Finite Group Databasebeta

← #22612866

Subgroups — #22612866

Order 9344.

588 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556551C211yesmaximal, characteristic
2#17988480C211yesmaximal, characteristic, complemented
3#17988474C211yesmaximal, characteristic, complemented
4#17988468C211yesmaximal, characteristic, complemented
5#17988463C211yesmaximal, characteristic
6#17988463C211yesmaximal, characteristic
7#17988454C211yesmaximal, characteristic, complemented
8#17988448C211yesmaximal, characteristic, complemented
9#17988444C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic73C211yesmaximal, characteristic, complemented
11C4×#11924005C211yesmaximal, characteristic, complemented
12#17988434C211yesmaximal, characteristic, complemented
13#17988433C211yesmaximal, characteristic, complemented
14#95×D73C211yesmaximal, characteristic, complemented
15#388×C73C211yesmaximal, characteristic, complemented
16C22×C22⋊D73C2211yescharacteristic
17C23×Dic73C2211yescharacteristic
18C22×C4×D73C2211yescharacteristic
19C22×C4×D73C2211yescharacteristic
20C22×C4×D73C2211yescharacteristic
21#14556551C418yescomplemented
22C2×C4⋊Dic73C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×C22⋊Dic73C2211yescharacteristic
25C2×C22⋊Dic73C2211yescharacteristic
26C2×#11924005C2211yescharacteristic
27C2×#11924005C2211yescharacteristic
28C2×#11924005C2211yescharacteristic
29C2×C4×Dic73C2211yescharacteristic
30C2×C4×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
44#14556498C2211yescharacteristic
45C2×C4⋊C4×C73C2211yescharacteristic
46C2×C22⋊C4×C73C2211yescharacteristic
47C2×C22⋊C4×C73C2211yescharacteristic
48C2×C22⋊C4×C73C2211yescharacteristic
49C2×C42×C73C2211yescharacteristic
50#95×C73C2211yescharacteristic
51#95×C73C2211yescharacteristic
52C23×D73C2311yescharacteristic
53C2×C22⋊D73—22no—
54C2×C22⋊D73—22no—
55C2×C22⋊D73C2×C414yes—
56C22×Dic73—41no—
57C22×Dic73—41no—
58C22×Dic73C2×C414yescomplemented
59C22×Dic73C2311yescharacteristic
60C22×Dic73C2311yescharacteristic
61C22×Dic73C2311yescharacteristic
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C22×Dic73C2311yescharacteristic
65C22×Dic73C2311yescharacteristic
66C2×C4×D73—22no—
67C2×C4×D73—22no—
68C2×C4×D73—22no—
69C2×C4×D73—22no—
70C2×C4×D73—41no—
71C2×C4×D73—41no—
72C2×C4×D73—41no—
73C2×C4×D73—41no—
74C2×C4×D73C2×C414yes—
75C4⋊Dic73—41no—
76#11924007C2×C414yescomplemented
77C22⋊Dic73—22no—
78C22⋊Dic73—41no—
79#11924005—22no—
80#11924005—22no—
81#11924005C2×C414yes—
82C4×Dic73—22no—
83C4×Dic73—41no—
84C4×Dic73—41no—
85C4×Dic73C2×C414yescomplemented
86C24×C73C2311yescharacteristic
87C22×C4×C73C2311yescharacteristic
88C22×C4×C73C2311yescharacteristic
89C22×C4×C73C2311yescharacteristic
90C22×C4×C73C2311yescharacteristic
91C22×C4×C73C2311yescharacteristic
92C22×C4×C73C2311yescharacteristic
93C4⋊C4×C73—41no—
94C22⋊C4×C73—22no—
95C22⋊C4×C73—41no—
96C22⋊C4×C73C2×C414yescomplemented
97C42×C73—22no—
98C23×C73—21no—
99C23×C73—21no—
100C23×C73—21no—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73—21no—
104C23×C73C22×C412yes—
105C23×C73C2411yescharacteristic
106C22×D73—21no—
107C22×D73—21no—
108C22×D73—21no—
109C22×D73—21no—
110C22×D73C22×C412yes—
111C22×D73#4112yes—
112C22×D73#4112yes—
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×C73C22×C412yes—
129C2×C4×C73C22×C412yes—
130C2×C4×C73#4112yes—
131C22⋊D73—28no—
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—44no—
150C2×Dic73C22×C412yes—
151C2×Dic73C22×C412yes—
152C2×Dic73C22×C412yes—
153C2×Dic73#4112yes—
154C4×D73—44no—
155C4×D73—44no—
156C4×D73—44no—
157C22×C73—22no—
158C22×C73—22no—
159C22×C73—22no—
160C22×C73—41no—
161C22×C73—41no—
162C22×C73—41no—
163C22×C73—41no—
164C22×C73C23×C411yescharacteristic
165C22×C73C2×#4111yescharacteristic
166C22×C73C2×#4111yescharacteristic
167C22×C73C2×#4111yescharacteristic
168C22×C73C2×#4111yescharacteristic
169C22×C73H(5,𝔽2)11yescharacteristic
170C22×C73H(5,𝔽2)11yescharacteristic
171C2×D73—22no—
172C2×D73—22no—
173C2×D73—22no—
174C2×D73—22no—
175C2×D73—22no—
176C2×D73—22no—
177C2×D73#11714yes—
178C4×C73—22no—
179C4×C73—22no—
180C4×C73—22no—
181C4×C73—41no—
182C4×C73—41no—
183C4×C73—41no—
184Dic73—22no—
185Dic73—22no—
186Dic73—22no—
187Dic73—22no—
188Dic73—41no—
189Dic73—41no—
