Finite Group Databasebeta

← #46813929

Subgroups — #46813929

Order 34432.

716 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575426C211yesmaximal, characteristic
2C2×#22575415C211yesmaximal, characteristic, complemented
3C2×#22575413C211yesmaximal, characteristic, complemented
4#31770494C211yesmaximal, characteristic, complemented
5#31770487C211yesmaximal, characteristic, complemented
6#31770486C211yesmaximal, characteristic, complemented
7#31770483C211yesmaximal, characteristic, complemented
8#31770482C211yesmaximal, characteristic, complemented
9#31770481C211yesmaximal, characteristic, complemented
10#31770481C211yesmaximal, characteristic, complemented
11C22⋊C4×Dic269C211yesmaximal, characteristic, complemented
12C4×#16864379C211yesmaximal, characteristic, complemented
13C4×#16864379C211yesmaximal, characteristic, complemented
14#95×D269C211yesmaximal, characteristic, complemented
15#388×C269C211yesmaximal, characteristic, complemented
16C22×D1076C2211yescharacteristic
17C22×C22⋊D269C2211yescharacteristic
18C22×C22⋊D269C2211yescharacteristic
19C23×Dic269C2211yescharacteristic
20C22×C4×D269C2211yescharacteristic
21C22×C4×D269C2211yescharacteristic
22C22×C4×D269C2211yescharacteristic
23C22×C4×D269C2211yescharacteristic
24#22575426C418yescomplemented
25#22575415—24no—
26#22575413—24no—
27C2×#16864381C2211yescharacteristic
28C2×#16864381C2211yescharacteristic
29C2×C22⋊Dic269C2211yescharacteristic
30C2×#16864379C2211yescharacteristic
31C2×#16864379C2211yescharacteristic
32C2×#16864379C2211yescharacteristic
33C2×#16864379C2211yescharacteristic
34C2×#16864379C2211yescharacteristic
35C2×#16864379C2211yescharacteristic
36C2×C4×Dic269C2211yescharacteristic
37C2×C4×Dic269C2211yescharacteristic
38C2×C4×Dic269C2211yescharacteristic
39#22575360C2211yescharacteristic
40#22575360C2211yescharacteristic
41#22575360C2211yescharacteristic
42#22575360C2211yescharacteristic
43#22575360C2211yescharacteristic
44#22575360C2211yescharacteristic
45#22575360C2211yescharacteristic
46#22575360C2211yescharacteristic
47C2×C4⋊C4×C269C2211yescharacteristic
48C2×C22⋊C4×C269C2211yescharacteristic
49C2×C22⋊C4×C269C2211yescharacteristic
50C2×C22⋊C4×C269C2211yescharacteristic
51C2×C42×C269C2211yescharacteristic
52#95×C269C2211yescharacteristic
53#95×C269C2211yescharacteristic
54C23×D269C2311yescharacteristic
55C23×D269C2311yescharacteristic
56C2×D1076—22no—
57C2×D1076—22no—
58C2×D1076C2×C414yescomplemented
59C2×C22⋊D269—22no—
60C2×C22⋊D269—22no—
61C2×C22⋊D269—41no—
62C2×C22⋊D269—41no—
63C2×C22⋊D269C2×C414yescomplemented
64C2×C22⋊D269C2×C414yescomplemented
65C22×Dic269—22no—
66C22×Dic269—22no—
67C22×Dic269—41no—
68C22×Dic269C2311yescharacteristic
69C22×Dic269C2311yescharacteristic
70C22×Dic269C2311yescharacteristic
71C22×Dic269C2311yescharacteristic
72C22×Dic269C2311yescharacteristic
