Finite Group Databasebeta

← #29576000

Subgroups — #29576000

Order 15616.

478 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 91 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#21454903C211yesmaximal, characteristic, complemented
2#21451682C211yesmaximal, characteristic
3C4×#14519695C211yesmaximal, characteristic, complemented
4#21444418C211yesmaximal, characteristic
5#21444416C211yesmaximal, characteristic
6#21443683C211yesmaximal, characteristic, complemented
7C61×#1288C211yesmaximal, characteristic, complemented
8C2×#14519765C2211yescharacteristic
9C2×C4×Dic122C2211yescharacteristic
10#16839891—22no—
11#16839890—22no—
12#16839819C2211yescharacteristic
13#16839816—21no—
14#16839812—21no—
15C2×#14519695—21no—
16C4×#11758194C2211yescharacteristic
17#16839699—21no—
18#16839683C411yescharacteristic
19#16839683C411yescharacteristic
20#16839680C411yescharacteristic
21#16839680C411yescharacteristic
22#16839675—21no—
23#16839654—21no—
24#16839654—21no—
25#16839530—21no—
26#16839501—22no—
27#16839501—22no—
28C61×#432C2211yescharacteristic
29C4×M16×C61C2211yescharacteristic
30C61×#383C2211yescharacteristic
31C22×Dic122C2×C411yescharacteristic
32C22×Dic122D411yescharacteristic
33C22×D244C2×C411yescharacteristic
34C2×#11758194—21no—
35#14519765—21no—
36#14519765—21no—
37#14519765—21no—
38#14519765—21no—
39C4×Dic122—21no—
40C4×Dic122—21no—
41C4×Dic122—21no—
42C4×Dic122—21no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61D411yescharacteristic
46C2×#11758196C2×C411yescharacteristic
47C2×#11758196C2×C411yescharacteristic
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×#11758198—21no—
53C2×#11758198—21no—
54C2×C4×Dic61D411yescharacteristic
55C2×C4×Dic61D411yescharacteristic
56C4⋊#92418—21no—
57#14519706—22no—
58#14519706—22no—
59#14519695—24no—
60C22⋊#92418—21no—
61#14519688—21no—
62#14519688D412yes—
63#14519687—22no—
64C4×#92418—21no—
65C8×Dic61—22no—
66#14519684—21no—
67#14519684—21no—
68C2×M16×C61—21no—
69C2×C42×C61C2311yescharacteristic
70C4⋊C8×C61—21no—
71C22⋊C8×C61—21no—
72#97×C61—21no—
73#97×C61D412yes—
74C4×C8×C61—21no—
75#95×C61—21no—
76#95×C61—21no—
77#95×C61C2×C411yescharacteristic
78#95×C61C2×C411yescharacteristic
79C23×D61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61C22×C411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×Dic61—21no—
86C22×Dic61C22⋊C411yescharacteristic
87C22×Dic61C22⋊C411yescharacteristic
88C22×Dic61C22⋊C411yescharacteristic
89C22×Dic61C22⋊C411yescharacteristic
90C2×D244—21no—
91C2×D244—21no—
92C2×D244—81no—
93C2×Dic122—21no—
94C2×Dic122—21no—
95C2×Dic122—22no—
96C2×Dic122—21no—
97C2×Dic122—21no—
98C2×Dic122—41no—
99C2×Dic122—81no—
100M16×C61—22no—
101M16×C61—41no—
102C2×C8×C61—22no—
103C2×C8×C61—41no—
104C42×C61C2×D411yescharacteristic
105C42×C61C2×D411yescharacteristic
106C42×C61#4111yescharacteristic
107C42×C61#4111yescharacteristic
108#11758198—42no—
109#11758198—41no—
110#11758198—41no—
111#11758198—41no—
