Finite Group Databasebeta

← #46822592

Subgroups — #46822592

Order 34432.

504 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575474C211yesmaximal, characteristic, complemented
2#31771266C211yesmaximal, characteristic, complemented
3#31771249C211yesmaximal, characteristic, complemented
4#31770986C211yesmaximal, characteristic, complemented
5#31770834C211yesmaximal, characteristic, complemented
6#31770831C211yesmaximal, characteristic, complemented
7#31770825C211yesmaximal, characteristic, complemented
8#31770822C211yesmaximal, characteristic, complemented
9#31770764C211yesmaximal, characteristic, complemented
10#31770761C211yesmaximal, characteristic, complemented
11#31770749C211yesmaximal, characteristic, complemented
12#31770739C211yesmaximal, characteristic, complemented
13SD16×Dic269C211yesmaximal, characteristic, complemented
14C8×C22⋊D269C211yesmaximal, characteristic, complemented
15C22×SD16×C269C211yesmaximal, characteristic, complemented
16C2×#16864403C2211yescharacteristic, complemented
17C2×#16864401C2211yescharacteristic
18#22575474—24no—
19C2×#16864392C2211yescharacteristic, complemented
20C2×#16864392C2211yescharacteristic, complemented
21C2×#16864391C2211yescharacteristic, complemented
22C2×#16864387C2211yescharacteristic
23C2×#16864387C2211yescharacteristic
24C2×C8×D269C2211yescharacteristic, complemented
25#22575442—21no—
26#22575442C2211yescharacteristic, complemented
27#22575440C2211yescharacteristic
28#22575434—21no—
29#22575432C2211yescharacteristic
30#22575429—21no—
31#22575429C2211yescharacteristic, complemented
32#22575427—21no—
33#22575427C2211yescharacteristic
34#22575425—21no—
35#22575424C2211yescharacteristic
36#22575422—21no—
37Q8×Dic269C2211yescharacteristic, complemented
38D4×Dic269C2211yescharacteristic
39C4×C22⋊D269—21no—
40C4×C22⋊D269C2211yescharacteristic
41C2×C22⋊Dic269—21no—
42#22575385C2211yescharacteristic, complemented
43#22575382C2211yescharacteristic, complemented
44#22575378C2211yescharacteristic, complemented
45#22575377C2211yescharacteristic, complemented
46#22575377C2211yescharacteristic, complemented
47#22575375C2211yescharacteristic, complemented
48#22575374C2211yescharacteristic
49#22575374C2211yescharacteristic
50C22⋊#14524130C2211yescharacteristic
51#22575365C2211yescharacteristic, complemented
52C8×Dic269C2211yescharacteristic, complemented
53C22×Q8×C269C2211yescharacteristic
54C22×D4×C269C2211yescharacteristic
55C2×SD16×C269—24no—
56C2×SD16×C269C2211yescharacteristic
57C2×SD16×C269C2211yescharacteristic
58C2×SD16×C269C2211yescharacteristic
59C2×SD16×C269C2211yescharacteristic
60C22×C8×C269C2211yescharacteristic
61#16864403—22no—
62#16864403—41no—
63#16864401—22no—
64#16864401—41no—
65C2×Dic538C2311yescharacteristic
66C2×D1076—21no—
67C2×D1076C2311yescharacteristic
68C2×C22⋊D269—21no—
