Finite Group Databasebeta

← #29580771

Subgroups — #29580771

Order 15616.

632 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 101 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#21455827C211yesmaximal, characteristic, complemented
2#21455616C211yesmaximal, characteristic, complemented
3#21444382C211yesmaximal, characteristic, complemented
4#21444244C211yesmaximal, characteristic, complemented
5#21444210C211yesmaximal, characteristic, complemented
6#21443677C211yesmaximal, characteristic, complemented
7C61×#2535C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16840092—21no—
10#16840062—22no—
11#16840052—21no—
12#16840052—21no—
13#16840042—21no—
14#16839967—21no—
15#16839913—21no—
16C4×#11758200—22no—
17#16839815C2211yescharacteristic
18#16839815C2211yescharacteristic
19#16839802—21no—
20#16839786C2211yescharacteristic
21#16839767—21no—
22#16839498—22no—
23D4⋊#92418—22no—
24D4⋊#92418—22no—
25C2×#121×C61—21no—
26C2×C4×D4×C61C2211yescharacteristic
27C2×C4×D4×C61C2211yescharacteristic
28C61×#397—21no—
29C61×#392—21no—
30C61×#386—22no—
31C61×#382C2211yescharacteristic
32C61×#380—21no—
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—
44#14519708—22no—
45#14519708—22no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49C4⋊#92418D412yescomplemented
50#14519700—22no—
51#14519698—22no—
52#14519698—22no—
53#14519698—22no—
54C22⋊#92418—21no—
55C22⋊#92418—21no—
56C4×#92418—21no—
57C4×#92418D412yescomplemented
58C22×D4×C61—22no—
59C22×D4×C61D411yescharacteristic
60C22×D4×C61D411yescharacteristic
61C23×C4×C61—21no—
62C23×C4×C61—21no—
63#121×C61—42no—
64#121×C61—42no—
65C4×D4×C61—21no—
66C4×D4×C61—21no—
67C4×D4×C61—21no—
68C4×D4×C61—21no—
69C4×D4×C61—21no—
70C4×D4×C61—21no—
71C4×D4×C61—21no—
72C4×D4×C61—21no—
73C2×C4⋊C4×C61—21no—
74C2×C4⋊C4×C61D411yescharacteristic
75C2×C4⋊C4×C61D411yescharacteristic
76C2×C22⋊C4×C61—22no—
77C2×C22⋊C4×C61—21no—
78C2×C22⋊C4×C61—21no—
79C2×C22⋊C4×C61—22no—
80C2×C42×C61C2311yescharacteristic
81#95×C61—22no—
82#95×C61—21no—
83#95×C61D412yes—
84C24×C61—21no—
85C24×C61—21no—
86C2×D4×C61—21no—
87C2×D4×C61—21no—
88C2×D4×C61—21no—
89C2×D4×C61—21no—
90C2×D4×C61—21no—
91C2×D4×C61—21no—
92C2×D4×C61—21no—
93C2×D4×C61—42no—
94C2×D4×C61—44no—
95C2×D4×C61—44no—
96C2×D4×C61—82no—
97C2×D4×C61SD1612yescomplemented
98C22×C4×C61—22no—
99C22×C4×C61—21no—
100C22×C4×C61—21no—
101C22×C4×C61—41no—
102C22×C4×C61—41no—
103C22×C4×C61—41no—
104C22×C4×C61—41no—
105C22×C4×C61—41no—
106C22×C4×C61—41no—
107C22×C4×C61—41no—
108C22×C4×C61—41no—
109C22×C4×C61—82no—
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C2×Dic122—21no—
114C2×Dic122—21no—
115C4⋊C4×C61—21no—
116C4⋊C4×C61—21no—
117C4⋊C4×C61—21no—
118C4⋊C4×C61—21no—
119C4⋊C4×C61—41no—
120C4⋊C4×C61—41no—
121C22⋊C4×C61—44no—
122C22⋊C4×C61—41no—
123C22⋊C4×C61—41no—
124C22⋊C4×C61—41no—
125C22⋊C4×C61—41no—
126C22⋊C4×C61—82no—
127C42×C61C2×D411yescharacteristic
128C42×C61C2×D411yescharacteristic
129C42×C61C2×D411yescharacteristic
130C42×C61#4111yescharacteristic
131C22⋊Dic61—41no—
132#11758200—44no—
133C4⋊Dic61—21no—
134C4⋊Dic61—21no—
135C4⋊Dic61—21no—
136C4⋊Dic61—21no—
137#11758196—41no—
138#11758196—41no—
139C4×Dic61—41no—
140#11758194—41no—
141#11758194—41no—
142C2×#92418—22no—
143C2×#92418—22no—
144C2×#92418—41no—
145C23×C61—22no—
146C23×C61—22no—
147C23×C61—41no—
148C23×C61—42no—
