Finite Group Databasebeta

← #46813867

Subgroups — #46813867

Order 34432.

928 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575423C211yesmaximal, characteristic
2C2×C4×D1076C211yesmaximal, characteristic, complemented
3C2×#22575413C211yesmaximal, characteristic, complemented
4C22×#16864379C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D269C211yesmaximal, characteristic, complemented
6#31770507C211yesmaximal, characteristic, complemented
7#31770497C211yesmaximal, characteristic, complemented
8#31770496C211yesmaximal, characteristic, complemented
9#31770484C211yesmaximal, characteristic, complemented
10#31770483C211yesmaximal, characteristic, complemented
11#31770483C211yesmaximal, characteristic, complemented
12#31770480C211yesmaximal, characteristic, complemented
13#31770479C211yesmaximal, characteristic, complemented
14C4×#16864379C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C269C211yesmaximal, characteristic, complemented
16C24×D269C2211yescharacteristic
17C22×D1076C2211yescharacteristic
18C22×D1076C2211yescharacteristic
19C22×C22⋊D269C2211yescharacteristic
20C23×Dic269C2211yescharacteristic
21C22×C4×D269C2211yescharacteristic
22C22×C4×D269C2211yescharacteristic
23C22×C4×D269C2211yescharacteristic, complemented
24#22575423C418yescomplemented
25C4×D1076—24no—
26#22575413—24no—
27C2×C4⋊Dic269C2211yescharacteristic, complemented
28C2×C4⋊Dic269C2211yescharacteristic, complemented
29C2×#16864381C2211yescharacteristic, complemented
30C2×C22⋊Dic269C2211yescharacteristic
31C2×#16864379—24no—
32C2×#16864379C2211yescharacteristic
33C2×#16864379C2211yescharacteristic
34C2×#16864379C2211yescharacteristic
35C2×#16864379C2211yescharacteristic
36C2×#16864379C2211yescharacteristic
37C2×#16864379C2211yescharacteristic
38C2×#16864379C2211yescharacteristic
39C2×#16864379C2211yescharacteristic
40C2×#16864379C2211yescharacteristic, complemented
41C2×#16864379C2211yescharacteristic, complemented
42C2×#16864379C2211yescharacteristic, complemented
43C22⋊C4×D269—24no—
44C2×C4×Dic269C2211yescharacteristic, complemented
45#22575360C2211yescharacteristic, complemented
46#22575360C2211yescharacteristic, complemented
47#22575360C2211yescharacteristic, complemented
48#22575360C2211yescharacteristic, complemented
49C23×C4×C269C2211yescharacteristic
50C2×C22⋊C4×C269C2211yescharacteristic
51C2×C22⋊C4×C269C2211yescharacteristic
52C2×C42×C269C2211yescharacteristic, complemented
53C2×C42×C269C2211yescharacteristic, complemented
54#95×C269C2211yescharacteristic, complemented
55#95×C269C2211yescharacteristic, complemented
56C23×D269—22no—
57C23×D269—22no—
58C23×D269—22no—
59C23×D269—22no—
60C23×D269—41no—
61C23×D269—41no—
62C23×D269C2×C414yescomplemented
63C23×D269C2311yescharacteristic
64C23×D269C2311yescharacteristic
