Finite Group Databasebeta

← #29576590

Subgroups — #29576590

Order 15616.

564 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 107 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#21456576C211yesmaximal, characteristic
2#21448899C211yesmaximal, characteristic, complemented
3#21446656C211yesmaximal, characteristic
4#21444392C211yesmaximal, characteristic, complemented
5#21443698C211yesmaximal, characteristic, complemented
6#21443666C211yesmaximal, characteristic, complemented
7C2×C61×#327C211yesmaximal, characteristic
8C2×#14519756C2211yescharacteristic
9#16840092C412yescomplemented
10#16840078—21no—
11#16839989—22no—
12#16839913C412yescomplemented
13#16839900—21no—
14C2×#14519692—21no—
15C2×#14519692—21no—
16C2×C22⋊#92418C2211yescharacteristic
17#16839666—21no—
18#16839647—21no—
19#16839644—21no—
20#16839635—21no—
21#16839622C2211yescharacteristic
22#16839613—21no—
23C4×C22⋊Dic61—21no—
24C4×C22⋊Dic61C2211yescharacteristic
25#16839500—22no—
26C2×#121×C61C2211yescharacteristic
27C2×C22⋊C8×C61C2211yescharacteristic
28C2×#95×C61C2211yescharacteristic
29C61×#327—21no—
30C61×#327—21no—
31C22×Dic122D411yescharacteristic
32C2×#11758200—22no—
33C22×#92418—21no—
34#14519756—21no—
35#14519756—21no—
36#14519756C2×C412yes—
37#14519756D412yes—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61D411yescharacteristic
46C2×C22⋊Dic61D411yescharacteristic
47C2×C4×Dic61—21no—
48C2×C4×Dic61—21no—
49C2×C4×Dic61—21no—
50#14519708—22no—
51#14519700—22no—
52#14519698—22no—
53#14519692—42no—
54#14519692—42no—
55C22⋊#92418—21no—
56C22⋊#92418C2×C412yes—
57#14519684—21no—
58#14519684—21no—
59#14519684—21no—
60#14519684—21no—
61#14519684—21no—
62#14519684—21no—
63C22×D4×C61—21no—
64C22×D4×C61C2×C411yescharacteristic
65C23×C4×C61—21no—
66C23×C4×C61C2311yescharacteristic
67C22×C8×C61—21no—
68#121×C61—21no—
69#121×C61—21no—
70#121×C61—21no—
71#121×C61—21no—
72C2×C4⋊C4×C61C2×C411yescharacteristic
73C2×C22⋊C4×C61—21no—
74C22⋊C8×C61—21no—
75C22⋊C8×C61—21no—
76#95×C61—21no—
77#95×C61D411yescharacteristic
78#95×C61D411yescharacteristic
79C24×C61—21no—
80C24×C61C2×D411yescharacteristic
81C2×D4×C61—21no—
82C2×D4×C61—21no—
83C2×D4×C61—41no—
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C2×D4×C61—41no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C2×D4×C61—81no—
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—21no—
93C22×C4×C61—42no—
94C22×C4×C61—41no—
95C22×C4×C61—41no—
96C22×C4×C61—81no—
97C22×C4×C61—81no—
98C22×C4×C61C22×C411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61#4111yescharacteristic
103C22×C4×C61#4111yescharacteristic
104C22×Dic61—21no—
105C22×Dic61—21no—
106C22×Dic61—21no—
107C22×Dic61—21no—
108C22×Dic61—41no—
109C2×Dic122—21no—
110C2×Dic122—81no—
111C2×Dic122C22⋊C412yes—
112C2×C8×C61—41no—
113C2×C8×C61—81no—
114C4⋊C4×C61—21no—
115C4⋊C4×C61—21no—
116C22⋊C4×C61—41no—
117C22⋊C4×C61—41no—
118C22⋊Dic61—22no—
119C22⋊Dic61—22no—
120C22⋊Dic61—21no—
121C22⋊Dic61—21no—
122C22⋊Dic61—21no—
123C22⋊Dic61—41no—
124C22⋊Dic61—41no—
125C22⋊Dic61SD1612yescomplemented
126#11758200—82no—
127C4⋊Dic61—21no—
128C4⋊Dic61—81no—
129C4⋊Dic61C22⋊C412yes—
130#11758196—22no—
131#11758196—22no—
132#11758196—42no—
133#11758196—81no—
134C4×Dic61—42no—
135C4×Dic61—81no—
136C4×Dic61—81no—
137C2×#92418—22no—
138C2×#92418—81no—
139C23×C61—41no—
140C23×C61—41no—