190Dic73—41no—
191C2×C73—42no—
192C2×C73C2×#11711yescharacteristic
193C2×C73C4×#4111yescharacteristic
194C2×C73#51811yescharacteristic
195C2×C73#55111yescharacteristic
196C2×C73#55111yescharacteristic
197C2×C73#55311yescharacteristic
198C2×C73#55311yescharacteristic
199D73—24no—
200#2353—731nomaximal, Sylow
201C73#235311yescharacteristic, complemented, Sylow
202C2×C4×D4—731no—
203#388—731no—
204#388D7311yescharacteristic, complemented
205#387—731no—
206#387—731no—
207#386—731no—
208#386—731no—
209#383—731no—
210#381—731no—
211#380—731no—
212C4×C22⋊C4—731no—
213C4×C22⋊C4—731no—
214C4×C22⋊C4—731no—
215#376—731no—
216C2×#95—731no—
217C22×D4—731no—
218C23×C4—731no—
219C23×C4—731no—
220C23×C4—731no—
221C23×C4—731no—
222C4×D4—738no—
223C2×C4⋊C4—731no—
224C2×C4⋊C4—731no—
225C2×C4⋊C4C2×D7311yescharacteristic
226C2×C22⋊C4—731no—
227C2×C22⋊C4—731no—
228C2×C22⋊C4—731no—
229C2×C22⋊C4—731no—
230C2×C22⋊C4—731no—
231C2×C22⋊C4C2×D7311yescharacteristic
232C2×C22⋊C4C2×D7311yescharacteristic
233C2×C22⋊C4C2×D7311yescharacteristic
234C2×C42—731no—
235C2×C42—731no—
236C2×C42—731no—
237C2×C42—731no—
238C2×C42C2×D7311yescharacteristic
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#95—731no—
250#95—731no—
251#95C2×D7311yescharacteristic
252#95C2×D7311yescharacteristic
253C24—731no—
254C24C22×D7311yescharacteristic
255C2×D4—734no—
256C2×D4—1462no—
257C2×D4—1462no—
258C22×C4—2921no—
259C22×C4—2921no—
260C22×C4—2921no—
261C22×C4—2921no—
262C22×C4—2921no—
263C22×C4—2921no—
264C22×C4—734no—
265C22×C4—734no—
266C22×C4—731no—
267C22×C4—731no—
268C22×C4—731no—
269C22×C4—731no—
270C22×C4—731no—
271C22×C4—731no—
272C22×C4—731no—
273C22×C4—1462no—
274C22×C4—1462no—
275C22×C4—1462no—
276C22×C4—1462no—
277C22×C4C22×D7311yescharacteristic
278C22×C4C22×D7311yescharacteristic
279C22×C4C22×D7311yescharacteristic
280C22×C4C22×D7311yescharacteristic
281C22×C4C22×D7311yescharacteristic
282C22×C4C22×D7311yescharacteristic
283C4⋊C4—41no—
284C4⋊C4—2921no—
285C4⋊C4—734no—
286C22⋊C4—22no—
287C22⋊C4—41no—
288C22⋊C4—2921no—
289C22⋊C4—734no—
290C22⋊C4—1462no—
291C22⋊C4—1462no—
292C22⋊C4—1462no—
293C22⋊C4C4×D7314yescomplemented
294C42—22no—
295C42—2921no—
296C42—2921no—
297C42—734no—
298C42—1462no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—732no—
306C23—732no—
307C23—732no—
308C23—1461no—
309C23—1461no—
310C23—1461no—
311C23—1461no—
312C23C2×C4×D7312yes—
313C23C23×D7311yescharacteristic
314D4—1468no—
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—2924no—
333C2×C4—2924no—
334C2×C4—732no—
335C2×C4—732no—
336C2×C4—732no—
337C2×C4—732no—
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—1461no—
354C2×C4—1461no—
355C2×C4C2×C4×D7312yes—
356C2×C4C2×C4×D7312yes—
357C2×C4#1192402712yes—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—734no—
366C22—1462no—
367C22—1462no—
368C22—1462no—
369C22—1462no—
370C22—1462no—
371C22—1462no—
372C22C22×C4×D7311yescharacteristic
373C22#41×D7311yescharacteristic
374C22#41×D7311yescharacteristic
375C22#41×D7311yescharacteristic
376C22C2×#1192402711yescharacteristic
377C22#1455663611yescharacteristic
378C22#1455663711yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—2921no—
386C4—2921no—
387C4—2921no—
388C4—1462no—
389C4—1462no—
390C4—1462no—
391C4—1462no—
392C2—42no—
393C2—1464no—
394C2#117×D7311yescharacteristic
395C2C4×#1192402711yescharacteristic
396C2#1798905911yescharacteristic
397C2#1798926011yescharacteristic
398C2#1798926711yescharacteristic
399C2#1798928411yescharacteristic
400C2#1798928811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutatorC22×C73C23×C4
Fitting#388×C73C2
socleC23×C73C24
hypercenter#388D73
hypocenterC73#2353
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #17988480C2semidirect
3. #17988474C2semidirect
4. #17988468C2semidirect
7. #17988454C2semidirect
8. #17988448C2semidirect
9. #17988444C2semidirect
10. C22⋊C4×Dic73C2semidirect
11. C4×#11924005C2semidirect
12. #17988434C2semidirect
13. #17988433C2semidirect
14. #95×D73C2semidirect
15. #388×C73C2semidirect
21. #14556551C4semidirect
58. C22×Dic73C2×C4semidirect
76. #11924007C2×C4semidirect
85. C4×Dic73C2×C4semidirect
96. C22⋊C4×C73C2×C4semidirect
201. C73#2353semidirect
204. #388D73semidirect
293. C22⋊C4C4×D73semidirect