Finite Group Databasebeta

← #29578019

Subgroups — #29578019

Order 15616.

520 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 91 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#21454846C211yesmaximal, characteristic
2#21451166C211yesmaximal, characteristic
3#21444155C211yesmaximal, characteristic
4#21444149C211yesmaximal, characteristic, complemented
5#21443726C211yesmaximal, characteristic, complemented
6#21443724C211yesmaximal, characteristic, complemented
7C61×#1463C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D61C2211yescharacteristic
9#16839836—22no—
10#16839831—22no—
11#16839816—21no—
12#16839726C2211yescharacteristic
13#16839726C2211yescharacteristic
14C22⋊C8×D61—21no—
15#16839695—21no—
16#16839684—21no—
17#16839643—21no—
18#16839641C411yescharacteristic
19#16839641C411yescharacteristic
20#16839635C411yescharacteristic
21#16839635C411yescharacteristic
22#16839633—21no—
23#16839622C2211yescharacteristic
24#16839488—22no—
25#16839487—21no—
26#16839485—21no—
27C22×C4⋊C4×C61C2211yescharacteristic
28C61×#407C2211yescharacteristic
29C61×#407C2211yescharacteristic
30C61×#324—22no—
31C22×C22⋊D61C2×C411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C2×#11758194—21no—
34C2×#11758194—21no—
35C2×C8×D61—22no—
36C4×C22⋊D61—21no—
37C4×C22⋊D61—21no—
38C4×C22⋊D61—21no—
39C4×C22⋊D61—21no—
40C2×C4⋊Dic61—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196D411yescharacteristic
44C2×C22⋊Dic61C2×C411yescharacteristic
45C2×C22⋊Dic61C2×C411yescharacteristic
46C2×C22⋊Dic61C2×C411yescharacteristic
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×#11758198D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51#14519706—22no—
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54C22⋊#92418—21no—
55C22⋊#92418D412yes—
56#14519689—22no—
57#14519687—22no—
58#14519684—21no—
59#14519684—21no—
60#14519684—21no—
61#14519684—21no—
62#14519684—21no—
63C23×C4×C61C2×C411yescharacteristic
64C23×C4×C61C2×C411yescharacteristic
65C23×C4×C61C2311yescharacteristic
66C2×M16×C61—21no—
67C2×M16×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61—21no—
74C22⋊C8×C61—21no—
75C22⋊C8×C61—21no—
76C22⋊C8×C61—21no—
77C22⋊C8×C61D412yes—
78C24×C61C22×C411yescharacteristic
79C23×D61C22⋊C411yescharacteristic
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61—42no—
87C22×C4×C61—81no—
88C22×C4×C61—81no—
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61#4111yescharacteristic
94C22×C4×C61#4111yescharacteristic
95C2×C22⋊D61—21no—
96C2×C22⋊D61—21no—
97C2×C22⋊D61—22no—
98C2×C22⋊D61—41no—
99C22×Dic61—21no—
100C22×Dic61—21no—
101C22×Dic61C22⋊C411yescharacteristic
102C22×Dic61C22⋊C411yescharacteristic
103C22×Dic61C22⋊C411yescharacteristic
104C2×C4×D61—21no—
105C2×C4×D61—21no—
106C2×C4×D61—81no—
107M16×C61—81no—
108M16×C61—81no—
109C2×C8×C61—22no—
110C2×C8×C61—41no—
111C4⋊C4×C61—41no—
112C4⋊C4×C61—41no—
113C4⋊C4×C61—41no—
114C4⋊C4×C61—41no—
115C22⋊Dic61—21no—
116C22⋊Dic61—21no—
117C22⋊Dic61—41no—
118C22⋊Dic61—41no—
119#11758198—21no—
120#11758198—21no—
121#11758198—42no—