141C23×C61—41no—
142C23×C61—41no—
143C23×C61—41no—
144C23×C61—81no—
145C23×C61—81no—
146C23×C61C4×D411yescharacteristic
147C23×C61#12011yescharacteristic
148C23×C61#12111yescharacteristic
149C23×C61C2×SD1611yescharacteristic
150C23×C61#13511yescharacteristic
151C23×C61AGL(1,ℤ/8)11yescharacteristic
152C23×C61#13711yescharacteristic
153D4×C61—42no—
154D4×C61—81no—
155D4×C61—81no—
156D4×C61—81no—
157D4×C61—81no—
158D4×C61—81no—
159C2×C4×C61—22no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—82no—
175C2×C4×C61—82no—
176C2×C4×C61C2×C22⋊C411yescharacteristic
177C2×C4×C61C4×D411yescharacteristic
178C2×C4×C61#12111yescharacteristic
179C2×C4×C61#12311yescharacteristic
180C2×Dic61—22no—
181C2×Dic61—22no—
182C2×Dic61—22no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—81no—
193C2×Dic61—81no—
194C2×Dic61—81no—
195Dic122—42no—
196Dic122—81no—
197C8×C61—81no—
198#92418—42no—
199#9278—611nomaximal, Sylow
200C22×C61—21no—
201C22×C61—21no—
202C22×C61—21no—
203C22×C61—21no—
204C22×C61—21no—
205C22×C61—21no—
206C22×C61—41no—
207C22×C61—41no—
208C22×C61—41no—
209C22×C61—41no—
210C22×C61—81no—
211C22×C61—81no—
212C22×C61—81no—
213C22×C61—161no—
214C22×C61—161no—
215C22×C61#38611yescharacteristic
216C22×C61C4×SD1611yescharacteristic
217C22×C61#44011yescharacteristic
218C22×C61#44811yescharacteristic
219C22×C61#44911yescharacteristic
220C22×C61#46011yescharacteristic
221C22×C61#46411yescharacteristic
222C4×C61—21no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—21no—
226C4×C61—42no—
227C4×C61—81no—
228C4×C61—81no—
229Dic61—42no—
230Dic61—42no—
231Dic61—42no—
232Dic61—81no—
233Dic61—161no—
234#3187—611no—
235#2368—611no—
236#1964—611no—
237#1520—611no—
238C2×#327D6111yescharacteristic
239#1294—611no—
240#1282—611no—
241C2×C61—21no—
242C2×C61—21no—
243C2×C61—21no—
244C2×C61—21no—
245C2×C61—21no—
246C2×C61—21no—
247C2×C61—161no—
248C2×C61#188011yescharacteristic
249C2×C61#190611yescharacteristic
250C2×C61#191311yescharacteristic
251C2×C22⋊Q8—611no—
252C2×#121C2×D6111yescharacteristic
253#483—612no—
254#481—1221no—
255#465—1222no—
256#450—612no—
257#448—1221no—
258C2×#99—1221no—
259C2×#99—1221no—
260C2×C22⋊C8—611no—
261C2×C22⋊C8C2×D6111yescharacteristic
262#391—1221no—
263#387—1221no—
264#387—1221no—
265#385—1221no—
266#380—611no—
267C4×C4⋊C4—1221no—
268C4×C22⋊C4—611no—
269C4×C22⋊C4—1221no—
270C2×#95C2×D6111yescharacteristic
271#328—1222no—
272#327—21no—
273#327—21no—
274C61#927811yescharacteristic, complemented, Sylow
275C22×Q8—611no—
276C22×D4—21no—
277C22×D4C4×D6111yescharacteristic
278C23×C4—21no—
279C23×C4C22×D6111yescharacteristic
280C2×SD16—1222no—
281C22×C8—21no—
282C22×C8—1221no—
283C22⋊Q8—612no—
284C22⋊Q8—612no—
285C22⋊Q8—1221no—
286C22⋊Q8—1221no—
287#121—21no—
288#121—21no—
289#121—21no—
290#121—21no—
291C2×C4⋊C4—611no—
292C2×C4⋊C4—1221no—
293C2×C4⋊C4—1221no—
294C2×C4⋊C4—1221no—
295C2×C4⋊C4—1221no—
296C2×C4⋊C4C4×D6111yescharacteristic
297C2×C22⋊C4—21no—
298C2×C22⋊C4—611no—
299C2×C22⋊C4—611no—
300C2×C22⋊C4—1221no—
301C2×C22⋊C4—1221no—
302C2×C42—1221no—
303C2×C42—1221no—
304C2×C42—1221no—
305#106—1222no—
306#103—1222no—
307#102—1222no—
308#99—2442no—
309#99—2442no—
310C22⋊C8—21no—
311C22⋊C8—21no—
312C22⋊C8—612no—
313C22⋊C8—1221no—
314#95—21no—
315#95—1221no—
316#95—1221no—
317#95—1221no—
318#95—1221no—
319#95—1221no—
