Finite Group Databasebeta

← #29575918

Subgroups — #29575918

Order 15616.

566 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455616C211yesmaximal, characteristic
2#21448729C211yesmaximal, characteristic
3#21444384C211yesmaximal, characteristic, complemented
4#21444319C211yesmaximal, characteristic, complemented
5#21443721C211yesmaximal, characteristic, complemented
6#21443678C211yesmaximal, characteristic, complemented
7C61×#1478C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9C2×D4×Dic61—21no—
10#16840062—22no—
11#16840052C412yescomplemented
12#16840042C412yescomplemented
13#16839802—21no—
14#16839786C2211yescharacteristic
15#16839767—21no—
16#16839661—21no—
17#16839637—22no—
18#16839628C2211yescharacteristic
19#16839622—21no—
20C4×C4⋊Dic61C2211yescharacteristic
21C2×#14519684—21no—
22#16839500—22no—
23#16839500—21no—
24#16839500—21no—
25C2×C4×D4×C61C2211yescharacteristic
26C61×#431C2211yescharacteristic
27C61×#431C2211yescharacteristic
28C61×D4⋊C8—22no—
29C23×Dic61—22no—
30C2×#11758194—21no—
31#14519777C2×C411yescharacteristic, complemented
32#14519777C2×C411yescharacteristic, complemented
33#14519769—21no—
34#14519756—21no—
35#14519756—21no—
36C4×Dic122—21no—
37C4×Dic122—21no—
38D4×Dic61—42no—
39D4×Dic61—42no—
40#14519736—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61—22no—
44C2×C22⋊Dic61—22no—
45C2×C4×Dic61—21no—
46#14519710—22no—
47#14519708—22no—
48C4⋊#92418—21no—
49C4⋊#92418C2×C412yescomplemented
50#14519698—22no—
51#14519698—22no—
52#14519684—22no—
53#14519684—21no—
54#14519684D411yescharacteristic
55#14519684D411yescharacteristic
56#14519684D412yes—
57C22×D4×C61D411yescharacteristic
58C23×C4×C61—21no—
59C4×D4×C61—21no—
60C4×D4×C61—21no—
61C4×D4×C61C2×C412yes—
62C4×D4×C61D412yes—
63C2×C4⋊C4×C61D411yescharacteristic
64C2×C22⋊C4×C61—21no—
65C2×C42×C61C2311yescharacteristic
66C4⋊C8×C61—21no—
67C4⋊C8×C61—21no—
68C22⋊C8×C61—21no—
69C22⋊C8×C61—21no—
70C4×C8×C61—21no—
71C4×C8×C61—21no—
72C24×C61—21no—
73C2×D4×C61—21no—
74C2×D4×C61—21no—
75C2×D4×C61—21no—
76C2×D4×C61C22⋊C412yes—
77C2×D4×C61SD1612yes—
78C2×D4×C61Q1612yes—
79C22×C4×C61—21no—
80C22×C4×C61—22no—
81C22×C4×C61—22no—
82C22×C4×C61—82no—
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×Dic61—21no—
87C22×Dic61—22no—
88C22×Dic61—21no—
89C22×Dic61—44no—
90C22×Dic61—44no—
91C22×Dic61—82no—
92C2×Dic122—21no—
93C2×Dic122—21no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C4⋊C4×C61—21no—
97C4⋊C4×C61C22⋊C412yes—
98C22⋊C4×C61—22no—
99C22⋊C4×C61—22no—
100C42×C61C22×C411yescharacteristic
101C42×C61C2×D411yescharacteristic
102C42×C61#4111yescharacteristic
103C42×C61#4111yescharacteristic
104C22⋊Dic61—44no—
105C22⋊Dic61—41no—
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110C4⋊Dic61—42no—
111C4⋊Dic61—41no—
112C4⋊Dic61—41no—
113C4⋊Dic61—82no—
114#11758196—41no—
115#11758196—41no—
116C4×Dic61—41no—
117C4×Dic61—41no—
118C4×Dic61—41no—
119#11758194—41no—
120#11758194—41no—
121C2×#92418—22no—
122C23×C61—22no—
123C23×C61—22no—
124C23×C61—22no—
125C23×C61—42no—
126C23×C61—42no—
