Finite Group Databasebeta

← #29590297

Subgroups — #29590297

Order 15616.

592 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 83 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#21451625C211yesmaximal, characteristic
2#342×D61C211yesmaximal, characteristic
3#323×D61C211yesmaximal, characteristic
4#21443843C211yesmaximal, characteristic, complemented
5#21443841C211yesmaximal, characteristic, complemented
6#21443839C211yesmaximal, characteristic, complemented
7C61×#1352C211yesmaximal, characteristic, complemented
8C2×#14519757C411yescharacteristic, complemented
9C2×C22⋊C4×D61—21no—
10C2×C22⋊C4×D61C2211yescharacteristic
11C22⋊C8×D61—21no—
12#16839697C411yescharacteristic, complemented
13#16839685—21no—
14#16839684—21no—
15#16839675C411yescharacteristic, complemented
16#16839674C2211yescharacteristic
17#16839633—21no—
18#16839621C411yescharacteristic, complemented
19#16839617—21no—
20#16839529C2211yescharacteristic
21#16839528—21no—
22#16839486C2211yescharacteristic
23#16839485—21no—
24C61×#399C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C24×D61D411yescharacteristic
28C22×Dic122C2×C411yescharacteristic, complemented
29C22×C4×D61—41no—
30C22×C4×D61C2×C411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C2×C8×D61—41no—
33#14519757—41no—
34#14519757—41no—
35C2×C4⋊Dic61—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61D411yescharacteristic
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—41no—
46C2×#11758198C2×C411yescharacteristic
47C2×#11758198D411yescharacteristic
48C22⋊C4×D61—24no—
49C22⋊C4×D61—41no—
50C22⋊C4×D61—41no—
51C22⋊C4×D61—42no—
52C22⋊#92418—21no—
53#14519689—41no—
54#14519684—21no—
55#14519684—21no—
56#14519684C2×C411yescharacteristic, complemented
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61C2311yescharacteristic
62C22⋊C8×C61—21no—
63#95×C61C2×C411yescharacteristic, complemented
64C24×C61C2×D411yescharacteristic
65C23×D61—21no—
66C23×D61—21no—
67C23×D61—22no—
68C23×D61—81no—
69C23×D61—81no—
70C23×D61C22⋊C411yescharacteristic
71C23×D61C22⋊C411yescharacteristic
72C23×D61SD1612yes—
73C23×D61Q1612yes—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—41no—
77C22×C4×C61C22×C411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—41no—
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—44no—
89C2×C4×D61—81no—
90C2×C4×D61—82no—
91C2×C4×D61—82no—
92C2×C4×D61—81no—
93C2×Dic122—41no—
94C2×Dic122—81no—
95C2×C8×C61—41no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—81no—
98C22⋊C4×C61—22no—
99C22⋊C4×C61—41no—
100C22⋊C4×C61—41no—
101C22⋊C4×C61—81no—
102C22⋊Dic61—22no—
103C22⋊Dic61—41no—
104C22⋊Dic61—41no—
105C22⋊Dic61—81no—
106#11758198—41no—
107#11758198—41no—
108#11758198—44no—
109#11758198—41no—
110#11758198—41no—
111#11758198—42no—
112#11758198—81no—
113#11758198—81no—
114C4⋊Dic61—42no—
115#11758196—81no—
116#11758196—81no—
117C2×#92418—41no—
118C8×D61—82no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61C2×C22⋊C411yescharacteristic
124C23×C61C2×SD1611yescharacteristic
125C23×C61C2×Q1611yescharacteristic
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—22no—
129C22×D61—22no—
130C22×D61—22no—
131C22×D61—22no—
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—42no—
