Finite Group Databasebeta

← #22623722

Subgroups — #22623722

Order 9344.

1540 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×#14556639C211yesmaximal, characteristic, complemented
2C2×#14556637C211yesmaximal, characteristic, complemented
3#17989249C211yesmaximal, characteristic, complemented
4#17989248C211yesmaximal, characteristic, complemented
5#17989244C211yesmaximal, characteristic, complemented
6#17989234C213yesmaximal, complemented
7#17989233C213yesmaximal, complemented
8#17989230C213yesmaximal, complemented
9#17989228C213yesmaximal, complemented
10#17989160C213yesmaximal, complemented
11#17989153C213yesmaximal, complemented
12#17989134C213yesmaximal, complemented
13#124×D73C213yesmaximal, complemented
14C4×#11924029C211yesmaximal, characteristic, complemented
15#548×C73C211yesmaximal, characteristic, complemented
16#14556639—28no—
17#14556637—28no—
18C2×#11924029C2211yescharacteristic
19C2×#11924029C2211yescharacteristic
20C2×#11924029C2213yescomplemented
21C2×#11924028C2213yes—
22C2×#11924028C2213yescomplemented
23C2×#11924028C2213yescomplemented
24C2×Q8×D73C2213yescomplemented
25C2×Q8×D73C2211yescharacteristic, complemented
26C22×D292C2213yes—
27C2×D4×D73C2213yes—
28C2×D4×D73C2213yes—
29#14556590C2213yescomplemented
30#14556587C2213yescomplemented
31#14556580C2213yescomplemented
32#14556579C2213yescomplemented
33#14556578C2213yescomplemented
34#14556577C2211yescharacteristic, complemented
35#14556577C2213yescomplemented
36#14556577C2216yescomplemented
37#14556576C2216yescomplemented
38#14556573C2216yescomplemented
39#14556571C2213yescomplemented
40#14556570C2213yescomplemented
41#14556567C2213yescomplemented
42#14556566C2213yescomplemented
43#14556566C2213yescomplemented
44#14556565C2213yescomplemented
45#14556564C2213yescomplemented
46#14556564C2213yescomplemented
47#14556562C2213yescomplemented
48#14556562C2213yescomplemented
49#14556561C2216yescomplemented
50#14556559C2216yescomplemented
51Q8×Dic73C2211yescharacteristic, complemented
52C4×D292C2213yescomplemented
53C4×D292C2213yescomplemented
54#14556553C2213yescomplemented
55C4×C22⋊D73C2213yescomplemented
56C4×C22⋊D73C2213yescomplemented
57#14556549C2213yescomplemented
58C22⋊C4×D73C2216yescomplemented
59C22⋊C4×D73C2216yescomplemented
60C42×D73C2213yescomplemented
61C2×#41×C73C2211yescharacteristic
62C22×Q8×C73C2211yescharacteristic, complemented
63#124×C73C2213yescomplemented
64C22⋊Q8×C73C2213yescomplemented
65#121×C73C2213yescomplemented
66C4×Q8×C73C2211yescharacteristic, complemented
67C4×D4×C73C2213yescomplemented
68C23×D73C2316yes—
69#11924029—24no—
70#11924029—212no—
71#11924029D418yescomplemented
72#11924028—212no—
73#11924028—212no—
74#11924028—212no—
75C2×Dic146C2313yes—
76C2×Dic146C2313yes—
77C2×Dic146C2311yescharacteristic
78Q8×D73—24no—
79Q8×D73—212no—
80C2×D292—212no—