127C23×C61#12011yescharacteristic
128D4×C61—22no—
129D4×C61—22no—
130D4×C61—22no—
131D4×C61#10314yes—
132C2×C4×C61—22no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—42no—
136C2×C4×C61—82no—
137C2×C4×C61—82no—
138C2×C4×C61C2×C22⋊C411yescharacteristic
139C2×C4×C61C4×D411yescharacteristic
140C2×C4×C61C4×D411yescharacteristic
141C2×C4×C61#12111yescharacteristic
142C2×C4×C61#12111yescharacteristic
143C2×C4×C61#12311yescharacteristic
144C2×C4×C61C2×SD1611yescharacteristic
145C2×C4×C61C2×Q1611yescharacteristic
146C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C61#13711yescharacteristic
148C2×Dic61—22no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—42no—
154C2×Dic61—42no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—42no—
159C2×Dic61—88no—
160Dic122—81no—
161Dic122—81no—
162C8×C61—81no—
163C8×C61—81no—
164#92418—42no—
165#9175—611nomaximal, Sylow
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—24no—
169C22×C61—44no—
170C22×C61—44no—
171C22×C61—42no—
172C22×C61—42no—
173C22×C61#38611yescharacteristic
174C22×C61#45011yescharacteristic
175C22×C61#45111yescharacteristic
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—42no—
181C4×C61C2×#10311yescharacteristic
182C4×C61#41711yescharacteristic
183C4×C61#48311yescharacteristic
184C4×C61#48411yescharacteristic
185Dic61—42no—
186Dic61—81no—
187Dic61—82no—
188Dic61—81no—
189Dic61—81no—
190#3077—611no—
191#2349—611no—
192#1518—611no—
193#1503—611no—
194#1478D6111yescharacteristic
195#1303—611no—
196#1286—611no—
197C2×C61—21no—
198C2×C61—21no—
199C2×C61—44no—
200C2×C61#187211yescharacteristic
201C2×C61#190411yescharacteristic
202C2×C61#190611yescharacteristic
203#533—611no—
204C2×C4×D4—1221no—
205C2×C4×D4C2×D6111yescharacteristic
206#478—1222no—
207#476—612no—
208#474—612no—
209#431C2×D6111yescharacteristic
210#431C2×D6111yescharacteristic
211#428—1221no—
212#423—611no—
213#418—1221no—
214#389—1221no—
215#385—1222no—
216#382—611no—
217#380—1221no—
218C4×C4⋊C4—611no—
219C2×#95—1221no—
220#328—1221no—
221#328—1221no—
222#328—1222no—
223D4⋊C8—22no—
224C61#917511yescharacteristic, complemented, Sylow
225C22×D4D24411yescharacteristic
226C23×C4—21no—
227C23×C4—1222no—
228C2×M16—1221no—
229C4⋊Q8—611no—
230C4⋊Q8—611no—
231#125—1221no—
232C22⋊Q8—1221no—
233C22⋊Q8—1221no—
234C4×Q8—1221no—
235C4×Q8—1221no—
236C4×D4—21no—
237C4×D4—21no—
238C4×D4—2442no—
239C4×D4—2442no—
240C4×D4C4×D6112yes—
241C4×D4C22⋊D6112yes—
242#117—1221no—
243C2×C4⋊C4—1222no—
244C2×C4⋊C4—1221no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4D24411yescharacteristic
247C2×C22⋊C4—21no—
248C2×C22⋊C4—1222no—
249C2×C42—1221no—
250C2×C42C22×D6111yescharacteristic
251#107—1222no—
252#106—1222no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—612no—
256C4⋊C8—1221no—
257#102—1222no—
258#102—1222no—
259C22⋊C8—21no—
260C22⋊C8—21no—
261C4×C8—21no—
262C4×C8—21no—
263#95—611no—
264#95—611no—
265#95—612no—
266#95—1222no—
267#95—1221no—
268C24—21no—
269C2×Q8—1221no—
270C2×Q8—1221no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4#1175819012yes—
