Finite Group Databasebeta

← #29737053

Subgroups — #29737053

Order 15616.

1082 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459622C211yesmaximal, characteristic
2#21450300C212yesmaximal, complemented
3#21446986C214yesmaximal, complemented
4#21446803C212yesmaximal, complemented
5#21446233C214yesmaximal
6C4×#14519692C211yesmaximal, characteristic
7C61×#2486C211yesmaximal, characteristic
8#16840471—24no—
9#16840469—22no—
10D4×Dic122—22no—
11#16840393—21no—
12#16840388—21no—
13#16840388C2212yes—
14#16840319—21no—
15C2×#14519756—21no—
16C2×#14519756C2212yes—
17#16840237C2212yes—
18C2×#14519692C2212yes—
19#16839700—24no—
20#16839667—22no—
21#16839627—22no—
22#16839625C2218yes—
23C4×C22⋊Dic61C2212yes—
24#16839529C2212yes—
25#16839528C2218yes—
26C2×#123×C61C2212yes—
27C2×C4×D4×C61C2211yescharacteristic
28C22×C4⋊C4×C61C2211yescharacteristic
29C61×#398—21no—
30C61×#397—21no—
31C61×#389—21no—
32C61×#381C2212yes—
33C61×#380—21no—
34C61×#380C2211yescharacteristic
35C22×Dic122—21no—
36C22×Dic122D412yes—
37#14519777—21no—
38#14519777—21no—
39#14519776—24no—
40#14519769—22no—
41#14519768—24no—
42#14519756—22no—
43#14519756—22no—
44#14519756—22no—
45#14519756—22no—
46#14519756—22no—
47#14519756—22no—
48#14519756—22no—
49#14519756—22no—
50#14519754—24no—
51#14519754—24no—
52#14519754—24no—
53#14519754—24no—
54C4×Dic122—22no—
55C4×Dic122—22no—
56D4×Dic61—24no—
57D4×Dic61—24no—
58#14519736—22no—
59C2×C4⋊Dic61—21no—
60C2×C4⋊Dic61D412yes—
61C2×#11758196—22no—
62C2×#11758196D414yes—
63C2×C22⋊Dic61—22no—
64C2×C22⋊Dic61C2314yes—
65C2×C22⋊Dic61C2314yes—
66C2×C4×Dic61—22no—
67#14519692—24no—
68#14519684—22no—
69#14519684—28no—
70#14519684—28no—
71C22×D4×C61C2311yescharacteristic
72C23×C4×C61D411yescharacteristic
73C23×C4×C61C2312yes—
74C23×C4×C61C2311yescharacteristic
75#123×C61—28no—
76C4×D4×C61—22no—
77C4×D4×C61—22no—
78C2×C4⋊C4×C61—22no—
79C2×C4⋊C4×C61—21no—
80C2×C4⋊C4×C61—21no—
81C2×C4⋊C4×C61—22no—
82C2×C4⋊C4×C61—21no—
83C2×C4⋊C4×C61—22no—
84C2×C4⋊C4×C61D411yescharacteristic
85C2×C22⋊C4×C61—22no—
86C2×C22⋊C4×C61D411yescharacteristic
87C2×C22⋊C4×C61C2312yes—
88C2×C22⋊C4×C61C2311yescharacteristic
89C2×C42×C61D411yescharacteristic
90#95×C61—22no—
91#95×C61—21no—
92#95×C61—22no—
93C24×C61C2×D411yescharacteristic
94C24×C61C2411yescharacteristic
95C2×D4×C61—22no—
96C2×D4×C61—22no—
97C2×D4×C61#4114yes—
98C22×C4×C61—21no—
99C22×C4×C61—21no—
100C22×C4×C61—22no—
101C22×C4×C61—22no—
102C22×C4×C61—24no—
103C22×C4×C61—24no—
104C22×C4×C61—24no—
105C22×C4×C61—42no—
106C22×C4×C61—42no—
107C22×C4×C61C2×D412yes—
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D412yes—
113C22×C4×C61C2×D411yescharacteristic
114C22×Dic61—22no—
115C22×Dic61—22no—
116C22×Dic61—24no—
117C22×Dic61C2×D414yes—
118C22×Dic61C2×D414yes—
119C2×Dic122—22no—
120C2×Dic122—22no—
121C2×Dic122—22no—
122C2×Dic122—22no—
123C2×Dic122—44no—
124C2×Dic122—82no—
125C4⋊C4×C61—22no—
126C4⋊C4×C61—42no—
127C4⋊C4×C61—41no—
128C4⋊C4×C61—42no—
129C4⋊C4×C61—41no—
130C4⋊C4×C61—44no—
131C22⋊C4×C61—22no—
132C22⋊C4×C61—22no—
133C22⋊C4×C61—24no—
134C22⋊C4×C61—44no—
135C42×C61—21no—
136C42×C61—21no—
137C22⋊Dic61—24no—
138C22⋊Dic61—24no—
139C22⋊Dic61—24no—
140C22⋊Dic61—24no—
141C22⋊Dic61—24no—
142C4⋊Dic61—22no—
143C4⋊Dic61—22no—
144C4⋊Dic61—22no—
145C4⋊Dic61—22no—
146C4⋊Dic61—22no—
147C4⋊Dic61—22no—
