Finite Group Databasebeta

← #22622251

Subgroups — #22622251

Order 9344.

430 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989256C211yesmaximal, characteristic, complemented
2#17989237C211yesmaximal, characteristic, complemented
3#17988932C211yesmaximal, characteristic, complemented
4#17988906C211yesmaximal, characteristic, complemented
5#17988904C211yesmaximal, characteristic, complemented
6#17988870C211yesmaximal, characteristic, complemented
7#17988838C211yesmaximal, characteristic, complemented
8#17988837C211yesmaximal, characteristic, complemented
9#17988780C211yesmaximal, characteristic, complemented
10#17988731C211yesmaximal, characteristic, complemented
11SD16×Dic73C211yesmaximal, characteristic, complemented
12#17988662C211yesmaximal, characteristic, complemented
13#17988588C211yesmaximal, characteristic, complemented
14#17988587C211yesmaximal, characteristic, complemented
15#449×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic
17C2×#11924027—21no—
18C2×#11924013C2211yescharacteristic
19C2×#11924012C2211yescharacteristic
20C2×#11924011C2211yescharacteristic
21#14556590C2211yescharacteristic
22#14556587—21no—
23#14556587C2211yescharacteristic
24#14556573—21no—
25#14556572—21no—
26#14556568—21no—
27#14556565—21no—
28#14556565C2211yescharacteristic
29#14556562—21no—
30#14556562C2211yescharacteristic
31#14556562C2211yescharacteristic
32Q8×Dic73C2211yescharacteristic
33D4×Dic73C2211yescharacteristic
34C4×C22⋊D73—21no—
35C4×C22⋊D73C2211yescharacteristic
36C2×C4⋊Dic73C2211yescharacteristic
37C4⋊C4×D73C2211yescharacteristic
38#14556523C2211yescharacteristic
39#14556523C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556520C2211yescharacteristic
42#14556515C2211yescharacteristic
43#14556515C2211yescharacteristic
44#14556513C2211yescharacteristic
45#14556513C2211yescharacteristic
46#14556512C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556512C2211yescharacteristic
49#14556511C2211yescharacteristic
50#14556503C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C2×#41×C73C2211yescharacteristic
53C2×SD16×C73C2211yescharacteristic
54C2×D8×C73C2211yescharacteristic
55#121×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59#11924029—22no—
60#11924029—41no—
61#11924027—44no—
62C2×Dic146—21no—
63C2×D292—21no—
64C2×D292C2311yescharacteristic
65C2×C22⋊D73—21no—
66C2×C22⋊D73—21no—
67C2×C22⋊D73—21no—
68C2×C22⋊D73—21no—
69C2×C22⋊D73—21no—
70C2×C22⋊D73D411yescharacteristic
71C22×Dic73—21no—
72C22×Dic73—21no—
73C2×C4×D73—21no—
74C2×C4×D73—21no—
75C2×C4×D73C2311yescharacteristic
76#11924013—41no—
77#11924012—41no—
78#11924011—41no—
79C2×#10596831C2311yescharacteristic
80C2×#10596831C2311yescharacteristic
81C4⋊Dic73—21no—
82C4⋊Dic73—21no—
83C4⋊Dic73C2311yescharacteristic
84C4⋊Dic73C2311yescharacteristic
85C4⋊Dic73C2311yescharacteristic
86#11924007—21no—
87#11924007—21no—
88#11924007D411yescharacteristic
89C22⋊Dic73—21no—
90C22⋊Dic73—21no—
91C22⋊Dic73—21no—
92C22⋊Dic73D411yescharacteristic
93#11924005—21no—
94#11924005D411yescharacteristic
95C4×Dic73—21no—
