group Databasebeta

← #22620124

Subgroups — #22620124

Order 9344.

396 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#17989067C211yesmaximal, characteristic, complemented
2#17988903C211yesmaximal, characteristic, complemented
3#17988898C211yesmaximal, characteristic, complemented
4#17988891C211yesmaximal, characteristic, complemented
5#17988884C211yesmaximal, characteristic, complemented
6#17988784C211yesmaximal, characteristic, complemented
7#17988779C211yesmaximal, characteristic, complemented
8#17988730C211yesmaximal, characteristic, complemented
9#17988730C211yesmaximal, characteristic, complemented
10#17988697C211yesmaximal, characteristic, complemented
11#17988687C211yesmaximal, characteristic, complemented
12C4×#11924016C211yesmaximal, characteristic, complemented
13C4×#11924013C211yesmaximal, characteristic, complemented
14#17988648C211yesmaximal, characteristic, complemented
15#540×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×#11924016C2211yescharacteristic
18C2×#11924016C2211yescharacteristic
19C2×#11924013C2211yescharacteristic
20C2×#11924013C2211yescharacteristic
21C4×Dic146C2211yescharacteristic
22C4×Dic146C2211yescharacteristic
23C4×D292C2211yescharacteristic
24C4×D292C2211yescharacteristic
25#14556551—21no—
26#14556551—21no—
27#14556549—21no—
28C2×C4⋊Dic73C2211yescharacteristic
29C4⋊C4×D73—21no—
30#14556524C2211yescharacteristic
31#14556524C2211yescharacteristic
32#14556522C2211yescharacteristic
33#14556522C2211yescharacteristic
34C4⋊#10596831C2211yescharacteristic
35C4⋊#10596831C2211yescharacteristic
36#14556514C2211yescharacteristic
37#14556514C2211yescharacteristic
38#14556512C2211yescharacteristic
39#14556512C2211yescharacteristic
40#14556512C2211yescharacteristic
41#14556512C2211yescharacteristic
42#14556511C2211yescharacteristic
43#14556511C2211yescharacteristic
44C22⋊#10596831C2211yescharacteristic
45C22⋊#10596831C2211yescharacteristic
46#14556502C2211yescharacteristic
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
59#11924028—22no—
60#11924028—22no—
61C2×Dic146C2311yescharacteristic
62C2×D292C2311yescharacteristic
63C2×C22⋊D73—21no—
64C22×Dic73—21no—
65C2×C4×D73—21no—
66C2×C4×D73—21no—
67C2×C4×D73—21no—
68#11924016—22no—
69#11924016—22no—
70#11924013—22no—
71#11924013—22no—
72C2×#10596831C2311yescharacteristic
73C2×#10596831C2311yescharacteristic
74C2×#10596831C2311yescharacteristic
75C2×#10596831C2311yescharacteristic
76C4⋊Dic73—21no—
77C4⋊Dic73C2311yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79#11924007—21no—
80#11924007—21no—
81#11924005—21no—
82#11924005—21no—
83C4×Dic73—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—24no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—81no—
137D292—21no—
138D292#4112yes—
139C4×D73—24no—
140C4×D73—81no—
141C4×D73—81no—
142Dic146—21no—
143Dic146#4112yes—
144#10596831—21no—
145#10596831—21no—
146#10596831—21no—
147#10596831—21no—
148C22×C73—21no—
149C22×C73—21no—
150C22×C73—21no—
151C22×C73—41no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73—41no—
155C22×C73—41no—
156C22×C73—41no—
157C22×C73C22×D411yescharacteristic
158C2×D73—22no—
159C2×D73—41no—
160C2×D73—41no—
161C4×C73—21no—
162C4×C73—21no—
163C4×C73—21no—
164C4×C73—21no—
165C4×C73—21no—
166C4×C73—41no—
167C4×C73—41no—
168C4×C73C2×#4111yescharacteristic
169C4×C73C2×#4111yescharacteristic
170Dic73—22no—
171Dic73—41no—
172Dic73—41no—
173C2×C73—41no—
174C2×C73—81no—
175C2×C73—81no—
176C2×C73#52511yescharacteristic
177C2×C73#57611yescharacteristic
178C2×C73#57711yescharacteristic
179D73—42no—
180#3119—731nomaximal, Sylow
181C73#311911yescharacteristic, complemented, Sylow
182#540D7311yescharacteristic, complemented
