Finite Group Databasebeta

← #22617633

Subgroups — #22617633

Order 9344.

472 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17988525C211yesmaximal, characteristic, complemented
2#17988509C211yesmaximal, characteristic, complemented
3#17988507C211yesmaximal, characteristic, complemented
4#17988500C211yesmaximal, characteristic, complemented
5#17988499C211yesmaximal, characteristic, complemented
6#17988487C211yesmaximal, characteristic
7#17988473C211yesmaximal, characteristic, complemented
8#17988472C211yesmaximal, characteristic, complemented
9#17988464C211yesmaximal, characteristic
10#17988463C211yesmaximal, characteristic
11#17988462C211yesmaximal, characteristic, complemented
12#17988458C211yesmaximal, characteristic, complemented
13#17988445C211yesmaximal, characteristic, complemented
14#17988444C211yesmaximal, characteristic, complemented
15#396×C73C211yesmaximal, characteristic, complemented
16C22×Dic146C2211yescharacteristic
17C22×C22⋊D73C2211yescharacteristic
18C23×Dic73C2211yescharacteristic
19C22×C4×D73C2211yescharacteristic
20C2×C4⋊Dic73C2211yescharacteristic
21C2×C4⋊Dic73C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×C22⋊Dic73C2211yescharacteristic
26C2×C22⋊Dic73C2211yescharacteristic
27C2×#11924005C2211yescharacteristic
28C2×#11924005C2211yescharacteristic
29C2×#11924005C2211yescharacteristic
30C2×#11924005C2211yescharacteristic
31C2×#11924005C2211yescharacteristic
32C2×C4×Dic73C2211yescharacteristic
33#14556498C2211yescharacteristic
34#14556498C2211yescharacteristic
35#14556498C2211yescharacteristic
36#14556498C2211yescharacteristic
37#14556498C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44C2×C4⋊C4×C73C2211yescharacteristic
45C2×C4⋊C4×C73C2211yescharacteristic
46C2×C4⋊C4×C73C2211yescharacteristic
47C2×C22⋊C4×C73C2211yescharacteristic
48C2×C22⋊C4×C73C2211yescharacteristic
49C2×C22⋊C4×C73C2211yescharacteristic
50#95×C73C2211yescharacteristic
51C23×D73C2311yescharacteristic
52C2×Dic146—41no—
53C2×Dic146—41no—
54C2×Dic146—41no—
55C2×C22⋊D73—41no—
56C2×C22⋊D73—41no—
57C2×C22⋊D73Q814yescomplemented
58C22×Dic73—22no—
59C22×Dic73—41no—
60C22×Dic73—41no—
61C22×Dic73C2311yescharacteristic
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C22×Dic73C2311yescharacteristic
65C22×Dic73C2311yescharacteristic
66C22×Dic73C2311yescharacteristic
67C22×Dic73C2311yescharacteristic
68C2×C4×D73—22no—
69C2×C4×D73—41no—
70C2×C4×D73—41no—
71C4⋊Dic73—22no—
72C4⋊Dic73—41no—
73#11924007—41no—
74#11924007—41no—
75#11924007—41no—
76C22⋊Dic73—41no—
77C22⋊Dic73—41no—
78#11924005—22no—
79#11924005—41no—
80#11924005—41no—
81#11924005—41no—
82#11924005—41no—
83C4×Dic73—41no—
84C24×C73C2311yescharacteristic
85C22×C4×C73C2311yescharacteristic
86C22×C4×C73C2311yescharacteristic
87C22×C4×C73C2311yescharacteristic
88C22×C4×C73C2311yescharacteristic
89C22×C4×C73C2311yescharacteristic
90C22×C4×C73C2311yescharacteristic
91C4⋊C4×C73—22no—
