Finite Group Databasebeta

← #29577316

Subgroups — #29577316

Order 15616.

530 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 103 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#21448634C211yesmaximal, characteristic, complemented
2#21446739C211yesmaximal, characteristic, complemented
3#21444417C211yesmaximal, characteristic, complemented
4#21444366C211yesmaximal, characteristic, complemented
5#21443685C211yesmaximal, characteristic, complemented
6#21443674C211yesmaximal, characteristic, complemented
7C61×#3213C211yesmaximal, characteristic
8#16839819C2211yescharacteristic
9C2×#14519704—21no—
10C2×#14519704—21no—
11C4×#11758194C2211yescharacteristic
12#16839669—21no—
13#16839655—21no—
14#16839655—21no—
15#16839642—21no—
16#16839637—21no—
17#16839630C2211yescharacteristic
18C4×C4⋊Dic61C2211yescharacteristic
19C22⋊C4×Dic61—21no—
20#16839502—22no—
21#16839496—21no—
22#16839496—21no—
23C61×#532C2211yescharacteristic
24C2×#124×C61C2211yescharacteristic
25C61×#496C412yescomplemented
26C61×#489C412yescomplemented
27C61×#463—22no—
28C61×#448—21no—
29C61×#447—21no—
30C61×#432C2211yescharacteristic
31C23×Dic61—21no—
32C2×#11758194—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C2×C4×Dic61—21no—
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C4⋊#92418—21no—
42#14519704—42no—
43#14519704—42no—
44C22⋊#92418—21no—
45#14519688—21no—
46#14519688—21no—
47C4×#92418—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684D411yescharacteristic
54#14519684D411yescharacteristic
55C2×#41×C61—21no—
56C22×Q8×C61D411yescharacteristic
57C22×D4×C61D411yescharacteristic
58C2×SD16×C61—22no—
59C2×D8×C61—22no—
60C4⋊Q8×C61C2×C411yescharacteristic, complemented
61#127×C61C2×C411yescharacteristic, complemented
62#124×C61—21no—
63#124×C61—21no—
64#124×C61—21no—
65#124×C61C2×C412yes—
66#124×C61D412yes—
67#121×C61—21no—
68#121×C61—21no—
69C4×D4×C61—21no—
70C4×D4×C61—21no—
71C2×C22⋊C4×C61—21no—
72C2×C22⋊C4×C61—21no—
73C2×C42×C61C2311yescharacteristic
74C4⋊C8×C61—21no—
75#103×C61—22no—
76#102×C61—22no—
77C22⋊C8×C61—21no—
78#97×C61C2×C412yescomplemented
79C24×C61—21no—
80#41×C61—41no—
81#41×C61—41no—
82#41×C61—41no—
83#41×C61—41no—
84C2×Q8×C61—21no—
85C2×Q8×C61—21no—
86C2×Q8×C61—81no—
87C2×Q8×C61C22⋊C412yes—
88C2×D4×C61—21no—
89C2×D4×C61—21no—
90C2×D4×C61—21no—
91C2×D4×C61—21no—
92C2×D4×C61—41no—
93C2×D4×C61—81no—
94C2×D4×C61C22⋊C412yes—
95C22×C4×C61—21no—
96C22×C4×C61—41no—
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×Dic61—21no—
101C22×Dic61—21no—
102C22×Dic61—21no—
103C22×Dic61—21no—
104C22×Dic61—42no—
105C22×Dic61—81no—
106C22×Dic61—81no—
107SD16×C61—82no—
108D8×C61—82no—
109C2×C8×C61—22no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61—21no—
112C22⋊C4×C61—22no—
113C22⋊C4×C61—22no—
114C22⋊C4×C61—22no—
115C22⋊C4×C61—22no—
116C22⋊C4×C61—41no—
117C22⋊C4×C61—41no—
118C42×C61C22×C411yescharacteristic
119C42×C61C2×D411yescharacteristic
120C42×C61#4111yescharacteristic
121C42×C61#4111yescharacteristic
122C22⋊Dic61—42no—
123C22⋊Dic61—81no—
124C22⋊Dic61—81no—
125C4⋊Dic61—42no—
126C4⋊Dic61—81no—
127C4×Dic61—41no—
128C4×Dic61—41no—
129C4×Dic61—81no—
130#11758194—22no—
131#11758194—41no—
132C2×#92418—41no—
133C2×#92418—41no—
134C23×C61—22no—