65C23×D269C2311yescharacteristic
66C2×D1076—22no—
67C2×D1076—22no—
68C2×D1076—41no—
69C2×D1076—41no—
70C2×D1076C2×C414yescomplemented
71C2×D1076C2×C414yescomplemented
72C2×C22⋊D269—22no—
73C2×C22⋊D269—22no—
74C2×C22⋊D269C2×C414yescomplemented
75C22×Dic269—22no—
76C22×Dic269—22no—
77C22×Dic269—41no—
78C22×Dic269C2311yescharacteristic
79C22×Dic269C2311yescharacteristic
80C22×Dic269C2311yescharacteristic
81C22×Dic269C2311yescharacteristic
82C22×Dic269C2311yescharacteristic
83C2×C4×D269—22no—
84C2×C4×D269—22no—
85C2×C4×D269—22no—
86C2×C4×D269—22no—
87C2×C4×D269—22no—
88C2×C4×D269—22no—
89C2×C4×D269—41no—
90C2×C4×D269—41no—
91C2×C4×D269—41no—
92C4⋊Dic269—22no—
93C4⋊Dic269—41no—
94#16864381—22no—
95C22⋊Dic269—22no—
96#16864379—22no—
97#16864379—22no—
98#16864379—22no—
99#16864379—22no—
100#16864379—22no—
101#16864379—22no—
102#16864379—22no—
103#16864379—41no—
104#16864379C2×C414yescomplemented
105#16864379C2×C414yescomplemented
106#16864379D414yescomplemented
107C4×Dic269—22no—
108C24×C269C2311yescharacteristic
109C22×C4×C269—22no—
110C22×C4×C269—22no—
111C22×C4×C269—41no—
112C22×C4×C269C2311yescharacteristic
113C22×C4×C269C2311yescharacteristic
114C22×C4×C269C2311yescharacteristic
115C22×C4×C269C2311yescharacteristic
116C22×C4×C269C2311yescharacteristic
117C22×C4×C269C2311yescharacteristic
118C22⋊C4×C269C2×C414yescomplemented
119C22⋊C4×C269D414yescomplemented
120C42×C269—22no—
121C42×C269—41no—
122C22×D269—21no—
123C22×D269—21no—
124C22×D269—21no—
125C22×D269—21no—
126C22×D269—28no—
127C22×D269—21no—
128C22×D269—21no—
129C22×D269—21no—
130C22×D269—21no—
131C22×D269—21no—
132C22×D269—21no—
133C22×D269—21no—
134C22×D269—21no—
135C22×D269—21no—
136C22×D269—21no—
137C22×D269—21no—
138C22×D269—21no—
139C22×D269—28no—
140C22×D269—44no—
141C22×D269—44no—
142C22×D269—44no—
143C22×D269—44no—
144C22×D269—44no—
145C22×D269C22×C412yes—
146C22×D269C22×C412yes—
147C22×D269C22×C412yes—
148C22×D269C2×D412yes—
149C22×D269#4112yes—
150D1076—28no—
151D1076—44no—
152C22⋊D269—28no—
153C2×Dic269—21no—
154C2×Dic269—21no—
155C2×Dic269—21no—
156C2×Dic269—21no—
157C2×Dic269—21no—
158C2×Dic269—21no—
159C2×Dic269—21no—
160C2×Dic269—21no—
161C2×Dic269—21no—
162C2×Dic269—21no—
163C2×Dic269—21no—
164C2×Dic269—21no—
165C2×Dic269—21no—
166C2×Dic269—44no—
167C2×Dic269C22×C412yes—
168C2×Dic269C2×D412yes—
169C4×D269—44no—
170C4×D269—44no—
171C4×D269—44no—
172C23×C269—21no—
173C23×C269—21no—
174C23×C269—21no—
175C23×C269—21no—
176C23×C269C22×C412yes—
177C23×C269C2×D412yes—
178C23×C269#4112yes—
179C23×C269C2411yescharacteristic
180C2×C4×C269—21no—
181C2×C4×C269—21no—
182C2×C4×C269—21no—
183C2×C4×C269—21no—
184C2×C4×C269—21no—
185C2×C4×C269—21no—
186C2×C4×C269—21no—
187C2×C4×C269—21no—
188C2×C4×C269—21no—
189C2×C4×C269—21no—
