Finite Group Databasebeta

← #29576592

Subgroups — #29576592

Order 15616.

564 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 109 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#21456577C211yesmaximal, characteristic
2#21448902C211yesmaximal, characteristic, complemented
3#21446655C211yesmaximal, characteristic
4#21444392C211yesmaximal, characteristic, complemented
5C2×#16839497C211yesmaximal, characteristic
6#21443699C211yesmaximal, characteristic, complemented
7C61×#1282C211yesmaximal, characteristic, complemented
8C2×#14519756C2211yescharacteristic
9C2×#14519751C2211yescharacteristic
10#16840093C412yescomplemented
11#16840081—21no—
12#16839991—22no—
13#16839915C412yescomplemented
14#16839903—21no—
15C2×#14519691—21no—
16C2×#14519691—21no—
17#16839666—21no—
18#16839646—21no—
19#16839645—21no—
20#16839634—21no—
21#16839622C2211yescharacteristic
22C4×#11758196—21no—
23C22⋊C4×Dic61—21no—
24C2×#14519684C2211yescharacteristic
25#16839500—22no—
26#16839497—21no—
27#16839497—21no—
28C2×C22⋊C8×C61C2211yescharacteristic
29C2×C22⋊C8×C61C2211yescharacteristic
30C4×C22⋊C4×C61C2211yescharacteristic
31C22×Dic122D411yescharacteristic
32C22×D244C2×C411yescharacteristic
33C22×C22⋊D61—21no—
34C23×Dic61—21no—
35C2×#11758190—22no—
36#14519756—21no—
37#14519756—21no—
38#14519756C2×C412yes—
39#14519756D412yes—
40#14519751—21no—
41#14519751—21no—
42#14519751—21no—
43#14519751—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61C2×C411yescharacteristic
46C2×C4⋊Dic61D411yescharacteristic
47C2×#11758196—21no—
48C2×#11758196—21no—
49C2×#11758196—21no—
50C2×C22⋊Dic61—21no—
51C2×C22⋊Dic61—21no—
52C2×#11758198—21no—
53C2×C4×Dic61—21no—
54C2×C4×Dic61—21no—
55#14519709—22no—
56#14519702—22no—
57#14519699—22no—
58#14519691—42no—
59#14519691—42no—
60#14519684—21no—
61#14519684—21no—
62#14519684—21no—
63#14519684—21no—
64#14519684—21no—
65#14519684—21no—
66#14519684D411yescharacteristic
67#14519684D411yescharacteristic
68C23×C4×C61C2311yescharacteristic
69C22×C8×C61—21no—
70C22×C8×C61—21no—
71C2×C22⋊C4×C61D411yescharacteristic
72C2×C22⋊C4×C61D411yescharacteristic
73C2×C42×C61—21no—
74C22⋊C8×C61—21no—
75C22⋊C8×C61—21no—
76C22⋊C8×C61—21no—
77C22⋊C8×C61C2×C412yes—
78#95×C61—21no—
79C24×C61C2×D411yescharacteristic
80C23×D61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—81no—
84C22×C4×C61C22×C411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61#4111yescharacteristic
89C22×C4×C61#4111yescharacteristic
90C2×C22⋊D61—41no—
91C2×C22⋊D61—41no—
92C2×C22⋊D61—41no—
93C2×C22⋊D61—41no—
94C2×C22⋊D61—41no—
95C2×C22⋊D61—41no—
96C22×Dic61—21no—
97C22×Dic61—21no—
98C22×Dic61—21no—
99C22×Dic61—21no—
100C22×Dic61—21no—
101C22×Dic61—42no—
102C22×Dic61—41no—
103C22×Dic61—41no—
104C22×Dic61—41no—
105C22×Dic61—81no—
106C2×D244—21no—
107C2×D244—21no—
108C2×D244—81no—
109C2×Dic122—21no—
110C2×Dic122—81no—
111C2×Dic122C22⋊C412yes—
112C2×C8×C61—22no—
113C2×C8×C61—41no—
114C2×C8×C61—81no—
115C2×C8×C61—81no—
116C22⋊C4×C61—21no—
117C22⋊C4×C61—21no—
118C22⋊C4×C61—21no—
119C22⋊C4×C61SD1612yescomplemented
120C42×C61—81no—
121C22⋊Dic61—22no—
122C22⋊Dic61—22no—
123C22⋊Dic61—41no—
124C22⋊Dic61—41no—
125#11758198—41no—
126#11758198—41no—
127C4⋊Dic61—21no—
128C4⋊Dic61—21no—
129C4⋊Dic61—21no—
130C4⋊Dic61—81no—
131C4⋊Dic61C22⋊C412yes—
132#11758196—22no—
133#11758196—22no—
