Finite Group Databasebeta

← #29583551

Subgroups — #29583551

Order 15616.

546 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450742C211yesmaximal, characteristic
2#21445975C211yesmaximal, 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×#14519708—22no—
12C2×#14519702—21no—
13C2×#14519699—21no—
14C2×C4×#92418C2211yescharacteristic
15#16839684—22no—
16#16839663—21no—
17#16839661—21no—
18#16839632C2211yescharacteristic
19#16839619—21no—
20#16839525—21no—
21#16839525—21no—
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#14519708—44no—
53#14519702—42no—
54#14519699—42no—
55C4×#92418—21no—
56C4×#92418D412yes—
57#14519684—22no—
58C22×C8×C61—21no—
59C22×C8×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61D412yes—
63C2×C42×C61C2311yescharacteristic
64C4⋊C8×C61—21no—
65C4⋊C8×C61—21no—
66C4⋊C8×C61—21no—
67C4⋊C8×C61—21no—
68C23×D61—21no—
69C22×C4×C61—22no—
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—41no—
77C2×D244—21no—
78C2×D244—21no—
79C2×D244—21no—
80C2×D244—21no—
81C2×D244—21no—
82C2×D244SD1612yes—
83C2×C4×D61—41no—
84C2×C4×D61—41no—
85C2×C4×D61—41no—
86C2×C4×D61—41no—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89C2×Dic122—21no—
90C2×Dic122—21no—
91C2×Dic122—21no—
92C2×Dic122—21no—
93C2×Dic122—21no—
94C2×Dic122SD1612yes—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C2×C8×C61—41no—
101C4⋊C4×C61—42no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—41no—
106C42×C61C2×D411yescharacteristic
107C42×C61#4111yescharacteristic
108C42×C61#4111yescharacteristic
109C42×C61#4111yescharacteristic
110#11758198—44no—
111#11758198—41no—
112#11758198—41no—
113#11758198—82no—
114C4⋊Dic61—21no—
115C4⋊Dic61—21no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118C4⋊Dic61—44no—
119C4⋊Dic61—42no—
120C4⋊Dic61—41no—
121C4⋊Dic61—41no—
122C4⋊Dic61—41no—
123C4⋊Dic61—41no—
124#11758196—41no—
125#11758196—41no—
126C4×Dic61—41no—
127C4×Dic61—41no—
128C2×#92418—22no—
129C2×#92418—22no—
130C2×#92418—22no—
131C23×C61#12011yescharacteristic
132C22×D61—22no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—41no—
138C22×D61—41no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—42no—
142C2×C4×C61—42no—
143C2×C4×C61—42no—
144C2×C4×C61#12111yescharacteristic
145C2×C4×C61#12111yescharacteristic
146C2×C4×C61#12111yescharacteristic
147C2×C4×C61#12311yescharacteristic
148C2×C4×C61#12311yescharacteristic
149C2×C4×C61#12411yescharacteristic
150C2×C4×C61C2×SD1611yescharacteristic
151C2×C4×C61C2×SD1611yescharacteristic
152C2×C4×C61#13511yescharacteristic
153C2×C4×C61#13511yescharacteristic
154C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C61#13711yescharacteristic
157C2×C4×C61#13711yescharacteristic
158C2×Dic61—22no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—81no—
168C2×Dic61—81no—
169C2×Dic61—81no—
170D244—22no—
171D244—22no—
172D244—41no—
173D244—41no—
174C4×D61—81no—
175C4×D61—81no—
176C4×D61—81no—
177C4×D61—81no—
178Dic122—22no—
179Dic122—22no—
180Dic122—41no—
181Dic122—41no—
182C8×C61—81no—
183C8×C61—81no—
184#92418—24no—
185#10435—611nomaximal, Sylow
