Finite Group Databasebeta

← #22623584

Subgroups — #22623584

Order 9344.

1536 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
1C2×#14556638C211yesmaximal, characteristic, complemented
2C2×#41×D73C211yesmaximal, characteristic, complemented
3#17989257C213yesmaximal, complemented
4#17989256C211yesmaximal, characteristic, complemented
5#17989255C213yesmaximal, complemented
6#17989249C211yesmaximal, characteristic, complemented
7#17989246C213yesmaximal, complemented
8#17989244C211yesmaximal, characteristic, complemented
9#17989243C213yesmaximal, complemented
10#17989153C213yesmaximal, complemented
11#17989150C213yesmaximal, complemented
12#17989097C213yesmaximal, complemented
13#17989096C213yesmaximal, complemented
14#17989063C211yesmaximal, characteristic, complemented
15#550×C73C211yesmaximal, characteristic, complemented
16#14556638—28no—
17C2×#11924029C2211yescharacteristic
18C2×#11924028C2213yes—
19C2×#11924028C2213yes—
20C2×#11924027C2213yes—
21C2×#11924027C2213yes—
22C2×#11924027C2213yescomplemented
23#41×D73—28no—
24C22×Dic146C2213yescomplemented
25C2×Q8×D73C2211yescharacteristic
26C2×Q8×D73C2211yescharacteristic, complemented
27C2×D4×D73C2213yes—
28C22×C4×D73C2213yes—
29#14556587C2213yescomplemented
30#14556587C2216yescomplemented
31#14556579C2213yescomplemented
32#14556578C2213yescomplemented
33#14556577C2216yescomplemented
34#14556576C2211yescharacteristic
35#14556573C2213yes—
36#14556571C2213yescomplemented
37#14556570C2213yescomplemented
38#14556569C2213yescomplemented
39#14556568C2213yescomplemented
40#14556566C2213yescomplemented
41#14556565C2213yescomplemented
42#14556564C2213yescomplemented
43#14556563C2216yescomplemented
44#14556563C2216yescomplemented
45#14556563C2213yescomplemented
46#14556562C2213yescomplemented
47#14556562C2213yescomplemented
48#14556561C2213yes—
49#14556559C2213yes—
50#14556559C2216yes—
51Q8×Dic73C2211yescharacteristic, complemented
52C4×Dic146C2213yescomplemented
53#14556556C2213yescomplemented
54C4×D292C2213yescomplemented
55D4×Dic73C2216yescomplemented
56C4×C22⋊D73C2213yescomplemented
57C4×C22⋊D73C2213yescomplemented
58#14556551C2216yescomplemented
59#14556549C2213yes—
60#14556548C2213yes—
61C2×#41×C73C2211yescharacteristic
62C2×#41×C73C2211yescharacteristic, complemented
63#127×C73C2213yescomplemented
64#121×C73C2213yescomplemented
65#121×C73C2213yescomplemented
66C4×Q8×C73C2211yescharacteristic, complemented
67C4×D4×C73C2213yescomplemented
68C23×D73C2313yes—
69#11924029—24no—
70#11924028—212no—
71#11924028—212no—
72#11924027—212no—
73#11924027—212no—
74#11924027—212no—
75C2×Dic146—212no—
76C2×Dic146C2313yes—
77C2×Dic146C2313yes—
78C2×Dic146C2313yes—
79Q8×D73—24no—
80Q8×D73D418yescomplemented
81C2×D292C2311yescharacteristic
