Finite Group Databasebeta

← #29578078

Subgroups — #29578078

Order 15616.

482 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455767C211yesmaximal, characteristic
2#21448575C211yesmaximal, characteristic
3#21445896C211yesmaximal, characteristic
4#21444353C211yesmaximal, characteristic
5#21443728C211yesmaximal, characteristic
6#21443672C211yesmaximal, characteristic
7C61×#1826C211yesmaximal, characteristic
8C2×#14519756C2211yescharacteristic
9#16840103—22no—
10#16840097C412yescomplemented
11#16840092C412yescomplemented
12#16839805—21no—
13#16839770—21no—
14#16839726C2211yescharacteristic
15#16839666—21no—
16#16839656—21no—
17#16839650—21no—
18#16839647—21no—
19#16839646—21no—
20#16839625C2211yescharacteristic
21#16839625C2211yescharacteristic
22C4×#11758196—21no—
23#16839529—21no—
24#16839529—21no—
25#16839500—22no—
26C2×#117×C61C2211yescharacteristic
27C61×#407C2211yescharacteristic
28C4×C22⋊C4×C61C2211yescharacteristic
29C61×#339—21no—
30C61×#339—21no—
31C22×Dic122D411yescharacteristic
32C2×#11758194—21no—
33#14519756—21no—
34#14519756—21no—
35#14519756C2×C412yes—
36#14519756D412yes—
37C2×C4⋊Dic61D411yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61D411yescharacteristic
44C2×C22⋊Dic61D411yescharacteristic
45C2×C4×Dic61—21no—
46C2×C4×Dic61—21no—
47#14519710—22no—
48#14519708—22no—
49#14519700—22no—
50#14519700—22no—
51C22⋊#92418—21no—
52C22⋊#92418C2×C412yes—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58#14519684—21no—
59#14519684—21no—
60#14519684—21no—
61C23×C4×C61C2311yescharacteristic
62C2×M16×C61—21no—
63#117×C61—21no—
64#117×C61—21no—
65#117×C61—21no—
66#117×C61—21no—
67C2×C4⋊C4×C61C2×C411yescharacteristic
68C2×C4⋊C4×C61C2×C411yescharacteristic
69C2×C22⋊C4×C61—21no—
70C2×C22⋊C4×C61—21no—
71C2×C42×C61—21no—
72C2×C42×C61D411yescharacteristic
73C2×C42×C61D411yescharacteristic
74C22⋊C8×C61—21no—
75C22⋊C8×C61—21no—
76#95×C61—21no—
77C24×C61C2×D411yescharacteristic
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61C22×C411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61#4111yescharacteristic
89C22×C4×C61#4111yescharacteristic
90C22×Dic61—21no—
91C22×Dic61—21no—
92C22×Dic61—21no—
93C22×Dic61—21no—
94C22×Dic61—41no—
95C2×Dic122—21no—
96C2×Dic122—41no—
97C2×Dic122—41no—
98C2×Dic122C22⋊C412yes—
99M16×C61—41no—
100M16×C61—41no—
101C2×C8×C61—41no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—21no—
106C22⋊C4×C61—42no—
107C22⋊C4×C61—41no—
108C22⋊C4×C61—41no—
109C42×C61—41no—
110C42×C61—41no—
111C42×C61—41no—
112C42×C61—41no—
113C22⋊Dic61—22no—
114C22⋊Dic61—22no—
115C22⋊Dic61—41no—
116C22⋊Dic61—41no—
117C22⋊Dic61—41no—
118C22⋊Dic61—41no—
119C4⋊Dic61—21no—
120C4⋊Dic61C22⋊C412yes—
121#11758196—22no—
122#11758196—22no—
123#11758196—42no—
124#11758196—81no—
125C4×Dic61—42no—
126C4×Dic61—81no—
127#11758194—41no—
128#11758194—41no—
129C2×#92418—22no—
130C23×C61—21no—
131C23×C61—21no—
132C23×C61—41no—
133C23×C61—41no—
134C23×C61C4×D411yescharacteristic
135C23×C61#12011yescharacteristic
136C23×C61#12111yescharacteristic
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—22no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—81no—
154C2×C4×C61—81no—
155C2×C4×C61C2×C22⋊C411yescharacteristic
156C2×C4×C61C4×D411yescharacteristic
157C2×C4×C61#12111yescharacteristic
158C2×C4×C61#12311yescharacteristic
159C2×Dic61—22no—
160C2×Dic61—22no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—81no—
172C2×Dic61—81no—
173C2×Dic61—81no—
174Dic122—42no—
175Dic122—81no—
176C8×C61—81no—
177#92418—42no—
178#9526—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—81no—
188C22×C61—81no—
189C22×C61#38611yescharacteristic
190C22×C61#45811yescharacteristic
191C22×C61#45811yescharacteristic
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—42no—
197C4×C61—81no—
198C4×C61—81no—
199C4×C61—81no—
200Dic61—42no—
201Dic61—42no—
202Dic61—81no—
203Dic61—81no—
204Dic61—161no—
205#3095—611no—
206#2332—611no—
207#1826D6111yescharacteristic
208#1820—611no—
209#1511—611no—
