Finite Group Databasebeta

← #29589531

Subgroups — #29589531

Order 15616.

460 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 69 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#21450090C211yesmaximal, characteristic
2#21444150C211yesmaximal, characteristic, complemented
3#21444130C211yesmaximal, characteristic, complemented
4#21443768C211yesmaximal, characteristic, complemented
5#21443766C211yesmaximal, characteristic, complemented
6#21443747C211yesmaximal, characteristic
7C61×#1316C211yesmaximal, characteristic
8C2×#14519733C2211yescharacteristic
9C22×C22⋊Dic61C411yescharacteristic
10#16839816—21no—
11#16839812—21no—
12#16839698—21no—
13#16839690—21no—
14#16839656—21no—
15#16839655—21no—
16#16839637C411yescharacteristic
17#16839634C2211yescharacteristic
18#16839623C411yescharacteristic
19#16839618C411yescharacteristic
20#16839487—21no—
21#16839487—21no—
22#16839486C2211yescharacteristic
23#16839486C2211yescharacteristic
24C61×#379C2211yescharacteristic
25C61×#323C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C23×Dic61C2×C411yescharacteristic
28C23×Dic61C2×C411yescharacteristic
29#14519733—41no—
30#14519733—41no—
31C2×C4⋊Dic61—21no—
32C2×#11758196—21no—
33C2×#11758196D411yescharacteristic
34C2×#11758196D411yescharacteristic
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—41no—
40C2×C22⋊Dic61—41no—
41C2×C22⋊Dic61C2×C411yescharacteristic
42C2×C22⋊Dic61C2×C411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45#14519706—41no—
46#14519706—41no—
47C22⋊#92418—21no—
48C22⋊#92418—21no—
49#14519687—41no—
50C8×Dic61—41no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55C25×C61C2×C411yescharacteristic
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61C2×C411yescharacteristic
59C2×C22⋊C4×C61C2311yescharacteristic
60C22⋊C8×C61—21no—
61C22⋊C8×C61—21no—
62C24×C61—21no—
63C24×C61—21no—
64C24×C61—21no—
65C24×C61—42no—
66C24×C61—41no—
67C24×C61—41no—
68C24×C61—81no—
69C24×C61C22×C411yescharacteristic
70C22×C4×C61—21no—
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—41no—
80C22×Dic61—41no—
81C22×Dic61—81no—
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C22⋊C411yescharacteristic
86C2×C8×C61—41no—
87C2×C8×C61—41no—
88C22⋊C4×C61—41no—
89C22⋊C4×C61—42no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—81no—
92C22⋊Dic61—21no—
93C22⋊Dic61—21no—
94C22⋊Dic61—41no—
95C22⋊Dic61—42no—
96C22⋊Dic61—42no—
97C22⋊Dic61—41no—
98C22⋊Dic61—41no—
99C22⋊Dic61—81no—
100C4⋊Dic61—81no—
101#11758196—41no—
102#11758196—41no—
103#11758196—81no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C2×#92418—41no—
109C2×#92418—41no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—22no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—42no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61—42no—
123C23×C61—81no—
124C23×C61—81no—
125C23×C61—84no—
126C23×C61—82no—
127C23×C61—82no—
128C23×C61—81no—
129C23×C61—81no—
130C23×C61C2×C22⋊C411yescharacteristic
131C23×C61#13111yescharacteristic
132C23×C61#13111yescharacteristic
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—82no—
160C2×Dic61#9911yescharacteristic
161C2×Dic61#9911yescharacteristic
162C8×C61—81no—
163C8×C61—81no—
164#92418—81no—
165#92418—81no—
166#11542—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61—42no—
174C22×C61—42no—
175C22×C61—42no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61—42no—
179C22×C61—81no—
180C22×C61—81no—
181C22×C61—82no—
182C22×C61—82no—
183C22×C61—82no—
184C22×C61—82no—
185C22×C61—81no—
186C22×C61—81no—
187C22×C61#40811yescharacteristic
188C22×C61C2×#9911yescharacteristic
189C22×C61#41311yescharacteristic
190C4×C61—41no—
191C4×C61—41no—
192C4×C61—81no—
193Dic61—21no—
194Dic61—21no—
195Dic61—41no—
196Dic61—41no—
197Dic61—41no—
198Dic61—81no—
199Dic61—81no—
200#2482—611no—
201#1464—611no—
202#1458—611no—
203#1326—611no—
204#1326—611no—
205#1316—611no—
