Finite Group Databasebeta

← #22617153

Subgroups — #22617153

Order 9344.

498 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17988527C211yesmaximal, characteristic, complemented
2#17988515C211yesmaximal, characteristic, complemented
3#17988509C211yesmaximal, characteristic, complemented
4#17988503C211yesmaximal, characteristic, complemented
5#17988496C211yesmaximal, characteristic
6#17988487C211yesmaximal, characteristic, complemented
7#17988476C211yesmaximal, characteristic, complemented
8#17988465C211yesmaximal, characteristic, complemented
9#17988465C211yesmaximal, characteristic, complemented
10#17988463C211yesmaximal, characteristic, complemented
11#17988463C211yesmaximal, characteristic, complemented
12#17988458C211yesmaximal, characteristic, complemented
13#17988454C211yesmaximal, characteristic, complemented
14#17988449C211yesmaximal, characteristic, complemented
15#397×C73C211yesmaximal, characteristic, complemented
16C22×D292C2211yescharacteristic
17C22×C22⋊D73C2211yescharacteristic
18C22×C22⋊D73C2211yescharacteristic
19C22×C4×D73C2211yescharacteristic
20C22×C4×D73C2211yescharacteristic
21C2×C4⋊Dic73C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×C22⋊Dic73C2211yescharacteristic
25C2×C22⋊Dic73C2211yescharacteristic
26C2×#11924005C2211yescharacteristic
27C2×#11924005C2211yescharacteristic
28C2×#11924005C2211yescharacteristic
29C2×#11924005C2211yescharacteristic
30C2×#11924005C2211yescharacteristic
31C2×#11924005C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
34C2×C4×Dic73C2211yescharacteristic
35#14556498C2211yescharacteristic
36#14556498C2211yescharacteristic
37#14556498C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44C2×C4⋊C4×C73C2211yescharacteristic
45C2×C22⋊C4×C73C2211yescharacteristic
46C2×C22⋊C4×C73C2211yescharacteristic
47C2×C22⋊C4×C73C2211yescharacteristic
48#95×C73C2211yescharacteristic
49#95×C73C2211yescharacteristic
50#95×C73C2211yescharacteristic
51C23×D73C2311yescharacteristic
52C23×D73C2311yescharacteristic
53C2×D292—22no—
54C2×D292—22no—
55C2×D292—41no—
56C2×C22⋊D73—22no—
57C2×C22⋊D73—22no—
58C2×C22⋊D73—22no—
59C2×C22⋊D73—41no—
60C2×C22⋊D73—41no—
61C2×C22⋊D73—41no—
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C22×Dic73C2311yescharacteristic
65C22×Dic73C2311yescharacteristic
66C22×Dic73C2311yescharacteristic
67C22×Dic73C2311yescharacteristic
68C2×C4×D73—22no—
69C2×C4×D73—41no—
70C2×C4×D73—41no—
71C2×C4×D73—41no—
72C2×C4×D73—41no—
73C2×C4×D73—41no—
74C4⋊Dic73—41no—
75#11924007—41no—
76#11924007—41no—
77C22⋊Dic73—41no—
78C22⋊Dic73—41no—
79#11924005—22no—
80#11924005—22no—
81#11924005—41no—
82#11924005—41no—
83#11924005—41no—
84#11924005—41no—
85#11924005—41no—
86#11924005—41no—
87C4×Dic73—22no—
88C24×C73C2311yescharacteristic
89C22×C4×C73C2311yescharacteristic
90C22×C4×C73C2311yescharacteristic
91C22×C4×C73C2311yescharacteristic
92C22×C4×C73C2311yescharacteristic
93C22×C4×C73C2311yescharacteristic
94C22×C4×C73C2311yescharacteristic
95C4⋊C4×C73—41no—
96C22⋊C4×C73—41no—
97C22⋊C4×C73—41no—
98C22⋊C4×C73—41no—
99C23×C73—21no—
100C23×C73—21no—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73—21no—
106C23×C73C2411yescharacteristic
107C22×D73—21no—
108C22×D73—21no—
109C22×D73—21no—
110C22×D73—21no—
111C22×D73—21no—
112C22×D73—21no—
113C22×D73—21no—
114C22×D73—21no—
115C22×D73—21no—
116C22×D73—21no—
117C22×D73—21no—
118C22×D73—21no—
119C22×D73#4112yes—
120C22×D73#4112yes—
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—21no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—21no—
136C2×C4×C73—21no—
137C2×C4×C73—21no—
138C2×C4×C73—21no—
139C22⋊D73—44no—
140C22⋊D73—44no—
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#4112yes—
159D292—44no—
160C4×D73—44no—
161C4×D73—44no—
162C22×C73—41no—
163C22×C73—41no—
164C22×C73—41no—
165C22×C73—41no—
166C22×C73—41no—
167C22×C73—41no—
168C22×C73—41no—
169C22×C73C2×#4111yescharacteristic
170C22×C73C2×#4111yescharacteristic
171C22×C73C2×#4111yescharacteristic
172C22×C73H(5,𝔽2)11yescharacteristic
173C22×C73H(5,𝔽2)11yescharacteristic
174C22×C73H(5,𝔽2)11yescharacteristic
175C22×C73H(5,𝔽2)11yescharacteristic
176C2×D73—22no—
177C2×D73—22no—
178C2×D73—22no—
179C2×D73—22no—
180C2×D73—22no—
181C2×D73—22no—
182C2×D73—41no—
183C2×D73—41no—
184C2×D73—41no—
185C2×D73—41no—
186C2×D73—41no—
187C2×D73—41no—
188C2×D73—41no—
189C2×D73—41no—
190C4×C73—41no—
191C4×C73—41no—
192C4×C73—41no—
193C4×C73—41no—
