Finite Group Databasebeta

← #29580391

Subgroups — #29580391

Order 15616.

768 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 768 conjugacy classes of subgroups — too many to draw. Only its 85 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#21455759C211yesmaximal, characteristic, complemented
2#21450750C211yesmaximal, characteristic
3#21445918C211yesmaximal, characteristic, complemented
4#21444347C211yesmaximal, characteristic, complemented
5#21444146C211yesmaximal, characteristic, complemented
6#21443671C211yesmaximal, characteristic, complemented
7C61×#2482C211yesmaximal, characteristic, complemented
8C2×#14519760—21no—
9C2×#14519751C2211yescharacteristic
10C2×#14519746—21no—
11#16840086—22no—
12#16840080—21no—
13#16840075—21no—
14#16839805—21no—
15#16839766—21no—
16#16839726C2211yescharacteristic
17#16839726C2211yescharacteristic
18#16839698—21no—
19#16839671—21no—
20#16839662—22no—
21C4×C22⋊Dic61C2211yescharacteristic
22#16839521—22no—
23#16839495—22no—
24#16839486—22no—
25C2×#117×C61C2211yescharacteristic
26C22×C22⋊C4×C61C2211yescharacteristic
27C61×#399—21no—
28C61×#397—21no—
29C61×#388—22no—
30C61×#385—21no—
31C61×#381C2211yescharacteristic
32C61×#379—21no—
33C22×D244D411yescharacteristic
34C22×C22⋊D61—21no—
35C22×C22⋊D61—22no—
36C2×#11758194—21no—
37C2×#11758194—21no—
38#14519760—44no—
39#14519751—21no—
40#14519751—21no—
41#14519751—21no—
42#14519751—21no—
43#14519746—44no—
44C2×C4⋊Dic61D411yescharacteristic
45C2×#11758196—22no—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61—22no—
48C2×#11758198—22no—
49C2×#11758198—21no—
50C2×C4×Dic61D412yes—
51#14519710—22no—
52#14519708—22no—
53#14519697—22no—
54#14519697—22no—
55C22⋊#92418—21no—
56C22⋊#92418—21no—
57C22⋊#92418—21no—
58C22⋊#92418D412yescomplemented
59#14519684—21no—
60C25×C61D411yescharacteristic
61C23×C4×C61D411yescharacteristic
62C23×C4×C61C2311yescharacteristic
63#117×C61—21no—
64#117×C61—21no—
65#117×C61—21no—
66#117×C61—21no—
67C2×C4⋊C4×C61—22no—
68C2×C4⋊C4×C61D411yescharacteristic, complemented
69C2×C4⋊C4×C61D411yescharacteristic, complemented
70C2×C22⋊C4×C61—22no—
71C2×C22⋊C4×C61—21no—
72C2×C22⋊C4×C61—21no—
73C2×C22⋊C4×C61—21no—
74C2×C22⋊C4×C61—21no—
75C2×C22⋊C4×C61—21no—
76C2×C22⋊C4×C61—21no—
77C2×C22⋊C4×C61—21no—
78C2×C22⋊C4×C61—21no—
79C2×C22⋊C4×C61—22no—
80C2×C42×C61—21no—
81#95×C61—22no—
82#95×C61—21no—
83#95×C61D412yescomplemented
84C24×C61—21no—
85C24×C61—21no—
86C24×C61—21no—
87C24×C61—42no—
88C24×C61—42no—
89C24×C61—42no—
90C24×C61C2×D411yescharacteristic
91C23×D61—21no—
92C22×C4×C61—22no—
93C22×C4×C61—21no—
94C22×C4×C61—21no—
95C22×C4×C61—21no—
96C22×C4×C61—21no—
97C22×C4×C61—21no—
98C22×C4×C61—42no—
99C22×C4×C61—42no—
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61#4111yescharacteristic
106C2×C22⋊D61—44no—
107C2×C22⋊D61—44no—
108C2×C22⋊D61—42no—
109C2×C22⋊D61—42no—
110C2×C22⋊D61—41no—
111C2×C22⋊D61—41no—
112C2×C22⋊D61—82no—
113C22×Dic61—22no—
114C22×Dic61—21no—
115C2×D244—21no—
116C2×D244—21no—
117C2×D244—42no—
118C4⋊C4×C61—21no—
119C4⋊C4×C61—21no—
120C4⋊C4×C61—21no—
121C4⋊C4×C61—21no—
122C4⋊C4×C61—82no—
123C22⋊C4×C61—42no—
124C22⋊C4×C61—44no—
125C22⋊C4×C61—41no—
126C22⋊C4×C61—41no—
127C22⋊C4×C61—41no—
128C22⋊C4×C61—41no—
129C22⋊C4×C61—41no—
130C22⋊C4×C61—41no—
131C22⋊C4×C61—82no—
132C42×C61—41no—
133C42×C61—41no—
134C22⋊Dic61—24no—
135C22⋊Dic61—44no—
136#11758198—44no—
137#11758198—41no—
138#11758198—41no—
139C4⋊Dic61—21no—
140C4⋊Dic61—21no—
