Finite Group Databasebeta

← #46822875

Subgroups — #46822875

Order 34432.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771263C211yesmaximal, characteristic, complemented
2#31771258C211yesmaximal, characteristic, complemented
3#31770939C211yesmaximal, characteristic, complemented
4#31770917C211yesmaximal, characteristic, complemented
5#31770897C211yesmaximal, characteristic, complemented
6#31770854C211yesmaximal, characteristic, complemented
7#31770840C211yesmaximal, characteristic, complemented
8#31770817C211yesmaximal, characteristic, complemented
9#31770751C211yesmaximal, characteristic, complemented
10#31770745C211yesmaximal, characteristic, complemented
11#31770707C211yesmaximal, characteristic, complemented
12#31770678C211yesmaximal, characteristic, complemented
13#31770603C211yesmaximal, characteristic, complemented
14#103×D269C211yesmaximal, characteristic, complemented
15#489×C269C211yesmaximal, characteristic, complemented
16C2×#16864403—21no—
17C2×#16864401C2211yescharacteristic
18C2×Q8×D269C2211yescharacteristic
19C2×#16864391C2211yescharacteristic
20C2×#16864389C2211yescharacteristic
21C2×#16864387C2211yescharacteristic
22C2×#16864385C2211yescharacteristic
23C2×C8×D269C2211yescharacteristic
24#22575439—21no—
25#22575438—21no—
26#22575438—21no—
27#22575430—21no—
28#22575429—21no—
29#22575429C2211yescharacteristic
30#22575428C2211yescharacteristic
31#22575428C2211yescharacteristic
32#22575426—21no—
33#22575424C2211yescharacteristic
34C4×Dic538C2211yescharacteristic
35C4×D1076C2211yescharacteristic
36C4×D1076C2211yescharacteristic
37#22575413—21no—
38C4⋊C4×D269C2211yescharacteristic
39C4⋊C4×D269C2211yescharacteristic
40#22575387C2211yescharacteristic
41#22575386C2211yescharacteristic
42#22575386C2211yescharacteristic
43C4⋊#14524130C2211yescharacteristic
44#22575378C2211yescharacteristic
45#22575377C2211yescharacteristic
46#22575376C2211yescharacteristic
47#22575376C2211yescharacteristic
48#22575375C2211yescharacteristic
49#22575374C2211yescharacteristic
50#22575365C2211yescharacteristic
51#22575365C2211yescharacteristic
52C4⋊Q8×C269C2211yescharacteristic
53#124×C269C2211yescharacteristic
54#103×C269C2211yescharacteristic
55#103×C269C2211yescharacteristic
56#102×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58#97×C269C2211yescharacteristic
59#16864403—44no—
60#16864401—22no—
61#16864401—41no—
62C2×Dic538—21no—
63C2×Dic538C2311yescharacteristic
64Q8×D269—22no—
65Q8×D269—41no—
66C2×D1076—21no—
67C2×D1076—21no—
68C2×D1076D411yescharacteristic
69C2×D1076C2311yescharacteristic
70C2×C22⋊D269—21no—
71C2×C22⋊D269—21no—
72C22×Dic269—21no—
73C2×C4×D269—21no—
74C2×C4×D269—21no—
75C2×C4×D269—21no—
76C2×C4×D269—21no—
77C2×C4×D269C2311yescharacteristic
78C2×C4×D269C2311yescharacteristic
79#16864391—22no—
80#16864389—41no—
81#16864387—41no—
82#16864385—41no—
83C2×#14524130C2311yescharacteristic
84C2×#14524130C2311yescharacteristic
85C8×D269—41no—
86C4⋊Dic269D411yescharacteristic
87C4⋊Dic269C2311yescharacteristic
88C4⋊Dic269C2311yescharacteristic
89#16864381—21no—
90#16864381—21no—
91#16864381—21no—
92#16864381—21no—
93C22⋊Dic269—21no—
94#16864379—21no—
95#16864379—21no—
96#16864379—21no—
97#16864379—21no—