190C2×C4×C269—21no—
191C2×C4×C269—21no—
192C2×C4×C269—21no—
193C2×C4×C269—44no—
194C2×C4×C269C22×C412yes—
195C2×C4×C269C22×C412yes—
196C2×C4×C269C2×D412yes—
197C2×C4×C269C2×D412yes—
198C2×C4×C269C2×D412yes—
199C22×C269—22no—
200C22×C269—22no—
201C22×C269—22no—
202C22×C269—22no—
203C22×C269—22no—
204C22×C269—22no—
205C22×C269C4×D414yescomplemented
206C22×C269C23×C411yescharacteristic
207C22×C269C22×D411yescharacteristic
208C22×C269C22×D411yescharacteristic
209C22×C269C2×#4111yescharacteristic
210C22×C269C2×#4111yescharacteristic
211C22×C269H(5,𝔽2)11yescharacteristic
212C22×C269H(5,𝔽2)11yescharacteristic
213C2×D269—22no—
214C2×D269—22no—
215C2×D269—22no—
216C2×D269—22no—
217C2×D269—22no—
218C2×D269—22no—
219C2×D269—22no—
220C2×D269—22no—
221C2×D269—22no—
222C2×D269—22no—
223C2×D269—22no—
224C2×D269—22no—
225C2×D269—416no—
226C2×D269—41no—
227C2×D269—41no—
228C2×D269—41no—
229C2×D269—41no—
230C2×D269—41no—
231C2×D269—41no—
232C2×D269—41no—
233C2×D269—41no—
234C2×D269C4×D414yescomplemented
235C4×C269—22no—
236C4×C269—22no—
237C4×C269—22no—
238C4×C269—22no—
239C4×C269—22no—
240C4×C269—41no—
241Dic269—22no—
242Dic269—22no—
243Dic269—41no—
244Dic269—41no—
245Dic269—41no—
246C2×C269—24no—
247C2×C269C2×C4×D411yescharacteristic
248C2×C269C2×C4×D411yescharacteristic
249C2×C269#51811yescharacteristic
250C2×C269D4211yescharacteristic
251C2×C269#54611yescharacteristic
252C2×C269#54611yescharacteristic
253C2×C269#55111yescharacteristic
254D269—24no—
255D269—42no—
256D269—42no—
257C269#235811yescharacteristic, complemented, Sylow
258#2358—2691nomaximal, Sylow
259C2×#120—2691no—
260C2×C4×D4—2691no—
261C2×C4×D4—2691no—
262C22×C22⋊C4—2691no—
263C22×C22⋊C4—2691no—
264#390—2691no—
265#388—2691no—
266#388—2691no—
267#386—2691no—
268#386—2691no—
269#386—2691no—
270#385—2691no—
271#385—2691no—
272C4×C22⋊C4—2691no—
273C4×C22⋊C4D26911yescharacteristic, complemented
274C25—2691no—
275C22×D4—2691no—
276C22×D4—2691no—
277C22×D4—2691no—
278C23×C4—2691no—
279C23×C4—2691no—
280C23×C4—2691no—
281C23×C4—2691no—
282C23×C4C2×D26911yescharacteristic
283#120—2698no—
284C4×D4—5384no—
285C4×D4—5384no—
286C2×C4⋊C4—2691no—
287C2×C4⋊C4—2691no—
288C2×C4⋊C4—2691no—
289C2×C22⋊C4—2691no—
290C2×C22⋊C4—2691no—
291C2×C22⋊C4—2691no—
292C2×C22⋊C4—2691no—
293C2×C22⋊C4—2691no—
294C2×C22⋊C4—2691no—
295C2×C22⋊C4—2691no—
296C2×C22⋊C4—2691no—
297C2×C22⋊C4—2691no—
298C2×C22⋊C4—2691no—
299C2×C22⋊C4—2691no—
300C2×C22⋊C4—2691no—
301C2×C22⋊C4—5384no—
302C2×C22⋊C4—5384no—
303C2×C22⋊C4C2×D26911yescharacteristic
304C2×C22⋊C4C2×D26911yescharacteristic
305C2×C42—2691no—
306C2×C42C2×D26911yescharacteristic, complemented
307C2×C42C2×D26911yescharacteristic, complemented
308#95—2691no—
309#95—2691no—
310#95—2691no—
311#95—2691no—
312#95C2×D26911yescharacteristic, complemented
