Finite Group Databasebeta

← #29583558

Subgroups — #29583558

Order 15616.

530 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450742C211yesmaximal, characteristic
2#21445946C211yesmaximal, characteristic, complemented
3#21445825C211yesmaximal, characteristic, complemented
4#21445820C211yesmaximal, characteristic
5C2×#16839492C211yesmaximal, characteristic, complemented
6C2×#16839489C211yesmaximal, characteristic
7C61×#1296C211yesmaximal, characteristic, complemented
8C2×#14519757—21no—
9C2×C4×Dic122C2211yescharacteristic
10C2×C4×D244C2211yescharacteristic
11C2×#14519702—21no—
12C2×#14519699—21no—
13C2×C4×#92418C2211yescharacteristic
14#16839684—22no—
15#16839663—21no—
16#16839661—21no—
17#16839632C2211yescharacteristic
18#16839619—21no—
19#16839525—21no—
20#16839525—21no—
21#16839524—22no—
22#16839492—22no—
23#16839489—22no—
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×C4⋊C8×C61C2211yescharacteristic
26C61×#384C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C22×D244D411yescharacteristic
29C22×C4×D61—21no—
30C22×#92418—21no—
31#14519757—42no—
32#14519757—42no—
33C4×Dic122—21no—
34C4×Dic122—21no—
35C4×Dic122—21no—
36C4×Dic122—21no—
37C4×D244—21no—
38C4×D244—21no—
39C4×D244—21no—
40C4×D244—21no—
41C2×C4⋊Dic61—22no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61D411yescharacteristic
46C2×C4⋊Dic61D411yescharacteristic
47C2×#11758196—21no—
48C2×#11758198—22no—
49C2×#11758198—21no—
50C2×#11758198—22no—
51C2×C4×Dic61—21no—
52#14519702—42no—
53#14519699—42no—
54C4×#92418—21no—
55C4×#92418D412yes—
56#14519684—22no—
57C22×C8×C61—21no—
58C22×C8×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61D412yes—
62C2×C42×C61C2311yescharacteristic
63C4⋊C8×C61—21no—
64C4⋊C8×C61—21no—
65C4⋊C8×C61—21no—
66C4⋊C8×C61—21no—
67C23×D61—21no—
68C22×C4×C61—22no—
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—41no—
76C2×D244—21no—
77C2×D244—21no—
78C2×D244—21no—
79C2×D244—21no—
80C2×D244—21no—
81C2×D244Q1612yes—
82C2×C4×D61—41no—
83C2×C4×D61—41no—
84C2×C4×D61—41no—
85C2×C4×D61—41no—
86C2×C4×D61—41no—
87C2×C4×D61—41no—
88C2×Dic122—21no—
89C2×Dic122—21no—
90C2×Dic122—21no—
91C2×Dic122—21no—
92C2×Dic122—21no—
93C2×Dic122SD1612yes—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C4⋊C4×C61—42no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C42×C61C2×D411yescharacteristic
106C42×C61#4111yescharacteristic
107C42×C61#4111yescharacteristic
108C42×C61#4111yescharacteristic
109#11758198—44no—
110#11758198—41no—
111#11758198—41no—
112#11758198—82no—
113C4⋊Dic61—21no—
114C4⋊Dic61—21no—
115C4⋊Dic61—21no—
116C4⋊Dic61—21no—
117C4⋊Dic61—44no—
118C4⋊Dic61—42no—
119C4⋊Dic61—41no—
120C4⋊Dic61—41no—
121C4⋊Dic61—41no—
122C4⋊Dic61—41no—
123#11758196—41no—
124#11758196—41no—
125C4×Dic61—41no—
126C4×Dic61—41no—
127C2×#92418—22no—
128C2×#92418—41no—
129C2×#92418—41no—
130C23×C61#12011yescharacteristic
131C22×D61—22no—
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—41no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—42no—
141C2×C4×C61—42no—
142C2×C4×C61—42no—
143C2×C4×C61#12111yescharacteristic
144C2×C4×C61#12111yescharacteristic
145C2×C4×C61#12111yescharacteristic
146C2×C4×C61#12311yescharacteristic
147C2×C4×C61#12311yescharacteristic
148C2×C4×C61#12411yescharacteristic
149C2×C4×C61C2×SD1611yescharacteristic
