Finite Group Databasebeta

← #29576570

Subgroups — #29576570

Order 15616.

606 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456576C211yesmaximal, characteristic
2#21448871C211yesmaximal, characteristic
3#21446803C211yesmaximal, characteristic, complemented
4C2×#16839500C211yesmaximal, characteristic, complemented
5#21443697C211yesmaximal, characteristic, complemented
6#21443666C211yesmaximal, characteristic, complemented
7C61×#1519C211yesmaximal, characteristic
8C2×#14519756C2211yescharacteristic
9C2×D4×Dic61—21no—
10#16840092—21no—
11#16840078C412yescomplemented
12#16839989—22no—
13#16839913—21no—
14#16839900C412yescomplemented
15C2×C22⋊#92418C2211yescharacteristic
16#16839655—21no—
17#16839648—21no—
18#16839642—21no—
19#16839642—21no—
20C22⋊C4×Dic61—21no—
21C4×C22⋊Dic61C2211yescharacteristic
22C2×#14519684C2211yescharacteristic
23#16839528—21no—
24#16839528—21no—
25#16839500—21no—
26#16839500—21no—
27C2×#121×C61C2211yescharacteristic
28C2×C22⋊C8×C61C2211yescharacteristic
29C61×#380C2211yescharacteristic
30C61×#327—22no—
31C22×Dic122C2×C411yescharacteristic, complemented
32C23×Dic61—21no—
33C23×Dic61—21no—
34C2×#11758200—22no—
35C22×#92418—21no—
36#14519756—21no—
37#14519756—21no—
38#14519756—21no—
39#14519756—21no—
40D4×Dic61—42no—
41D4×Dic61—42no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61C2×C411yescharacteristic, complemented
44C2×#11758196—21no—
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61—21no—
48C2×C22⋊Dic61—21no—
49C2×C22⋊Dic61D411yescharacteristic
50C2×C22⋊Dic61D411yescharacteristic
51C2×C4×Dic61—21no—
52C2×C4×Dic61—21no—
53#14519708—22no—
54#14519700—22no—
55#14519698—22no—
56C22⋊#92418—21no—
57C22⋊#92418C2×C412yescomplemented
58#14519684—21no—
59#14519684—21no—
60#14519684—21no—
61#14519684—21no—
62#14519684D411yescharacteristic
63#14519684D411yescharacteristic
64C22×D4×C61—21no—
65C22×D4×C61D411yescharacteristic
66C23×C4×C61C2311yescharacteristic
67C22×C8×C61—21no—
68#121×C61—21no—
69#121×C61—21no—
70#121×C61C2×C412yes—
71#121×C61D412yes—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61D411yescharacteristic
74C2×C22⋊C4×C61—21no—
75C2×C22⋊C4×C61—21no—
76C22⋊C8×C61—21no—
77C22⋊C8×C61—21no—
78#95×C61—21no—
79C24×C61—21no—
80C24×C61C2×D411yescharacteristic
81C2×D4×C61—22no—
82C2×D4×C61—22no—
83C2×D4×C61—21no—
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C2×D4×C61—41no—
87C2×D4×C61—41no—
88C2×D4×C61—81no—
89C2×D4×C61C22⋊C412yes—
90C22×C4×C61—21no—
91C22×C4×C61—41no—
92C22×C4×C61—81no—
93C22×C4×C61C22×C411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61#4111yescharacteristic
98C22×C4×C61#4111yescharacteristic
99C22×Dic61—21no—
100C22×Dic61—21no—
101C22×Dic61—21no—
102C22×Dic61—21no—
103C22×Dic61—21no—
104C22×Dic61—21no—
105C22×Dic61—42no—
106C22×Dic61—42no—
107C22×Dic61—42no—
108C22×Dic61—41no—
109C22×Dic61—41no—
110C22×Dic61—81no—
111C22×Dic61—81no—
112C2×Dic122—21no—
113C2×Dic122—21no—
114C2×Dic122—81no—
115C2×C8×C61—41no—
116C2×C8×C61—81no—
117C4⋊C4×C61—21no—
118C4⋊C4×C61—81no—
119C4⋊C4×C61C22⋊C412yes—
120C22⋊C4×C61—22no—
121C22⋊C4×C61—22no—
122C22⋊C4×C61—41no—
123C22⋊C4×C61—41no—
124C22⋊Dic61—21no—
125C22⋊Dic61—21no—
126C22⋊Dic61—21no—
127C22⋊Dic61—42no—
128C22⋊Dic61—42no—
129C22⋊Dic61—41no—
130C22⋊Dic61—41no—
131C22⋊Dic61—81no—
132C22⋊Dic61SD1612yescomplemented
133#11758200—82no—
134C4⋊Dic61—21no—
135C4⋊Dic61—21no—
136C4⋊Dic61—42no—
137#11758196—41no—
138#11758196—41no—
139C4×Dic61—42no—
140C4×Dic61—81no—
141C2×#92418—22no—
142C2×#92418—81no—
