Finite Group Databasebeta

← #29580747

Subgroups — #29580747

Order 15616.

622 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 99 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#21455287C211yesmaximal, characteristic, complemented
2#21450728C211yesmaximal, characteristic, complemented
3#21444379C211yesmaximal, characteristic, complemented
4#21444244C211yesmaximal, characteristic, complemented
5#21444215C211yesmaximal, characteristic, complemented
6#21443678C211yesmaximal, characteristic, complemented
7C61×#3100C211yesmaximal, characteristic
8C2×#14519807—21no—
9C2×#14519756—21no—
10C2×C4×Dic122C2211yescharacteristic
11#16839981—22no—
12#16839969—21no—
13#16839959—21no—
14#16839815C2211yescharacteristic
15#16839786C2211yescharacteristic
16#16839763—21no—
17#16839693—21no—
18#16839676—21no—
19#16839650—22no—
20#16839628C2211yescharacteristic
21#16839622—21no—
22#16839496—22no—
23#16839494—22no—
24D4⋊#92418—22no—
25C61×#532C2211yescharacteristic
26C2×C4×D4×C61C2211yescharacteristic
27C61×#480—21no—
28C61×#474—21no—
29C61×#459—21no—
30C61×#447—21no—
31C4×D8×C61—22no—
32C61×#431C2211yescharacteristic
33C22×Dic122D411yescharacteristic
34#14519807—42no—
35#14519807—42no—
36C2×#11758202—22no—
37C2×#11758200—22no—
38C2×#11758194—21no—
39#14519756—42no—
40#14519756—42no—
41C4×Dic122—21no—
42C4×Dic122—21no—
43C4×Dic122—21no—
44C4×Dic122—21no—
45C2×C4⋊Dic61—21no—
46C2×C4⋊Dic61D411yescharacteristic
47C2×#11758196—22no—
48C2×#11758196—21no—
49C2×C22⋊Dic61—22no—
50C2×C22⋊Dic61—22no—
51C2×C4×Dic61—21no—
52C4⋊#92418—21no—
53C4⋊#92418—21no—
54C4⋊#92418D412yes—
55#14519701—22no—
56#14519698—22no—
57C22⋊#92418—21no—
58C4×#92418—21no—
59#14519684—22no—
60#14519684—21no—
61#14519684D412yes—
62C2×#41×C61—21no—
63C22×D4×C61D411yescharacteristic
64C23×C4×C61—21no—
65C2×D8×C61—22no—
66C4⋊Q8×C61D411yescharacteristic
67#127×C61D411yescharacteristic
68#124×C61—21no—
69#121×C61—21no—
70#121×C61—21no—
71C4×D4×C61—21no—
72C4×D4×C61—21no—
73C4×D4×C61—21no—
74C4×D4×C61—21no—
75C4×D4×C61—21no—
76C4×D4×C61—21no—
77C2×C4⋊C4×C61D411yescharacteristic
78C2×C22⋊C4×C61—21no—
79C2×C42×C61C2311yescharacteristic
80#107×C61—22no—
81C4⋊C8×C61—21no—
82#102×C61—22no—
83#102×C61—22no—
84C22⋊C8×C61—21no—
85C4×C8×C61D412yes—
86C24×C61—21no—
87#41×C61—41no—
88#41×C61—41no—
89#41×C61—41no—
90#41×C61—41no—
91C2×Q8×C61—21no—
92C2×D4×C61—21no—
93C2×D4×C61—21no—
94C2×D4×C61—21no—
95C2×D4×C61—21no—
96C2×D4×C61—21no—
97C2×D4×C61—42no—
98C2×D4×C61—41no—
99C22×C4×C61—21no—
100C22×C4×C61—41no—
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×C61C2×D411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×Dic61—21no—
111C22×Dic61—22no—
112C22×Dic61—21no—
113C2×Dic122—21no—
114C2×Dic122—21no—
115C2×Dic122—21no—
116C2×Dic122—21no—
117C2×Dic122—21no—
118C2×Dic122D812yescomplemented
119D8×C61—44no—
120C2×C8×C61—22no—
121C4⋊C4×C61—21no—
122C4⋊C4×C61—21no—
123C4⋊C4×C61—21no—
124C4⋊C4×C61—21no—
125C22⋊C4×C61—41no—
126C22⋊C4×C61—41no—
127C22⋊C4×C61—41no—
128C22⋊C4×C61—41no—
129C42×C61C2×D411yescharacteristic
130C42×C61C2×D411yescharacteristic
131C42×C61C2×D411yescharacteristic
132C42×C61#4111yescharacteristic
133C22⋊Dic61—44no—
134C22⋊Dic61—44no—
135#11758202—44no—
136#11758200—44no—
137C4⋊Dic61—21no—
138C4⋊Dic61—21no—
139C4⋊Dic61—41no—
140C4⋊Dic61—41no—
141#11758196—44no—
142#11758196—41no—
