Finite Group Databasebeta

← #46820571

Subgroups — #46820571

Order 34432.

472 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575482C211yesmaximal, characteristic, complemented
2C2×#22575461C211yesmaximal, characteristic, complemented
3#31771184C211yesmaximal, characteristic
4#31771178C211yesmaximal, characteristic, complemented
5#31770863C211yesmaximal, characteristic, complemented
6#31770862C211yesmaximal, characteristic, complemented
7#31770850C211yesmaximal, characteristic, complemented
8#31770847C211yesmaximal, characteristic, complemented
9#31770844C211yesmaximal, characteristic, complemented
10#31770832C211yesmaximal, characteristic, complemented
11#31770831C211yesmaximal, characteristic, complemented
12#31770646C211yesmaximal, characteristic, complemented
13#31770598C211yesmaximal, characteristic, complemented
14#103×D269C211yesmaximal, characteristic, complemented
15#468×C269C211yesmaximal, characteristic, complemented
16C2×#16864402C2211yescharacteristic
17C2×#16864401C2211yescharacteristic
18C2×Q8×D269C2211yescharacteristic
19#22575482—24no—
20C2×Dic1076C2211yescharacteristic
21C2×#16864392C2211yescharacteristic
22C2×#16864390C2211yescharacteristic
23#22575461—24no—
24C2×#16864385C2211yescharacteristic
25C2×#16864385C2211yescharacteristic
26C22×#14524130C2211yescharacteristic
27C2×C8×D269C2211yescharacteristic
28C2×C8×D269C2211yescharacteristic
29#22575452—21no—
30#22575439—21no—
31#22575438—21no—
32#22575435—21no—
33#22575433C2211yescharacteristic
34#22575433C2211yescharacteristic
35#22575432C2211yescharacteristic
36#22575432C2211yescharacteristic
37#22575430—21no—
38#22575429C2211yescharacteristic
39#22575426—21no—
40#22575425—21no—
41#22575424—21no—
42#22575424C2211yescharacteristic
43#22575411C2211yescharacteristic
44C4⋊C4×D269C2211yescharacteristic
45#22575386C2211yescharacteristic
46#22575385C2211yescharacteristic
47#22575384C2211yescharacteristic
48#22575378C2211yescharacteristic
49#22575378C2211yescharacteristic
50#22575377C2211yescharacteristic
51#22575376C2211yescharacteristic
52#22575376C2211yescharacteristic
53#22575374C2211yescharacteristic
54C2×SD16×C269C2211yescharacteristic
55C2×M16×C269C2211yescharacteristic
56C22⋊Q8×C269C2211yescharacteristic
57#121×C269C2211yescharacteristic
58#107×C269C2211yescharacteristic
59#103×C269C2211yescharacteristic
60#102×C269C2211yescharacteristic
61#16864402—22no—
62#16864402—22no—
63#16864401—22no—
64#16864401—22no—
65C2×Dic538—21no—
66C2×Dic538D411yescharacteristic
67C2×Dic538C2311yescharacteristic
68C2×Dic538C2311yescharacteristic
69Q8×D269—22no—
70Q8×D269—22no—
71C2×D1076D411yescharacteristic
72C2×C22⋊D269—21no—
73C2×C22⋊D269—21no—
74C2×C22⋊D269D411yescharacteristic
75C2×C22⋊D269D411yescharacteristic
76C22×Dic269—21no—
77C2×C4×D269—21no—
78C2×C4×D269—21no—
79C2×C4×D269C2311yescharacteristic
80C2×C4×D269C2311yescharacteristic
81Dic1076—22no—
82#16864392—22no—
83#16864390—22no—
84#16864385—22no—
85#16864385D414yescomplemented
86C2×#14524130—22no—
87C2×#14524130C2311yescharacteristic
88C2×#14524130C2311yescharacteristic
89C8×D269—22no—
90C8×D269—22no—
91C4⋊Dic269—21no—
92C4⋊Dic269—21no—
93C4⋊Dic269C2311yescharacteristic
94C4⋊Dic269C2311yescharacteristic
95#16864381—21no—
96#16864381—21no—
97#16864381—21no—
98#16864381—21no—
99C22⋊Dic269—21no—