141#11758196—44no—
142C4×Dic61—42no—
143#11758194—42no—
144#11758194—42no—
145C2×#92418—22no—
146C2×#92418—41no—
147C23×C61—22no—
148C23×C61—22no—
149C23×C61—22no—
150C23×C61—22no—
151C23×C61—22no—
152C23×C61—41no—
153C23×C61—42no—
154C23×C61—41no—
155C23×C61—41no—
156C23×C61—42no—
157C23×C61—41no—
158C23×C61—41no—
159C23×C61—42no—
160C23×C61—42no—
161C23×C61—81no—
162C23×C61—81no—
163C23×C61—88no—
164C23×C61#12011yescharacteristic
165C23×C61#12011yescharacteristic
166C23×C61#12111yescharacteristic
167C22×D61—41no—
168C22×D61—41no—
169C22×D61—42no—
170C22×D61—41no—
171C22×D61—42no—
172C2×C4×C61—22no—
173C2×C4×C61—22no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—42no—
179C2×C4×C61—42no—
180C2×C4×C61—42no—
181C2×C4×C61—42no—
182C2×C4×C61—41no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—42no—
186C2×C4×C61—42no—
187C2×C4×C61—42no—
188C2×C4×C61—81no—
189C2×C4×C61#12011yescharacteristic
190C2×C4×C61#12111yescharacteristic
191C2×C4×C61#12111yescharacteristic
192C2×C4×C61#12711yescharacteristic
193C22⋊D61—88no—
194C22⋊D61—82no—
195C22⋊D61—82no—
196C2×Dic61—24no—
197C2×Dic61—42no—
198C2×Dic61—42no—
199C2×Dic61—41no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202D244—42no—
203D244—81no—
204#92418—42no—
205#92418—81no—
206#9940—611nomaximal, Sylow
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—21no—
212C22×C61—21no—
213C22×C61—21no—
214C22×C61—44no—
215C22×C61—44no—
216C22×C61—44no—
217C22×C61—42no—
218C22×C61—82no—
219C22×C61—82no—
220C22×C61—82no—
221C22×C61—82no—
222C22×C61—81no—
223C22×C61—81no—
224C22×C61#39211yescharacteristic
225C22×C61#45312yes—
226C22×C61#45812yes—
227C2×D61—82no—
228C2×D61—82no—
229C2×D61—81no—
230C2×D61—81no—
231C2×D61—81no—
232C4×C61—21no—
233C4×C61—21no—
234C4×C61—21no—
235C4×C61—21no—
236C4×C61—82no—
237C4×C61—81no—
238C4×C61—81no—
239C4×C61—81no—
240Dic61—44no—
241Dic61—81no—
242#3094—611no—
243#2539—611no—
244#2482D6111yescharacteristic, complemented
245#1826—611no—
246#1510—611no—
247#1462—611no—
248#1284—611no—
249C2×C61—22no—
250C2×C61—22no—
251C2×C61—41no—
252C2×C61—82no—
253C2×C61#200211yescharacteristic
254C2×C61#201011yescharacteristic
255C2×C61#202211yescharacteristic
256D61—161no—
257C2×#123—1221no—
258C2×#121—611no—
259C2×#120—1221no—
260C2×#117C2×D6111yescharacteristic
261C22×C22⋊C4C2×D6111yescharacteristic
262#482—1222no—
263#481—1221no—
264#480—1221no—
265#428—1221no—
266#418—1221no—
267#407—611no—
268#407—611no—
269#399—21no—
270#399—1221no—
271#397—21no—
272#392—1221no—
273#390—1222no—
274#388—22no—
275#385—21no—
276#381C2×D6111yescharacteristic
277#379—21no—
278C4×C22⋊C4—611no—
279#339—1222no—
280#327—1222no—
281#323—1222no—
282C61#994011yescharacteristic, complemented, Sylow
283C25C22⋊D6111yescharacteristic
284C22×D4—611no—
285C22×D4—1222no—
286C22×D4—1221no—
287C23×C4C22⋊D6111yescharacteristic
288C23×C4C22×D6111yescharacteristic
289C2×M16—1221no—
290C2×M16—1221no—
291#123—2444no—
292#121—1221no—
293#121—1221no—
294#121—1221no—
295#121—1221no—
296#120—2444no—
297#117—21no—
298#117—21no—
299#117—21no—
300#117—21no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—611no—
303C2×C4⋊C4—1222no—
304C2×C4⋊C4C22⋊D6111yescharacteristic, complemented
305C2×C4⋊C4C22⋊D6111yescharacteristic, complemented
306C2×C22⋊C4—22no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—1221no—
317C2×C22⋊C4—1222no—
318C2×C22⋊C4—1222no—
319C2×C22⋊C4—1221no—
320C2×C42—21no—
321C2×C42—612no—
322#107—1222no—