81C2×D292C2313yes—
82C2×D292C2313yes—
83C2×D292C2313yes—
84C2×D292C2313yes—
85C2×D292C2313yes—
86C2×C22⋊D73C2313yes—
87C2×C22⋊D73C2313yes—
88C2×C22⋊D73C2313yes—
89C2×C22⋊D73C2311yescharacteristic
90C2×C22⋊D73C2313yes—
91C2×C22⋊D73C2313yes—
92D4×D73—212no—
93D4×D73—212no—
94C2×C4×D73C2316yes—
95C2×C4×D73C2313yes—
96C2×C4×D73C2313yes—
97C2×C4×D73C2313yes—
98C2×C4×D73C2313yes—
99C2×C4×D73C2313yes—
100C4⋊Dic73C2313yes—
101C4⋊Dic73C2313yes—
102#11924007C2313yes—
103#11924007C2313yes—
104C22⋊Dic73C2313yes—
105C22⋊Dic73C2316yes—
106C22⋊Dic73C2311yescharacteristic
107#11924005C2313yes—
108#11924005C2313yes—
109#11924005C2316yes—
110#11924005C2316yes—
111#11924005C2316yes—
112#11924005C2311yescharacteristic
113#11924005C2311yescharacteristic
114C4×Dic73C2311yescharacteristic
115C4×Dic73C2313yes—
116C4×Dic73C2313yes—
117#41×C73—24no—
118C2×Q8×C73—24no—
119C2×Q8×C73C2313yes—
120C2×Q8×C73C2311yescharacteristic
121C2×D4×C73C2313yes—
122C2×D4×C73C2313yes—
123C22×C4×C73C2313yes—
124C22×C4×C73C2313yes—
125C4⋊C4×C73C2313yes—
126C4⋊C4×C73C2313yes—
127C22⋊C4×C73C2311yescharacteristic
128C22⋊C4×C73C2313yes—
129C22⋊C4×C73C2316yes—
130C42×C73C2313yes—
131C23×C73C2413yes—
132C23×C73C2411yescharacteristic
133C22×D73—212no—
134C22×D73—46no—
135C22×D73—46no—
136C22×D73C2413yes—
137C22×D73C2411yescharacteristic
138C22×D73C2413yes—
139Q8×C73—26no—
140Q8×C73C2×D414yes—
141D4×C73—26no—
142D4×C73—43no—
143C2×C4×C73—26no—
144C2×C4×C73—26no—
145C2×C4×C73C2411yescharacteristic
146C2×C4×C73C2413yes—
147C2×C4×C73C2413yes—
148C2×C4×C73C2411yescharacteristic
149C2×C4×C73C2413yes—
150C22⋊D73—26no—
151C22⋊D73—26no—
152C22⋊D73—26no—
153C22⋊D73—22no—
154C22⋊D73—43no—
155C22⋊D73—43no—
156C2×Dic73C2411yescharacteristic
157C2×Dic73C2413yes—
158C2×Dic73C2413yes—
159C2×Dic73C2411yescharacteristic
160C2×Dic73C2411yescharacteristic
161D292—26no—
162D292—26no—
163D292—26no—
164D292—43no—
165D292C2×D4112yes—
166C4×D73—212no—
167C4×D73—26no—
168C4×D73—26no—
169C4×D73—43no—
170C4×D73—43no—
171C4×D73C2×D4112yes—
172Dic146—26no—
173Dic146—26no—
174Dic146—22no—
175C22×C73—21no—
176C22×C73—23no—
177C22×C73—21no—
178C22×C73—23no—
179C22×C73—21no—
180C22×C73—23no—
181C22×C73C2511yescharacteristic
182C2×D73—23no—
183C2×D73—23no—
184C2×D73—21no—
185C2×D73—23no—
186C2×D73—21no—
187C2×D73—23no—
188C2×D73—21no—
189C2×D73—23no—
190C2×D73—812no—
191C2×D73C22×D416yes—
192C4×C73—23no—
193C4×C73—21no—
194C4×C73—21no—
195C4×C73—23no—
196C4×C73C22×D416yes—
197Dic73—23no—
198Dic73—21no—
199Dic73—21no—
200Dic73—23no—
201Dic73C22×D412yes—
202C2×C73—43no—
203C2×C73—41no—
204C2×C73C23×D411yescharacteristic
205C2×C73#58511yescharacteristic
206C2×C73#58511yescharacteristic
207D73—26no—
208D73—41no—
209D73—43no—
210#3500—731nomaximal, Sylow
211C73#350011yescharacteristic, complemented, Sylow
212C2×2−1+4—731no—
213C2×H(5,𝔽2)—731no—