112#11758198—41no—
113#11758198—42no—
114#11758198—81no—
115#11758198—81no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118C4⋊Dic61—81no—
119C4⋊Dic61—81no—
120#11758196—21no—
121#11758196—21no—
122#11758196—21no—
123#11758196—21no—
124C4×Dic61—21no—
125C4×Dic61—21no—
126C4×Dic61—21no—
127C4×Dic61—21no—
128#11758194—22no—
129#11758194—41no—
130C2×#92418—22no—
131C2×#92418—41no—
132C23×C61C2×C22⋊C411yescharacteristic
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—41no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
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×C61C4×D411yescharacteristic
151C2×C4×C61C4×D411yescharacteristic
152C2×C4×C61#12011yescharacteristic
153C2×C4×C61#12111yescharacteristic
154C2×C4×C61#12111yescharacteristic
155C2×C4×C61#12311yescharacteristic
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61#10412yes—
169D244—81no—
170D244—81no—
171Dic122—42no—
172Dic122—42no—
173Dic122—81no—
174Dic122—81no—
175C8×C61—42no—
176C8×C61—42no—
177#92418—42no—
178#92418—42no—
179#9188—611nomaximal, Sylow
180C22×C61—21no—
181C22×C61—21no—
182C22×C61#38611yescharacteristic
183C22×C61C2×#10411yescharacteristic
184C22×C61#42111yescharacteristic
185C2×D61—81no—
186C2×D61—81no—
187C2×D61—81no—
188C2×D61—81no—
189C2×D61—81no—
190C2×D61—81no—
191C2×D61—81no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61—21no—
198C4×C61—81no—
199C4×C61—81no—
200Dic61—22no—
201Dic61—41no—
202Dic61—41no—
203Dic61—41no—
204Dic61—81no—
205#2983—611no—
206#2632—611no—
207C4×#101—611no—
208#1527—611no—
209#1527—611no—
210#1288—611no—
211#1288D6111yescharacteristic, complemented
212C2×C61—21no—
213C2×C61—21no—
214C2×C61#187111yescharacteristic
215C2×C61#191211yescharacteristic
216C2×C61#191411yescharacteristic
217D61—161no—
218C2×#124—611no—
219C2×C4×Q8—611no—
220#446—1222no—
221#446—1222no—
222#432—611no—
223#432—1221no—
224#432C2×D6111yescharacteristic
225#431—1221no—
226C2×#101—1221no—
227C4×M16—611no—
228C4×M16C2×D6111yescharacteristic
229#399—1221no—
230#395—611no—
231#395—611no—
232#394—611no—
233#394—611no—
234#393—1221no—
235#388—1221no—
236#388—1221no—
237#383C2×D6111yescharacteristic
238#343—1221no—
239#329—1222no—
240#329—1222no—
241C61#918811yescharacteristic, complemented, Sylow
242C22×Q8—611no—
243C22×Q8—611no—
244C22×D4—611no—
245C2×M16—21no—
246C2×M16—1221no—
247#124—1221no—
248#124—1221no—
249#124—1221no—
250#124—1221no—
251C4×Q8—1221no—
252C4×Q8—1221no—
253C4×Q8—1221no—
254C4×Q8—1221no—
255C2×C4⋊C4—611no—
256C2×C4⋊C4—611no—
257C2×C4⋊C4—611no—
258C2×C4⋊C4—1221no—
259C2×C4⋊C4—1221no—
260C2×C22⋊C4—1221no—
261C2×C22⋊C4—1221no—
262C2×C22⋊C4—1221no—
263C2×C22⋊C4—1221no—
264C2×C22⋊C4—1221no—
265C2×C22⋊C4—1221no—
266C2×C42—611no—
267C2×C42—611no—
268C2×C42C22×D6111yescharacteristic
269C4⋊C8—21no—
270C4⋊C8—1222no—
271C4⋊C8—1222no—
272C4⋊C8—1221no—
273#101—1224no—
274C22⋊C8—21no—
275C22⋊C8—1221no—
276#97—21no—
277#97—612no—
278#97—1222no—
279#97—1221no—
280#97D24412yes—
