Finite Group Databasebeta

← #29580750

Subgroups — #29580750

Order 15616.

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

normal subgroups only

This group has 622 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#21455819C211yesmaximal, characteristic
2#21455291C211yesmaximal, characteristic, complemented
3#21444378C211yesmaximal, characteristic, complemented
4#21444244C211yesmaximal, characteristic, complemented
5#21444214C211yesmaximal, characteristic, complemented
6#21443677C211yesmaximal, characteristic, complemented
7C61×#2536C211yesmaximal, characteristic, complemented
8C2×#14519808—21no—
9#16840312C2211yescharacteristic
10#16840075—21no—
11#16840042—21no—
12#16839984—22no—
13#16839972—21no—
14#16839962—21no—
15#16839957—21no—
16#16839896—21no—
17C4×#11758199—22no—
18#16839815C2211yescharacteristic
19#16839815C2211yescharacteristic
20#16839786C2211yescharacteristic
21#16839761—21no—
22#16839495—22no—
23Q8⋊#92418—22no—
24D4⋊#92418—22no—
25C2×C22⋊Q8×C61—21no—
26C2×C4×Q8×C61C2211yescharacteristic
27C2×C4×D4×C61C2211yescharacteristic
28C61×#398—21no—
29C61×#394—21no—
30C61×#388—22no—
31C61×#382C2211yescharacteristic
32C61×#380—21no—
33C2×#11758222—21no—
34#14519808—42no—
35#14519808—42no—
36C2×#11758202—22no—
37C2×#11758201—22no—
38C2×#11758199—22no—
39C2×#11758194—21no—
40#14519777D411yescharacteristic
41#14519774D411yescharacteristic
42#14519765—21no—
43#14519751—21no—
44#14519751—21no—
45C4×D244—21no—
46C4×D244—21no—
47#14519710—22no—
48C4⋊#92418—21no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51C4⋊#92418D412yes—
52#14519700—22no—
53#14519698—22no—
54#14519697—22no—
55#14519697—22no—
56C22⋊#92418—21no—
57C22⋊#92418—21no—
58C4×#92418—21no—
59C4×#92418D412yes—
60C22×Q8×C61D411yescharacteristic
61C22×D4×C61D411yescharacteristic
62C23×C4×C61—21no—
63C22⋊Q8×C61—42no—
64C22⋊Q8×C61—42no—
65C4×Q8×C61—21no—
66C4×Q8×C61—21no—
67C4×Q8×C61—21no—
68C4×Q8×C61—21no—
69C4×D4×C61—21no—
70C4×D4×C61—21no—
71C4×D4×C61—21no—
72C4×D4×C61—21no—
73C2×C4⋊C4×C61—22no—
74C2×C4⋊C4×C61—21no—
75C2×C4⋊C4×C61—21no—
76C2×C4⋊C4×C61D411yescharacteristic
77C2×C4⋊C4×C61D411yescharacteristic
78C2×C22⋊C4×C61—22no—
79C2×C22⋊C4×C61—22no—
80C2×C22⋊C4×C61—21no—
81C2×C42×C61—21no—
82C2×C42×C61C2311yescharacteristic
83#95×C61—22no—
84#95×C61—21no—
85#95×C61D412yes—
86C24×C61—21no—
87C2×Q8×C61—21no—
88C2×Q8×C61—21no—
89C2×Q8×C61—21no—
90C2×Q8×C61—21no—
91C2×Q8×C61—21no—
92C2×Q8×C61D812yescomplemented
93C2×D4×C61—21no—
94C2×D4×C61—21no—
95C2×D4×C61—42no—
96C22×C4×C61—21no—
97C22×C4×C61—22no—
98C22×C4×C61—21no—
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×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C2×C22⋊D61—41no—
110#11758222—41no—
111#11758222—41no—
112#11758222—41no—
113#11758222—41no—
114C2×D244—21no—
115C2×D244—21no—
116C2×D244—21no—
117C2×C4×D61—41no—
118C2×Dic122—21no—
119C4⋊C4×C61—21no—
120C4⋊C4×C61—21no—
121C4⋊C4×C61—21no—
122C4⋊C4×C61—21no—
123C4⋊C4×C61—44no—
124C4⋊C4×C61—41no—
125C4⋊C4×C61—41no—
126C4⋊C4×C61—41no—
127C4⋊C4×C61—41no—
128C22⋊C4×C61—44no—
129C22⋊C4×C61—44no—
130C22⋊C4×C61—41no—
131C22⋊C4×C61—41no—
132C42×C61—41no—
133C42×C61—41no—
134C42×C61C2×D411yescharacteristic
135C42×C61C2×D411yescharacteristic
136C42×C61C2×D411yescharacteristic
137C42×C61#4111yescharacteristic
138#11758202—44no—
139#11758201—44no—
140#11758199—44no—
141#11758198—41no—
142#11758198—41no—