149C23×C61—42no—
150C23×C61—41no—
151C23×C61—41no—
152C23×C61—41no—
153C23×C61—41no—
154C23×C61—41no—
155C23×C61—41no—
156C23×C61—41no—
157C23×C61#12011yescharacteristic
158D4×C61—22no—
159D4×C61—22no—
160D4×C61—22no—
161D4×C61—22no—
162D4×C61—41no—
163D4×C61—41no—
164D4×C61—41no—
165D4×C61—41no—
166D4×C61—88no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—42no—
170C2×C4×C61—42no—
171C2×C4×C61—42no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—42no—
176C2×C4×C61—41no—
177C2×C4×C61—82no—
178C2×C4×C61—82no—
179C2×C4×C61—81no—
180C2×C4×C61—81no—
181C2×C4×C61—81no—
182C2×C4×C61—81no—
183C2×C4×C61#12011yescharacteristic
184C2×C4×C61#12011yescharacteristic
185C2×C4×C61#12111yescharacteristic
186C2×C4×C61#12111yescharacteristic
187C2×C4×C61#12111yescharacteristic
188C2×C4×C61#12711yescharacteristic
189C2×C4×C61C2×SD1611yescharacteristic
190C2×C4×C61#13511yescharacteristic
191C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C61#13711yescharacteristic
193C2×Dic61—41no—
194C2×Dic61—41no—
195Dic122—42no—
196Dic122—81no—
197#92418—42no—
198#92418—42no—
199#92418—81no—
200#10000—611nomaximal, Sylow
201C22×C61—21no—
202C22×C61—21no—
203C22×C61—42no—
204C22×C61—44no—
205C22×C61—42no—
206C22×C61—42no—
207C22×C61—42no—
208C22×C61—81no—
209C22×C61—82no—
210C22×C61—81no—
211C22×C61—81no—
212C22×C61—81no—
213C22×C61—81no—
214C22×C61—81no—
215C22×C61#39211yescharacteristic
216C22×C61#45011yescharacteristic
217C22×C61#45211yescharacteristic
218C4×C61—21no—
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—21no—
222C4×C61—82no—
223C4×C61—81no—
224C4×C61—81no—
225C4×C61#44811yescharacteristic
226C4×C61#44911yescharacteristic
227C4×C61#46511yescharacteristic
228C4×C61#46811yescharacteristic
229Dic61—81no—
230Dic61—81no—
231#3101—611no—
232#3077—611no—
233#2535D6111yescharacteristic
234#1518—611no—
235#1486—611no—
236#1478—611no—
237#1286—611no—
238C2×C61—21no—
239C2×C61—21no—
240C2×C61—82no—
241C2×C61—82no—
242C2×C61#200011yescharacteristic
243C2×C61#200811yescharacteristic
244C2×C61#201011yescharacteristic
245#533—611no—
246C2×#121—21no—
247C2×C4×D4C2×D6111yescharacteristic
248C2×C4×D4C2×D6111yescharacteristic
249#483—1221no—
250#478—1222no—
251#476—1221no—
252#476—1221no—
253#474—1221no—
254#461—1221no—
255#450—1221no—
256C4×SD16—1222no—
257#431—611no—
258#431—611no—
259#428—1221no—
260#423—611no—
261#418—1221no—
262#397—21no—
263#392—21no—
264#386—22no—
265#382C2×D6111yescharacteristic
266#380—21no—
267#328—1222no—
268D4⋊C8—1222no—
269D4⋊C8—1222no—
270C61#1000011yescharacteristic, complemented, Sylow
271C22×D4—22no—
272C22×D4C22⋊D6111yescharacteristic
273C22×D4C22⋊D6111yescharacteristic
274C23×C4—21no—
275C23×C4—21no—
276C2×SD16—1222no—
277C2×M16—1221no—
278C4⋊Q8—611no—
279C4⋊Q8—611no—
280#125—1221no—
281C22⋊Q8—1221no—
282C22⋊Q8—1221no—
283#121—42no—
284#121—42no—
285C4×Q8—1221no—
286C4×Q8—1221no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4—21no—
290C4×D4—21no—
291C4×D4—21no—
292C4×D4—21no—
293C4×D4—21no—
294C4×D4—21no—
295#117—1221no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4C22⋊D6111yescharacteristic
298C2×C4⋊C4C22⋊D6111yescharacteristic
299C2×C22⋊C4—22no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—22no—
303C2×C42C22×D6111yescharacteristic
304#107—1222no—
305#106—1222no—
306#106—1222no—
307C4⋊C8—612no—
308C4⋊C8—1221no—
