Finite Group Databasebeta

← #29577904

Subgroups — #29577904

Order 15616.

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

normal subgroups only

This group has 514 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#21454455C211yesmaximal, characteristic, complemented
2#21451379C211yesmaximal, characteristic
3#21444262C211yesmaximal, characteristic, complemented
4#21444151C211yesmaximal, characteristic, complemented
5#21443685C211yesmaximal, characteristic, complemented
6#21443684C211yesmaximal, characteristic, complemented
7C61×#1490C211yesmaximal, characteristic, complemented
8C2×#14519734C2211yescharacteristic
9#16839824—22no—
10#16839821—22no—
11#16839819C2211yescharacteristic
12#16839785—21no—
13#16839725—21no—
14C4×#11758194C2211yescharacteristic
15#16839700C411yescharacteristic
16#16839697C411yescharacteristic
17#16839676C411yescharacteristic
18#16839670C411yescharacteristic
19#16839650—21no—
20#16839641—21no—
21#16839638—21no—
22#16839635—21no—
23#16839630C2211yescharacteristic
24D4⋊#92418—22no—
25#16839487—21no—
26#16839485—21no—
27C2×C4×D4×C61C2211yescharacteristic
28C61×#432C2211yescharacteristic
29C4×M16×C61C2211yescharacteristic
30C61×D4⋊C8—22no—
31C22×C22⋊D61—21no—
32C22×C4×D61D411yescharacteristic
33C2×#11758194—21no—
34#14519734—21no—
35#14519734—21no—
36#14519734—21no—
37#14519734—21no—
38C2×#11758196—21no—
39C2×#11758196C2×C411yescharacteristic
40C2×#11758196D411yescharacteristic
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×#11758198—21no—
45C2×#11758198C2×C411yescharacteristic
46C2×#11758198D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C4⋊#92418—21no—
49#14519706—24no—
50C22⋊#92418—21no—
51#14519689—24no—
52#14519688—21no—
53#14519688—21no—
54C4×#92418D412yescomplemented
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58#14519684—21no—
59#14519684C2×C411yescharacteristic
60#14519684C2×C411yescharacteristic
61C22×D4×C61C2×C411yescharacteristic
62C23×C4×C61—21no—
63C2×M16×C61—21no—
64C4×D4×C61—21no—
65C4×D4×C61—21no—
66C4×D4×C61—21no—
67C4×D4×C61—21no—
68C2×C4⋊C4×C61C2×C411yescharacteristic
69C2×C22⋊C4×C61—21no—
70C2×C42×C61C2311yescharacteristic
71C4⋊C8×C61—21no—
72C22⋊C8×C61—21no—
73#97×C61—21no—
74#97×C61—21no—
75C4×C8×C61D412yescomplemented
76C24×C61—21no—
77C23×D61C22⋊C411yescharacteristic
78C2×D4×C61—21no—
79C2×D4×C61—21no—
80C2×D4×C61—42no—
81C22×C4×C61—21no—
82C22×C4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61—81no—
85C22×C4×C61—81no—
86C22×C4×C61C22×C411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C2×C22⋊D61—42no—
90C2×C22⋊D61—42no—
91C2×C22⋊D61—81no—
92C22×Dic61—21no—
93C22×Dic61—21no—
94C22×Dic61C22⋊C411yescharacteristic
95C22×Dic61C22⋊C411yescharacteristic
96C22×Dic61C22⋊C411yescharacteristic
97C2×C4×D61—21no—
98C2×C4×D61—21no—
99C2×C4×D61—41no—
100C2×C4×D61—41no—
101M16×C61—41no—
102M16×C61—41no—
103C2×C8×C61—22no—
104C2×C8×C61—41no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—21no—
107C22⋊C4×C61—41no—
108C22⋊C4×C61—41no—
109C42×C61C2×D411yescharacteristic
110C42×C61C2×D411yescharacteristic
111C42×C61#4111yescharacteristic
112C42×C61#4111yescharacteristic
113C22⋊Dic61—42no—
114C22⋊Dic61—42no—
115C22⋊Dic61—81no—
116#11758198—21no—
117#11758198—21no—
118#11758198—21no—
