Finite Group Databasebeta

← #22621723

Subgroups — #22621723

Order 9344.

460 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989399C211yesmaximal, characteristic, complemented
2#17989397C211yesmaximal, characteristic, complemented
3#17989396C211yesmaximal, characteristic, complemented
4#17989393C211yesmaximal, characteristic, complemented
5#17988958C211yesmaximal, characteristic, complemented
6#17988853C211yesmaximal, characteristic, complemented
7#17988851C211yesmaximal, characteristic, complemented
8#17988849C211yesmaximal, characteristic, complemented
9#17988772C211yesmaximal, characteristic, complemented
10#17988768C211yesmaximal, characteristic, complemented
11#17988757C211yesmaximal, characteristic, complemented
12#17988753C211yesmaximal, characteristic, complemented
13#17988703C211yesmaximal, characteristic, complemented
14#17988702C211yesmaximal, characteristic, complemented
15#471×C73C211yesmaximal, characteristic, complemented
16#14556639C2211yescharacteristic
17#14556638C2211yescharacteristic
18#14556637C2211yescharacteristic, complemented
19#14556636C2211yescharacteristic, complemented
20#14556624—21no—
21#14556624C2211yescharacteristic, complemented
22#14556624C2211yescharacteristic, complemented
23#14556623—21no—
24#14556622C2211yescharacteristic, complemented
25#14556620—21no—
26#14556620—21no—
27#14556619—21no—
28#14556619C2211yescharacteristic
29#14556619C2211yescharacteristic
30#14556618—21no—
31#14556618—21no—
32#14556617C2211yescharacteristic
33#14556615—21no—
34#14556614—21no—
35#14556613—21no—
36#14556613C2211yescharacteristic
37#14556612—21no—
38#14556611C2211yescharacteristic
39#14556610—21no—
40C2×#11924017—21no—
41C2×#11924017C2211yescharacteristic, complemented
42C2×#11924016C2211yescharacteristic, complemented
43C2×#11924015C2211yescharacteristic, complemented
44SD16×D73—21no—
45SD16×D73—21no—
46SD16×D73—21no—
47#14556599C2211yescharacteristic, complemented
48#14556599C2211yescharacteristic, complemented
49#14556597C2211yescharacteristic, complemented
50#14556589C2211yescharacteristic, complemented
51#14556587C2211yescharacteristic
52#14556526C2211yescharacteristic, complemented
53#14556518C2211yescharacteristic, complemented
54#14556517C2211yescharacteristic, complemented
55#14556517C2211yescharacteristic, complemented
56#14556517C2211yescharacteristic, complemented
57#14556509C2211yescharacteristic, complemented
58#14556507C2211yescharacteristic, complemented
59C8×Dic73C2211yescharacteristic, complemented
60#137×C73C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C73C2211yescharacteristic
62C2×SD16×C73C2211yescharacteristic, complemented
63#131×C73C2211yescharacteristic, complemented
64#108×C73C2211yescharacteristic, complemented
65#101×C73C2211yescharacteristic, complemented
66#100×C73C2211yescharacteristic, complemented
67#11924029—21no—
68#11924029—21no—
69#11924029—21no—
70#11924028—21no—
71#11924028—21no—
72#11924028—41no—
73#11924028C2311yescharacteristic
74#11924028C2311yescharacteristic
75#11924028C2311yescharacteristic
