Finite Group Databasebeta

← #22622924

Subgroups — #22622924

Order 9344.

372 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989319C211yesmaximal, characteristic, complemented
2#17989306C211yesmaximal, characteristic, complemented
3#17988968C211yesmaximal, characteristic, complemented
4#17988958C211yesmaximal, characteristic, complemented
5#17988811C211yesmaximal, characteristic, complemented
6#17988806C211yesmaximal, characteristic, complemented
7#17988800C211yesmaximal, characteristic, complemented
8#17988799C211yesmaximal, characteristic, complemented
9#17988795C211yesmaximal, characteristic, complemented
10#17988780C211yesmaximal, characteristic
11C8×Dic146C211yesmaximal, characteristic, complemented
12C4×#11924017C211yesmaximal, characteristic, complemented
13SD16×Dic73C211yesmaximal, characteristic, complemented
14SD16×Dic73C211yesmaximal, characteristic, complemented
15#495×C73C211yesmaximal, characteristic, complemented
16C2×#11924018C2211yescharacteristic
17C2×#11924017C2211yescharacteristic
18C2×#11924016C2211yescharacteristic
19C2×#11924015C2211yescharacteristic
20C2×#11924013C2211yescharacteristic
21#14556589C2211yescharacteristic
22#14556587C2211yescharacteristic
23#14556584—21no—
24#14556584—21no—
25#14556580C2211yescharacteristic
26#14556578C2211yescharacteristic
27#14556577—21no—
28#14556575—21no—
29#14556573—21no—
30#14556568—21no—
31Q8×Dic73C2211yescharacteristic
32Q8×Dic73C2211yescharacteristic
33C4×Dic146C2211yescharacteristic
34C4×Dic146C2211yescharacteristic
35C4×D292C2211yescharacteristic
36D4×Dic73C2211yescharacteristic
37D4×Dic73C2211yescharacteristic
38#14556551—21no—
39#14556547—21no—
40#14556523C2211yescharacteristic
41C4⋊#10596831C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556520C2211yescharacteristic
44#14556516C2211yescharacteristic
45#14556515C2211yescharacteristic
46#14556515C2211yescharacteristic
47#14556513C2211yescharacteristic
48#14556512C2211yescharacteristic
49#14556512C2211yescharacteristic
50C8×Dic73C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C2×Q16×C73C2211yescharacteristic
53C2×SD16×C73C2211yescharacteristic
54C2×SD16×C73C2211yescharacteristic
55C2×D8×C73C2211yescharacteristic
56#124×C73C2211yescharacteristic
57#124×C73C2211yescharacteristic
58C4×C8×C73C2211yescharacteristic
59C2×Dic146D411yescharacteristic
60C2×Dic146C2311yescharacteristic
61C2×D292C2311yescharacteristic
62C2×C22⋊D73—21no—
63C2×C22⋊D73—21no—
64C22×Dic73—21no—
65C22×Dic73—21no—
66C2×C4×D73—21no—
67#11924018—41no—
68#11924017—22no—
69#11924016—41no—
70#11924015—41no—
71#11924013—41no—
72C2×#10596831C2311yescharacteristic
73C2×#10596831C2311yescharacteristic
74C4⋊Dic73—21no—
75C4⋊Dic73—21no—
76C4⋊Dic73D411yescharacteristic
77C4⋊Dic73C2311yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007D411yescharacteristic
83#11924007D411yescharacteristic
84C22⋊Dic73—21no—
85C22⋊Dic73—21no—
86C22⋊Dic73—21no—
87C22⋊Dic73—21no—
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91C4×Dic73—21no—
92C4×Dic73—21no—
93C4×Dic73—21no—
94C4×Dic73C2311yescharacteristic
95C4×Dic73C2311yescharacteristic
96C2×Q8×C73C2311yescharacteristic
97C2×Q8×C73C2311yescharacteristic
98C2×D4×C73C2311yescharacteristic
99C2×D4×C73C2311yescharacteristic
100Q16×C73—41no—
101SD16×C73—22no—
102SD16×C73—22no—
103D8×C73—41no—
104C2×C8×C73C2311yescharacteristic
105C2×C8×C73C2311yescharacteristic
106C22⋊C4×C73—21no—
107C22⋊C4×C73—21no—
108C22⋊C4×C73—21no—
109C22⋊C4×C73—21no—
110C42×C73C2311yescharacteristic
111C23×C73—21no—
112C23×C73—21no—
113C22×D73—21no—
114Q8×C73—21no—
115Q8×C73—21no—
116Q8×C73—21no—
117Q8×C73—21no—
118D4×C73—21no—
119D4×C73—21no—
120D4×C73—21no—
121D4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73C2×D411yescharacteristic
125C2×C4×C73C2×D411yescharacteristic
126C2×C4×C73C2411yescharacteristic
127C22⋊D73—42no—
128C22⋊D73—81no—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—42no—
133C2×Dic73—81no—
134C2×Dic73C2×D411yescharacteristic
135C2×Dic73C2×D411yescharacteristic
136C2×Dic73C2×D411yescharacteristic
137C2×Dic73C2×D411yescharacteristic
138D292—21no—
139D292—21no—
140C4×D73—81no—
141Dic146—22no—
142Dic146—21no—
143Dic146—21no—
144C8×C73—21no—
145C8×C73#4112yes—
146#10596831—21no—
147#10596831—21no—
148C22×C73—41no—
149C22×C73—41no—
150C22×C73—41no—