119#11758198—21no—
120#11758198—81no—
121#11758196—21no—
122#11758196—21no—
123#11758196—21no—
124#11758196—21no—
125#11758196—81no—
126C4×Dic61—21no—
127C4×Dic61—21no—
128#11758194—41no—
129#11758194—41no—
130C2×#92418—22no—
131C2×#92418—41no—
132C23×C61—22no—
133C23×C61—41no—
134C23×C61—41no—
135C23×C61—41no—
136C23×C61—41no—
137C23×C61—41no—
138C23×C61—41no—
139C23×C61C2×C22⋊C411yescharacteristic
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—21no—
143C22×D61—41no—
144C22×D61—41no—
145D4×C61—22no—
146D4×C61—22no—
147D4×C61—41no—
148D4×C61—41no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—82no—
157C2×C4×C61—82no—
158C2×C4×C61C4×D411yescharacteristic
159C2×C4×C61C4×D411yescharacteristic
160C2×C4×C61#12011yescharacteristic
161C2×C4×C61#12111yescharacteristic
162C2×C4×C61#12111yescharacteristic
163C2×C4×C61#12311yescharacteristic
164C22⋊D61—84no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C4×D61—42no—
179C4×D61—42no—
180C8×C61—42no—
181C8×C61—81no—
182#92418—42no—
183#92418—81no—
184#9494—611nomaximal, Sylow
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—42no—
188C22×C61—42no—
189C22×C61—42no—
190C22×C61—81no—
191C22×C61—81no—
192C22×C61—81no—
193C22×C61—81no—
194C22×C61#38611yescharacteristic
195C22×C61#42111yescharacteristic
196C22×C61#42111yescharacteristic
197C2×D61—42no—
198C2×D61—41no—
199C2×D61—41no—
200C2×D61—41no—
201C2×D61—81no—
202C4×C61—21no—
203C4×C61—21no—
204C4×C61—21no—
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—81no—
209Dic61—41no—
210Dic61—41no—
211Dic61—41no—
212Dic61—81no—
213Dic61—81no—
214#2921—611no—
215#2598—611no—
216#1490—611no—
217#1490D6111yescharacteristic, complemented
218#1464—611no—
219#1288—611no—
220#1288—611no—
221C2×C61—21no—
222C2×C61—21no—
223C2×C61—82no—
224C2×C61#189111yescharacteristic
225C2×C61#189711yescharacteristic
226C2×C61#191011yescharacteristic
227D61—81no—
228C2×C4×D4C2×D6111yescharacteristic
229C2×#117—611no—
230#433—1222no—
231#433—1222no—
232#432—611no—
233#432C2×D6111yescharacteristic
234#423—1221no—
235#407—1221no—
236C4×M16—611no—
237C4×M16C2×D6111yescharacteristic
238#400—611no—
239#399—611no—
240#394—611no—
241#392—611no—
242#388—1221no—
243#386—1221no—
244#386—1221no—
245#385—1221no—
246#383—611no—
247D4⋊C8—22no—
248D4⋊C8—1222no—
249#324—1221no—
250#323—1221no—
251C61#949411yescharacteristic, complemented, Sylow
252C22×D4—1221no—
253C22×D4C4×D6111yescharacteristic
254C23×C4—21no—
255C23×C4—611no—
256C2×M16—21no—
257C2×M16—1221no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4—21no—
261C4×D4—21no—
262#117—1221no—
263#117—1221no—
264#117—1221no—
265#117—1221no—
266C2×C4⋊C4—611no—
267C2×C4⋊C4—611no—
268C2×C4⋊C4—1221no—
269C2×C4⋊C4C4×D6111yescharacteristic
270C2×C22⋊C4—21no—
271C2×C22⋊C4—611no—
272C2×C22⋊C4—611no—
273C2×C22⋊C4—1221no—
274C2×C22⋊C4—1221no—
275C2×C22⋊C4—1221no—
276C2×C22⋊C4—1221no—
277C2×C42—611no—
278C2×C42C22×D6111yescharacteristic
279C4⋊C8—21no—
280C4⋊C8—1224no—
281C4⋊C8—1221no—
282C22⋊C8—21no—
283C22⋊C8—1224no—
284C22⋊C8—1221no—
285#97—21no—
286#97—21no—
287#97—1221no—
288#97—1221no—
289C4×C8—612no—
290C4×C8C22⋊D6112yescomplemented
291#95—611no—
292#95—611no—
293#95—1221no—
294#95—1221no—
295#95—1221no—
296#95—1221no—
297C24—21no—
