Finite Group Databasebeta

← #29583178

Subgroups — #29583178

Order 15616.

464 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 89 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#21451043C211yesmaximal, characteristic, complemented
2#21446654C211yesmaximal, characteristic
3#21444388C211yesmaximal, characteristic
4C2×#16839495C211yesmaximal, characteristic
5#21443686C211yesmaximal, characteristic, complemented
6#21443666C211yesmaximal, characteristic, complemented
7C61×#1294C211yesmaximal, characteristic, complemented
8C2×#14519751C2211yescharacteristic
9C2×#14519691—21no—
10C2×#14519691—21no—
11C2×C22⋊#92418C2211yescharacteristic
12#16839704—21no—
13#16839694—21no—
14#16839649—21no—
15#16839645—21no—
16#16839635—21no—
17#16839622—21no—
18#16839622C2211yescharacteristic
19C4×C22⋊Dic61C2211yescharacteristic
20#16839497—21no—
21#16839497—21no—
22#16839495—21no—
23#16839495—21no—
24C2×C22⋊C8×C61C2211yescharacteristic
25C61×#380C2211yescharacteristic
26C2×#95×C61C2211yescharacteristic
27C22×D244Q811yescharacteristic
28C22×C22⋊D61—21no—
29C22×#92418—21no—
30#14519751—21no—
31#14519751—21no—
32#14519751—21no—
33#14519751—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61Q811yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61D411yescharacteristic
42C2×C22⋊Dic61D411yescharacteristic
43C2×#11758198—21no—
44C2×C4×Dic61—21no—
45#14519691—42no—
46#14519691—42no—
47C22⋊#92418—21no—
48C22⋊#92418—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684D411yescharacteristic
55#14519684D411yescharacteristic
56C23×C4×C61—21no—
57C23×C4×C61C2311yescharacteristic
58C22×C8×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C22⋊C4×C61—21no—
61C22⋊C8×C61—21no—
62C22⋊C8×C61—21no—
63#95×C61—21no—
64#95×C61—21no—
65#95×C61D411yescharacteristic
66#95×C61D411yescharacteristic
67C24×C61C2×D411yescharacteristic
68C23×D61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—42no—
72C22×C4×C61—41no—
73C22×C4×C61—41no—
74C22×C4×C61—41no—
75C22×C4×C61—81no—
76C22×C4×C61—81no—
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×Q811yescharacteristic
80C22×C4×C61#4111yescharacteristic
81C22×C4×C61#4111yescharacteristic
82C22×C4×C61#4111yescharacteristic
83C2×C22⋊D61—41no—
84C2×C22⋊D61—41no—
85C2×C22⋊D61—41no—
86C2×C22⋊D61—41no—
87C2×C22⋊D61—41no—
88C2×C22⋊D61—41no—
89C22×Dic61—21no—
90C22×Dic61—21no—
91C22×Dic61—21no—
92C22×Dic61—21no—
93C22×Dic61—21no—
94C2×D244—21no—
95C2×D244—21no—
96C2×D244—81no—
97C2×C8×C61—41no—
98C2×C8×C61—81no—
99C4⋊C4×C61—81no—
100C22⋊C4×C61—41no—
101C22⋊C4×C61—41no—
102C22⋊Dic61—21no—
103C22⋊Dic61—21no—
104C22⋊Dic61—21no—
105C22⋊Dic61—21no—
106C22⋊Dic61—41no—
107C22⋊Dic61—41no—
108#11758198—41no—
109#11758198—41no—
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112C4⋊Dic61—42no—
113C4⋊Dic61—81no—
114C4⋊Dic61—81no—
115#11758196—42no—
116#11758196—81no—
117C4×Dic61—81no—
118C2×#92418—41no—
119C2×#92418—81no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61#12011yescharacteristic
123C23×C61C22⋊Q811yescharacteristic
124C23×C61#12411yescharacteristic
125C23×C61#13511yescharacteristic