214#548—731no—
215#548—731no—
216#548—731no—
217#548D7311yescharacteristic, complemented
218#546—733no—
219#546—733no—
220#546—733no—
221#546—733no—
222#536—733no—
223#535—733no—
224#532—733no—
225C2×#124—733no—
226C4×#41—731no—
2272−1+4—1468no—
228H(5,𝔽2)—1468no—
229C2×#41—731no—
230C2×#41—733no—
231C2×#41—731no—
232C2×#41—733no—
233C2×#41—733no—
234C2×#41—733no—
235C2×#41C2×D7311yescharacteristic
236C22×Q8—733no—
237C22×Q8—731no—
238C22×Q8C2×D7311yescharacteristic, complemented
239C22×D4—733no—
240C22×D4—733no—
241C22×D4—733no—
242C4⋊Q8—733no—
243#127—733no—
244#124—733no—
245#124—733no—
246#124—733no—
247#124—736no—
248#124—731no—
249#124—733no—
250#124C2×D7313yescomplemented
251#123—736no—
252#123—736no—
253C22⋊Q8—733no—
254C22⋊Q8—733no—
255C22⋊Q8—733no—
256C22⋊Q8C2×D7313yescomplemented
257#121—733no—
258#121—733no—
259#121—733no—
260#121—733no—
261#121—733no—
262#121—733no—
263#121—733no—
264#121C2×D7313yescomplemented
265#120—736no—
266#120—736no—
267C4×Q8—731no—
268C4×Q8C2×D7311yescharacteristic, complemented
269C4×D4—733no—
270C4×D4—733no—
271C4×D4—733no—
272C4×D4—733no—
273C4×D4—733no—
274C4×D4C2×D7313yescomplemented
275#117—733no—
276C2×C22⋊C4—736no—
277C2×C22⋊C4—736no—
278C2×C42—733no—
279C24—736no—
280#41—24no—
281#41—738no—
282#41—14612no—
283#41—14612no—
284#41—14612no—
285#41—14612no—
286#41—1464no—
287C2×Q8—24no—
288C2×Q8—733no—
289C2×Q8—733no—
290C2×Q8—731no—
291C2×Q8—14612no—
292C2×Q8—1464no—
293C2×Q8C22×D7313yes—
294C2×Q8C22×D7311yescharacteristic
295C2×D4—733no—
296C2×D4—733no—
297C2×D4—733no—
298C2×D4—733no—
299C2×D4—733no—
300C2×D4—731no—
301C2×D4—733no—
302C2×D4—733no—
303C2×D4—733no—
304C2×D4—733no—
305C2×D4—733no—
306C2×D4—14612no—
307C2×D4—14612no—
308C2×D4—14612no—
309C2×D4C22×D7313yes—
310C2×D4C22×D7313yes—
311C22×C4—733no—
312C22×C4—733no—
313C22×C4—733no—
314C22×C4—736no—
315C22×C4—733no—
316C22×C4—733no—
317C22×C4C22×D7313yes—
318C22×C4C22×D7313yes—
319C4⋊C4—733no—
320C4⋊C4—733no—
321C4⋊C4—733no—
322C4⋊C4—733no—
323C4⋊C4C22×D7313yes—
324C4⋊C4C22×D7313yes—
325C22⋊C4—733no—
326C22⋊C4—736no—
327C22⋊C4—731no—
328C22⋊C4—733no—
329C22⋊C4—733no—
330C22⋊C4—736no—
331C22⋊C4—736no—
332C22⋊C4—736no—
333C22⋊C4—731no—
334C22⋊C4—731no—
335C22⋊C4C22×D7313yes—
336C22⋊C4C22×D7316yes—
337C22⋊C4C22×D7311yescharacteristic
338C42—731no—
339C42—733no—
340C42—733no—
341C42C22×D7313yes—
342C23—2926no—
343C23—2926no—
344C23—733no—
345C23—733no—
346C23—731no—
347C23—14612no—
348C23C23×D7313yes—
349C23C23×D7311yescharacteristic
350Q8—26no—
351Q8—1466no—
352Q8—1462no—
353Q8—1466no—
354Q8D4×D7314yes—
355D4—26no—
356D4—43no—
357D4—2923no—
358D4—2923no—
359D4—2923no—
360D4—7312no—
361D4—1466no—
362D4—1466no—
363D4—1466no—
364D4—1462no—
365D4—1466no—
366D4—1466no—
367D4—1466no—
368C2×C4—26no—
369C2×C4—26no—
370C2×C4—2923no—
371C2×C4—2923no—
372C2×C4—731no—
