Finite Group Databasebeta

← #22620187

Subgroups — #22620187

Order 9344.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989067C211yesmaximal, characteristic, complemented
2#17988920C211yesmaximal, characteristic, complemented
3#17988898C211yesmaximal, characteristic, complemented
4#17988879C211yesmaximal, characteristic, complemented
5#17988864C211yesmaximal, characteristic, complemented
6#17988806C211yesmaximal, characteristic, complemented
7#17988799C211yesmaximal, characteristic, complemented
8#17988747C211yesmaximal, characteristic, complemented
9#17988730C211yesmaximal, characteristic
10#17988687C211yesmaximal, characteristic, complemented
11#17988685C211yesmaximal, characteristic, complemented
12C4×#11924018C211yesmaximal, characteristic, complemented
13C4×#11924013C211yesmaximal, characteristic, complemented
14#17988648C211yesmaximal, characteristic, complemented
15#542×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×#11924018C2211yescharacteristic
18C2×#11924016C2211yescharacteristic
19C2×#11924015C2211yescharacteristic
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#14556524C2211yescharacteristic
33#14556524C2211yescharacteristic
34C4⋊#10596831C2211yescharacteristic
35C4⋊#10596831C2211yescharacteristic
36#14556515C2211yescharacteristic
37#14556515C2211yescharacteristic
38#14556514C2211yescharacteristic
39#14556514C2211yescharacteristic
40#14556512C2211yescharacteristic
41#14556512C2211yescharacteristic
42#14556511C2211yescharacteristic
43#14556511C2211yescharacteristic
44C22⋊#10596831C2211yescharacteristic
45C22⋊#10596831C2211yescharacteristic
46#14556502C2211yescharacteristic
47C4×#10596831C2211yescharacteristic
48C4⋊Q8×C73C2211yescharacteristic
49#126×C73—21no—
50#124×C73—21no—
51#124×C73C2211yescharacteristic
52#123×C73—21no—
53C22⋊Q8×C73—21no—
54C22⋊Q8×C73C2211yescharacteristic
55#121×C73C2211yescharacteristic
56C4×Q8×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#11924018—22no—
69#11924016—22no—
70#11924015—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×Q8×C73—21no—
86C2×Q8×C73C2311yescharacteristic
87C2×D4×C73—21no—
88C2×D4×C73C2311yescharacteristic
89C22×C4×C73—21no—
90C22×C4×C73C2311yescharacteristic
91C4⋊C4×C73—21no—
92C4⋊C4×C73—21no—
93C4⋊C4×C73—21no—
94C4⋊C4×C73D411yescharacteristic
95C4⋊C4×C73D411yescharacteristic
96C4⋊C4×C73C2311yescharacteristic
97C4⋊C4×C73C2311yescharacteristic
98C22⋊C4×C73—21no—
99C22⋊C4×C73—21no—
100C22⋊C4×C73—21no—
101C22⋊C4×C73—21no—
102C22⋊C4×C73—21no—
103C22⋊C4×C73D411yescharacteristic
104C22⋊C4×C73D411yescharacteristic
105C42×C73—21no—
106C42×C73C2311yescharacteristic
107C42×C73C2311yescharacteristic
108C23×C73—21no—
109C23×C73C2×D411yescharacteristic
110C22×D73—21no—
111Q8×C73—21no—
112Q8×C73—21no—
113Q8×C73—81no—
114D4×C73—21no—
115D4×C73—21no—
116D4×C73—81no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—81no—
123C2×C4×C73C2×D411yescharacteristic
124C2×C4×C73C2×D411yescharacteristic
125C2×C4×C73C2×D411yescharacteristic
126C2×C4×C73C2×D411yescharacteristic
127C2×C4×C73C2×D411yescharacteristic
128C2×C4×C73C2411yescharacteristic
129C22⋊D73—24no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—81no—
134D292—21no—
135D292#4112yes—
136C4×D73—24no—
137C4×D73—81no—
138C4×D73—81no—
139Dic146—21no—
140Dic146#4112yes—
141#10596831—21no—
142#10596831—21no—
143#10596831—21no—
144#10596831—21no—
145C22×C73—21no—
146C22×C73—21no—
147C22×C73—21no—
148C22×C73—41no—
149C22×C73—41no—
150C22×C73—41no—
151C22×C73C22×D411yescharacteristic
152C2×D73—22no—
153C2×D73—41no—
154C2×D73—41no—
155C4×C73—21no—
156C4×C73—21no—
157C4×C73—21no—
158C4×C73—21no—
159C4×C73—21no—
160C4×C73—41no—
161C4×C73—41no—
162C4×C73—41no—
163C4×C73C2×#4111yescharacteristic
164C4×C73C2×#4111yescharacteristic
165Dic73—22no—
166Dic73—41no—
167Dic73—41no—
168C2×C73—41no—
169C2×C73—81no—