96C4×Dic73C2311yescharacteristic
97#41×C73—22no—
98#41×C73—41no—
99C2×Q8×C73C2311yescharacteristic
100C2×D4×C73—21no—
101C2×D4×C73—21no—
102C2×D4×C73C2311yescharacteristic
103C2×D4×C73C2311yescharacteristic
104C22×C4×C73—21no—
105C22×C4×C73C2311yescharacteristic
106SD16×C73—22no—
107D8×C73—41no—
108C2×C8×C73C2311yescharacteristic
109C2×C8×C73C2311yescharacteristic
110C4⋊C4×C73C2311yescharacteristic
111C22⋊C4×C73—21no—
112C23×C73—21no—
113C23×C73—21no—
114C23×C73C2×D411yescharacteristic
115C22×D73—21no—
116C22×D73C2×D411yescharacteristic
117Q8×C73—21no—
118Q8×C73#4112yescomplemented
119D4×C73—21no—
120D4×C73—21no—
121D4×C73—21no—
122D4×C73—21no—
123D4×C73—42no—
124D4×C73—42no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—42no—
130C2×C4×C73C2×D411yescharacteristic
131C2×C4×C73C2411yescharacteristic
132C22⋊D73—22no—
133C22⋊D73—42no—
134C22⋊D73—42no—
135C22⋊D73—81no—
136C22⋊D73—81no—
137C22⋊D73—81no—
138C2×Dic73—21no—
139C2×Dic73—21no—
140C2×Dic73—21no—
141C2×Dic73—42no—
142C2×Dic73—42no—
143C2×Dic73C2×D411yescharacteristic
144C2×Dic73C2×D411yescharacteristic
145C2×Dic73C2×D411yescharacteristic
146D292—21no—
147D292—21no—
148D292—42no—
149C4×D73—21no—
150C4×D73—21no—
151C4×D73—42no—
152C4×D73—42no—
153Dic146—42no—
154C8×C73—21no—
155C8×C73—21no—
156#10596831—21no—
157#10596831—21no—
158C22×C73—21no—
159C22×C73—21no—
160C22×C73—21no—
161C22×C73—41no—
162C22×C73—41no—
163C22×C73—41no—
164C22×C73—41no—
165C22×C73—41no—
166C22×C73—41no—
167C22×C73C22×D411yescharacteristic
168C2×D73—21no—
169C2×D73—21no—
170C2×D73—21no—
171C2×D73—41no—
172C2×D73—41no—
173C2×D73—41no—
174C4×C73—22no—
175C4×C73—21no—
176C4×C73—41no—
177C4×C73C2×#4111yescharacteristic
178C4×C73H(5,𝔽2)11yescharacteristic
179Dic73—21no—
180Dic73—21no—
181Dic73—41no—
182Dic73—41no—
183Dic73—41no—
184Dic73AGL(1,ℤ/8)12yes—
185C2×C73—41no—
186C2×C73—81no—
187C2×C73—81no—
188C2×C73#54611yescharacteristic
189C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C73#57711yescharacteristic
191D73—41no—
192D73—81no—
193#3332—731nomaximal, Sylow
194C73#333211yescharacteristic, complemented, Sylow
195#550—731no—
196#547—731no—
197#486—731no—
198#481—731no—
199#481—731no—
200#475—731no—
201#469—731no—
202#469—731no—
203#459—731no—
204#449—731no—
205#449D7311yescharacteristic, complemented
206C4×SD16—731no—
207#436—731no—
208#417—731no—
209#417—731no—
210C2×#41—731no—
211C2×#41—1461no—
212C2×#41C2×D7311yescharacteristic
213C2×SD16C2×D7311yescharacteristic
214C2×D8—731no—
215C2×D8C2×D7311yescharacteristic
216C2×M16—731no—
217C2×M16—731no—
218C4⋊Q8—731no—
219#127—731no—
220#127—1461no—
221#123—1461no—
222#123—1461no—
223C22⋊Q8—1461no—
224#121—731no—
225#121—731no—
226#121—731no—
227#121—1461no—
228#121—1461no—
229#121C2×D7311yescharacteristic
230C4×Q8—731no—
231C4×D4—731no—
232C4×D4—731no—
233C4×D4—1461no—
234C2×C4⋊C4—731no—
235C2×C4⋊C4—731no—
236#106—731no—
237#106—731no—
238#106—731no—
239C4⋊C8—731no—
240#103—731no—
241#103—731no—
242#103C2×D7311yescharacteristic
243#102—731no—
244#102—731no—
245#102—731no—
246#102—731no—
247#102—731no—
