Finite Group Databasebeta

← #46813902

Subgroups — #46813902

Order 34432.

788 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575425C211yesmaximal, characteristic
2C2×C4×C22⋊D269C211yesmaximal, characteristic, complemented
3C2×#22575413C211yesmaximal, characteristic, complemented
4C22×#16864381C211yesmaximal, characteristic, complemented
5#31770505C211yesmaximal, characteristic, complemented
6#31770500C211yesmaximal, characteristic, complemented
7#31770496C211yesmaximal, characteristic, complemented
8#31770493C211yesmaximal, characteristic, complemented
9#31770485C211yesmaximal, characteristic, complemented
10#31770484C211yesmaximal, characteristic, complemented
11#31770478C211yesmaximal, characteristic, complemented
12#31770476C211yesmaximal, characteristic, complemented
13C4×#16864381C211yesmaximal, characteristic, complemented
14C22⋊C4×Dic269C211yesmaximal, characteristic, complemented
15C2×C4×D4×C269C211yesmaximal, characteristic, complemented
16C22×C22⋊D269C2211yescharacteristic
17C22×C22⋊D269C2211yescharacteristic
18C23×Dic269C2211yescharacteristic
19C23×Dic269C2211yescharacteristic
20C22×C4×D269C2211yescharacteristic
21#22575425C418yescomplemented
22C4×C22⋊D269—24no—
23#22575413—24no—
24C2×#16864381—24no—
25C2×#16864381C2211yescharacteristic
26C2×#16864381C2211yescharacteristic
27C2×#16864381C2211yescharacteristic
28C2×#16864381C2211yescharacteristic
29C2×#16864381C2211yescharacteristic
30C2×#16864381C2211yescharacteristic
31C2×C22⋊Dic269C2211yescharacteristic
32C2×C22⋊Dic269C2211yescharacteristic
33C2×C22⋊Dic269C2211yescharacteristic
34C2×C22⋊Dic269C2211yescharacteristic
35C2×#16864379C2211yescharacteristic
36C2×#16864379C2211yescharacteristic
37C2×#16864379C2211yescharacteristic
38C2×#16864379C2211yescharacteristic
39C2×C4×Dic269C2211yescharacteristic
40C2×C4×Dic269C2211yescharacteristic
41C2×C4×Dic269C2211yescharacteristic
42#22575360C2211yescharacteristic
43#22575360C2211yescharacteristic
44#22575360C2211yescharacteristic
45#22575360C2211yescharacteristic
46#22575360C2211yescharacteristic
47#22575360C2211yescharacteristic
48C22×D4×C269C2211yescharacteristic
49C23×C4×C269C2211yescharacteristic
50C23×C4×C269C2211yescharacteristic
51C4×D4×C269—24no—
52C2×C4⋊C4×C269C2211yescharacteristic
53C2×C22⋊C4×C269C2211yescharacteristic
54C2×C22⋊C4×C269C2211yescharacteristic
55C2×C42×C269C2211yescharacteristic
56C23×D269C2311yescharacteristic
57C2×C22⋊D269—22no—
58C2×C22⋊D269—22no—
59C2×C22⋊D269—22no—
60C2×C22⋊D269—22no—
61C2×C22⋊D269C2×C414yescomplemented
62C2×C22⋊D269C2×C414yescomplemented
63C22×Dic269—22no—
64C22×Dic269—22no—
65C22×Dic269—22no—
66C22×Dic269—22no—
67C22×Dic269—41no—
68C22×Dic269C2×C414yescomplemented
69C22×Dic269C2311yescharacteristic
70C22×Dic269C2311yescharacteristic
71C22×Dic269C2311yescharacteristic
72C22×Dic269C2311yescharacteristic
73C22×Dic269C2311yescharacteristic
74C22×Dic269C2311yescharacteristic
75C22×Dic269C2311yescharacteristic
76C2×C4×D269—22no—
77C2×C4×D269—22no—
78C2×C4×D269—41no—
