Finite Group Databasebeta

← #29580917

Subgroups — #29580917

Order 15616.

576 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 81 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#21456205C211yesmaximal, characteristic, complemented
2#21455918C211yesmaximal, characteristic, complemented
3#21444443C211yesmaximal, characteristic, complemented
4#21444369C211yesmaximal, characteristic, complemented
5#21444262C211yesmaximal, characteristic, complemented
6#21443683C211yesmaximal, characteristic, complemented
7C61×#2631C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16840121—21no—
10#16840121—21no—
11#16840116—22no—
12#16840097—21no—
13#16840042—21no—
14#16839967—21no—
15#16839913—21no—
16#16839862—22no—
17#16839819C2211yescharacteristic
18#16839819C2211yescharacteristic
19#16839771—21no—
20#16839767—21no—
21C4×#11758194C2211yescharacteristic
22#16839502—22no—
23#16839498—22no—
24D4⋊#92418—22no—
25C2×#124×C61C2211yescharacteristic
26C2×C4×D4×C61C2211yescharacteristic
27C61×#397—21no—
28C61×#393—21no—
29C61×#392—21no—
30C61×#392—21no—
31C61×#386—22no—
32C61×#383C2211yescharacteristic
33C2×#11758200—22no—
34C2×#11758194—21no—
35#14519777D411yescharacteristic, complemented
36#14519777D411yescharacteristic, complemented
37#14519769—21no—
38#14519756—21no—
39#14519756—21no—
40C4×Dic122—21no—
41C4×Dic122—21no—
42#14519736—21no—
43#14519710—22no—
44C4⋊#92418—21no—
45C4⋊#92418—21no—
46#14519701—22no—
47#14519701—22no—
48#14519700—22no—
49#14519698—22no—
50#14519698—22no—
51#14519698—22no—
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54#14519688—21no—
55#14519688—21no—
56#14519688D412yescomplemented
57C4×#92418D412yescomplemented
58C22×Q8×C61D411yescharacteristic
59C22×D4×C61—22no—
60C22×D4×C61D411yescharacteristic
61C22×D4×C61D411yescharacteristic
62C23×C4×C61—21no—
63#124×C61—21no—
64#124×C61—21no—
65#124×C61—21no—
66#124×C61—21no—
67C4×D4×C61—21no—
68C4×D4×C61—21no—
69C4×D4×C61—21no—
70C4×D4×C61—21no—
71C2×C4⋊C4×C61D411yescharacteristic
72C2×C22⋊C4×C61—21no—
73C2×C22⋊C4×C61—21no—
74C2×C22⋊C4×C61—21no—
75C2×C22⋊C4×C61—22no—
76C2×C22⋊C4×C61—22no—
77C2×C42×C61C2311yescharacteristic
78#95×C61—22no—
79#95×C61—21no—
80#95×C61—21no—
81#95×C61D412yes—
82C24×C61—21no—
83C24×C61—21no—
84C2×Q8×C61—21no—
85C2×Q8×C61—21no—
86C2×Q8×C61—42no—
87C2×D4×C61—21no—
88C2×D4×C61—21no—
89C2×D4×C61—21no—
90C2×D4×C61—21no—
91C2×D4×C61—42no—
92C2×D4×C61—42no—
93C2×D4×C61—44no—
94C2×D4×C61—82no—
95C2×D4×C61—82no—
96C22×C4×C61—22no—
97C22×C4×C61—21no—
98C22×C4×C61—21no—
99C22×C4×C61—41no—
100C22×C4×C61—41no—
101C22×C4×C61—82no—
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61C2×D411yescharacteristic
105C2×Dic122—21no—
106C2×Dic122—21no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—21no—
109C22⋊C4×C61—41no—
110C22⋊C4×C61—41no—
111C22⋊C4×C61—41no—
112C22⋊C4×C61—41no—
113C22⋊C4×C61—41no—
114C22⋊C4×C61—41no—
115C22⋊C4×C61—82no—
116C22⋊C4×C61—82no—
117C42×C61C2×D411yescharacteristic
118C42×C61C2×D411yescharacteristic
119C42×C61C2×D411yescharacteristic
120C42×C61#4111yescharacteristic
121C22⋊Dic61—41no—
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—41no—
140C23×C61—41no—
141C23×C61—42no—
142C23×C61—41no—
143C23×C61—42no—
144C23×C61#12011yescharacteristic
145Q8×C61—42no—
146Q8×C61—81no—
147D4×C61—22no—
148D4×C61—22no—
149D4×C61—41no—
150D4×C61—41no—
151D4×C61—42no—
152D4×C61—81no—
153D4×C61—88no—
154C2×C4×C61—22no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—42no—
158C2×C4×C61—42no—
159C2×C4×C61—42no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—42no—
163C2×C4×C61—42no—
164C2×C4×C61—82no—
165C2×C4×C61—82no—
166C2×C4×C61#12011yescharacteristic
167C2×C4×C61#12011yescharacteristic
168C2×C4×C61#12111yescharacteristic
169C2×C4×C61#12111yescharacteristic
170C2×C4×C61#12111yescharacteristic
171C2×C4×C61#12711yescharacteristic
172C2×Dic61—41no—
173C2×Dic61—41no—
174Dic122—42no—
175Dic122—81no—
176#92418—42no—
177#92418—42no—
178#92418—81no—
179#10022—611nomaximal, Sylow
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—44no—
183C22×C61—42no—
184C22×C61—82no—
185C22×C61—82no—
186C22×C61—82no—
187C22×C61—81no—
188C22×C61—81no—
189C22×C61—81no—
190C22×C61—81no—
191C22×C61—81no—
192C22×C61#39211yescharacteristic
193C22×C61#45512yes—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—82no—
201C4×C61—81no—
202C4×C61—81no—
203Dic61—81no—
204Dic61—81no—
205#3140—611no—