135C23×C61—41no—
136C23×C61—41no—
137C23×C61—41no—
138C23×C61—41no—
139C23×C61—41no—
140C23×C61—41no—
141C23×C61—41no—
142C23×C61#12011yescharacteristic
143Q8×C61—42no—
144Q8×C61—41no—
145Q8×C61—41no—
146Q8×C61—81no—
147D4×C61—42no—
148D4×C61—42no—
149D4×C61—41no—
150D4×C61—41no—
151D4×C61—81no—
152D4×C61—81no—
153D4×C61—81no—
154D4×C61—81no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—22no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—81no—
164C2×C4×C61—81no—
165C2×C4×C61C2×C22⋊C411yescharacteristic
166C2×C4×C61C4×D411yescharacteristic
167C2×C4×C61C4×D411yescharacteristic
168C2×C4×C61#12111yescharacteristic
169C2×C4×C61#12111yescharacteristic
170C2×C4×C61#12311yescharacteristic
171C2×Dic61—22no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—84no—
184C8×C61—42no—
185#92418—42no—
186#92418—81no—
187#9381—611nomaximal, Sylow
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—42no—
191C22×C61—42no—
192C22×C61—42no—
193C22×C61—81no—
194C22×C61—81no—
195C22×C61—81no—
196C22×C61—81no—
197C22×C61—81no—
198C22×C61—81no—
199C22×C61—81no—
200C22×C61#38611yescharacteristic
201C22×C61#45311yescharacteristic
202C22×C61#45411yescharacteristic
203C4×C61—21no—
204C4×C61—21no—
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—42no—
210C4×C61—81no—
211Dic61—42no—
212Dic61—81no—
213Dic61—81no—
214Dic61—81no—
215#3213D6111yescharacteristic
216#2337—611no—
217#1980—611no—
218#1527—611no—
219#1514—611no—
220#1288—611no—
221#1285—611no—
222C2×C61—21no—
223C2×C61—21no—
224C2×C61—82no—
225C2×C61—161no—
226C2×C61#188311yescharacteristic
227C2×C61#190611yescharacteristic
228C2×C61#191111yescharacteristic
229#532C2×D6111yescharacteristic
230C2×#124C2×D6111yescharacteristic
231#496Dic6112yescomplemented
232#489Dic6112yescomplemented
233#463—22no—
234#448—21no—
235#447—21no—
236#432—611no—
237#432C2×D6111yescharacteristic
238C2×#104—1221no—
239C2×#104—1221no—
240C4×M16—611no—
241#391—1221no—
242#388—1221no—
243#388—1221no—
244#386—1221no—
245#385—1221no—
246#383—611no—
247C4×C4⋊C4—611no—
248C4×C22⋊C4—1221no—
249#329—1222no—
250#327—1221no—
251#327—1221no—
252C61#938111yescharacteristic, complemented, Sylow
253C2×#41—21no—
254C22×Q8C22⋊D6111yescharacteristic
255C22×D4C22⋊D6111yescharacteristic
256C23×C4—1221no—
257C2×SD16—22no—
258C2×D8—22no—
259C2×M16—1221no—
260C4⋊Q8C2×Dic6111yescharacteristic, complemented
261#127C2×Dic6111yescharacteristic, complemented
262#124—21no—
263#124—21no—
264#124—21no—
265#124C2×Dic6112yes—
266#124C22⋊D6112yes—
267#121—21no—
268#121—21no—
269C4×D4—21no—
270C4×D4—21no—
271C2×C4⋊C4—1221no—
272C2×C4⋊C4—1221no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—1221no—
276C2×C22⋊C4—1221no—
277C2×C22⋊C4—1221no—
278C2×C42—611no—
279C2×C42—611no—
280C2×C42—1221no—
281C2×C42C22×D6111yescharacteristic
282C4⋊C8—21no—
283C4⋊C8—1221no—
284#104—2442no—
285#104—2442no—
286#103—22no—
287#102—22no—
288C22⋊C8—21no—
289C22⋊C8—1221no—
290#97—1221no—
291#97—1221no—
292#97C2×Dic6112yescomplemented
293C4×C8—1221no—
294#95—611no—
295#95—611no—
296#95—1221no—
297#95—1221no—
298#95—1221no—
299#95—1221no—
300#95—1221no—
301C24—21no—
302#41—41no—
303#41—41no—
304#41—41no—
305#41—41no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—81no—