134#11758196—42no—
135#11758196—81no—
136C4×Dic61—42no—
137C4×Dic61—81no—
138#11758190—82no—
139C23×C61—41no—
140C23×C61—41no—
141C23×C61C4×D411yescharacteristic
142C23×C61#12011yescharacteristic
143C23×C61#12111yescharacteristic
144C23×C61C2×SD1611yescharacteristic
145C23×C61#13511yescharacteristic
146C23×C61AGL(1,ℤ/8)11yescharacteristic
147C23×C61#13711yescharacteristic
148C22×D61—41no—
149C22×D61—41no—
150C22×D61—41no—
151C22×D61—81no—
152C22×D61—81no—
153C2×C4×C61—22no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61C2×C22⋊C411yescharacteristic
166C2×C4×C61C4×D411yescharacteristic
167C2×C4×C61#12111yescharacteristic
168C2×C4×C61#12311yescharacteristic
169C22⋊D61—81no—
170C22⋊D61—81no—
171C22⋊D61—81no—
172C22⋊D61—81no—
173C2×Dic61—22no—
174C2×Dic61—22no—
175C2×Dic61—22no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61—82no—
189C2×Dic61—82no—
190C2×Dic61—81no—
191C2×Dic61—81no—
192C2×Dic61—81no—
193D244—42no—
194D244—81no—
195Dic122—42no—
196Dic122—81no—
197C8×C61—42no—
198C8×C61—81no—
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#38611yescharacteristic
211C22×C61C4×SD1611yescharacteristic
212C22×C61#44011yescharacteristic
213C22×C61#44811yescharacteristic
214C22×C61#44911yescharacteristic
215C22×C61#46011yescharacteristic
216C22×C61#46411yescharacteristic
217C2×D61—81no—
218C2×D61—81no—
219C2×D61—81no—
220C2×D61—161no—
221C2×D61—161no—
222C4×C61—21no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—21no—
226C4×C61—42no—
227C4×C61—81no—
228Dic61—42no—
229Dic61—42no—
230Dic61—42no—
231Dic61—81no—
232Dic61—81no—
233Dic61—161no—
234#3187—611no—
235#2368—611no—
236#1964—611no—
237#1520—611no—
238C2×#327—611no—
239#1294—611no—
240#1282D6111yescharacteristic, complemented
241C2×C61—21no—
242C2×C61—21no—
243C2×C61—21no—
244C2×C61—21no—
245C2×C61—21no—
246C2×C61—21no—
247C2×C61#188011yescharacteristic
248C2×C61#190611yescharacteristic
249C2×C61#191311yescharacteristic
250D61—161no—
251C2×C22⋊Q8—611no—
252C2×#121—611no—
253#483—612no—
254#481—1221no—
255#465—1222no—
256#450—612no—
257#448—1221no—
258C2×#99—1221no—
259C2×#99—1221no—
260C2×C22⋊C8C2×D6111yescharacteristic
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—1221no—
269C4×C22⋊C4C2×D6111yescharacteristic
270C2×#95—611no—
271#328—1222no—
272#327—1221no—
273#327—1221no—
274C61#927811yescharacteristic, complemented, Sylow
275C22×Q8—611no—
276C22×D4—611no—
277C22×D4—1221no—
278C23×C4—1221no—
279C23×C4C22×D6111yescharacteristic
280C2×SD16—1222no—
281C22×C8—21no—
282C22×C8—21no—
283C22⋊Q8—612no—
284C22⋊Q8—612no—
285C22⋊Q8—1221no—
286C22⋊Q8—1221no—
287#121—1221no—
288#121—1221no—
289#121—1221no—
290#121—1221no—
291C2×C4⋊C4—611no—
292C2×C4⋊C4—611no—
293C2×C4⋊C4—1221no—
294C2×C4⋊C4—1221no—
295C2×C4⋊C4—1221no—
296C2×C4⋊C4—1221no—
297C2×C22⋊C4—1221no—
298C2×C22⋊C4—1221no—
299C2×C22⋊C4—1221no—
300C2×C22⋊C4D24411yescharacteristic
301C2×C22⋊C4D24411yescharacteristic
302C2×C42—21no—
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—21no—
313C22⋊C8C4×D6112yes—
314#95—21no—
315#95—611no—
316#95—611no—
317#95—1221no—
318#95—1221no—
319#95—1221no—
320#95—1221no—
321#95—1221no—
322#95—1221no—
323C24—1221no—
324C24C2×D24411yescharacteristic
325C2×Q8—612no—
326C2×Q8—1221no—
327C2×Q8—4881no—
328C2×D4—1221no—
329C2×D4—1221no—
330C2×D4—4881no—
331C2×D4—2441no—
332C2×D4—2441no—