82C2×D292C2313yes—
83C2×D292C2313yes—
84C2×C22⋊D73C2313yes—
85C2×C22⋊D73C2316yes—
86C2×C22⋊D73C2313yes—
87C2×C22⋊D73C2316yes—
88C2×C22⋊D73C2313yes—
89C2×C22⋊D73C2313yes—
90D4×D73—212no—
91C22×Dic73C2316yes—
92C22×Dic73C2313yes—
93C2×C4×D73—212no—
94C2×C4×D73C2313yes—
95C2×C4×D73C2313yes—
96C2×C4×D73C2313yes—
97C2×C4×D73C2311yescharacteristic
98C2×C4×D73C2313yes—
99C4⋊Dic73C2313yes—
100C4⋊Dic73C2313yes—
101#11924007C2313yes—
102#11924007C2313yes—
103#11924007C2313yes—
104#11924007C2311yescharacteristic
105C22⋊Dic73C2313yes—
106C22⋊Dic73C2313yes—
107C22⋊Dic73C2316yes—
108#11924005C2311yescharacteristic
109#11924005C2313yes—
110#11924005C2316yes—
111#11924005C2311yescharacteristic
112#11924005C2313yes—
113#11924005C2311yescharacteristic
114#11924005C2313yes—
115C4×Dic73C2313yes—
116C4×Dic73C2316yes—
117#41×C73—24no—
118#41×C73—24no—
119C2×Q8×C73C2311yescharacteristic
120C2×D4×C73C2313yes—
121C2×D4×C73C2313yes—
122C2×D4×C73C2313yes—
123C2×D4×C73C2316yes—
124C22×C4×C73C2313yes—
125C22×C4×C73C2313yes—
126C4⋊C4×C73C2311yescharacteristic
127C4⋊C4×C73C2313yes—
128C22⋊C4×C73C2313yes—
129C22⋊C4×C73C2313yes—
130C42×C73C2313yes—
131C23×C73C2413yes—
132C23×C73C2413yes—
133C22×D73—26no—
134C22×D73—43no—
135C22×D73—43no—
136C22×D73C2413yes—
137C22×D73C2411yescharacteristic
138C22×D73C2411yescharacteristic
139Q8×C73C2×D414yes—
140D4×C73—26no—
141D4×C73—26no—
142D4×C73—46no—
143D4×C73—43no—
144C2×C4×C73—26no—
145C2×C4×C73—26no—
146C2×C4×C73C2411yescharacteristic
147C2×C4×C73C2413yes—
148C2×C4×C73C2411yescharacteristic
149C2×C4×C73C2411yescharacteristic
150C2×C4×C73C2413yes—
151C22⋊D73—26no—
152C22⋊D73—212no—
153C22⋊D73—26no—
154C22⋊D73—43no—
155C22⋊D73—43no—
156C22⋊D73—46no—
157C2×Dic73—26no—
158C2×Dic73—212no—
159C2×Dic73C2411yescharacteristic
160C2×Dic73C2413yes—
161C2×Dic73C2413yes—
162C2×Dic73C2411yescharacteristic
163C2×Dic73C2413yes—
164D292—22no—
165D292—26no—
166D292—43no—
167C4×D73—22no—
168C4×D73—26no—
169C4×D73—26no—
170C4×D73—26no—
171C4×D73C2×D4112yes—
172Dic146—26no—
173Dic146—26no—
174Dic146C2×D4112yes—
175C22×C73—23no—
176C22×C73—23no—
177C22×C73—23no—
178C22×C73—23no—
179C22×C73—23no—
180C22×C73—23no—
181C22×C73C2511yescharacteristic
182C2×D73—21no—
183C2×D73—21no—
184C2×D73—21no—
185C2×D73—23no—
186C2×D73—21no—
187C2×D73—23no—
188C2×D73—21no—
189C2×D73—23no—
190C2×D73—412no—
191C2×D73C22×D412yes—
192C4×C73—21no—
193C4×C73—21no—
194C4×C73—23no—
195C4×C73—21no—
196C4×C73C22×D416yes—
197Dic73—23no—
198Dic73—21no—
199Dic73—21no—
200Dic73—23no—
201Dic73C22×D416yes—
202C2×C73—43no—
203C2×C73—43no—
204C2×C73C23×D411yescharacteristic
205C2×C73#58511yescharacteristic
206C2×C73#58511yescharacteristic
207D73—22no—
208D73—41no—
209D73—43no—
210#3487—731nomaximal, Sylow
