Finite Group Databasebeta

← #29571829

Subgroups — #29571829

Order 15616.

868 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840393C211yesmaximal, characteristic
2#21446124C212yesmaximal
3C2×#16839500C212yesmaximal
4#21444072C211yesmaximal, characteristic
5C2×C61×#324C211yesmaximal, characteristic
6#16840393—24no—
7#16840393—22no—
8#16840393C414yescomplemented
9C2×#14519776—22no—
10C2×#14519768—22no—
11C2×#14519756—21no—
12C2×#14519756C2212yes—
13C2×#14519736—21no—
14C22×C4⋊Dic61C2211yescharacteristic
15C2×#14519702—22no—
16C2×#14519684—21no—
17C2×#14519684—21no—
18C2×#14519684C2211yescharacteristic
19#16839525—22no—
20#16839500—24no—
21C22×C4⋊C4×C61C2211yescharacteristic
22C2×C22⋊C8×C61C2212yes—
23C61×#324—22no—
24C22×Dic122—21no—
25C22×Dic122D412yes—
26C23×Dic61—21no—
27C23×Dic61—21no—
28#14519776—28no—
29#14519776—28no—
30#14519768—28no—
31#14519768—28no—
32#14519756—24no—
33#14519756—24no—
34#14519756—22no—
35#14519756—22no—
36#14519756C2×C414yes—
37#14519756D414yes—
38#14519736—24no—
39#14519736—24no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61—22no—
44C2×C4⋊Dic61—42no—
45C2×C4⋊Dic61D412yes—
46C2×#11758196—22no—
47C2×#11758196—22no—
48C2×C22⋊Dic61—22no—
49C2×C4×Dic61—22no—
50#14519702—44no—
51#14519684—22no—
52#14519684—42no—
53#14519684—42no—
54C23×C4×C61D411yescharacteristic
55C23×C4×C61D411yescharacteristic
56C23×C4×C61C2311yescharacteristic
57C22×C8×C61—22no—
58C2×C4⋊C4×C61—22no—
59C2×C4⋊C4×C61—22no—
60C2×C4⋊C4×C61C2×C412yes—
61C2×C4⋊C4×C61D412yes—
62C22⋊C8×C61—22no—
63C22⋊C8×C61—22no—
64C24×C61C2×D411yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—41no—
72C22×C4×C61—41no—
73C22×C4×C61—41no—
74C22×C4×C61—41no—
75C22×C4×C61C22⋊C412yes—
76C22×C4×C61C22⋊C412yes—
77C22×C4×C61SD1612yes—
78C22×C4×C61Q1612yes—
79C22×C4×C61C22×C411yescharacteristic
80C22×C4×C61C2×D412yes—
81C22×C4×C61C2×D412yes—
82C22×C4×C61C2×D411yescharacteristic
83C22×Dic61—22no—
84C22×Dic61—22no—
85C22×Dic61—22no—
86C22×Dic61—22no—
87C22×Dic61—41no—
88C22×Dic61—41no—
89C22×Dic61—41no—
90C22×Dic61—41no—
91C22×Dic61—41no—
92C22×Dic61—41no—
93C22×Dic61—41no—
94C22×Dic61—41no—
95C22×Dic61—41no—
96C22×Dic61—41no—
97C22×Dic61—41no—
98C22×Dic61—41no—
99C2×Dic122—24no—
100C2×Dic122—22no—
101C2×Dic122—42no—
102C2×Dic122—42no—
103C2×Dic122—81no—
104C2×Dic122—81no—
105C2×Dic122C22⋊C414yes—
106C2×C8×C61—42no—
107C2×C8×C61—42no—
108C2×C8×C61—42no—
109C4⋊C4×C61—24no—
110C4⋊C4×C61—24no—
111C22⋊Dic61—24no—
112C22⋊Dic61—24no—
113C4⋊Dic61—24no—
114C4⋊Dic61—24no—
115C4⋊Dic61—24no—
116C4⋊Dic61—22no—
117C4⋊Dic61—24no—
118C4⋊Dic61—42no—
119C4⋊Dic61C22⋊C414yes—
120#11758196—28no—
121#11758196—24no—
122#11758196—24no—
123C4×Dic61—28no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61C2×C22⋊C411yescharacteristic
129C23×C61#12011yescharacteristic
130C23×C61#12011yescharacteristic
131C23×C61C2×SD1611yescharacteristic
132C23×C61C2×Q1611yescharacteristic
133C23×C61#13711yescharacteristic
134C23×C61#13711yescharacteristic
135C2×C4×C61—22no—
136C2×C4×C61—22no—
137C2×C4×C61—22no—
138C2×C4×C61—22no—
139C2×C4×C61—22no—