194C4×C73—41no—
195C4×C73—41no—
196Dic73—22no—
197Dic73—41no—
198Dic73—41no—
199Dic73—41no—
200Dic73—41no—
201Dic73—41no—
202C2×C73—81no—
203C2×C73#53811yescharacteristic
204C2×C73#53811yescharacteristic
205C2×C73#54011yescharacteristic
206C2×C73#55111yescharacteristic
207C2×C73#55111yescharacteristic
208C2×C73#55311yescharacteristic
209C2×C73#56011yescharacteristic
210D73—42no—
211D73—42no—
212#2749—731nomaximal, Sylow
213C73#274911yescharacteristic, complemented, Sylow
214#400—731no—
215#397—731no—
216#397D7311yescharacteristic, complemented
217#396—731no—
218#394—731no—
219#392—731no—
220#390—731no—
221#388—731no—
222#386—731no—
223#386—731no—
224#386—731no—
225#386—731no—
226#385—731no—
227#383—731no—
228#381—731no—
229C22×D4—731no—
230C22×D4—731no—
231C22×D4—731no—
232C23×C4—731no—
233C23×C4—731no—
234C2×C4⋊C4—731no—
235C2×C4⋊C4—731no—
236C2×C4⋊C4—731no—
237C2×C4⋊C4C2×D7311yescharacteristic
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⋊C4—731no—
248C2×C22⋊C4C2×D7311yescharacteristic
249C2×C22⋊C4C2×D7311yescharacteristic
250C2×C22⋊C4C2×D7311yescharacteristic
251C2×C42—731no—
252#95—731no—
253#95—731no—
254#95—731no—
255#95—731no—
256#95—731no—
257#95—731no—
258#95—731no—
259#95—731no—
260#95—731no—
261#95C2×D7311yescharacteristic
262#95C2×D7311yescharacteristic
263#95C2×D7311yescharacteristic
264C24—731no—
265C24—731no—
266C24C22×D7311yescharacteristic
267C2×D4—2921no—
268C2×D4—2921no—
269C2×D4—2921no—
270C2×D4—2921no—
271C2×D4—1462no—
272C2×D4—1462no—
273C2×D4—1462no—
274C2×D4—1462no—
275C2×D4—1462no—
276C22×C4—2921no—
277C22×C4—2921no—
278C22×C4—2921no—
279C22×C4—2921no—
280C22×C4—2921no—
281C22×C4—731no—
282C22×C4—731no—
283C22×C4—731no—
284C22×C4—731no—
285C22×C4—731no—
286C22×C4—731no—
287C22×C4—1462no—
288C22×C4C22×D7311yescharacteristic
289C22×C4C22×D7311yescharacteristic
290C22×C4C22×D7311yescharacteristic
291C22×C4C22×D7311yescharacteristic
292C22×C4C22×D7311yescharacteristic
293C22×C4C22×D7311yescharacteristic
294C4⋊C4—41no—
295C4⋊C4—2921no—
296C4⋊C4—2921no—
297C4⋊C4—2921no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—2921no—
302C22⋊C4—2921no—
303C22⋊C4—2921no—
304C22⋊C4—2921no—
305C22⋊C4—2921no—
306C22⋊C4—2921no—
307C22⋊C4—2921no—
308C22⋊C4—2921no—
309C22⋊C4—1462no—
310C22⋊C4—1462no—
311C42—1462no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—732no—
320C23—732no—
321C23—1461no—
322C23—1461no—
323C23—1461no—
324C23—1461no—
325C23—1461no—
326C23—1461no—
327C23—1461no—
328C23—1461no—
329C23—1461no—
330C23—1461no—
331C23—1461no—
332C23—1461no—
333C23C23×D7311yescharacteristic
334D4—2924no—
335D4—2924no—
336D4—2924no—
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—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—2924no—
356C2×C4—2924no—
357C2×C4—732no—
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—1461no—
370C2×C4—1461no—
371C2×C4—1461no—
372C2×C4—1461no—
373C2×C4—1461no—
374C2×C4—1461no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—2921no—
383C22—2921no—
384C22—2921no—
385C22—2921no—
386C22—2921no—
387C22—2921no—
388C22—2921no—
389C22—2921no—
390C22—1462no—
391C22—1462no—
392C22—1462no—
393C22—1462no—
394C22—1462no—
395C22—1462no—
396C22#41×D7311yescharacteristic
397C22#41×D7311yescharacteristic
398C22#41×D7311yescharacteristic
399C22#1455663611yescharacteristic
400C22#1455663611yescharacteristic
401C22#1455663711yescharacteristic
402C22#1455663711yescharacteristic
403C4—41no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—41no—
408C4—41no—
409C4—2921no—
410C4—2921no—
411C4—2921no—
412C4—2921no—
413C4—2921no—
414C4—1462no—
415C2—81no—
416C2—2922no—
417C2—2922no—
418C2#1798917311yescharacteristic
419C2#1798917611yescharacteristic
420C2#1798918911yescharacteristic
421C2#1798926211yescharacteristic
422C2#1798926711yescharacteristic
423C2#1798928211yescharacteristic
424C2#1798932511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#397×C73C2
hypercenter#397D73
hypocenterC73#2749
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. #17988527C2semidirect
2. #17988515C2semidirect
3. #17988509C2semidirect
4. #17988503C2semidirect
6. #17988487C2semidirect
7. #17988476C2semidirect
8. #17988465C2semidirect
9. #17988465C2semidirect
10. #17988463C2semidirect
11. #17988463C2semidirect
12. #17988458C2semidirect
13. #17988454C2semidirect
14. #17988449C2semidirect
15. #397×C73C2semidirect
213. C73#2749semidirect
216. #397D73semidirect