211C73#348711yescharacteristic, complemented, Sylow
212C2×2−1+4—731no—
213C22×#41—731no—
214#550—731no—
215#550—733no—
216#550—733no—
217#550D7311yescharacteristic, complemented
218#548—731no—
219#548—733no—
220#548—731no—
221#548—733no—
222#535—733no—
223#535—733no—
224#525—733no—
225#525—733no—
226#519—731no—
2272−1+4—1468no—
228C2×#41—731no—
229C2×#41—733no—
230C2×#41—733no—
231C2×#41—733no—
232C2×#41—733no—
233C2×#41—733no—
234C2×#41—1468no—
235C2×#41C2×D7311yescharacteristic
236C2×#41C2×D7311yescharacteristic, complemented
237C22×Q8—731no—
238C22×Q8—731no—
239C22×Q8—733no—
240C22×D4—733no—
241C23×C4—733no—
242#127—733no—
243#127—736no—
244#127C2×D7313yescomplemented
245#124—733no—
246#124—736no—
247#124—733no—
248#123—731no—
249#123—733no—
250C22⋊Q8—733no—
251C22⋊Q8—733no—
252C22⋊Q8—733no—
253C22⋊Q8—733no—
254#121—733no—
255#121—733no—
256#121—733no—
257#121—736no—
258#121—736no—
259#121—733no—
260#121—733no—
261#121—733no—
262#121C2×D7313yescomplemented
263#121C2×D7313yescomplemented
264#120—736no—
265#120—733no—
266#120—733no—
267C4×Q8—731no—
268C4×Q8—733no—
269C4×Q8—733no—
270C4×Q8C2×D7311yescharacteristic, complemented
271C4×D4—736no—
272C4×D4—733no—
273C4×D4—733no—
274C4×D4—736no—
275C4×D4—733no—
276C4×D4C2×D7313yescomplemented
277#117—733no—
278#117—733no—
279C24—733no—
280#41—24no—
281#41—24no—
282#41—14612no—
283#41—14612no—
284#41—14612no—
285#41—14612no—
286#41—14612no—
287#41—1464no—
288C2×Q8—738no—
289C2×Q8—733no—
290C2×Q8—733no—
291C2×Q8—733no—
292C2×Q8—14612no—
293C2×Q8—1464no—
294C2×Q8C22×D7311yescharacteristic
295C2×D4—736no—
296C2×D4—733no—
297C2×D4—733no—
298C2×D4—733no—
299C2×D4—736no—
300C2×D4—733no—
301C2×D4—733no—
302C2×D4—731no—
303C2×D4—733no—
304C2×D4—14612no—
305C2×D4C22×D7313yes—
306C2×D4C22×D7313yes—
307C2×D4C22×D7316yes—
308C2×D4C22×D7313yes—
309C22×C4—733no—
310C22×C4—736no—
311C22×C4—733no—
312C22×C4—733no—
313C22×C4—733no—
314C22×C4—733no—
315C22×C4—731no—
316C22×C4—14612no—
317C22×C4C22×D7313yes—
318C22×C4C22×D7313yes—
319C4⋊C4—733no—
320C4⋊C4—733no—
321C4⋊C4—733no—
322C4⋊C4—731no—
323C4⋊C4—733no—
324C4⋊C4—733no—
325C4⋊C4C22×D7313yes—
326C4⋊C4C22×D7311yescharacteristic
327C22⋊C4—733no—
328C22⋊C4—733no—
329C22⋊C4—736no—
330C22⋊C4—733no—
331C22⋊C4—731no—
332C22⋊C4—731no—
333C22⋊C4—731no—
334C22⋊C4—733no—
335C22⋊C4—736no—
336C22⋊C4—733no—
337C22⋊C4C22×D7313yes—
338C22⋊C4C22×D7313yes—
339C42—736no—
340C42—733no—
341C42C22×D7313yes—
342C23—2923no—
343C23—2923no—
344C23—731no—
345C23—733no—
346C23—731no—
347C23—1466no—
348C23C23×D7313yes—
349C23C23×D7313yes—
350Q8—7312no—
351Q8—1466no—
352Q8—1466no—
353Q8D4×D7314yes—
354D4—26no—
355D4—26no—
356D4—46no—
357D4—43no—
358D4—2923no—
359D4—2923no—
360D4—2926no—
361D4—2923no—
362D4—1462no—
