Finite Group Databasebeta

← #22616971

Subgroups — #22616971

Order 9344.

552 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17988524C211yesmaximal, characteristic, complemented
2#17988516C211yesmaximal, characteristic, complemented
3#17988516C211yesmaximal, characteristic, complemented
4#17988510C211yesmaximal, characteristic, complemented
5#17988509C211yesmaximal, characteristic, complemented
6#17988480C211yesmaximal, characteristic, complemented
7#17988480C211yesmaximal, characteristic, complemented
8#17988479C211yesmaximal, characteristic, complemented
9#17988479C211yesmaximal, characteristic, complemented
10#17988477C211yesmaximal, characteristic, complemented
11#17988476C211yesmaximal, characteristic, complemented
12#17988442C211yesmaximal, characteristic
13#17988442C211yesmaximal, characteristic
14#17988442C211yesmaximal, characteristic
15#397×C73C211yesmaximal, characteristic, complemented
16C24×D73C2211yescharacteristic
17C2×C4⋊Dic73C2211yescharacteristic, complemented
18C2×C4⋊Dic73C2211yescharacteristic, complemented
19C2×C4⋊Dic73C2211yescharacteristic, complemented
20C2×#11924007C2211yescharacteristic, complemented
21C2×#11924007C2211yescharacteristic, complemented
22C2×C22⋊Dic73C2211yescharacteristic
23C2×C22⋊Dic73C2211yescharacteristic
24C2×C22⋊Dic73C2211yescharacteristic
25C2×#11924005C2211yescharacteristic
26C2×#11924005C2211yescharacteristic
27C2×#11924005C2211yescharacteristic
28C2×#11924005C2211yescharacteristic
29C2×#11924005C2211yescharacteristic
30C2×#11924005C2211yescharacteristic
31C2×#11924005C2211yescharacteristic
32C2×#11924005C2211yescharacteristic
33C2×#11924005C2211yescharacteristic
34C2×#11924005C2211yescharacteristic
35C2×#11924005C2211yescharacteristic
36C2×#11924005C2211yescharacteristic
37C2×C4×Dic73C2211yescharacteristic, complemented
38C2×C4×Dic73C2211yescharacteristic, complemented
39#14556498C2211yescharacteristic, complemented
40#14556498C2211yescharacteristic, complemented
41#14556498C2211yescharacteristic, complemented
42#14556498C2211yescharacteristic, complemented
43#14556498C2211yescharacteristic, complemented
44C2×C4⋊C4×C73C2211yescharacteristic, complemented
45C2×C22⋊C4×C73C2211yescharacteristic
46C2×C22⋊C4×C73C2211yescharacteristic
47C2×C22⋊C4×C73C2211yescharacteristic
48#95×C73C2211yescharacteristic, complemented
49#95×C73C2211yescharacteristic, complemented
50#95×C73C2211yescharacteristic, complemented
51C23×D73—22no—
52C23×D73—22no—
53C23×D73—22no—
54C23×D73—41no—
55C23×D73—41no—
56C23×D73—41no—
57C23×D73—41no—
58C23×D73C2311yescharacteristic
59C23×D73C2311yescharacteristic
60C22×Dic73C2311yescharacteristic
61C22×Dic73C2311yescharacteristic
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C22×Dic73C2311yescharacteristic
65C22×Dic73C2311yescharacteristic
66C4⋊Dic73—41no—
67C4⋊Dic73—41no—
68C4⋊Dic73—41no—
69#11924007—41no—
70#11924007—41no—
71C22⋊Dic73—41no—
72C22⋊Dic73—41no—
73C22⋊Dic73—41no—
74#11924005—22no—
75#11924005—22no—
76#11924005—22no—
77#11924005—22no—
78#11924005—41no—
79#11924005—41no—
80#11924005—41no—
81#11924005—41no—
82#11924005—41no—
83#11924005—41no—
84#11924005—41no—
85#11924005—41no—
86C4×Dic73—41no—
