Finite Group Databasebeta

← #49130475

Subgroups — #49130475

Order 36224.

764 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D283C211yesmaximal, characteristic, complemented
2C2×#22583630C211yesmaximal, characteristic, complemented
3#31826972C211yesmaximal, characteristic, complemented
4#31826626C211yesmaximal, characteristic, complemented
5#31826624C211yesmaximal, characteristic, complemented
6#31826619C211yesmaximal, characteristic, complemented
7#31826614C211yesmaximal, characteristic, complemented
8#31826609C211yesmaximal, characteristic, complemented
9#31826607C211yesmaximal, characteristic, complemented
10#31826602C211yesmaximal, characteristic, complemented
11#31826597C211yesmaximal, characteristic, complemented
12#31826462C211yesmaximal, characteristic, complemented
13#31826461C211yesmaximal, characteristic, complemented
14C2×(C2×D283)⋊C8C211yesmaximal, characteristic, complemented
15C2×#135×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×#17985392—21no—
18C2×#17985392C2211yescharacteristic
19C2×#17985391—21no—
20C2×#17985391C2211yescharacteristic
21#41×D283—24no—
22#41×D283—24no—
23C2×Q8×D283C2211yescharacteristic
24C2×D4×D283—21no—
25C2×D4×D283C2211yescharacteristic
26C22×C4×D283—21no—
27C22×C4×D283C2211yescharacteristic
28#22583630—24no—
29C2×#17985382C2211yescharacteristic, complemented
30C2×#17985380C2211yescharacteristic, complemented
31C2×#17985379C2211yescharacteristic, complemented
32C2×#17985377C2211yescharacteristic, complemented
33C22×C283⋊C8C2211yescharacteristic, complemented
34#22583591—21no—
35#22583586C2211yescharacteristic
36#22583586C2211yescharacteristic, complemented
37#22583581C2211yescharacteristic
38#22583581C2211yescharacteristic, complemented
39#22583578—21no—
40C4×C22⋊D283—21no—
41C4×C22⋊D283—21no—
42#22583569C2211yescharacteristic, complemented
43#22583535C2211yescharacteristic, complemented
44#22583535C2211yescharacteristic, complemented
45#22583534C2211yescharacteristic, complemented
46#22583534C2211yescharacteristic, complemented
47#22583532C2211yescharacteristic, complemented
48#22583532C2211yescharacteristic, complemented
49#22583531C2211yescharacteristic, complemented
50#22583531C2211yescharacteristic, complemented
51(C2×D283)⋊C8C2211yescharacteristic
52(C2×D283)⋊C8C2211yescharacteristic
53(C2×D283)⋊C8C2211yescharacteristic, complemented
54(C2×D283)⋊C8C2211yescharacteristic, complemented
55C2×#41×C283C2211yescharacteristic
56C2×#41×C283C2211yescharacteristic, complemented
57#135×C283—24no—
58C2×Q16×C283C2211yescharacteristic, complemented
59C2×SD16×C283C2211yescharacteristic, complemented
60C2×SD16×C283C2211yescharacteristic, complemented
61C2×D8×C283C2211yescharacteristic, complemented
62C22×C8×C283C2211yescharacteristic, complemented
63C23×D283—21no—
64C23×D283D411yescharacteristic
65#17985393—22no—
66#17985393—22no—
67#17985392—28no—
68#17985392—22no—
69#17985392D414yescomplemented
70#17985391—28no—
71#17985391—22no—
72#17985391—22no—
73C2×Dic566—21no—
74C2×Dic566C2311yescharacteristic
75Q8×D283—22no—
76Q8×D283—22no—
77C2×D1132—21no—
78C2×D1132C2311yescharacteristic
79C2×C22⋊D283—21no—
80C2×C22⋊D283—21no—
81C2×C22⋊D283—21no—
82C2×C22⋊D283—21no—
83C2×C22⋊D283—21no—
84D4×D283—28no—
