Finite Group Databasebeta

← #29576437

Subgroups — #29576437

Order 15616.

552 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840092C211yesmaximal, characteristic
2#21448688C211yesmaximal, characteristic
3#21446803C211yesmaximal, characteristic
4#21444392C211yesmaximal, characteristic
5#21443686C211yesmaximal, characteristic
6#21443665C211yesmaximal, characteristic
7C61×#1823C211yesmaximal, characteristic
8C2×#14519756C2211yescharacteristic
9C2×#14519736—21no—
10#16840092—21no—
11#16840092—21no—
12#16840092—22no—
13C2×#14519708C412yescomplemented
14C2×#14519700C412yescomplemented
15C2×C22⋊#92418C2211yescharacteristic
16#16839661—21no—
17#16839648—22no—
18#16839625—21no—
19#16839622C2211yescharacteristic
20C4⋊C4×Dic61—21no—
21C4×C22⋊Dic61C2211yescharacteristic
22#16839528—21no—
23#16839528—21no—
24#16839500—22no—
25C22×C4⋊C4×C61C2211yescharacteristic
26C2×C22⋊C8×C61C2211yescharacteristic
27C61×#380C2211yescharacteristic
28C61×#340—22no—
29C22×Dic122C2×C411yescharacteristic
30C22×#92418C2×C412yes—
31#14519756—21no—
32#14519756—21no—
33#14519756—21no—
34#14519756—21no—
35#14519736—42no—
36#14519736—42no—
37C2×C4⋊Dic61—22no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×#11758196—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61D411yescharacteristic
44C2×C22⋊Dic61D411yescharacteristic
45C2×C4×Dic61—22no—
46C2×C4×Dic61—21no—
47#14519708—22no—
48#14519708—22no—
49#14519700—22no—
50#14519700—22no—
51C22⋊#92418—21no—
52C22⋊#92418—21no—
53#14519684—22no—
54#14519684—22no—
55#14519684—21no—
56#14519684D412yes—
57C23×C4×C61—21no—
58C23×C4×C61C2311yescharacteristic
59C22×C8×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61C2×C412yes—
65C2×C4⋊C4×C61D411yescharacteristic
66C2×C4⋊C4×C61D411yescharacteristic
67C2×C4⋊C4×C61D412yes—
68C2×C22⋊C4×C61—21no—
69C22⋊C8×C61—21no—
70C22⋊C8×C61—21no—
71#95×C61—21no—
72C24×C61C2×D411yescharacteristic
73C22×C4×C61—22no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—22no—
77C22×C4×C61—42no—
78C22×C4×C61—41no—
79C22×C4×C61—41no—
80C22×C4×C61—41no—
81C22×C4×C61—41no—
82C22×C4×C61—41no—
83C22×C4×C61C22×C411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61#4111yescharacteristic
88C22×C4×C61#4111yescharacteristic
89C22×Dic61—21no—
90C22×Dic61—21no—
91C22×Dic61—22no—
92C22×Dic61—21no—
93C22×Dic61—21no—
94C2×Dic122—21no—
95C2×Dic122—21no—
96C2×Dic122—42no—
97C2×C8×C61—42no—
98C2×C8×C61—41no—
99C4⋊C4×C61—22no—
100C4⋊C4×C61—22no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—42no—
104C4⋊C4×C61C22⋊C412yes—
105C4⋊C4×C61C22⋊C412yes—
106C22⋊C4×C61—41no—
107C22⋊C4×C61—41no—
108C22⋊Dic61—21no—
109C22⋊Dic61—21no—
110C22⋊Dic61—21no—
111C22⋊Dic61—41no—
112C22⋊Dic61—41no—
113C22⋊Dic61—41no—
114C22⋊Dic61—41no—
115C22⋊Dic61SD1612yes—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118C4⋊Dic61—44no—
119C4⋊Dic61—42no—
120#11758196—41no—
121#11758196—41no—
122C4×Dic61—44no—
123C4×Dic61—42no—
124C2×#92418—22no—
125C2×#92418—42no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61C4×D411yescharacteristic
129C23×C61#12011yescharacteristic
130C23×C61#12111yescharacteristic
131C23×C61C2×SD1611yescharacteristic
132C23×C61#13511yescharacteristic
133C23×C61AGL(1,ℤ/8)11yescharacteristic
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—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—42no—
144C2×C4×C61—42no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—42no—
150C2×C4×C61—42no—
151C2×C4×C61—81no—
152C2×C4×C61—81no—
153C2×C4×C61—81no—
154C2×C4×C61C2×C22⋊C411yescharacteristic
155C2×C4×C61C4×D411yescharacteristic
156C2×C4×C61#12111yescharacteristic
157C2×C4×C61#12311yescharacteristic
158C2×Dic61—22no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—42no—
163C2×Dic61—41no—
164C2×Dic61—42no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—42no—
168C2×Dic61—41no—
169C2×Dic61—81no—
170C2×Dic61—81no—
171Dic122—42no—
172Dic122—81no—
173C8×C61—81no—
174#92418—42no—
175#9256—611nomaximal, Sylow
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61—41no—
186C22×C61#38611yescharacteristic
187C22×C61C4×SD1611yescharacteristic
188C22×C61#44011yescharacteristic
189C22×C61#45011yescharacteristic
190C22×C61#45211yescharacteristic
191C22×C61#46111yescharacteristic
192C22×C61#46311yescharacteristic
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—42no—
197C4×C61—42no—
198C4×C61—161no—
199C4×C61#41012yes—
200Dic61—42no—
201Dic61—82no—
202Dic61—81no—
203Dic61—81no—
204Dic61—81no—
205C2×#483—611no—