76#11924027—21no—
77#11924027—21no—
78#11924027—21no—
79#11924027—41no—
80C2×Dic146—21no—
81C2×Dic146C2311yescharacteristic
82Q8×D73—21no—
83Q8×D73—21no—
84Q8×D73—21no—
85C2×D292—21no—
86C2×D292C2311yescharacteristic
87C2×C22⋊D73—41no—
88C2×C22⋊D73—41no—
89D4×D73—21no—
90D4×D73—21no—
91D4×D73—21no—
92D4×D73—41no—
93Dic292—21no—
94Dic292—21no—
95Dic292D411yescharacteristic, complemented
96#11924018—21no—
97#11924018D411yescharacteristic, complemented
98#11924017—21no—
99#11924017—21no—
100#11924017—21no—
101#11924017—21no—
102#11924017—21no—
103#11924017—21no—
104#11924017D411yescharacteristic, complemented
105#11924017D411yescharacteristic, complemented
106#11924016—21no—
107#11924016—21no—
108#11924016—21no—
109#11924016D411yescharacteristic, complemented
110#11924015—21no—
111#11924015—21no—
112#11924015—21no—
113#11924015D411yescharacteristic, complemented
114D584—21no—
115D584—21no—
116D584D411yescharacteristic, complemented
117#11924013—21no—
118#11924013D411yescharacteristic, complemented
119#11924012C2311yescharacteristic
120#11924011—21no—
121#11924011—21no—
122#11924011—21no—
123C2×#10596831C2311yescharacteristic
124C8×D73—21no—
125C8×D73—21no—
126C8×D73—21no—
127#11924007—41no—
128C4×Dic73C2311yescharacteristic
129#41×C73C2311yescharacteristic
130C2×Q8×C73C2311yescharacteristic
131C2×D4×C73C2311yescharacteristic
132Q16×C73—21no—
133SD16×C73—21no—
134SD16×C73—21no—
135SD16×C73—21no—
136SD16×C73—21no—
137D8×C73—21no—
138M16×C73—21no—
139M16×C73C2311yescharacteristic
140M16×C73C2311yescharacteristic
141M16×C73C2311yescharacteristic
142C2×C8×C73—21no—
143C2×C8×C73C2311yescharacteristic
144C23×C73—21no—
145C22×D73—21no—
146C22×D73—41no—
147C22×D73—41no—
148Q8×C73—21no—
149Q8×C73—21no—
150Q8×C73C2×D411yescharacteristic
151D4×C73—21no—
152D4×C73—21no—
153D4×C73—21no—
154D4×C73C2×D411yescharacteristic
155C2×C4×C73—21no—
156C2×C4×C73—21no—
157C2×C4×C73C2411yescharacteristic
158C22⋊D73—21no—
159C22⋊D73—21no—
160C22⋊D73—21no—
161C22⋊D73—41no—
162C22⋊D73—41no—
163C22⋊D73—41no—
164C22⋊D73—41no—
165C22⋊D73—82no—
166C2×Dic73—21no—
167C2×Dic73—21no—
168C2×Dic73—41no—
169C2×Dic73—41no—
170D292—21no—
171D292—21no—
172D292—41no—
173D292—41no—
174D292C2×D411yescharacteristic
175D292C2×D411yescharacteristic
176D292C2×D411yescharacteristic
177C4×D73—21no—
178C4×D73—21no—
179C4×D73—21no—
180C4×D73—41no—
181C4×D73—41no—
182C4×D73—41no—
183C4×D73—41no—
184Dic146—21no—
185Dic146—21no—
186Dic146—41no—
187Dic146—41no—
188Dic146C2×D411yescharacteristic
189Dic146C2×D411yescharacteristic
190Dic146C2×D411yescharacteristic
191C8×C73—21no—
192C8×C73—21no—
193C8×C73—21no—
194C8×C73C2×D411yescharacteristic
195C8×C73C2×D411yescharacteristic
196#10596831—21no—
197#10596831C2×D411yescharacteristic
198#10596831C2×D411yescharacteristic
199C22×C73—21no—
200C22×C73—41no—
201C22×C73—81no—
202C22×C73H(5,𝔽2)11yescharacteristic
203C2×D73—21no—
204C2×D73—21no—
205C2×D73—21no—
206C2×D73—41no—
207C2×D73—81no—
208C2×D73—161no—
209C2×D73—161no—
210C4×C73—21no—
211C4×C73—41no—