87C4×Dic73—41no—
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—22no—
97C22⋊C4×C73—22no—
98C22⋊C4×C73—41no—
99C23×C73—21no—
100C23×C73—21no—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73#4112yes—
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—44no—
120C22×D73—44no—
121C22×D73—44no—
122C22×D73—44no—
123C22×D73—44no—
124C22×D73—44no—
125C22×D73—44no—
126C22×D73#4112yes—
127C22×D73#4112yes—
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—
139C2×C4×C73—21no—
140C2×C4×C73—21no—
141C2×C4×C73—21no—
142C2×C4×C73—21no—
143C2×C4×C73—21no—
144C2×C4×C73—21no—
145C2×C4×C73—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—21no—
160C2×Dic73—21no—
161C2×Dic73—21no—
162C2×Dic73—21no—
163C2×Dic73—21no—
164C22×C73—22no—
165C22×C73—22no—
166C22×C73—22no—
167C22×C73—41no—
168C22×C73—41no—
169C22×C73—41no—
170C22×C73—41no—
171C22×C73C2×#4111yescharacteristic
172C22×C73C2×#4111yescharacteristic
173C22×C73C2×#4111yescharacteristic
174C22×C73H(5,𝔽2)11yescharacteristic
175C22×C73H(5,𝔽2)11yescharacteristic
176C22×C73H(5,𝔽2)11yescharacteristic
177C22×C73H(5,𝔽2)11yescharacteristic
178C2×D73—22no—
179C2×D73—22no—
180C2×D73—22no—
181C2×D73—22no—
182C2×D73—22no—
183C2×D73—22no—
184C2×D73—416no—
185C2×D73—41no—
186C2×D73—41no—
187C2×D73—41no—
188C2×D73—41no—
189C2×D73—41no—
190C2×D73—41no—
191C2×D73—41no—
192C2×D73—41no—
193C4×C73—41no—
194C4×C73—41no—
195C4×C73—41no—
196C4×C73—41no—
197C4×C73—41no—
198C4×C73—41no—
199Dic73—41no—
200Dic73—41no—
201Dic73—41no—
202Dic73—41no—
203Dic73—41no—
204Dic73—41no—
205C2×C73—42no—
206C2×C73#53811yescharacteristic
207C2×C73#53811yescharacteristic
208C2×C73#53811yescharacteristic
209C2×C73#55111yescharacteristic
210C2×C73#55111yescharacteristic
211C2×C73#55111yescharacteristic
212C2×C73#56011yescharacteristic
213D73—42no—
214D73—42no—
215#2735—731nomaximal, Sylow
216C73#273511yescharacteristic, complemented, Sylow
217#399—731no—
218#397—731no—
219#397—731no—
220#397D7311yescharacteristic, complemented
221#396—731no—
222#396—731no—
223#388—731no—
224#388—731no—
225#388—731no—
226#388—731no—
227#388—731no—
228#388—731no—
229#379—731no—
230#379—731no—
231#379—731no—
232C25—731no—
233C2×C4⋊C4—731no—
234C2×C4⋊C4—731no—
235C2×C4⋊C4—731no—
236C2×C4⋊C4—731no—
237C2×C4⋊C4—731no—
238C2×C4⋊C4C2×D7311yescharacteristic, complemented
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⋊C4—731no—
249C2×C22⋊C4—731no—
250C2×C22⋊C4—731no—
251C2×C22⋊C4—731no—
252C2×C22⋊C4—731no—
253C2×C22⋊C4—731no—
254C2×C22⋊C4C2×D7311yescharacteristic
255C2×C22⋊C4C2×D7311yescharacteristic
256C2×C22⋊C4C2×D7311yescharacteristic
257C2×C42—731no—
258C2×C42—731no—
259#95—731no—
260#95—731no—
261#95—731no—
262#95—731no—
263#95—731no—
264#95C2×D7311yescharacteristic, complemented
265#95C2×D7311yescharacteristic, complemented
266#95C2×D7311yescharacteristic, complemented
267C24—2921no—
268C24—2921no—
269C24—2921no—
270C24—2921no—
271C24—731no—
272C24—731no—
273C24—1462no—
274C24—1462no—
275C24—1462no—
276C24C22×D7311yescharacteristic
277C22×C4—731no—
278C22×C4—731no—
279C22×C4—731no—
280C22×C4—731no—
281C22×C4—731no—
282C22×C4—731no—
283C22×C4C22×D7311yescharacteristic
