Finite Group Databasebeta

← #29583176

Subgroups — #29583176

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#21451038C211yesmaximal, characteristic, complemented
2#21446655C211yesmaximal, characteristic
3#21444388C211yesmaximal, characteristic
4C2×#16839497C211yesmaximal, characteristic
5#21443699C211yesmaximal, characteristic, complemented
6#21443687C211yesmaximal, characteristic, complemented
7C61×#1282C211yesmaximal, characteristic, complemented
8C2×#14519751C2211yescharacteristic
9C2×#14519691—21no—
10C2×#14519691—21no—
11#16839704—21no—
12#16839696—21no—
13#16839646—21no—
14#16839646—21no—
15#16839634—21no—
16#16839622C2211yescharacteristic
17#16839622C2211yescharacteristic
18#16839620—21no—
19C2×#14519684C2211yescharacteristic
20#16839497—21no—
21#16839497—21no—
22#16839497—21no—
23#16839497—21no—
24C2×C22⋊C8×C61C2211yescharacteristic
25C2×C22⋊C8×C61C2211yescharacteristic
26C4×C22⋊C4×C61C2211yescharacteristic
27C22×D244Q811yescharacteristic
28C22×C22⋊D61—21no—
29C23×Dic61—21no—
30#14519751—21no—
31#14519751—21no—
32#14519751—21no—
33#14519751—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61Q811yescharacteristic
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×#11758198—21no—
44#14519691—42no—
45#14519691—42no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684D411yescharacteristic
53#14519684D411yescharacteristic
54#14519684D411yescharacteristic
55#14519684D411yescharacteristic
56C23×C4×C61C2311yescharacteristic
57C22×C8×C61—21no—
58C22×C8×C61—21no—
59C2×C22⋊C4×C61D411yescharacteristic
60C2×C22⋊C4×C61D411yescharacteristic
61C2×C42×C61—21no—
62C22⋊C8×C61—21no—
63C22⋊C8×C61—21no—
64C22⋊C8×C61—21no—
65C22⋊C8×C61—21no—
66#95×C61—21no—
67C24×C61C2×D411yescharacteristic
68C23×D61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—81no—
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×Q811yescharacteristic
75C22×C4×C61#4111yescharacteristic
76C22×C4×C61#4111yescharacteristic
77C22×C4×C61#4111yescharacteristic
78C2×C22⋊D61—41no—
79C2×C22⋊D61—41no—
80C2×C22⋊D61—41no—
81C2×C22⋊D61—41no—
82C2×C22⋊D61—41no—
83C2×C22⋊D61—41no—
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—42no—
90C22×Dic61—41no—
91C22×Dic61—41no—
92C22×Dic61—41no—
93C22×Dic61—81no—
94C2×D244—21no—
95C2×D244—21no—
96C2×D244—81no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61—81no—
100C2×C8×C61—81no—
101C22⋊C4×C61—21no—
102C22⋊C4×C61—21no—
103C22⋊C4×C61—21no—
104C22⋊C4×C61—21no—
105C42×C61—81no—
106C22⋊Dic61—41no—
107C22⋊Dic61—41no—
108C22⋊Dic61—41no—
109C22⋊Dic61—41no—
110#11758198—41no—
111#11758198—41no—
112C4⋊Dic61—21no—
113C4⋊Dic61—21no—
114C4⋊Dic61—81no—
115C4⋊Dic61—81no—
116#11758196—42no—
117#11758196—42no—
118#11758196—81no—
119#11758196—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—41no—
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×C61C22⋊Q811yescharacteristic
147C2×C4×C61C22⋊Q811yescharacteristic
148C2×C4×C61#12411yescharacteristic
149C2×C4×C61#12411yescharacteristic
150C22⋊D61—81no—
151C22⋊D61—81no—
152C22⋊D61—81no—
153C22⋊D61—81no—
154C2×Dic61—22no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
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—82no—
170C2×Dic61—82no—
171C2×Dic61—81no—
172C2×Dic61—81no—
173C2×Dic61—81no—
174D244—81no—
175D244—81no—
176C8×C61—81no—
177C8×C61—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—81no—
206C4×C61—81no—
207Dic61—42no—
208Dic61—81no—
209Dic61—81no—
210Dic61—81no—
211Dic61—81no—
212Dic61—161no—
213#2569—611no—
214#1964—611no—
215#1519—611no—
216C2×#327—611no—
217#1294—611no—
218#1289—611no—
219#1282D6111yescharacteristic, complemented
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⋊C8C2×D6111yescharacteristic
234C2×C22⋊C8C2×D6111yescharacteristic
235#400—1221no—
236#398—1221no—
237#387—1221no—
238#387—1221no—
239#385—1221no—
240#380—611no—
241#380—611no—
242#380—1221no—