150C2×C4×C61C2×Q1611yescharacteristic
151C2×C4×C61#13511yescharacteristic
152C2×C4×C61#13511yescharacteristic
153C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C61#13711yescharacteristic
157C2×Dic61—22no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—81no—
167C2×Dic61—81no—
168C2×Dic61—81no—
169D244—22no—
170D244—22no—
171D244—41no—
172D244—41no—
173C4×D61—81no—
174C4×D61—81no—
175C4×D61—81no—
176C4×D61—81no—
177Dic122—22no—
178Dic122—22no—
179Dic122—41no—
180Dic122—41no—
181C8×C61—81no—
182C8×C61—81no—
183#92418—42no—
184#10436—611nomaximal, Sylow
185C22×C61#39411yescharacteristic
186C22×C61#44911yescharacteristic
187C22×C61#44911yescharacteristic
188C22×C61#45011yescharacteristic
189C22×C61#45111yescharacteristic
190C22×C61#45411yescharacteristic
191C22×C61#45511yescharacteristic
192C2×D61—42no—
193C2×D61—42no—
194C2×D61—42no—
195C2×D61—81no—
196C2×D61—81no—
197C2×D61—81no—
198C2×D61—81no—
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—82no—
202C4×C61#46511yescharacteristic
203C4×C61#46711yescharacteristic
204C4×C61#46811yescharacteristic
205C4×C61#46911yescharacteristic
206C4×C61#48111yescharacteristic
207C4×C61#48211yescharacteristic
208C4×C61#48411yescharacteristic
209C4×C61#48511yescharacteristic
210Dic61—42no—
211Dic61—81no—
212Dic61—81no—
213Dic61—161no—
214#2538—611no—
215#1834—611no—
216#1803—611no—
217#1802—611no—
218C2×Q8⋊C8—611no—
219C2×D4⋊C8—611no—
220#1296D6111yescharacteristic, complemented
221C2×C61#162811yescharacteristic
222C2×C61#163711yescharacteristic
223C2×C61#164211yescharacteristic
224C2×C61#164411yescharacteristic
225C2×C61#203411yescharacteristic
226C2×C61#203611yescharacteristic
227C2×C61#204011yescharacteristic
228D61—82no—
229C2×C22⋊Q8—1221no—
230C2×C4×Q8—611no—
231C2×C4×D4—611no—
232C2×C4⋊C8C2×D6111yescharacteristic
233C2×C4⋊C8C2×D6111yescharacteristic
234C2×#103—1221no—
235C2×#102—1221no—
236C2×C4×C8—611no—
237#396—1222no—
238#390—1221no—
239#389—1221no—
240#384—611no—
241#384C2×D6111yescharacteristic
242#380—1221no—
243#340—1221no—
244#340—1221no—
245#340—1222no—
246Q8⋊C8—1222no—
247D4⋊C8—1222no—
248C61#1043611yescharacteristic, complemented, Sylow
249C22×Q8—611no—
250C22×D4—611no—
251C23×C4—1221no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—1221no—
255C22⋊Q8—2442no—
256C22⋊Q8—2442no—
257C4×Q8—1221no—
258C4×Q8—1221no—
259C4×Q8—1221no—
260C4×Q8—1221no—
261C4×D4—1221no—
262C4×D4—1221no—
263C4×D4—1221no—
264C4×D4—1221no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—611no—
268C2×C4⋊C4—611no—
269C2×C4⋊C4—1222no—
270C2×C4⋊C4—1221no—
271C2×C4⋊C4—1221no—
272C2×C4⋊C4—1221no—
273C2×C4⋊C4—1221no—
274C2×C4⋊C4D24412yes—
275C2×C22⋊C4—1222no—
276C2×C22⋊C4—1222no—
277C2×C22⋊C4—1221no—
278C2×C42—1221no—
279C2×C42C22×D6111yescharacteristic
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284#103—2442no—
285#102—2442no—
286C4×C8—612no—
287C4×C8—1221no—
288#95—1222no—
289C24—1221no—
290C2×Q8—612no—
291C2×Q8—1221no—
292C2×Q8—1221no—
293C2×Q8—1221no—
294C2×Q8—1221no—
295C2×Q8—1221no—
296C2×D4—612no—
297C2×D4—1221no—
298C2×D4—1221no—
299C2×D4—1221no—
300C2×D4—1221no—
301C2×D4—1221no—
302C22×C4—22no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4—2441no—
307C22×C4—2441no—
308C22×C4—2441no—
309C22×C4—2441no—
310C22×C4—2441no—
311C22×C4—2441no—
312C22×C4—2441no—
313C22×C4C2×D24411yescharacteristic
