Finite Group Databasebeta

← #46813862

Subgroups — #46813862

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×#22575421C211yesmaximal, characteristic
2C2×C4×C22⋊D269C211yesmaximal, characteristic, complemented
3C22×#16864379C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D269C211yesmaximal, characteristic, complemented
5#31770505C211yesmaximal, characteristic, complemented
6#31770496C211yesmaximal, characteristic, complemented
7#31770495C211yesmaximal, characteristic, complemented
8#31770485C211yesmaximal, characteristic, complemented
9#31770484C211yesmaximal, characteristic, complemented
10#31770481C211yesmaximal, characteristic, complemented
11#31770478C211yesmaximal, characteristic, complemented
12#31770476C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic269C211yesmaximal, characteristic, complemented
14C4×#16864379C211yesmaximal, characteristic, complemented
15C2×C4×D4×C269C211yesmaximal, characteristic, complemented
16C24×D269C2211yescharacteristic
17C22×C22⋊D269C2211yescharacteristic
18C22×C22⋊D269C2211yescharacteristic
19C23×Dic269C2211yescharacteristic
20C22×C4×D269C2211yescharacteristic
21C22×C4×D269C2211yescharacteristic
22#22575421C418yescomplemented
23C4×C22⋊D269—24no—
24C2×#16864381C2211yescharacteristic, complemented
25C2×#16864381C2211yescharacteristic, complemented
26C2×C22⋊Dic269C2211yescharacteristic
27C2×C22⋊Dic269C2211yescharacteristic
28C2×C22⋊Dic269C2211yescharacteristic, complemented
29C2×C22⋊Dic269C2211yescharacteristic, complemented
30C2×#16864379—24no—
31C2×#16864379C2211yescharacteristic
32C2×#16864379C2211yescharacteristic
33C2×#16864379C2211yescharacteristic
34C2×#16864379C2211yescharacteristic
35C2×#16864379C2211yescharacteristic
36C2×#16864379C2211yescharacteristic
37C2×#16864379C2211yescharacteristic
38C2×#16864379C2211yescharacteristic
39C22⋊C4×D269—24no—
40C2×C4×Dic269C2211yescharacteristic, complemented
41C2×C4×Dic269C2211yescharacteristic, complemented
42#22575360C2211yescharacteristic, complemented
43#22575360C2211yescharacteristic, complemented
44#22575360C2211yescharacteristic, complemented
45#22575360C2211yescharacteristic, complemented
46#22575360C2211yescharacteristic, complemented
47#22575360C2211yescharacteristic, complemented
48C22×D4×C269C2211yescharacteristic
49C23×C4×C269C2211yescharacteristic
50C23×C4×C269C2211yescharacteristic, complemented
51C4×D4×C269—24no—
52C2×C4⋊C4×C269C2211yescharacteristic, complemented
53C2×C22⋊C4×C269C2211yescharacteristic
54C2×C22⋊C4×C269C2211yescharacteristic, complemented
55C2×C42×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
65C2×C22⋊D269—22no—
66C2×C22⋊D269—22no—
67C2×C22⋊D269—41no—
68C2×C22⋊D269—41no—
69C2×C22⋊D269C2×C414yescomplemented
70C2×C22⋊D269C2×C414yescomplemented
71C22×Dic269—22no—
72C22×Dic269—22no—
73C22×Dic269—41no—
74C22×Dic269C2311yescharacteristic
75C22×Dic269C2311yescharacteristic
76C22×Dic269C2311yescharacteristic
77C22×Dic269C2311yescharacteristic
78C22×Dic269C2311yescharacteristic
79C22×Dic269C2311yescharacteristic
80C2×C4×D269—22no—
