Finite Group Databasebeta

← #29577809

Subgroups — #29577809

Order 15616.

958 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 958 conjugacy classes of subgroups — too many to draw. Only its 97 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#21449134C211yesmaximal, characteristic
2#21448171C211yesmaximal, characteristic, complemented
3#21445763C211yesmaximal, characteristic, complemented
4#21444145C211yesmaximal, characteristic, complemented
5#21443673C211yesmaximal, characteristic, complemented
6#21443672C211yesmaximal, characteristic, complemented
7C61×#1789C211yesmaximal, characteristic, complemented
8C2×#14519745—21no—
9C22×#11758198C2211yescharacteristic
10C2×C22⋊C4×D61—21no—
11C2×#14519704—22no—
12#16839726C2211yescharacteristic
13#16839673C412yescomplemented
14#16839670C412yescomplemented
15#16839642—21no—
16#16839641—22no—
17#16839625C2211yescharacteristic
18C22⋊C4×Dic61—21no—
19C4×#11758198—22no—
20C4×C22⋊Dic61C2211yescharacteristic
21#16839609—22no—
22#16839485—22no—
23C22×#41×C61C2211yescharacteristic
24C2×#104×C61—22no—
25C61×#407C2211yescharacteristic
26C4×C22⋊C4×C61C2211yescharacteristic
27C24×D61D411yescharacteristic
28C22×C22⋊D61—22no—
29C23×Dic61D411yescharacteristic
30C22×C4×D61—22no—
31C2×#11758194—21no—
32#14519745—44no—
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—22no—
36C2×#11758198—22no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—22no—
42C2×#11758198C2×C412yes—
43C2×#11758198D412yes—
44C22⋊C4×D61—28no—
45C2×C4×Dic61—22no—
46C2×C4×Dic61D412yescomplemented
47#14519704—44no—
48C22⋊#92418—21no—
49C22⋊#92418—21no—
50#14519684—22no—
51#14519684—21no—
52#14519684—21no—
53#14519684—22no—
54#14519684C2×C412yescomplemented
55C2×#41×C61—21no—
56C2×#41×C61—21no—
57C2×#41×C61—21no—
58C2×#41×C61—21no—
59C2×#41×C61—44no—
60C22×Q8×C61C2×C411yescharacteristic, complemented
61C22×D4×C61—21no—
62C22×D4×C61C2×C411yescharacteristic, complemented
63C23×C4×C61—21no—
64C23×C4×C61C2311yescharacteristic
65C2×M16×C61—21no—
66C2×C22⋊C4×C61—21no—
67C2×C42×C61D412yescomplemented
68#104×C61—44no—
69C22⋊C8×C61—21no—
70C22⋊C8×C61—21no—
71#95×C61—21no—
72C24×C61—21no—
73C24×C61C2×D411yescharacteristic
74C23×D61—21no—
75C23×D61—21no—
76C23×D61—24no—
77C23×D61—42no—
78C23×D61—81no—
79C23×D61C22⋊C412yes—
80#41×C61—24no—
81#41×C61—24no—
82#41×C61—42no—
83#41×C61—42no—
84#41×C61—42no—
85#41×C61—42no—
86#41×C61—42no—
87#41×C61—42no—
88C2×Q8×C61—21no—
89C2×Q8×C61—21no—
90C2×Q8×C61—42no—
91C2×D4×C61—24no—
92C2×D4×C61—21no—
93C2×D4×C61—21no—
94C2×D4×C61—42no—
95C2×D4×C61—42no—
96C2×D4×C61—41no—
97C2×D4×C61—41no—
98C22×C4×C61—21no—
99C22×C4×C61—22no—
100C22×C4×C61—42no—
101C22×C4×C61—42no—
102C22×C4×C61—42no—
103C22×C4×C61—41no—
104C22×C4×C61—41no—
105C22×C4×C61C22×C411yescharacteristic
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61#4111yescharacteristic
110C22×C4×C61#4111yescharacteristic
111C2×C22⋊D61—44no—
112C2×C22⋊D61—44no—
113C2×C22⋊D61—82no—
114C22×Dic61—22no—
115C22×Dic61—21no—
116C22×Dic61—21no—
117C22×Dic61—22no—
118C22×Dic61—81no—
119C22×Dic61C22⋊C412yes—
120C2×C4×D61—28no—
121C2×C4×D61—82no—
122C2×C4×D61—82no—
123M16×C61—42no—
124C2×C8×C61—41no—
125C22⋊C4×C61—24no—
126C42×C61—42no—
127C22⋊Dic61—24no—
128C22⋊Dic61—42no—
129C22⋊Dic61—82no—
130#11758198—28no—
131#11758198—22no—
132#11758198—22no—
133#11758198—22no—
134#11758198—22no—
135#11758198—44no—
136C4×Dic61—42no—
137C4×Dic61—82no—
138#11758194—42no—
139C2×#92418—41no—
140C23×C61—22no—
141C23×C61—22no—
142C23×C61—22no—
143C23×C61—41no—
144C23×C61—42no—