126C23×C61#13511yescharacteristic
127C23×C61AGL(1,ℤ/8)11yescharacteristic
128C23×C61AGL(1,ℤ/8)11yescharacteristic
129C22×D61—41no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—81no—
133C22×D61—81no—
134C2×C4×C61—22no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—82no—
147C2×C4×C61—82no—
148C2×C4×C61—81no—
149C2×C4×C61—81no—
150C2×C4×C61—81no—
151C2×C4×C61C22⋊Q811yescharacteristic
152C2×C4×C61C22⋊Q811yescharacteristic
153C2×C4×C61#12411yescharacteristic
154C2×C4×C61#12411yescharacteristic
155C22⋊D61—81no—
156C22⋊D61—81no—
157C22⋊D61—81no—
158C22⋊D61—81no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
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—41no—
173C2×Dic61—41no—
174D244—81no—
175D244—81no—
176C8×C61—81no—
177#92418—81no—
178#10376—611nomaximal, Sylow
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—41no—
188C22×C61—41no—
189C22×C61#39311yescharacteristic
190C22×C61#44911yescharacteristic
191C22×C61#44911yescharacteristic
192C22×C61#47811yescharacteristic
193C22×C61#47811yescharacteristic
194C22×C61#48811yescharacteristic
195C22×C61#49011yescharacteristic
196C2×D61—81no—
197C2×D61—81no—
198C2×D61—81no—
199C2×D61—161no—
200C2×D61—161no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—21no—
204C4×C61—21no—
205C4×C61—42no—
206C4×C61—81no—
207C4×C61—161no—
208Dic61—81no—
209Dic61—81no—
210Dic61—81no—
211Dic61—81no—
212Dic61—81no—
213#2569—611no—
214#1964—611no—
215#1519—611no—
216C2×#327—611no—
217#1294D6111yescharacteristic, complemented
218#1289—611no—
219#1282—611no—
220C2×C61—21no—
221C2×C61—21no—
222C2×C61—21no—
223C2×C61—21no—
224C2×C61—21no—
225C2×C61—21no—
226C2×C61#202511yescharacteristic
227C2×C61#203111yescharacteristic
228C2×C61#203211yescharacteristic
229D61—161no—
230C2×#121—611no—
231C2×#99—1221no—
232C2×#99—1221no—
233C2×C22⋊C8—611no—
234C2×C22⋊C8C2×D6111yescharacteristic
235#400—1221no—
236#398—1221no—
237#387—1221no—
238#387—1221no—
239#385—1221no—
240#380—611no—
241#380—1221no—
242#380C2×D6111yescharacteristic
243C4×C22⋊C4—611no—
244C2×#95C2×D6111yescharacteristic
245#327—1221no—
246#327—1221no—
247#327—1221no—
248#327—1221no—
249C61#1037611yescharacteristic, complemented, Sylow
250C22×D4—611no—
251C22×D4—1221no—
252C23×C4—21no—
253C23×C4C22×D6111yescharacteristic
254C22×C8—21no—
255C22×C8—1221no—
256#121—1221no—
257#121—1221no—
258#121—1221no—
259#121—1221no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—611no—
262C2×C4⋊C4—1221no—
263C2×C4⋊C4—1221no—
264C2×C4⋊C4—1221no—
265C2×C4⋊C4—1221no—
266C2×C4⋊C4—1221no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—611no—
269C2×C22⋊C4—611no—
270C2×C22⋊C4—1221no—
271C2×C22⋊C4—1221no—
272C2×C42—1221no—
273#99—2442no—
274#99—2442no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8—1221no—
278C22⋊C8—1221no—
279#95—21no—
280#95—21no—
281#95—611no—
282#95—611no—
283#95—1221no—
284#95—1221no—
285#95—1221no—
286#95—1221no—
287#95—1221no—
288#95D24411yescharacteristic
289#95D24411yescharacteristic
290C24—1221no—
291C24D4×D6111yescharacteristic
292C2×D4—1221no—
293C2×D4—1221no—
294C2×D4—4881no—