148#11758196—24no—
149#11758196—24no—
150#11758196—24no—
151#11758196—24no—
152C4×Dic61—24no—
153C4×Dic61—44no—
154C23×C61—21no—
155C23×C61—21no—
156C23×C61—41no—
157C23×C61—41no—
158C23×C61—41no—
159C23×C61—41no—
160C23×C61#12412yes—
161C23×C61C22×D411yescharacteristic
162C23×C61C22×D412yes—
163C23×C61C2×#4112yes—
164C23×C612−1+412yes—
165D4×C61—28no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—24no—
169C2×C4×C61—22no—
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—41no—
173C2×C4×C61—42no—
174C2×C4×C61—42no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—42no—
178C2×C4×C61—42no—
179C2×C4×C61—42no—
180C2×C4×C61—42no—
181C2×C4×C61—42no—
182C2×C4×C61—42no—
183C2×C4×C61—48no—
184C2×C4×C61—81no—
185C2×C4×C61#12011yescharacteristic
186C2×C4×C61#12012yes—
187C2×C4×C61#12011yescharacteristic
188C2×C4×C61#12412yes—
189C2×Dic61—24no—
190C2×Dic61—24no—
191C2×Dic61—44no—
192C2×Dic61—44no—
193C2×Dic61—44no—
194C2×Dic61—44no—
195C2×Dic61—44no—
196C2×Dic61—82no—
197C2×Dic61—82no—
198Dic122—44no—
199Dic122—82no—
200Dic122—82no—
201Dic122—82no—
202#25948—611nomaximal, Sylow
203C22×C61—22no—
204C22×C61—21no—
205C22×C61—22no—
206C22×C61—21no—
207C22×C61—22no—
208C22×C61—42no—
209C22×C61—42no—
210C22×C61—42no—
211C22×C61—41no—
212C22×C61—41no—
213C22×C61—81no—
214C22×C61C2×#12011yescharacteristic
215C22×C61C2×#12411yescharacteristic
216C22×C61#53611yescharacteristic
217C22×C61#54814yes—
218C4×C61—22no—
219C4×C61—22no—
220C4×C61—21no—
221C4×C61—41no—
222C4×C61—41no—
223C4×C61—82no—
224C4×C61—82no—
225C4×C61#45812yes—
226Dic61—44no—
227Dic61—44no—
228Dic61—84no—
229#3501—611no—
230#2503—612no—
231#2486D6111yescharacteristic
232#2030—614no—
233#1996—612no—
234#1890—614no—
235C4×#99—611no—
236C2×C61—24no—
237C2×C61—21no—
238C2×C61—21no—
239C2×C61—42no—
240C2×C61#243611yescharacteristic
241C2×C61C2×#45811yescharacteristic
242C2×C61#302811yescharacteristic
243#554—1222no—
244#554—1224no—
245D4×Q8—1222no—
246#544—1221no—
247#543—612no—
248#543—1221no—
249#533—1221no—
250C2×#123C2×D6112yes—
251C2×C22⋊Q8—612no—
252C2×C22⋊Q8—1221no—
253#518—612no—
254C2×C4×D4C2×D6111yescharacteristic
255C22×C4⋊C4C2×D6111yescharacteristic
256C2×#99—612no—
257#400—1224no—
258#398—21no—
259#397—21no—
260#391—1222no—
261#389—21no—
262#382—1222no—
263#381—618no—
264#381C2×D6112yes—
265#380—21no—
266#380C2×D6111yescharacteristic
267C4×C22⋊C4—612no—
268#342—618no—
269#342—612no—
270C61#2594811yescharacteristic, complemented, Sylow
271C22×Q8—612no—
272C22×Q8—1221no—
273C22×D4C22×D6111yescharacteristic
274C23×C4C22⋊D6111yescharacteristic
275C23×C4C22×D6112yes—
276C23×C4C22×D6111yescharacteristic
277C4⋊Q8—1221no—
278C4⋊Q8—1221no—
279C4⋊Q8—1224no—
280#125—1222no—
281#125—1224no—
282#123—28no—
283C22⋊Q8—1224no—
284C22⋊Q8—1224no—
285C22⋊Q8—1224no—
286C22⋊Q8—1224no—
287C22⋊Q8—1222no—
288C22⋊Q8—1222no—
289C22⋊Q8—1222no—
290C22⋊Q8—1222no—
291C22⋊Q8—1222no—
292C22⋊Q8—1222no—
293C22⋊Q8—1222no—
294C22⋊Q8—1222no—
295C4×Q8—1222no—
296C4×Q8—1222no—
297C4×D4—22no—
298C4×D4—22no—
299C4×D4—1224no—
300C4×D4—1224no—
301#117—1222no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—612no—
309C2×C4⋊C4—614no—
310C2×C4⋊C4—1222no—
311C2×C4⋊C4—1221no—
312C2×C4⋊C4C22⋊D6111yescharacteristic
313C2×C22⋊C4—22no—
314C2×C22⋊C4—614no—
315C2×C22⋊C4—614no—
316C2×C22⋊C4—1222no—