320#95—1221no—
321#95C22⋊D6111yescharacteristic
322#95C22⋊D6111yescharacteristic
323C24—21no—
324C24D4×D6111yescharacteristic
325C2×Q8—612no—
326C2×Q8—1221no—
327C2×Q8—4881no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—81no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—42no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—81no—
344C22×C4—81no—
345C22×C4—1221no—
346C22×C4—1221no—
347C22×C4—1221no—
348C22×C4—1221no—
349C22×C4—2441no—
350C22×C4C2×C4×D6111yescharacteristic
351C22×C4#1175822211yescharacteristic
352C22×C4D4×D6111yescharacteristic
353C22×C4D4×D6111yescharacteristic
354C22×C4#1175822411yescharacteristic
355C22×C4C2×C22⋊D6111yescharacteristic
356SD16—4882no—
357C2×C8—41no—
358C2×C8—81no—
359C2×C8—1222no—
360C2×C8—4881no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—612no—
364C4⋊C4—1222no—
365C4⋊C4—1222no—
366C4⋊C4—1221no—
367C4⋊C4—4881no—
368C4⋊C4—4881no—
369C4⋊C4—2442no—
370C22⋊C4—41no—
371C22⋊C4—41no—
372C22⋊C4—612no—
373C22⋊C4—1222no—
374C22⋊C4—1222no—
375C22⋊C4—1221no—
376C22⋊C4—1221no—
377C22⋊C4—1221no—
378C22⋊C4—2441no—
379C22⋊C4—2441no—
380C42—4881no—
381C42—4881no—
382C42—2442no—
383C23—41no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23—81no—
389C23—81no—
390C23#1451973711yescharacteristic
391C23#1451974511yescharacteristic
392C23#1451975011yescharacteristic
393C23SD16×D6111yescharacteristic
394C23#1451979611yescharacteristic
395C23#1451980111yescharacteristic
396C23#1451980611yescharacteristic
397Q8—4881no—
398Q8—2442no—
399D4—42no—
400D4—81no—
401D4—81no—
402D4—81no—
403D4—81no—
404D4—81no—
405C2×C4—22no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4—1222no—
423C2×C4—1222no—
424C2×C4—1222no—
425C2×C4—4881no—
426C2×C4—4881no—
427C2×C4—4881no—
428C2×C4—2441no—
429C2×C4—2441no—
430C2×C4—2441no—
431C2×C4—2441no—
432C2×C4—2441no—
433C2×C4—2441no—
434C2×C4—2441no—
435C2×C4—2441no—
436C2×C4—2441no—
437C2×C4C22⋊C4×D6111yescharacteristic
438C2×C4C4×C22⋊D6111yescharacteristic
439C2×C4#1451974811yescharacteristic
440C2×C4#1451975911yescharacteristic
441C8—81no—
442C8—2442no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—161no—
457C22—161no—
458C22#1683963811yescharacteristic
459C22#1683985311yescharacteristic
460C22#1683985911yescharacteristic
461C22#1683989911yescharacteristic
462C22#1683990411yescharacteristic
463C22#1683996111yescharacteristic
464C22#1683998311yescharacteristic
465C4—21no—
466C4—21no—
467C4—21no—
468C4—21no—
469C4—42no—
470C4—81no—
471C4—81no—
472C4—9761no—
473C4—4881no—
474C4—2442no—
475C4—2442no—
476C4—2442no—
477C2—21no—
478C2—21no—
479C2—21no—
480C2—21no—
481C2—21no—
482C2—21no—
483C2—161no—
484C2#2144617111yescharacteristic
485C2#2144632311yescharacteristic
486C2#2144635811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#327C2
socleC22×C61#386
prime radicalC2×#121×C61C22
cosocleC23×C4×C61C23
hypercenterC2×#327D61
hypocenterC61#9278
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. #21448899C2semidirect
4. #21444392C2semidirect
5. #21443698C2semidirect
6. #21443666C2semidirect
9. #16840092C4semidirect
12. #16839913C4semidirect
125. C22⋊Dic61SD16semidirect
274. C61#9278semidirect

Maximal subgroups

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

subgroupindex
#214565762
#214488992
#214466562
#214443922
#214436982
#214436662
C2×C61×#3272
#927861