186C22×C61#39411yescharacteristic
187C22×C61#44811yescharacteristic
188C22×C61#44911yescharacteristic
189C22×C61#45011yescharacteristic
190C22×C61#45211yescharacteristic
191C22×C61#45311yescharacteristic
192C22×C61#45611yescharacteristic
193C2×D61—42no—
194C2×D61—42no—
195C2×D61—42no—
196C2×D61—81no—
197C2×D61—81no—
198C2×D61—81no—
199C2×D61—81no—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—82no—
203C4×C61#46511yescharacteristic
204C4×C61#46511yescharacteristic
205C4×C61#46911yescharacteristic
206C4×C61#47011yescharacteristic
207C4×C61#48111yescharacteristic
208C4×C61#48211yescharacteristic
209C4×C61#48311yescharacteristic
210C4×C61#48511yescharacteristic
211Dic61—42no—
212Dic61—81no—
213Dic61—81no—
214Dic61—161no—
215#2538—611no—
216#1844—611no—
217#1803—611no—
218#1802—611no—
219C2×Q8⋊C8—611no—
220C2×D4⋊C8—611no—
221#1296D6111yescharacteristic, complemented
222C2×C61#162211yescharacteristic
223C2×C61#163111yescharacteristic
224C2×C61#165111yescharacteristic
225C2×C61#165211yescharacteristic
226C2×C61#203411yescharacteristic
227C2×C61#203511yescharacteristic
228C2×C61#203911yescharacteristic
229D61—82no—
230C2×C22⋊Q8—1221no—
231C2×C4×Q8—611no—
232C2×C4×D4—611no—
233C2×#106—1222no—
234C2×C4⋊C8C2×D6111yescharacteristic
235C2×C4⋊C8C2×D6111yescharacteristic
236C2×#103—1221no—
237C2×#102—1221no—
238C2×C4×C8—611no—
239#396—1222no—
240#390—1221no—
241#389—1221no—
242#384—611no—
243#384C2×D6111yescharacteristic
244#380—1221no—
245#340—1221no—
246#340—1221no—
247Q8⋊C8—1222no—
248D4⋊C8—1222no—
249C61#1043511yescharacteristic, complemented, Sylow
250C22×Q8—611no—
251C22×D4—611no—
252C23×C4—1221no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—1221no—
256C22⋊Q8—2442no—
257C22⋊Q8—2442no—
258C4×Q8—1221no—
259C4×Q8—1221no—
260C4×Q8—1221no—
261C4×Q8—1221no—
262C4×D4—1221no—
263C4×D4—1221no—
264C4×D4—1221no—
265C4×D4—1221no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—611no—
269C2×C4⋊C4—611no—
270C2×C4⋊C4—1222no—
271C2×C4⋊C4—1221no—
272C2×C4⋊C4—1221no—
273C2×C4⋊C4—1221no—
274C2×C4⋊C4—1221no—
275C2×C4⋊C4D24412yes—
276C2×C22⋊C4—1222no—
277C2×C22⋊C4—1222no—
278C2×C22⋊C4—1221no—
279C2×C42—1221no—
280C2×C42C22×D6111yescharacteristic
281#106—2444no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8—21no—
286#103—2442no—
287#102—2442no—
288C4×C8—612no—
289C4×C8—1221no—
290#95—1222no—
291C24—1221no—
292C2×Q8—612no—
293C2×Q8—1221no—
294C2×Q8—1221no—
295C2×Q8—1221no—
296C2×Q8—1221no—
297C2×Q8—1221no—
298C2×D4—612no—
299C2×D4—1221no—
300C2×D4—1221no—
301C2×D4—1221no—
302C2×D4—1221no—
303C2×D4—1221no—
304C22×C4—22no—
305C22×C4—1221no—
306C22×C4—1221no—
307C22×C4—1221no—
308C22×C4—2441no—
309C22×C4—2441no—
310C22×C4—2441no—
311C22×C4—2441no—
312C22×C4—2441no—
313C22×C4—2441no—
314C22×C4—2441no—
315C22×C4C2×D24411yescharacteristic
316C22×C4D4×D6111yescharacteristic
317C22×C4D4×D6111yescharacteristic
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—1222no—
325C2×C8—1222no—
326C2×C8—1222no—
327C4⋊C4—42no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—1221no—