143C23×C61—22no—
144C23×C61—41no—
145C23×C61—41no—
146C23×C61—41no—
147C23×C61—41no—
148C23×C61—41no—
149C23×C61—41no—
150C23×C61—41no—
151C23×C61—41no—
152C23×C61C4×D411yescharacteristic
153C23×C61#12011yescharacteristic
154C23×C61#12111yescharacteristic
155C23×C61C2×SD1611yescharacteristic
156C23×C61#13511yescharacteristic
157C23×C61AGL(1,ℤ/8)11yescharacteristic
158C23×C61#13711yescharacteristic
159D4×C61—42no—
160D4×C61—42no—
161D4×C61—42no—
162D4×C61—42no—
163D4×C61—42no—
164D4×C61—81no—
165C2×C4×C61—22no—
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—81no—
175C2×C4×C61—81no—
176C2×C4×C61—81no—
177C2×C4×C61C2×C22⋊C411yescharacteristic
178C2×C4×C61C4×D411yescharacteristic
179C2×C4×C61#12111yescharacteristic
180C2×C4×C61#12311yescharacteristic
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—41no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—84no—
196C2×Dic61—82no—
197C2×Dic61—82no—
198C2×Dic61—81no—
199C2×Dic61—81no—
200Dic122—42no—
201Dic122—81no—
202C8×C61—81no—
203#92418—42no—
204#9275—611nomaximal, Sylow
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—41no—
212C22×C61—41no—
213C22×C61—41no—
214C22×C61—41no—
215C22×C61—42no—
216C22×C61—42no—
217C22×C61—42no—
218C22×C61—81no—
219C22×C61—81no—
220C22×C61—81no—
221C22×C61—81no—
222C22×C61#38611yescharacteristic
223C22×C61C4×SD1611yescharacteristic
224C22×C61#44011yescharacteristic
225C22×C61#45011yescharacteristic
226C22×C61#45211yescharacteristic
227C22×C61#46111yescharacteristic
228C22×C61#46311yescharacteristic
229C4×C61—21no—
230C4×C61—21no—
231C4×C61—21no—
232C4×C61—21no—
233C4×C61—42no—
234C4×C61—161no—
235Dic61—42no—
236Dic61—42no—
237Dic61—81no—
238Dic61—81no—
239Dic61—81no—
240Dic61—81no—
241#3187—611no—
242#2364—611no—
243#1996—611no—
244#1519D6111yescharacteristic
245C2×#328—611no—
246#1294—611no—
247#1282—611no—
248C2×C61—21no—
249C2×C61—21no—
250C2×C61—21no—
251C2×C61—21no—
252C2×C61—21no—
253C2×C61—21no—
254C2×C61—82no—
255C2×C61#187711yescharacteristic
256C2×C61#190611yescharacteristic
257C2×C61#191311yescharacteristic
258C2×C22⋊Q8—611no—
259C2×#121C2×D6111yescharacteristic
260C2×C4×D4—1221no—
261#483—1221no—
262#481—612no—
263#465—1222no—
264#450—1221no—
265#448—612no—
266C2×C22⋊C8—611no—
267C2×C22⋊C8C2×D6111yescharacteristic
268#388—1221no—
269#387—1221no—
270#386—1221no—
271#386—1221no—
272#380C2×D6111yescharacteristic
273C4×C22⋊C4—611no—
274C4×C22⋊C4—1221no—
275C2×#95—611no—
276#342—1221no—
277#342—1221no—
278#328—1221no—
279#328—1221no—
280#327—22no—
281C61#927511yescharacteristic, complemented, Sylow
282C22×Q8—611no—
283C22×D4—21no—
284C22×D4D24411yescharacteristic
285C23×C4—1221no—
286C23×C4—1221no—
287C23×C4C22×D6111yescharacteristic
288C2×SD16—1222no—
289C22×C8—21no—
290C22×C8—1221no—
291C22⋊Q8—1221no—
292C22⋊Q8—1221no—
293C22⋊Q8—1221no—
294C22⋊Q8—1221no—
295#121—21no—
296#121—21no—
297#121C4×D6112yes—
298#121C22⋊D6112yes—
299C4×D4—2442no—
300C4×D4—2442no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—611no—
303C2×C4⋊C4—1221no—
304C2×C4⋊C4—1221no—
305C2×C4⋊C4D24411yescharacteristic
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—611no—
309C2×C22⋊C4—611no—
310C2×C22⋊C4—1221no—
311C2×C22⋊C4—1221no—
312C2×C22⋊C4—1221no—
313C2×C22⋊C4—1221no—
314C2×C42—1221no—
315C2×C42—1221no—
316#106—1222no—
317#103—1222no—
318#102—1222no—
319C22⋊C8—21no—
320C22⋊C8—21no—
321C22⋊C8—612no—
322C22⋊C8—1221no—
323#95—21no—
324#95—611no—
325#95—611no—
326#95—1221no—
327#95—1221no—
328#95—1221no—
329#95—1221no—