85D4×D283—22no—
86D4×D283—22no—
87C22×Dic283—21no—
88C22×Dic283D411yescharacteristic
89C2×C4×D283—28no—
90C2×C4×D283—21no—
91C2×C4×D283—21no—
92C2×C4×D283—21no—
93C2×C4×D283—22no—
94C2×C4×D283—22no—
95C2×C4×D283D411yescharacteristic
96C2×C4×D283D411yescharacteristic
97C2×C4×D283C2311yescharacteristic
98C2×C4×D283C2311yescharacteristic
99#17985382—22no—
100#17985380—22no—
101#17985379—22no—
102#17985377—22no—
103C2×C283⋊C8—22no—
104C2×C283⋊C8C2311yescharacteristic
105C2×C283⋊C8C2311yescharacteristic
106C4⋊Dic283C2311yescharacteristic
107C4⋊Dic283C2311yescharacteristic
108Dic283⋊C4—21no—
109Dic283⋊C4—21no—
110C22⋊Dic283—21no—
111C22⋊Dic283—21no—
112C22⋊Dic283—21no—
113(C2×D283)⋊C4—21no—
114(C2×D283)⋊C4—21no—
115C4×Dic283—21no—
116#41×C283—22no—
117#41×C283—22no—
118#41×C283—22no—
119#41×C283D414yescomplemented
120C2×Q8×C283C2311yescharacteristic
121C2×Q8×C283C2311yescharacteristic
122C2×D4×C283—21no—
123C2×D4×C283—21no—
124C2×D4×C283C2311yescharacteristic
125C2×D4×C283C2311yescharacteristic
126C22×C4×C283—21no—
127C22×C4×C283—21no—
128C22×C4×C283C2311yescharacteristic
129Q16×C283—22no—
130SD16×C283—22no—
131SD16×C283—22no—
132D8×C283—22no—
133C2×C8×C283—22no—
134C2×C8×C283C2311yescharacteristic
135C2×C8×C283C2311yescharacteristic
136C22×D283—24no—
137C22×D283—22no—
138C22×D283—21no—
139C22×D283—22no—
140C22×D283—41no—
141C22×D283—42no—
142C22×D283—42no—
143C22×D283C2×D411yescharacteristic
144C22×D283C2×D411yescharacteristic
145Dic566—24no—
146Dic566—21no—
147Dic566C2×D412yes—
148D1132—24no—
149D1132—21no—
150D1132C2×D412yes—
151C22⋊D283—24no—
152C22⋊D283—24no—
153C22⋊D283—24no—
154C22⋊D283—42no—
155C22⋊D283—42no—
156C2×Dic283—24no—
157C2×Dic283—22no—
158C2×Dic283—21no—
159C2×Dic283—21no—
160C2×Dic283—21no—
161C2×Dic283C2×D411yescharacteristic
162C2×Dic283C2×D411yescharacteristic
163C4×D283—24no—
164C4×D283—24no—
165C4×D283—22no—
166C4×D283—24no—
167C4×D283—22no—
168C4×D283—21no—
169C4×D283—21no—
170C4×D283—21no—
171C4×D283—21no—
172C283⋊C8—21no—
173C283⋊C8—21no—
174C23×C283—21no—
175C23×C283—21no—
176C23×C283C2×D411yescharacteristic
177Q8×C283—21no—
178Q8×C283—21no—
179Q8×C283—21no—
180Q8×C283C2×D412yes—
181D4×C283—24no—
182D4×C283—21no—
183D4×C283—21no—
184D4×C283—21no—
185D4×C283—42no—
186D4×C283C2×D412yes—
187C2×C4×C283—21no—
188C2×C4×C283—24no—
189C2×C4×C283—21no—
190C2×C4×C283—42no—
191C2×C4×C283C2×D412yes—
192C2×C4×C283C2×D411yescharacteristic
193C2×C4×C283C2×D412yes—
194C2×C4×C283C2411yescharacteristic
195C8×C283—21no—
196C8×C283—21no—
197C22×C283—21no—
198C22×C283—21no—
199C22×C283—22no—
200C22×C283—41no—
201C22×C283—41no—
202C22×C283—41no—
203C22×C283—41no—
204C22×C283—41no—
205C22×C283#12012yes—
206C22×C283C22×D411yescharacteristic
207C2×D283—21no—
208C2×D283—21no—
209C2×D283—21no—
210C2×D283—22no—
211C2×D283—21no—
212C2×D283—21no—
213C2×D283—44no—
214C2×D283—48no—
215C2×D283—41no—
216C2×D283—41no—
217C2×D283#13512yescomplemented
218C4×C283—22no—
219C4×C283—41no—
220C4×C283#12012yes—
221C4×C283C22×D411yescharacteristic
222C4×C283C22×D411yescharacteristic
223Dic283—21no—
224Dic283—22no—
225Dic283—21no—
226Dic283—41no—
227Dic283—41no—
228C2×C283—22no—
229C2×C283—42no—
230C2×C283—81no—
231C2×C283C2×#12011yescharacteristic
