Finite Group Databasebeta

← #29575980

Subgroups — #29575980

Order 15616.

530 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 91 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#21454858C211yesmaximal, characteristic
2#21451739C211yesmaximal, characteristic
3C4×#14519691C211yesmaximal, characteristic
4#21444340C211yesmaximal, characteristic, complemented
5#21444338C211yesmaximal, characteristic, complemented
6#21443671C211yesmaximal, characteristic, complemented
7C61×#1284C211yesmaximal, characteristic, complemented
8C2×#14519756C2211yescharacteristic
9C2×C4×C22⋊D61C2211yescharacteristic
10#16839838—22no—
11#16839837—22no—
12#16839812—21no—
13C2×#14519691—21no—
14#16839726C2211yescharacteristic
15#16839724—21no—
16#16839694C411yescharacteristic, complemented
17#16839689C411yescharacteristic, complemented
18#16839687—21no—
19#16839683C411yescharacteristic, complemented
20#16839678—21no—
21#16839675C411yescharacteristic, complemented
22#16839647—21no—
23#16839636—21no—
24C4×C22⋊Dic61C2211yescharacteristic
25#16839528—21no—
26#16839500—22no—
27#16839498—22no—
28C61×#407C2211yescharacteristic
29C61×#381C2211yescharacteristic
30C4×C22⋊C4×C61C2211yescharacteristic
31C22×Dic122C2×C411yescharacteristic
32C22×C22⋊D61D411yescharacteristic
33C22×C4×D61D411yescharacteristic
34C2×#11758194—21no—
35C2×#11758189—22no—
36#14519756—21no—
37#14519756—21no—
38#14519756—21no—
39#14519756—21no—
40C4×C22⋊D61—21no—
41C4×C22⋊D61—21no—
42C4×C22⋊D61—21no—
43C4×C22⋊D61—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61—21no—
46C2×C4⋊Dic61C2×C411yescharacteristic
47C2×#11758196—21no—
48C2×#11758196C2×C411yescharacteristic
49C2×C22⋊Dic61—21no—
50C2×C22⋊Dic61—21no—
51C2×C22⋊Dic61D411yescharacteristic
52C2×#11758198—21no—
53C2×#11758198—21no—
54C2×#11758198C2×C411yescharacteristic
55C2×C4×Dic61—21no—
56C2×C4×Dic61D411yescharacteristic
57#14519706—22no—
58#14519691—24no—
59C22⋊#92418—21no—
60C22⋊#92418D412yes—
61#14519689—22no—
62C8×Dic61—22no—
63#14519684—21no—
64#14519684—21no—
65#14519684—21no—
66#14519684—21no—
67#14519684—21no—
68C23×C4×C61C2311yescharacteristic
69C2×M16×C61—21no—
70C2×C22⋊C4×C61—21no—
71C2×C22⋊C4×C61—21no—
72C2×C42×C61—21no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61D412yes—
75#95×C61—21no—
76#95×C61—21no—
77#95×C61C2×C411yescharacteristic
78#95×C61C2×C411yescharacteristic
79C24×C61C2×D411yescharacteristic
80C23×D61C22⋊C411yescharacteristic
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—41no—
84C22×C4×C61—81no—
85C22×C4×C61C22×C411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61#4111yescharacteristic
90C22×C4×C61#4111yescharacteristic
91C2×C22⋊D61—21no—
92C2×C22⋊D61—21no—
93C2×C22⋊D61—22no—
94C2×C22⋊D61—41no—
95C22×Dic61—21no—
96C22×Dic61—21no—
97C22×Dic61—41no—
98C22×Dic61C22⋊C411yescharacteristic
99C22×Dic61C22⋊C411yescharacteristic
100C22×Dic61C22⋊C411yescharacteristic
101C2×C4×D61—21no—
102C2×C4×D61—21no—
103C2×C4×D61—81no—
104C2×Dic122—21no—
105C2×Dic122—21no—
106C2×Dic122—81no—
107M16×C61—81no—
108C2×C8×C61—22no—
109C22⋊C4×C61—22no—
110C22⋊C4×C61—41no—
111C22⋊C4×C61—81no—
112C42×C61—81no—
113C22⋊Dic61—21no—
114C22⋊Dic61—21no—
115C22⋊Dic61—22no—
116C22⋊Dic61—41no—
117C22⋊Dic61—41no—
118C22⋊Dic61—41no—
119#11758198—21no—
120#11758198—21no—
121#11758198—42no—
122#11758198—81no—