295C2×D4—2441no—
296C2×D4—2441no—
297C2×D4—2441no—
298C2×D4—2441no—
299C2×D4—2441no—
300C2×D4—2441no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—42no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—81no—
308C22×C4—81no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4—1221no—
314C22×C4C2×D24411yescharacteristic
315C22×C4#1175822211yescharacteristic
316C22×C4#1175822211yescharacteristic
317C22×C4D4×D6111yescharacteristic
318C22×C4#1175822411yescharacteristic
319C22×C4Q8×D6111yescharacteristic
320C2×C8—41no—
321C2×C8—81no—
322C2×C8—4881no—
323C2×C8—2441no—
324C4⋊C4—81no—
325C4⋊C4—1221no—
326C4⋊C4—1221no—
327C4⋊C4—4881no—
328C4⋊C4—4881no—
329C4⋊C4—4881no—
330C4⋊C4—2442no—
331C4⋊C4—2442no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—1221no—
335C22⋊C4—1221no—
336C22⋊C4—1221no—
337C22⋊C4—1221no—
338C22⋊C4—2441no—
339C22⋊C4—2441no—
340C22⋊C4—2441no—
341C22⋊C4—2441no—
342C42—4881no—
343C23—41no—
344C23—41no—
345C23—4881no—
346C23—4881no—
347C23—2441no—
348C23—2441no—
349C23—2441no—
350C23#1451974711yescharacteristic
351C23#1451975511yescharacteristic
352C23#1451976311yescharacteristic
353C23#1451979811yescharacteristic
354C23#1451980011yescharacteristic
355C23#1451980111yescharacteristic
356C23#1451980411yescharacteristic
357D4—4881no—
358D4—4881no—
359D4—4881no—
360D4—4881no—
361D4—4881no—
362D4—4881no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4—2441no—
384C2×C4—2441no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4—2441no—
388C2×C4—2441no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4—2441no—
392C2×C4—2441no—
393C2×C4—2441no—
394C2×C4—2441no—
395C2×C4#1451975511yescharacteristic
396C2×C4#1451975711yescharacteristic
397C2×C4#1451976311yescharacteristic
398C2×C4#1451976511yescharacteristic
399C8—81no—
400C8—4881no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—9761no—
412C22—9761no—
413C22—4881no—
414C22—4881no—
415C22—4881no—
416C22#1683967511yescharacteristic
417C22#1683990811yescharacteristic
418C22#1683991011yescharacteristic
419C22#1684006111yescharacteristic
420C22#1684006511yescharacteristic
421C22#1684011811yescharacteristic
422C22#1684012511yescharacteristic
423C4—21no—
424C4—21no—
425C4—21no—
426C4—21no—
427C4—42no—
428C4—81no—
429C4—161no—
430C4—4881no—
431C4—4881no—
432C4—4881no—
433C4—4881no—
434C4—4881no—
435C2—21no—
436C2—21no—
437C2—21no—
438C2—21no—
439C2—21no—
440C2—21no—
441C2—9761no—
442C2#2144696411yescharacteristic
443C2#2144699211yescharacteristic
444C2#2144699711yescharacteristic
subgroupG/H
centerC22#16839675
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1294C2
socleC22×C61#393
prime radicalC2×#14519751C22
hypercenter#1294D61
hypocenterC61#10376
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
1. #21451043C2semidirect
5. #21443686C2semidirect
6. #21443666C2semidirect
7. C61×#1294C2semidirect
217. #1294D61semidirect
249. C61#10376semidirect

Maximal subgroups

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

subgroupindex
#214510432
#214466542
#214443882
C2×#168394952
#214436862
#214436662
C61×#12942
#1037661