Finite Group Databasebeta

← #46813863

Subgroups — #46813863

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×#22575415C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D269C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D269C211yesmaximal, characteristic, complemented
6#31770505C211yesmaximal, characteristic, complemented
7#31770498C211yesmaximal, characteristic, complemented
8#31770483C211yesmaximal, characteristic, complemented
9#31770483C211yesmaximal, characteristic, complemented
10#31770481C211yesmaximal, characteristic, complemented
11#31770479C211yesmaximal, characteristic, complemented
12#31770476C211yesmaximal, characteristic, complemented
13C4×#16864379C211yesmaximal, characteristic, complemented
14#31770452C211yesmaximal, characteristic, complemented
15#388×C269C211yesmaximal, characteristic, complemented
16C24×D269C2211yescharacteristic
17C22×D1076C2211yescharacteristic
18C22×D1076C2211yescharacteristic
19C22×C22⋊D269C2211yescharacteristic
20C22×C4×D269C2211yescharacteristic
21C22×C4×D269C2211yescharacteristic
22C22×C4×D269C2211yescharacteristic
23C22×C4×D269C2211yescharacteristic
24C22×C4×D269C2211yescharacteristic, complemented
25#22575423C418yescomplemented
26C4×D1076—24no—
27#22575415—24no—
28C2×C4⋊Dic269C2211yescharacteristic, complemented
29C2×#16864381C2211yescharacteristic, complemented
30C2×C22⋊Dic269C2211yescharacteristic
31C2×C22⋊Dic269C2211yescharacteristic
32C2×#16864379C2211yescharacteristic
33C2×#16864379C2211yescharacteristic
34C2×#16864379C2211yescharacteristic
35C2×#16864379C2211yescharacteristic
36C2×#16864379C2211yescharacteristic
37C2×#16864379C2211yescharacteristic
38C2×#16864379C2211yescharacteristic, complemented
39C2×#16864379C2211yescharacteristic, complemented
40C2×#16864379C2211yescharacteristic, complemented
41C22⋊C4×D269—24no—
42C22⋊C4×D269—24no—
43C2×C4×Dic269C2211yescharacteristic, complemented
44C2×C4×Dic269C2211yescharacteristic, complemented
45#22575360C2211yescharacteristic, complemented
46#22575360C2211yescharacteristic, complemented
47#22575360C2211yescharacteristic, complemented
48#22575360C2211yescharacteristic, complemented
49C2×C4⋊C4×C269C2211yescharacteristic, complemented
50C2×C22⋊C4×C269C2211yescharacteristic
51C2×C22⋊C4×C269C2211yescharacteristic
52C2×C22⋊C4×C269C2211yescharacteristic
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—22no—
69C2×D1076—22no—
70C2×D1076C2×C414yescomplemented
71C2×D1076C2×C414yescomplemented
72C2×C22⋊D269—41no—
73C2×C22⋊D269—41no—
74C2×C22⋊D269C2×C414yescomplemented
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—22no—
85C2×C4×D269—22no—
86C2×C4×D269—22no—
87C2×C4×D269—22no—
88C2×C4×D269—22no—
89C2×C4×D269—22no—
90C2×C4×D269—41no—
91C2×C4×D269—41no—
92C2×C4×D269—41no—
93C2×C4×D269—41no—
94C2×C4×D269—41no—
95C4⋊Dic269—22no—
96#16864381—41no—
97C22⋊Dic269—22no—
98C22⋊Dic269—22no—
99#16864379—22no—
100#16864379—22no—
101#16864379—22no—
102#16864379—22no—
103#16864379—41no—
104#16864379C2×C414yescomplemented
105#16864379C2×C414yescomplemented
106#16864379D414yescomplemented
107#16864379D414yescomplemented
108C4×Dic269—22no—
109C4×Dic269—41no—
110C24×C269C2311yescharacteristic
111C22×C4×C269C2311yescharacteristic
112C22×C4×C269C2311yescharacteristic