98#16864379D411yescharacteristic
99#16864379D411yescharacteristic
100C4×Dic269—21no—
101C2×Q8×C269—21no—
102C2×Q8×C269C2311yescharacteristic
103C2×D4×C269C2311yescharacteristic
104C2×C8×C269C2311yescharacteristic
105C2×C8×C269C2311yescharacteristic
106C4⋊C4×C269—21no—
107C4⋊C4×C269C2311yescharacteristic
108C4⋊C4×C269C2311yescharacteristic
109C22⋊C4×C269—21no—
110C22⋊C4×C269—21no—
111C42×C269C2311yescharacteristic
112C22×D269—21no—
113C22×D269C2×D411yescharacteristic
114C22×D269C2×D411yescharacteristic
115Dic538—21no—
116Dic538—42no—
117Dic538#4112yescomplemented
118D1076—22no—
119D1076—21no—
120D1076—21no—
121D1076—42no—
122D1076—42no—
123C22⋊D269—42no—
124C22⋊D269—42no—
125C2×Dic269—21no—
126C2×Dic269—21no—
127C2×Dic269—21no—
128C2×Dic269—42no—
129C2×Dic269C2×D411yescharacteristic
130C2×Dic269C2×D411yescharacteristic
131C4×D269—21no—
132C4×D269—21no—
133C4×D269—21no—
134C4×D269—21no—
135C4×D269—42no—
136C4×D269—42no—
137C4×D269—42no—
138C4×D269—42no—
139#14524130—21no—
140#14524130—21no—
141C23×C269—21no—
142Q8×C269—21no—
143Q8×C269—21no—
144Q8×C269—42no—
145D4×C269—21no—
146D4×C269—21no—
147C2×C4×C269—21no—
148C2×C4×C269—21no—
149C2×C4×C269—21no—
150C2×C4×C269C2×D411yescharacteristic
151C2×C4×C269C2×D411yescharacteristic
152C2×C4×C269C2411yescharacteristic
153C8×C269—21no—
154C8×C269—21no—
155C22×C269—41no—
156C22×C269—41no—
157C22×C269—41no—
158C22×C269C22×D411yescharacteristic
159C2×D269—21no—
160C2×D269—21no—
161C2×D269—21no—
162C2×D269—21no—
163C2×D269—21no—
164C2×D269—41no—
165C2×D269—41no—
166C2×D269—41no—
167C2×D269AGL(1,ℤ/8)12yes—
168C4×C269—21no—
169C4×C269—21no—
170C4×C269—41no—
171C4×C269—41no—
172C4×C269—41no—
173C4×C269C2×#4111yescharacteristic
174C4×C269H(5,𝔽2)11yescharacteristic
175Dic269—21no—
176Dic269—21no—
177Dic269—22no—
178Dic269—41no—
179Dic269—41no—
180C2×C269—81no—
181C2×C269#54611yescharacteristic
182C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
183C2×C269#57811yescharacteristic
184D269—22no—
185D269—41no—
186D269—81no—
187C269#330811yescharacteristic, complemented, Sylow
188#3308—2691nomaximal, Sylow
189#548—2691no—
190#547—2691no—
191#489D26911yescharacteristic, complemented
192#484—2691no—
193#480—2691no—
194#477—2691no—
195#468—2691no—
196#466—2691no—
197#463—2691no—
198#449—2691no—
199#448—2691no—
200#440—2691no—
201#435—2691no—
202#417—2691no—
203C2×#103—2691no—
204C2×#41—2691no—
205C2×#41—5381no—
206C22×Q8—2691no—
207C2×SD16—2691no—
208C2×SD16—2691no—
209C2×D8—2691no—
210C2×M16—2691no—
211C22×C8—2691no—
212C4⋊Q8C2×D26911yescharacteristic
213#124—5381no—
214#124C2×D26911yescharacteristic
215#123—5381no—
216#123—5381no—
217C22⋊Q8—2691no—
218C22⋊Q8—5381no—
219C22⋊Q8—5381no—
220#121—2691no—
221#121—2691no—
222#121—2691no—
223#121—5381no—
224C4×Q8—2691no—
225C4×D4—2691no—
226C4×D4—2691no—
227C4×D4—5381no—
228C2×C4⋊C4—2691no—
229C2×C4⋊C4—2691no—
230#107—2691no—
231#107—2691no—
232#107—2691no—
233C4⋊C8—2691no—
234#103—2691no—
235#103—2691no—
236#103—2691no—
237#103—2691no—
238#103C2×D26911yescharacteristic
239#103C2×D26911yescharacteristic
240#102—2691no—
241#102—2691no—
242#102C2×D26911yescharacteristic
243#102C2×D26911yescharacteristic
244C22⋊C8—2691no—
245C22⋊C8—2691no—
246#97C2×D26911yescharacteristic
