Finite Group Databasebeta

← #22617652

Subgroups — #22617652

Order 9344.

434 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17988517C211yesmaximal, characteristic, complemented
2#17988515C211yesmaximal, characteristic, complemented
3#17988515C211yesmaximal, characteristic, complemented
4#17988512C211yesmaximal, characteristic, complemented
5#17988510C211yesmaximal, characteristic, complemented
6#17988490C211yesmaximal, characteristic
7#17988481C211yesmaximal, characteristic, complemented
8#17988475C211yesmaximal, characteristic, complemented
9#17988473C211yesmaximal, characteristic, complemented
10#17988470C211yesmaximal, characteristic, complemented
11#17988470C211yesmaximal, characteristic, complemented
12#17988467C211yesmaximal, characteristic
13#17988462C211yesmaximal, characteristic, complemented
14#17988445C211yesmaximal, characteristic, complemented
15#394×C73C211yesmaximal, characteristic
16C23×Dic73C2211yescharacteristic
17C2×C4⋊Dic73C2211yescharacteristic
18C2×C4⋊Dic73C2211yescharacteristic
19C2×C4⋊Dic73C2211yescharacteristic
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×C22⋊Dic73C2211yescharacteristic
25C2×C22⋊Dic73C2211yescharacteristic
26C2×C22⋊Dic73C2211yescharacteristic
27C2×C22⋊Dic73C2211yescharacteristic
28C2×C22⋊Dic73C2211yescharacteristic
29C2×C22⋊Dic73C2211yescharacteristic
30C2×C22⋊Dic73C2211yescharacteristic
31C2×C4×Dic73C2211yescharacteristic
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
44C22×D4×C73C2211yescharacteristic
45C2×C4⋊C4×C73C2211yescharacteristic
46C2×C22⋊C4×C73C2211yescharacteristic
47C2×C22⋊C4×C73C2211yescharacteristic
48C2×C22⋊C4×C73C2211yescharacteristic
49C2×C22⋊C4×C73C2211yescharacteristic
50#95×C73C2211yescharacteristic
51C22×Dic73—22no—
52C22×Dic73—41no—
53C22×Dic73—41no—
54C22×Dic73C2311yescharacteristic
55C22×Dic73C2311yescharacteristic
56C22×Dic73C2311yescharacteristic
57C22×Dic73C2311yescharacteristic
58C22×Dic73C2311yescharacteristic
59C22×Dic73C2311yescharacteristic
60C22×Dic73C2311yescharacteristic
61C22×Dic73C2311yescharacteristic
62C4⋊Dic73—22no—
63C4⋊Dic73—22no—
64C4⋊Dic73—41no—
65#11924007—41no—
66#11924007—41no—
67#11924007—41no—
68#11924007—41no—
69C22⋊Dic73—22no—
70C22⋊Dic73—22no—
71C22⋊Dic73—41no—
72C22⋊Dic73—41no—
73C22⋊Dic73—41no—
74C22⋊Dic73—41no—
75C22⋊Dic73—41no—
76C4×Dic73—41no—
77C4×Dic73—41no—
78C24×C73C2311yescharacteristic
79C24×C73C2311yescharacteristic
80C2×D4×C73—22no—
81C2×D4×C73—22no—
82C2×D4×C73—41no—
83C22×C4×C73C2311yescharacteristic
84C22×C4×C73C2311yescharacteristic
85C22×C4×C73C2311yescharacteristic
86C22×C4×C73C2311yescharacteristic
87C22×C4×C73C2311yescharacteristic
88C4⋊C4×C73—22no—
89C22⋊C4×C73—22no—
90C22⋊C4×C73—41no—
91C22⋊C4×C73—41no—
92C22⋊C4×C73—41no—
93C23×C73—21no—
94C23×C73—21no—
95C23×C73—21no—
96C23×C73—21no—
97C23×C73—21no—
98C23×C73—21no—
99C23×C73—21no—
100C23×C73—21no—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73—21no—
106C23×C73#4112yes—
107C23×C73C2411yescharacteristic
108D4×C73—44no—
109C2×C4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
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#4112yes—
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73—21no—
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—44no—
148C2×Dic73#4112yes—
149C22×C73—22no—
150C22×C73—22no—
151C22×C73—22no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73—41no—
155C22×C73—41no—
156C22×C73—41no—
157C22×C73—41no—
158C22×C73—41no—
159C22×C73—41no—
160C22×C73—41no—
161C22×C73—41no—
162C22×C73—41no—
163C22×C73C2×#4111yescharacteristic
164C22×C73C2×#4111yescharacteristic
165C22×C73C2×#4111yescharacteristic
166C22×C73H(5,𝔽2)11yescharacteristic
167C22×C73H(5,𝔽2)11yescharacteristic
168C22×C73H(5,𝔽2)11yescharacteristic
169C22×C732−1+411yescharacteristic
170C4×C73—22no—
171C4×C73—41no—
172C4×C73—41no—
173C4×C73—41no—
174C4×C73—41no—
175Dic73—22no—
176Dic73—41no—
177Dic73—41no—
178Dic73—41no—
179Dic73—41no—
180Dic73—41no—
181Dic73—41no—
182Dic73—41no—
183C2×C73—42no—