333C4⋊C4—1221no—
334C4⋊C4—1221no—
335C4⋊C4—1221no—
336C4⋊C4—2442no—
337C4⋊C4—2444no—
338C4⋊C4—2441no—
339C4⋊C4—2441no—
340C4⋊C4—2441no—
341C4⋊C4—2441no—
342C4⋊C4—2441no—
343C4⋊C4—2441no—
344C22⋊C4—4882no—
345C22⋊C4—2444no—
346C22⋊C4—2441no—
347C22⋊C4—2441no—
348C42—2441no—
349C42—2441no—
350C42#1175822211yescharacteristic
351C42#1175822211yescharacteristic
352C42D4×D6111yescharacteristic
353C42#1175822611yescharacteristic
354C23—1222no—
355C23—2441no—
356C23—2441no—
357C23—2441no—
358C23—2441no—
359C23—2441no—
360C23—2441no—
361C23#1451974711yescharacteristic
362Q8—1222no—
363Q8—1222no—
364Q8—2441no—
365Q8—2441no—
366D4—1222no—
367D4—1222no—
368D4—2441no—
369D4—2441no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—1222no—
376C2×C4—4881no—
377C2×C4—4881no—
378C2×C4—4881no—
379C2×C4—4881no—
380C2×C4—4881no—
381C2×C4—4881no—
382C2×C4—4881no—
383C2×C4—2441no—
384C2×C4—2441no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4—2441no—
388C2×C4—2441no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4#1451975011yescharacteristic
392C2×C4#1451975011yescharacteristic
393C2×C4#1451975211yescharacteristic
394C2×C4#1451976211yescharacteristic
395C2×C4#1451976211yescharacteristic
396C2×C4#1451976511yescharacteristic
397C2×C4SD16×D6111yescharacteristic
398C2×C4SD16×D6111yescharacteristic
399C2×C4#1451979611yescharacteristic
400C2×C4#1451980011yescharacteristic
401C2×C4#1451980111yescharacteristic
402C2×C4#1451980411yescharacteristic
403C2×C4#1451980611yescharacteristic
404C2×C4#1451980911yescharacteristic
405C8—81no—
406C8—81no—
407C8—1224no—
408C22—4881no—
409C22—4881no—
410C22—4881no—
411C22—4881no—
412C22—2442no—
413C22—2442no—
414C22—2442no—
415C22#1683968011yescharacteristic
416C22#1683990211yescharacteristic
417C22#1683991011yescharacteristic
418C22#1683991411yescharacteristic
419C22#1683992511yescharacteristic
420C22#1683993211yescharacteristic
421C22#1683994711yescharacteristic
422C4—21no—
423C4—21no—
424C4—82no—
425C4—9761no—
426C4—4881no—
427C4—4881no—
428C4—2442no—
429C4#1683999011yescharacteristic
430C4#1683999411yescharacteristic
431C4#1684001411yescharacteristic
432C4#1684001911yescharacteristic
433C4#1684008211yescharacteristic
434C4#1684008911yescharacteristic
435C4#1684009411yescharacteristic
436C4#1684010511yescharacteristic
437C2—4882no—
438C2#2144489211yescharacteristic
439C2#2144494711yescharacteristic
440C2#2144508311yescharacteristic
441C2#2144509011yescharacteristic
442C2#2144701111yescharacteristic
443C2#2144701811yescharacteristic
444C2#2144704411yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1296C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#1296D61
hypocenterC61#10435
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. #21445975C2semidirect
3. #21445825C2semidirect
5. C2×#16839492C2semidirect
7. C61×#1296C2semidirect
221. #1296D61semidirect
249. C61#10435semidirect

Maximal subgroups

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

subgroupindex
#214507422
#214459752
#214458252
#214458202
C2×#168394922
C2×#168394892
C61×#12962
#1043561