247#41—5382no—
248#41—10761no—
249#41—10764no—
250C2×Q8—21no—
251C2×Q8—2691no—
252C2×Q8—5381no—
253C2×Q8—5382no—
254C2×Q8—10761no—
255C2×Q8C22×D26911yescharacteristic
256C2×D4—2691no—
257C2×D4—2691no—
258C2×D4—5381no—
259C2×D4—5381no—
260C2×D4—5381no—
261C2×D4—5381no—
262C2×D4C22×D26911yescharacteristic
263C22×C4—2691no—
264C22×C4—2691no—
265C22×C4—5381no—
266C22×C4—5381no—
267C22×C4—5381no—
268C22×C4—5381no—
269C22×C4—5381no—
270SD16—5382no—
271SD16—10761no—
272D8—10761no—
273M16—10761no—
274C2×C8—2691no—
275C2×C8—2691no—
276C2×C8—10761no—
277C2×C8C22×D26911yescharacteristic
278C2×C8C22×D26911yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—2691no—
281C4⋊C4—2691no—
282C4⋊C4—2691no—
283C4⋊C4—5381no—
284C4⋊C4—5381no—
285C4⋊C4—5381no—
286C4⋊C4—5381no—
287C4⋊C4C22×D26911yescharacteristic
288C4⋊C4C22×D26911yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—2691no—
292C22⋊C4—2691no—
293C22⋊C4—5381no—
294C22⋊C4—5381no—
295C22⋊C4—5381no—
296C22⋊C4—5381no—
297C22⋊C4—5381no—
298C42—5381no—
299C42C22×D26911yescharacteristic
300C23—21no—
301C23—2691no—
302C23—2691no—
303C23—5381no—
304Q8—21no—
305Q8—21no—
306Q8—42no—
307Q8—2692no—
308Q8—5381no—
309Q8—10762no—
310D4—21no—
311D4—21no—
312D4—5382no—
313D4—5381no—
314D4—5381no—
315D4—10762no—
316D4—10762no—
317D4—10762no—
318D4—10762no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—2691no—
323C2×C4—2691no—
324C2×C4—5381no—
325C2×C4—5381no—
326C2×C4—5381no—
327C2×C4—5381no—
328C2×C4—5381no—
329C2×C4—5381no—
330C2×C4—5381no—
331C2×C4—10762no—
332C2×C4—10762no—
333C2×C4—10762no—
334C2×C4—10762no—
335C2×C4—10762no—
336C2×C4D4×D26911yescharacteristic
337C2×C4D4×D26911yescharacteristic
338C2×C4C23×D26911yescharacteristic
339C8—21no—
340C8—21no—
341C8—5381no—
342C8—5381no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—2692no—
347C22—5381no—
348C22—5381no—
349C22—5381no—
350C22—5381no—
351C22—5381no—
352C22—10761no—
353C22—10761no—
354C22—10761no—
355C22C2×D4×D26911yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—5381no—
362C4—5381no—
363C4—5382no—
364C4—10761no—
365C4—10761no—
366C4#41×D26911yescharacteristic
367C4#2257549911yescharacteristic
368C2—81no—
369C2—5382no—
370C2—10761no—
371C2—21521no—
372C2#3177124811yescharacteristic
373C2AGL(1,ℤ/8)×D26911yescharacteristic
374C2#3177142111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#489×C269C2
socleC22×C269C22×D4
hypercenter#489D269
hypocenterC269#3308
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #31771263C2semidirect
2. #31771258C2semidirect
3. #31770939C2semidirect
4. #31770917C2semidirect
5. #31770897C2semidirect
6. #31770854C2semidirect
7. #31770840C2semidirect
8. #31770817C2semidirect
9. #31770751C2semidirect
10. #31770745C2semidirect
11. #31770707C2semidirect
12. #31770678C2semidirect
13. #31770603C2semidirect
14. #103×D269C2semidirect
15. #489×C269C2semidirect
117. Dic538#41semidirect
187. C269#3308semidirect
191. #489D269semidirect

Maximal subgroups

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

subgroupindex
#317712632
#317712582
#317709392
#317709172
#317708972
#317708542
#317708402
#317708172
#317707512
#317707452
#317707072
#317706782
#317706032
#103×D2692
#489×C2692
#3308269