232C2×C283C2×#13511yescharacteristic
233C2×C283#57511yescharacteristic
234D283—22no—
235D283—41no—
236D283—42no—
237C283#300211yescharacteristic, complemented, Sylow
238#3002—2831nomaximal, Sylow
239C22×#41—2831no—
240C2×#135—2831no—
241C2×#135D28311yescharacteristic, complemented
242#525—2831no—
243#452—2831no—
244#452—2831no—
245#451—2831no—
246#450—2831no—
247#449—2831no—
248#449—2831no—
249#448—2831no—
250#447—2831no—
251#416—2831no—
252#416—2831no—
253C2×C22⋊C8—2831no—
254C2×#41—2831no—
255C2×#41—2831no—
256C2×#41—2831no—
257C2×#41—5661no—
258C2×#41—5661no—
259C2×#41—5664no—
260C2×#41—5664no—
261C2×#41C2×D28311yescharacteristic
262C2×#41C2×D28311yescharacteristic, complemented
263C22×Q8—2831no—
264C22×D4—2831no—
265C22×D4—5661no—
266C23×C4—2831no—
267C23×C4—5661no—
268#135—24no—
269#135—5664no—
270C2×Q16—2831no—
271C2×Q16C2×D28311yescharacteristic, complemented
272C2×SD16—2831no—
273C2×SD16—2831no—
274C2×SD16C2×D28311yescharacteristic, complemented
275C2×SD16C2×D28311yescharacteristic, complemented
276C2×D8—2831no—
277C2×D8C2×D28311yescharacteristic, complemented
278C22×C8—2831no—
279C22×C8C2×D28311yescharacteristic, complemented
280#123—5661no—
281C22⋊Q8—2831no—
282C22⋊Q8—2831no—
283#121—2831no—
284#121—2831no—
285#120—5661no—
286C4×D4—5661no—
287C4×D4—5661no—
288#117—2831no—
289#103—2831no—
290#103—2831no—
291#103—2831no—
292#103—2831no—
293#102—2831no—
294#102—2831no—
295#102—2831no—
296#102—2831no—
297C22⋊C8—2831no—
298C22⋊C8—2831no—
299C22⋊C8—2831no—
300C22⋊C8—2831no—
301C24—2831no—
302C24—5661no—
303#41—22no—
304#41—22no—
305#41—22no—
306#41—2834no—
307#41—5668no—
308#41—5662no—
309#41—5668no—
310#41—5662no—
311#41—5662no—
312#41—5662no—
313#41—5662no—
314#41C22⋊D28314yescomplemented
315C2×Q8—2831no—
316C2×Q8—5661no—
317C2×Q8—5662no—
318C2×Q8—5662no—
319C2×Q8C22×D28311yescharacteristic
320C2×Q8C22×D28311yescharacteristic
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—2831no—
324C2×D4—5661no—
325C2×D4—5661no—
326C2×D4—5662no—
327C2×D4—5668no—
328C2×D4—5661no—
329C2×D4—5661no—
330C2×D4—5662no—
331C2×D4—5661no—
332C2×D4—5661no—
333C2×D4C22×D28311yescharacteristic
334C2×D4C22×D28311yescharacteristic
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—2831no—
338C22×C4—2831no—
339C22×C4—2831no—
340C22×C4—2831no—
341C22×C4—2831no—
342C22×C4—5661no—
343C22×C4—5661no—
344C22×C4—5668no—
345C22×C4—5661no—
346C22×C4—5662no—
347C22×C4—5661no—
348C22×C4—5662no—
349C22×C4C22×D28311yescharacteristic
350Q16—22no—
351Q16—5662no—
352SD16—22no—
353SD16—22no—
354SD16—5662no—
355SD16—5662no—
356D8—22no—
357D8—5662no—
358C2×C8—22no—
359C2×C8—2831no—
360C2×C8—2831no—
361C2×C8—5662no—
362C2×C8C22×D28311yescharacteristic
363C2×C8C22×D28311yescharacteristic
364C4⋊C4—2831no—
365C4⋊C4—2831no—
366C4⋊C4—5661no—
367C4⋊C4—5661no—
368C22⋊C4—5661no—
369C22⋊C4—5661no—
370C22⋊C4—5661no—
371C22⋊C4—5661no—
372C22⋊C4—5661no—
373C42—5661no—
374C23—21no—
375C23—21no—
376C23—2831no—
377C23—2831no—
378C23—5662no—
379C23—5664no—
380C23—5662no—
381C23—5661no—
382C23—11321no—
383C23—11322no—
384C23—11322no—
385C23D4×D28311yescharacteristic
386Q8—21no—
387Q8—21no—
388Q8—21no—
389Q8—2832no—
390Q8—5664no—
391Q8—5661no—
392Q8C2×C22⋊D28312yes—
393D4—24no—
394D4—21no—
