Finite Group Databasebeta

← #29580877

Subgroups — #29580877

Order 15616.

560 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 97 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#21455858C211yesmaximal, characteristic, complemented
2#21455827C211yesmaximal, characteristic
3#21446800C211yesmaximal, characteristic, complemented
4#21444248C211yesmaximal, characteristic, complemented
5#21444244C211yesmaximal, characteristic
6#21443648C211yesmaximal, characteristic, complemented
7C61×#2398C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16840097—21no—
10#16840092—21no—
11#16840057—21no—
12#16840052—21no—
13#16839972—21no—
14#16839967—21no—
15#16839918—21no—
16#16839913—21no—
17C4×#11758202—22no—
18C4×#11758200—22no—
19#16839815C2211yescharacteristic
20#16839815C2211yescharacteristic
21#16839786C2211yescharacteristic
22#16839522—22no—
23Q8⋊#92418—22no—
24D4⋊#92418—22no—
25C2×C4×Q8×C61C2211yescharacteristic
26C2×C4×D4×C61C2211yescharacteristic
27C61×#400—21no—
28C61×#397—21no—
29C61×#394—21no—
30C61×#393—21no—
31C4×C22⋊C4×C61—22no—
32C61×#376C2211yescharacteristic
33C2×#11758202—22no—
34C2×#11758200—22no—
35C2×#11758194—21no—
36#14519777D411yescharacteristic
37#14519777D411yescharacteristic
38#14519769—21no—
39#14519756—21no—
40#14519756—21no—
41C4×Dic122—21no—
42C4×Dic122—21no—
43#14519736—21no—
44#14519710—22no—
45#14519708—22no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49C4⋊#92418—21no—
50#14519701—22no—
51#14519700—22no—
52#14519700—22no—
53#14519698—22no—
54C22⋊#92418—21no—
55C22⋊#92418—21no—
56C4×#92418D412yes—
57C4×#92418D412yes—
58C22×Q8×C61D411yescharacteristic
59C22×D4×C61D411yescharacteristic
60C23×C4×C61—21no—
61C4×Q8×C61—21no—
62C4×Q8×C61—21no—
63C4×Q8×C61—21no—
64C4×Q8×C61—21no—
65C4×D4×C61—21no—
66C4×D4×C61—21no—
67C4×D4×C61—21no—
68C4×D4×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61D411yescharacteristic
71C2×C4⋊C4×C61D411yescharacteristic
72C2×C22⋊C4×C61—22no—
73C2×C22⋊C4×C61—22no—
74C2×C22⋊C4×C61—21no—
75C2×C42×C61—21no—
76C2×C42×C61D412yes—
77C2×C42×C61C2311yescharacteristic
78#95×C61—22no—
79#95×C61—22no—
80#95×C61—21no—
81#95×C61—21no—
82C24×C61—21no—
83C2×Q8×C61—21no—
84C2×Q8×C61—21no—
85C2×Q8×C61—42no—
86C2×D4×C61—21no—
87C2×D4×C61—21no—
88C2×D4×C61—42no—
89C22×C4×C61—21no—
90C22×C4×C61—22no—
91C22×C4×C61—21no—
92C22×C4×C61—21no—
93C22×C4×C61—41no—
94C22×C4×C61—41no—
95C22×C4×C61—42no—
96C22×C4×C61—42no—
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C2×Dic122—21no—
101C2×Dic122—21no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—41no—
107C4⋊C4×C61—41no—
108C22⋊C4×C61—44no—
109C22⋊C4×C61—44no—
110C22⋊C4×C61—41no—
111C22⋊C4×C61—41no—
112C42×C61—22no—
113C42×C61—22no—
114C42×C61—41no—
115C42×C61—41no—
116C42×C61C2×D411yescharacteristic
117C42×C61C2×D411yescharacteristic
118C42×C61C2×D411yescharacteristic
119C42×C61#4111yescharacteristic
120C22⋊Dic61—41no—
121#11758202—44no—
122#11758200—44no—
123C4⋊Dic61—21no—
124C4⋊Dic61—21no—
125C4⋊Dic61—21no—
126C4⋊Dic61—21no—
127#11758196—41no—
128#11758196—41no—
129C4×Dic61—41no—
130#11758194—42no—
131C2×#92418—22no—
132C2×#92418—22no—
133C2×#92418—41no—
134C23×C61—22no—
135C23×C61—42no—
136C23×C61—41no—
137C23×C61—41no—
138C23×C61—42no—
139C23×C61#12011yescharacteristic
140Q8×C61—22no—
141Q8×C61—22no—
142Q8×C61—41no—
143Q8×C61—41no—
144D4×C61—22no—
145D4×C61—22no—
146D4×C61—41no—
147D4×C61—41no—
148C2×C4×C61—22no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—42no—
154C2×C4×C61—42no—
155C2×C4×C61—42no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—42no—
159C2×C4×C61—42no—
160C2×C4×C61—82no—
161C2×C4×C61—81no—
162C2×C4×C61—81no—
163C2×C4×C61#12011yescharacteristic
164C2×C4×C61#12011yescharacteristic
165C2×C4×C61#12111yescharacteristic
166C2×C4×C61#12111yescharacteristic
167C2×C4×C61#12111yescharacteristic
168C2×C4×C61#12711yescharacteristic
169C2×C4×C61#13512yes—
170C2×C4×C61#13712yes—
171C2×Dic61—41no—
172C2×Dic61—41no—
173Dic122—42no—
174Dic122—42no—
175#92418—42no—
176#92418—42no—
177#92418—81no—
178#10016—611nomaximal, Sylow
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—44no—
182C22×C61—42no—
183C22×C61—82no—
184C22×C61—81no—
185C22×C61—81no—
186C22×C61#39211yescharacteristic
187C22×C61#45212yes—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—42no—
193C4×C61—82no—
194C4×C61—81no—
195C4×C61—81no—
196C4×C61#46412yes—
197C4×C61#49511yescharacteristic