140C2×C4×C61—22no—
141C2×C4×C61—22no—
142C2×C4×C61—22no—
143C2×C4×C61—22no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—42no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—42no—
150C2×C4×C61—81no—
151C2×C4×C61#10314yescomplemented
152C2×C4×C61C2×C22⋊C412yes—
153C2×C4×C61#12012yes—
154C2×Dic61—24no—
155C2×Dic61—24no—
156C2×Dic61—42no—
157C2×Dic61—42no—
158C2×Dic61—42no—
159C2×Dic61—42no—
160C2×Dic61—42no—
161C2×Dic61—42no—
162C2×Dic61—42no—
163C2×Dic61—42no—
164C2×Dic61—42no—
165C2×Dic61—42no—
166C2×Dic61—81no—
167C2×Dic61—81no—
168C2×Dic61—81no—
169C2×Dic61—81no—
170C2×Dic61—81no—
171C2×Dic61—81no—
172C2×Dic61—81no—
173C2×Dic61—81no—
174Dic122—44no—
175Dic122—82no—
176Dic122—84no—
177C8×C61—82no—
178#8406—611nomaximal, Sylow
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—21no—
191C22×C61#37911yescharacteristic
192C22×C61C2×#10311yescharacteristic
193C22×C61#41911yescharacteristic
194C22×C61#44811yescharacteristic
195C22×C61#44811yescharacteristic
196C22×C61#45111yescharacteristic
197C22×C61#45111yescharacteristic
198C22×C61#45411yescharacteristic
199C22×C61#45611yescharacteristic
200C22×C61B(4,𝔽2)11yescharacteristic
201C22×C61#45811yescharacteristic
202C4×C61—24no—
203C4×C61—22no—
204C4×C61—22no—
205C4×C61—42no—
206Dic61—44no—
207Dic61—44no—
208Dic61—82no—
209Dic61—82no—
210C2×#544—611no—
211#1872—612no—
212C2×#328—612no—
213C2×#324D6111yescharacteristic
214#1441—611no—
215C2×C61—21no—
216C2×C61—21no—
217C2×C61—21no—
218C2×C61—21no—
219C2×C61#159911yescharacteristic
220C2×C61#160511yescharacteristic
221C2×C61#161111yescharacteristic
222C2×C61#161711yescharacteristic
223C2×C61#178711yescharacteristic
224C2×C61#179011yescharacteristic
225C2×C61#179311yescharacteristic
226#544—614no—
227#544—1224no—
228#544—1222no—
229C2×C4⋊Q8—1222no—
230C2×#125—1222no—
231C2×C22⋊Q8—612no—
232C2×C22⋊Q8—1221no—
233C2×#117—1221no—
234C22×C4⋊C4—611no—
235C22×C4⋊C4C2×D6111yescharacteristic
236C2×#103—1222no—
237C2×C22⋊C8C2×D6112yes—
238C2×#95—611no—
239C2×#95—1221no—
240C2×#95—1221no—
241#340—1222no—
242#328—1224no—
243#324—22no—
244C61#840611yescharacteristic, complemented, Sylow
245C22×Q8—612no—
246C22×Q8—1221no—
247C23×C4—1221no—
248C23×C4—1221no—
249C23×C4D24411yescharacteristic
250C23×C4D24411yescharacteristic
251C23×C4C22×D6111yescharacteristic
252C22×C8—22no—
253C4⋊Q8—1228no—
254C4⋊Q8—1228no—
255#125—1228no—
256#125—1228no—
257C22⋊Q8—614no—
258C22⋊Q8—614no—
259C22⋊Q8—1224no—
260C22⋊Q8—1224no—
261C22⋊Q8—1222no—
262C22⋊Q8—1222no—
263#117—1224no—
264#117—1224no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—612no—
268C2×C4⋊C4—1221no—
269C2×C4⋊C4—1221no—
270C2×C4⋊C4—1221no—
271C2×C4⋊C4—1222no—
272C2×C4⋊C4—1222no—
273C2×C4⋊C4—1222no—
274C2×C4⋊C4—2442no—
275C2×C4⋊C4C4×D6112yes—
276C2×C4⋊C4C22⋊D6112yes—
277C2×C22⋊C4—1222no—
278C2×C42—1222no—
279#103—2444no—
280C22⋊C8—22no—
281C22⋊C8—22no—
282#95—1222no—
283#95—2442no—
284#95—2442no—
285C24C2×D24411yescharacteristic
286C2×Q8—614no—
287C2×Q8—1224no—
288C2×Q8—1222no—
289C2×Q8—4881no—
290C2×Q8—4881no—
291C2×Q8—2442no—