81C2×C4×D269—22no—
82C2×C4×D269—22no—
83C2×C4×D269—22no—
84C2×C4×D269—41no—
85C2×C4×D269—41no—
86#16864381—22no—
87#16864381—41no—
88C22⋊Dic269—22no—
89C22⋊Dic269—22no—
90C22⋊Dic269—41no—
91C22⋊Dic269C2×C414yescomplemented
92#16864379—22no—
93#16864379—22no—
94#16864379—22no—
95#16864379—22no—
96#16864379—22no—
97#16864379C2×C414yescomplemented
98#16864379C2×C414yescomplemented
99#16864379D414yescomplemented
100C4×Dic269—22no—
101C4×Dic269—41no—
102C24×C269C2311yescharacteristic
103C24×C269C2311yescharacteristic
104C2×D4×C269—22no—
105C2×D4×C269—22no—
106C2×D4×C269C2×C414yescomplemented
107C22×C4×C269—22no—
108C22×C4×C269—22no—
109C22×C4×C269—22no—
110C22×C4×C269—22no—
111C22×C4×C269—41no—
112C22×C4×C269—41no—
113C22×C4×C269C2311yescharacteristic
114C22×C4×C269C2311yescharacteristic
115C22×C4×C269C2311yescharacteristic
116C22×C4×C269C2311yescharacteristic
117C22×C4×C269C2311yescharacteristic
118C4⋊C4×C269—22no—
119C22⋊C4×C269—22no—
120C22⋊C4×C269D414yescomplemented
121C42×C269—22no—
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—28no—
134C22×D269—44no—
135C22×D269—44no—
136C22×D269—44no—
137C22×D269—44no—
138C22×D269—44no—
139C22×D269C22×C412yes—
140C22×D269C22×C412yes—
141C22×D269C2×D412yes—
142C22×D269#4112yes—
143C22⋊D269—28no—
144C22⋊D269—44no—
145C2×Dic269—21no—
146C2×Dic269—21no—
147C2×Dic269—21no—
148C2×Dic269—21no—
149C2×Dic269—21no—
150C2×Dic269—21no—
151C2×Dic269—21no—
152C2×Dic269—21no—
153C2×Dic269—21no—
154C2×Dic269—21no—
155C2×Dic269—21no—
156C2×Dic269—21no—
157C2×Dic269—21no—
158C2×Dic269—21no—
159C2×Dic269—21no—
160C2×Dic269—44no—
161C2×Dic269C22×C412yes—
162C2×Dic269C22×C412yes—
163C2×Dic269C2×D412yes—
164C4×D269—44no—
165C4×D269—44no—
166C23×C269—21no—
167C23×C269—21no—
168C23×C269—21no—
169C23×C269—21no—
170C23×C269—21no—
171C23×C269—21no—
172C23×C269—21no—
173C23×C269—21no—
174C23×C269—21no—
175C23×C269—21no—
176C23×C269C22×C412yes—
177C23×C269C22×C412yes—
178C23×C269C2×D412yes—
179C23×C269#4112yes—
180C23×C269C2411yescharacteristic
181D4×C269—28no—
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×C269—44no—
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×C269—22no—
206C22×C269—22no—
207C22×C269—22no—
208C22×C269—41no—
209C22×C269—41no—
210C22×C269—41no—
211C22×C269—41no—
212C22×C269C4×D414yescomplemented
213C22×C269C23×C411yescharacteristic
214C22×C269C22×D411yescharacteristic
215C22×C269C22×D411yescharacteristic
216C22×C269C2×#4111yescharacteristic
217C22×C269C2×#4111yescharacteristic
218C22×C269H(5,𝔽2)11yescharacteristic
219C22×C269H(5,𝔽2)11yescharacteristic
220C2×D269—22no—
221C2×D269—22no—
222C2×D269—22no—
223C2×D269—22no—
224C2×D269—22no—
225C2×D269—22no—
226C2×D269—22no—
227C2×D269—22no—
228C2×D269—22no—
229C2×D269—416no—
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—41no—
240Dic269—22no—
241Dic269—22no—
242Dic269—22no—
243Dic269—41no—
244Dic269—41no—
245Dic269—41no—
246C2×C269—24no—
247C2×C269—42no—
248C2×C269C2×C4×D411yescharacteristic
249C2×C269C2×C4×D411yescharacteristic