143#11758196—41no—
144C4×Dic61—41no—
145C4×Dic61—41no—
146#11758194—41no—
147#11758194—41no—
148C2×#92418—22no—
149C2×#92418—41no—
150C23×C61—22no—
151C23×C61—41no—
152C23×C61—41no—
153C23×C61—41no—
154C23×C61—41no—
155C23×C61—41no—
156C23×C61—41no—
157C23×C61—41no—
158C23×C61#12011yescharacteristic
159Q8×C61—41no—
160Q8×C61—41no—
161D4×C61—22no—
162D4×C61—22no—
163D4×C61—41no—
164D4×C61—41no—
165D4×C61—42no—
166D4×C61—41no—
167D4×C61—41no—
168D4×C61—81no—
169D4×C61—81no—
170D4×C61—81no—
171C2×C4×C61—41no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—81no—
178C2×C4×C61—81no—
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×D811yescharacteristic
190C2×C4×C61#13511yescharacteristic
191C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
193C2×Dic61—22no—
194C2×Dic61—41no—
195C2×Dic61—41no—
196C2×Dic61—42no—
197C2×Dic61—42no—
198C2×Dic61—42no—
199C2×Dic61—41no—
200C2×Dic61—42no—
201Dic122—22no—
202Dic122—22no—
203Dic122—41no—
204Dic122—41no—
205C8×C61—42no—
206#92418—42no—
207#92418—81no—
208#9997—611nomaximal, Sylow
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—42no—
212C22×C61—42no—
213C22×C61—42no—
214C22×C61—81no—
215C22×C61—81no—
216C22×C61—81no—
217C22×C61—81no—
218C22×C61—81no—
219C22×C61—81no—
220C22×C61—81no—
221C22×C61#39211yescharacteristic
222C22×C61#44711yescharacteristic
223C22×C61#44911yescharacteristic
224C4×C61—21no—
225C4×C61—21no—
226C4×C61—21no—
227C4×C61—21no—
228C4×C61—81no—
229C4×C61—81no—
230C4×C61#44711yescharacteristic
231C4×C61#44911yescharacteristic
232C4×C61#46611yescharacteristic
233C4×C61#46911yescharacteristic
234Dic61—42no—
235Dic61—82no—
236Dic61—81no—
237#3100D6111yescharacteristic
238#3037—611no—
239#2536—611no—
240#1517—611no—
241#1486—611no—
242#1479—611no—
243#1286—611no—
244C2×C61—21no—
245C2×C61—21no—
246C2×C61—82no—
247C2×C61—161no—
248C2×C61#199911yescharacteristic
249C2×C61#200911yescharacteristic
250C2×C61#201011yescharacteristic
251C2×#137—1221no—
252#532C2×D6111yescharacteristic
253C2×C22⋊Q8—1221no—
254C2×C4×Q8—611no—
255C2×C4×D4C2×D6111yescharacteristic
256#480—21no—
257#474—21no—
258#464—1222no—
259#462—1221no—
260#460—1221no—
261#459—21no—
262#447—21no—
263C4×D8—22no—
264#431—611no—
265#431C2×D6111yescharacteristic
266#423—611no—
267#417—1221no—
268#398—1221no—
269#394—1221no—
270#388—1222no—
271#382—611no—
272#380—1221no—
273#327—1222no—
274Q8⋊C8—1222no—
275D4⋊C8—1222no—
276C61#999711yescharacteristic, complemented, Sylow
277C2×#41—21no—
278C22×Q8—611no—
279C22×D4C22⋊D6111yescharacteristic
280C23×C4—21no—
281#137—2442no—
282#137—2442no—
283C2×Q16—1222no—
284C2×SD16—1222no—
285C2×D8—22no—
286C2×M16—1221no—
287C4⋊Q8C22⋊D6111yescharacteristic
288#127C22⋊D6111yescharacteristic
289#124—21no—
290C22⋊Q8—2442no—
291C22⋊Q8—2442no—
292#121—21no—
293#121—21no—
294C4×Q8—1221no—
295C4×Q8—1221no—
296C4×Q8—1221no—
297C4×Q8—1221no—
298C4×D4—21no—
299C4×D4—21no—
300C4×D4—21no—
301C4×D4—21no—
302C4×D4—21no—
303C4×D4—21no—
304C2×C4⋊C4—611no—
305C2×C4⋊C4—1222no—
306C2×C4⋊C4—1221no—
307C2×C4⋊C4—1221no—
308C2×C4⋊C4C22⋊D6111yescharacteristic
309C2×C22⋊C4—21no—
310C2×C22⋊C4—1222no—
311C2×C22⋊C4—1222no—
312C2×C42—1221no—
313C2×C42C22×D6111yescharacteristic
314#107—22no—
315C4⋊C8—21no—
316C4⋊C8—612no—
317C4⋊C8—1221no—
318C4⋊C8—1221no—
319#103—1222no—
320#102—22no—
321#102—22no—