281C4×C8—21no—
282C4×C8—1222no—
283C4×C8—1221no—
284#95—21no—
285#95—21no—
286#95—1221no—
287#95—1221no—
288#95C4×D6111yescharacteristic
289#95C4×D6111yescharacteristic
290C24—1221no—
291C2×Q8—1222no—
292C2×Q8—1221no—
293C2×Q8—1221no—
294C2×Q8—1221no—
295C2×Q8—1221no—
296C2×Q8—4881no—
297C2×Q8—2441no—
298C2×D4—1221no—
299C2×D4—1221no—
300C2×D4—4881no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—611no—
304C22×C4—611no—
305C22×C4—611no—
306C22×C4—611no—
307C22×C4—1221no—
308C22×C4C2×C4×D6111yescharacteristic
309C22×C4D4×D6111yescharacteristic
310C22×C4D4×D6111yescharacteristic
311M16—22no—
312M16—41no—
313M16—1222no—
314M16—2441no—
315C2×C8—22no—
316C2×C8—41no—
317C2×C8—1222no—
318C2×C8—2441no—
319C4⋊C4—1221no—
320C4⋊C4—1221no—
321C4⋊C4—1221no—
322C4⋊C4—1221no—
323C4⋊C4—1221no—
324C4⋊C4—1221no—
325C4⋊C4—4881no—
326C4⋊C4—4881no—
327C22⋊C4—4881no—
328C22⋊C4—4881no—
329C22⋊C4—2442no—
330C22⋊C4—2442no—
331C22⋊C4—2441no—
332C22⋊C4—2441no—
333C22⋊C4—2441no—
334C22⋊C4—2441no—
335C42—1221no—
336C42—1221no—
337C42—1221no—
338C42—1221no—
339C42C2×D24411yescharacteristic
340C42#1175822211yescharacteristic
341C42D4×D6111yescharacteristic
342C42#1175822611yescharacteristic
343C23—2441no—
344C23—2441no—
345C23—2441no—
346C23—2441no—
347C23—2441no—
348C23—2441no—
349C23—2441no—
350C23C22⋊C4×D6111yescharacteristic
351Q8—4881no—
352Q8—4881no—
353Q8—2442no—
354Q8—2442no—
355D4—4881no—
356D4—4881no—
357C2×C4—21no—
358C2×C4—21no—
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—612no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4#1451973911yescharacteristic
381C2×C4C4×D24411yescharacteristic
382C2×C4#1451974711yescharacteristic
383C2×C4#1451975011yescharacteristic
384C2×C4#1451975211yescharacteristic
385C2×C4#1451976211yescharacteristic
386C8—42no—
387C8—42no—
388C8—2442no—
389C8—2442no—
390C22—21no—
391C22—21no—
392C22—4881no—
393C22—4881no—
394C22—4881no—
395C22—4881no—
396C22—4881no—
397C22—4881no—
398C22—4881no—
399C22#1683964011yescharacteristic
400C22#104×D6111yescharacteristic
401C22#1683977711yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—81no—
409C4—81no—
410C4—1222no—
411C4—4881no—
412C4—2441no—
413C4—2441no—
414C4—2441no—
415C2—21no—
416C2—21no—
417C2—9761no—
418C2#2144612011yescharacteristic
419C2#2144635511yescharacteristic
420C2#2144636511yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1288C2
socleC22×C61#386
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1288D61
hypocenterC61#9188
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1288

Complements

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

NH ≅ G/Ntype
1. #21454903C2semidirect
3. C4×#14519695C2semidirect
6. #21443683C2semidirect
7. C61×#1288C2semidirect
211. #1288D61semidirect
241. C61#9188semidirect

Maximal subgroups

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

subgroupindex
#214549032
#214516822
C4×#145196952
#214444182
#214444162
#214436832
C61×#12882
#918861