Finite Group Databasebeta

← #22621923

Subgroups — #22621923

Order 9344.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989244C211yesmaximal, characteristic, complemented
2#17989238C211yesmaximal, characteristic, complemented
3#17988945C211yesmaximal, characteristic, complemented
4#17988922C211yesmaximal, characteristic, complemented
5#17988899C211yesmaximal, characteristic, complemented
6#17988880C211yesmaximal, characteristic, complemented
7#17988833C211yesmaximal, characteristic, complemented
8#17988822C211yesmaximal, characteristic, complemented
9#17988801C211yesmaximal, characteristic, complemented
10#17988732C211yesmaximal, characteristic, complemented
11#17988727C211yesmaximal, characteristic, complemented
12#17988690C211yesmaximal, characteristic, complemented
13#17988656C211yesmaximal, characteristic, complemented
14#103×D73C211yesmaximal, characteristic, complemented
15#417×C73C211yesmaximal, characteristic, complemented
16C2×#11924028—21no—
17C2×Q8×D73C2211yescharacteristic
18C2×#11924017C2211yescharacteristic
19C2×#11924015C2211yescharacteristic
20C2×#11924013C2211yescharacteristic
21C2×C8×D73C2211yescharacteristic
22#14556590C2211yescharacteristic
23#14556578—21no—
24#14556578C2211yescharacteristic
25#14556576—21no—
26#14556574—21no—
27#14556570—21no—
28#14556570C2211yescharacteristic
29#14556569—21no—
30#14556566C2211yescharacteristic
31#14556565C2211yescharacteristic
32#14556562—21no—
33#14556562C2211yescharacteristic
34Q8×Dic73C2211yescharacteristic
35#14556553C2211yescharacteristic
36C4×C22⋊D73—21no—
37C4×C22⋊D73C2211yescharacteristic
38C4⋊C4×D73C2211yescharacteristic
39#14556525C2211yescharacteristic
40#14556524C2211yescharacteristic
41#14556524C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556515C2211yescharacteristic
45#14556514C2211yescharacteristic
46#14556514C2211yescharacteristic
47#14556513C2211yescharacteristic
48#14556512C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic
51#14556501C2211yescharacteristic
52C2×#41×C73C2211yescharacteristic
53C2×M16×C73C2211yescharacteristic
54C2×C4⋊C4×C73C2211yescharacteristic
55#103×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59#11924028—44no—
60C2×Dic146—21no—
61C2×Dic146—21no—
62C2×Dic146C2311yescharacteristic
63Q8×D73—22no—
64Q8×D73—41no—
65C2×D292—21no—
66C2×D292C2311yescharacteristic
67C2×C22⋊D73—21no—
68C2×C22⋊D73—21no—
69C2×C22⋊D73D411yescharacteristic
70C2×C4×D73—21no—
71C2×C4×D73—21no—
72C2×C4×D73—21no—
73C2×C4×D73C2311yescharacteristic
74#11924017—41no—
75#11924015—22no—
76#11924013—41no—
77C2×#10596831C2311yescharacteristic
78C2×#10596831C2311yescharacteristic
79C8×D73—41no—
80C4⋊Dic73—21no—
81C4⋊Dic73C2311yescharacteristic
82C4⋊Dic73C2311yescharacteristic
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86#11924007D411yescharacteristic
87C22⋊Dic73—21no—
88C22⋊Dic73—21no—
89C22⋊Dic73—21no—
90C22⋊Dic73—21no—
91C22⋊Dic73D411yescharacteristic
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005D411yescharacteristic