322#102—1222no—
323C22⋊C8—21no—
324C22⋊C8—1221no—
325C4×C8—1221no—
326C4×C8C22⋊D6112yes—
327#95—612no—
328#95—1222no—
329#95—1221no—
330C24—21no—
331#41—41no—
332#41—41no—
333#41—41no—
334#41—41no—
335C2×Q8—21no—
336C2×Q8—612no—
337C2×Q8—1221no—
338C2×Q8—1221no—
339C2×Q8—1221no—
340C2×Q8—1221no—
341C2×Q8—1221no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—42no—
348C2×D4—41no—
349C22×C4—21no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—1221no—
358C22×C4—1222no—
359C22×C4—1221no—
360C22×C4D4×D6111yescharacteristic
361C22×C4D4×D6111yescharacteristic
362C22×C4C2×C22⋊D6111yescharacteristic
363Q16—2444no—
364SD16—2444no—
365D8—44no—
366M16—2441no—
367M16—2441no—
368C2×C8—22no—
369C2×C8—1222no—
370C2×C8—2441no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—1221no—
376C4⋊C4—1221no—
377C4⋊C4—2444no—
378C4⋊C4—2441no—
379C4⋊C4—2441no—
380C4⋊C4—2441no—
381C4⋊C4—2441no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—2444no—
387C22⋊C4—2444no—
388C42—2441no—
389C42—2441no—
390C42D4×D6111yescharacteristic
391C42#1175822411yescharacteristic
392C42C2×C22⋊D6111yescharacteristic
393C42C2×C22⋊D6111yescharacteristic
394C23—22no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23#1451974511yescharacteristic
403Q8—41no—
404Q8—41no—
405Q8—1222no—
406Q8—1222no—
407Q8—2441no—
408Q8—2441no—
409D4—22no—
410D4—22no—
411D4—41no—
412D4—41no—
413D4—42no—
414D4—41no—
415D4—41no—
416D4—81no—
417D4—81no—
418D4—81no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—81no—
431C2×C4—1222no—
432C2×C4—2442no—
433C2×C4—2442no—
434C2×C4—2442no—
435C2×C4—2442no—
436C2×C4—2441no—
437C2×C4—2441no—
438C2×C4—2441no—
439C2×C4#1451974511yescharacteristic
440C2×C4#1451974611yescharacteristic
441C2×C4#1451974811yescharacteristic
442C2×C4#1451974911yescharacteristic
443C2×C4#1451974911yescharacteristic
444C2×C4#1451977311yescharacteristic
445C2×C4D8×D6111yescharacteristic
446C2×C4#1451979611yescharacteristic
447C2×C4#1451980111yescharacteristic
448C2×C4#1451980111yescharacteristic
449C8—42no—
450C8—4881no—
451C8—2442no—
452C22—21no—
453C22—21no—
454C22—42no—
455C22—42no—
456C22—42no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22#1683967011yescharacteristic
465C22#1683989411yescharacteristic
466C22#1683990411yescharacteristic
467C4—21no—
468C4—21no—
469C4—21no—
470C4—21no—
471C4—81no—
472C4—81no—
473C4—4882no—
474C4—4881no—
475C4—2442no—
476C4#1683989411yescharacteristic
477C4#1683990411yescharacteristic
478C4#1683999511yescharacteristic
479C4#1684001211yescharacteristic
480C2—21no—
481C2—21no—
482C2—82no—
483C2—161no—
484C2#2144681411yescharacteristic
485C2#2144687611yescharacteristic
486C2#2144688411yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
Fitting, prime radicalC61×#3100C2
socleC22×C61#392
hypercenter#3100D61
hypocenterC61#9997
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3100

Complements

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

NH ≅ G/Ntype
1. #21455287C2semidirect
2. #21450728C2semidirect
3. #21444379C2semidirect
4. #21444244C2semidirect
5. #21444215C2semidirect
6. #21443678C2semidirect
118. C2×Dic122D8semidirect
276. C61#9997semidirect

Maximal subgroups

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

subgroupindex
#214552872
#214507282
#214443792
#214442442
#214442152
#214436782
C61×#31002
#999761