206#3110—611no—
207#2631D6111yescharacteristic
208#1533—611no—
209#1515—611no—
210#1490—611no—
211#1288—611no—
212C2×C61—22no—
213C2×C61—82no—
214C2×C61—161no—
215C2×C61#200411yescharacteristic
216C2×C61#200811yescharacteristic
217C2×C61#201011yescharacteristic
218#533—611no—
219C2×#124C2×D6111yescharacteristic
220C2×C4×D4C2×D6111yescharacteristic
221#489—1221no—
222#489—1221no—
223#488—1222no—
224#484—1221no—
225#474—1221no—
226#461—1221no—
227#450—1221no—
228#440—1222no—
229#432—611no—
230#432—611no—
231#419—1221no—
232#418—1221no—
233C4×M16—611no—
234#397—21no—
235#393—21no—
236#392—21no—
237#392—21no—
238#386—22no—
239#383C2×D6111yescharacteristic
240#329—1222no—
241#328—1222no—
242D4⋊C8—1222no—
243C61#1002211yescharacteristic, complemented, Sylow
244C22×Q8C22⋊D6111yescharacteristic
245C22×D4—22no—
246C22×D4C22⋊D6111yescharacteristic
247C22×D4C22⋊D6111yescharacteristic
248C23×C4—21no—
249C2×SD16—1222no—
250C2×M16—1221no—
251C4⋊Q8—611no—
252C4⋊Q8—611no—
253#125—1221no—
254#124—21no—
255#124—21no—
256#124—21no—
257#124—21no—
258C22⋊Q8—1221no—
259C22⋊Q8—1221no—
260C4×Q8—1221no—
261C4×Q8—1221no—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—21no—
266#117—1221no—
267C2×C4⋊C4C22⋊D6111yescharacteristic
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—22no—
273C2×C42C22×D6111yescharacteristic
274#107—1222no—
275C4⋊C8—1221no—
276C4⋊C8—1221no—
277#103—1222no—
278#103—1222no—
279#103—1222no—
280#102—1222no—
281#102—1222no—
282#102—1222no—
283C22⋊C8—1221no—
284C22⋊C8—1221no—
285#97—612no—
286#97—1221no—
287#97—1221no—
288C4×C8—612no—
289#95—22no—
290#95—21no—
291#95—21no—
292#95C22⋊D6112yes—
293C24—21no—
294C24—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—42no—
298C2×Q8—1221no—
299C2×Q8—1221no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—42no—
305C2×D4—42no—
306C2×D4—44no—
307C2×D4—82no—
308C2×D4—82no—
309C22×C4—22no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—82no—
315C22×C4C2×C22⋊D6111yescharacteristic
316C22×C4C2×C22⋊D6111yescharacteristic
317C22×C4C2×C22⋊D6111yescharacteristic
318SD16—2444no—
319M16—2442no—
320C2×C8—1222no—
321C2×C8—1222no—
322C2×C8—2441no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—1221no—
326C4⋊C4—1221no—
327C4⋊C4—1221no—
328C4⋊C4—1221no—
329C4⋊C4—2441no—
330C4⋊C4—2441no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—82no—
338C22⋊C4—82no—
339C22⋊C4—2441no—
340C42—2441no—
341C42D4×D6111yescharacteristic
342C42D4×D6111yescharacteristic
343C42D4×D6111yescharacteristic
344C42#1175822411yescharacteristic
345C23—22no—
346C23—42no—
347C23—41no—
348C23—41no—
349C23—42no—
350C23—41no—
351C23—42no—
352C23—41no—
353C23—42no—
354C23—41no—
355C23#1451974611yescharacteristic
356Q8—42no—
357Q8—81no—
358Q8—4881no—
359Q8—2442no—
360D4—22no—
361D4—22no—
362D4—41no—
363D4—41no—
364D4—42no—
365D4—81no—
366D4—88no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—82no—
378C2×C4—82no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4#1451974511yescharacteristic
382C2×C4#1451974511yescharacteristic
383C2×C4#1451974811yescharacteristic
384C2×C4#1451974911yescharacteristic
385C2×C4#1451974911yescharacteristic
386C2×C4#1451977311yescharacteristic
387C8—4881no—
388C8—2442no—
389C8—2442no—
390C22—21no—
391C22—21no—
392C22—44no—
393C22—42no—
394C22—82no—
395C22—82no—
396C22—82no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22#1683967011yescharacteristic
403C22#1683994012yes—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—21no—
410C4—82no—
411C4—81no—
412C4—81no—
413C4—4881no—
414C4—4881no—
415C2—22no—
416C2—82no—
417C2—161no—
418C2#2144684611yescharacteristic
419C2#2144687211yescharacteristic
420C2#2144688411yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
Fitting, prime radicalC61×#2631C2
socleC22×C61#392
hypercenter#2631D61
hypocenterC61#10022
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2631

Complements

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

NH ≅ G/Ntype
1. #21456205C2semidirect
2. #21455918C2semidirect
3. #21444443C2semidirect
4. #21444369C2semidirect
5. #21444262C2semidirect
6. #21443683C2semidirect
35. #14519777D4semidirect
36. #14519777D4semidirect
56. #14519688D4semidirect
57. C4×#92418D4semidirect
243. C61#10022semidirect

Maximal subgroups

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

subgroupindex
#214562052
#214559182
#214444432
#214443692
#214442622
#214436832
C61×#26312
#1002261