210#1306—611no—
211#1284—611no—
212C2×C61—21no—
213C2×C61—21no—
214C2×C61—41no—
215C2×C61—41no—
216C2×C61#189011yescharacteristic
217C2×C61#190511yescharacteristic
218C2×C61#190611yescharacteristic
219C2×C22⋊Q8—611no—
220C2×#117C2×D6111yescharacteristic
221#485—1222no—
222#484—612no—
223#483—612no—
224#428—1221no—
225#419—1221no—
226#407—611no—
227#407C2×D6111yescharacteristic
228#391—1221no—
229#388—1221no—
230#388—1221no—
231#387—1221no—
232#387—1221no—
233#381—611no—
234#381—611no—
235C4×C4⋊C4—1221no—
236C4×C22⋊C4C2×D6111yescharacteristic
237#342—1221no—
238#342—1221no—
239#339—21no—
240#339—21no—
241#328—1222no—
242C61#952611yescharacteristic, complemented, Sylow
243C22×Q8—611no—
244C23×C4C22×D6111yescharacteristic
245C2×M16—21no—
246C2×M16—1221no—
247C22⋊Q8—612no—
248C22⋊Q8—612no—
249C22⋊Q8—1221no—
250C22⋊Q8—1221no—
251#117—21no—
252#117—21no—
253#117—21no—
254#117—21no—
255C2×C4⋊C4—611no—
256C2×C4⋊C4—1221no—
257C2×C4⋊C4—1221no—
258C2×C4⋊C4—1221no—
259C2×C4⋊C4C4×D6111yescharacteristic
260C2×C4⋊C4C4×D6111yescharacteristic
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—611no—
264C2×C22⋊C4—611no—
265C2×C22⋊C4—1221no—
266C2×C22⋊C4—1221no—
267C2×C42—21no—
268C2×C42—1221no—
269C2×C42—1221no—
270C2×C42C22⋊D6111yescharacteristic
271C2×C42C22⋊D6111yescharacteristic
272#107—1222no—
273#106—1222no—
274#103—1222no—
275#103—1222no—
276C22⋊C8—21no—
277C22⋊C8—21no—
278C22⋊C8—612no—
279C22⋊C8—1221no—
280#95—21no—
281#95—1221no—
282#95—1221no—
283#95—1221no—
284#95—1221no—
285#95—1221no—
286#95—1221no—
287#95—1221no—
288#95—1221no—
289C24D4×D6111yescharacteristic
290C2×Q8—612no—
291C2×Q8—1221no—
292C2×Q8—2441no—
293C2×Q8—2441no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—1221no—
301C22×C4—1221no—
302C22×C4—1221no—
303C22×C4—1221no—
304C22×C4—2441no—
305C22×C4C2×C4×D6111yescharacteristic
306C22×C4#1175822211yescharacteristic
307C22×C4D4×D6111yescharacteristic
308C22×C4D4×D6111yescharacteristic
309C22×C4#1175822411yescharacteristic
310C22×C4C2×C22⋊D6111yescharacteristic
311M16—41no—
312M16—41no—
313M16—2441no—
314M16—2441no—
315C2×C8—41no—
316C2×C8—1222no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—612no—
322C4⋊C4—1222no—
323C4⋊C4—1222no—
324C4⋊C4—1221no—
325C4⋊C4—4881no—
326C4⋊C4—2442no—
327C22⋊C4—42no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—1222no—
331C22⋊C4—1222no—
332C22⋊C4—2441no—
333C22⋊C4—2441no—
334C22⋊C4—2441no—
335C22⋊C4—2441no—
336C42—41no—
337C42—41no—
338C42—41no—
339C42—41no—
340C42—4881no—
341C42—2442no—
342C23—21no—
343C23—21no—
344C23—41no—
345C23—41no—
346C23#1451973711yescharacteristic
347C23#1451974511yescharacteristic
348C23#1451975011yescharacteristic
349Q8—4881no—
350Q8—2442no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—1222no—
370C2×C4—1222no—
371C2×C4—4881no—
372C2×C4—4881no—
373C2×C4—4881no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4—2441no—
384C2×C4C22⋊C4×D6111yescharacteristic
385C2×C4C4×C22⋊D6111yescharacteristic
386C2×C4#1451974811yescharacteristic
387C2×C4#1451975911yescharacteristic
388C8—81no—
389C8—2442no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—81no—
399C22—81no—
400C22#1683963811yescharacteristic
401C22#1683995111yescharacteristic
402C22#1683995111yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—42no—
408C4—81no—
409C4—81no—
410C4—81no—
411C4—9761no—
412C4—4881no—
413C4—4881no—
414C4—2442no—
415C4—2442no—
416C2—21no—
417C2—21no—
418C2—41no—
419C2—41no—
420C2#2144622911yescharacteristic
421C2#2144631011yescharacteristic
422C2#2144632311yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1826C2
socleC22×C61#386
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenter#1826D61
hypocenterC61#9526
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
10. #16840097C4semidirect
11. #16840092C4semidirect
242. C61#9526semidirect

Maximal subgroups

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

subgroupindex
#214557672
#214485752
#214458962
#214443532
#214437282
#214436722
C61×#18262
#952661