96C4×Dic73—21no—
97C4×Dic73C2311yescharacteristic
98#41×C73—22no—
99#41×C73—41no—
100C2×Q8×C73C2311yescharacteristic
101C2×D4×C73—21no—
102C2×D4×C73C2311yescharacteristic
103C22×C4×C73—21no—
104C22×C4×C73—21no—
105C22×C4×C73C2311yescharacteristic
106M16×C73—41no—
107C2×C8×C73C2311yescharacteristic
108C2×C8×C73C2311yescharacteristic
109C4⋊C4×C73—21no—
110C4⋊C4×C73C2311yescharacteristic
111C4⋊C4×C73C2311yescharacteristic
112C23×C73—21no—
113C23×C73C2×D411yescharacteristic
114C22×D73—21no—
115C22×D73C2×D411yescharacteristic
116Q8×C73—21no—
117Q8×C73#4112yescomplemented
118D4×C73—21no—
119D4×C73—21no—
120D4×C73—42no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—42no—
127C2×C4×C73—42no—
128C2×C4×C73C2×D411yescharacteristic
129C2×C4×C73C2411yescharacteristic
130C22⋊D73—22no—
131C22⋊D73—42no—
132C22⋊D73—42no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73C2×D411yescharacteristic
137C2×Dic73C2×D411yescharacteristic
138C2×Dic73C2×D411yescharacteristic
139D292—21no—
140D292—21no—
141D292—42no—
142C4×D73—21no—
143C4×D73—21no—
144C4×D73—42no—
145C4×D73—42no—
146C4×D73—42no—
147Dic146—21no—
148Dic146—21no—
149Dic146—42no—
150Dic146—42no—
151C8×C73—21no—
152C8×C73—21no—
153#10596831—21no—
154#10596831—21no—
155C22×C73—21no—
156C22×C73—21no—
157C22×C73—21no—
158C22×C73—41no—
159C22×C73—41no—
160C22×C73—41no—
161C22×C73C22×D411yescharacteristic
162C2×D73—21no—
163C2×D73—21no—
164C2×D73—41no—
165C2×D73—41no—
166C2×D73—41no—
167C2×D73AGL(1,ℤ/8)12yes—
168C4×C73—22no—
169C4×C73—21no—
170C4×C73—41no—
171C4×C73—41no—
172C4×C73C2×#4111yescharacteristic
173C4×C73H(5,𝔽2)11yescharacteristic
174Dic73—21no—
175Dic73—21no—
176Dic73—21no—
177Dic73—41no—
178Dic73—41no—
179Dic73—41no—
180C2×C73—41no—
181C2×C73—81no—
182C2×C73#54611yescharacteristic
183C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
184C2×C73#57811yescharacteristic
185D73—22no—
186D73—81no—
187#3308—731nomaximal, Sylow
188C73#330811yescharacteristic, complemented, Sylow
189#548—731no—
190#547—731no—
191#489—731no—
192#484—731no—
193#480—731no—
194#477—731no—
195#468—731no—
196#466—731no—
197#463—731no—
198#449—731no—
199#448—731no—
200#440—731no—
201#435—731no—
202#417D7311yescharacteristic, complemented
203C2×#103—731no—
204C2×#41—1461no—
205C2×#41C2×D7311yescharacteristic
206C22×Q8—731no—
207C2×SD16—731no—
208C2×SD16—731no—
209C2×D8—731no—
210C2×M16C2×D7311yescharacteristic
211C22×C8—731no—
212C4⋊Q8—731no—
213#124—731no—
214#124—1461no—
215#123—1461no—
216#123—1461no—
217C22⋊Q8—731no—
218C22⋊Q8—1461no—
219C22⋊Q8—1461no—
220#121—731no—
221#121—731no—
222#121—731no—
223#121—1461no—
224C4×Q8—731no—
225C4×D4—731no—
226C4×D4—731no—
227C4×D4—1461no—
228C2×C4⋊C4—731no—
229C2×C4⋊C4C2×D7311yescharacteristic
230#107—731no—
231#107—731no—
232#107—731no—
233C4⋊C8—731no—
234#103—731no—
235#103—731no—
236#103—731no—
237#103—731no—
238#103C2×D7311yescharacteristic
239#103C2×D7311yescharacteristic
240#102—731no—