113C22×C4×C269C2311yescharacteristic
114C22×C4×C269C2311yescharacteristic
115C22×C4×C269C2311yescharacteristic
116C22×C4×C269C2311yescharacteristic
117C4⋊C4×C269—22no—
118C22⋊C4×C269—22no—
119C22⋊C4×C269—22no—
120C22⋊C4×C269C2×C414yescomplemented
121C42×C269—22no—
122C22×D269—21no—
123C22×D269—21no—
124C22×D269—21no—
125C22×D269—21no—
126C22×D269—21no—
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—28no—
137C22×D269—28no—
138C22×D269—44no—
139C22×D269—44no—
140C22×D269—44no—
141C22×D269—44no—
142C22×D269—44no—
143C22×D269C22×C412yes—
144C22×D269C22×C412yes—
145C22×D269C22×C412yes—
146C22×D269C2×D412yes—
147C22×D269C2×D412yes—
148C22×D269#4112yes—
149C22×D269#4112yes—
150D1076—28no—
151D1076—28no—
152C22⋊D269—44no—
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×Dic269C22×C412yes—
166C2×Dic269C2×D412yes—
167C2×Dic269C2×D412yes—
168C4×D269—44no—
169C4×D269—44no—
170C4×D269—44no—
171C4×D269—44no—
172C4×D269—44no—
173C23×C269—21no—
174C23×C269—21no—
175C23×C269—21no—
176C23×C269—21no—
177C23×C269—21no—
178C23×C269—21no—
179C23×C269C22×C412yes—
180C23×C269C2411yescharacteristic
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—21no—
194C2×C4×C269—21no—
195C2×C4×C269C22×C412yes—
196C2×C4×C269C22×C412yes—
197C2×C4×C269C2×D412yes—
198C2×C4×C269C2×D412yes—
199C22×C269—22no—
200C22×C269—22no—
201C22×C269—22no—
202C22×C269—41no—
203C22×C269—41no—
204C22×C269—41no—
205C22×C269—41no—
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—22no—
226C2×D269—22no—
227C2×D269—22no—
228C2×D269—416no—
229C2×D269—41no—
230C2×D269—41no—
231C2×D269—41no—
232C2×D269—41no—
233C2×D269C4×D414yescomplemented
234C2×D269C4×D414yescomplemented
235C4×C269—22no—
236C4×C269—22no—
237C4×C269—22no—
238C4×C269—22no—
239C4×C269—41no—
240C4×C269—41no—
241Dic269—22no—
242Dic269—22no—
243Dic269—22no—
244Dic269—41no—
245Dic269—41no—
246C2×C269—42no—
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—24no—
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#388D26911yescharacteristic, complemented
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×D4—2691no—
278C23×C4—2691no—
279C23×C4—2691no—
280C23×C4—2691no—
281C23×C4—2691no—
282C23×C4—2691no—
283#120—2698no—
284C4×D4—5384no—
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—5384no—
301C2×C22⋊C4—5384no—
302C2×C22⋊C4C2×D26911yescharacteristic
303C2×C22⋊C4C2×D26911yescharacteristic
304C2×C22⋊C4C2×D26911yescharacteristic
305C2×C42—2691no—
306C2×C42—2691no—
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—2691no—
335C22×C4—2691no—
336C22×C4—2691no—
337C22×C4—2691no—
338C22×C4—2691no—
339C22×C4—5382no—
340C22×C4—5382no—
341C22×C4—5382no—
342C22×C4—5382no—
343C22×C4—5382no—
344C22×C4—5382no—
345C22×C4—5382no—
346C22×C4—5382no—
347C22×C4—5382no—
348C22×C4—5382no—
349C22×C4—10761no—
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—22no—
361C4⋊C4—5382no—
362C4⋊C4—10761no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—2694no—
366C22⋊C4—2694no—
367C22⋊C4—2694no—
368C22⋊C4—2694no—
369C22⋊C4—5382no—
370C22⋊C4—5382no—
371C22⋊C4—5382no—
372C22⋊C4—5382no—
373C22⋊C4—5382no—
374C22⋊C4—5382no—
375C22⋊C4—10761no—
376C22⋊C4C4×D26914yescomplemented
377C42—22no—
378C42—5382no—
