Finite Group Databasebeta

← #22621344

Subgroups — #22621344

Order 9344.

358 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989208C211yesmaximal, characteristic, complemented
2#17989192C211yesmaximal, characteristic, complemented
3#17988895C211yesmaximal, characteristic, complemented
4#17988888C211yesmaximal, characteristic, complemented
5#17988878C211yesmaximal, characteristic, complemented
6#17988868C211yesmaximal, characteristic, complemented
7#17988840C211yesmaximal, characteristic, complemented
8#17988833C211yesmaximal, characteristic, complemented
9#17988823C211yesmaximal, characteristic, complemented
10#17988816C211yesmaximal, characteristic, complemented
11#17988803C211yesmaximal, characteristic, complemented
12#17988803C211yesmaximal, characteristic, complemented
13#17988788C211yesmaximal, characteristic, complemented
14#17988783C211yesmaximal, characteristic, complemented
15#424×C73C211yesmaximal, characteristic, complemented
16C2×#11924017C2211yescharacteristic
17C2×#11924017C2211yescharacteristic
18C2×D584C2211yescharacteristic
19C2×D584C2211yescharacteristic
20#14556591C2211yescharacteristic
21#14556588C2211yescharacteristic
22#14556586—21no—
23#14556583C2211yescharacteristic
24#14556579C2211yescharacteristic
25#14556577—21no—
26#14556576—21no—
27#14556576—21no—
28#14556573—21no—
29#14556570C2211yescharacteristic
30#14556569—21no—
31#14556565C2211yescharacteristic
32#14556565C2211yescharacteristic
33#14556565C2211yescharacteristic
34#14556564—21no—
35#14556564—21no—
36C4×Dic146C2211yescharacteristic
37C4×D292C2211yescharacteristic
38C4×D292C2211yescharacteristic
39C4×D292C2211yescharacteristic
40#14556525C2211yescharacteristic
41#14556525C2211yescharacteristic
42#14556523C2211yescharacteristic
43#14556523C2211yescharacteristic
44#14556516C2211yescharacteristic
45#14556516C2211yescharacteristic
46#14556513C2211yescharacteristic
47#14556513C2211yescharacteristic
48#14556513C2211yescharacteristic
49#14556513C2211yescharacteristic
50#14556513C2211yescharacteristic
51#14556513C2211yescharacteristic
52C2×M16×C73C2211yescharacteristic
53C22×C8×C73C2211yescharacteristic
54#117×C73C2211yescharacteristic
55C4⋊C8×C73C2211yescharacteristic
56C4⋊C8×C73C2211yescharacteristic
57C4⋊C8×C73C2211yescharacteristic
58C4⋊C8×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146C2311yescharacteristic
61C2×D292—21no—
62C2×D292—21no—
63C2×D292C2311yescharacteristic
64C2×D292C2311yescharacteristic
65C2×D292C2311yescharacteristic
66C2×C22⋊D73—21no—
67C2×C22⋊D73—21no—
68C2×C22⋊D73—21no—
69C2×C4×D73—21no—
70C2×C4×D73—21no—
71C2×C4×D73—21no—
72#11924017—41no—
73#11924017—41no—
74D584—41no—
75D584—41no—
76C4⋊Dic73—21no—
77C4⋊Dic73C2311yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79C4⋊Dic73C2311yescharacteristic
80C4⋊Dic73C2311yescharacteristic
81#11924007—21no—
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85C22⋊Dic73—21no—
86#11924005—21no—
87#11924005—21no—