309C4⋊C8—1221no—
310C4⋊C8—1221no—
311#103—1222no—
312#102—1222no—
313#102—1222no—
314#102—1222no—
315C22⋊C8—1221no—
316C22⋊C8—1221no—
317C4×C8—612no—
318C4×C8—1221no—
319#95—22no—
320#95—21no—
321#95C22⋊D6112yes—
322C24—21no—
323C24—21no—
324C2×Q8—1221no—
325C2×Q8—1221no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—42no—
334C2×D4—44no—
335C2×D4—44no—
336C2×D4—82no—
337C2×D4#1175820012yescomplemented
338C22×C4—22no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—82no—
350C22×C4C2×C22⋊D6111yescharacteristic
351C22×C4C2×C22⋊D6111yescharacteristic
352C22×C4C2×C22⋊D6111yescharacteristic
353SD16—2444no—
354M16—2441no—
355M16—2441no—
356C2×C8—1222no—
357C2×C8—1222no—
358C2×C8—2441no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—1221no—
366C4⋊C4—1221no—
367C4⋊C4—1221no—
368C4⋊C4—1221no—
369C4⋊C4—2441no—
370C4⋊C4—2441no—
371C22⋊C4—44no—
372C22⋊C4—41no—
373C22⋊C4—41no—
374C22⋊C4—41no—
375C22⋊C4—41no—
376C22⋊C4—82no—
377C22⋊C4—2441no—
378C42—2441no—
379C42D4×D6111yescharacteristic
380C42D4×D6111yescharacteristic
381C42D4×D6111yescharacteristic
382C42#1175822411yescharacteristic
383C23—22no—
384C23—22no—
385C23—41no—
386C23—42no—
387C23—42no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23#1451974611yescharacteristic
396Q8—4881no—
397Q8—2442no—
398D4—22no—
399D4—22no—
400D4—22no—
401D4—22no—
402D4—41no—
403D4—41no—
404D4—41no—
405D4—41no—
406D4—88no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—82no—
418C2×C4—82no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—2441no—
424C2×C4—2441no—
425C2×C4#1451974511yescharacteristic
426C2×C4#1451974511yescharacteristic
427C2×C4#1451974811yescharacteristic
428C2×C4#1451974911yescharacteristic
429C2×C4#1451974911yescharacteristic
430C2×C4#1451977311yescharacteristic
431C2×C4C2×#1175820011yescharacteristic
432C2×C4#1451979711yescharacteristic
433C2×C4#1451980311yescharacteristic
434C2×C4#1451980711yescharacteristic
435C8—4881no—
436C8—2442no—
437C8—2442no—
438C22—21no—
439C22—21no—
440C22—42no—
441C22—44no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—81no—
446C22—82no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22#1683967011yescharacteristic
453C22#1683991311yescharacteristic
454C22#1683992411yescharacteristic
455C4—21no—
456C4—21no—
457C4—21no—
458C4—21no—
459C4—82no—
460C4—81no—
461C4—81no—
462C4—4881no—
463C4—4881no—
464C4#1683990011yescharacteristic
465C4#1683990511yescharacteristic
466C4#1683998911yescharacteristic
467C4#1684000611yescharacteristic
468C2—21no—
469C2—21no—
470C2—82no—
471C2—82no—
472C2#2144682211yescharacteristic
473C2#2144687211yescharacteristic
474C2#2144688411yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
Fitting, prime radicalC61×#2535C2
socleC22×C61#392
hypercenter#2535D61
hypocenterC61#10000
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. #21455827C2semidirect
2. #21455616C2semidirect
3. #21444382C2semidirect
4. #21444244C2semidirect
5. #21444210C2semidirect
6. #21443677C2semidirect
35. #14519777D4semidirect
36. #14519777D4semidirect
49. C4⋊#92418D4semidirect
57. C4×#92418D4semidirect
97. C2×D4×C61SD16semidirect
270. C61#10000semidirect
337. C2×D4#11758200semidirect

Maximal subgroups

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

subgroupindex
#214558272
#214556162
#214443822
#214442442
#214442102
#214436772
C61×#25352
#1000061