212C4×C73C22×D411yescharacteristic
213C4×C73C22×D411yescharacteristic
214Dic73—22no—
215Dic73—21no—
216Dic73—21no—
217Dic73—21no—
218Dic73—41no—
219C2×C73—21no—
220C2×C73—41no—
221C2×C73—81no—
222C2×C73D4211yescharacteristic
223D73—41no—
224D73—41no—
225D73—41no—
226D73—81no—
227#3291—731nomaximal, Sylow
228C73#329111yescharacteristic, complemented, Sylow
229#577—731no—
230#577—731no—
231#577—731no—
232#577—731no—
233#492—731no—
234#471—731no—
235#471—731no—
236#471—731no—
237#471D7311yescharacteristic, complemented
238#456—731no—
239#456—731no—
240#453—731no—
241#453—731no—
242#443—731no—
243#443—731no—
2442−1+4—731no—
2452−1+4—731no—
246H(5,𝔽2)—731no—
247H(5,𝔽2)—731no—
248#137—731no—
249#137—731no—
250#137—731no—
251#137—1461no—
252#137—1461no—
253#137—1461no—
254#137—1461no—
255#137C2×D7311yescharacteristic, complemented
256AGL(1,ℤ/8)—731no—
257AGL(1,ℤ/8)—731no—
258AGL(1,ℤ/8)—731no—
259AGL(1,ℤ/8)—1461no—
260AGL(1,ℤ/8)—1461no—
261AGL(1,ℤ/8)—1461no—
262AGL(1,ℤ/8)—1461no—
263AGL(1,ℤ/8)C2×D7311yescharacteristic
264#135—731no—
265#135—731no—
266#135—1461no—
267#135—1461no—
268#135—1461no—
269#135—1461no—
270C2×SD16—731no—
271C2×SD16—731no—
272C2×SD16—731no—
273C2×SD16—1461no—
274C2×SD16—1461no—
275C2×SD16—1461no—
276C2×SD16—1461no—
277C2×SD16C2×D7311yescharacteristic, complemented
278#131—731no—
279#131—731no—
280#131—731no—
281#131C2×D7311yescharacteristic, complemented
282C4⋊Q8—731no—
283#127—731no—
284#108—731no—
285#108C2×D7311yescharacteristic, complemented
286#104—731no—
287#104—731no—
288#104—731no—
289#104—731no—
290#101—731no—
291#101C2×D7311yescharacteristic, complemented
292#100—731no—
293#100C2×D7311yescharacteristic, complemented
294C4×C8—731no—
295#41—2921no—
296#41—2921no—
297#41—731no—
298#41—731no—
299#41—731no—
300#41—1461no—
301#41—1461no—
302#41—1461no—
303#41—1461no—
304#41—1461no—
305#41—1461no—
306#41—1461no—
307#41—1461no—
308#41C22×D7311yescharacteristic
309C2×Q8—731no—
310C2×Q8—1461no—
311C2×Q8—1461no—
312C2×Q8—1461no—
313C2×Q8—1461no—
314C2×Q8C22×D7311yescharacteristic
315C2×D4—2921no—
316C2×D4—2921no—
317C2×D4—2921no—
318C2×D4—731no—
319C2×D4—1461no—
320C2×D4—1461no—
321C2×D4—1461no—
322C2×D4—1461no—
323C2×D4C22×D7311yescharacteristic
324Q16—21no—
325Q16—731no—
326Q16—731no—
327Q16—1461no—
328Q16—1461no—
329Q16—1461no—
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—731no—
335SD16—731no—
336SD16—731no—
337SD16—731no—
338SD16—1461no—
339SD16—1461no—
340SD16—1461no—
341SD16—1461no—
342SD16—1461no—
343SD16—1461no—
344SD16—1461no—
345SD16—1461no—
346SD16—1461no—
347SD16—1461no—
348SD16—1461no—
349SD16—1461no—
350D8—21no—
351D8—731no—
352D8—731no—
353D8—1461no—
354D8—1461no—
355D8—1461no—
356M16—21no—
357M16—731no—
358M16—1461no—
359M16—1461no—
360M16—1461no—
361M16C22×D7311yescharacteristic
362M16C22×D7311yescharacteristic
363M16C22×D7311yescharacteristic
364C2×C8—21no—
365C2×C8—731no—
366C2×C8—1461no—
367C2×C8—1461no—
368C2×C8—1461no—
369C2×C8C22×D7311yescharacteristic
370C4⋊C4—2921no—
371C42—731no—
372C23—21no—
373C23—2921no—
374C23—2921no—