313#95C2×D26911yescharacteristic, complemented
314C24—2691no—
315C24—2691no—
316C24—2691no—
317C24—2694no—
318C24—5382no—
319C24—5382no—
320C24—5382no—
321C24—5382no—
322C24—10761no—
323C24—10761no—
324C24C22×D26911yescharacteristic
325C2×D4—2694no—
326C2×D4—2694no—
327C2×D4—2694no—
328C2×D4—5382no—
329C2×D4—5382no—
330C2×D4—5382no—
331C2×D4—5382no—
332C2×D4—10761no—
333C2×D4—10761no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—41no—
337C22×C4—2691no—
338C22×C4—2691no—
339C22×C4—2691no—
340C22×C4—2691no—
341C22×C4—2691no—
342C22×C4—5382no—
343C22×C4—5382no—
344C22×C4—5382no—
345C22×C4—5382no—
346C22×C4—5382no—
347C22×C4—5382no—
348C22×C4—5382no—
349C22×C4—5382no—
350C22×C4—10761no—
351C22×C4—10761no—
352C22×C4—10761no—
353C22×C4—10761no—
354C22×C4C22×D26911yescharacteristic
355C22×C4C22×D26911yescharacteristic
356C22×C4C22×D26911yescharacteristic
357C22×C4C22×D26911yescharacteristic
358C22×C4C22×D26911yescharacteristic
359C22×C4C22×D26911yescharacteristic
360C4⋊C4—5382no—
361C4⋊C4—5382no—
362C4⋊C4—10761no—
363C22⋊C4—2694no—
364C22⋊C4—2694no—
365C22⋊C4—2694no—
366C22⋊C4—5382no—
367C22⋊C4—5382no—
368C22⋊C4—5382no—
369C22⋊C4—5382no—
370C22⋊C4—5382no—
371C22⋊C4—5382no—
372C22⋊C4—5382no—
373C22⋊C4—5382no—
374C22⋊C4—10761no—
375C22⋊C4C4×D26914yescomplemented
376C22⋊C4D107614yescomplemented
377C42—22no—
378C42—41no—
379C42—5382no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—2692no—
385C23—2692no—
386C23—2692no—
387C23—2692no—
388C23—2692no—
389C23—5388no—
390C23—5381no—
391C23—5381no—
392C23—5381no—
393C23—5381no—
394C23—5388no—
395C23—5381no—
396C23—5381no—
397C23—5381no—
398C23—5381no—
399C23—5381no—
400C23—5381no—
401C23—5381no—
402C23—5381no—
403C23—5381no—
404C23—5381no—
405C23—5381no—
406C23—5381no—
407C23—10764no—
408C23—10764no—
409C23—10764no—
410C23—10764no—
411C23—10764no—
412C23C2×C4×D26912yes—
413C23C2×D107612yes—
414C23#1686440212yes—
415C23C23×D26911yescharacteristic
416D4—5388no—
417D4—5388no—
418D4—10764no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—44no—
433C2×C4—2692no—
434C2×C4—2692no—
435C2×C4—5381no—
436C2×C4—5381no—
437C2×C4—5381no—
438C2×C4—5381no—
439C2×C4—5381no—
440C2×C4—5381no—
441C2×C4—5381no—
442C2×C4—5381no—
443C2×C4—5381no—
444C2×C4—5381no—
445C2×C4—5381no—
446C2×C4—5381no—
447C2×C4—5381no—
448C2×C4—10764no—
449C2×C4—10764no—
450C2×C4—10764no—
451C2×C4—10764no—
452C2×C4C2×C4×D26912yes—
453C2×C4C2×C4×D26912yes—
454C2×C4D4×D26912yes—
455C2×C4C2×D107612yes—
456C2×C4C2×D107612yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—2694no—
464C22—5382no—
465C22—5382no—
466C22—5382no—
467C22—5382no—
468C22—5382no—
469C22—5382no—
470C22—5382no—
471C22—5382no—
472C22—5382no—
473C22—5382no—
474C22—5382no—
475C22—5382no—
476C22—107616no—
477C22—10761no—