135C22×D61—42no—
136C22×D61—41no—
137C22×D61—41no—
138C22×D61—81no—
139C22×D61—81no—
140C22×D61—82no—
141C22×D61—82no—
142C22×D61—84no—
143C22×D61#9911yescharacteristic
144C22×D61#9911yescharacteristic
145C22×D61#10312yes—
146C22×D61#10312yes—
147C22×D61#10412yes—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—42no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—81no—
160C2×C4×C61—81no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—42no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—81no—
173C2×Dic61—81no—
174C4×D61—42no—
175C4×D61—81no—
176C4×D61—81no—
177C4×D61—81no—
178C4×D61—88no—
179Dic122—82no—
180C8×C61—81no—
181#92418—81no—
182#11716—611nomaximal, Sylow
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—41no—
188C22×C61—41no—
189C22×C61—41no—
190C22×C61—41no—
191C22×C61—81no—
192C22×C61C2×#9911yescharacteristic
193C22×C61C2×#10311yescharacteristic
194C22×C61C2×#10411yescharacteristic
195C2×D61—21no—
196C2×D61—21no—
197C2×D61—21no—
198C2×D61—21no—
199C2×D61—22no—
200C2×D61—42no—
201C2×D61—42no—
202C2×D61—44no—
203C2×D61—44no—
204C2×D61—41no—
205C2×D61—41no—
206C2×D61—42no—
207C2×D61—82no—
208C2×D61—82no—
209C2×D61—81no—
210C2×D61#32812yes—
211C2×D61#32812yes—
212C4×C61—41no—
213C4×C61—41no—
214C4×C61—81no—
215C4×C61—82no—
216C4×C61—81no—
217Dic61—41no—
218Dic61—41no—
219Dic61—81no—
220Dic61—82no—
221Dic61—81no—
222#2626—611no—
223C2×#342—611no—
224C2×#323—611no—
225#1352—611no—
226#1352D6111yescharacteristic, complemented
227#1351—611no—
228#1351—611no—
229C2×C61—21no—
230C2×C61—21no—
231C2×C61—41no—
232C2×C61—41no—
233C2×C61C2×#32811yescharacteristic
234C2×C61#212111yescharacteristic
235C2×C61#212711yescharacteristic
236D61—22no—
237D61—22no—
238D61—42no—
239C2×C22⋊Q8—611no—
240C22×C22⋊C4—611no—
241C22×C22⋊C4—1221no—
242C2×C22⋊C8—1221no—
243#399—611no—
244#399C2×D6111yescharacteristic
245#396—1221no—
246#396—1221no—
247#393—611no—
248#393—611no—
249#385—1221no—
250#380—611no—
251#379—1221no—
252#342—611no—
253#342—1221no—
254#342C2×D6111yescharacteristic
255#323—611no—
256#323—1221no—
257#323C2×D6111yescharacteristic
258C61#1171611yescharacteristic, complemented, Sylow
259C25—611no—
260C22×Q8—611no—
261C23×C4—611no—
262C23×C4—611no—
263C23×C4—2441no—
264C22×C8—2441no—
265C22⋊Q8—2441no—
266C22⋊Q8—2441no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—1221no—
269C2×C4⋊C4—1221no—
270C2×C4⋊C4—1221no—
271C2×C4⋊C4C4×D6111yescharacteristic, complemented
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—611no—
275C2×C22⋊C4—611no—
276C2×C22⋊C4—611no—
277C2×C22⋊C4—1224no—
278C2×C22⋊C4—1221no—
279C2×C22⋊C4—1221no—
280C2×C22⋊C4—1221no—
281C2×C22⋊C4—1221no—
282C2×C22⋊C4—1221no—
283C2×C22⋊C4—1221no—
284C2×C22⋊C4—2441no—
285C2×C22⋊C4—2441no—
286C2×C22⋊C4—2442no—
287C2×C22⋊C4—2441no—
288C2×C22⋊C4C22×D6111yescharacteristic
289C22⋊C8—21no—
290C22⋊C8—1221no—
291C22⋊C8—2441no—
292#95—611no—
293#95—1221no—
294#95—1221no—
295#95C4×D6111yescharacteristic, complemented
296C24—611no—
297C24—612no—
298C24—612no—
299C24—611no—
300C24—1222no—
301C24—1221no—
302C24—1221no—
303C24—4881no—
304C24—4881no—
305C24D4×D6111yescharacteristic
306C2×Q8—4881no—