79#16864381—22no—
80#16864381—22no—
81#16864381—22no—
82#16864381—22no—
83#16864381C2×C414yescomplemented
84#16864381D414yescomplemented
85C22⋊Dic269—22no—
86C22⋊Dic269—22no—
87C22⋊Dic269—41no—
88C22⋊Dic269C2×C414yescomplemented
89#16864379—22no—
90#16864379—22no—
91#16864379—41no—
92#16864379C2×C414yescomplemented
93C4×Dic269—22no—
94C4×Dic269—22no—
95C4×Dic269—22no—
96C24×C269C2311yescharacteristic
97C24×C269C2311yescharacteristic
98C2×D4×C269—22no—
99C2×D4×C269—22no—
100C2×D4×C269C2×C414yescomplemented
101C22×C4×C269—22no—
102C22×C4×C269—22no—
103C22×C4×C269—22no—
104C22×C4×C269—22no—
105C22×C4×C269—41no—
106C22×C4×C269—41no—
107C22×C4×C269C2311yescharacteristic
108C22×C4×C269C2311yescharacteristic
109C22×C4×C269C2311yescharacteristic
110C22×C4×C269C2311yescharacteristic
111C22×C4×C269C2311yescharacteristic
112C4⋊C4×C269—22no—
113C22⋊C4×C269—22no—
114C22⋊C4×C269D414yescomplemented
115C42×C269—22no—
116C22×D269—21no—
117C22×D269—21no—
118C22×D269—21no—
119C22×D269—21no—
120C22×D269—21no—
121C22×D269—21no—
122C22×D269C22×C412yes—
123C22⋊D269—28no—
124C22⋊D269—28no—
125C2×Dic269—21no—
126C2×Dic269—21no—
127C2×Dic269—21no—
128C2×Dic269—21no—
129C2×Dic269—21no—
130C2×Dic269—21no—
131C2×Dic269—28no—
132C2×Dic269—21no—
133C2×Dic269—21no—
134C2×Dic269—21no—
135C2×Dic269—21no—
136C2×Dic269—21no—
137C2×Dic269—21no—
138C2×Dic269—21no—
139C2×Dic269—21no—
140C2×Dic269—21no—
141C2×Dic269—44no—
142C2×Dic269C22×C412yes—
143C2×Dic269C22×C412yes—
144C2×Dic269C22×C412yes—
145C2×Dic269C2×D412yes—
146C2×Dic269C2×D412yes—
147C2×Dic269#4112yes—
148C4×D269—44no—
149C23×C269—21no—
150C23×C269—21no—
151C23×C269—21no—
152C23×C269—21no—
153C23×C269—21no—
154C23×C269—21no—
155C23×C269—21no—
156C23×C269—21no—
157C23×C269—21no—
158C23×C269—21no—
159C23×C269C22×C412yes—
160C23×C269C22×C412yes—
161C23×C269C2×D412yes—
162C23×C269#4112yes—
163C23×C269C2411yescharacteristic
164D4×C269—28no—
165C2×C4×C269—21no—
166C2×C4×C269—21no—
167C2×C4×C269—21no—
168C2×C4×C269—21no—
169C2×C4×C269—21no—
170C2×C4×C269—21no—
171C2×C4×C269—21no—
172C2×C4×C269—21no—
173C2×C4×C269—21no—
174C2×C4×C269—21no—
175C2×C4×C269—21no—
176C2×C4×C269—44no—
177C2×C4×C269—44no—
178C2×C4×C269C22×C412yes—
179C2×C4×C269C2×D412yes—
180C2×C4×C269C2×D412yes—
181C2×C4×C269C2×D412yes—
182C22×C269—22no—
183C22×C269—22no—
184C22×C269—22no—
185C22×C269—22no—
186C22×C269—22no—
187C22×C269—22no—
188C22×C269—22no—
189C22×C269—22no—
190C22×C269—22no—
191C22×C269—41no—
192C22×C269—41no—
193C22×C269—41no—
194C22×C269—41no—
195C22×C269C4×D414yescomplemented
196C22×C269C23×C411yescharacteristic
197C22×C269C22×D411yescharacteristic
198C22×C269C22×D411yescharacteristic
199C22×C269C2×#4111yescharacteristic
200C22×C269C2×#4111yescharacteristic
201C22×C269H(5,𝔽2)11yescharacteristic
202C22×C2692−1+411yescharacteristic
203C2×D269—22no—
204C2×D269—22no—
205C2×D269—22no—
206C2×D269—41no—
207C2×D269—41no—
208C2×D269—41no—
209C2×D269—41no—
210C4×C269—22no—
211C4×C269—22no—
212C4×C269—22no—
213C4×C269—22no—