73C22×Dic269C2311yescharacteristic
74C2×C4×D269—22no—
75C2×C4×D269—22no—
76C2×C4×D269—22no—
77C2×C4×D269—22no—
78C2×C4×D269—22no—
79C2×C4×D269—22no—
80C2×C4×D269—41no—
81C2×C4×D269—41no—
82C2×C4×D269—41no—
83C2×C4×D269—41no—
84C2×C4×D269—41no—
85C2×C4×D269C2×C414yescomplemented
86#16864381—22no—
87#16864381C2×C414yescomplemented
88C22⋊Dic269—22no—
89#16864379—22no—
90#16864379—22no—
91#16864379—22no—
92#16864379—41no—
93#16864379C2×C414yescomplemented
94#16864379D414yescomplemented
95C4×Dic269—22no—
96C4×Dic269—22no—
97C4×Dic269—41no—
98C24×C269C2311yescharacteristic
99C22×C4×C269C2311yescharacteristic
100C22×C4×C269C2311yescharacteristic
101C22×C4×C269C2311yescharacteristic
102C22×C4×C269C2311yescharacteristic
103C22×C4×C269C2311yescharacteristic
104C22×C4×C269C2311yescharacteristic
105C4⋊C4×C269—22no—
106C22⋊C4×C269—22no—
107C22⋊C4×C269—41no—
108C22⋊C4×C269C2×C414yescomplemented
109C42×C269—41no—
110C22×D269—21no—
111C22×D269—21no—
112C22×D269—21no—
113C22×D269—21no—
114C22×D269—21no—
115C22×D269—21no—
116C22×D269—21no—
117C22×D269—21no—
118C22×D269—21no—
119C22×D269—21no—
120C22×D269C22×C412yes—
121C22×D269C22×C412yes—
122C22×D269C2×D412yes—
123C22×D269#4112yes—
124D1076—28no—
125C22⋊D269—28no—
126C22⋊D269—44no—
127C2×Dic269—21no—
128C2×Dic269—21no—
129C2×Dic269—21no—
130C2×Dic269—21no—
131C2×Dic269—21no—
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—44no—
141C2×Dic269C22×C412yes—
142C2×Dic269C22×C412yes—
143C2×Dic269C2×D412yes—
144C2×Dic269#4112yes—
145C2×Dic269#4112yes—
146C4×D269—44no—
147C4×D269—44no—
148C4×D269—44no—
149C4×D269—44no—
150C23×C269—21no—
151C23×C269—21no—
152C23×C269—21no—
153C23×C269—21no—
154C23×C269—21no—
155C23×C269—21no—
156C23×C269C22×C412yes—
157C23×C269C2411yescharacteristic
158C2×C4×C269—21no—
159C2×C4×C269—21no—
160C2×C4×C269—21no—
161C2×C4×C269—21no—
162C2×C4×C269—21no—
163C2×C4×C269—21no—
164C2×C4×C269—21no—
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×C269C22×C412yes—
174C2×C4×C269C22×C412yes—
175C2×C4×C269C2×D412yes—
176C22×C269—22no—
177C22×C269—22no—
178C22×C269—22no—
179C22×C269—41no—
180C22×C269—41no—
181C22×C269—41no—
182C22×C269—41no—
183C22×C269C23×C411yescharacteristic
184C22×C269C22×D411yescharacteristic
185C22×C269C2×#4111yescharacteristic
186C22×C269C2×#4111yescharacteristic
187C22×C269C2×#4111yescharacteristic
188C22×C269H(5,𝔽2)11yescharacteristic
189C22×C269H(5,𝔽2)11yescharacteristic
190C2×D269—22no—
191C2×D269—22no—
192C2×D269—22no—
193C2×D269—22no—
194C2×D269—22no—
195C2×D269—22no—
196C2×D269—22no—
197C2×D269—22no—
198C2×D269—22no—
199C2×D269—41no—
200C2×D269—41no—
201C2×D269—41no—
202C2×D269—41no—
203C2×D269C4×D414yes—
204C4×C269—22no—
205C4×C269—22no—
206C4×C269—22no—
207C4×C269—41no—
208C4×C269—41no—
209C4×C269—41no—
210Dic269—22no—
211Dic269—22no—
212Dic269—22no—