373C2×C4—7312no—
374C2×C4—731no—
375C2×C4—733no—
376C2×C4—733no—
377C2×C4—731no—
378C2×C4—14612no—
379C2×C4—1466no—
380C2×C4—1466no—
381C2×C4C23×D7311yescharacteristic
382C2×C4C23×D7313yes—
383C2×C4C23×D7313yes—
384C2×C4C23×D7311yescharacteristic
385C2×C4C23×D7313yes—
386C22—21no—
387C22—23no—
388C22—21no—
389C22—23no—
390C22—21no—
391C22—23no—
392C22—58412no—
393C22—736no—
394C22—1461no—
395C22—1463no—
396C22—1461no—
397C22—1463no—
398C22—1461no—
399C22—1463no—
400C22—1463no—
401C22—1463no—
402C22C24×D7311yescharacteristic
403C4—21no—
404C4—23no—
405C4—23no—
406C4—21no—
407C4—732no—
408C4—1461no—
409C4—1463no—
410C4—1461no—
411C4—1463no—
412C4C2×D4×D7316yes—
413C2—43no—
414C2—41no—
415C2—2923no—
416C2—2921no—
417C2—1466no—
418C2C22×D4×D7311yescharacteristic
419C2#1798942311yescharacteristic
420C2#1798942411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D73
commutator, socleC22×C73C25
Fitting#548×C73C2
hypercenter#548D73
hypocenterC73#3500
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#14556639C2semidirect
2. C2×#14556637C2semidirect
3. #17989249C2semidirect
4. #17989248C2semidirect
5. #17989244C2semidirect
6. #17989234C2semidirect
7. #17989233C2semidirect
8. #17989230C2semidirect
9. #17989228C2semidirect
10. #17989160C2semidirect
11. #17989153C2semidirect
12. #17989134C2semidirect
13. #124×D73C2semidirect
14. C4×#11924029C2semidirect
15. #548×C73C2semidirect
20. C2×#11924029C22semidirect
22. C2×#11924028C22semidirect
23. C2×#11924028C22semidirect
24. C2×Q8×D73C22semidirect
25. C2×Q8×D73C22semidirect
29. #14556590C22semidirect
30. #14556587C22semidirect
31. #14556580C22semidirect
32. #14556579C22semidirect
33. #14556578C22semidirect
34. #14556577C22semidirect
35. #14556577C22semidirect
36. #14556577C22semidirect
37. #14556576C22semidirect
38. #14556573C22semidirect
39. #14556571C22semidirect
40. #14556570C22semidirect
41. #14556567C22semidirect
42. #14556566C22semidirect
43. #14556566C22semidirect
44. #14556565C22semidirect
45. #14556564C22semidirect
46. #14556564C22semidirect
47. #14556562C22semidirect
48. #14556562C22semidirect
49. #14556561C22semidirect
50. #14556559C22semidirect
51. Q8×Dic73C22semidirect
52. C4×D292C22semidirect
53. C4×D292C22semidirect
54. #14556553C22semidirect
55. C4×C22⋊D73C22semidirect
56. C4×C22⋊D73C22semidirect
57. #14556549C22semidirect
58. C22⋊C4×D73C22semidirect
59. C22⋊C4×D73C22semidirect
60. C42×D73C22semidirect
62. C22×Q8×C73C22semidirect
63. #124×C73C22semidirect
64. C22⋊Q8×C73C22semidirect
65. #121×C73C22semidirect
66. C4×Q8×C73C22semidirect
67. C4×D4×C73C22semidirect
71. #11924029D4semidirect
211. C73#3500semidirect
217. #548D73semidirect
238. C22×Q8C2×D73semidirect
250. #124C2×D73semidirect
256. C22⋊Q8C2×D73semidirect
264. #121C2×D73semidirect
268. C4×Q8C2×D73semidirect
274. C4×D4C2×D73semidirect