123C4⋊Dic61—21no—
124C4⋊Dic61—21no—
125C4⋊Dic61—42no—
126C4⋊Dic61—81no—
127#11758196—21no—
128#11758196—21no—
129#11758196—41no—
130#11758196—41no—
131C4×Dic61—21no—
132C4×Dic61—21no—
133C4×Dic61—81no—
134#11758194—81no—
135C2×#92418—22no—
136#11758189—82no—
137C23×C61—21no—
138C23×C61—21no—
139C23×C61—41no—
140C23×C61—41no—
141C23×C61C2×C22⋊C411yescharacteristic
142C23×C61#12111yescharacteristic
143C23×C61#12111yescharacteristic
144C22×D61—21no—
145C22×D61—21no—
146C22×D61—21no—
147C22×D61—41no—
148C22×D61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—42no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—81no—
163C2×C4×C61—81no—
164C2×C4×C61C4×D411yescharacteristic
165C2×C4×C61C4×D411yescharacteristic
166C2×C4×C61#12011yescharacteristic
167C2×C4×C61#12311yescharacteristic
168C22⋊D61—42no—
169C22⋊D61—42no—
170C2×Dic61—21no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—42no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—81no—
184C2×Dic61—81no—
185C2×Dic61#10412yes—
186C4×D61—42no—
187C4×D61—81no—
188Dic122—81no—
189Dic122—81no—
190C8×C61—42no—
191#92418—42no—
192#9184—611nomaximal, Sylow
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61—21no—
197C22×C61—21no—
198C22×C61—21no—
199C22×C61—21no—
200C22×C61—21no—
201C22×C61—81no—
202C22×C61—81no—
203C22×C61#38611yescharacteristic
204C22×C61C2×#10411yescharacteristic
205C22×C61#42111yescharacteristic
206C2×D61—42no—
207C2×D61—41no—
208C2×D61—41no—
209C2×D61—41no—
210C2×D61—81no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—81no—
216C4×C61—81no—
217C4×C61—82no—
218Dic61—22no—
219Dic61—41no—
220Dic61—41no—
221Dic61—82no—
222Dic61—81no—
223Dic61—81no—
224#2975—611no—
225#2638—611no—
226C4×#99—611no—
227#1508—611no—
228#1508—611no—
229#1284—611no—
230#1284D6111yescharacteristic, complemented
231C2×C61—21no—
232C2×C61—21no—
233C2×C61—41no—
234C2×C61—41no—
235C2×C61#187111yescharacteristic
236C2×C61#190911yescharacteristic
237C2×C61#191311yescharacteristic
238D61—81no—
239C2×C22⋊Q8—611no—
240C2×C4×D4—611no—
241#436—1222no—
242#436—1222no—
243#431—1221no—
244C2×#99—1221no—
245#407—611no—
246#407—1221no—
247#407C2×D6111yescharacteristic
248#398—611no—
249#397—611no—
250#397—1221no—
251#395—611no—
252#394—1221no—
253#393—611no—
254#387—1221no—
255#385—1221no—
256#381C2×D6111yescharacteristic
257C4×C22⋊C4—611no—
258C4×C22⋊C4C2×D6111yescharacteristic
259#342—1221no—
260#328—1222no—
261#328—1222no—
262C61#918411yescharacteristic, complemented, Sylow
263C22×Q8—611no—
264C22×D4—611no—
265C23×C4—611no—
266C23×C4C22×D6111yescharacteristic
267C2×M16—21no—
268C2×M16—1222no—
269C2×M16—1221no—
270C22⋊Q8—1221no—
271C22⋊Q8—1221no—
272C22⋊Q8—1221no—
273C22⋊Q8—1221no—
274C4×D4—1221no—
275C4×D4—1221no—
276C4×D4—1221no—
277C4×D4—1221no—
278C2×C4⋊C4—611no—
279C2×C4⋊C4—611no—
280C2×C4⋊C4—1221no—
281C2×C4⋊C4—1221no—
282C2×C4⋊C4—1221no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—611no—
286C2×C22⋊C4—611no—
287C2×C22⋊C4—1221no—
288C2×C22⋊C4—1221no—
289C2×C22⋊C4—1221no—
290C2×C22⋊C4—1221no—
291C2×C42—21no—
292C2×C42—611no—
293C2×C42—1221no—
294C4⋊C8—1222no—
295#99—1224no—
296C22⋊C8—21no—
297C22⋊C8—612no—
298C22⋊C8—1222no—
299C22⋊C8—1221no—
300C22⋊C8D24412yes—
301C4×C8—1222no—
302#95—21no—
303#95—21no—
304#95—1221no—
305#95—1221no—
306#95—1221no—
307#95—1221no—