184C2×C73—81no—
185C2×C73#53811yescharacteristic
186C2×C73#53911yescharacteristic
187C2×C73#54011yescharacteristic
188C2×C73#55111yescharacteristic
189C2×C73#55311yescharacteristic
190C2×C73#55611yescharacteristic
191C2×C73#56211yescharacteristic
192#2786—731nomaximal, Sylow
193C73#278611yescharacteristic, complemented, Sylow
194#398—731no—
195#397—731no—
196#397—731no—
197#397—731no—
198#396—731no—
199#394D7311yescharacteristic
200#390—731no—
201#388—731no—
202#388—731no—
203#387—731no—
204#387—731no—
205#387—731no—
206#386—731no—
207#385—731no—
208#380—731no—
209C22×D4C2×D7311yescharacteristic
210C23×C4—731no—
211C2×C4⋊C4—731no—
212C2×C4⋊C4—731no—
213C2×C4⋊C4—731no—
214C2×C4⋊C4—731no—
215C2×C4⋊C4—731no—
216C2×C4⋊C4—731no—
217C2×C4⋊C4—731no—
218C2×C4⋊C4C2×D7311yescharacteristic
219C2×C22⋊C4—731no—
220C2×C22⋊C4—731no—
221C2×C22⋊C4—731no—
222C2×C22⋊C4—731no—
223C2×C22⋊C4—731no—
224C2×C22⋊C4—731no—
225C2×C22⋊C4—731no—
226C2×C22⋊C4C2×D7311yescharacteristic
227C2×C22⋊C4C2×D7311yescharacteristic
228C2×C22⋊C4C2×D7311yescharacteristic
229C2×C22⋊C4C2×D7311yescharacteristic
230C2×C42—731no—
231C2×C42—731no—
232#95—731no—
233#95—731no—
234#95—731no—
235#95—731no—
236#95—731no—
237#95—731no—
238#95—731no—
239#95—731no—
240#95—731no—
241#95—731no—
242#95—731no—
243#95C2×D7311yescharacteristic
244C24C22×D7311yescharacteristic
245C24C22×D7311yescharacteristic
246C2×D4—22no—
247C2×D4—22no—
248C2×D4—41no—
249C22×C4—2921no—
250C22×C4—2921no—
251C22×C4—731no—
252C22×C4—731no—
253C22×C4—731no—
254C22×C4—731no—
255C22×C4—731no—
256C22×C4—731no—
257C22×C4—731no—
258C22×C4—731no—
259C22×C4—1462no—
260C22×C4C22×D7311yescharacteristic
261C22×C4C22×D7311yescharacteristic
262C22×C4C22×D7311yescharacteristic
263C22×C4C22×D7311yescharacteristic
264C22×C4C22×D7311yescharacteristic
265C4⋊C4—22no—
266C4⋊C4—2921no—
267C4⋊C4—2921no—
268C4⋊C4—2921no—
269C4⋊C4—2921no—
270C4⋊C4—2921no—
271C4⋊C4—1462no—
272C4⋊C4—1462no—
273C22⋊C4—22no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—2921no—
278C22⋊C4—2921no—
279C22⋊C4—2921no—
280C22⋊C4—2921no—
281C22⋊C4—2921no—
282C22⋊C4—1462no—
283C22⋊C4—1462no—
284C42—2921no—
285C42—2921no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23#1192402712yes—
300C23C23×D7311yescharacteristic
301D4—44no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—2924no—
317C2×C4—732no—
318C2×C4—1461no—
319C2×C4—1461no—
320C2×C4—1461no—
321C2×C4—1461no—
322C2×C4—1461no—
323C2×C4—1461no—
324C2×C4—1461no—
325C2×C4—1461no—
326C2×C4—1461no—
327C2×C4—1461no—
328C2×C4—1461no—
329C2×C4—1461no—
330C2×C4—1461no—
331C2×C4—1461no—
332C2×C4—1461no—
333C2×C4—1461no—
334C2×C4—1461no—
335C2×C4—1461no—
336C2×C4—1461no—
337C2×C4—1461no—
338C2×C4—1461no—
339C2×C4—1461no—
340C2×C4—1461no—
341C2×C4#1192402712yes—
342C22—22no—
343C22—22no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22#41×D7311yescharacteristic
357C22C2×#1192402711yescharacteristic
358C22C2×#1192402711yescharacteristic
359C22#1455663611yescharacteristic
360C22#1455663611yescharacteristic
361C22#1455663711yescharacteristic
362C22#1455663811yescharacteristic
363C4—22no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—2921no—
369C4—2921no—
370C4—2921no—
371C4—2921no—
372C4—2921no—
373C4—2921no—
374C4—2921no—
375C4—1462no—
376C2—42no—
377C2—81no—
378C2#1798917311yescharacteristic
379C2#1798918111yescharacteristic
380C2#1798919011yescharacteristic
381C2#1798926811yescharacteristic
382C2#1798928011yescharacteristic
383C2#1798930611yescharacteristic
384C2#1798933211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#394×C73C2
hypercenter#394D73
hypocenterC73#2786
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #17988517C2semidirect
2. #17988515C2semidirect
3. #17988515C2semidirect
4. #17988512C2semidirect
5. #17988510C2semidirect
7. #17988481C2semidirect
8. #17988475C2semidirect
9. #17988473C2semidirect
10. #17988470C2semidirect
11. #17988470C2semidirect
13. #17988462C2semidirect
14. #17988445C2semidirect
193. C73#2786semidirect