363D4—14612no—
364D4—1466no—
365D4—1466no—
366D4—1466no—
367C2×C4—26no—
368C2×C4—26no—
369C2×C4—733no—
370C2×C4—7312no—
371C2×C4—731no—
372C2×C4—733no—
373C2×C4—733no—
374C2×C4—731no—
375C2×C4—1466no—
376C2×C4—1462no—
377C2×C4—1466no—
378C2×C4—14612no—
379C2×C4—1466no—
380C2×C4—1466no—
381C2×C4C23×D7313yes—
382C2×C4C23×D7311yescharacteristic
383C2×C4C23×D7311yescharacteristic
384C2×C4C23×D7311yescharacteristic
385C2×C4C23×D7313yes—
386C22—23no—
387C22—23no—
388C22—23no—
389C22—23no—
390C22—23no—
391C22—23no—
392C22—29212no—
393C22—732no—
394C22—1461no—
395C22—1463no—
396C22—1461no—
397C22—1463no—
398C22—1461no—
399C22—1463no—
400C22—1461no—
401C22—1461no—
402C22C24×D7311yescharacteristic
403C4—21no—
404C4—21no—
405C4—23no—
406C4—21no—
407C4—736no—
408C4—1461no—
409C4—1463no—
410C4—1461no—
411C4—1463no—
412C4C2×D4×D7316yes—
413C2—43no—
414C2—43no—
415C2—2923no—
416C2—2921no—
417C2—1462no—
418C2C22×D4×D7311yescharacteristic
419C2#1798942211yescharacteristic
420C2#1798942311yescharacteristic
subgroupG/H
center, FrattiniC22C24×D73
commutator, socleC22×C73C25
Fitting#550×C73C2
hypercenter#550D73
hypocenterC73#3487
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#14556638C2semidirect
2. C2×#41×D73C2semidirect
3. #17989257C2semidirect
4. #17989256C2semidirect
5. #17989255C2semidirect
6. #17989249C2semidirect
7. #17989246C2semidirect
8. #17989244C2semidirect
9. #17989243C2semidirect
10. #17989153C2semidirect
11. #17989150C2semidirect
12. #17989097C2semidirect
13. #17989096C2semidirect
14. #17989063C2semidirect
15. #550×C73C2semidirect
22. C2×#11924027C22semidirect
24. C22×Dic146C22semidirect
26. C2×Q8×D73C22semidirect
29. #14556587C22semidirect
30. #14556587C22semidirect
31. #14556579C22semidirect
32. #14556578C22semidirect
33. #14556577C22semidirect
36. #14556571C22semidirect
37. #14556570C22semidirect
38. #14556569C22semidirect
39. #14556568C22semidirect
40. #14556566C22semidirect
41. #14556565C22semidirect
42. #14556564C22semidirect
43. #14556563C22semidirect
44. #14556563C22semidirect
45. #14556563C22semidirect
46. #14556562C22semidirect
47. #14556562C22semidirect
51. Q8×Dic73C22semidirect
52. C4×Dic146C22semidirect
53. #14556556C22semidirect
54. C4×D292C22semidirect
55. D4×Dic73C22semidirect
56. C4×C22⋊D73C22semidirect
57. C4×C22⋊D73C22semidirect
58. #14556551C22semidirect
62. C2×#41×C73C22semidirect
63. #127×C73C22semidirect
64. #121×C73C22semidirect
65. #121×C73C22semidirect
66. C4×Q8×C73C22semidirect
67. C4×D4×C73C22semidirect
80. Q8×D73D4semidirect
211. C73#3487semidirect
217. #550D73semidirect
236. C2×#41C2×D73semidirect
244. #127C2×D73semidirect
262. #121C2×D73semidirect
263. #121C2×D73semidirect
270. C4×Q8C2×D73semidirect
276. C4×D4C2×D73semidirect