206#1316D6111yescharacteristic
207C2×C61—21no—
208C2×C61—21no—
209C2×C61—41no—
210C2×C61—41no—
211C2×C61—82no—
212C2×C61#146811yescharacteristic
213C2×C61#212011yescharacteristic
214C2×C61#212211yescharacteristic
215C2×#117—611no—
216C22×C22⋊C4—611no—
217#432—1221no—
218#431—1221no—
219#399—1221no—
220#397—1221no—
221#388—1221no—
222#388—1221no—
223#385—611no—
224#385—611no—
225#381—611no—
226#379—611no—
227#379C2×D6111yescharacteristic
228#324—1221no—
229#324—1221no—
230#323—611no—
231#323—611no—
232#323C2×D6111yescharacteristic
233#323C2×D6111yescharacteristic
234C61#1154211yescharacteristic, complemented, Sylow
235C25C4×D6111yescharacteristic
236C23×C4—611no—
237C23×C4—611no—
238#117—2441no—
239#117—2441no—
240C2×C4⋊C4—611no—
241C2×C4⋊C4—611no—
242C2×C4⋊C4—1221no—
243C2×C4⋊C4—1221no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—611no—
247C2×C22⋊C4—611no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1221no—
250C2×C22⋊C4—1221no—
251C2×C22⋊C4—1221no—
252C2×C22⋊C4—2441no—
253C2×C22⋊C4—2441no—
254C2×C22⋊C4C4×D6111yescharacteristic
255C2×C22⋊C4C22×D6111yescharacteristic
256C2×C42—611no—
257C2×C42—611no—
258C4⋊C8—2441no—
259C4⋊C8—2441no—
260C22⋊C8—21no—
261C22⋊C8—21no—
262C22⋊C8—1221no—
263C22⋊C8—1221no—
264#97—2441no—
265C4×C8—2441no—
266#95—1221no—
267#95—1221no—
268#95—1221no—
269#95—1221no—
270C24—21no—
271C24—21no—
272C24—21no—
273C24—41no—
274C24—42no—
275C24—41no—
276C24—81no—
277C24C2×C4×D6111yescharacteristic
278C22×C4—21no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—4881no—
290C22×C4—2441no—
291C22×C4—2441no—
292C22×C4D4×D6111yescharacteristic
293C22×C4D4×D6111yescharacteristic
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—2441no—
297C2×C8—2441no—
298C4⋊C4—4881no—
299C4⋊C4—4881no—
300C4⋊C4—2441no—
301C4⋊C4—2441no—
302C22⋊C4—41no—
303C22⋊C4—42no—
304C22⋊C4—41no—
305C22⋊C4—81no—
306C22⋊C4—1221no—
307C22⋊C4—1221no—
308C22⋊C4—4881no—
309C22⋊C4—2441no—
310C22⋊C4—2441no—
311C22⋊C4—2441no—
312C22⋊C4—2442no—
313C22⋊C4—2442no—
314C42—1221no—
315C42—1221no—
316C42—1221no—
317C42—1221no—
318C23—21no—
319C23—21no—
320C23—22no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—42no—
327C23—42no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—81no—
332C23—81no—
333C23—82no—
334C23—82no—
335C23—84no—
336C23—81no—
337C23—81no—
338C23C22⋊C4×D6111yescharacteristic
339C23#1451978311yescharacteristic
340C23#1451978511yescharacteristic
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—4882no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C8—81no—
371C8—81no—
372C8—4881no—
373C8—4881no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—42no—
381C22—42no—
382C22—42no—
383C22—41no—
384C22—41no—
385C22—42no—
386C22—81no—
387C22—81no—
388C22—82no—
389C22—82no—
390C22—82no—
391C22—82no—
392C22—81no—
393C22—81no—
394C22#1683972711yescharacteristic
395C22#99×D6111yescharacteristic
396C22#1683974311yescharacteristic
397C4—41no—
398C4—41no—
399C4—81no—
400C4—1221no—
401C4—1221no—
402C4—4881no—
403C4—4881no—
404C4—2441no—
405C4—2441no—
406C4—2441no—
407C2—21no—
408C2—21no—
409C2—41no—
410C2—41no—
411C2—82no—
412C2#2144416411yescharacteristic
413C2#2144745711yescharacteristic
414C2#2144746711yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC24×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1316C2
socleC22×C61C2×#99
prime radicalC25×C61C2×C4
cosocleC2×C22⋊C4×C61C23
hypercenter#1316D61
hypocenterC61#11542
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1316

Complements

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

NH ≅ G/Ntype
2. #21444150C2semidirect
3. #21444130C2semidirect
4. #21443768C2semidirect
5. #21443766C2semidirect
234. C61#11542semidirect

Maximal subgroups

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

subgroupindex
#214500902
#214441502
#214441302
#214437682
#214437662
#214437472
C61×#13162
#1154261