Finite Group Databasebeta

← #29575998

Subgroups — #29575998

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#21451680C211yesmaximal, characteristic
3C4×#14519695C211yesmaximal, characteristic, complemented
4#21444417C211yesmaximal, characteristic
5#21443685C211yesmaximal, characteristic, complemented
6#21443684C211yesmaximal, characteristic, complemented
7C61×#1527C211yesmaximal, characteristic
8C2×C4×Dic122C2211yescharacteristic
9#16839891—22no—
10#16839890—22no—
11#16839819C2211yescharacteristic
12#16839816—21no—
13#16839812—21no—
14C2×#14519695—21no—
15C4×#11758194C2211yescharacteristic
16#16839698—21no—
17#16839681C411yescharacteristic
18#16839681C411yescharacteristic
19#16839676C411yescharacteristic
20#16839676C411yescharacteristic
21#16839674—21no—
22#16839650—21no—
23#16839650—21no—
24#16839630C2211yescharacteristic
25#16839530—21no—
26#16839502—22no—
27C2×#124×C61C2211yescharacteristic
28C61×#432C2211yescharacteristic
29C4×M16×C61C2211yescharacteristic
30C61×#329—22no—
31C22×Dic122D411yescharacteristic
32C2×#11758194—21no—
33C4×Dic122—21no—
34C4×Dic122—21no—
35C4×Dic122—21no—
36C4×Dic122—21no—
37C2×C4⋊Dic61D411yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196C2×C411yescharacteristic
41C2×#11758196C2×C411yescharacteristic
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61—21no—
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C4⋊#92418—21no—
49#14519706—22no—
50#14519706—22no—
51#14519695—24no—
52C22⋊#92418—21no—
53#14519688—21no—
54#14519688D412yes—
55#14519687—22no—
56C4×#92418—21no—
57C8×Dic61—22no—
58#14519684—21no—
59#14519684—21no—
60#14519684—21no—
61#14519684—21no—
62#14519684C2×C411yescharacteristic
63#14519684C2×C411yescharacteristic
64C22×Q8×C61C2×C411yescharacteristic
65C22×D4×C61C2×C411yescharacteristic
66C2×M16×C61—21no—
67#124×C61—21no—
68#124×C61—21no—
69#124×C61—21no—
70#124×C61—21no—
71C2×C22⋊C4×C61—21no—
72C2×C22⋊C4×C61—21no—
73C2×C42×C61C2311yescharacteristic
74C4⋊C8×C61—21no—
75C22⋊C8×C61—21no—
76#97×C61—21no—
77#97×C61D412yes—
78C4×C8×C61—21no—
79C24×C61—21no—
80C2×Q8×C61—21no—
81C2×Q8×C61—21no—
82C2×Q8×C61—81no—
83C2×D4×C61—21no—
84C2×D4×C61—21no—
85C2×D4×C61—81no—
86C22×C4×C61—21no—
87C22×C4×C61C22×C411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×Dic61—21no—
91C22×Dic61—21no—
92C22×Dic61C22⋊C411yescharacteristic
93C22×Dic61C22⋊C411yescharacteristic
94C22×Dic61C22⋊C411yescharacteristic
95C22×Dic61C22⋊C411yescharacteristic
96C2×Dic122—21no—
97C2×Dic122—21no—
98C2×Dic122—22no—
99C2×Dic122—41no—
100M16×C61—22no—
101M16×C61—41no—
102C2×C8×C61—22no—
103C2×C8×C61—41no—
104C22⋊C4×C61—41no—
105C22⋊C4×C61—41no—
106C22⋊C4×C61—41no—
107C22⋊C4×C61—41no—
108C42×C61C2×D411yescharacteristic
109C42×C61C2×D411yescharacteristic
110C42×C61#4111yescharacteristic
111C42×C61#4111yescharacteristic
112C22⋊Dic61—42no—
113C22⋊Dic61—42no—
114C22⋊Dic61—81no—
115C22⋊Dic61—81no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118#11758196—21no—
119#11758196—21no—
120#11758196—21no—
121#11758196—21no—
122#11758196—81no—
123#11758196—81no—
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×C61—41no—
133C23×C61—41no—
134C23×C61—41no—
135C23×C61—41no—
136C23×C61—41no—
137C23×C61—41no—
138C23×C61—41no—
139C23×C61C2×C22⋊C411yescharacteristic
140Q8×C61—81no—
141Q8×C61—81no—
142D4×C61—81no—
143D4×C61—81no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61C4×D411yescharacteristic
152C2×C4×C61C4×D411yescharacteristic
153C2×C4×C61#12011yescharacteristic
154C2×C4×C61#12111yescharacteristic
155C2×C4×C61#12111yescharacteristic
156C2×C4×C61#12311yescharacteristic
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61#10412yes—
173Dic122—42no—
174Dic122—42no—
175C8×C61—42no—
176C8×C61—42no—