145C23×C61—41no—
146C23×C61—41no—
147C23×C61—42no—
148C23×C61C2×C22⋊C411yescharacteristic
149C23×C61#12011yescharacteristic
150C23×C61#12311yescharacteristic
151C22×D61—22no—
152C22×D61—22no—
153C22×D61—22no—
154C22×D61—24no—
155C22×D61—22no—
156C22×D61—42no—
157C22×D61—42no—
158C22×D61—42no—
159C22×D61—42no—
160C22×D61—88no—
161C22×D61—81no—
162C22×D61—81no—
163C22×D61#10414yescomplemented
164Q8×C61—22no—
165Q8×C61—22no—
166Q8×C61—41no—
167Q8×C61—41no—
168D4×C61—22no—
169D4×C61—22no—
170D4×C61—41no—
171D4×C61—41no—
172D4×C61—44no—
173D4×C61—44no—
174C2×C4×C61—22no—
175C2×C4×C61—22no—
176C2×C4×C61—24no—
177C2×C4×C61—22no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61—44no—
183C2×C4×C61—44no—
184C2×C4×C61—42no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—42no—
188C2×C4×C61C4×D411yescharacteristic
189C2×C4×C61C4×D411yescharacteristic
190C2×C4×C61#12111yescharacteristic
191C2×C4×C61#12111yescharacteristic
192C22⋊D61—88no—
193C2×Dic61—24no—
194C2×Dic61—22no—
195C2×Dic61—42no—
196C2×Dic61—42no—
197C2×Dic61—42no—
198C2×Dic61—42no—
199C2×Dic61—42no—
200C2×Dic61—42no—
201C2×Dic61—42no—
202C2×Dic61—81no—
203C4×D61—88no—
204C8×C61—81no—
205#92418—81no—
206#9475—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—42no—
217C22×C61—82no—
218C22×C61—81no—
219C22×C61—81no—
220C22×C61#38611yescharacteristic
221C22×C61C2×#10412yes—
222C22×C61B(4,𝔽2)12yes—
223C2×D61—24no—
224C2×D61—44no—
225C2×D61—44no—
226C2×D61—42no—
227C2×D61—42no—
228C2×D61—44no—
229C2×D61—82no—
230C2×D61—84no—
231C4×C61—21no—
232C4×C61—21no—
233C4×C61—21no—
234C4×C61—21no—
235C4×C61—44no—
236C4×C61—42no—
237Dic61—44no—
238Dic61—42no—
239Dic61—82no—
240#2404—611no—
241#2273—611no—
242#1789—611no—
243#1789D6111yescharacteristic, complemented
244#1462—611no—
245#1284—611no—
246#1284—611no—
247C2×C61—22no—
248C2×C61—22no—
249C2×C61—41no—
250C2×C61—82no—
251C2×C61#188911yescharacteristic
252C2×C61#189611yescharacteristic
253C2×C61#191111yescharacteristic
254D61—44no—
255C22×#41C2×D6111yescharacteristic
256C2×#120—1221no—
257C22×C22⋊C4—611no—
258C22×C22⋊C4—1221no—
259C2×#104—22no—
260C2×#104—1222no—
261#407—611no—
262#407C2×D6111yescharacteristic
263#393—612no—
264#392—612no—
265#386—1222no—
266#386—1221no—
267#381—611no—
268C4×C22⋊C4—611no—
269C4×C22⋊C4—1222no—
270C4×C22⋊C4—1221no—
271C4×C22⋊C4—1222no—
272C4×C22⋊C4C2×D6111yescharacteristic
273#323—1222no—
274C61#947511yescharacteristic, complemented, Sylow
275C25—611no—
276C2×#41—21no—
277C2×#41—21no—
278C2×#41—21no—
279C2×#41—21no—
280C2×#41—44no—
281C22×Q8C4×D6111yescharacteristic, complemented
282C22×D4—21no—
283C22×D4—1222no—
284C22×D4C4×D6111yescharacteristic, complemented
285C23×C4—21no—
286C23×C4—611no—
287C23×C4—1222no—
288C23×C4C22×D6111yescharacteristic
289C2×M16—21no—
290C2×M16—1221no—
291#120—2444no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—612no—
294C2×C22⋊C4—612no—
295C2×C22⋊C4—1228no—
296C2×C22⋊C4—1222no—
297C2×C22⋊C4—1221no—
298C2×C22⋊C4—1221no—
299C2×C22⋊C4—1221no—
300C2×C22⋊C4—1221no—
301C2×C22⋊C4—1221no—
302C2×C22⋊C4—1222no—
303C2×C22⋊C4—1222no—
304C2×C22⋊C4—1221no—
305C2×C42—612no—
306C2×C42—1222no—
307C2×C42C22⋊D6112yescomplemented
308#104—44no—
309#104—2444no—
310C22⋊C8—21no—
311C22⋊C8—21no—
312C22⋊C8—1221no—
313C22⋊C8—1221no—
314#95—21no—
315#95—612no—
316#95—1222no—
317#95—1222no—
318#95—1221no—
319#95—1221no—
320C24—21no—
321C24—612no—
322C24—1224no—
323C24—1221no—
324C24—1221no—
325C24—4881no—
326C24—2442no—
327C24D4×D6111yescharacteristic
328#41—24no—
329#41—24no—
330#41—42no—