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005—21no—
93#11924005—21no—
94C4×Dic73—21no—
95C22×C4×C73C2311yescharacteristic
96M16×C73—41no—
97C2×C8×C73—41no—
98C2×C8×C73C2311yescharacteristic
99C2×C8×C73C2311yescharacteristic
100C2×C8×C73C2311yescharacteristic
101C2×C8×C73C2311yescharacteristic
102C4⋊C4×C73D411yescharacteristic
103C4⋊C4×C73D411yescharacteristic
104C22⋊C4×C73D411yescharacteristic
105C22⋊C4×C73D411yescharacteristic
106C42×C73C2311yescharacteristic
107C42×C73C2311yescharacteristic
108C23×C73C2×D411yescharacteristic
109C22×D73—21no—
110C22×D73—21no—
111C22×D73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73C2×D411yescharacteristic
115C2×C4×C73C2×D411yescharacteristic
116C2×C4×C73C2×D411yescharacteristic
117C2×C4×C73C2×D411yescharacteristic
118C2×C4×C73C2×D411yescharacteristic
119C2×C4×C73C2411yescharacteristic
120C22⋊D73—81no—
121C22⋊D73—81no—
122C22⋊D73—81no—
123C2×Dic73—21no—
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128D292—21no—
129D292—21no—
130D292—21no—
131D292—21no—
132D292—21no—
133D292—21no—
134D292—81no—
135D292—81no—
136C4×D73—81no—
137C4×D73—81no—
138C4×D73—81no—
139Dic146—21no—
140Dic146—21no—
141Dic146—81no—
142C8×C73—21no—
143C8×C73—21no—
144C8×C73—21no—
145C8×C73—21no—
146C22×C73—21no—
147C22×C73—21no—
148C22×C73—21no—
149C22×C73C22×D411yescharacteristic
150C2×D73—41no—
151C2×D73—41no—
152C2×D73—41no—
153C2×D73—41no—
154C2×D73—41no—
155C2×D73—41no—
156C2×D73—41no—
157C2×D73—41no—
158C2×D73—41no—
159C4×C73—21no—
160C4×C73—21no—
161C4×C73—21no—
162C4×C73—21no—
163C4×C73—21no—
164C4×C73H(5,𝔽2)11yescharacteristic
165C4×C732−1+411yescharacteristic
166Dic73—41no—
167Dic73—41no—
168Dic73—41no—
169Dic73—41no—
170Dic73—41no—
171C2×C73—41no—
172C2×C73#53711yescharacteristic
173C2×C73#57611yescharacteristic
174C2×C73#57711yescharacteristic
175D73—81no—
176D73—81no—
177D73—81no—
178#3257—731nomaximal, Sylow
179C73#325711yescharacteristic, complemented, Sylow
180#542—731no—
181#540—731no—
182#479—731no—
183#478—731no—
184#476—731no—
185#474—731no—
186#469—731no—
187#468—731no—
188#466—731no—
189#465—731no—
190#463—731no—
191#463—731no—
192#460—731no—
193#459—731no—
194#424D7311yescharacteristic, complemented
195C2×SD16—731no—
196C2×SD16—731no—
197C2×D8—731no—
198C2×D8—731no—
199C2×M16C2×D7311yescharacteristic
200C22×C8C2×D7311yescharacteristic
201C4⋊Q8—731no—
202#127—731no—
203#126—1461no—
204#125—731no—
205#124—731no—
206#124—1461no—
207#123—1461no—
208#123—1461no—
209#123—1461no—
210C22⋊Q8—731no—
211C22⋊Q8—1461no—
212#121—731no—
213#121—731no—
214#121—731no—
215#121—1461no—
216#121—1461no—
217C4×Q8—731no—
218C4×D4—731no—
219C4×D4—731no—
220C4×D4—731no—
221#117C2×D7311yescharacteristic
222#107—731no—
223#107—731no—
224#106—731no—
225#106—731no—
226C4⋊C8C2×D7311yescharacteristic
227C4⋊C8C2×D7311yescharacteristic
228C4⋊C8C2×D7311yescharacteristic
229C4⋊C8C2×D7311yescharacteristic
230#103—731no—
231#103—731no—