69C2×C22⋊D269—21no—
70C2×C22⋊D269—21no—
71C2×C22⋊D269D411yescharacteristic
72C22×Dic269—21no—
73C22×Dic269—21no—
74C2×C4×D269—21no—
75C2×C4×D269C2311yescharacteristic
76#16864392—22no—
77#16864392—41no—
78#16864391—22no—
79#16864387—22no—
80#16864387—41no—
81C2×#14524130C2311yescharacteristic
82C2×#14524130C2311yescharacteristic
83C8×D269—22no—
84C4⋊Dic269—21no—
85C4⋊Dic269C2311yescharacteristic
86C4⋊Dic269C2311yescharacteristic
87#16864381—21no—
88#16864381—21no—
89#16864381D411yescharacteristic
90C22⋊Dic269—21no—
91C22⋊Dic269—21no—
92C22⋊Dic269—21no—
93C22⋊Dic269—21no—
94C22⋊Dic269—21no—
95C22⋊Dic269D411yescharacteristic
96#16864379—21no—
97#16864379—21no—
98#16864379—21no—
99#16864379—21no—
100#16864379D411yescharacteristic
101C4×Dic269—21no—
102C4×Dic269C2311yescharacteristic
103C24×C269—21no—
104C2×Q8×C269—21no—
105C2×Q8×C269—22no—
106C2×Q8×C269—41no—
107C2×Q8×C269C2311yescharacteristic
108C2×Q8×C269C2311yescharacteristic
109C2×D4×C269—22no—
110C2×D4×C269—21no—
111C2×D4×C269—41no—
112C2×D4×C269C2311yescharacteristic
113C2×D4×C269C2311yescharacteristic
114C22×C4×C269—21no—
115C22×C4×C269C2311yescharacteristic
116SD16×C269—22no—
117SD16×C269—22no—
118SD16×C269—22no—
119SD16×C269D414yescomplemented
120C2×C8×C269—22no—
121C2×C8×C269C2311yescharacteristic
122C2×C8×C269C2311yescharacteristic
123C22×D269—21no—
124C22×D269C2×D411yescharacteristic
125Dic538—21no—
126Dic538—21no—
127D1076—21no—
128D1076—21no—
129D1076—42no—
130C22⋊D269—22no—
131C22⋊D269—42no—
132C22⋊D269—42no—
133C22⋊D269—81no—
134C2×Dic269—21no—
135C2×Dic269—21no—
136C2×Dic269—21no—
137C2×Dic269—42no—
138C2×Dic269—81no—
139C2×Dic269C2×D411yescharacteristic
140C2×Dic269C2×D411yescharacteristic
141C2×Dic269C2×D411yescharacteristic
142C4×D269—21no—
143C4×D269—21no—
144C4×D269—42no—
145#14524130—21no—
146#14524130—21no—
147C23×C269—21no—
148C23×C269—21no—
149C23×C269—42no—
150C23×C269—42no—
151C23×C269—81no—
152C23×C269C2×D411yescharacteristic
153Q8×C269—21no—
154Q8×C269—21no—
155Q8×C269—21no—
156Q8×C269—42no—
157Q8×C269C2×D412yes—
158D4×C269—21no—
159D4×C269—21no—
160D4×C269—21no—
161D4×C269—42no—
162D4×C269C2×D412yes—
163C2×C4×C269—21no—
164C2×C4×C269—21no—
165C2×C4×C269—21no—
166C2×C4×C269—21no—
167C2×C4×C269—42no—
168C2×C4×C269C2×D411yescharacteristic
169C2×C4×C269C2411yescharacteristic
170C8×C269—21no—
171C8×C269C2×D412yes—
172C22×C269—21no—
173C22×C269—21no—
174C22×C269—22no—
175C22×C269—41no—
176C22×C269—41no—
177C22×C269—41no—
178C22×C269—41no—
179C22×C269—41no—
180C22×C269—84no—
181C22×C269#13512yescomplemented
182C22×C269C22×D411yescharacteristic
183C2×D269—21no—
184C2×D269—21no—
185C2×D269—21no—
186C2×D269—41no—
187C2×D269—41no—
188C2×D269—41no—
189C4×C269—21no—
190C4×C269—22no—
191C4×C269—41no—
192C4×C269C22×D411yescharacteristic
193C4×C269H(5,𝔽2)11yescharacteristic