143C4⋊Dic61—21no—
144C4⋊Dic61—21no—
145#11758194—41no—
146#11758194—41no—
147C2×#92418—22no—
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#12011yescharacteristic
158C22×D61—41no—
159Q8×C61—22no—
160Q8×C61—22no—
161Q8×C61—41no—
162Q8×C61—41no—
163D4×C61—22no—
164D4×C61—22no—
165D4×C61—41no—
166D4×C61—41no—
167C2×C4×C61—22no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
172C2×C4×C61—42no—
173C2×C4×C61—42no—
174C2×C4×C61—42no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—42no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—81no—
181C2×C4×C61—81no—
182C2×C4×C61—81no—
183C2×C4×C61—81no—
184C2×C4×C61#12011yescharacteristic
185C2×C4×C61#12011yescharacteristic
186C2×C4×C61#12111yescharacteristic
187C2×C4×C61#12111yescharacteristic
188C2×C4×C61#12111yescharacteristic
189C2×C4×C61#12711yescharacteristic
190C2×C4×C61C2×D811yescharacteristic
191C2×C4×C61#13511yescharacteristic
192C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
193C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
194C22⋊D61—81no—
195C22⋊D61—81no—
196C2×Dic61—41no—
197D244—42no—
198D244—41no—
199D244—41no—
200D244—81no—
201C4×D61—81no—
202C4×D61—81no—
203Dic122—41no—
204Dic122—41no—
205#92418—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#39211yescharacteristic
219C22×C61#44711yescharacteristic
220C22×C61#44911yescharacteristic
221C2×D61—81no—
222C2×D61—81no—
223C2×D61—81no—
224C4×C61—21no—
225C4×C61—21no—
226C4×C61—21no—
227C4×C61—21no—
228C4×C61—42no—
229C4×C61—82no—
230C4×C61—81no—
231C4×C61—81no—
232C4×C61#44711yescharacteristic
233C4×C61#44911yescharacteristic
234C4×C61#46611yescharacteristic
235C4×C61#46911yescharacteristic
236Dic61—81no—
237#3100—611no—
238#3037—611no—
239#2536D6111yescharacteristic, complemented
240#1517—611no—
241#1486—611no—
242#1479—611no—
243#1286—611no—
244C2×C61—21no—
245C2×C61—21no—
246C2×C61—82no—
247C2×C61#199911yescharacteristic
248C2×C61#200911yescharacteristic
249C2×C61#201011yescharacteristic
250D61—161no—
251C2×#137—1221no—
252#532—611no—
253C2×C22⋊Q8—21no—
254C2×C4×Q8C2×D6111yescharacteristic
255C2×C4×D4C2×D6111yescharacteristic
256#480—1221no—
257#474—1221no—
258#464—1222no—
259#462—1221no—
260#460—1221no—
261#459—1221no—
262#447—1221no—
263C4×D8—1222no—
264#431—611no—
265#431—611no—
266#423—611no—
267#417—1221no—
268#398—21no—
269#394—21no—
270#388—22no—
271#382C2×D6111yescharacteristic
272#380—21no—
273#327—1222no—
274Q8⋊C8—1222no—
275D4⋊C8—1222no—
276C61#999711yescharacteristic, complemented, Sylow
277C2×#41—1221no—
278C22×Q8C22⋊D6111yescharacteristic
279C22×D4C22⋊D6111yescharacteristic
280C23×C4—21no—
281#137—2442no—
282#137—2442no—
283C2×Q16—1222no—
284C2×SD16—1222no—
285C2×D8—1222no—
286C2×M16—1221no—
287C4⋊Q8—611no—
288#127—611no—
289#124—1221no—
290C22⋊Q8—42no—
291C22⋊Q8—42no—
292#121—1221no—
293#121—1221no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8—21no—
298C4×D4—21no—
299C4×D4—21no—
300C4×D4—21no—
301C4×D4—21no—
302C4×D4—1221no—
303C4×D4—1221no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4C22⋊D6111yescharacteristic
308C2×C4⋊C4C22⋊D6111yescharacteristic
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—21no—
312C2×C42—21no—
313C2×C42C22×D6111yescharacteristic
314#107—1222no—
315C4⋊C8—612no—
316C4⋊C8—1221no—
317C4⋊C8—1221no—
318C4⋊C8—1221no—
319#103—1222no—
320#102—1222no—
321#102—1222no—
322#102—1222no—
323C22⋊C8—1221no—
