Finite Group Databasebeta

← #22619657

Subgroups — #22619657

Order 9344.

466 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989383C211yesmaximal, characteristic, complemented
2C2×#14556615C211yesmaximal, characteristic, complemented
3AGL(1,ℤ/8)×D73C211yesmaximal, characteristic, complemented
4#17989352C211yesmaximal, characteristic, complemented
5#17988856C211yesmaximal, characteristic, complemented
6#17988855C211yesmaximal, characteristic, complemented
7#17988854C211yesmaximal, characteristic, complemented
8#17988851C211yesmaximal, characteristic, complemented
9#17988850C211yesmaximal, characteristic, complemented
10#17988849C211yesmaximal, characteristic, complemented
11#17988848C211yesmaximal, characteristic, complemented
12#17988634C211yesmaximal, characteristic, complemented
13#17988568C211yesmaximal, characteristic, complemented
14#100×D73C211yesmaximal, characteristic, complemented
15#472×C73C211yesmaximal, characteristic, complemented
16C2×#11924027C2211yescharacteristic
17#41×D73C2211yescharacteristic
18C2×D4×D73C2211yescharacteristic
19#14556624C2211yescharacteristic, complemented
20#14556621C2211yescharacteristic, complemented
21#14556620—21no—
22#14556619C2211yescharacteristic
23#14556618—21no—
24#14556617C2211yescharacteristic
25#14556617C2211yescharacteristic, complemented
26#14556616C2211yescharacteristic
27#14556615—21no—
28#14556615—21no—
29#14556615—21no—
30#14556615—21no—
31#14556615—21no—
32#14556615—21no—
33#14556612—21no—
34#14556610—21no—
35C2×#11924017C2211yescharacteristic, complemented
36C2×#11924016C2211yescharacteristic, complemented
37SD16×D73—21no—
38C2×#11924013C2211yescharacteristic, complemented
39D8×D73—21no—
40#14556599—21no—
41#14556599C2211yescharacteristic, complemented
42#14556598C2211yescharacteristic, complemented
43#14556597—21no—
44#14556597C2211yescharacteristic, complemented
45C2×#11924011—21no—
46C2×#11924011C2211yescharacteristic
47M16×D73—21no—
48M16×D73C2211yescharacteristic
49M16×D73C2211yescharacteristic
50M16×D73C2211yescharacteristic
51#14556527C2211yescharacteristic, complemented
52#14556526C2211yescharacteristic, complemented
53#14556526C2211yescharacteristic, complemented
54#14556509C2211yescharacteristic, complemented
55#14556509C2211yescharacteristic, complemented
56#14556508C2211yescharacteristic, complemented
57#14556508C2211yescharacteristic, complemented
58#14556507C2211yescharacteristic, complemented
59#14556507C2211yescharacteristic, complemented
60AGL(1,ℤ/8)×C73C2211yescharacteristic
61AGL(1,ℤ/8)×C73C2211yescharacteristic, complemented
62C2×D8×C73C2211yescharacteristic, complemented
63#131×C73C2211yescharacteristic, complemented
64#108×C73C2211yescharacteristic, complemented
65#100×C73C2211yescharacteristic, complemented
66#100×C73C2211yescharacteristic, complemented
67C23×D73—21no—
68#11924029D411yescharacteristic
69#11924028—21no—
70#11924028C2311yescharacteristic
71#11924027—21no—
72#11924027—21no—
73#11924027—21no—
74#11924027—21no—
75#11924027—21no—
76#11924027D411yescharacteristic
77C2×Dic146C2311yescharacteristic
78Q8×D73D411yescharacteristic
79C2×D292C2311yescharacteristic
80C2×C22⋊D73—21no—
81C2×C22⋊D73—21no—
82D4×D73—21no—
83D4×D73—21no—
84D4×D73—21no—
85D4×D73—21no—
86D4×D73—21no—
87D4×D73D411yescharacteristic
88C22×Dic73—21no—
89C2×C4×D73—21no—
90C2×C4×D73C2311yescharacteristic
91Dic292—21no—
92#11924018—21no—
93#11924017—21no—
94#11924017—21no—
95#11924017—21no—
96#11924017—21no—
97#11924016—21no—
98#11924016—21no—
99#11924016—21no—
100#11924016—21no—
101#11924016—21no—
