Finite Group Databasebeta

← #29577994

Subgroups — #29577994

Order 15616.

558 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 89 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#21454454C211yesmaximal, characteristic, complemented
2#21450093C211yesmaximal, characteristic
3#21445900C211yesmaximal, characteristic, complemented
4#21444146C211yesmaximal, characteristic
5#21443728C211yesmaximal, characteristic, complemented
6#21443728C211yesmaximal, characteristic, complemented
7C61×#1462C211yesmaximal, characteristic
8C2×#14519736C2211yescharacteristic
9#16839820—22no—
10#16839820—22no—
11#16839785—21no—
12#16839726C2211yescharacteristic
13#16839726C2211yescharacteristic
14M16×Dic61—21no—
15#16839698—21no—
16#16839687—21no—
17#16839650—21no—
18#16839650—21no—
19#16839635C411yescharacteristic
20#16839635C411yescharacteristic
21#16839625C2211yescharacteristic
22#16839618C411yescharacteristic
23#16839618C411yescharacteristic
24#16839530—21no—
25#16839530—21no—
26#16839486—22no—
27C22×C22⋊C4×C61C2211yescharacteristic
28C61×#407C2211yescharacteristic
29C61×#407C2211yescharacteristic
30C61×#323—22no—
31C2×#11758194—21no—
32C2×#11758194—21no—
33#14519736—21no—
34#14519736—21no—
35#14519736—21no—
36#14519736—21no—
37C2×C4⋊Dic61D411yescharacteristic
38C2×C4⋊Dic61D411yescharacteristic
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61C2×C411yescharacteristic
46C2×C22⋊Dic61C2×C411yescharacteristic
47C2×C22⋊Dic61C2×C411yescharacteristic
48C2×C22⋊Dic61C2×C411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51#14519706—24no—
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54C22⋊#92418—21no—
55C22⋊#92418D412yes—
56#14519687—22no—
57C8×Dic61—22no—
58#14519684—21no—
59#14519684—21no—
60#14519684—21no—
61#14519684—21no—
62C25×C61C2×C411yescharacteristic
63C23×C4×C61C2×C411yescharacteristic
64C23×C4×C61C2311yescharacteristic
65C2×M16×C61—21no—
66C2×M16×C61—21no—
67C2×C22⋊C4×C61—21no—
68C2×C22⋊C4×C61—21no—
69C2×C22⋊C4×C61—21no—
70C2×C22⋊C4×C61—21no—
71C2×C22⋊C4×C61—21no—
72C2×C22⋊C4×C61—21no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61—21no—
75C22⋊C8×C61—21no—
76C22⋊C8×C61D412yes—
77C24×C61—21no—
78C24×C61—21no—
79C24×C61—21no—
80C24×C61—42no—
81C24×C61—41no—
82C24×C61—41no—
83C24×C61—81no—
84C24×C61C22×C411yescharacteristic
85C22×C4×C61—21no—
86C22×C4×C61—21no—
87C22×C4×C61—21no—
88C22×C4×C61—41no—
89C22×C4×C61—41no—
90C22×C4×C61—81no—
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61#4111yescharacteristic
96C22×C4×C61#4111yescharacteristic
97C22×Dic61—21no—
98C22×Dic61—21no—
99C22×Dic61C22⋊C411yescharacteristic
100C22×Dic61C22⋊C411yescharacteristic
101C22×Dic61C22⋊C411yescharacteristic
102C22×Dic61C22⋊C411yescharacteristic
103M16×C61—41no—
104M16×C61—41no—
105M16×C61—41no—
106M16×C61—41no—
107C2×C8×C61—22no—
108C2×C8×C61—41no—
109C22⋊C4×C61—41no—
110C22⋊C4×C61—41no—
111C22⋊C4×C61—41no—
112C22⋊C4×C61—41no—
113C22⋊Dic61—21no—
114C22⋊Dic61—21no—
115C22⋊Dic61—21no—
116C22⋊Dic61—21no—
117C22⋊Dic61—42no—
118C22⋊Dic61—42no—
119C22⋊Dic61—41no—
120C22⋊Dic61—41no—
121C22⋊Dic61—81no—
122C22⋊Dic61—81no—
123C4⋊Dic61—21no—
124C4⋊Dic61—21no—
125C4⋊Dic61—21no—
126C4⋊Dic61—21no—
127#11758196—81no—