177#92418—42no—
178#92418—42no—
179#9188—611nomaximal, Sylow
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—81no—
183C22×C61—81no—
184C22×C61—81no—
185C22×C61—81no—
186C22×C61—81no—
187C22×C61—81no—
188C22×C61—81no—
189C22×C61#38611yescharacteristic
190C22×C61C2×#10411yescharacteristic
191C22×C61#42111yescharacteristic
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61—21no—
198C4×C61—81no—
199Dic61—22no—
200Dic61—41no—
201Dic61—41no—
202Dic61—41no—
203Dic61—81no—
204Dic61—81no—
205#2983—611no—
206#2632—611no—
207C4×#101—611no—
208#1527—611no—
209#1527D6111yescharacteristic
210#1288—611no—
211#1288—611no—
212C2×C61—21no—
213C2×C61—21no—
214C2×C61—161no—
215C2×C61#187111yescharacteristic
216C2×C61#191211yescharacteristic
217C2×C61#191411yescharacteristic
218C2×#124C2×D6111yescharacteristic
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#383—611no—
238#343—1221no—
239#329—22no—
240#329—1222no—
241C61#918811yescharacteristic, complemented, Sylow
242C22×Q8—611no—
243C22×Q8C4×D6111yescharacteristic
244C22×D4C4×D6111yescharacteristic
245C2×M16—21no—
246C2×M16—1221no—
247#124—21no—
248#124—21no—
249#124—21no—
250#124—21no—
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—21no—
261C2×C22⋊C4—21no—
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#97C22⋊D6112yes—
281C4×C8—21no—
282C4×C8—1222no—
283C4×C8—1221no—
284#95—611no—
285#95—611no—
286#95—1221no—
287#95—1221no—
288#95—1221no—
289#95—1221no—
290C24—21no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×Q8—81no—
294C2×Q8—1222no—
295C2×Q8—1221no—
296C2×Q8—1221no—
297C2×Q8—2441no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—81no—
301C22×C4—21no—
302C22×C4—611no—
303C22×C4—611no—
304C22×C4—611no—
305C22×C4—611no—
306C22×C4—1221no—
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—41no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—4881no—
332C22⋊C4—4881no—
333C22⋊C4—2442no—
334C22⋊C4—2442no—
335C42—1221no—
336C42—1221no—
337C42—1221no—
338C42—1221no—
339C42#1175822211yescharacteristic
340C42D4×D6111yescharacteristic
341C42#1175822411yescharacteristic
342C42C2×C22⋊D6111yescharacteristic
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23C22⋊C4×D6111yescharacteristic
351Q8—81no—
352Q8—81no—
353Q8—2442no—
354Q8—2442no—
355D4—81no—
356D4—81no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—612no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4#1451973711yescharacteristic
381C2×C4C4×C22⋊D6111yescharacteristic
382C2×C4#1451974511yescharacteristic
383C2×C4#1451974811yescharacteristic
384C2×C4#1451975011yescharacteristic
385C2×C4#1451975911yescharacteristic
386C8—42no—
387C8—42no—
388C8—2442no—
389C8—2442no—
390C22—21no—
391C22—21no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22#1683963811yescharacteristic
400C22#104×D6111yescharacteristic
401C22#1683977711yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—81no—
409C4—1222no—
410C4—4881no—
411C4—4881no—
412C4—2441no—
413C4—2441no—
414C4—2441no—
415C2—21no—
416C2—21no—
417C2—161no—
418C2#2144611811yescharacteristic
419C2#2144635311yescharacteristic
420C2#2144636311yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1527C2
socleC22×C61#386
prime radicalC22×D4×C61C2×C4
cosocleC2×C42×C61C23
hypercenter#1527D61
hypocenterC61#9188
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1527

Complements

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

NH ≅ G/Ntype
1. #21454903C2semidirect
3. C4×#14519695C2semidirect
5. #21443685C2semidirect
6. #21443684C2semidirect
241. C61#9188semidirect

Maximal subgroups

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

subgroupindex
#214549032
#214516802
C4×#145196952
#214444172
#214436852
#214436842
C61×#15272
#918861