Finite Group Databasebeta

← #29652308

Subgroups — #29652308

Order 15616.

928 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459224C211yesmaximal, characteristic
2#21455858C212yesmaximal, complemented
3#21444860C212yesmaximal, complemented
4#21444843C212yesmaximal
5#21444792C212yesmaximal, complemented
6#21444775C212yesmaximal
7#21444317C212yesmaximal, complemented
8#21444133C211yesmaximal, characteristic
9C61×#2396C211yesmaximal, characteristic
10#16840393—21no—
11#16840393C2212yes—
12#16840390—22no—
13#16840390—22no—
14#16840388—21no—
15#16840388C2212yes—
16#16840319—21no—
17#16840319C2212yes—
18#16840315—24no—
19C2×#14519736—21no—
20#16840097C2214yes—
21#16840057—22no—
22#16839972—22no—
23#16839918C2214yes—
24C4×#11758202—24no—
25#16839815C2212yes—
26#16839498C2214yes—
27#16839498C2214yes—
28#16839488C2212yes—
29#16839486C2212yes—
30C2×C4×Q8×C61C2211yescharacteristic
31C2×#117×C61C2211yescharacteristic
32C61×#400C2211yescharacteristic
33C61×#399C2211yescharacteristic
34C61×#398—21no—
35C61×#396—21no—
36C61×#395C2211yescharacteristic
37C61×#393C2211yescharacteristic
38C4×C4⋊C4×C61—21no—
39C4×C4⋊C4×C61C2211yescharacteristic
40C4×C22⋊C4×C61—21no—
41C2×#11758202—24no—
42#14519777—21no—
43#14519777—21no—
44#14519777D412yes—
45#14519777D412yes—
46#14519776—24no—
47#14519776—24no—
48#14519769—22no—
49#14519769—22no—
50#14519768—24no—
51#14519768—24no—
52#14519756—22no—
53#14519756—22no—
54#14519756—22no—
55#14519756C2314yes—
56#14519754—24no—
57#14519754—24no—
58#14519754—24no—
59#14519754—24no—
60C4×Dic122—22no—
61C4×Dic122—22no—
62C4×Dic122—22no—
63C4×Dic122D414yes—
64#14519736—22no—
65#14519736—22no—
66#14519736—22no—
67#14519736—22no—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61—21no—
70C2×C22⋊Dic61—22no—
71C2×C4×Dic61—22no—
72#14519710—24no—
73C4⋊#92418—22no—
74#14519701—24no—
75#14519700—24no—
76C22⋊#92418C2314yes—
77C4×#92418—22no—
78C22×Q8×C61C2311yescharacteristic
79C23×C4×C61D411yescharacteristic
80C4×Q8×C61—22no—
81C4×Q8×C61—22no—
82#117×C61—22no—
83#117×C61—22no—
84C2×C4⋊C4×C61—21no—
85C2×C4⋊C4×C61—21no—
86C2×C4⋊C4×C61—21no—
87C2×C4⋊C4×C61—21no—
88C2×C4⋊C4×C61D411yescharacteristic
89C2×C4⋊C4×C61C2311yescharacteristic
90C2×C4⋊C4×C61C2311yescharacteristic
91C2×C22⋊C4×C61—21no—
92C2×C22⋊C4×C61—21no—
93C2×C22⋊C4×C61D411yescharacteristic
94C2×C22⋊C4×C61C2311yescharacteristic
95C2×C42×C61—21no—
96C2×C42×C61—21no—
97C2×C42×C61D411yescharacteristic
98C2×C42×C61C2311yescharacteristic
99#95×C61—21no—
100#95×C61—21no—
101#95×C61—21no—
102#95×C61—21no—
103#95×C61C2311yescharacteristic
104#95×C61C2311yescharacteristic
105C24×C61C2×D411yescharacteristic
106C2×Q8×C61—22no—
107C2×Q8×C61—42no—
108C22×C4×C61—21no—
109C22×C4×C61—21no—
110C22×C4×C61—22no—
111C22×C4×C61—21no—
112C22×C4×C61—21no—
113C22×C4×C61—21no—
114C22×C4×C61—21no—
115C22×C4×C61Q1614yescomplemented
116C22×C4×C61C2×D411yescharacteristic
117C22×C4×C61C2×D411yescharacteristic
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2×D411yescharacteristic
120C22×C4×C61C2×D411yescharacteristic
121C22×C4×C61C2411yescharacteristic
122C22×Dic61—22no—
123C22×Dic61—22no—
124C2×Dic122—22no—
125C2×Dic122—22no—
126C2×Dic122—22no—
127C2×Dic122C2×D414yes—
128C4⋊C4×C61—22no—
129C4⋊C4×C61—22no—
130C4⋊C4×C61—22no—
131C4⋊C4×C61—42no—
132C4⋊C4×C61—42no—
133C4⋊C4×C61—42no—
134C4⋊C4×C61—42no—
135C22⋊C4×C61—22no—
136C22⋊C4×C61—22no—
137C22⋊C4×C61—42no—