92C4⋊C4×C73—41no—
93C4⋊C4×C73—41no—
94C22⋊C4×C73—22no—
95C22⋊C4×C73—41no—
96C22⋊C4×C73—41no—
97C23×C73—21no—
98C23×C73—21no—
99C23×C73—21no—
100C23×C73—21no—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73C2×Q812yes—
104C23×C73C2411yescharacteristic
105C22×D73—21no—
106C22×D73—21no—
107C22×D73—21no—
108C22×D73—21no—
109C22×D73—21no—
110C22×D73—21no—
111C22×D73C2×Q812yes—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73#4112yes—
130C22⋊D73—44no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—21no—
138C2×Dic73—21no—
139C2×Dic73—21no—
140C2×Dic73—21no—
141C2×Dic73—21no—
142C2×Dic73—21no—
143C2×Dic73—21no—
144C2×Dic73—21no—
145C2×Dic73—21no—
146C2×Dic73—21no—
147C2×Dic73—21no—
148C2×Dic73—21no—
149C2×Dic73—21no—
150C2×Dic73—44no—
151C2×Dic73C2×Q812yes—
152C2×Dic73#4112yes—
153C4×D73—44no—
154Dic146—44no—
155C22×C73—22no—
156C22×C73—22no—
157C22×C73—22no—
158C22×C73—41no—
159C22×C73—41no—
160C22×C73—41no—
161C22×C73—41no—
162C22×C73C22×Q811yescharacteristic
163C22×C73C2×#4111yescharacteristic
164C22×C73C2×#4111yescharacteristic
165C22×C73H(5,𝔽2)11yescharacteristic
166C22×C73H(5,𝔽2)11yescharacteristic
167C22×C73H(5,𝔽2)11yescharacteristic
168C22×C73H(5,𝔽2)11yescharacteristic
169C2×D73—22no—
170C2×D73—22no—
171C2×D73—22no—
172C2×D73—41no—
173C2×D73—41no—
174C2×D73—41no—
175C2×D73—41no—
176C4×C73—22no—
177C4×C73—41no—
178C4×C73—41no—
179C4×C73—41no—
180C4×C73—41no—
181C4×C73—41no—
182Dic73—22no—
183Dic73—22no—
184Dic73—41no—
185Dic73—41no—
186Dic73—41no—
187Dic73—41no—
188Dic73—41no—
189C2×C73—42no—
190C2×C73#53811yescharacteristic
191C2×C73#53811yescharacteristic
192C2×C73#54311yescharacteristic
193C2×C73#55411yescharacteristic
194C2×C73#55411yescharacteristic
195C2×C73#55511yescharacteristic
196C2×C73#56011yescharacteristic
197D73—42no—
198#2784—731nomaximal, Sylow
199C73#278411yescharacteristic, complemented, Sylow
200#400—731no—
201#396—731no—
202#396D7311yescharacteristic, complemented
203#395—731no—
204#393—731no—
205#393—731no—
206#390—731no—
207#387—731no—
208#387—731no—
209#386—731no—
210#386—731no—
211#385—731no—
212#385—731no—
213#380—731no—
214#380—731no—
215C22×Q8—731no—
216C22×D4—731no—
217C23×C4—731no—
218C23×C4—731no—
219C2×C4⋊C4—731no—
220C2×C4⋊C4—731no—
221C2×C4⋊C4—731no—
222C2×C4⋊C4—731no—
223C2×C4⋊C4—731no—
224C2×C4⋊C4C2×D7311yescharacteristic
225C2×C4⋊C4C2×D7311yescharacteristic
226C2×C4⋊C4C2×D7311yescharacteristic
227C2×C22⋊C4—731no—
228C2×C22⋊C4—731no—
229C2×C22⋊C4—731no—
230C2×C22⋊C4—731no—
231C2×C22⋊C4—731no—
232C2×C22⋊C4—731no—
233C2×C22⋊C4—731no—
234C2×C22⋊C4C2×D7311yescharacteristic
235C2×C22⋊C4C2×D7311yescharacteristic
236C2×C22⋊C4C2×D7311yescharacteristic
237C2×C42—731no—
238#95—731no—
239#95—731no—
240#95—731no—
241#95—731no—
242#95—731no—
243#95—731no—
244#95—731no—
245#95—731no—
246#95—731no—
247#95—731no—
248#95—731no—
249#95C2×D7311yescharacteristic
250C24—731no—
251C24C22×D7311yescharacteristic