375C23—1461no—
376Q8—21no—
377Q8—21no—
378Q8—2921no—
379Q8—2921no—
380Q8—731no—
381Q8—731no—
382Q8—731no—
383Q8—1461no—
384Q8—1461no—
385Q8D4×D7311yescharacteristic
386D4—21no—
387D4—21no—
388D4—21no—
389D4—2921no—
390D4—2921no—
391D4—2921no—
392D4—2921no—
393D4—2921no—
394D4—2921no—
395D4—5842no—
396D4—731no—
397D4—731no—
398D4—731no—
399D4—1461no—
400D4—1461no—
401D4—1461no—
402D4—1461no—
403D4—1461no—
404D4D4×D7311yescharacteristic
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—2921no—
408C2×C4—2921no—
409C2×C4—2921no—
410C2×C4—2921no—
411C2×C4—2921no—
412C2×C4—2921no—
413C2×C4—1461no—
414C2×C4—1461no—
415C2×C4—1461no—
416C2×C4—1461no—
417C2×C4—1461no—
418C2×C4C23×D7311yescharacteristic
419C8—21no—
420C8—21no—
421C8—21no—
422C8—731no—
423C8—731no—
424C8—1461no—
425C8D4×D7311yescharacteristic
426C8D4×D7311yescharacteristic
427C22—21no—
428C22—41no—
429C22—81no—
430C22—2921no—
431C22—5841no—
432C22—11681no—
433C22—11681no—
434C22—1461no—
435C22—1461no—
436C22—1461no—
437C22#1455663711yescharacteristic
438C4—21no—
439C4—41no—
440C4—2921no—
441C4—1462no—
442C4—1461no—
443C4—1461no—
444C4—1461no—
445C4C2×D4×D7311yescharacteristic
446C4C2×D4×D7311yescharacteristic
447C2—21no—
448C2—41no—
449C2—81no—
450C2—2921no—
451C2—2921no—
452C2—2921no—
453C2—5841no—
454C2#1798922111yescharacteristic
subgroupG/H
centerC2#17989221
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#471×C73C2
socleC2×C73D42
hypercenter#471D73
hypocenterC73#3291
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #17989399C2semidirect
2. #17989397C2semidirect
3. #17989396C2semidirect
4. #17989393C2semidirect
5. #17988958C2semidirect
6. #17988853C2semidirect
7. #17988851C2semidirect
8. #17988849C2semidirect
9. #17988772C2semidirect
10. #17988768C2semidirect
11. #17988757C2semidirect
12. #17988753C2semidirect
13. #17988703C2semidirect
14. #17988702C2semidirect
15. #471×C73C2semidirect
18. #14556637C22semidirect
19. #14556636C22semidirect
21. #14556624C22semidirect
22. #14556624C22semidirect
24. #14556622C22semidirect
41. C2×#11924017C22semidirect
42. C2×#11924016C22semidirect
43. C2×#11924015C22semidirect
47. #14556599C22semidirect
48. #14556599C22semidirect
49. #14556597C22semidirect
50. #14556589C22semidirect
52. #14556526C22semidirect
53. #14556518C22semidirect
54. #14556517C22semidirect
55. #14556517C22semidirect
56. #14556517C22semidirect
57. #14556509C22semidirect
58. #14556507C22semidirect
59. C8×Dic73C22semidirect
60. #137×C73C22semidirect
62. C2×SD16×C73C22semidirect
63. #131×C73C22semidirect
64. #108×C73C22semidirect
65. #101×C73C22semidirect
66. #100×C73C22semidirect
95. Dic292D4semidirect
97. #11924018D4semidirect
104. #11924017D4semidirect
105. #11924017D4semidirect
109. #11924016D4semidirect
113. #11924015D4semidirect
116. D584D4semidirect
118. #11924013D4semidirect
228. C73#3291semidirect
237. #471D73semidirect
255. #137C2×D73semidirect
277. C2×SD16C2×D73semidirect
281. #131C2×D73semidirect
285. #108C2×D73semidirect
291. #101C2×D73semidirect
293. #100C2×D73semidirect