102#11924015—21no—
103D584—21no—
104#11924013—21no—
105#11924013—21no—
106#11924013—21no—
107#11924013—21no—
108#11924013—21no—
109#11924012—21no—
110#11924012C2311yescharacteristic
111#11924012C2311yescharacteristic
112#11924012C2311yescharacteristic
113#11924011—21no—
114#11924011—21no—
115#11924011—21no—
116#11924011—21no—
117#11924011—21no—
118#11924011D411yescharacteristic
119#11924011D411yescharacteristic
120#11924011D411yescharacteristic
121#11924011D411yescharacteristic
122C2×#10596831—21no—
123C2×#10596831C2311yescharacteristic
124C8×D73—21no—
125C8×D73—21no—
126C8×D73—21no—
127C8×D73—21no—
128C8×D73—21no—
129#41×C73C2311yescharacteristic
130C2×D4×C73C2311yescharacteristic
131C2×D4×C73C2311yescharacteristic
132SD16×C73—21no—
133SD16×C73—21no—
134D8×C73—21no—
135D8×C73—21no—
136D8×C73—21no—
137D8×C73—21no—
138M16×C73—21no—
139M16×C73C2311yescharacteristic
140M16×C73C2311yescharacteristic
141M16×C73C2311yescharacteristic
142C2×C8×C73—21no—
143C2×C8×C73C2311yescharacteristic
144C23×C73—21no—
145C23×C73—21no—
146C22×D73—21no—
147C22×D73—21no—
148C22×D73—41no—
149C22×D73—41no—
150C22×D73—82no—
151C22×D73#4111yescharacteristic
152Q8×C73C2×D411yescharacteristic
153D4×C73—21no—
154D4×C73—21no—
155D4×C73—21no—
156D4×C73—21no—
157D4×C73—21no—
158D4×C73C2×D411yescharacteristic
159C2×C4×C73—21no—
160C2×C4×C73C2411yescharacteristic
161C22⋊D73—21no—
162C22⋊D73—21no—
163C22⋊D73—21no—
164C22⋊D73—41no—
165C22⋊D73—41no—
166C22⋊D73—41no—
167C22⋊D73—41no—
168C2×Dic73—21no—
169C2×Dic73—21no—
170C2×Dic73—41no—
171C2×Dic73—41no—
172C2×Dic73#4111yescharacteristic
173D292—21no—
174D292—21no—
175D292—21no—
176D292C2×D411yescharacteristic
177C4×D73—21no—
178C4×D73—21no—
179C4×D73—21no—
180C4×D73C2×D411yescharacteristic
181C4×D73C2×D411yescharacteristic
182C4×D73C2×D411yescharacteristic
183C4×D73C2×D411yescharacteristic
184Dic146—21no—
185Dic146—21no—
186Dic146—21no—
187Dic146C2×D411yescharacteristic
188C8×C73—21no—
189C8×C73—21no—
190C8×C73—21no—
191C8×C73C2×D411yescharacteristic
192C8×C73C2×D411yescharacteristic
193#10596831—21no—
194#10596831—21no—
195#10596831—21no—
196#10596831C2×D411yescharacteristic
197#10596831C2×D411yescharacteristic
198C22×C73—21no—
199C22×C73—41no—
200C22×C73—41no—
201C22×C73—81no—
202C22×C73—81no—
203C22×C73C2×#4111yescharacteristic
204C2×D73—21no—
205C2×D73—41no—
206C2×D73—41no—
207C2×D73—81no—
208C2×D73—82no—
209C2×D73—82no—
210C2×D73—81no—
211C2×D73#12111yescharacteristic
212C2×D73#12111yescharacteristic
213C4×C73—21no—
214C4×C73C22×D411yescharacteristic
215C4×C73C22×D411yescharacteristic
216Dic73—21no—
217Dic73—41no—
218Dic73#12111yescharacteristic
219Dic73#12111yescharacteristic
220C2×C73—21no—
221C2×C73—41no—
222C2×C73—81no—
223C2×C73—81no—
224C2×C73C2×#12111yescharacteristic
225D73—21no—
226D73—21no—
227D73—41no—
228D73—81no—
229#3068—731nomaximal, Sylow
230C73#306811yescharacteristic, complemented, Sylow
231#575—731no—
232C2×AGL(1,ℤ/8)—731no—
233C2×AGL(1,ℤ/8)—731no—
234#568—731no—
235#472—731no—
236#472—731no—
237#472—731no—
238#472D7311yescharacteristic, complemented
239#471—731no—
240#471—731no—
241#471—731no—
242#471—731no—
243#430—731no—
244#413—731no—
245C2×#100—731no—
246C2×#41—731no—
247C2×#41—731no—
248C22×D4—731no—
249#137—731no—
250#137—731no—
251#137—1461no—
252AGL(1,ℤ/8)—731no—
253AGL(1,ℤ/8)—731no—
254AGL(1,ℤ/8)—731no—
255AGL(1,ℤ/8)—731no—
256AGL(1,ℤ/8)—1461no—
257AGL(1,ℤ/8)—1461no—
258AGL(1,ℤ/8)—1461no—
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
264AGL(1,ℤ/8)C2×D7311yescharacteristic, complemented
265#135—1461no—