194Dic269—21no—
195Dic269—21no—
196Dic269—21no—
197Dic269—41no—
198Dic269—41no—
199Dic269—41no—
200C2×C269—22no—
201C2×C269—42no—
202C2×C269—81no—
203C2×C269D4211yescharacteristic
204C2×C269C2×#13511yescharacteristic
205C2×C269#57711yescharacteristic
206D269—41no—
207D269—81no—
208C269#328211yescharacteristic, complemented, Sylow
209#3282—2691nomaximal, Sylow
210C2×#135—2691no—
211C22×SD16D26911yescharacteristic, complemented
212#548—2691no—
213#546—2691no—
214#495—2691no—
215#465—2691no—
216#465—2691no—
217#464—2691no—
218#463—2691no—
219#452—2691no—
220#451—2691no—
221#449—2691no—
222#447—2691no—
223C4×SD16—2691no—
224C8×D4—2691no—
225C2×#41—2691no—
226C2×#41—2691no—
227C22×Q8C2×D26911yescharacteristic
228C22×D4C2×D26911yescharacteristic
229#135—5384no—
230C2×Q16—2691no—
231C2×Q16—2691no—
232C2×SD16—24no—
233C2×SD16—2691no—
234C2×SD16C2×D26911yescharacteristic
235C2×SD16C2×D26911yescharacteristic
236C2×SD16C2×D26911yescharacteristic
237C2×SD16C2×D26911yescharacteristic
238C2×D8—2691no—
239C2×D8—2691no—
240C22×C8—2691no—
241C22×C8C2×D26911yescharacteristic
242#124—2691no—
243#124—2691no—
244#124—5381no—
245#123—5381no—
246C22⋊Q8—2691no—
247C22⋊Q8—2691no—
248C22⋊Q8—5381no—
249#121—2691no—
250#121—2691no—
251#121—5381no—
252#121—5381no—
253#120—5381no—
254C4×Q8—2691no—
255C4×D4—2691no—
256C4×D4—2691no—
257C4×D4—5381no—
258C2×C22⋊C4—5381no—
259#106—2691no—
260C4⋊C8—2691no—
261#103—2691no—
262#103—2691no—
263#103—2691no—
264#102—2691no—
265#102—2691no—
266#102—2691no—
267C22⋊C8—2691no—
268C22⋊C8—2691no—
269C4×C8—2691no—
270C24—21no—
271#41—5382no—
272#41—5382no—
273#41—10761no—
274#41—10761no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—2691no—
279C2×Q8C22×D26911yescharacteristic
280C2×Q8C22×D26911yescharacteristic
281C2×D4—22no—
282C2×D4—21no—
283C2×D4—41no—
284C2×D4—2691no—
285C2×D4—2691no—
286C2×D4—5381no—
287C2×D4—5381no—
288C2×D4—5381no—
289C2×D4—5381no—
290C2×D4C22×D26911yescharacteristic
291C2×D4C22×D26911yescharacteristic
292C22×C4—21no—
293C22×C4—2691no—
294C22×C4—5381no—
295C22×C4—5381no—
296C22×C4—5381no—
297C22×C4C22×D26911yescharacteristic
298Q16—5382no—
299Q16—10761no—
300SD16—22no—
301SD16—22no—
302SD16—22no—
303SD16—5382no—
304SD16C22⋊D26914yescomplemented
305D8—5382no—
306D8—10761no—
307C2×C8—22no—
308C2×C8—2691no—
309C2×C8—2691no—
310C2×C8—5382no—
311C2×C8C22×D26911yescharacteristic
312C2×C8C22×D26911yescharacteristic
313C4⋊C4—2691no—
314C4⋊C4—2691no—
315C4⋊C4—2691no—
316C4⋊C4—5381no—
317C4⋊C4—5381no—
318C4⋊C4—5381no—
319C22⋊C4—2691no—
320C22⋊C4—2691no—
321C22⋊C4—5381no—
322C22⋊C4—5381no—
323C22⋊C4—5381no—
324C22⋊C4—5381no—
325C22⋊C4—5381no—
326C22⋊C4—5381no—
327C22⋊C4—5381no—
328C22⋊C4—5381no—
329C22⋊C4—5381no—
330C42—2691no—
331C42—5381no—
332C23—21no—
333C23—21no—
334C23—42no—
335C23—42no—
336C23—81no—