128#11758196—81no—
129C4×Dic61—21no—
130C4×Dic61—21no—
131C4×Dic61—21no—
132C4×Dic61—21no—
133#11758194—41no—
134#11758194—41no—
135#11758194—41no—
136#11758194—41no—
137C2×#92418—22no—
138C2×#92418—41no—
139C23×C61—21no—
140C23×C61—21no—
141C23×C61—22no—
142C23×C61—22no—
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×C61—41no—
153C23×C61—41no—
154C23×C61—81no—
155C23×C61—81no—
156C23×C61—81no—
157C23×C61—81no—
158C23×C61—84no—
159C23×C61—84no—
160C23×C61C2×C22⋊C411yescharacteristic
161C23×C61C4×D411yescharacteristic
162C23×C61C4×D411yescharacteristic
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
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#12011yescharacteristic
177C2×C4×C61#12111yescharacteristic
178C2×C4×C61#12111yescharacteristic
179C2×C4×C61#12311yescharacteristic
180C2×Dic61—21no—
181C2×Dic61—21no—
182C2×Dic61—21no—
183C2×Dic61—21no—
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—
194C8×C61—42no—
195C8×C61—81no—
196#92418—42no—
197#92418—81no—
198#9512—611nomaximal, Sylow
199C22×C61—21no—
200C22×C61—21no—
201C22×C61—21no—
202C22×C61—21no—
203C22×C61—21no—
204C22×C61—21no—
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—42no—
208C22×C61—42no—
209C22×C61—42no—
210C22×C61—42no—
211C22×C61—42no—
212C22×C61—81no—
213C22×C61—81no—
214C22×C61—82no—
215C22×C61—82no—
216C22×C61—82no—
217C22×C61—82no—
218C22×C61—81no—
219C22×C61—81no—
220C22×C61#38611yescharacteristic
221C22×C61#41011yescharacteristic
222C22×C61#41011yescharacteristic
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—21no—
226C4×C61—21no—
227C4×C61—81no—
228Dic61—41no—
229Dic61—41no—
230Dic61—41no—
231Dic61—41no—
232Dic61—81no—
233Dic61—81no—
234#2921—611no—
235#2482—611no—
236#1822—611no—
237#1462—611no—
238#1462D6111yescharacteristic
239#1306—611no—
240#1306—611no—
241C2×C61—21no—
242C2×C61—21no—
243C2×C61—41no—
244C2×C61—41no—
245C2×C61—82no—
246C2×C61#189111yescharacteristic
247C2×C61#189911yescharacteristic
248C2×C61#191411yescharacteristic
249C2×#117—611no—
250C22×C22⋊C4C2×D6111yescharacteristic
251#433—1222no—
252#433—1222no—
253#423—1221no—
254#407—611no—
255#407—611no—
256#407C2×D6111yescharacteristic
257#407C2×D6111yescharacteristic
258C4×M16—1221no—
259#399—1221no—
260#397—1221no—
261#388—1221no—
262#388—1221no—
263#385—611no—
264#385—611no—
265#381—611no—
266#379—611no—
267#379—611no—
268#343—1221no—
269#343—1221no—
270#323—22no—
271#323—1222no—
272C61#951211yescharacteristic, complemented, Sylow
273C25C4×D6111yescharacteristic
274C23×C4C4×D6111yescharacteristic
275C23×C4C22×D6111yescharacteristic
276C2×M16—21no—
277C2×M16—21no—
278C2×M16—1221no—
279C2×M16—1221no—
280#117—1221no—
281#117—1221no—
282#117—1221no—
283#117—1221no—
284C2×C4⋊C4—611no—
285C2×C4⋊C4—611no—
286C2×C4⋊C4—1221no—
287C2×C4⋊C4—1221no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—611no—
295C2×C22⋊C4—611no—
296C2×C22⋊C4—611no—
297C2×C22⋊C4—611no—
298C2×C22⋊C4—1221no—
299C2×C22⋊C4—1221no—
300C2×C22⋊C4—1221no—
301C2×C22⋊C4—1221no—
302C2×C42—611no—
303C2×C42—611no—
304C4⋊C8—1224no—
305C22⋊C8—21no—
306C22⋊C8—21no—
307C22⋊C8—21no—
308C22⋊C8—612no—
309C22⋊C8—1221no—
310C22⋊C8—1221no—
311C22⋊C8—1221no—
312C22⋊C8C22⋊D6112yes—
313#97—1222no—