266#135—1461no—
267C2×SD16—731no—
268C2×SD16—731no—
269C2×SD16—1461no—
270C2×D8—731no—
271C2×D8—1461no—
272C2×D8C2×D7311yescharacteristic, complemented
273#131—731no—
274#131—731no—
275#131—731no—
276#131—1461no—
277#131—1461no—
278#131C2×D7311yescharacteristic, complemented
279C2×M16—731no—
280C2×M16—731no—
281C2×M16—731no—
282C2×M16—731no—
283C2×M16—1461no—
284C2×M16—1461no—
285#108—731no—
286#108—731no—
287#108—731no—
288#108C2×D7311yescharacteristic, complemented
289#101—731no—
290#101—731no—
291#100—731no—
292#100—731no—
293#100—731no—
294#100—731no—
295#100C2×D7311yescharacteristic, complemented
296#100C2×D7311yescharacteristic, complemented
297C24—1461no—
298#41—731no—
299#41—731no—
300#41—731no—
301#41—1461no—
302#41—1461no—
303#41—1461no—
304#41—1461no—
305#41—1461no—
306#41—1461no—
307#41C22×D7311yescharacteristic
308C2×Q8—731no—
309C2×Q8—731no—
310C2×D4—731no—
311C2×D4—731no—
312C2×D4—1461no—
313C2×D4—1461no—
314C2×D4—1461no—
315C2×D4—1461no—
316C2×D4—1461no—
317C2×D4—1461no—
318C2×D4—1461no—
319C2×D4C22×D7311yescharacteristic
320C2×D4C22×D7311yescharacteristic
321C22×C4—731no—
322C22×C4—1461no—
323C22×C4—1461no—
324Q16—1461no—
325Q16—1461no—
326SD16—21no—
327SD16—21no—
328SD16—1461no—
329SD16—1461no—
330SD16—1461no—
331SD16—1461no—
332SD16—1461no—
333SD16—1461no—
334SD16—1461no—
335SD16—1461no—
336SD16—1461no—
337SD16—1461no—
338D8—21no—
339D8—21no—
340D8—21no—
341D8—21no—
342D8—1461no—
343D8—1461no—
344D8—1461no—
345D8—1461no—
346D8—1461no—
347D8—1461no—
348M16—21no—
349M16—731no—
350M16—731no—
351M16—731no—
352M16—731no—
353M16—731no—
354M16—731no—
355M16—731no—
356M16—1461no—
357M16—1461no—
358M16—1461no—
359M16—1461no—
360M16—1461no—
361M16—1461no—
362M16C22×D7311yescharacteristic
363M16C22×D7311yescharacteristic
364M16C22×D7311yescharacteristic
365C2×C8—21no—
366C2×C8—731no—
367C2×C8—1461no—
368C2×C8—1461no—
369C2×C8—1461no—
370C2×C8—1461no—
371C2×C8—1461no—
372C2×C8—1461no—
373C2×C8C22×D7311yescharacteristic
374C23—21no—
375C23—21no—
376C23—2921no—
377C23—2921no—
378C23—5842no—
379C23—731no—
380C23—1461no—
381C23—1461no—
382Q8—731no—
383Q8—1461no—
384Q8—1461no—
385Q8—1461no—
386Q8D4×D7311yescharacteristic
387D4—21no—
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—2921no—
393D4—2921no—
394D4—2921no—
395D4—2921no—
396D4—731no—
397D4—1461no—
398D4—1461no—
399D4—1461no—
400D4—1461no—
401D4—1461no—
402D4—1461no—
403D4D4×D7311yescharacteristic
404C2×C4—21no—
405C2×C4—2921no—
406C2×C4—2921no—
407C2×C4—731no—
408C2×C4—731no—
409C2×C4—731no—
410C2×C4—731no—
411C2×C4—731no—
412C2×C4—1461no—
413C2×C4—1461no—
414C2×C4—1461no—
415C2×C4—1461no—
416C2×C4—1461no—
417C2×C4C23×D7311yescharacteristic
418C8—21no—
419C8—21no—
420C8—21no—
421C8—731no—
422C8—731no—
423C8—1461no—
424C8—1461no—
425C8—1461no—
426C8D4×D7311yescharacteristic
427C8D4×D7311yescharacteristic
428C22—21no—
429C22—41no—
430C22—41no—
431C22—81no—
432C22—81no—
433C22—2921no—
434C22—2921no—
435C22—5841no—
436C22—5841no—
437C22—5842no—
438C22—5842no—
439C22—731no—
440C22—731no—
441C22—1461no—
442C22#41×D7311yescharacteristic
443C4—21no—
444C4—2921no—
445C4—731no—
446C4—731no—
447C4—1461no—
448C4C2×D4×D7311yescharacteristic
449C4C2×D4×D7311yescharacteristic
450C2—21no—
451C2—41no—
452C2—81no—
453C2—81no—
454C2—2921no—
455C2—5841no—
456C2—1461no—
457C2—1461no—
458C2#121×D7311yescharacteristic
subgroupG/H
centerC2#121×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#472×C73C2
socleC2×C73C2×#121
hypercenter#472D73
hypocenterC73#3068
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