275C2×D4Dic24412yes—
276C2×D4#1175819812yes—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—82no—
281C22×C4—1221no—
282C22×C4—1222no—
283C22×C4—1221no—
284C22×C4—4882no—
285C22×C4—2444no—
286C22×C4—2444no—
287C22×C4C2×D24411yescharacteristic
288C22×C4D4×D6111yescharacteristic
289C22×C4D4×D6111yescharacteristic
290M16—2441no—
291M16—2441no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—1222no—
295C4⋊C4—21no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C4⋊C4—1221no—
299C4⋊C4—1221no—
300C4⋊C4—4882no—
301C4⋊C4—2442no—
302C4⋊C4—2441no—
303C4⋊C4—2441no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C4⋊C4#1175819812yes—
307C22⋊C4—22no—
308C22⋊C4—22no—
309C22⋊C4—2444no—
310C22⋊C4—2441no—
311C42—2441no—
312C42—2441no—
313C42—2441no—
314C42C2×C4×D6111yescharacteristic
315C42#1175822411yescharacteristic
316C42#1175822411yescharacteristic
317C42C2×C22⋊D6111yescharacteristic
318C23—22no—
319C23—22no—
320C23—22no—
321C23—42no—
322C23—42no—
323C23#1451974711yescharacteristic
324Q8—4881no—
325Q8—4881no—
326D4—22no—
327D4—22no—
328D4—22no—
329D4#1451970214yes—
330C2×C4—22no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—1222no—
337C2×C4—4888no—
338C2×C4—2441no—
339C2×C4—2442no—
340C2×C4—2441no—
341C2×C4—2442no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2442no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4C2×#1175819811yescharacteristic
349C2×C4#1451973711yescharacteristic
350C2×C4#1451973711yescharacteristic
351C2×C4#1451974911yescharacteristic
352C2×C4#1451974911yescharacteristic
353C2×C4#1451976111yescharacteristic
354C2×C4C2×#1175819011yescharacteristic
355C2×C4C2×Dic24411yescharacteristic
356C2×C4#1451980511yescharacteristic
357C2×C4#1451981011yescharacteristic
358C8—81no—
359C8—81no—
360C8—2442no—
361C22—21no—
362C22—21no—
363C22—24no—
364C22—44no—
365C22—44no—
366C22—42no—
367C22—42no—
368C22#1683963911yescharacteristic
369C22#1683991511yescharacteristic
370C22#1683992011yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—4882no—
377C4—4881no—
378C4—4881no—
379C4—4881no—
380C4—2442no—
381C4C2×#1451970211yescharacteristic
382C4#1683976411yescharacteristic
383C4#1684009311yescharacteristic
384C4#1684009811yescharacteristic
385C2—21no—
386C2—21no—
387C2—44no—
388C2#2144612411yescharacteristic
389C2#2144630411yescharacteristic
390C2#2144631811yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1478C2
socleC22×C61#386
prime radicalC22×D4×C61D4
cosocleC2×C42×C61C23
hypercenter#1478D61
hypocenterC61#9175
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
3. #21444384C2semidirect
4. #21444319C2semidirect
5. #21443721C2semidirect
6. #21443678C2semidirect
11. #16840052C4semidirect
12. #16840042C4semidirect
31. #14519777C2×C4semidirect
32. #14519777C2×C4semidirect
49. C4⋊#92418C2×C4semidirect
224. C61#9175semidirect

Maximal subgroups

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

subgroupindex
#214556162
#214487292
#214443842
#214443192
#214437212
#214436782
C61×#14782
#917561