314C4×C8—1222no—
315#95—1221no—
316#95—1221no—
317#95—1221no—
318#95—1221no—
319C24—21no—
320C24—21no—
321C24—21no—
322C24—42no—
323C24—41no—
324C24—41no—
325C24—81no—
326C24C2×C4×D6111yescharacteristic
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—81no—
333C22×C4—611no—
334C22×C4—611no—
335C22×C4—611no—
336C22×C4—611no—
337C22×C4—1221no—
338C22×C4—1221no—
339C22×C4#1175822211yescharacteristic
340C22×C4D4×D6111yescharacteristic
341C22×C4D4×D6111yescharacteristic
342C22×C4D4×D6111yescharacteristic
343C22×C4#1175822411yescharacteristic
344C22×C4C2×C22⋊D6111yescharacteristic
345M16—41no—
346M16—41no—
347M16—41no—
348M16—41no—
349M16—2441no—
350M16—2441no—
351M16—2441no—
352M16—2441no—
353C2×C8—22no—
354C2×C8—41no—
355C2×C8—1222no—
356C2×C8—2441no—
357C4⋊C4—1221no—
358C4⋊C4—1221no—
359C4⋊C4—1221no—
360C4⋊C4—1221no—
361C4⋊C4—4881no—
362C4⋊C4—4881no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—1221no—
368C22⋊C4—1221no—
369C22⋊C4—1221no—
370C22⋊C4—1221no—
371C22⋊C4—4881no—
372C22⋊C4—4881no—
373C22⋊C4—2442no—
374C22⋊C4—2442no—
375C22⋊C4—2441no—
376C22⋊C4—2441no—
377C42—1221no—
378C42—1221no—
379C42—1221no—
380C42—1221no—
381C23—21no—
382C23—21no—
383C23—22no—
384C23—22no—
385C23—22no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—81no—
397C23—81no—
398C23—81no—
399C23—81no—
400C23—84no—
401C23—84no—
402C23C22⋊C4×D6111yescharacteristic
403C23#1451973711yescharacteristic
404C23C4×C22⋊D6111yescharacteristic
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—1221no—
419C2×C4—1221no—
420C2×C4—1221no—
421C2×C4—1221no—
422C2×C4—2441no—
423C2×C4—2441no—
424C2×C4—2441no—
425C2×C4—2441no—
426C2×C4—2441no—
427C2×C4—2441no—
428C2×C4—2441no—
429C2×C4—2441no—
430C2×C4—2441no—
431C2×C4—2441no—
432C2×C4#1451974511yescharacteristic
433C2×C4#1451974811yescharacteristic
434C2×C4#1451975011yescharacteristic
435C2×C4#1451975911yescharacteristic
436C8—42no—
437C8—81no—
438C8—4881no—
439C8—2442no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—42no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—42no—
453C22—81no—
454C22—81no—
455C22—82no—
456C22—82no—
457C22—82no—
458C22—82no—
459C22—81no—
460C22—81no—
461C22#1683963811yescharacteristic
462C22#1683973411yescharacteristic
463C22#1683973411yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—81no—
469C4—4881no—
470C4—4881no—
471C4—2441no—
472C4—2441no—
473C4—2441no—
474C4—2441no—
475C2—21no—
476C2—21no—
477C2—41no—
478C2—41no—
479C2—82no—
480C2#2144623411yescharacteristic
481C2#2144627411yescharacteristic
482C2#2144636311yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC24×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1462C2
socleC22×C61#386
prime radicalC25×C61C2×C4
cosocleC23×C4×C61C23
hypercenter#1462D61
hypocenterC61#9512
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1462

Complements

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

NH ≅ G/Ntype
1. #21454454C2semidirect
3. #21445900C2semidirect
5. #21443728C2semidirect
6. #21443728C2semidirect
272. C61#9512semidirect

Maximal subgroups

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

subgroupindex
#214544542
#214500932
#214459002
#214441462
#214437282
C61×#14622
#951261