317C2×C22⋊C4C22⋊D6111yescharacteristic
318C2×C22⋊C4C22×D6112yes—
319C2×C22⋊C4C22×D6111yescharacteristic
320C2×C42—1222no—
321C2×C42C22⋊D6111yescharacteristic
322#99—1224no—
323#95—22no—
324#95—21no—
325#95—22no—
326#95—1228no—
327#95—1228no—
328#95—1222no—
329C24C2×C22⋊D6111yescharacteristic
330C24C23×D6111yescharacteristic
331C2×Q8—1222no—
332C2×Q8—1222no—
333C2×Q8—1222no—
334C2×Q8—1222no—
335C2×Q8—4882no—
336C2×Q8—2444no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4#1175822414yes—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—24no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—614no—
350C22×C4—614no—
351C22×C4—1222no—
352C22×C4—1222no—
353C22×C4—1224no—
354C22×C4D4×D6112yes—
355C22×C4D4×D6112yes—
356C22×C4C2×C22⋊D6111yescharacteristic
357C22×C4C2×C22⋊D6111yescharacteristic
358C22×C4C2×C22⋊D6111yescharacteristic
359C22×C4C2×C22⋊D6111yescharacteristic
360C22×C4C2×C22⋊D6111yescharacteristic
361C4⋊C4—22no—
362C4⋊C4—42no—
363C4⋊C4—41no—
364C4⋊C4—42no—
365C4⋊C4—41no—
366C4⋊C4—44no—
367C4⋊C4—1224no—
368C4⋊C4—1222no—
369C4⋊C4—1224no—
370C4⋊C4—1222no—
371C4⋊C4—1222no—
372C4⋊C4—1222no—
373C4⋊C4—1224no—
374C4⋊C4—1222no—
375C4⋊C4—1224no—
376C4⋊C4—1222no—
377C22⋊C4—22no—
378C22⋊C4—22no—
379C22⋊C4—24no—
380C22⋊C4—44no—
381C22⋊C4—1224no—
382C22⋊C4—1224no—
383C22⋊C4—1224no—
384C22⋊C4—1224no—
385C22⋊C4—1224no—
386C42—21no—
387C42—21no—
388C42—1224no—
389C42—2444no—
390C23—21no—
391C23—21no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23#1451976412yes—
397C23C2×D4×D6112yes—
398C23C22×C22⋊D6111yescharacteristic
399C23C2×#1175822412yes—
400C23#1451982412yes—
401Q8—4882no—
402Q8—4882no—
403Q8—4882no—
404Q8—2444no—
405D4—28no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—24no—
409C2×C4—22no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—48no—
424C2×C4—81no—
425C2×C4—1224no—
426C2×C4—1224no—
427C2×C4—4882no—
428C2×C4—4882no—
429C2×C4—2444no—
430C2×C4—2444no—
431C2×C4—2444no—
432C2×C4—2444no—
433C2×C4—2444no—
434C2×C4#1451974511yescharacteristic
435C2×C4#1451974512yes—
436C2×C4#1451974511yescharacteristic
437C2×C4#1451976412yes—
438C22—21no—
439C22—22no—
440C22—21no—
441C22—22no—
442C22—22no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22—41no—
447C22—41no—
448C22—81no—
449C22C2×#1451974511yescharacteristic
450C22C2×#1451976411yescharacteristic
451C22#1684033311yescharacteristic
452C22#1684041814yes—
453C4—22no—
454C4—21no—
455C4—22no—
456C4—41no—
457C4—41no—
458C4—82no—
459C4—82no—
460C4—4884no—
461C4—2444no—
462C4—2444no—
463C4#1683995112yes—
464C2—21no—
465C2—24no—
466C2—21no—
467C2—42no—
468C2#2144947811yescharacteristic
469C2C2×#1683995111yescharacteristic
470C2#2145522411yescharacteristic
subgroupG/H
centerC22C2×#14519745
commutator, cosocleC24×C61C24
FrattiniC24C23×D61
FittingC61×#2486C2
socleC22×C61C2×#120
prime radicalC22×D4×C61C23
hypercenter#2486D61
hypocenterC61#25948
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2486

Complements

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

NH ≅ G/Ntype
2. #21450300C2semidirect
3. #21446986C2semidirect
4. #21446803C2semidirect
270. C61#25948semidirect

Maximal subgroups

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

subgroupindex
#214596222
#214503002
#214469862
#214468032
#214462332
C4×#145196922
C61×#24862
#2594861