122#11758198—81no—
123C4⋊Dic61—81no—
124#11758196—21no—
125#11758196—21no—
126#11758196—42no—
127#11758196—81no—
128C4×Dic61—21no—
129C4×Dic61—21no—
130#11758194—81no—
131#11758194—81no—
132C2×#92418—22no—
133C2×#92418—41no—
134C8×D61—82no—
135C23×C61—21no—
136C23×C61—21no—
137C23×C61—41no—
138C23×C61—41no—
139C23×C61C2×C22⋊C411yescharacteristic
140C23×C61C4×D411yescharacteristic
141C23×C61C4×D411yescharacteristic
142C22×D61—21no—
143C22×D61—21no—
144C22×D61—41no—
145C22×D61—41no—
146C22×D61#10112yes—
147C2×C4×C61—22no—
148C2×C4×C61—22no—
149C2×C4×C61—22no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
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—81no—
164C2×C4×C61—81no—
165C2×C4×C61#12011yescharacteristic
166C2×C4×C61#12111yescharacteristic
167C2×C4×C61#12111yescharacteristic
168C2×C4×C61#12311yescharacteristic
169C22⋊D61—42no—
170C22⋊D61—42no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—21no—
175C2×Dic61—21no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C4×D61—42no—
185C4×D61—81no—
186C8×C61—42no—
187C8×C61—81no—
188#92418—42no—
189#92418—81no—
190#9517—611nomaximal, Sylow
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61—21no—
197C22×C61—21no—
198C22×C61—21no—
199C22×C61—42no—
200C22×C61—42no—
201C22×C61#38611yescharacteristic
202C22×C61C2×#10111yescharacteristic
203C22×C61#41311yescharacteristic
204C2×D61—22no—
205C2×D61—41no—
206C2×D61—41no—
207C2×D61—42no—
208C2×D61—81no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—42no—
214C4×C61—81no—
215Dic61—41no—
216Dic61—41no—
217Dic61—41no—
218Dic61—81no—
219Dic61—81no—
220#2973—611no—
221#2579—611no—
222#1465—611no—
223#1463—611no—
224#1463D6111yescharacteristic, complemented
225#1305—611no—
226#1305—611no—
227C2×C61—21no—
228C2×C61—21no—
229C2×C61—41no—
230C2×C61—41no—
231C2×C61#189111yescharacteristic
232C2×C61#190111yescharacteristic
233C2×C61#191311yescharacteristic
234D61—42no—
235C2×C4×D4—611no—
236C22×C4⋊C4C2×D6111yescharacteristic
237#435—1222no—
238#435—1222no—
239#432—1221no—
240#407—611no—
241#407—611no—
242#407C2×D6111yescharacteristic
243#407C2×D6111yescharacteristic
244C2×C22⋊C8—1221no—
245#398—1221no—
246#396—1221no—
247#387—1221no—
248#386—611no—
249#386—611no—
250#385—611no—
251#385—611no—
252#385—1221no—
253#380—611no—
254#324—22no—
255#324—1221no—
256#324—1222no—
257#323—1221no—
258C61#951711yescharacteristic, complemented, Sylow
259C22×D4—611no—
260C23×C4—611no—
261C23×C4C4×D6111yescharacteristic
262C23×C4C4×D6111yescharacteristic
263C23×C4C22×D6111yescharacteristic
264C2×M16—21no—
265C2×M16—21no—
266C2×M16—1221no—
267C2×M16—1221no—
268C22×C8—1222no—
269C4×D4—1221no—
270C4×D4—1221no—
271C4×D4—1221no—
272C4×D4—1221no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—611no—
280C2×C4⋊C4—1221no—
281C2×C4⋊C4—1221no—
282C2×C4⋊C4—1221no—
283C2×C22⋊C4—611no—
284C2×C22⋊C4—611no—
285C2×C22⋊C4—611no—
286C2×C22⋊C4—611no—
287C2×C22⋊C4—1221no—
288C2×C22⋊C4—1221no—
289C2×C42—611no—
290C4⋊C8—1222no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8—612no—