138C22⋊C4×C61—42no—
139C42×C61—21no—
140C42×C61—21no—
141C42×C61—41no—
142C42×C61—41no—
143C42×C61—42no—
144C42×C61C2×D412yes—
145C42×C61C2×D412yes—
146C22⋊Dic61—24no—
147C22⋊Dic61—24no—
148#11758202—48no—
149C4⋊Dic61—22no—
150C4⋊Dic61—22no—
151C4⋊Dic61—22no—
152C4⋊Dic61—22no—
153C4⋊Dic61—22no—
154C4⋊Dic61—22no—
155C4⋊Dic61—22no—
156C4⋊Dic61C2×D414yes—
157#11758196—24no—
158#11758196—24no—
159#11758196—24no—
160#11758196—24no—
161C4×Dic61—24no—
162C4×Dic61—24no—
163C2×#92418—24no—
164C23×C61—21no—
165C23×C61—21no—
166C23×C61—41no—
167C23×C61—41no—
168C23×C61C2×Q1612yes—
169C23×C61C22×D411yescharacteristic
170Q8×C61—24no—
171Q8×C61—42no—
172C2×C4×C61—21no—
173C2×C4×C61—21no—
174C2×C4×C61—24no—
175C2×C4×C61—24no—
176C2×C4×C61—22no—
177C2×C4×C61—22no—
178C2×C4×C61—21no—
179C2×C4×C61—21no—
180C2×C4×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61—41no—
193C2×C4×C61—41no—
194C2×C4×C61#12012yes—
195C2×C4×C61#12011yescharacteristic
196C2×C4×C61#12011yescharacteristic
197C2×C4×C61C2×Q1612yes—
198C2×C4×C61C2×Q1612yes—
199C2×C4×C61#13712yes—
200C2×C4×C61C22×D412yes—
201C2×Dic61—24no—
202C2×Dic61—24no—
203C2×Dic61—82no—
204C2×Dic61—82no—
205Dic122—44no—
206Dic122—82no—
207Dic122—82no—
208Dic122—82no—
209#92418—44no—
210#18125—611nomaximal, Sylow
211C22×C61—21no—
212C22×C61—21no—
213C22×C61—22no—
214C22×C61—42no—
215C22×C61—41no—
216C22×C61—41no—
217C22×C61—81no—
218C22×C61C2×#12011yescharacteristic
219C22×C61C22×Q1611yescharacteristic
220C22×C61C2×#13711yescharacteristic
221C4×C61—22no—
222C4×C61—22no—
223C4×C61—22no—
224C4×C61—42no—
225C4×C61—41no—
226C4×C61—41no—
227C4×C61—42no—
228C4×C61—81no—
229C4×C61—81no—
230C4×C61#45112yes—
231C4×C61#45112yes—
232Dic61—44no—
233Dic61—44no—
234#3458—611no—
235#3104—612no—
236#2396D6111yescharacteristic
237#1617—612no—
238#1614—612no—
239#1605—612no—
240#1602—612no—
241#1503—612no—
242#1458—611no—
243C2×C61—21no—
244C2×C61—21no—
245C2×C61—42no—
246C2×C61C2×#45111yescharacteristic
247C2×C61#301811yescharacteristic
248C2×C61#302511yescharacteristic
249#544—612no—
250#544—1222no—
251#544—1222no—
252#544—1221no—
253#543—612no—
254#543—1221no—
255#533—612no—
256#533—1224no—
257#533—1221no—
258C2×C4×Q8C2×D6111yescharacteristic
259C2×#117—1221no—
260C2×#117C2×D6111yescharacteristic
261#484—614no—
262#477—1222no—
263#462—1222no—
264#451—614no—
265C4×Q16—1224no—
266#431—612no—
267#400C2×D6111yescharacteristic
268#399C2×D6111yescharacteristic
269#398—21no—
270#396—21no—
271#395C2×D6111yescharacteristic
272#393C2×D6111yescharacteristic
273C4×C4⋊C4—21no—
274C4×C4⋊C4C2×D6111yescharacteristic
275C4×C22⋊C4—21no—
276#328—614no—
277#328—614no—
278#324—612no—
279#323—612no—
280C61#1812511yescharacteristic, complemented, Sylow
281C22×Q8C22×D6111yescharacteristic
282C23×C4C22⋊D6111yescharacteristic
283C2×Q16—1224no—
284C4⋊Q8—612no—
285C4⋊Q8—612no—
286C4⋊Q8—1221no—
287C4⋊Q8—1221no—
288C4⋊Q8—1224no—
289C4⋊Q8—1224no—
290#125—1222no—
291#125—1224no—
292#125—1224no—
293#125—1222no—
294C22⋊Q8—614no—
295C22⋊Q8—1224no—
296C22⋊Q8—1224no—
297C22⋊Q8—1224no—
298C22⋊Q8—1224no—
299C22⋊Q8—1222no—
300C22⋊Q8—1222no—
301C22⋊Q8—1222no—
302C4×Q8—22no—
303C4×Q8—22no—
304C4×Q8—614no—
305C4×Q8—1222no—
306C4×Q8—1222no—
307C4×Q8—1222no—
308#117—22no—
309#117—22no—
310#117—1222no—
311#117—1222no—
312#117—1222no—
313#117—1222no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—1221no—
319C2×C4⋊C4—1221no—
