Finite Group Databasebeta

← #29577894

Subgroups — #29577894

Order 15616.

600 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 93 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#21454236C211yesmaximal, 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×M16×D61—21no—
9C2×#14519734C2211yescharacteristic
10#16839819C2211yescharacteristic
11#16839719—22no—
12#16839716—22no—
13C4×#11758194C2211yescharacteristic
14M16×Dic61—21no—
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—
34C2×#11758189—22no—
35M16×D61—24no—
36M16×D61—24no—
37C2×C8×D61—22no—
38#14519734—21no—
39#14519734—21no—
40#14519734—21no—
41#14519734—21no—
42C2×#11758196—21no—
43C2×#11758196C2×C411yescharacteristic
44C2×#11758196D411yescharacteristic
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61—21no—
48C2×#11758198—21no—
49C2×#11758198C2×C411yescharacteristic
50C2×#11758198D411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C4⋊#92418—21no—
53C22⋊#92418—21no—
54#14519688—21no—
55#14519688—21no—
56#14519687—22no—
57C4×#92418D412yescomplemented
58C8×Dic61—22no—
59#14519684—21no—
60#14519684—21no—
61#14519684—21no—
62#14519684—21no—
63#14519684C2×C411yescharacteristic
64#14519684C2×C411yescharacteristic
65C22×D4×C61C2×C411yescharacteristic
66C23×C4×C61—21no—
67C2×M16×C61—21no—
68C4×D4×C61—21no—
69C4×D4×C61—21no—
70C4×D4×C61—21no—
71C4×D4×C61—21no—
72C2×C4⋊C4×C61C2×C411yescharacteristic
73C2×C22⋊C4×C61—21no—
74C2×C42×C61C2311yescharacteristic
75C4⋊C8×C61—21no—
76C22⋊C8×C61—21no—
77#97×C61—21no—
78#97×C61—21no—
79C4×C8×C61D412yescomplemented
80C24×C61—21no—
81C23×D61C22⋊C411yescharacteristic
82C2×D4×C61—21no—
83C2×D4×C61—21no—
84C2×D4×C61—42no—
85C22×C4×C61—21no—
86C22×C4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61—81no—
89C22×C4×C61—81no—
90C22×C4×C61C22×C411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C2×C22⋊D61—42no—
94C2×C22⋊D61—42no—
95C2×C22⋊D61—81no—
96C22×Dic61—21no—
97C22×Dic61—21no—
98C22×Dic61C22⋊C411yescharacteristic
99C22×Dic61C22⋊C411yescharacteristic
100C22×Dic61C22⋊C411yescharacteristic
101C2×C4×D61—22no—
102C2×C4×D61—21no—
103C2×C4×D61—21no—
104C2×C4×D61—22no—
105M16×C61—22no—
106M16×C61—22no—
107C2×C8×C61—22no—
108C2×C8×C61—41no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61—21no—
111C22⋊C4×C61—41no—
112C22⋊C4×C61—41no—
113C42×C61C2×D411yescharacteristic
114C42×C61C2×D411yescharacteristic
115C42×C61#4111yescharacteristic
116C42×C61#4111yescharacteristic
117C22⋊Dic61—42no—
118C22⋊Dic61—42no—
119C22⋊Dic61—81no—
120#11758198—21no—
121#11758198—21no—
122#11758198—21no—
123#11758198—21no—
124#11758198—81no—
125#11758196—21no—
126#11758196—21no—
127#11758196—21no—
128#11758196—21no—
129#11758196—81no—
130C4×Dic61—21no—
131C4×Dic61—21no—
132#11758194—22no—
133#11758194—22no—
134C2×#92418—22no—
135C2×#92418—41no—
136#11758189—28no—
137C8×D61—28no—
138C23×C61—22no—
139C23×C61—41no—
140C23×C61—41no—
141C23×C61—41no—
142C23×C61—41no—
143C23×C61—41no—
144C23×C61—41no—
145C23×C61C2×C22⋊C411yescharacteristic
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—41no—
149C22×D61—41no—
150C22×D61#10412yes—
151D4×C61—22no—
152D4×C61—22no—
153D4×C61—41no—
154D4×C61—41no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—82no—
163C2×C4×C61—82no—
164C2×C4×C61C4×D411yescharacteristic
165C2×C4×C61C4×D411yescharacteristic
166C2×C4×C61#12011yescharacteristic
167C2×C4×C61#12111yescharacteristic
168C2×C4×C61#12111yescharacteristic
169C2×C4×C61#12311yescharacteristic
170C22⋊D61—84no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—21no—
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#10412yes—
184C4×D61—22no—
185C4×D61—22no—
186C4×D61—24no—
187C8×C61—24no—
188C8×C61—81no—
189#92418—24no—
190#92418—81no—
191#9492—611nomaximal, Sylow
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—42no—
195C22×C61—42no—
196C22×C61—42no—
197C22×C61—81no—
198C22×C61—81no—
199C22×C61—81no—
200C22×C61—81no—
201C22×C61#38611yescharacteristic
202C22×C61C2×#10411yescharacteristic
203C22×C61C2×#10411yescharacteristic
204C2×D61—22no—
205C2×D61—41no—
206C2×D61—41no—
207C2×D61—42no—
208C2×D61—81no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—81no—
216Dic61—22no—
217Dic61—41no—
218Dic61—41no—
219Dic61—81no—
220Dic61—81no—
221#2873—611no—
222#2598—611no—
223#1490—611no—
224#1490D6111yescharacteristic, complemented
225#1464—611no—
226#1288—611no—
227#1288—611no—
228C2×C61—21no—
229C2×C61—21no—
230C2×C61—82no—
231C2×C61#189111yescharacteristic