100C22⋊Dic269—21no—
101C22⋊Dic269—21no—
102#16864379—21no—
103#16864379—21no—
104#16864379—21no—
105#16864379—21no—
106C4×Dic269—21no—
107C2×Q8×C269C2311yescharacteristic
108C2×D4×C269—21no—
109C2×D4×C269C2311yescharacteristic
110C22×C4×C269C2311yescharacteristic
111SD16×C269—22no—
112M16×C269—22no—
113C2×C8×C269C2311yescharacteristic
114C2×C8×C269C2311yescharacteristic
115C4⋊C4×C269—21no—
116C4⋊C4×C269C2311yescharacteristic
117C4⋊C4×C269C2311yescharacteristic
118C22⋊C4×C269—21no—
119C22⋊C4×C269—21no—
120C22×D269C2×D411yescharacteristic
121C22×D269C2×D411yescharacteristic
122Dic538—22no—
123Dic538—21no—
124Dic538—21no—
125Dic538—21no—
126Dic538—21no—
127Dic538—42no—
128D1076—22no—
129C22⋊D269—22no—
130C22⋊D269—22no—
131C22⋊D269—42no—
132C22⋊D269—81no—
133C2×Dic269—21no—
134C2×Dic269—21no—
135C2×Dic269—21no—
136C2×Dic269—21no—
137C2×Dic269—42no—
138C2×Dic269C2×D411yescharacteristic
139C2×Dic269C2×D411yescharacteristic
140C4×D269—21no—
141C4×D269—21no—
142C4×D269—42no—
143C4×D269—81no—
144C4×D269C2×D412yes—
145C4×D269#4112yes—
146#14524130—21no—
147#14524130C2×D412yes—
148C23×C269—21no—
149C23×C269C2×D411yescharacteristic
150Q8×C269—21no—
151Q8×C269—21no—
152D4×C269—21no—
153D4×C269—21no—
154D4×C269—81no—
155C2×C4×C269—21no—
156C2×C4×C269—21no—
157C2×C4×C269—21no—
158C2×C4×C269—21no—
159C2×C4×C269—21no—
160C2×C4×C269C2×D411yescharacteristic
161C2×C4×C269C2411yescharacteristic
162C8×C269—21no—
163C8×C269C2×D412yes—
164C22×C269—21no—
165C22×C269—21no—
166C22×C269—21no—
167C22×C269—41no—
168C22×C269—41no—
169C22×C269—41no—
170C22×C269C22×D411yescharacteristic
171C2×D269—21no—
172C2×D269—21no—
173C2×D269—21no—
174C2×D269—21no—
175C2×D269—21no—
176C2×D269#12112yes—
177C4×C269—21no—
178C4×C269—41no—
179C4×C269—41no—
180C4×C269—41no—
181C4×C269C22×D411yescharacteristic
182C4×C269C2×#4111yescharacteristic
183Dic269—21no—
184Dic269—41no—
185Dic269—41no—
186Dic269—41no—
187Dic269—41no—
188Dic269#12112yes—
189C2×C269—41no—
190C2×C269—81no—
191C2×C269C2×#12111yescharacteristic
192C2×C269#57711yescharacteristic
193C2×C269#57811yescharacteristic
194D269—22no—
195D269—41no—
196C269#306311yescharacteristic, complemented, Sylow
197#3063—2691nomaximal, Sylow
198C2×#137—2691no—
199C2×#131—2691no—
200#537—2691no—
201#536—2691no—
202#470—2691no—
203#470—2691no—
204#468—2691no—
205#468D26911yescharacteristic, complemented
206#467—2691no—
207#467—2691no—
208#465—2691no—
209#465—2691no—
210#428—2691no—
211#416—2691no—
212C2×#103—2691no—
213C2×#41—2691no—
214C2×#41—2691no—
215C22×Q8—2691no—
216#137—5384no—
217C2×Q16—2691no—
218C2×Q16—2691no—
219C2×SD16—2691no—
220C2×SD16C2×D26911yescharacteristic
221#131—5384no—
222C2×M16—2691no—
223C2×M16—2691no—
224C2×M16C2×D26911yescharacteristic
225C22×C8—2691no—
226C22×C8—2691no—
227C22×C8—2691no—
228C4⋊Q8—5381no—
229#124—5381no—
230#123—5381no—
231#123—5381no—
232C22⋊Q8—2691no—
233C22⋊Q8—2691no—
234C22⋊Q8—2691no—
235C22⋊Q8—2691no—
236C22⋊Q8—2691no—
237C22⋊Q8—5381no—
238C22⋊Q8C2×D26911yescharacteristic
239#121—2691no—
240#121—5381no—
241#121—5381no—
242#121—5381no—
243#121C2×D26911yescharacteristic
244#117—2691no—
245C2×C4⋊C4—2691no—
246#107—2691no—
247#107C2×D26911yescharacteristic
248#106—2691no—
249#106—2691no—
250#103—2691no—
251#103—2691no—
252#103—2691no—
253#103—2691no—