214C4×C269—41no—
215Dic269—22no—
216Dic269—22no—
217Dic269—22no—
218Dic269—41no—
219Dic269—41no—
220Dic269—41no—
221Dic269C4×D414yescomplemented
222C2×C269—24no—
223C2×C269—42no—
224C2×C269C2×C4×D411yescharacteristic
225C2×C269C2×C4×D411yescharacteristic
226C2×C269#52011yescharacteristic
227C2×C269D4211yescharacteristic
228C2×C269#54711yescharacteristic
229C2×C269#54811yescharacteristic
230C2×C269#55311yescharacteristic
231D269—42no—
232C269#236111yescharacteristic, complemented, Sylow
233#2361—2691nomaximal, Sylow
234C2×#121—2691no—
235C2×C4×D4—2691no—
236C2×C4×D4—2691no—
237C2×C4×D4D26911yescharacteristic, complemented
238C22×C4⋊C4—2691no—
239#390—2691no—
240#389—2691no—
241#388—2691no—
242#388—2691no—
243#386—2691no—
244#386—2691no—
245#385—2691no—
246#385—2691no—
247C4×C4⋊C4—2691no—
248C4×C22⋊C4—2691no—
249C22×D4—2691no—
250C22×D4—2691no—
251C22×D4C2×D26911yescharacteristic
252C23×C4—2691no—
253C23×C4—2691no—
254C23×C4—2691no—
255C23×C4C2×D26911yescharacteristic
256C23×C4C2×D26911yescharacteristic
257#121—2698no—
258C4×D4—24no—
259C4×D4—5384no—
260C4×D4—5384no—
261C2×C4⋊C4—2691no—
262C2×C4⋊C4—2691no—
263C2×C4⋊C4—2691no—
264C2×C4⋊C4—2691no—
265C2×C4⋊C4—2691no—
266C2×C4⋊C4—2691no—
267C2×C4⋊C4—5384no—
268C2×C4⋊C4C2×D26911yescharacteristic
269C2×C22⋊C4—2691no—
270C2×C22⋊C4—2691no—
271C2×C22⋊C4—2691no—
272C2×C22⋊C4—2691no—
273C2×C22⋊C4—2691no—
274C2×C22⋊C4—2691no—
275C2×C22⋊C4—2691no—
276C2×C22⋊C4—2691no—
277C2×C22⋊C4C2×D26911yescharacteristic
278C2×C22⋊C4C2×D26911yescharacteristic
279C2×C42—2691no—
280C2×C42—2691no—
281C2×C42—2691no—
282C2×C42C2×D26911yescharacteristic
283#95—2691no—
284#95—2691no—
285#95—2691no—
286#95—2691no—
287#95—2691no—
288#95—2691no—
289C24—2691no—
290C24C22×D26911yescharacteristic
291C24C22×D26911yescharacteristic
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—2694no—
295C2×D4—2694no—
296C2×D4—5382no—
297C2×D4—5382no—
298C2×D4—5382no—
299C2×D4—5382no—
300C2×D4C4×D26914yescomplemented
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—2691no—
308C22×C4—2694no—
309C22×C4—2691no—
310C22×C4—2691no—
311C22×C4—2691no—
312C22×C4—2691no—
313C22×C4—2691no—
314C22×C4—2691no—
315C22×C4—5382no—
316C22×C4—5382no—
317C22×C4—5382no—
318C22×C4—5382no—
319C22×C4—5382no—
320C22×C4—5382no—
321C22×C4—10761no—
322C22×C4—10761no—
323C22×C4C22×D26911yescharacteristic
324C22×C4C22×D26911yescharacteristic
325C22×C4C22×D26911yescharacteristic
326C22×C4C22×D26911yescharacteristic
327C22×C4C22×D26911yescharacteristic
328C4⋊C4—22no—
329C4⋊C4—2694no—
330C4⋊C4—2694no—
331C4⋊C4—5382no—
332C4⋊C4—5382no—
333C4⋊C4—5382no—
334C4⋊C4—5382no—
335C22⋊C4—22no—
336C22⋊C4—2694no—
337C22⋊C4—2694no—
338C22⋊C4—5382no—
339C22⋊C4—5382no—
340C22⋊C4—5382no—
341C22⋊C4—5382no—
342C22⋊C4—10761no—
343C22⋊C4—10761no—
344C22⋊C4C22⋊D26914yescomplemented
345C42—22no—
346C42—5382no—
347C42—5382no—
348C42—5382no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—2692no—
360C23—5381no—
361C23—5381no—
362C23—5381no—
363C23—5381no—