243C4×C22⋊C4C2×D6111yescharacteristic
244C2×#95—611no—
245#327—1221no—
246#327—1221no—
247#327—1221no—
248#327—1221no—
249C61#1037611yescharacteristic, complemented, Sylow
250C22×D4—611no—
251C22×D4—1221no—
252C23×C4—1221no—
253C23×C4C22×D6111yescharacteristic
254C22×C8—21no—
255C22×C8—21no—
256#121—1221no—
257#121—1221no—
258#121—1221no—
259#121—1221no—
260C2×C4⋊C4—611no—
261C2×C4⋊C4—1221no—
262C2×C4⋊C4—1221no—
263C2×C4⋊C4—1221no—
264C2×C4⋊C4—1221no—
265C2×C4⋊C4—1221no—
266C2×C4⋊C4—1221no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4—1221no—
269C2×C22⋊C4—1221no—
270C2×C22⋊C4D24411yescharacteristic
271C2×C22⋊C4D24411yescharacteristic
272C2×C42—21no—
273#99—2442no—
274#99—2442no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279#95—21no—
280#95—611no—
281#95—611no—
282#95—611no—
283#95—611no—
284#95—1221no—
285#95—1221no—
286#95—1221no—
287#95—1221no—
288#95—1221no—
289#95—1221no—
290C24—1221no—
291C24C2×D24411yescharacteristic
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—81no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4—1221no—
307C22×C4—1221no—
308C22×C4—1221no—
309C22×C4—4881no—
310C22×C4—2442no—
311C22×C4—2441no—
312C22×C4—2441no—
313C22×C4—2441no—
314C22×C4#1175822211yescharacteristic
315C22×C4#1175822211yescharacteristic
316C22×C4D4×D6111yescharacteristic
317C22×C4D4×D6111yescharacteristic
318C22×C4#1175822411yescharacteristic
319C22×C4Q8×D6111yescharacteristic
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—81no—
323C2×C8—81no—
324C4⋊C4—1221no—
325C4⋊C4—1221no—
326C4⋊C4—4881no—
327C4⋊C4—4881no—
328C4⋊C4—4881no—
329C4⋊C4—4881no—
330C4⋊C4—2442no—
331C4⋊C4—2442no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—21no—
336C22⋊C4—2441no—
337C22⋊C4—2441no—
338C22⋊C4—2441no—
339C22⋊C4—2441no—
340C22⋊C4—2441no—
341C22⋊C4—2441no—
342C42—81no—
343C23—41no—
344C23—41no—
345C23—4881no—
346C23—4881no—
347C23—2441no—
348C23—2441no—
349C23—2441no—
350C23#1451974711yescharacteristic
351C23#1451975711yescharacteristic
352C23#1451976511yescharacteristic
353C23#1451979911yescharacteristic
354C23#1451979911yescharacteristic
355C23#1451980511yescharacteristic
356C23#1451980511yescharacteristic
357D4—4881no—
358D4—4881no—
359D4—4881no—
360D4—4881no—
361D4—4881no—
362D4—4881no—
363C2×C4—41no—
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—1222no—
376C2×C4—4881no—
377C2×C4—4881no—
378C2×C4—4881no—
379C2×C4—4882no—
380C2×C4—4882no—
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#1451975511yescharacteristic
397C2×C4#1451976311yescharacteristic
398C2×C4#1451976311yescharacteristic
399C8—81no—
400C8—81no—
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#1683990911yescharacteristic
418C22#1683990911yescharacteristic
419C22#1684006311yescharacteristic
420C22#1684006311yescharacteristic
421C22#1684011711yescharacteristic
422C22#1684012711yescharacteristic
423C4—21no—
424C4—21no—
425C4—21no—
426C4—21no—
427C4—81no—
428C4—81no—
429C4—9761no—
430C4—4881no—
431C4—4881no—
432C4—4881no—
433C4—4881no—
434C4—2442no—
435C2—21no—
436C2—21no—
437C2—21no—
438C2—21no—
439C2—21no—
440C2—21no—
441C2—9761no—
442C2#2144696611yescharacteristic
443C2#2144699411yescharacteristic
444C2#2144699711yescharacteristic
subgroupG/H
centerC22#16839675
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1282C2
socleC22×C61#393
prime radicalC2×#14519751C22
hypercenter#1282D61
hypocenterC61#10376
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1282

Complements

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

NH ≅ G/Ntype
1. #21451038C2semidirect
5. #21443699C2semidirect
6. #21443687C2semidirect
7. C61×#1282C2semidirect
219. #1282D61semidirect
249. C61#10376semidirect

Maximal subgroups

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

subgroupindex
#214510382
#214466552
#214443882
C2×#168394972
#214436992
#214436872
C61×#12822
#1037661