324C22⋊C8—1221no—
325C4×C8—612no—
326C4×C8—1221no—
327#95—22no—
328#95—21no—
329#95C22⋊D6112yes—
330C24—21no—
331#41—2441no—
332#41—2441no—
333#41—2441no—
334#41—2441no—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—1221no—
341C2×Q8#1175819912yescomplemented
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—42no—
345C2×D4—1221no—
346C2×D4—1221no—
347C2×D4—1221no—
348C2×D4—2441no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—2441no—
360C22×C4C2×C22⋊D6111yescharacteristic
361C22×C4C2×C22⋊D6111yescharacteristic
362C22×C4C2×C22⋊D6111yescharacteristic
363Q16—2444no—
364SD16—2444no—
365D8—2444no—
366M16—2441no—
367M16—2441no—
368C2×C8—1222no—
369C2×C8—1222no—
370C2×C8—2441no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—44no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—1221no—
381C4⋊C4—1221no—
382C22⋊C4—44no—
383C22⋊C4—44no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—2441no—
387C22⋊C4—2441no—
388C42—41no—
389C42—41no—
390C42D4×D6111yescharacteristic
391C42D4×D6111yescharacteristic
392C42D4×D6111yescharacteristic
393C42#1175822411yescharacteristic
394C23—22no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—2441no—
402C23#1451974611yescharacteristic
403Q8—22no—
404Q8—22no—
405Q8—41no—
406Q8—41no—
407Q8—2441no—
408Q8—2441no—
409D4—22no—
410D4—22no—
411D4—41no—
412D4—41no—
413D4—4881no—
414D4—4881no—
415D4—4881no—
416D4—2442no—
417D4—2441no—
418D4—2441no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—81no—
433C2×C4—81no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4—4881no—
437C2×C4—4881no—
438C2×C4—2441no—
439C2×C4#1451974511yescharacteristic
440C2×C4#1451974511yescharacteristic
441C2×C4#1451974811yescharacteristic
442C2×C4#1451974911yescharacteristic
443C2×C4#1451974911yescharacteristic
444C2×C4#1451977311yescharacteristic
445C2×C4C2×#1175819911yescharacteristic
446C2×C4#1451979711yescharacteristic
447C2×C4#1451980211yescharacteristic
448C2×C4#1451980311yescharacteristic
449C8—4881no—
450C8—2442no—
451C8—2442no—
452C22—21no—
453C22—21no—
454C22—42no—
455C22—42no—
456C22—42no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22—4881no—
462C22—4881no—
463C22—4881no—
464C22#1683967011yescharacteristic
465C22#1683989611yescharacteristic
466C22#1683990711yescharacteristic
467C4—21no—
468C4—21no—
469C4—21no—
470C4—21no—
471C4—42no—
472C4—82no—
473C4—81no—
474C4—81no—
475C4—4881no—
476C4#1683989511yescharacteristic
477C4#1683990511yescharacteristic
478C4#1683999611yescharacteristic
479C4#1684001311yescharacteristic
480C2—21no—
481C2—21no—
482C2—82no—
483C2—9761no—
484C2#2144681511yescharacteristic
485C2#2144687911yescharacteristic
486C2#2144688411yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2536C2
socleC22×C61#392
prime radical#21455819C2
hypercenter#2536D61
hypocenterC61#9997
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2536

Complements

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

NH ≅ G/Ntype
2. #21455291C2semidirect
3. #21444378C2semidirect
4. #21444244C2semidirect
5. #21444214C2semidirect
6. #21443677C2semidirect
7. C61×#2536C2semidirect
92. C2×Q8×C61D8semidirect
239. #2536D61semidirect
276. C61#9997semidirect
341. C2×Q8#11758199semidirect

Maximal subgroups

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

subgroupindex
#214558192
#214552912
#214443782
#214442442
#214442142
#214436772
C61×#25362
#999761