331#41—42no—
332#41—42no—
333#41—42no—
334#41—42no—
335#41—42no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—42no—
339C2×D4—24no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—42no—
343C2×D4—42no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—4882no—
347C2×D4—2444no—
348C2×D4—2444no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—612no—
357C22×C4—1228no—
358C22×C4—1221no—
359C22×C4—1222no—
360C22×C4—1221no—
361C22×C4—1222no—
362C22×C4—4882no—
363C22×C4—4882no—
364C22×C4—4881no—
365C22×C4C2×C4×D6111yescharacteristic
366C22×C4#1175822211yescharacteristic
367C22×C4D4×D6111yescharacteristic
368C22×C4D4×D6111yescharacteristic
369C22×C4#1175822411yescharacteristic
370C22×C4C2×C22⋊D6111yescharacteristic
371M16—42no—
372M16—2442no—
373C2×C8—41no—
374C2×C8—2441no—
375C22⋊C4—24no—
376C22⋊C4—1228no—
377C22⋊C4—1224no—
378C22⋊C4—1222no—
379C22⋊C4—1222no—
380C22⋊C4—1222no—
381C22⋊C4—1222no—
382C22⋊C4—4882no—
383C22⋊C4—2444no—
384C22⋊C4—2442no—
385C42—42no—
386C42—4882no—
387C42—2442no—
388C23—22no—
389C23—22no—
390C23—22no—
391C23—41no—
392C23—42no—
393C23—41no—
394C23—42no—
395C23—41no—
396C23—614no—
397C23—1224no—
398C23—1222no—
399C23—1222no—
400C23—1222no—
401C23—1222no—
402C23—4881no—
403C23—4881no—
404C23—4888no—
405C23—2442no—
406C23—2442no—
407C23—2442no—
408C23—2442no—
409C23C22⋊C4×D6111yescharacteristic
410C23#1451974511yescharacteristic
411C23#1451975911yescharacteristic
412Q8—22no—
413Q8—22no—
414Q8—41no—
415Q8—41no—
416D4—22no—
417D4—22no—
418D4—41no—
419D4—41no—
420D4—44no—
421D4—44no—
422D4—4888no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—22no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—44no—
432C2×C4—44no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—1224no—
438C2×C4—1222no—
439C2×C4—4888no—
440C2×C4—4881no—
441C2×C4—2442no—
442C2×C4—2442no—
443C2×C4—2442no—
444C2×C4—2442no—
445C2×C4—2442no—
446C2×C4—2442no—
447C2×C4—2442no—
448C2×C4#1451973711yescharacteristic
449C2×C4C4×C22⋊D6111yescharacteristic
450C2×C4#1451974811yescharacteristic
451C2×C4#1451975011yescharacteristic
452C8—81no—
453C8—4881no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—44no—
462C22—44no—
463C22—42no—
464C22—82no—
465C22—81no—
466C22—81no—
467C22—1224no—
468C22—4882no—
469C22—4884no—
470C22—2444no—
471C22—2444no—
472C22—2444no—
473C22—2442no—
474C22—2442no—
475C22#1683963811yescharacteristic
476C22#104×D6112yes—
477C22#1683994812yes—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—44no—
483C4—42no—
484C4—4882no—
485C4—2444no—
486C4—2442no—
487C2—22no—
488C2—22no—
489C2—41no—
490C2—82no—
491C2—2444no—
492C2#2144622411yescharacteristic
493C2#2144625911yescharacteristic
494C2#2144634811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1789C2
socleC22×C61#386
prime radical#21449134C2
cosocleC23×C4×C61C23
hypercenter#1789D61
hypocenterC61#9475
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. #21448171C2semidirect
3. #21445763C2semidirect
4. #21444145C2semidirect
5. #21443673C2semidirect
6. #21443672C2semidirect
7. C61×#1789C2semidirect
13. #16839673C4semidirect
14. #16839670C4semidirect
46. C2×C4×Dic61D4semidirect
54. #14519684C2×C4semidirect
60. C22×Q8×C61C2×C4semidirect
62. C22×D4×C61C2×C4semidirect
67. C2×C42×C61D4semidirect
163. C22×D61#104semidirect
243. #1789D61semidirect
274. C61#9475semidirect
281. C22×Q8C4×D61semidirect
284. C22×D4C4×D61semidirect
307. C2×C42C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214491342
#214481712
#214457632
#214441452
#214436732
#214436722
C61×#17892
#947561