364C23—5381no—
365C23—5381no—
366C23C2×C4×D26912yes—
367C23C2×C4×D26912yes—
368C23C2×C22⋊D26912yes—
369C23#1686440212yes—
370C23C23×D26911yescharacteristic
371D4—28no—
372D4—5388no—
373D4—5388no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—44no—
386C2×C4—44no—
387C2×C4—2692no—
388C2×C4—2692no—
389C2×C4—2692no—
390C2×C4—2692no—
391C2×C4—2692no—
392C2×C4—2692no—
393C2×C4—5388no—
394C2×C4—5381no—
395C2×C4—5381no—
396C2×C4—5381no—
397C2×C4—5381no—
398C2×C4—5381no—
399C2×C4—5381no—
400C2×C4—5381no—
401C2×C4—5381no—
402C2×C4—5381no—
403C2×C4—5381no—
404C2×C4—5381no—
405C2×C4—5381no—
406C2×C4—5381no—
407C2×C4—5381no—
408C2×C4—5381no—
409C2×C4—10764no—
410C2×C4—10764no—
411C2×C4C2×C4×D26912yes—
412C2×C4D4×D26912yes—
413C2×C4C2×C22⋊D26912yes—
414C2×C4C2×C22⋊D26912yes—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—5382no—
429C22—5382no—
430C22—5382no—
431C22—10761no—
432C22—10761no—
433C22—10761no—
434C22—10761no—
435C22C4×C22⋊D26914yescomplemented
436C22C22×C4×D26911yescharacteristic
437C22C2×D4×D26911yescharacteristic
438C22C22×C22⋊D26911yescharacteristic
439C22#41×D26911yescharacteristic
440C22C2×#1686440211yescharacteristic
441C22#2257549811yescharacteristic
442C22#2257550011yescharacteristic
443C4—22no—
444C4—22no—
445C4—22no—
446C4—22no—
447C4—41no—
448C4—2694no—
449C4—5382no—
450C4—5382no—
451C4—5382no—
452C4—10761no—
453C4—10761no—
454C4—10761no—
455C2—24no—
456C2—42no—
457C2—10762no—
458C2C4×D4×D26911yescharacteristic
459C2C2×C4×C22⋊D26911yescharacteristic
460C2#3177108411yescharacteristic
461C2D4×C22⋊D26911yescharacteristic
462C2#3177125411yescharacteristic
463C2#3177126411yescharacteristic
464C2#3177130411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D269
commutatorC22×C269C23×C4
FittingC2×C4×D4×C269C2
socle, cosocleC23×C269C24
prime radicalC2×#22575425C2
hypercenterC2×C4×D4D269
hypocenterC269#2361
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. C2×#22575413C2semidirect
4. C22×#16864381C2semidirect
5. #31770505C2semidirect
6. #31770500C2semidirect
7. #31770496C2semidirect
8. #31770493C2semidirect
9. #31770485C2semidirect
10. #31770484C2semidirect
11. #31770478C2semidirect
12. #31770476C2semidirect
13. C4×#16864381C2semidirect
14. C22⋊C4×Dic269C2semidirect
15. C2×C4×D4×C269C2semidirect
21. #22575425C4semidirect
61. C2×C22⋊D269C2×C4semidirect
62. C2×C22⋊D269C2×C4semidirect
68. C22×Dic269C2×C4semidirect
83. #16864381C2×C4semidirect
84. #16864381D4semidirect
88. C22⋊Dic269C2×C4semidirect
92. #16864379C2×C4semidirect
100. C2×D4×C269C2×C4semidirect
114. C22⋊C4×C269D4semidirect
195. C22×C269C4×D4semidirect
221. Dic269C4×D4semidirect
232. C269#2361semidirect
237. C2×C4×D4D269semidirect
300. C2×D4C4×D269semidirect
344. C22⋊C4C22⋊D269semidirect
435. C22C4×C22⋊D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754252
C2×C4×C22⋊D2692
C2×#225754132
C22×#168643812
#317705052
#317705002
#317704962
#317704932
#317704852
#317704842
#317704782
#317704762
C4×#168643812
C22⋊C4×Dic2692
C2×C4×D4×C2692
#2361269