206#2344—611no—
207#1996—611no—
208#1823D6111yescharacteristic
209#1520—611no—
210#1289—611no—
211#1282—611no—
212C2×C61—21no—
213C2×C61—21no—
214C2×C61—21no—
215C2×C61—21no—
216C2×C61—21no—
217C2×C61—21no—
218C2×C61#187711yescharacteristic
219C2×C61#189911yescharacteristic
220C2×C61#190511yescharacteristic
221C2×C22⋊Q8—611no—
222C2×#117—1221no—
223C22×C4⋊C4C2×D6111yescharacteristic
224#483—1221no—
225#483—1221no—
226#483—1222no—
227C2×#106—612no—
228C2×#103—612no—
229C2×C22⋊C8—611no—
230C2×C22⋊C8C2×D6111yescharacteristic
231#389—1221no—
232#387—1222no—
233#381—1221no—
234#380—611no—
235#380C2×D6111yescharacteristic
236C4×C4⋊C4—1221no—
237C4×C22⋊C4—611no—
238#342—1221no—
239#342—1221no—
240#340—22no—
241#328—1222no—
242C61#925611yescharacteristic, complemented, Sylow
243C22×Q8—611no—
244C23×C4—21no—
245C23×C4C22×D6111yescharacteristic
246C22×C8—21no—
247C22×C8—612no—
248C22⋊Q8—1221no—
249C22⋊Q8—1221no—
250C22⋊Q8—1221no—
251C22⋊Q8—1221no—
252#117—2442no—
253#117—2442no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—611no—
259C2×C4⋊C4—1222no—
260C2×C4⋊C4—1221no—
261C2×C4⋊C4—1221no—
262C2×C4⋊C4C4×D6112yes—
263C2×C4⋊C4D24411yescharacteristic
264C2×C4⋊C4D24411yescharacteristic
265C2×C4⋊C4C22⋊D6112yes—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—611no—
268C2×C22⋊C4—611no—
269C2×C22⋊C4—1221no—
270C2×C22⋊C4—1221no—
271C2×C42—1222no—
272C2×C42—1221no—
273#106—1222no—
274#106—1222no—
275#103—1222no—
276#103—1222no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279C22⋊C8—1221no—
280C22⋊C8—1221no—
281#95—21no—
282#95—612no—
283#95—1222no—
284#95—1222no—
285#95—1221no—
286C24D4×D6111yescharacteristic
287C2×Q8—1221no—
288C2×Q8—1221no—
289C2×Q8—2442no—
290C22×C4—22no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—22no—
294C22×C4—42no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—1221no—
301C22×C4—1221no—
302C22×C4—1221no—
303C22×C4—1222no—
304C22×C4—1221no—
305C22×C4C2×C4×D6111yescharacteristic
306C22×C4C2×D24411yescharacteristic
307C22×C4D4×D6111yescharacteristic
308C22×C4#1175822411yescharacteristic
309C22×C4#1175822411yescharacteristic
310C22×C4C2×C22⋊D6111yescharacteristic
311C2×C8—42no—
312C2×C8—41no—
313C2×C8—1222no—
314C2×C8—2442no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—42no—
320C4⋊C4—1221no—
321C4⋊C4—1221no—
322C4⋊C4—2442no—
323C4⋊C4—2444no—
324C4⋊C4—2441no—
325C4⋊C4—2441no—
326C4⋊C4#1175819812yes—
327C4⋊C4#1175819812yes—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—612no—
331C22⋊C4—1221no—
332C22⋊C4—1221no—
333C22⋊C4—1221no—
334C22⋊C4—2441no—
335C22⋊C4—2441no—
336C22⋊C4—2441no—
337C22⋊C4—2441no—
338C42—2442no—
339C42—2444no—
340C23—41no—
341C23—41no—
342C23#1451973711yescharacteristic
343C23#1451974711yescharacteristic
344C23#1451974911yescharacteristic
345C23SD16×D6111yescharacteristic
346C23#1451979611yescharacteristic
347C23#1451980111yescharacteristic
348C23#1451980611yescharacteristic
349Q8—4881no—
350Q8—2442no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—1222no—
371C2×C4—4881no—
372C2×C4—4881no—
373C2×C4—2441no—
374C2×C4—2442no—
375C2×C4—2442no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2442no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4C2×#1175819811yescharacteristic
384C2×C4#1451973711yescharacteristic
385C2×C4#1451974911yescharacteristic
386C2×C4#1451976111yescharacteristic
387C8—81no—
388C8—2442no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22#1683963911yescharacteristic
400C22#1683985311yescharacteristic
401C22#1683985911yescharacteristic
402C22#1683991411yescharacteristic
403C22#1683992511yescharacteristic
404C22#1683996511yescharacteristic
405C22#1683997511yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—42no—
410C4—42no—
411C4—161no—
412C4—4882no—
413C4—4881no—
414C4—4881no—
415C4—4881no—
416C4—2442no—
417C4#1683973512yes—
418C2—21no—
419C2—21no—
420C2—21no—
421C2—21no—
422C2—21no—
423C2—21no—
424C2#2144615111yescharacteristic
425C2#2144627511yescharacteristic
426C2#2144631111yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1823C2
socleC22×C61#386
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenter#1823D61
hypocenterC61#9256
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
13. C2×#14519708C4semidirect
14. C2×#14519700C4semidirect
242. C61#9256semidirect

Maximal subgroups

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

subgroupindex
C2×#168400922
#214486882
#214468032
#214443922
#214436862
#214436652
C61×#18232
#925661