213Dic269—22no—
214Dic269—22no—
215Dic269—41no—
216C2×C269—42no—
217C2×C269C2×C4×D411yescharacteristic
218C2×C269C4×#4111yescharacteristic
219C2×C269#51811yescharacteristic
220C2×C269#54611yescharacteristic
221C2×C269#54611yescharacteristic
222C2×C269#55311yescharacteristic
223C2×C269#55311yescharacteristic
224D269—24no—
225D269—42no—
226C269#236411yescharacteristic, complemented, Sylow
227#2364—2691nomaximal, Sylow
228C2×#121—2691no—
229C2×C4×D4—2691no—
230C2×C4×D4—2691no—
231#388—2691no—
232#388D26911yescharacteristic, complemented
233#387—2691no—
234#387—2691no—
235#386—2691no—
236#386—2691no—
237#386—2691no—
238#386—2691no—
239C4×C22⋊C4—2691no—
240C4×C22⋊C4—2691no—
241C4×C22⋊C4—2691no—
242C2×#95—2691no—
243C22×D4—2691no—
244C22×D4—2691no—
245C22×D4—2691no—
246C23×C4—2691no—
247C23×C4—2691no—
248C23×C4—2691no—
249C23×C4—2691no—
250C23×C4—2691no—
251#121—2698no—
252C4×D4—5384no—
253C4×D4—5384no—
254C2×C4⋊C4—2691no—
255C2×C4⋊C4—2691no—
256C2×C4⋊C4C2×D26911yescharacteristic
257C2×C22⋊C4—2691no—
258C2×C22⋊C4—2691no—
259C2×C22⋊C4—2691no—
260C2×C22⋊C4—2691no—
261C2×C22⋊C4—2691no—
262C2×C22⋊C4—2691no—
263C2×C22⋊C4—2691no—
264C2×C22⋊C4C2×D26911yescharacteristic
265C2×C22⋊C4C2×D26911yescharacteristic
266C2×C22⋊C4C2×D26911yescharacteristic
267C2×C42—2691no—
268C2×C42—2691no—
269C2×C42—2691no—
270C2×C42C2×D26911yescharacteristic
271#95—2691no—
272#95—2691no—
273#95—2691no—
274#95—2691no—
275#95—2691no—
276#95—2691no—
277#95—2691no—
278#95—2691no—
279#95C2×D26911yescharacteristic
280#95C2×D26911yescharacteristic
281C24—2691no—
282C24—2691no—
283C24C22×D26911yescharacteristic
284C2×D4—2694no—
285C2×D4—2694no—
286C2×D4—2694no—
287C2×D4—5382no—
288C2×D4—5382no—
289C2×D4—5382no—
290C2×D4—5382no—
291C2×D4—10761no—
292C2×D4—10761no—
293C22×C4—2691no—
294C22×C4—2691no—
295C22×C4—2691no—
296C22×C4—2691no—
297C22×C4—2691no—
298C22×C4—2694no—
299C22×C4—2691no—
300C22×C4—5382no—
301C22×C4—5382no—
302C22×C4—5382no—
303C22×C4—5382no—
304C22×C4—5382no—
305C22×C4—5382no—
306C22×C4—5382no—
307C22×C4—5382no—
308C22×C4—10761no—
309C22×C4—10761no—
310C22×C4—10761no—
311C22×C4—10761no—
312C22×C4—10761no—
313C22×C4—10761no—
314C22×C4C22×D26911yescharacteristic
315C22×C4C22×D26911yescharacteristic
316C22×C4C22×D26911yescharacteristic
317C22×C4C22×D26911yescharacteristic
318C22×C4C22×D26911yescharacteristic
319C22×C4C22×D26911yescharacteristic
320C4⋊C4—22no—
321C4⋊C4—2694no—
322C4⋊C4—5382no—
323C22⋊C4—22no—
324C22⋊C4—41no—
325C22⋊C4—2694no—
326C22⋊C4—2694no—
327C22⋊C4—5382no—
328C22⋊C4—5382no—
329C22⋊C4—5382no—
330C22⋊C4—5382no—
331C22⋊C4—10761no—
332C22⋊C4C4×D26914yescomplemented
333C42—41no—
334C42—5382no—
335C42—5382no—
336C42—10761no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—2692no—
344C23—2692no—
345C23—2692no—
346C23—2692no—
347C23—5381no—
348C23—5381no—
349C23—5381no—