379C42—10761no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—2692no—
387C23—2692no—
388C23—2692no—
389C23—2692no—
390C23—2692no—
391C23—2692no—
392C23—2692no—
393C23—5388no—
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—5381no—
408C23—5381no—
409C23—10764no—
410C23—10764no—
411C23—10764no—
412C23—10764no—
413C23—10764no—
414C23C2×C4×D26912yes—
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—21no—
433C2×C4—2692no—
434C2×C4—2692no—
435C2×C4—2692no—
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×C4—10764no—
453C2×C4C2×C4×D26912yes—
454C2×C4C2×C4×D26912yes—
455C2×C4D4×D26912yes—
456C2×C4D4×D26912yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—2694no—
465C22—2694no—
466C22—5382no—
467C22—5382no—
468C22—5382no—
469C22—5382no—
470C22—5382no—
471C22—5382no—
472C22—5382no—
473C22—5382no—
474C22—5382no—
475C22—5382no—
476C22—5382no—
477C22—5382no—
478C22—5382no—
479C22—5382no—
480C22—5382no—
481C22—107616no—
482C22—10761no—
483C22—10761no—
484C22—10761no—
485C22—10761no—
486C22C22×C4×D26911yescharacteristic
487C22C2×D4×D26911yescharacteristic
488C22C2×D4×D26911yescharacteristic
489C22#41×D26911yescharacteristic
490C22#41×D26911yescharacteristic
491C22#2257549911yescharacteristic
492C22#2257549911yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—41no—
498C4—41no—
499C4—5382no—
500C4—5382no—
501C4—5382no—
502C4—10761no—
503C4—10761no—
504C2—42no—
505C2—5384no—
506C2—5384no—
507C2—10762no—
508C2C4×D4×D26911yescharacteristic
509C2C4×D4×D26911yescharacteristic
510C2#3177107911yescharacteristic
511C2#3177123911yescharacteristic
512C2#3177124711yescharacteristic
513C2#3177124811yescharacteristic
514C2#3177128011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D269
commutatorC22×C269C23×C4
Fitting#388×C269C2
socle, cosocleC23×C269C24
prime radicalC2×#22575423C2
hypercenter#388D269
hypocenterC269#2358
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×C4×D1076C2semidirect
3. C2×#22575415C2semidirect
4. C2×C22⋊C4×D269C2semidirect
5. C2×C22⋊C4×D269C2semidirect
6. #31770505C2semidirect
7. #31770498C2semidirect
8. #31770483C2semidirect
9. #31770483C2semidirect
10. #31770481C2semidirect
11. #31770479C2semidirect
12. #31770476C2semidirect
13. C4×#16864379C2semidirect
14. #31770452C2semidirect
15. #388×C269C2semidirect
24. C22×C4×D269C22semidirect
25. #22575423C4semidirect
28. C2×C4⋊Dic269C22semidirect
29. C2×#16864381C22semidirect
38. C2×#16864379C22semidirect
39. C2×#16864379C22semidirect
40. C2×#16864379C22semidirect
43. C2×C4×Dic269C22semidirect
44. C2×C4×Dic269C22semidirect
45. #22575360C22semidirect
46. #22575360C22semidirect
47. #22575360C22semidirect
48. #22575360C22semidirect
49. C2×C4⋊C4×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
107. #16864379D4semidirect
120. C22⋊C4×C269C2×C4semidirect
233. C2×D269C4×D4semidirect
234. C2×D269C4×D4semidirect
257. C269#2358semidirect
266. #388D269semidirect
288. C2×C4⋊C4C2×D269semidirect
307. C2×C42C2×D269semidirect
312. #95C2×D269semidirect
313. #95C2×D269semidirect
376. C22⋊C4C4×D269semidirect

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×#225754152
C2×C22⋊C4×D2692
#317705052
#317704982
#317704832
#317704812
#317704792
#317704762
C4×#168643792
#317704522
#388×C2692
#2358269