183#520—731no—
184#481—731no—
185#480—731no—
186#479—731no—
187#478—731no—
188#460—731no—
189#459—731no—
190#449—731no—
191#449—731no—
192#442—731no—
193#440—731no—
194C4×SD16—731no—
195C4×D8—731no—
196#433—731no—
197C2×#41—731no—
198C2×SD16—731no—
199C2×SD16—731no—
200C2×D8—731no—
201C2×D8—731no—
202#127C2×D7311yescharacteristic
203#125C2×D7311yescharacteristic
204#123—21no—
205#123—21no—
206#121—21no—
207#121—21no—
208#121C2×D7311yescharacteristic
209#121C2×D7311yescharacteristic
210C4×Q8—731no—
211C4×Q8—731no—
212C4×D4—731no—
213C4×D4—731no—
214C4×D4—1461no—
215C4×D4—1461no—
216C4×D4C2×D7311yescharacteristic
217C4×D4C2×D7311yescharacteristic
218#117—1461no—
219#117C2×D7311yescharacteristic
220C2×C4⋊C4—731no—
221C2×C4⋊C4—1461no—
222#107—731no—
223#107—731no—
224#106—731no—
225#106—731no—
226C4⋊C8—731no—
227C4⋊C8—731no—
228#103—731no—
229#103—731no—
230#102—731no—
231#102—731no—
232#102—731no—
233#102—731no—
234#102—731no—
235#102—731no—
236C22⋊C8—731no—
237C22⋊C8—731no—
238#97—731no—
239C4×C8—731no—
240#41—1462no—
241#41—1462no—
242C2×Q8—731no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—731no—
248C2×D4—1461no—
249C2×D4C22×D7311yescharacteristic
250C2×D4C22×D7311yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—1461no—
254C22×C4—1461no—
255C22×C4—1461no—
256C22×C4—1461no—
257C22×C4C22×D7311yescharacteristic
258SD16—1462no—
259SD16—1462no—
260D8—1462no—
261D8—1462no—
262C2×C8—731no—
263C2×C8—731no—
264C2×C8—731no—
265C2×C8—731no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—731no—
269C4⋊C4—731no—
270C4⋊C4—1461no—
271C4⋊C4—1461no—
272C4⋊C4—1461no—
273C4⋊C4C22⋊D7311yescharacteristic
274C4⋊C4C22⋊D7311yescharacteristic
275C4⋊C4C22×D7311yescharacteristic
276C4⋊C4C22×D7311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—1461no—
282C22⋊C4—1461no—
283C22⋊C4C22⋊D7311yescharacteristic
284C22⋊C4C22⋊D7311yescharacteristic
285C42—1461no—
286C42—1461no—
287C42C22×D7311yescharacteristic
288C42C22×D7311yescharacteristic
289C23—21no—
290C23—21no—
291C23—1461no—
292C23C2×C22⋊D7311yescharacteristic
293Q8—732no—
294Q8—1461no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—81no—
301D4—81no—
302D4—81no—
303D4—732no—
304D4—1464no—
305D4—1461no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—5841no—
313C2×C4—5841no—
314C2×C4—5841no—
315C2×C4—1464no—
316C2×C4—1461no—
317C2×C4—1461no—
318C2×C4—1461no—
319C2×C4C2×C22⋊D7311yescharacteristic
320C2×C4C2×C22⋊D7311yescharacteristic
321C2×C4C2×C22⋊D7311yescharacteristic
322C2×C4C2×C22⋊D7311yescharacteristic
323C2×C4C2×C22⋊D7311yescharacteristic
324C2×C4C23×D7311yescharacteristic
325C8—1461no—
326C8—1461no—
327C8—1461no—
328C8—1461no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—2921no—
339C22—2921no—
340C22—1462no—
341C22C22×C22⋊D7311yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—2921no—
350C4—2921no—
351C4—1462no—
352C4#41×D7311yescharacteristic
353C4#41×D7311yescharacteristic
354C2—41no—
355C2—81no—
356C2—81no—
357C2—2922no—
358C2#1798909411yescharacteristic
359C2#1798939011yescharacteristic
360C2#1798939811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#540×C73C2
socleC22×C73C22×D4
hypercenter#540D73
hypocenterC73#3119
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. #17989067C2semidirect
2. #17988903C2semidirect
3. #17988898C2semidirect
4. #17988891C2semidirect
5. #17988884C2semidirect
6. #17988784C2semidirect
7. #17988779C2semidirect
8. #17988730C2semidirect
9. #17988730C2semidirect
10. #17988697C2semidirect
11. #17988687C2semidirect
12. C4×#11924016C2semidirect
13. C4×#11924013C2semidirect
14. #17988648C2semidirect
15. #540×C73C2semidirect
181. C73#3119semidirect
182. #540D73semidirect