232C2×C61#189611yescharacteristic
233C2×C61#191011yescharacteristic
234D61—42no—
235C22×M16—1221no—
236C2×C4×D4C2×D6111yescharacteristic
237C2×#117—611no—
238#432—611no—
239#432C2×D6111yescharacteristic
240#405—1222no—
241#405—1222no—
242C4×M16—611no—
243C4×M16—1221no—
244C4×M16C2×D6111yescharacteristic
245#400—611no—
246#399—611no—
247#394—611no—
248#392—611no—
249#388—1221no—
250#386—1221no—
251#386—1221no—
252#385—1221no—
253#383—611no—
254D4⋊C8—22no—
255D4⋊C8—1222no—
256#324—1221no—
257#323—1221no—
258C61#949211yescharacteristic, complemented, Sylow
259C22×D4—1221no—
260C22×D4C4×D6111yescharacteristic
261C23×C4—21no—
262C23×C4—611no—
263C2×M16—21no—
264C2×M16—1222no—
265C2×M16—1224no—
266C2×M16—1224no—
267C2×M16—1221no—
268C22×C8—1222no—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4—21no—
272C4×D4—21no—
273#117—1221no—
274#117—1221no—
275#117—1221no—
276#117—1221no—
277C2×C4⋊C4—611no—
278C2×C4⋊C4—611no—
279C2×C4⋊C4—1221no—
280C2×C4⋊C4C4×D6111yescharacteristic
281C2×C22⋊C4—21no—
282C2×C22⋊C4—611no—
283C2×C22⋊C4—611no—
284C2×C22⋊C4—1221no—
285C2×C22⋊C4—1221no—
286C2×C22⋊C4—1221no—
287C2×C22⋊C4—1221no—
288C2×C42—611no—
289C2×C42C22×D6111yescharacteristic
290C4⋊C8—21no—
291C4⋊C8—1221no—
292C22⋊C8—21no—
293C22⋊C8—1221no—
294#97—21no—
295#97—21no—
296#97—1222no—
297#97—1221no—
298#97—1221no—
299C4×C8—612no—
300C4×C8—1222no—
301C4×C8C22⋊D6112yescomplemented
302#95—611no—
303#95—611no—
304#95—1221no—
305#95—1221no—
306#95—1221no—
307#95—1221no—
308C24—21no—
309C24—611no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—42no—
313C2×D4—4881no—
314C2×D4—2442no—
315C2×D4—2442no—
316C22×C4—21no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—81no—
320C22×C4—81no—
321C22×C4—611no—
322C22×C4—611no—
323C22×C4—611no—
324C22×C4—1222no—
325C22×C4—1222no—
326C22×C4—1221no—
327C22×C4—1221no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4C2×C4×D6111yescharacteristic
331C22×C4D4×D6111yescharacteristic
332C22×C4D4×D6111yescharacteristic
333M16—22no—
334M16—22no—
335M16—1228no—
336M16—1222no—
337M16—1222no—
338C2×C8—22no—
339C2×C8—41no—
340C2×C8—1228no—
341C2×C8—1222no—
342C2×C8—2441no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—1221no—
346C4⋊C4—1221no—
347C4⋊C4—1221no—
348C4⋊C4—1221no—
349C4⋊C4—4881no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—1221no—
353C22⋊C4—1221no—
354C22⋊C4—1221no—
355C22⋊C4—1221no—
356C22⋊C4—4881no—
357C22⋊C4—4881no—
358C22⋊C4—2442no—
359C22⋊C4—2442no—
360C42—1221no—
361C42—1221no—
362C42#1175822211yescharacteristic
363C42D4×D6111yescharacteristic
364C42#1175822411yescharacteristic
365C42C2×C22⋊D6111yescharacteristic
366C23—22no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—612no—
374C23—1221no—
375C23—1221no—
376C23—2441no—
377C23—2441no—
378C23C22⋊C4×D6111yescharacteristic
379D4—22no—
380D4—22no—
381D4—41no—
382D4—41no—
383D4—4884no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—82no—
392C2×C4—82no—
393C2×C4—612no—
394C2×C4—1222no—
395C2×C4—1222no—
396C2×C4—1224no—
397C2×C4—1221no—
398C2×C4—1221no—
399C2×C4—1221no—
400C2×C4—1221no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4#1451973711yescharacteristic
410C2×C4C4×C22⋊D6111yescharacteristic
411C2×C4#1451974511yescharacteristic
412C2×C4#1451974811yescharacteristic
413C2×C4#1451975011yescharacteristic
414C2×C4#1451975911yescharacteristic
415C8—24no—
416C8—81no—
417C8—1224no—
418C8—4881no—
419C22—21no—
420C22—21no—
421C22—42no—
422C22—42no—
423C22—42no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22—1222no—
429C22—4881no—
430C22—2442no—
431C22—2441no—
432C22—2441no—
433C22#1683963811yescharacteristic
434C22#104×D6111yescharacteristic
435C22#104×D6111yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—21no—
442C4—81no—
443C4—1222no—
444C4—4881no—
445C4—4881no—
446C4—2441no—
447C4—2441no—
448C2—21no—
449C2—21no—
450C2—82no—
451C2—2442no—
452C2#2144623411yescharacteristic
453C2#2144625911yescharacteristic
454C2#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#9492
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. #21454236C2semidirect
3. #21444262C2semidirect
4. #21444151C2semidirect
5. #21443685C2semidirect
6. #21443684C2semidirect
7. C61×#1490C2semidirect
57. C4×#92418D4semidirect
79. C4×C8×C61D4semidirect
224. #1490D61semidirect
258. C61#9492semidirect
301. C4×C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214542362
#214513792
#214442622
#214441512
#214436852
#214436842
C61×#14902
#949261