250C2×C269#51811yescharacteristic
251C2×C269D4211yescharacteristic
252C2×C269#54611yescharacteristic
253C2×C269#54611yescharacteristic
254C2×C269#55111yescharacteristic
255D269—24no—
256D269—42no—
257C269#235811yescharacteristic, complemented, Sylow
258#2358—2691nomaximal, Sylow
259C2×#120—2691no—
260C2×C4×D4—2691no—
261C2×C4×D4D26911yescharacteristic, complemented
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⋊C4—2691no—
274C25—2691no—
275C22×D4—2691no—
276C22×D4—2691no—
277C22×D4C2×D26911yescharacteristic
278C23×C4—2691no—
279C23×C4—2691no—
280C23×C4—2691no—
281C23×C4C2×D26911yescharacteristic
282C23×C4C2×D26911yescharacteristic, complemented
283#120—2698no—
284C4×D4—24no—
285C4×D4—5384no—
286C2×C4⋊C4—2691no—
287C2×C4⋊C4—2691no—
288C2×C4⋊C4C2×D26911yescharacteristic, complemented
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, complemented
305C2×C42—2691no—
306C2×C42—2691no—
307C2×C42C2×D26911yescharacteristic, complemented
308#95—2691no—
309#95—2691no—
310#95—2691no—
311#95—2691no—
312#95—2691no—
313#95—2691no—
314C24—2691no—
315C24—2691no—
316C24—2694no—
317C24—5382no—
318C24—5382no—
319C24—5382no—
320C24—5382no—
321C24—10761no—
322C24—10761no—
323C24C22×D26911yescharacteristic
324C24C22×D26911yescharacteristic
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—2694no—
328C2×D4—2694no—
329C2×D4—5382no—
330C2×D4—5382no—
331C2×D4—10761no—
332C2×D4—10761no—
333C2×D4C4×D26914yescomplemented
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—2691no—
341C22×C4—2691no—
342C22×C4—2691no—
343C22×C4—2691no—
344C22×C4—2691no—
345C22×C4—2691no—
346C22×C4—5382no—
347C22×C4—5382no—
348C22×C4—5382no—
349C22×C4—5382no—
350C22×C4—5382no—
351C22×C4—5382no—
352C22×C4—10761no—
353C22×C4—10761no—
354C22×C4—10761no—
355C22×C4C22×D26911yescharacteristic
356C22×C4C22×D26911yescharacteristic
357C22×C4C22×D26911yescharacteristic
358C22×C4C22×D26911yescharacteristic
359C22×C4C22×D26911yescharacteristic
360C4⋊C4—22no—
361C4⋊C4—5382no—
362C4⋊C4—10761no—
363C22⋊C4—22no—
364C22⋊C4—2694no—
365C22⋊C4—2694no—
366C22⋊C4—2694no—
367C22⋊C4—2694no—
368C22⋊C4—5382no—
369C22⋊C4—5382no—
370C22⋊C4—5382no—
371C22⋊C4—5382no—
372C22⋊C4—5382no—
373C22⋊C4—5382no—
374C22⋊C4—5382no—
375C22⋊C4—10761no—
376C22⋊C4C22⋊D26914yescomplemented
377C42—22no—
378C42—5382no—
379C42—10761no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—2692no—
391C23—2692no—
392C23—2692no—
393C23—2692no—
394C23—5388no—
395C23—5381no—
396C23—5381no—
397C23—5381no—
398C23—5381no—
399C23—5388no—
400C23—5381no—
401C23—5381no—
402C23—5381no—
403C23—5381no—
404C23—5381no—
405C23—5381no—
406C23—10764no—
407C23—10764no—
408C23—10764no—
409C23—10764no—
410C23—10764no—
411C23C2×C4×D26912yes—
412C23C2×C4×D26912yes—
413C23C2×C22⋊D26912yes—
414C23#1686440212yes—
415C23C23×D26911yescharacteristic
416D4—28no—
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—44no—
431C2×C4—44no—
432C2×C4—2692no—
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—5381no—
449C2×C4—5381no—
450C2×C4—10764no—
451C2×C4—10764no—
452C2×C4—10764no—