292C2×Q8—2442no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—1222no—
304C22×C4—1222no—
305C22×C4—1222no—
306C22×C4—1222no—
307C22×C4—2441no—
308C22×C4—2441no—
309C22×C4—2441no—
310C22×C4—2441no—
311C22×C4—2441no—
312C22×C4—2441no—
313C22×C4—2441no—
314C22×C4—2441no—
315C22×C4—2441no—
316C22×C4—2441no—
317C22×C4—2441no—
318C22×C4—2441no—
319C22×C4#1175819012yes—
320C22×C4Dic24412yes—
321C22×C4#1175819812yes—
322C22×C4#1175819812yes—
323C22×C4C2×C4×D6111yescharacteristic
324C22×C4D4×D6112yes—
325C22×C4D4×D6112yes—
326C22×C4C2×C22⋊D6111yescharacteristic
327C2×C8—42no—
328C2×C8—42no—
329C2×C8—42no—
330C4⋊C4—24no—
331C4⋊C4—24no—
332C4⋊C4—614no—
333C4⋊C4—1228no—
334C4⋊C4—1224no—
335C4⋊C4—1224no—
336C4⋊C4—1224no—
337C4⋊C4—1224no—
338C4⋊C4—1224no—
339C4⋊C4—1222no—
340C4⋊C4—1224no—
341C4⋊C4—2442no—
342C22⋊C4—1224no—
343C22⋊C4—1224no—
344C42—1228no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23C2×#1175819811yescharacteristic
350C23#1451974711yescharacteristic
351C23#1451974711yescharacteristic
352C23C2×#1175819011yescharacteristic
353C23C2×Dic24411yescharacteristic
354C23#1451981011yescharacteristic
355C23#1451981011yescharacteristic
356Q8—4882no—
357Q8—4884no—
358Q8—2444no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—81no—
375C2×C4—1224no—
376C2×C4—1224no—
377C2×C4—4881no—
378C2×C4—4881no—
379C2×C4—4881no—
380C2×C4—4881no—
381C2×C4—4881no—
382C2×C4—4881no—
383C2×C4—4881no—
384C2×C4—4881no—
385C2×C4—2442no—
386C2×C4—2442no—
387C2×C4—2442no—
388C2×C4—2442no—
389C2×C4—2442no—
390C2×C4—2442no—
391C2×C4—2442no—
392C2×C4—2442no—
393C2×C4—2442no—
394C2×C4—2442no—
395C2×C4#1451970214yescomplemented
396C2×C4C22⋊C4×D6112yes—
397C2×C4#1451974512yes—
398C8—82no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22#1683961711yescharacteristic
412C22C2×#1451970211yescharacteristic
413C22#1683977211yescharacteristic
414C22#1683990311yescharacteristic
415C22#1683990311yescharacteristic
416C22#1683992011yescharacteristic
417C22#1683992011yescharacteristic
418C22#1683993711yescharacteristic
419C22#1683994711yescharacteristic
420C22#1683995011yescharacteristic
421C22#1683995311yescharacteristic
422C4—24no—
423C4—22no—
424C4—22no—
425C4—42no—
426C4—4882no—
427C4—4882no—
428C4—2444no—
429C4—2444no—
430C2—21no—
431C2—21no—
432C2—21no—
433C2—21no—
434C2#2144476111yescharacteristic
435C2#2144479511yescharacteristic
436C2#2144482911yescharacteristic
437C2#2144486311yescharacteristic
438C2#2144575511yescharacteristic
439C2#2144576511yescharacteristic
440C2#2144578011yescharacteristic
subgroupG/H
centerC23#14519747
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#324C2
socleC23×C61#120
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenterC2×#324D61
hypocenterC61#8406
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
8. #16840393C4semidirect
151. C2×C4×C61#103semidirect
244. C61#8406semidirect
395. C2×C4#14519702semidirect

Maximal subgroups

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

subgroupindex
C2×#168403932
#214461242
C2×#168395002
#214440722
C2×C61×#3242
#840661