314C22×C4D4×D6111yescharacteristic
315C22×C4D4×D6111yescharacteristic
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—1222no—
323C2×C8—2441no—
324C2×C8—2441no—
325C4⋊C4—42no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—1221no—
331C4⋊C4—1221no—
332C4⋊C4—1221no—
333C4⋊C4—1221no—
334C4⋊C4—2442no—
335C4⋊C4—2444no—
336C4⋊C4—2441no—
337C4⋊C4—2441no—
338C4⋊C4—2441no—
339C4⋊C4—2441no—
340C4⋊C4—2441no—
341C4⋊C4—2441no—
342C22⋊C4—4882no—
343C22⋊C4—2444no—
344C22⋊C4—2441no—
345C22⋊C4—2441no—
346C42—2441no—
347C42—2441no—
348C42#1175822211yescharacteristic
349C42#1175822211yescharacteristic
350C42D4×D6111yescharacteristic
351C42#1175822611yescharacteristic
352C23—1222no—
353C23—2441no—
354C23—2441no—
355C23—2441no—
356C23—2441no—
357C23—2441no—
358C23—2441no—
359C23#1451974711yescharacteristic
360Q8—1222no—
361Q8—1222no—
362Q8—2441no—
363Q8—2441no—
364D4—1222no—
365D4—1222no—
366D4—2441no—
367D4—2441no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—1222no—
374C2×C4—4881no—
375C2×C4—4881no—
376C2×C4—4881no—
377C2×C4—4881no—
378C2×C4—4881no—
379C2×C4—4881no—
380C2×C4—4881no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4—2441no—
384C2×C4—2441no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4—2441no—
388C2×C4—2441no—
389C2×C4#1451975011yescharacteristic
390C2×C4#1451975011yescharacteristic
391C2×C4#1451975211yescharacteristic
392C2×C4#1451976211yescharacteristic
393C2×C4#1451976211yescharacteristic
394C2×C4#1451976511yescharacteristic
395C2×C4SD16×D6111yescharacteristic
396C2×C4Q16×D6111yescharacteristic
397C2×C4#1451979811yescharacteristic
398C2×C4#1451980011yescharacteristic
399C2×C4#1451980111yescharacteristic
400C2×C4#1451980111yescharacteristic
401C2×C4#1451980411yescharacteristic
402C2×C4#1451980611yescharacteristic
403C8—81no—
404C8—81no—
405C8—2442no—
406C22—4881no—
407C22—4881no—
408C22—4881no—
409C22—4881no—
410C22—2442no—
411C22—2442no—
412C22—2442no—
413C22#1683968011yescharacteristic
414C22#1683990811yescharacteristic
415C22#1683991011yescharacteristic
416C22#1683991411yescharacteristic
417C22#1683991911yescharacteristic
418C22#1683993711yescharacteristic
419C22#1683994211yescharacteristic
420C4—21no—
421C4—21no—
422C4—82no—
423C4—9761no—
424C4—4881no—
425C4—4881no—
426C4—2442no—
427C4#1683999411yescharacteristic
428C4#1684000211yescharacteristic
429C4#1684000711yescharacteristic
430C4#1684001411yescharacteristic
431C4#1684008211yescharacteristic
432C4#1684008911yescharacteristic
433C4#1684009911yescharacteristic
434C4#1684010611yescharacteristic
435C2—4882no—
436C2#2144493011yescharacteristic
437C2#2144498511yescharacteristic
438C2#2144502011yescharacteristic
439C2#2144503411yescharacteristic
440C2#2144701111yescharacteristic
441C2#2144702511yescharacteristic
442C2#2144704911yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1296C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#1296D61
hypocenterC61#10436
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #21445946C2semidirect
3. #21445825C2semidirect
5. C2×#16839492C2semidirect
7. C61×#1296C2semidirect
220. #1296D61semidirect
248. C61#10436semidirect

Maximal subgroups

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

subgroupindex
#214507422
#214459462
#214458252
#214458202
C2×#168394922
C2×#168394892
C61×#12962
#1043661