453C2×C4C2×C4×D26912yes—
454C2×C4D4×D26912yes—
455C2×C4C2×C22⋊D26912yes—
456C2×C4C2×C22⋊D26912yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—2694no—
471C22—5382no—
472C22—5382no—
473C22—5382no—
474C22—5382no—
475C22—5382no—
476C22—5382no—
477C22—5382no—
478C22—5382no—
479C22—5382no—
480C22—107616no—
481C22—10761no—
482C22—10761no—
483C22—10761no—
484C22—10761no—
485C22C4×C22⋊D26914yescomplemented
486C22C22×C4×D26911yescharacteristic
487C22C2×D4×D26911yescharacteristic
488C22C22×C22⋊D26911yescharacteristic
489C22#41×D26911yescharacteristic
490C22C2×#1686440211yescharacteristic
491C22#2257549811yescharacteristic
492C22#2257549911yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—41no—
498C4—5382no—
499C4—5382no—
500C4—5382no—
501C4—10761no—
502C4—10761no—
503C4—10761no—
504C2—24no—
505C2—42no—
506C2—5384no—
507C2—10762no—
508C2C4×D4×D26911yescharacteristic
509C2C2×C4×C22⋊D26911yescharacteristic
510C2#3177107711yescharacteristic
511C2D4×C22⋊D26911yescharacteristic
512C2#3177124311yescharacteristic
513C2#3177125111yescharacteristic
514C2#3177128411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D269
commutatorC22×C269C23×C4
FittingC2×C4×D4×C269C2
socle, cosocleC23×C269C24
prime radicalC2×#22575421C2
hypercenterC2×C4×D4D269
hypocenterC269#2358
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D269C2semidirect
3. C22×#16864379C2semidirect
4. C2×C22⋊C4×D269C2semidirect
5. #31770505C2semidirect
6. #31770496C2semidirect
7. #31770495C2semidirect
8. #31770485C2semidirect
9. #31770484C2semidirect
10. #31770481C2semidirect
11. #31770478C2semidirect
12. #31770476C2semidirect
13. C22⋊C4×Dic269C2semidirect
14. C4×#16864379C2semidirect
15. C2×C4×D4×C269C2semidirect
22. #22575421C4semidirect
24. C2×#16864381C22semidirect
25. C2×#16864381C22semidirect
28. C2×C22⋊Dic269C22semidirect
29. C2×C22⋊Dic269C22semidirect
40. C2×C4×Dic269C22semidirect
41. C2×C4×Dic269C22semidirect
42. #22575360C22semidirect
43. #22575360C22semidirect
44. #22575360C22semidirect
45. #22575360C22semidirect
46. #22575360C22semidirect
47. #22575360C22semidirect
50. C23×C4×C269C22semidirect
52. C2×C4⋊C4×C269C22semidirect
54. C2×C22⋊C4×C269C22semidirect
55. C2×C42×C269C22semidirect
62. C23×D269C2×C4semidirect
69. C2×C22⋊D269C2×C4semidirect
70. C2×C22⋊D269C2×C4semidirect
91. C22⋊Dic269C2×C4semidirect
97. #16864379C2×C4semidirect
98. #16864379C2×C4semidirect
99. #16864379D4semidirect
106. C2×D4×C269C2×C4semidirect
120. C22⋊C4×C269D4semidirect
212. C22×C269C4×D4semidirect
234. C2×D269C4×D4semidirect
257. C269#2358semidirect
261. C2×C4×D4D269semidirect
282. C23×C4C2×D269semidirect
288. C2×C4⋊C4C2×D269semidirect
304. C2×C22⋊C4C2×D269semidirect
307. C2×C42C2×D269semidirect
333. C2×D4C4×D269semidirect
376. C22⋊C4C22⋊D269semidirect
485. C22C4×C22⋊D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754212
C2×C4×C22⋊D2692
C22×#168643792
C2×C22⋊C4×D2692
#317705052
#317704962
#317704952
#317704852
#317704842
#317704812
#317704782
#317704762
C22⋊C4×Dic2692
C4×#168643792
C2×C4×D4×C2692
#2358269