254#103—2691no—
255#103C2×D26911yescharacteristic
256#102—2691no—
257#102C2×D26911yescharacteristic
258#41—5382no—
259#41—5382no—
260#41—5382no—
261#41—5382no—
262C2×Q8—2691no—
263C2×Q8—2691no—
264C2×Q8—2691no—
265C2×Q8—5381no—
266C2×Q8—5382no—
267C2×Q8—5382no—
268C2×Q8C22×D26911yescharacteristic
269C2×D4—21no—
270C2×D4—2691no—
271C2×D4—2691no—
272C2×D4—2691no—
273C2×D4—5381no—
274C2×D4—5381no—
275C2×D4C22×D26911yescharacteristic
276C22×C4—2691no—
277C22×C4—2691no—
278C22×C4—5381no—
279C22×C4—5381no—
280C22×C4—5381no—
281C22×C4C22×D26911yescharacteristic
282Q16—5382no—
283Q16—5382no—
284SD16—22no—
285SD16—5382no—
286M16—22no—
287M16—2694no—
288M16—5382no—
289C2×C8—2691no—
290C2×C8—2691no—
291C2×C8—5382no—
292C2×C8—5382no—
293C2×C8—5382no—
294C2×C8C22×D26911yescharacteristic
295C2×C8C22×D26911yescharacteristic
296C4⋊C4—21no—
297C4⋊C4—2691no—
298C4⋊C4—2691no—
299C4⋊C4—5381no—
300C4⋊C4—5381no—
301C4⋊C4—5381no—
302C4⋊C4—5381no—
303C4⋊C4—5381no—
304C4⋊C4—5381no—
305C4⋊C4C22×D26911yescharacteristic
306C4⋊C4C22×D26911yescharacteristic
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—5381no—
310C22⋊C4—5381no—
311C22⋊C4—5381no—
312C22⋊C4—5381no—
313C22⋊C4—5381no—
314C22⋊C4—5381no—
315C22⋊C4—5381no—
316C42—5381no—
317C23—21no—
318C23—2691no—
319C23—2691no—
320C23D4×D26911yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—5382no—
324Q8—5381no—
325Q8—5381no—
326Q8—5381no—
327Q8—5381no—
328Q8—10762no—
329D4—21no—
330D4—21no—
331D4—81no—
332D4—5382no—
333D4—5382no—
334D4—5382no—
335D4—10762no—
336D4—21521no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—2691no—
343C2×C4—2692no—
344C2×C4—2692no—
345C2×C4—2691no—
346C2×C4—5381no—
347C2×C4—5381no—
348C2×C4—5381no—
349C2×C4—5381no—
350C2×C4—5381no—
351C2×C4—5381no—
352C2×C4—10762no—
353C2×C4—10762no—
354C2×C4—21521no—
355C2×C4D4×D26911yescharacteristic
356C2×C4C23×D26911yescharacteristic
357C8—21no—
358C8—2692no—
359C8—5381no—
360C8D4×D26912yes—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—2692no—
368C22—5381no—
369C22—5381no—
370C22—5381no—
371C22—5381no—
372C22—5381no—
373C22C2×D4×D26911yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—2692no—
379C4—5381no—
380C4—10761no—
381C4—10761no—
382C4—10761no—
383C4—10761no—
384C4C2×D4×D26911yescharacteristic
385C4#41×D26911yescharacteristic
386C2—41no—
387C2—81no—
388C2—5382no—
389C2—10761no—
390C2#121×D26911yescharacteristic
391C2#3177141511yescharacteristic
392C2#3177142111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#468×C269C2
socleC22×C269C22×D4
prime radical#31771184C2
hypercenter#468D269
hypocenterC269#3063
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#22575482C2semidirect
2. C2×#22575461C2semidirect
4. #31771178C2semidirect
5. #31770863C2semidirect
6. #31770862C2semidirect
7. #31770850C2semidirect
8. #31770847C2semidirect
9. #31770844C2semidirect
10. #31770832C2semidirect
11. #31770831C2semidirect
12. #31770646C2semidirect
13. #31770598C2semidirect
14. #103×D269C2semidirect
15. #468×C269C2semidirect
85. #16864385D4semidirect
196. C269#3063semidirect
205. #468D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754822
C2×#225754612
#317711842
#317711782
#317708632
#317708622
#317708502
#317708472
#317708442
#317708322
#317708312
#317706462
#317705982
#103×D2692
#468×C2692
#3063269