478C22—10761no—
479C22—10761no—
480C22—10761no—
481C22—10761no—
482C22—10761no—
483C22—10761no—
484C22—10761no—
485C22C4×D107614yescomplemented
486C22C22×C4×D26911yescharacteristic
487C22C2×D4×D26911yescharacteristic
488C22C22×D107611yescharacteristic
489C22#41×D26911yescharacteristic
490C22C2×#1686440211yescharacteristic
491C22#2257549811yescharacteristic
492C22#2257549911yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—22no—
498C4—41no—
499C4—5382no—
500C4—5382no—
501C4—10761no—
502C4—10761no—
503C4—10761no—
504C2—24no—
505C2—5384no—
506C2—10762no—
507C2—10762no—
508C2C4×D4×D26911yescharacteristic
509C2C2×C4×D107611yescharacteristic
510C2#3177107711yescharacteristic
511C2D4×D107611yescharacteristic
512C2#3177124511yescharacteristic
513C2#3177125011yescharacteristic
514C2#3177127911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D269
commutatorC22×C269C23×C4
FittingC4×C22⋊C4×C269C2
socle, cosocleC23×C269C24
prime radicalC2×#22575423C2
hypercenterC4×C22⋊C4D269
hypocenterC269#2358
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D1076C2semidirect
3. C2×#22575413C2semidirect
4. C22×#16864379C2semidirect
5. C2×C22⋊C4×D269C2semidirect
6. #31770507C2semidirect
7. #31770497C2semidirect
8. #31770496C2semidirect
9. #31770484C2semidirect
10. #31770483C2semidirect
11. #31770483C2semidirect
12. #31770480C2semidirect
13. #31770479C2semidirect
14. C4×#16864379C2semidirect
15. C4×C22⋊C4×C269C2semidirect
23. C22×C4×D269C22semidirect
24. #22575423C4semidirect
27. C2×C4⋊Dic269C22semidirect
28. C2×C4⋊Dic269C22semidirect
29. C2×#16864381C22semidirect
40. C2×#16864379C22semidirect
41. C2×#16864379C22semidirect
42. C2×#16864379C22semidirect
44. C2×C4×Dic269C22semidirect
45. #22575360C22semidirect
46. #22575360C22semidirect
47. #22575360C22semidirect
48. #22575360C22semidirect
52. C2×C42×C269C22semidirect
53. C2×C42×C269C22semidirect
54. #95×C269C22semidirect
55. #95×C269C22semidirect
62. C23×D269C2×C4semidirect
70. C2×D1076C2×C4semidirect
71. C2×D1076C2×C4semidirect
74. C2×C22⋊D269C2×C4semidirect
104. #16864379C2×C4semidirect
105. #16864379C2×C4semidirect
106. #16864379D4semidirect
118. C22⋊C4×C269C2×C4semidirect
119. C22⋊C4×C269D4semidirect
205. C22×C269C4×D4semidirect
234. C2×D269C4×D4semidirect
257. C269#2358semidirect
273. C4×C22⋊C4D269semidirect
306. C2×C42C2×D269semidirect
307. C2×C42C2×D269semidirect
312. #95C2×D269semidirect
313. #95C2×D269semidirect
375. C22⋊C4C4×D269semidirect
376. C22⋊C4D1076semidirect
485. C22C4×D1076semidirect

Maximal subgroups

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

subgroupindex
C2×#225754232
C2×C4×D10762
C2×#225754132
C22×#168643792
C2×C22⋊C4×D2692
#317705072
#317704972
#317704962
#317704842
#317704832
#317704802
#317704792
C4×#168643792
C4×C22⋊C4×C2692
#2358269