307C2×Q8—2441no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—41no—
311C22×C4—611no—
312C22×C4—611no—
313C22×C4—1221no—
314C22×C4—1221no—
315C22×C4—1221no—
316C22×C4—1221no—
317C22×C4—1221no—
318C22×C4—1221no—
319C22×C4—4881no—
320C22×C4—4881no—
321C22×C4—4882no—
322C22×C4—4882no—
323C22×C4—2444no—
324C22×C4—2441no—
325C22×C4C2×C4×D6111yescharacteristic
326C22×C4D4×D6111yescharacteristic
327C2×C8—41no—
328C2×C8—4882no—
329C2×C8—2441no—
330C4⋊C4—41no—
331C4⋊C4—81no—
332C4⋊C4—4881no—
333C4⋊C4—4881no—
334C4⋊C4—2442no—
335C22⋊C4—22no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—81no—
339C22⋊C4—1222no—
340C22⋊C4—4881no—
341C22⋊C4—4881no—
342C22⋊C4—4881no—
343C22⋊C4—2441no—
344C22⋊C4—2441no—
345C22⋊C4—2442no—
346C22⋊C4—2441no—
347C22⋊C4—2441no—
348C22⋊C4—2444no—
349C22⋊C4—2441no—
350C22⋊C4—2441no—
351C23—21no—
352C23—21no—
353C23—41no—
354C23—41no—
355C23—611no—
356C23—611no—
357C23—612no—
358C23—612no—
359C23—612no—
360C23—1222no—
361C23—1222no—
362C23—1222no—
363C23—1222no—
364C23—1221no—
365C23—1221no—
366C23—4881no—
367C23—4881no—
368C23—4882no—
369C23—4882no—
370C23—4884no—
371C23—2441no—
372C23—2441no—
373C23—2441no—
374C23—2441no—
375C23—2442no—
376C23—2442no—
377C23C22⋊C4×D6111yescharacteristic
378C23SD16×D6111yescharacteristic
379C23Q16×D6111yescharacteristic
380Q8—4882no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—4881no—
397C2×C4—4881no—
398C2×C4—4881no—
399C2×C4—4888no—
400C2×C4—4881no—
401C2×C4—4881no—
402C2×C4—2442no—
403C2×C4—2442no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4—2441no—
410C2×C4—2441no—
411C2×C4—2441no—
412C8—81no—
413C8—4881no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—81no—
423C22—612no—
424C22—612no—
425C22—1221no—
426C22—1221no—
427C22—1221no—
428C22—1221no—
429C22—1222no—
430C22—4881no—
431C22—4882no—
432C22—4882no—
433C22—2442no—
434C22—2442no—
435C22—2442no—
436C22—2444no—
437C22—2444no—
438C22—2441no—
439C22—2441no—
440C22#99×D6111yescharacteristic
441C22#103×D6111yescharacteristic
442C22#104×D6111yescharacteristic
443C4—41no—
444C4—41no—
445C4—81no—
446C4—82no—
447C4—81no—
448C4—4881no—
449C4—4882no—
450C4—4881no—
451C4—2441no—
452C4—2441no—
453C2—21no—
454C2—21no—
455C2—41no—
456C2—41no—
457C2—1222no—
458C2—1222no—
459C2—2442no—
460C2#328×D6111yescharacteristic
461C2#2144746411yescharacteristic
462C2#2144748511yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1352C2
socleC22×C61C2×#99
prime radicalC24×D61D4
cosocleC2×C22⋊C4×C61C23
hypercenter#1352D61
hypocenterC61#11716
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1352

Complements

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

NH ≅ G/Ntype
4. #21443843C2semidirect
5. #21443841C2semidirect
6. #21443839C2semidirect
7. C61×#1352C2semidirect
8. C2×#14519757C4semidirect
12. #16839697C4semidirect
15. #16839675C4semidirect
18. #16839621C4semidirect
28. C22×Dic122C2×C4semidirect
56. #14519684C2×C4semidirect
58. C2×C4⋊C4×C61C2×C4semidirect
63. #95×C61C2×C4semidirect
226. #1352D61semidirect
258. C61#11716semidirect
271. C2×C4⋊C4C4×D61semidirect
295. #95C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214516252
#342×D612
#323×D612
#214438432
#214438412
#214438392
C61×#13522
#1171661