241#102—731no—
242#102C2×D7311yescharacteristic
243#102C2×D7311yescharacteristic
244C22⋊C8—731no—
245C22⋊C8—731no—
246#97—731no—
247#41—22no—
248#41—41no—
249#41—2924no—
250C2×Q8—2921no—
251C2×Q8—731no—
252C2×Q8—1461no—
253C2×Q8—1461no—
254C2×Q8—1462no—
255C2×Q8C22×D7311yescharacteristic
256C2×D4—21no—
257C2×D4—731no—
258C2×D4—731no—
259C2×D4—1461no—
260C2×D4—1461no—
261C2×D4—1461no—
262C2×D4C22×D7311yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—731no—
266C22×C4—1461no—
267C22×C4—1461no—
268C22×C4—1461no—
269C22×C4C22×D7311yescharacteristic
270SD16—2921no—
271SD16—1462no—
272D8—2921no—
273M16—41no—
274C2×C8—2921no—
275C2×C8—731no—
276C2×C8—731no—
277C2×C8C22×D7311yescharacteristic
278C2×C8C22×D7311yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—731no—
281C4⋊C4—731no—
282C4⋊C4—731no—
283C4⋊C4—1461no—
284C4⋊C4—1461no—
285C4⋊C4—1461no—
286C4⋊C4—1461no—
287C4⋊C4C22×D7311yescharacteristic
288C4⋊C4C22×D7311yescharacteristic
289C22⋊C4—731no—
290C22⋊C4—731no—
291C22⋊C4—1461no—
292C22⋊C4—1461no—
293C22⋊C4—1461no—
294C22⋊C4—1461no—
295C22⋊C4—1461no—
296C22⋊C4—1461no—
297C22⋊C4—1461no—
298C42—731no—
299C42—1461no—
300C23—21no—
301C23—731no—
302C23—1461no—
303C23D4×D7311yescharacteristic
304Q8—21no—
305Q8—2922no—
306Q8—2922no—
307Q8—1461no—
308Q8—1461no—
309Q8#1192402812yescomplemented
310D4—21no—
311D4—21no—
312D4—42no—
313D4—2922no—
314D4—2922no—
315D4—2922no—
316D4—1462no—
317D4—1461no—
318D4—1461no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—2922no—
327C2×C4—2922no—
328C2×C4—2922no—
329C2×C4—731no—
330C2×C4—731no—
331C2×C4—731no—
332C2×C4—1461no—
333C2×C4—1461no—
334C2×C4—1461no—
335C2×C4—1461no—
336C2×C4—1461no—
337C2×C4D4×D7311yescharacteristic
338C2×C4C23×D7311yescharacteristic
339C8—21no—
340C8—21no—
341C8—1461no—
342C8—1461no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—2921no—
350C22—2921no—
351C22—2921no—
352C22—732no—
353C22—1461no—
354C22—1461no—
355C22C2×D4×D7311yescharacteristic
356C4—21no—
357C4—22no—
358C4—41no—
359C4—41no—
360C4—2921no—
361C4—2921no—
362C4—2921no—
363C4—1461no—
364C4—1461no—
365C4—1461no—
366C4C2×#1192402811yescharacteristic
367C4#1455663611yescharacteristic
368C2—41no—
369C2—81no—
370C2—5841no—
371C2—1462no—
372C2#1798922711yescharacteristic
373C2AGL(1,ℤ/8)×D7311yescharacteristic
374C2#1798940311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#417×C73C2
socleC22×C73C22×D4
hypercenter#417D73
hypocenterC73#3308
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #17989244C2semidirect
2. #17989238C2semidirect
3. #17988945C2semidirect
4. #17988922C2semidirect
5. #17988899C2semidirect
6. #17988880C2semidirect
7. #17988833C2semidirect
8. #17988822C2semidirect
9. #17988801C2semidirect
10. #17988732C2semidirect
11. #17988727C2semidirect
12. #17988690C2semidirect
13. #17988656C2semidirect
14. #103×D73C2semidirect
15. #417×C73C2semidirect
117. Q8×C73#41semidirect
188. C73#3308semidirect
202. #417D73semidirect
309. Q8#11924028semidirect