Complements

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

NH ≅ G/Ntype
1. #17989383C2semidirect
2. C2×#14556615C2semidirect
3. AGL(1,ℤ/8)×D73C2semidirect
4. #17989352C2semidirect
5. #17988856C2semidirect
6. #17988855C2semidirect
7. #17988854C2semidirect
8. #17988851C2semidirect
9. #17988850C2semidirect
10. #17988849C2semidirect
11. #17988848C2semidirect
12. #17988634C2semidirect
13. #17988568C2semidirect
14. #100×D73C2semidirect
15. #472×C73C2semidirect
19. #14556624C22semidirect
20. #14556621C22semidirect
25. #14556617C22semidirect
35. C2×#11924017C22semidirect
36. C2×#11924016C22semidirect
38. C2×#11924013C22semidirect
41. #14556599C22semidirect
42. #14556598C22semidirect
44. #14556597C22semidirect
51. #14556527C22semidirect
52. #14556526C22semidirect
53. #14556526C22semidirect
54. #14556509C22semidirect
55. #14556509C22semidirect
56. #14556508C22semidirect
57. #14556508C22semidirect
58. #14556507C22semidirect
59. #14556507C22semidirect
61. AGL(1,ℤ/8)×C73C22semidirect
62. C2×D8×C73C22semidirect
63. #131×C73C22semidirect
64. #108×C73C22semidirect
65. #100×C73C22semidirect
66. #100×C73C22semidirect
230. C73#3068semidirect
238. #472D73semidirect
264. AGL(1,ℤ/8)C2×D73semidirect
272. C2×D8C2×D73semidirect
278. #131C2×D73semidirect
288. #108C2×D73semidirect
295. #100C2×D73semidirect
296. #100C2×D73semidirect