248#102—731no—
249#102C2×D7311yescharacteristic
250C22⋊C8—731no—
251C22⋊C8C2×D7311yescharacteristic
252C4×C8—731no—
253#41—22no—
254#41—41no—
255#41—2924no—
256#41—2921no—
257#41—1462no—
258C2×Q8—1461no—
259C2×Q8C22×D7311yescharacteristic
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—731no—
263C2×D4—731no—
264C2×D4—1461no—
265C2×D4—1461no—
266C2×D4—1461no—
267C2×D4—1461no—
268C2×D4—1461no—
269C2×D4—1461no—
270C2×D4C22×D7311yescharacteristic
271C2×D4C22×D7311yescharacteristic
272C22×C4—21no—
273C22×C4—731no—
274C22×C4—1461no—
275C22×C4—1461no—
276C22×C4—1461no—
277C22×C4—1461no—
278C22×C4C22×D7311yescharacteristic
279SD16—22no—
280D8—41no—
281D8—2921no—
282M16—2921no—
283M16—2921no—
284C2×C8—731no—
285C2×C8—731no—
286C2×C8C22×D7311yescharacteristic
287C2×C8C22×D7311yescharacteristic
288C4⋊C4—731no—
289C4⋊C4—731no—
290C4⋊C4—731no—
291C4⋊C4—731no—
292C4⋊C4—1461no—
293C4⋊C4—1461no—
294C4⋊C4—1461no—
295C4⋊C4—1461no—
296C4⋊C4C22×D7311yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—731no—
299C22⋊C4—731no—
300C22⋊C4—1461no—
301C22⋊C4—1461no—
302C22⋊C4—1461no—
303C22⋊C4—1461no—
304C42—731no—
305C42—1461no—
306C23—21no—
307C23—21no—
308C23—731no—
309C23—1461no—
310C23D4×D7311yescharacteristic
311Q8—21no—
312Q8—2922no—
313Q8#1192402712yescomplemented
314D4—21no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—42no—
319D4—42no—
320D4—2922no—
321D4—2922no—
322D4—2922no—
323D4—5841no—
324D4—5841no—
325D4—5841no—
326D4—1462no—
327D4—1461no—
328D4—1461no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—42no—
334C2×C4—2922no—
335C2×C4—2922no—
336C2×C4—2922no—
337C2×C4—2922no—
338C2×C4—731no—
339C2×C4—731no—
340C2×C4—731no—
341C2×C4—1461no—
342C2×C4—1461no—
343C2×C4—1461no—
344C2×C4—1461no—
345C2×C4—1461no—
346C2×C4D4×D7311yescharacteristic
347C2×C4C23×D7311yescharacteristic
348C8—21no—
349C8—21no—
350C8—1461no—
351C8—1461no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—2921no—
362C22—2921no—
363C22—2921no—
364C22—1461no—
365C22—1461no—
366C22—1461no—
367C22C2×D4×D7311yescharacteristic
368C4—21no—
369C4—22no—
370C4—41no—
371C4—2921no—
372C4—2921no—
373C4—2921no—
374C4—732no—
375C4—1461no—
376C4—1461no—
377C4C2×#1192402711yescharacteristic
378C4#1455663611yescharacteristic
379C2—41no—
380C2—81no—
381C2—81no—
382C2—2921no—
383C2—5841no—
384C2#1798922411yescharacteristic
385C2AGL(1,ℤ/8)×D7311yescharacteristic
386C2#1798939411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#449×C73C2
socleC22×C73C22×D4
hypercenter#449D73
hypocenterC73#3332
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #17989256C2semidirect
2. #17989237C2semidirect
3. #17988932C2semidirect
4. #17988906C2semidirect
5. #17988904C2semidirect
6. #17988870C2semidirect
7. #17988838C2semidirect
8. #17988837C2semidirect
9. #17988780C2semidirect
10. #17988731C2semidirect
11. SD16×Dic73C2semidirect
12. #17988662C2semidirect
13. #17988588C2semidirect
14. #17988587C2semidirect
15. #449×C73C2semidirect
118. Q8×C73#41semidirect
194. C73#3332semidirect
205. #449D73semidirect
313. Q8#11924027semidirect