395D4—21no—
396D4—21no—
397D4—42no—
398D4—2832no—
399D4—5664no—
400D4—5664no—
401D4—5664no—
402D4—5664no—
403D4—5661no—
404D4—11322no—
405D4—11322no—
406D4C2×C22⋊D28312yes—
407C2×C4—21no—
408C2×C4—24no—
409C2×C4—21no—
410C2×C4—42no—
411C2×C4—2831no—
412C2×C4—2831no—
413C2×C4—5664no—
414C2×C4—5664no—
415C2×C4—5664no—
416C2×C4—5662no—
417C2×C4—5661no—
418C2×C4—5662no—
419C2×C4—5662no—
420C2×C4—5664no—
421C2×C4—5661no—
422C2×C4—5661no—
423C2×C4—5661no—
424C2×C4—5661no—
425C2×C4—5661no—
426C2×C4—5661no—
427C2×C4D4×D28312yes—
428C2×C4D4×D28311yescharacteristic
429C2×C4C2×C22⋊D28312yes—
430C2×C4C23×D28311yescharacteristic
431C8—21no—
432C8—21no—
433C8—5661no—
434C8—5661no—
435C22—21no—
436C22—21no—
437C22—22no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—2832no—
444C22—5661no—
445C22—5661no—
446C22—5662no—
447C22—5661no—
448C22—5661no—
449C22—5661no—
450C22—11324no—
451C22—11328no—
452C22—11321no—
453C22—11321no—
454C22#2258357812yes—
455C22C2×D4×D28311yescharacteristic
456C4—22no—
457C4—41no—
458C4—5661no—
459C4—5661no—
460C4—5662no—
461C4—11321no—
462C4—11321no—
463C4#2258357812yes—
464C4C2×D4×D28311yescharacteristic
465C4C22×C22⋊D28311yescharacteristic
466C2—22no—
467C2—42no—
468C2—81no—
469C2—5662no—
470C2—11321no—
471C2—11322no—
472C2C2×#2258357811yescharacteristic
473C2#135×D28311yescharacteristic
474C2#3182726211yescharacteristic
subgroupG/H
centerC2×C4D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#135×C283C2
socleC22×C283C22×D4
hypercenterC2×#135D283
hypocenterC283#3002
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#41×D283C2semidirect
2. C2×#22583630C2semidirect
3. #31826972C2semidirect
4. #31826626C2semidirect
5. #31826624C2semidirect
6. #31826619C2semidirect
7. #31826614C2semidirect
8. #31826609C2semidirect
9. #31826607C2semidirect
10. #31826602C2semidirect
11. #31826597C2semidirect
12. #31826462C2semidirect
13. #31826461C2semidirect
14. C2×(C2×D283)⋊C8C2semidirect
15. C2×#135×C283C2semidirect
29. C2×#17985382C22semidirect
30. C2×#17985380C22semidirect
31. C2×#17985379C22semidirect
32. C2×#17985377C22semidirect
33. C22×C283⋊C8C22semidirect
36. #22583586C22semidirect
38. #22583581C22semidirect
42. #22583569C22semidirect
43. #22583535C22semidirect
44. #22583535C22semidirect
45. #22583534C22semidirect
46. #22583534C22semidirect
47. #22583532C22semidirect
48. #22583532C22semidirect
49. #22583531C22semidirect
50. #22583531C22semidirect
53. (C2×D283)⋊C8C22semidirect
54. (C2×D283)⋊C8C22semidirect
56. C2×#41×C283C22semidirect
58. C2×Q16×C283C22semidirect
59. C2×SD16×C283C22semidirect
60. C2×SD16×C283C22semidirect
61. C2×D8×C283C22semidirect
62. C22×C8×C283C22semidirect
69. #17985392D4semidirect
119. #41×C283D4semidirect
217. C2×D283#135semidirect
237. C283#3002semidirect
241. C2×#135D283semidirect
262. C2×#41C2×D283semidirect
271. C2×Q16C2×D283semidirect
274. C2×SD16C2×D283semidirect
275. C2×SD16C2×D283semidirect
277. C2×D8C2×D283semidirect
279. C22×C8C2×D283semidirect
314. #41C22⋊D283semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#41×D2832
C2×#225836302
#318269722
#318266262
#318266242
#318266192
#318266142
#318266092
#318266072
#318266022
#318265972
#318264622
#318264612
C2×(C2×D283)⋊C82
C2×#135×C2832
#3002283