Finite Group Databasebeta

← #22617865

Subgroups — #22617865

Order 9344.

470 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17988515C211yesmaximal, characteristic, complemented
2#17988503C211yesmaximal, characteristic, complemented
3#17988503C211yesmaximal, characteristic, complemented
4#17988502C211yesmaximal, characteristic, complemented
5#17988501C211yesmaximal, characteristic, complemented
6#17988495C211yesmaximal, characteristic
7#17988487C211yesmaximal, characteristic, complemented
8#17988485C211yesmaximal, characteristic, complemented
9#17988480C211yesmaximal, characteristic, complemented
10#17988480C211yesmaximal, characteristic, complemented
11#17988478C211yesmaximal, characteristic, complemented
12#17988477C211yesmaximal, characteristic, complemented
13#17988475C211yesmaximal, characteristic, complemented
14#17988468C211yesmaximal, characteristic, complemented
15#390×C73C211yesmaximal, characteristic, complemented
16C22×C22⋊D73C2211yescharacteristic
17C22×C22⋊D73C2211yescharacteristic
18C2×C4⋊Dic73C2211yescharacteristic
19C2×C4⋊Dic73C2211yescharacteristic
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×C22⋊Dic73C2211yescharacteristic
24C2×C22⋊Dic73C2211yescharacteristic
25C2×C22⋊Dic73C2211yescharacteristic
26C2×C22⋊Dic73C2211yescharacteristic
27C2×C22⋊Dic73C2211yescharacteristic
28C2×C22⋊Dic73C2211yescharacteristic
29C2×#11924005C2211yescharacteristic
30C2×#11924005C2211yescharacteristic
31C2×#11924005C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
34C2×C4×Dic73C2211yescharacteristic
35C2×C4×Dic73C2211yescharacteristic
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
50C2×C42×C73C2211yescharacteristic
51C23×D73C2311yescharacteristic
52C2×C22⋊D73—22no—
53C2×C22⋊D73—41no—
54C2×C22⋊D73—41no—
55C2×C22⋊D73—41no—
56C2×C22⋊D73—41no—
57C2×C22⋊D73—41no—
58C22×Dic73C2311yescharacteristic
59C22×Dic73C2311yescharacteristic
60C22×Dic73C2311yescharacteristic
61C22×Dic73C2311yescharacteristic
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C22×Dic73C2311yescharacteristic
65C4⋊Dic73—22no—
66C4⋊Dic73—41no—
67#11924007—22no—
68#11924007—41no—
69#11924007—41no—
70C22⋊Dic73—22no—
71C22⋊Dic73—41no—
72C22⋊Dic73—41no—
73C22⋊Dic73—41no—
74C22⋊Dic73—41no—
75C22⋊Dic73—41no—
76#11924005—22no—
77#11924005—22no—
78#11924005—41no—
79#11924005—41no—
80#11924005—41no—
81C4×Dic73—41no—
82C4×Dic73—41no—
83C24×C73C2311yescharacteristic
84C24×C73C2311yescharacteristic
85C2×D4×C73—22no—
86C2×D4×C73—41no—
87C2×D4×C73—41no—
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—22no—
96C22⋊C4×C73—41no—
97C22⋊C4×C73—41no—
98C42×C73—41no—
99C23×C73—21no—
100C23×C73—21no—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73—21no—
106C23×C73—21no—
107C23×C73—21no—
108C23×C73—21no—
109C23×C73—21no—
110C23×C73—21no—
111C23×C73—21no—
112C23×C73—21no—
113C23×C73C2411yescharacteristic
114C22×D73—21no—