323#106—1222no—
324#102—1222no—
325#102—1222no—
326C22⋊C8—612no—
327C22⋊C8—1221no—
328C22⋊C8—1221no—
329C22⋊C8—1221no—
330#95—22no—
331#95—21no—
332#95—1221no—
333#95C22⋊D6112yescomplemented
334C24—21no—
335C24—21no—
336C24—21no—
337C24—42no—
338C24—42no—
339C24—42no—
340C24—1221no—
341C24C2×C22⋊D6111yescharacteristic
342C2×D4—1221no—
343C2×D4—1221no—
344C2×D4—4882no—
345C2×D4—2442no—
346C2×D4—2444no—
347C2×D4—2442no—
348C2×D4—2442no—
349C2×D4—2444no—
350C2×D4—2441no—
351C2×D4—2441no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—1222no—
361C22×C4—1221no—
362C22×C4D4×D6111yescharacteristic
363C22×C4D4×D6111yescharacteristic
364C22×C4D4×D6111yescharacteristic
365C22×C4#1175822411yescharacteristic
366C22×C4C2×C22⋊D6111yescharacteristic
367C22×C4C2×C22⋊D6111yescharacteristic
368M16—2442no—
369M16—2442no—
370C2×C8—1222no—
371C2×C8—2441no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—82no—
377C4⋊C4—1221no—
378C4⋊C4—1221no—
379C4⋊C4—2444no—
380C22⋊C4—42no—
381C22⋊C4—44no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—82no—
389C22⋊C4—1224no—
390C22⋊C4—2444no—
391C22⋊C4—2444no—
392C22⋊C4—2441no—
393C22⋊C4—2441no—
394C42—41no—
395C42—41no—
396C42—2442no—
397C23—22no—
398C23—22no—
399C23—22no—
400C23—22no—
401C23—22no—
402C23—41no—
403C23—42no—
404C23—42no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—42no—
409C23—41no—
410C23—42no—
411C23—81no—
412C23—81no—
413C23—88no—
414C23—2441no—
415C23—2441no—
416C23—2442no—
417C23—2442no—
418C23—2441no—
419C23#1451974511yescharacteristic
420C23#1451974611yescharacteristic
421C23#1451974911yescharacteristic
422D4—4881no—
423D4—4882no—
424D4—4882no—
425D4—4888no—
426D4—2442no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—81no—
444C2×C4—1224no—
445C2×C4—2441no—
446C2×C4—2441no—
447C2×C4—2441no—
448C2×C4—2442no—
449C2×C4—2442no—
450C2×C4#1451974511yescharacteristic
451C2×C4#1451974811yescharacteristic
452C2×C4#1451974911yescharacteristic
453C2×C4#1451977311yescharacteristic
454C8—4881no—
455C8—2442no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—44no—
464C22—44no—
465C22—44no—
466C22—42no—
467C22—82no—
468C22—82no—
469C22—82no—
470C22—82no—
471C22—81no—
472C22—81no—
473C22—4882no—
474C22—4882no—
475C22—4881no—
476C22—4881no—
477C22—4881no—
478C22#1683967011yescharacteristic
479C22#1683993012yes—
480C22#1683995112yes—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—21no—
485C4—82no—
486C4—81no—
487C4—81no—
488C4—81no—
489C4—4881no—
490C4—2444no—
491C2—22no—
492C2—22no—
493C2—41no—
494C2—82no—
495C2—9761no—
496C2#2144683211yescharacteristic
497C2#2144688411yescharacteristic
498C2#2144694711yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#2482C2
socleC22×C61#392
prime radical#21450750C2
hypercenter#2482D61
hypocenterC61#9940
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2482

Complements

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

NH ≅ G/Ntype
1. #21455759C2semidirect
3. #21445918C2semidirect
4. #21444347C2semidirect
5. #21444146C2semidirect
6. #21443671C2semidirect
7. C61×#2482C2semidirect
58. C22⋊#92418D4semidirect
68. C2×C4⋊C4×C61D4semidirect
69. C2×C4⋊C4×C61D4semidirect
83. #95×C61D4semidirect
244. #2482D61semidirect
282. C61#9940semidirect
304. C2×C4⋊C4C22⋊D61semidirect
305. C2×C4⋊C4C22⋊D61semidirect
333. #95C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214557592
#214507502
#214459182
#214443472
#214441462
#214436712
C61×#24822
#994061