198C4×C61#49711yescharacteristic
199Dic61—81no—
200Dic61—81no—
201#3104—611no—
202#3101—611no—
203#2398D6111yescharacteristic
204#1995—611no—
205#1487—611no—
206#1486—611no—
207#1274—611no—
208C2×C61—22no—
209C2×C61—82no—
210C2×C61#201011yescharacteristic
211C2×C61#201011yescharacteristic
212C2×C61#201511yescharacteristic
213#533—611no—
214C2×C4×Q8C2×D6111yescharacteristic
215C2×C4×D4C2×D6111yescharacteristic
216#484—1221no—
217#483—1221no—
218#477—1221no—
219#476—1221no—
220#462—1221no—
221#461—1221no—
222#451—1221no—
223#450—1221no—
224C4×Q16—1222no—
225C4×SD16—1222no—
226#431—611no—
227#431—611no—
228#423—611no—
229#400—21no—
230#397—21no—
231#394—21no—
232#393—21no—
233C4×C22⋊C4—22no—
234#376C2×D6111yescharacteristic
235#339—1222no—
236Q8⋊C8—1222no—
237D4⋊C8—1222no—
238C61#1001611yescharacteristic, complemented, Sylow
239C22×Q8C22⋊D6111yescharacteristic
240C22×D4C22⋊D6111yescharacteristic
241C23×C4—21no—
242C2×Q16—1222no—
243C2×SD16—1222no—
244C2×M16—1221no—
245C4⋊Q8—611no—
246C4⋊Q8—611no—
247#125—1221no—
248C22⋊Q8—1221no—
249C22⋊Q8—1221no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8—21no—
254C4×Q8—1221no—
255C4×Q8—1221no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—21no—
259C4×D4—21no—
260#117—1221no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4C22⋊D6111yescharacteristic
263C2×C4⋊C4C22⋊D6111yescharacteristic
264C2×C22⋊C4—22no—
265C2×C22⋊C4—22no—
266C2×C22⋊C4—21no—
267C2×C42—21no—
268C2×C42C22⋊D6112yes—
269C2×C42C22×D6111yescharacteristic
270#107—1222no—
271#106—1222no—
272C4⋊C8—1221no—
273C4⋊C8—1221no—
274C4⋊C8—1221no—
275C4⋊C8—1221no—
276#103—1222no—
277#103—1222no—
278#103—1222no—
279#102—1222no—
280C22⋊C8—1221no—
281C22⋊C8—1221no—
282C4×C8—612no—
283C4×C8—612no—
284#95—22no—
285#95—22no—
286#95—21no—
287#95—21no—
288C24—21no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—42no—
292C2×Q8—1221no—
293C2×Q8—1221no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—42no—
297C22×C4—21no—
298C22×C4—22no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4C2×C22⋊D6111yescharacteristic
306C22×C4C2×C22⋊D6111yescharacteristic
307C22×C4C2×C22⋊D6111yescharacteristic
308Q16—2444no—
309SD16—2444no—
310M16—2442no—
311C2×C8—1222no—
312C2×C8—1222no—
313C2×C8—2441no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—1221no—
321C4⋊C4—1221no—
322C4⋊C4—1221no—
323C4⋊C4—1221no—
324C4⋊C4—2441no—
325C4⋊C4—2441no—
326C22⋊C4—44no—
327C22⋊C4—44no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—2441no—
331C42—22no—
332C42—22no—
333C42—41no—
334C42—41no—
335C42—2441no—
336C42D4×D6111yescharacteristic
337C42D4×D6111yescharacteristic
338C42D4×D6111yescharacteristic
339C42#1175822411yescharacteristic
340C23—22no—
341C23—42no—
342C23—41no—
343C23—42no—
344C23—41no—
345C23#1451974611yescharacteristic
346Q8—22no—
347Q8—22no—
348Q8—41no—
349Q8—41no—
350Q8—2442no—
351Q8—2442no—
352D4—22no—
353D4—22no—
354D4—41no—
355D4—41no—
356C2×C4—22no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—82no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4#1451974511yescharacteristic
374C2×C4#1451974511yescharacteristic
375C2×C4#1451974811yescharacteristic
376C2×C4#1451974911yescharacteristic
377C2×C4#1451974911yescharacteristic
378C2×C4#1451977311yescharacteristic
379C2×C4#1451979712yes—
380C2×C4#1451980712yes—
381C8—4881no—
382C8—2442no—
383C8—2442no—
384C22—21no—
385C22—21no—
386C22—44no—
387C22—42no—
388C22—82no—
389C22—81no—
390C22—81no—
391C22#1683967011yescharacteristic
392C22#1683992412yes—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—42no—
398C4—82no—
399C4—81no—
400C4—81no—
401C4—4881no—
402C4—4881no—
403C4#1683998112yes—
404C4#1684014411yescharacteristic
405C4#1684015711yescharacteristic
406C2—22no—
407C2—82no—
408C2#2144688411yescharacteristic
409C2#2144688411yescharacteristic
410C2#2144691311yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2398C2
socleC22×C61#392
prime radicalC22×D4×C61D4
hypercenter#2398D61
hypocenterC61#10016
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2398

Complements

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

NH ≅ G/Ntype
1. #21455858C2semidirect
3. #21446800C2semidirect
4. #21444248C2semidirect
6. #21443648C2semidirect
238. C61#10016semidirect

Maximal subgroups

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

subgroupindex
#214558582
#214558272
#214468002
#214442482
#214442442
#214436482
C61×#23982
#1001661