115C22×D73—21no—
116C22×D73—21no—
117C22×D73—21no—
118C22×D73—21no—
119C22×D73—21no—
120C22×D73—21no—
121D4×C73—44no—
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—21no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73#4112yes—
136C2×C4×C73#4112yes—
137C22⋊D73—44no—
138C22⋊D73—44no—
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—21no—
151C2×Dic73—21no—
152C2×Dic73—21no—
153C2×Dic73—21no—
154C2×Dic73—21no—
155C2×Dic73—21no—
156C2×Dic73—21no—
157C2×Dic73—21no—
158C2×Dic73—21no—
159C2×Dic73#4112yes—
160C22×C73—41no—
161C22×C73—41no—
162C22×C73—41no—
163C22×C73—41no—
164C22×C73—41no—
165C22×C73—41no—
166C22×C73—41no—
167C22×C73—41no—
168C22×C73—41no—
169C22×C73—41no—
170C22×C73—41no—
171C22×C73—41no—
172C22×C73—41no—
173C22×C73—41no—
174C22×C73C2×#4111yescharacteristic
175C22×C73C2×#4111yescharacteristic
176C22×C73C2×#4111yescharacteristic
177C22×C73H(5,𝔽2)11yescharacteristic
178C22×C73H(5,𝔽2)11yescharacteristic
179C22×C73H(5,𝔽2)11yescharacteristic
180C22×C73H(5,𝔽2)11yescharacteristic
181C2×D73—41no—
182C2×D73—41no—
183C2×D73—41no—
184C2×D73—41no—
185C2×D73—41no—
186C2×D73—41no—
187C2×D73—41no—
188C4×C73—22no—
189C4×C73—22no—
190C4×C73—41no—
191C4×C73—41no—
192C4×C73—41no—
193Dic73—22no—
194Dic73—41no—
195Dic73—41no—
196Dic73—41no—
197Dic73—41no—
198Dic73—41no—
199Dic73—41no—
200C2×C73—81no—
201C2×C73—81no—
202C2×C73#53811yescharacteristic
203C2×C73#53811yescharacteristic
204C2×C73#54011yescharacteristic
205C2×C73#55311yescharacteristic
206C2×C73#55511yescharacteristic
207C2×C73#55911yescharacteristic
208C2×C73#56011yescharacteristic
209D73—81no—
210#2803—731nomaximal, Sylow
211C73#280311yescharacteristic, complemented, Sylow
212#397—731no—
213#394—731no—
214#394—731no—
215#394—731no—
216#394—731no—
217#392—731no—
218#390—731no—
219#390D7311yescharacteristic, complemented
220#389—731no—
221#388—731no—
222#388—731no—
223#388—731no—
224#388—731no—
225#388—731no—
226#387—731no—
227C22×D4—731no—
228C22×D4—731no—
229C22×D4C2×D7311yescharacteristic
230C2×C4⋊C4—731no—
231C2×C4⋊C4—731no—
232C2×C4⋊C4—731no—
233C2×C4⋊C4—731no—
234C2×C4⋊C4—731no—
235C2×C4⋊C4C2×D7311yescharacteristic
236C2×C22⋊C4—731no—
237C2×C22⋊C4—731no—
238C2×C22⋊C4—731no—
239C2×C22⋊C4—731no—
240C2×C22⋊C4—731no—
241C2×C22⋊C4—731no—
242C2×C22⋊C4—731no—
243C2×C22⋊C4—731no—
244C2×C22⋊C4—731no—
245C2×C22⋊C4—731no—
246C2×C22⋊C4—731no—
247C2×C22⋊C4C2×D7311yescharacteristic
248C2×C22⋊C4C2×D7311yescharacteristic
249C2×C22⋊C4C2×D7311yescharacteristic
250C2×C22⋊C4C2×D7311yescharacteristic
251C2×C42—731no—
252C2×C42—731no—
253C2×C42C2×D7311yescharacteristic
254#95—731no—
255#95—731no—
256#95—731no—
257#95—731no—
258#95—731no—
259#95—731no—
260#95—731no—
261#95—731no—
262C24—731no—
263C24C22×D7311yescharacteristic
264C24C22×D7311yescharacteristic
265C2×D4—22no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—2921no—