284C22×C4C22×D7311yescharacteristic
285C22×C4C22×D7311yescharacteristic
286C22×C4C22×D7311yescharacteristic
287C22×C4C22×D7311yescharacteristic
288C22×C4C22×D7311yescharacteristic
289C4⋊C4—41no—
290C4⋊C4—2921no—
291C4⋊C4—2921no—
292C4⋊C4—2921no—
293C4⋊C4—2921no—
294C4⋊C4—2921no—
295C22⋊C4—22no—
296C22⋊C4—22no—
297C22⋊C4—41no—
298C22⋊C4—2921no—
299C22⋊C4—2921no—
300C22⋊C4—2921no—
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—
311C22⋊C4—1462no—
312C22⋊C4—1462no—
313C42—2921no—
314C42—2921no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—2924no—
322C23—2924no—
323C23—2924no—
324C23—2924no—
325C23—2924no—
326C23—2924no—
327C23—2924no—
328C23—732no—
329C23—732no—
330C23—1461no—
331C23—1461no—
332C23—1461no—
333C23—1461no—
334C23—1461no—
335C23—1461no—
336C23—1461no—
337C23—1461no—
338C23—1461no—
339C23—1461no—
340C23—1461no—
341C23—1461no—
342C23#1192402712yes—
343C23C23×D7311yescharacteristic
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—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
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—
375C2×C4—1461no—
376C2×C4—1461no—
377C2×C4—1461no—
378C2×C4—1461no—
379C2×C4—1461no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—29216no—
388C22—2921no—
389C22—2921no—
390C22—2921no—
391C22—2921no—
392C22—2921no—
393C22—2921no—
394C22—2921no—
395C22—2921no—
396C22—1462no—
397C22—1462no—
398C22—1462no—
399C22—1462no—
400C22—1462no—
401C22—1462no—
402C22#41×D7311yescharacteristic
403C22#41×D7311yescharacteristic
404C22C2×#1192402711yescharacteristic
405C22#1455663611yescharacteristic
406C22#1455663711yescharacteristic
407C22#1455663711yescharacteristic
408C22#1455663711yescharacteristic
409C4—41no—
410C4—41no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—2921no—
416C4—2921no—
417C4—2921no—
418C4—2921no—
419C4—2921no—
420C4—2921no—
421C2—42no—
422C2—2922no—
423C2—2922no—
424C2#1798917111yescharacteristic
425C2#1798917311yescharacteristic
426C2#1798917411yescharacteristic
427C2#1798926011yescharacteristic
428C2#1798926011yescharacteristic
429C2#1798926211yescharacteristic
430C2#1798932811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#397×C73C2
hypercenter#397D73
hypocenterC73#2735
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. #17988524C2semidirect
2. #17988516C2semidirect
3. #17988516C2semidirect
4. #17988510C2semidirect
5. #17988509C2semidirect
6. #17988480C2semidirect
7. #17988480C2semidirect
8. #17988479C2semidirect
9. #17988479C2semidirect
10. #17988477C2semidirect
11. #17988476C2semidirect
15. #397×C73C2semidirect
17. C2×C4⋊Dic73C22semidirect
18. C2×C4⋊Dic73C22semidirect
19. C2×C4⋊Dic73C22semidirect
20. C2×#11924007C22semidirect
21. C2×#11924007C22semidirect
37. C2×C4×Dic73C22semidirect
38. C2×C4×Dic73C22semidirect
39. #14556498C22semidirect
40. #14556498C22semidirect
41. #14556498C22semidirect
42. #14556498C22semidirect
43. #14556498C22semidirect
44. C2×C4⋊C4×C73C22semidirect
48. #95×C73C22semidirect
49. #95×C73C22semidirect
50. #95×C73C22semidirect
216. C73#2735semidirect
220. #397D73semidirect
238. C2×C4⋊C4C2×D73semidirect
264. #95C2×D73semidirect
265. #95C2×D73semidirect
266. #95C2×D73semidirect