295C22⋊C8—1222no—
296C22⋊C8—1221no—
297C22⋊C8—1221no—
298C22⋊C8—1221no—
299C22⋊C8C22⋊D6112yes—
300#97—1222no—
301#95—1221no—
302#95—1221no—
303#95—1221no—
304#95—1221no—
305#95—1221no—
306C24—611no—
307C24C2×C4×D6111yescharacteristic
308C2×D4—1222no—
309C2×D4—1221no—
310C2×D4—1221no—
311C2×D4—2441no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—42no—
319C22×C4—81no—
320C22×C4—81no—
321C22×C4—611no—
322C22×C4—611no—
323C22×C4—611no—
324C22×C4—1221no—
325C22×C4—1221no—
326C22×C4—1221no—
327C22×C4—1221no—
328C22×C4—4881no—
329C22×C4#1175822211yescharacteristic
330C22×C4D4×D6111yescharacteristic
331C22×C4D4×D6111yescharacteristic
332C22×C4D4×D6111yescharacteristic
333C22×C4#1175822411yescharacteristic
334C22×C4C2×C22⋊D6111yescharacteristic
335M16—81no—
336M16—81no—
337M16—4881no—
338M16—4881no—
339C2×C8—22no—
340C2×C8—41no—
341C2×C8—1222no—
342C2×C8—4882no—
343C2×C8—2441no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—1221no—
349C4⋊C4—1221no—
350C4⋊C4—4881no—
351C4⋊C4—4881no—
352C4⋊C4—2442no—
353C22⋊C4—1221no—
354C22⋊C4—1221no—
355C22⋊C4—1221no—
356C22⋊C4—1221no—
357C22⋊C4—4881no—
358C22⋊C4—2442no—
359C22⋊C4—2441no—
360C22⋊C4—2441no—
361C42—1221no—
362C42—1221no—
363C23—21no—
364C23—21no—
365C23—41no—
366C23—41no—
367C23—612no—
368C23—1221no—
369C23—1221no—
370C23—2441no—
371C23—2441no—
372C23C22⋊C4×D6111yescharacteristic
373C23#1451973711yescharacteristic
374C23C4×C22⋊D6111yescharacteristic
375D4—2442no—
376D4—2442no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—1221no—
396C2×C4—1221no—
397C2×C4—1221no—
398C2×C4—1221no—
399C2×C4—1221no—
400C2×C4—4881no—
401C2×C4—2442no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4—2441no—
410C2×C4#1451974511yescharacteristic
411C2×C4#1451974811yescharacteristic
412C2×C4#1451975011yescharacteristic
413C2×C4#1451975911yescharacteristic
414C8—42no—
415C8—81no—
416C8—4881no—
417C8—2442no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—42no—
427C22—42no—
428C22—1222no—
429C22—4881no—
430C22—2442no—
431C22—2441no—
432C22—2441no—
433C22#1683963811yescharacteristic
434C22#101×D6111yescharacteristic
435C22#1683974511yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—42no—
441C4—81no—
442C4—4881no—
443C4—4881no—
444C4—2441no—
445C4—2441no—
446C4—2441no—
447C2—21no—
448C2—21no—
449C2—41no—
450C2—41no—
451C2—2442no—
452C2#2144623411yescharacteristic
453C2#2144628411yescharacteristic
454C2#2144635811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC24×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1463C2
socleC22×C61#386
prime radicalC22×C22⋊D61C2×C4
cosocleC23×C4×C61C23
hypercenter#1463D61
hypocenterC61#9517
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
4. #21444149C2semidirect
5. #21443726C2semidirect
6. #21443724C2semidirect
7. C61×#1463C2semidirect
224. #1463D61semidirect
258. C61#9517semidirect

Maximal subgroups

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

subgroupindex
#214548462
#214511662
#214441552
#214441492
#214437262
#214437242
C61×#14632
#951761