269C2×D4—2921no—
270C2×D4—2921no—
271C2×D4—2921no—
272C2×D4—2921no—
273C2×D4—1462no—
274C22×C4—731no—
275C22×C4—731no—
276C22×C4—731no—
277C22×C4—731no—
278C22×C4—731no—
279C22×C4—731no—
280C22×C4—731no—
281C22×C4C22×D7311yescharacteristic
282C22×C4C22×D7311yescharacteristic
283C22×C4C22×D7311yescharacteristic
284C22×C4C22×D7311yescharacteristic
285C22×C4C22×D7311yescharacteristic
286C4⋊C4—41no—
287C4⋊C4—2921no—
288C4⋊C4—2921no—
289C4⋊C4—2921no—
290C4⋊C4—1462no—
291C4⋊C4—1462no—
292C22⋊C4—22no—
293C22⋊C4—22no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—2921no—
297C22⋊C4—2921no—
298C22⋊C4—2921no—
299C22⋊C4—2921no—
300C22⋊C4—2921no—
301C22⋊C4—2921no—
302C22⋊C4—2921no—
303C22⋊C4—2921no—
304C22⋊C4—1462no—
305C22⋊C4—1462no—
306C22⋊C4—1462no—
307C42—41no—
308C42—2921no—
309C42—2921no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—1461no—
325C23—1461no—
326C23—1461no—
327C23—1461no—
328C23—1461no—
329C23—1461no—
330C23—1461no—
331C23C23×D7311yescharacteristic
332D4—44no—
333D4—2924no—
334D4—2924no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—732no—
349C2×C4—1461no—
350C2×C4—1461no—
351C2×C4—1461no—
352C2×C4—1461no—
353C2×C4—1461no—
354C2×C4—1461no—
355C2×C4—1461no—
356C2×C4—1461no—
357C2×C4—1461no—
358C2×C4—1461no—
359C2×C4—1461no—
360C2×C4—1461no—
361C2×C4—1461no—
362C2×C4—1461no—
363C2×C4—1461no—
364C2×C4—1461no—
365C2×C4—1461no—
366C2×C4—1461no—
367C2×C4—1461no—
368C2×C4—1461no—
369C2×C4#1192402712yes—
370C2×C4#1192402812yes—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—2921no—
386C22—2921no—
387C22—2921no—
388C22—2921no—
389C22—2921no—
390C22—2921no—
391C22—2921no—
392C22#41×D7311yescharacteristic
393C22C2×#1192402711yescharacteristic
394C22C2×#1192402811yescharacteristic
395C22#1455663611yescharacteristic
396C22#1455663611yescharacteristic
397C22#1455663611yescharacteristic
398C22#1455663711yescharacteristic
399C4—22no—
400C4—22no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—2921no—
405C4—2921no—
406C4—2921no—
407C4—2921no—
408C4—2921no—
409C4—2921no—
410C4—1462no—
411C2—81no—
412C2—81no—
413C2—5841no—
414C2#1798917111yescharacteristic
415C2#1798917511yescharacteristic
416C2#1798919111yescharacteristic
417C2#1798928011yescharacteristic
418C2#1798930211yescharacteristic
419C2#1798932011yescharacteristic
420C2#1798932511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#390×C73C2
hypercenter#390D73
hypocenterC73#2803
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #17988515C2semidirect
2. #17988503C2semidirect
3. #17988503C2semidirect
4. #17988502C2semidirect
5. #17988501C2semidirect
7. #17988487C2semidirect
8. #17988485C2semidirect
9. #17988480C2semidirect
10. #17988480C2semidirect
11. #17988478C2semidirect
12. #17988477C2semidirect
13. #17988475C2semidirect
14. #17988468C2semidirect
15. #390×C73C2semidirect
211. C73#2803semidirect
219. #390D73semidirect