252C2×Q8—2921no—
253C2×Q8—2921no—
254C2×Q8—2921no—
255C2×D4—2921no—
256C2×D4—2921no—
257C2×D4—734no—
258C22×C4—2921no—
259C22×C4—2921no—
260C22×C4—2921no—
261C22×C4—2921no—
262C22×C4—731no—
263C22×C4—731no—
264C22×C4—731no—
265C22×C4—731no—
266C22×C4—731no—
267C22×C4—731no—
268C22×C4—731no—
269C22×C4—1462no—
270C22×C4—1462no—
271C22×C4C22×D7311yescharacteristic
272C22×C4C22×D7311yescharacteristic
273C22×C4C22×D7311yescharacteristic
274C22×C4C22×D7311yescharacteristic
275C22×C4C22×D7311yescharacteristic
276C22×C4C22×D7311yescharacteristic
277C4⋊C4—22no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—2921no—
281C4⋊C4—2921no—
282C4⋊C4—2921no—
283C4⋊C4—2921no—
284C4⋊C4—1462no—
285C22⋊C4—22no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—2921no—
289C22⋊C4—2921no—
290C22⋊C4—2921no—
291C22⋊C4—2921no—
292C22⋊C4—2921no—
293C22⋊C4—2921no—
294C22⋊C4—1462no—
295C42—2921no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—732no—
303C23—1461no—
304C23—1461no—
305C23—1461no—
306C23—1461no—
307C23—1461no—
308C23—1461no—
309C23Q8×D7312yes—
310C23C23×D7311yescharacteristic
311Q8—2924no—
312D4—2924no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—2924no—
331C2×C4—2924no—
332C2×C4—732no—
333C2×C4—732no—
334C2×C4—1461no—
335C2×C4—1461no—
336C2×C4—1461no—
337C2×C4—1461no—
338C2×C4—1461no—
339C2×C4—1461no—
340C2×C4—1461no—
341C2×C4—1461no—
342C2×C4—1461no—
343C2×C4—1461no—
344C2×C4—1461no—
345C2×C4—1461no—
346C2×C4—1461no—
347C2×C4—1461no—
348C2×C4—1461no—
349C2×C4—1461no—
350C2×C4—1461no—
351C2×C4—1461no—
352C2×C4—1461no—
353C2×C4#1192402712yes—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—2921no—
362C22—2921no—
363C22—2921no—
364C22—2921no—
365C22—1462no—
366C22—1462no—
367C22—1462no—
368C22C2×Q8×D7311yescharacteristic
369C22#41×D7311yescharacteristic
370C22C2×#1192402711yescharacteristic
371C22#1455663611yescharacteristic
372C22#1455663611yescharacteristic
373C22#1455663711yescharacteristic
374C22#1455663711yescharacteristic
375C4—22no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—2921no—
382C4—2921no—
383C4—2921no—
384C4—2921no—
385C4—2921no—
386C4—1462no—
387C4—1462no—
388C2—42no—
389C2—2922no—
390C2#1798917411yescharacteristic
391C2#1798917611yescharacteristic
392C2#1798921211yescharacteristic
393C2#1798929111yescharacteristic
394C2#1798929511yescharacteristic
395C2#1798930111yescharacteristic
396C2#1798932511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#396×C73C2
hypercenter#396D73
hypocenterC73#2784
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. #17988525C2semidirect
2. #17988509C2semidirect
3. #17988507C2semidirect
4. #17988500C2semidirect
5. #17988499C2semidirect
7. #17988473C2semidirect
8. #17988472C2semidirect
11. #17988462C2semidirect
12. #17988458C2semidirect
13. #17988445C2semidirect
14. #17988444C2semidirect
15. #396×C73C2semidirect
57. C2×C22⋊D73Q8semidirect
199. C73#2784semidirect
202. #396D73semidirect