298C24—611no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—42no—
302C2×D4—4881no—
303C2×D4—2442no—
304C2×D4—2442no—
305C22×C4—21no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—81no—
309C22×C4—81no—
310C22×C4—611no—
311C22×C4—611no—
312C22×C4—611no—
313C22×C4—1221no—
314C22×C4—1221no—
315C22×C4—1221no—
316C22×C4—1221no—
317C22×C4—2441no—
318C22×C4—2441no—
319C22×C4C2×C4×D6111yescharacteristic
320C22×C4D4×D6111yescharacteristic
321C22×C4D4×D6111yescharacteristic
322M16—41no—
323M16—41no—
324M16—2441no—
325M16—2441no—
326C2×C8—22no—
327C2×C8—41no—
328C2×C8—1222no—
329C2×C8—2441no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—1221no—
333C4⋊C4—1221no—
334C4⋊C4—1221no—
335C4⋊C4—1221no—
336C4⋊C4—4881no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—1221no—
340C22⋊C4—1221no—
341C22⋊C4—1221no—
342C22⋊C4—1221no—
343C22⋊C4—4881no—
344C22⋊C4—4881no—
345C22⋊C4—2442no—
346C22⋊C4—2442no—
347C42—1221no—
348C42—1221no—
349C42#1175822211yescharacteristic
350C42D4×D6111yescharacteristic
351C42#1175822411yescharacteristic
352C42C2×C22⋊D6111yescharacteristic
353C23—22no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—1221no—
361C23—1221no—
362C23—1221no—
363C23—2441no—
364C23—2441no—
365C23C22⋊C4×D6111yescharacteristic
366D4—22no—
367D4—22no—
368D4—41no—
369D4—41no—
370D4—4884no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—82no—
379C2×C4—82no—
380C2×C4—1221no—
381C2×C4—1221no—
382C2×C4—1221no—
383C2×C4—1221no—
384C2×C4—1221no—
385C2×C4—2442no—
386C2×C4—2442no—
387C2×C4—2441no—
388C2×C4—2441no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4—2441no—
392C2×C4—2441no—
393C2×C4—2441no—
394C2×C4—2441no—
395C2×C4#1451973711yescharacteristic
396C2×C4C4×C22⋊D6111yescharacteristic
397C2×C4#1451974511yescharacteristic
398C2×C4#1451974811yescharacteristic
399C2×C4#1451975011yescharacteristic
400C2×C4#1451975911yescharacteristic
401C8—42no—
402C8—81no—
403C8—4881no—
404C8—2442no—
405C22—21no—
406C22—21no—
407C22—42no—
408C22—42no—
409C22—42no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—4881no—
415C22—2442no—
416C22—2441no—
417C22—2441no—
418C22—2441no—
419C22#1683963811yescharacteristic
420C22#1683977711yescharacteristic
421C22#1683977711yescharacteristic
422C4—21no—
423C4—21no—
424C4—21no—
425C4—21no—
426C4—21no—
427C4—21no—
428C4—81no—
429C4—4881no—
430C4—4881no—
431C4—2441no—
432C4—2441no—
433C4—2441no—
434C2—21no—
435C2—21no—
436C2—82no—
437C2—4881no—
438C2#2144623411yescharacteristic
439C2#2144626411yescharacteristic
440C2#2144634311yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1490C2
socleC22×C61#386
prime radical#16839670C4
cosocleC2×C42×C61C23
hypercenter#1490D61
hypocenterC61#9494
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1490

Complements

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

NH ≅ G/Ntype
1. #21454455C2semidirect
3. #21444262C2semidirect
4. #21444151C2semidirect
5. #21443685C2semidirect
6. #21443684C2semidirect
7. C61×#1490C2semidirect
54. C4×#92418D4semidirect
75. C4×C8×C61D4semidirect
217. #1490D61semidirect
251. C61#9494semidirect
290. C4×C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214544552
#214513792
#214442622
#214441512
#214436852
#214436842
C61×#14902
#949461