330C24—21no—
331C24D4×D6111yescharacteristic
332C2×Q8—1221no—
333C2×Q8—1221no—
334C2×Q8—4881no—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—21no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—81no—
343C2×D4#1175819812yes—
344C22×C4—21no—
345C22×C4—41no—
346C22×C4—81no—
347C22×C4—1221no—
348C22×C4—1221no—
349C22×C4—1221no—
350C22×C4—1221no—
351C22×C4—1221no—
352C22×C4—1221no—
353C22×C4—4881no—
354C22×C4—4881no—
355C22×C4—2442no—
356C22×C4—2442no—
357C22×C4—2442no—
358C22×C4—2441no—
359C22×C4—2441no—
360C22×C4C2×C4×D6111yescharacteristic
361C22×C4C2×D24411yescharacteristic
362C22×C4D4×D6111yescharacteristic
363C22×C4#1175822411yescharacteristic
364C22×C4#1175822411yescharacteristic
365C22×C4C2×C22⋊D6111yescharacteristic
366SD16—4882no—
367C2×C8—41no—
368C2×C8—81no—
369C2×C8—1222no—
370C2×C8—4881no—
371C4⋊C4—21no—
372C4⋊C4—81no—
373C4⋊C4—1221no—
374C4⋊C4—1221no—
375C4⋊C4—2442no—
376C4⋊C4—2441no—
377C4⋊C4—2441no—
378C4⋊C4#1175819812yes—
379C22⋊C4—22no—
380C22⋊C4—22no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—612no—
384C22⋊C4—1221no—
385C22⋊C4—1221no—
386C22⋊C4—1221no—
387C22⋊C4—4881no—
388C22⋊C4—2442no—
389C22⋊C4—2442no—
390C22⋊C4—2441no—
391C22⋊C4—2441no—
392C42—4881no—
393C42—2442no—
394C23—22no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23#1451973711yescharacteristic
404C23#1451974711yescharacteristic
405C23#1451974911yescharacteristic
406C23SD16×D6111yescharacteristic
407C23#1451979611yescharacteristic
408C23#1451980111yescharacteristic
409C23#1451980611yescharacteristic
410Q8—4881no—
411Q8—2442no—
412D4—42no—
413D4—42no—
414D4—42no—
415D4—42no—
416D4—42no—
417D4—81no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—1222no—
431C2×C4—1222no—
432C2×C4—4882no—
433C2×C4—4882no—
434C2×C4—4881no—
435C2×C4—4881no—
436C2×C4—4884no—
437C2×C4—2441no—
438C2×C4—2441no—
439C2×C4—2441no—
440C2×C4—2441no—
441C2×C4—2441no—
442C2×C4—2441no—
443C2×C4—2441no—
444C2×C4—2441no—
445C2×C4—2441no—
446C2×C4—2441no—
447C2×C4—2441no—
448C2×C4—2441no—
449C2×C4C2×#1175819811yescharacteristic
450C2×C4#1451973711yescharacteristic
451C2×C4#1451974911yescharacteristic
452C2×C4#1451976111yescharacteristic
453C8—81no—
454C8—2442no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22#1683963911yescharacteristic
473C22#1683985311yescharacteristic
474C22#1683985911yescharacteristic
475C22#1683991411yescharacteristic
476C22#1683992511yescharacteristic
477C22#1683996511yescharacteristic
478C22#1683997511yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—42no—
484C4—161no—
485C4—4881no—
486C4—4881no—
487C4—4881no—
488C4—4881no—
489C4—2442no—
490C4—2442no—
491C2—21no—
492C2—21no—
493C2—21no—
494C2—21no—
495C2—21no—
496C2—21no—
497C2—82no—
498C2#2144615111yescharacteristic
499C2#2144631811yescharacteristic
500C2#2144635911yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1519C2
socleC22×C61#386
prime radicalC2×#121×C61C22
cosocleC23×C4×C61C23
hypercenter#1519D61
hypocenterC61#9275
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
3. #21446803C2semidirect
4. C2×#16839500C2semidirect
5. #21443697C2semidirect
6. #21443666C2semidirect
11. #16840078C4semidirect
14. #16839900C4semidirect
31. C22×Dic122C2×C4semidirect
43. C2×C4⋊Dic61C2×C4semidirect
57. C22⋊#92418C2×C4semidirect
132. C22⋊Dic61SD16semidirect
281. C61#9275semidirect

Maximal subgroups

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

subgroupindex
#214565762
#214488712
#214468032
C2×#168395002
#214436972
#214436662
C61×#15192
#927561