308#95—1221no—
309#95C4×D6111yescharacteristic
310#95C4×D6111yescharacteristic
311C24—611no—
312C24D4×D6111yescharacteristic
313C2×Q8—1221no—
314C2×Q8—1221no—
315C2×Q8—4881no—
316C2×D4—1222no—
317C2×D4—1221no—
318C2×D4—1221no—
319C2×D4—2441no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—41no—
323C22×C4—81no—
324C22×C4—611no—
325C22×C4—611no—
326C22×C4—611no—
327C22×C4—1221no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4—1221no—
331C22×C4—4881no—
332C22×C4—2441no—
333C22×C4C2×C4×D6111yescharacteristic
334C22×C4C2×D24411yescharacteristic
335C22×C4#1175822211yescharacteristic
336C22×C4D4×D6111yescharacteristic
337C22×C4D4×D6111yescharacteristic
338C22×C4#1175822611yescharacteristic
339M16—81no—
340M16—4882no—
341M16—4881no—
342C2×C8—22no—
343C2×C8—1222no—
344C4⋊C4—1221no—
345C4⋊C4—1221no—
346C4⋊C4—1221no—
347C4⋊C4—1221no—
348C4⋊C4—4881no—
349C4⋊C4—2442no—
350C4⋊C4—2441no—
351C4⋊C4—2441no—
352C22⋊C4—22no—
353C22⋊C4—41no—
354C22⋊C4—81no—
355C22⋊C4—1221no—
356C22⋊C4—1221no—
357C22⋊C4—1221no—
358C22⋊C4—1221no—
359C22⋊C4—1222no—
360C22⋊C4—4881no—
361C22⋊C4—2442no—
362C22⋊C4—2441no—
363C22⋊C4—2441no—
364C22⋊C4—2441no—
365C42—81no—
366C42—1221no—
367C42—1221no—
368C42—4881no—
369C23—21no—
370C23—21no—
371C23—41no—
372C23—41no—
373C23—1221no—
374C23—1221no—
375C23—1221no—
376C23—2441no—
377C23—2441no—
378C23C22⋊C4×D6111yescharacteristic
379C23#1451975011yescharacteristic
380C23#1451975211yescharacteristic
381Q8—4881no—
382Q8—4881no—
383D4—2442no—
384D4—2442no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—612no—
401C2×C4—1221no—
402C2×C4—1221no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—4881no—
406C2×C4—4881no—
407C2×C4—4881no—
408C2×C4—2442no—
409C2×C4—2442no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4—2441no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4#1451973911yescharacteristic
419C2×C4C4×D24411yescharacteristic
420C2×C4#1451974711yescharacteristic
421C2×C4#1451976211yescharacteristic
422C8—42no—
423C8—2442no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—81no—
433C22—81no—
434C22—4881no—
435C22—2442no—
436C22—2441no—
437C22—2441no—
438C22—2441no—
439C22#1683964011yescharacteristic
440C22#104×D6111yescharacteristic
441C22#1683977711yescharacteristic
442C4—21no—
443C4—21no—
444C4—21no—
445C4—21no—
446C4—81no—
447C4—81no—
448C4—82no—
449C4—1222no—
450C4—4882no—
451C4—4881no—
452C4—4881no—
453C4—2441no—
454C4—2441no—
455C2—21no—
456C2—21no—
457C2—41no—
458C2—41no—
459C2—4881no—
460C2#2144612011yescharacteristic
461C2#2144634011yescharacteristic
462C2#2144636011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1284C2
socleC22×C61#386
prime radicalC22×C22⋊D61D4
cosocleC23×C4×C61C23
hypercenter#1284D61
hypocenterC61#9184
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

Complements

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

NH ≅ G/Ntype
4. #21444340C2semidirect
5. #21444338C2semidirect
6. #21443671C2semidirect
7. C61×#1284C2semidirect
16. #16839694C4semidirect
17. #16839689C4semidirect
19. #16839683C4semidirect
21. #16839675C4semidirect
230. #1284D61semidirect
262. C61#9184semidirect

Maximal subgroups

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

subgroupindex
#214548582
#214517392
C4×#145196912
#214443402
#214443382
#214436712
C61×#12842
#918461