232#102—731no—
233#102—731no—
234#102—731no—
235#102—731no—
236#102—731no—
237#102—731no—
238C2×Q8—731no—
239C2×Q8—1461no—
240C2×D4—731no—
241C2×D4—731no—
242C2×D4—731no—
243C2×D4—1461no—
244C2×D4—1461no—
245C2×D4—1461no—
246C2×D4—1461no—
247C2×D4—1461no—
248C22×C4—1461no—
249C22×C4—1461no—
250C22×C4—1461no—
251C22×C4C22×D7311yescharacteristic
252SD16—2921no—
253SD16—2921no—
254D8—2921no—
255D8—2921no—
256M16—41no—
257C2×C8—41no—
258C2×C8C22×D7311yescharacteristic
259C2×C8C22×D7311yescharacteristic
260C2×C8C22×D7311yescharacteristic
261C2×C8C22×D7311yescharacteristic
262C4⋊C4—731no—
263C4⋊C4—731no—
264C4⋊C4—731no—
265C4⋊C4—731no—
266C4⋊C4—1461no—
267C4⋊C4—1461no—
268C4⋊C4—1461no—
269C4⋊C4—1461no—
270C4⋊C4—1461no—
271C4⋊C4D29211yescharacteristic
272C4⋊C4D29211yescharacteristic
273C22⋊C4—1461no—
274C22⋊C4—1461no—
275C22⋊C4—1461no—
276C22⋊C4—1461no—
277C22⋊C4—1461no—
278C22⋊C4—1461no—
279C22⋊C4—1461no—
280C22⋊C4—1461no—
281C22⋊C4—1461no—
282C22⋊C4D29211yescharacteristic
283C22⋊C4D29211yescharacteristic
284C42—1461no—
285C42C22×D7311yescharacteristic
286C42C22×D7311yescharacteristic
287C23—1461no—
288C23—1461no—
289C23—1461no—
290C23C2×D29211yescharacteristic
291Q8—5841no—
292Q8—1461no—
293Q8—1461no—
294D4—5841no—
295D4—5841no—
296D4—5841no—
297D4—5841no—
298D4—5841no—
299D4—1461no—
300D4—1461no—
301D4—1461no—
302D4—1461no—
303D4—1461no—
304D4—1461no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—5841no—
308C2×C4—5841no—
309C2×C4—5841no—
310C2×C4—1461no—
311C2×C4—1461no—
312C2×C4—1461no—
313C2×C4—1461no—
314C2×C4—1461no—
315C2×C4C2×D29211yescharacteristic
316C2×C4C2×D29211yescharacteristic
317C2×C4C2×D29211yescharacteristic
318C2×C4C2×D29211yescharacteristic
319C2×C4C2×D29211yescharacteristic
320C2×C4C23×D7311yescharacteristic
321C8—21no—
322C8—21no—
323C8—21no—
324C8—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—2921no—
329C22—2921no—
330C22—2921no—
331C22—2921no—
332C22—2921no—
333C22—2921no—
334C22—2921no—
335C22—2921no—
336C22—2921no—
337C22C22×D29211yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—2921no—
344C4—2921no—
345C4—2921no—
346C4—2921no—
347C4—2921no—
348C4#1455663611yescharacteristic
349C4#1455663911yescharacteristic
350C2—41no—
351C2—5841no—
352C2—5841no—
353C2—5841no—
354C2#1798916811yescharacteristic
355C2#1798939211yescharacteristic
356C2#1798939911yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#424×C73C2
socleC22×C73C22×D4
hypercenter#424D73
hypocenterC73#3257
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #17989208C2semidirect
2. #17989192C2semidirect
3. #17988895C2semidirect
4. #17988888C2semidirect
5. #17988878C2semidirect
6. #17988868C2semidirect
7. #17988840C2semidirect
8. #17988833C2semidirect
9. #17988823C2semidirect
10. #17988816C2semidirect
11. #17988803C2semidirect
12. #17988803C2semidirect
13. #17988788C2semidirect
14. #17988783C2semidirect
15. #424×C73C2semidirect
179. C73#3257semidirect
194. #424D73semidirect