320C2×C4⋊C4C22⋊D6111yescharacteristic
321C2×C4⋊C4C22×D6111yescharacteristic
322C2×C4⋊C4C22×D6111yescharacteristic
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—1222no—
326C2×C22⋊C4C22⋊D6111yescharacteristic
327C2×C22⋊C4C22×D6111yescharacteristic
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—1222no—
331C2×C42C22⋊D6111yescharacteristic
332C2×C42C22×D6111yescharacteristic
333#107—1224no—
334C4⋊C8—1222no—
335#103—1224no—
336#103—1224no—
337C22⋊C8—614no—
338C4×C8—1222no—
339#95—21no—
340#95—21no—
341#95—21no—
342#95—21no—
343#95C22×D6111yescharacteristic
344#95C22×D6111yescharacteristic
345C24C2×C22⋊D6111yescharacteristic
346C2×Q8—22no—
347C2×Q8—42no—
348C2×Q8—614no—
349C2×Q8—1222no—
350C2×Q8—1222no—
351C2×Q8—1222no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—1222no—
360C22×C4—1222no—
361C22×C4#1175820214yescomplemented
362C22×C4C2×C22⋊D6111yescharacteristic
363C22×C4C2×C22⋊D6111yescharacteristic
364C22×C4C2×C22⋊D6111yescharacteristic
365C22×C4C2×C22⋊D6111yescharacteristic
366C22×C4C2×C22⋊D6111yescharacteristic
367C22×C4C23×D6111yescharacteristic
368Q16—2448no—
369C2×C8—1224no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—42no—
374C4⋊C4—42no—
375C4⋊C4—42no—
376C4⋊C4—42no—
377C4⋊C4—614no—
378C4⋊C4—1222no—
379C4⋊C4—1222no—
380C4⋊C4—1224no—
381C4⋊C4—1224no—
382C4⋊C4—1222no—
383C4⋊C4—1222no—
384C4⋊C4—1224no—
385C4⋊C4—1222no—
386C4⋊C4—1222no—
387C4⋊C4—1224no—
388C4⋊C4—1222no—
389C22⋊C4—22no—
390C22⋊C4—22no—
391C22⋊C4—42no—
392C22⋊C4—42no—
393C22⋊C4—1224no—
394C22⋊C4—1224no—
395C42—21no—
396C42—21no—
397C42—41no—
398C42—41no—
399C42—42no—
400C42—1224no—
401C42—1224no—
402C42D4×D6112yes—
403C42D4×D6112yes—
404C23—21no—
405C23—21no—
406C23—41no—
407C23—41no—
408C23C2×#1175820212yes—
409C23C22×C22⋊D6111yescharacteristic
410Q8—24no—
411Q8—42no—
412Q8—4882no—
413Q8—4882no—
414Q8—4882no—
415Q8—2444no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—1224no—
439C2×C4—1224no—
440C2×C4—4882no—
441C2×C4—4882no—
442C2×C4#1451974512yes—
443C2×C4#1451974511yescharacteristic
444C2×C4#1451974511yescharacteristic
445C2×C4C2×#1175820212yes—
446C2×C4C2×#1175820212yes—
447C2×C4#1451980712yes—
448C2×C4C2×D4×D6112yes—
449C8—2444no—
450C22—21no—
451C22—21no—
452C22—22no—
453C22—42no—
454C22—41no—
455C22—41no—
456C22—81no—
457C22C2×#1451974511yescharacteristic
458C22C22×#1175820211yescharacteristic
459C22C2×#1451980711yescharacteristic
460C4—22no—
461C4—22no—
462C4—22no—
463C4—42no—
464C4—41no—
465C4—42no—
466C4—41no—
467C4—81no—
468C4—81no—
469C4—2444no—
470C4—2444no—
471C4#1683991712yes—
472C4#1683991712yes—
473C2—21no—
474C2—21no—
475C2—42no—
476C2C2×#1683991711yescharacteristic
477C2#2145516711yescharacteristic
478C2#2145521011yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2396C2
socleC22×C61C2×#120
prime radicalC24×C61C2×D4
hypercenter#2396D61
hypocenterC61#18125
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2396

Complements

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

NH ≅ G/Ntype
2. #21455858C2semidirect
3. #21444860C2semidirect
5. #21444792C2semidirect
7. #21444317C2semidirect
115. C22×C4×C61Q16semidirect
280. C61#18125semidirect
361. C22×C4#11758202semidirect

Maximal subgroups

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

subgroupindex
#214592242
#214558582
#214448602
#214448432
#214447922
#214447752
#214443172
#214441332
C61×#23962
#1812561