309C2×Q8C22⋊Dic6112yes—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—41no—
315C2×D4—81no—
316C2×D4C22⋊Dic6112yes—
317C22×C4—21no—
318C22×C4—41no—
319C22×C4—1221no—
320C22×C4—1221no—
321C22×C4—1221no—
322C22×C4—1221no—
323C22×C4—4881no—
324C22×C4—4881no—
325C22×C4—2442no—
326C22×C4D4×D6111yescharacteristic
327C22×C4D4×D6111yescharacteristic
328C22×C4C2×C22⋊D6111yescharacteristic
329SD16—82no—
330D8—82no—
331M16—1222no—
332M16—2441no—
333C2×C8—22no—
334C2×C8—2441no—
335C2×C8—2441no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—4881no—
339C4⋊C4—2442no—
340C22⋊C4—22no—
341C22⋊C4—22no—
342C22⋊C4—22no—
343C22⋊C4—22no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—4881no—
347C22⋊C4—4881no—
348C22⋊C4—2442no—
349C42—4881no—
350C42—2441no—
351C42—2441no—
352C42#1175822411yescharacteristic
353C42#1175822411yescharacteristic
354C42C22×Dic6111yescharacteristic
355C42C2×C22⋊D6111yescharacteristic
356C23—22no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23#1451974511yescharacteristic
365Q8—42no—
366Q8—41no—
367Q8—41no—
368Q8—81no—
369D4—42no—
370D4—42no—
371D4—41no—
372D4—41no—
373D4—81no—
374D4—81no—
375D4—81no—
376D4—81no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—22no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—1222no—
388C2×C4—4884no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4—2441no—
392C2×C4—2441no—
393C2×C4—2441no—
394C2×C4—2441no—
395C2×C4—2441no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4C2×C22⋊Dic6111yescharacteristic
401C2×C4D4×Dic6111yescharacteristic
402C2×C4D4×Dic6111yescharacteristic
403C2×C4#1451974911yescharacteristic
404C2×C4#1451974911yescharacteristic
405C2×C4#1451975811yescharacteristic
406C8—42no—
407C8—4881no—
408C8—2442no—
409C22—21no—
410C22—21no—
411C22—42no—
412C22—42no—
413C22—42no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22#1683964211yescharacteristic
422C22#1683992811yescharacteristic
423C22#1683993311yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—21no—
428C4—21no—
429C4—21no—
430C4—42no—
431C4—81no—
432C4—4881no—
433C4—4881no—
434C4—4881no—
435C4—2442no—
436C2—21no—
437C2—21no—
438C2—82no—
439C2—161no—
440C2#2144619711yescharacteristic
441C2#2144632211yescharacteristic
442C2#2144635211yescharacteristic
subgroupG/H
centerC22#16839642
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
Fitting, prime radicalC61×#3213C2
socleC22×C61#386
cosocleC2×C42×C61C23
hypercenter#3213D61
hypocenterC61#9381
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3213

Complements

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

NH ≅ G/Ntype
1. #21448634C2semidirect
2. #21446739C2semidirect
3. #21444417C2semidirect
4. #21444366C2semidirect
5. #21443685C2semidirect
6. #21443674C2semidirect
25. C61×#496C4semidirect
26. C61×#489C4semidirect
60. C4⋊Q8×C61C2×C4semidirect
61. #127×C61C2×C4semidirect
78. #97×C61C2×C4semidirect
231. #496Dic61semidirect
232. #489Dic61semidirect
252. C61#9381semidirect
260. C4⋊Q8C2×Dic61semidirect
261. #127C2×Dic61semidirect
292. #97C2×Dic61semidirect

Maximal subgroups

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

subgroupindex
#214486342
#214467392
#214444172
#214443662
#214436852
#214436742
C61×#32132
#938161