170C2×C73#52511yescharacteristic
171C2×C73#57611yescharacteristic
172C2×C73#57811yescharacteristic
173D73—42no—
174#3124—731nomaximal, Sylow
175C73#312411yescharacteristic, complemented, Sylow
176#542D7311yescharacteristic, complemented
177#520—731no—
178#484—731no—
179#480—731no—
180#477—731no—
181#474—731no—
182#464—731no—
183#463—731no—
184#452—731no—
185#449—731no—
186#440—731no—
187#440—731no—
188C4×Q16—731no—
189C4×D8—731no—
190#433—731no—
191C2×#41—731no—
192C2×Q16—731no—
193C2×SD16—731no—
194C2×SD16—731no—
195C2×D8—731no—
196C4⋊Q8C2×D7311yescharacteristic
197#126—21no—
198#124—21no—
199#124C2×D7311yescharacteristic
200#123—21no—
201C22⋊Q8—21no—
202C22⋊Q8C2×D7311yescharacteristic
203#121C2×D7311yescharacteristic
204C4×Q8—731no—
205C4×Q8—731no—
206C4×Q8C2×D7311yescharacteristic
207C4×D4—731no—
208C4×D4—731no—
209C4×D4—1461no—
210C4×D4—1461no—
211C4×D4C2×D7311yescharacteristic
212#117—1461no—
213#117C2×D7311yescharacteristic
214C2×C4⋊C4—731no—
215C2×C4⋊C4—1461no—
216#107—731no—
217#107—731no—
218#107—731no—
219#107—731no—
220C4⋊C8—731no—
221C4⋊C8—731no—
222#103—731no—
223#103—731no—
224#103—731no—
225#103—731no—
226#102—731no—
227#102—731no—
228#102—731no—
229#102—731no—
230C22⋊C8—731no—
231C22⋊C8—731no—
232#97—731no—
233C4×C8—731no—
234#41—1462no—
235#41—1462no—
236C2×Q8—21no—
237C2×Q8—731no—
238C2×Q8C22×D7311yescharacteristic
239C2×D4—21no—
240C2×D4—731no—
241C2×D4—1461no—
242C2×D4C22×D7311yescharacteristic
243C22×C4—21no—
244C22×C4—1461no—
245C22×C4—1461no—
246C22×C4—1461no—
247C22×C4—1461no—
248C22×C4C22×D7311yescharacteristic
249Q16—1462no—
250SD16—1462no—
251SD16—1462no—
252D8—1462no—
253C2×C8—731no—
254C2×C8—731no—
255C2×C8—731no—
256C2×C8—731no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—731no—
261C4⋊C4—731no—
262C4⋊C4—1461no—
263C4⋊C4—1461no—
264C4⋊C4—1461no—
265C4⋊C4C22⋊D7311yescharacteristic
266C4⋊C4C22⋊D7311yescharacteristic
267C4⋊C4C22×D7311yescharacteristic
268C4⋊C4C22×D7311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—1461no—
275C22⋊C4—1461no—
276C22⋊C4C22⋊D7311yescharacteristic
277C22⋊C4C22⋊D7311yescharacteristic
278C42—21no—
279C42—1461no—
280C42—1461no—
281C42C22×D7311yescharacteristic
282C42C22×D7311yescharacteristic
283C23—21no—
284C23—1461no—
285C23C2×C22⋊D7311yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—81no—
289Q8—732no—
290Q8—1461no—
291D4—21no—
292D4—21no—
293D4—81no—
294D4—732no—
295D4—1464no—
296D4—1461no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—5841no—
304C2×C4—5841no—
305C2×C4—5841no—
306C2×C4—1464no—
307C2×C4—1461no—
308C2×C4—1461no—
309C2×C4—1461no—
310C2×C4C2×C22⋊D7311yescharacteristic
311C2×C4C2×C22⋊D7311yescharacteristic
312C2×C4C2×C22⋊D7311yescharacteristic
313C2×C4C2×C22⋊D7311yescharacteristic
314C2×C4C2×C22⋊D7311yescharacteristic
315C2×C4C23×D7311yescharacteristic
316C8—1461no—
317C8—1461no—
318C8—1461no—
319C8—1461no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—2921no—
327C22—2921no—
328C22—1462no—
329C22C22×C22⋊D7311yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—2921no—
339C4—2921no—
340C4—1462no—
341C4#41×D7311yescharacteristic
342C4#41×D7311yescharacteristic
343C2—41no—
344C2—81no—
345C2—2922no—
346C2#1798909411yescharacteristic
347C2#1798939011yescharacteristic
348C2#1798940211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#542×C73C2
socleC22×C73C22×D4
hypercenter#542D73
hypocenterC73#3124
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #17989067C2semidirect
2. #17988920C2semidirect
3. #17988898C2semidirect
4. #17988879C2semidirect
5. #17988864C2semidirect
6. #17988806C2semidirect
7. #17988799C2semidirect
8. #17988747C2semidirect
10. #17988687C2semidirect
11. #17988685C2semidirect
12. C4×#11924018C2semidirect
13. C4×#11924013C2semidirect
14. #17988648C2semidirect
15. #542×C73C2semidirect
175. C73#3124semidirect
176. #542D73semidirect