333C2×D4—2441no—
334C2×D4—2441no—
335C2×D4—2441no—
336C2×D4—2441no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—81no—
340C22×C4—1221no—
341C22×C4—1221no—
342C22×C4—1221no—
343C22×C4—1221no—
344C22×C4—1221no—
345C22×C4—4881no—
346C22×C4—2442no—
347C22×C4—2441no—
348C22×C4—2441no—
349C22×C4—2441no—
350C22×C4C2×C4×D6111yescharacteristic
351C22×C4#1175822211yescharacteristic
352C22×C4D4×D6111yescharacteristic
353C22×C4D4×D6111yescharacteristic
354C22×C4D4×D6111yescharacteristic
355C22×C4#1175822611yescharacteristic
356SD16—4882no—
357C2×C8—22no—
358C2×C8—41no—
359C2×C8—81no—
360C2×C8—81no—
361C4⋊C4—612no—
362C4⋊C4—1222no—
363C4⋊C4—1222no—
364C4⋊C4—1221no—
365C4⋊C4—1221no—
366C4⋊C4—1221no—
367C4⋊C4—4881no—
368C4⋊C4—4881no—
369C4⋊C4—2442no—
370C22⋊C4—21no—
371C22⋊C4—21no—
372C22⋊C4—21no—
373C22⋊C4—1222no—
374C22⋊C4—1222no—
375C22⋊C4—2441no—
376C22⋊C4—2441no—
377C22⋊C4—2441no—
378C22⋊C4—2441no—
379C22⋊C4#1175819012yescomplemented
380C42—81no—
381C42—4881no—
382C42—2442no—
383C23—41no—
384C23—41no—
385C23—4881no—
386C23—4881no—
387C23—2441no—
388C23—2441no—
389C23—2441no—
390C23C4×D24411yescharacteristic
391C23#1451974711yescharacteristic
392C23#1451975211yescharacteristic
393C23C2×#1175819011yescharacteristic
394C23#1451979911yescharacteristic
395C23#1451980511yescharacteristic
396C23#1451981011yescharacteristic
397Q8—4881no—
398Q8—2442no—
399D4—4881no—
400D4—4881no—
401D4—4881no—
402D4—4881no—
403D4—4881no—
404D4—2442no—
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—1222no—
418C2×C4—1222no—
419C2×C4—1222no—
420C2×C4—4881no—
421C2×C4—4881no—
422C2×C4—4881no—
423C2×C4—4882no—
424C2×C4—4882no—
425C2×C4—2441no—
426C2×C4—2441no—
427C2×C4—2441no—
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×C4#1451973911yescharacteristic
439C2×C4#1451975011yescharacteristic
440C2×C4#1451976211yescharacteristic
441C8—42no—
442C8—81no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—9761no—
454C22—9761no—
455C22—4881no—
456C22—4881no—
457C22—4881no—
458C22#1683964011yescharacteristic
459C22C4×#1175819011yescharacteristic
460C22#1683986411yescharacteristic
461C22#1683990311yescharacteristic
462C22#1683990911yescharacteristic
463C22#1683996311yescharacteristic
464C22#1683998511yescharacteristic
465C4—21no—
466C4—21no—
467C4—21no—
468C4—21no—
469C4—42no—
470C4—81no—
471C4—9761no—
472C4—4881no—
473C4—4881no—
474C4—2442no—
475C4—2442no—
476C4—2442no—
477C2—21no—
478C2—21no—
479C2—21no—
480C2—21no—
481C2—21no—
482C2—21no—
483C2—9761no—
484C2#2144617311yescharacteristic
485C2#2144632111yescharacteristic
486C2#2144636011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1282C2
socleC22×C61#386
prime radicalC2×#14519751C22
cosocleC23×C4×C61C23
hypercenter#1282D61
hypocenterC61#9278
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1282

Complements

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

NH ≅ G/Ntype
2. #21448902C2semidirect
4. #21444392C2semidirect
6. #21443699C2semidirect
7. C61×#1282C2semidirect
10. #16840093C4semidirect
13. #16839915C4semidirect
119. C22⋊C4×C61SD16semidirect
240. #1282D61semidirect
274. C61#9278semidirect
379. C22⋊C4#11758190semidirect

Maximal subgroups

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

subgroupindex
#214565772
#214489022
#214466552
#214443922
C2×#168394972
#214436992
C61×#12822
#927861