151C22×C73—41no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73C22×D411yescharacteristic
155C2×D73—41no—
156C2×D73—41no—
157C2×D73—41no—
158C4×C73—21no—
159C4×C73—21no—
160C4×C73—41no—
161C4×C73—41no—
162C4×C73C2×#4111yescharacteristic
163C4×C73H(5,𝔽2)11yescharacteristic
164Dic73—21no—
165Dic73—21no—
166Dic73—21no—
167Dic73—41no—
168Dic73—41no—
169Dic73—41no—
170Dic73#13512yes—
171C2×C73—81no—
172C2×C73—81no—
173C2×C73#55011yescharacteristic
174C2×C73C2×#13511yescharacteristic
175C2×C73#57711yescharacteristic
176D73—81no—
177#3394—731nomaximal, Sylow
178C73#339411yescharacteristic, complemented, Sylow
179#559—731no—
180#556—731no—
181#495—731no—
182#495D7311yescharacteristic, complemented
183#492—731no—
184#464—731no—
185#464—731no—
186#463—731no—
187#463—731no—
188#462—731no—
189#459—731no—
190C8×Q8—731no—
191C4×SD16—731no—
192C4×SD16—731no—
193C4×SD16—731no—
194C2×Q16—731no—
195C2×Q16C2×D7311yescharacteristic
196C2×SD16—731no—
197C2×SD16—731no—
198C2×SD16—731no—
199C2×SD16C2×D7311yescharacteristic
200C2×SD16C2×D7311yescharacteristic
201C2×D8—731no—
202C2×D8C2×D7311yescharacteristic
203C4⋊Q8—731no—
204#127—731no—
205#126—1461no—
206#126—1461no—
207#124—731no—
208#124—731no—
209#124—1461no—
210#124C2×D7311yescharacteristic
211#124C2×D7311yescharacteristic
212#123—1461no—
213#123—1461no—
214C22⋊Q8—1461no—
215C4×Q8—731no—
216C4×Q8—731no—
217C4×Q8—731no—
218C4×Q8—731no—
219C4×D4—731no—
220C4×D4—731no—
221C4×D4—731no—
222C4×D4—1461no—
223#117—1461no—
224#106—731no—
225C4⋊C8—731no—
226C4⋊C8—731no—
227C4⋊C8—731no—
228#103—731no—
229#103—731no—
230#103—731no—
231#102—731no—
232#102—731no—
233#102—731no—
234C4×C8—731no—
235C4×C8—731no—
236C4×C8C2×D7311yescharacteristic
237C2×Q8—731no—
238C2×Q8—731no—
239C2×Q8C22×D7311yescharacteristic
240C2×Q8C22×D7311yescharacteristic
241C2×D4—731no—
242C2×D4—1461no—
243C2×D4—1461no—
244C2×D4C22×D7311yescharacteristic
245C2×D4C22×D7311yescharacteristic
246C22×C4—1461no—
247C22×C4—1461no—
248C22×C4—1461no—
249Q16—41no—
250Q16—2921no—
251SD16—22no—
252SD16—22no—
253SD16—2921no—
254SD16—2921no—
255SD16—1462no—
256D8—41no—
257D8—2921no—
258C2×C8—731no—
259C2×C8—731no—
260C2×C8C22×D7311yescharacteristic
261C2×C8C22×D7311yescharacteristic
262C4⋊C4—731no—
263C4⋊C4—731no—
264C4⋊C4—731no—
265C4⋊C4—731no—
266C4⋊C4—731no—
267C4⋊C4—1461no—
268C4⋊C4—1461no—
269C4⋊C4—1461no—
270C4⋊C4—1461no—
271C4⋊C4—1461no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—1461no—
277C22⋊C4—1461no—
278C22⋊C4—1461no—
279C22⋊C4—1461no—
280C22⋊C4—1461no—
281C22⋊C4—1461no—
282C22⋊C4—1461no—
283C42—731no—
284C42—731no—
285C42—1461no—
286C42—1461no—
287C42—1461no—
288C42C22×D7311yescharacteristic
289C23—21no—
290C23—21no—
291C23—1461no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—1462no—
297Q8—1461no—
298Q8—1461no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—2922no—
304D4—5841no—
305D4—1461no—
306D4—1461no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—2922no—
310C2×C4—5841no—
311C2×C4—5841no—
312C2×C4—731no—
313C2×C4—731no—
314C2×C4—731no—
315C2×C4—731no—
316C2×C4—1461no—
317C2×C4—1461no—
318C2×C4—1461no—
319C2×C4D4×D7311yescharacteristic
320C2×C4D4×D7311yescharacteristic
321C2×C4C23×D7311yescharacteristic
322C8—21no—
323C8—1461no—
324C8—1461no—
325C8#1192402712yes—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—2921no—
333C22—2921no—
334C22—2921no—
335C22C2×D4×D7311yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—2921no—
341C4—2921no—
342C4—2921no—
343C4—732no—
344C4—1461no—
345C4—1461no—
346C4—1461no—
347C4C2×#1192402711yescharacteristic
348C4#1455663611yescharacteristic
349C2—81no—
350C2—81no—
351C2—5841no—
352C2#1798925711yescharacteristic
353C2#135×D7311yescharacteristic
354C2#1798939411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#495×C73C2
socleC22×C73C22×D4
hypercenter#495D73
hypocenterC73#3394
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #17989319C2semidirect
2. #17989306C2semidirect
3. #17988968C2semidirect
4. #17988958C2semidirect
5. #17988811C2semidirect
6. #17988806C2semidirect
7. #17988800C2semidirect
8. #17988799C2semidirect
9. #17988795C2semidirect
11. C8×Dic146C2semidirect
12. C4×#11924017C2semidirect
13. SD16×Dic73C2semidirect
14. SD16×Dic73C2semidirect
15. #495×C73C2semidirect
178. C73#3394semidirect
182. #495D73semidirect