337C23—2691no—
338C23—5381no—
339C23D4×D26911yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—42no—
344Q8—5381no—
345Q8—5381no—
346Q8C2×C22⋊D26912yes—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—42no—
351D4—5382no—
352D4—5381no—
353D4—5381no—
354D4—10762no—
355D4—10762no—
356D4—10762no—
357D4—21521no—
358D4C2×C22⋊D26912yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—42no—
364C2×C4—2691no—
365C2×C4—2691no—
366C2×C4—2691no—
367C2×C4—5381no—
368C2×C4—5381no—
369C2×C4—5381no—
370C2×C4—5381no—
371C2×C4—5381no—
372C2×C4—10762no—
373C2×C4—10762no—
374C2×C4—21521no—
375C2×C4D4×D26911yescharacteristic
376C2×C4C23×D26911yescharacteristic
377C8—21no—
378C8—5381no—
379C8—5381no—
380C8C2×C22⋊D26912yes—
381C22—21no—
382C22—21no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—84no—
390C22—5381no—
391C22—5381no—
392C22—5381no—
393C22—10761no—
394C22—10761no—
395C22—10761no—
396C22#2257547412yescomplemented
397C22C2×D4×D26911yescharacteristic
398C4—21no—
399C4—22no—
400C4—41no—
401C4—5381no—
402C4—5381no—
403C4—5381no—
404C4—10761no—
405C4—10761no—
406C4—10761no—
407C4C22×C22⋊D26911yescharacteristic
408C4#2257549811yescharacteristic
409C2—22no—
410C2—42no—
411C2—81no—
412C2—10761no—
413C2—21521no—
414C2D4×C22⋊D26911yescharacteristic
415C2C2×#2257547411yescharacteristic
416C2#3177141111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
FittingC22×SD16×C269C2
socleC22×C269C22×D4
hypercenterC22×SD16D269
hypocenterC269#3282
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#22575474C2semidirect
2. #31771266C2semidirect
3. #31771249C2semidirect
4. #31770986C2semidirect
5. #31770834C2semidirect
6. #31770831C2semidirect
7. #31770825C2semidirect
8. #31770822C2semidirect
9. #31770764C2semidirect
10. #31770761C2semidirect
11. #31770749C2semidirect
12. #31770739C2semidirect
13. SD16×Dic269C2semidirect
14. C8×C22⋊D269C2semidirect
15. C22×SD16×C269C2semidirect
16. C2×#16864403C22semidirect
19. C2×#16864392C22semidirect
20. C2×#16864392C22semidirect
21. C2×#16864391C22semidirect
24. C2×C8×D269C22semidirect
26. #22575442C22semidirect
31. #22575429C22semidirect
37. Q8×Dic269C22semidirect
42. #22575385C22semidirect
43. #22575382C22semidirect
44. #22575378C22semidirect
45. #22575377C22semidirect
46. #22575377C22semidirect
47. #22575375C22semidirect
51. #22575365C22semidirect
52. C8×Dic269C22semidirect
119. SD16×C269D4semidirect
181. C22×C269#135semidirect
208. C269#3282semidirect
211. C22×SD16D269semidirect
304. SD16C22⋊D269semidirect
396. C22#22575474semidirect

Maximal subgroups

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

subgroupindex
C2×#225754742
#317712662
#317712492
#317709862
#317708342
#317708312
#317708252
#317708222
#317707642
#317707612
#317707492
#317707392
SD16×Dic2692
C8×C22⋊D2692
C22×SD16×C2692
#3282269