350C23—5381no—
351C23—5381no—
352C23—5381no—
353C23—5381no—
354C23—5381no—
355C23—5381no—
356C23—5381no—
357C23C2×C4×D26912yes—
358C23C23×D26911yescharacteristic
359D4—5388no—
360D4—5388no—
361D4—10764no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—2692no—
378C2×C4—2692no—
379C2×C4—2692no—
380C2×C4—2692no—
381C2×C4—2692no—
382C2×C4—5381no—
383C2×C4—5381no—
384C2×C4—5381no—
385C2×C4—5381no—
386C2×C4—5381no—
387C2×C4—5381no—
388C2×C4—5381no—
389C2×C4—5381no—
390C2×C4—5381no—
391C2×C4—5381no—
392C2×C4—5381no—
393C2×C4—5381no—
394C2×C4—5381no—
395C2×C4—10764no—
396C2×C4—10764no—
397C2×C4—10764no—
398C2×C4—10764no—
399C2×C4—10764no—
400C2×C4C2×C4×D26912yes—
401C2×C4C2×C4×D26912yes—
402C2×C4D4×D26912yes—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—2694no—
411C22—5382no—
412C22—5382no—
413C22—5382no—
414C22—5382no—
415C22—5382no—
416C22—5382no—
417C22—5382no—
418C22—5382no—
419C22—5382no—
420C22—10761no—
421C22—10761no—
422C22—10761no—
423C22—10761no—
424C22C22×C4×D26911yescharacteristic
425C22C2×D4×D26911yescharacteristic
426C22#41×D26911yescharacteristic
427C22#41×D26911yescharacteristic
428C22#41×D26911yescharacteristic
429C22#2257549811yescharacteristic
430C22#2257549911yescharacteristic
431C4—22no—
432C4—22no—
433C4—22no—
434C4—41no—
435C4—41no—
436C4—41no—
437C4—5382no—
438C4—5382no—
439C4—5382no—
440C4—5382no—
441C4—5382no—
442C4—10761no—
443C2—42no—
444C2—5384no—
445C2—10762no—
446C2C4×D4×D26911yescharacteristic
447C2#3177107311yescharacteristic
448C2#3177107711yescharacteristic
449C2#3177124411yescharacteristic
450C2#3177124811yescharacteristic
451C2#3177130011yescharacteristic
452C2#3177130611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D269
commutatorC22×C269C23×C4
Fitting#388×C269C2
socle, cosocleC23×C269C24
prime radicalC2×#22575426C2
hypercenter#388D269
hypocenterC269#2364
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×#22575415C2semidirect
3. C2×#22575413C2semidirect
4. #31770494C2semidirect
5. #31770487C2semidirect
6. #31770486C2semidirect
7. #31770483C2semidirect
8. #31770482C2semidirect
9. #31770481C2semidirect
10. #31770481C2semidirect
11. C22⋊C4×Dic269C2semidirect
12. C4×#16864379C2semidirect
13. C4×#16864379C2semidirect
14. #95×D269C2semidirect
15. #388×C269C2semidirect
24. #22575426C4semidirect
58. C2×D1076C2×C4semidirect
63. C2×C22⋊D269C2×C4semidirect
64. C2×C22⋊D269C2×C4semidirect
85. C2×C4×D269C2×C4semidirect
87. #16864381C2×C4semidirect
93. #16864379C2×C4semidirect
94. #16864379D4semidirect
108. C22⋊C4×C269C2×C4semidirect
226. C269#2364semidirect
232. #388D269semidirect
332. C22⋊C4C4×D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754262
C2×#225754152
C2×#225754132
#317704942
#317704872
#317704862
#317704832
#317704822
#317704812
C22⋊C4×Dic2692
C4×#168643792
#95×D2692
#388×C2692
#2364269