Finite Group Databasebeta

← #29577944

Subgroups — #29577944

Order 15616.

660 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 93 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#21450097C211yesmaximal, characteristic
2#21448415C211yesmaximal, characteristic
3#21445893C211yesmaximal, characteristic
4#21445891C211yesmaximal, characteristic
5#21443723C211yesmaximal, characteristic
6#21443723C211yesmaximal, characteristic
7C61×#1819C211yesmaximal, characteristic
8C22×C22⋊Dic61C2211yescharacteristic
9#16839690—22no—
10#16839656—22no—
11#16839650—22no—
12#16839635C412yescomplemented
13#16839634—21no—
14#16839625C412yescomplemented
15#16839623—21no—
16#16839620—21no—
17#16839618C2211yescharacteristic
18#16839618C2211yescharacteristic
19#16839618C2211yescharacteristic
20C22⋊C4×Dic61—21no—
21#16839529—22no—
22#16839528—22no—
23C22×C22⋊C4×C61C2211yescharacteristic
24C61×#379C2211yescharacteristic
25C61×#379C2211yescharacteristic
26C61×#342—22no—
27C23×Dic61D411yescharacteristic
28C23×Dic61D411yescharacteristic
29C2×#11758196—22no—
30C2×#11758196—22no—
31C2×C22⋊Dic61—21no—
32C2×C22⋊Dic61—21no—
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61C2×C412yes—
43C2×C22⋊Dic61C2×C412yes—
44C2×C22⋊Dic61D412yes—
45C2×C22⋊Dic61D412yes—
46C2×C4×Dic61—22no—
47#14519684—22no—
48#14519684—22no—
49#14519684—22no—
50#14519684—22no—
51#14519684—22no—
52C25×C61C2311yescharacteristic
53C23×C4×C61C2×C411yescharacteristic
54C23×C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61—21no—
63C2×C22⋊C4×C61—21no—
64C2×C22⋊C4×C61—21no—
65C2×C22⋊C4×C61—21no—
66C2×C22⋊C4×C61D412yes—
67C24×C61—42no—
68C24×C61—42no—
69C24×C61—81no—
70C24×C61C22×C411yescharacteristic
71C24×C61C2×D411yescharacteristic
72C24×C61C2×D411yescharacteristic
73C24×C61C2×D411yescharacteristic
74C24×C61C2×D411yescharacteristic
75C24×C61#4111yescharacteristic
76C24×C61#4111yescharacteristic
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—22no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—42no—
85C22×C4×C61—41no—
86C22×C4×C61—81no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—21no—
90C22×Dic61—21no—
91C22×Dic61—22no—
92C22×Dic61—22no—
93C22×Dic61—42no—
94C22×Dic61—41no—
95C22×Dic61—81no—
96C22×Dic61C22⋊C412yes—
97C22×Dic61C22⋊C412yes—
98C22⋊C4×C61—42no—
99C22⋊C4×C61—41no—
100C22⋊C4×C61—41no—
101C22⋊C4×C61—41no—
102C22⋊C4×C61—41no—
103C22⋊C4×C61—42no—
104C22⋊C4×C61—42no—
105C22⋊C4×C61—42no—
106C22⋊C4×C61—81no—
107C22⋊C4×C61—81no—
108C22⋊Dic61—22no—
109C22⋊Dic61—22no—
110C22⋊Dic61—22no—
111C22⋊Dic61—22no—
112C22⋊Dic61—42no—
113C22⋊Dic61—42no—
114C22⋊Dic61—42no—
115C22⋊Dic61—42no—
116C22⋊Dic61—42no—
117C22⋊Dic61—42no—
118C22⋊Dic61—81no—
119C22⋊Dic61—81no—
120C22⋊Dic61—81no—
121#11758196—82no—
122#11758196—82no—
123C4×Dic61—82no—
124C23×C61—22no—
125C23×C61—22no—
126C23×C61—22no—
127C23×C61—22no—
128C23×C61—22no—
129C23×C61—22no—
130C23×C61—41no—
131C23×C61—41no—
132C23×C61—41no—
133C23×C61—41no—
134C23×C61—41no—
135C23×C61—41no—
136C23×C61—41no—
137C23×C61—41no—
138C23×C61—41no—
139C23×C61—41no—
140C23×C61—41no—
141C23×C61—41no—
142C23×C61—41no—
143C23×C61—41no—
144C23×C61—41no—
145C23×C61—88no—
146C23×C61C2×C22⋊C411yescharacteristic
147C23×C61C4×D411yescharacteristic
148C23×C61C4×D411yescharacteristic
149C23×C61#12011yescharacteristic
150C23×C61#12111yescharacteristic
151C23×C61#12111yescharacteristic
152C23×C61#12311yescharacteristic
153C2×C4×C61—42no—
154C2×C4×C61—42no—
155C2×C4×C61—42no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—42no—
159C2×C4×C61—42no—
160C2×C4×C61—81no—
161C2×C4×C61—81no—
162C2×C4×C61—81no—
163C2×C4×C61—81no—
164C2×C4×C61—81no—
165C2×C4×C61—81no—
166C2×C4×C61—81no—
167C2×Dic61—22no—
168C2×Dic61—22no—
169C2×Dic61—42no—
170C2×Dic61—42no—
171C2×Dic61—42no—
172C2×Dic61—42no—
173C2×Dic61—42no—
174C2×Dic61—42no—
175C2×Dic61—42no—
176C2×Dic61—42no—
177C2×Dic61—42no—
178C2×Dic61—42no—
179C2×Dic61—81no—
180C2×Dic61—81no—
181C2×Dic61—81no—
182C2×Dic61—81no—
183C2×Dic61—81no—
184#9502—611nomaximal, Sylow
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—21no—
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—21no—
200C22×C61—21no—
201C22×C61—21no—
202C22×C61—21no—
203C22×C61—21no—
204C22×C61—44no—
205C22×C61—44no—
206C22×C61—82no—
207C22×C61—82no—
208C22×C61—82no—
209C22×C61—82no—
210C22×C61—82no—
211C22×C61#38611yescharacteristic
212C22×C61#41012yes—
213C22×C61#45812yes—
214C4×C61—82no—
215C4×C61—81no—
216C4×C61—81no—
217C4×C61—161no—
218Dic61—42no—
219Dic61—42no—
220Dic61—82no—
221Dic61—82no—
222Dic61—161no—
223#2483—611no—
224#2312—611no—
225#1819—611no—
226#1819—611no—
227#1819D6111yescharacteristic
228#1304—611no—
229#1304—611no—
230C2×C61—22no—
231C2×C61—22no—
232C2×C61—41no—
233C2×C61—41no—
234C2×C61—41no—
235C2×C61—41no—
236C2×C61—41no—
237C2×C61#189011yescharacteristic
238C2×C61#189911yescharacteristic
239C2×C61#191311yescharacteristic
240C22×C22⋊C4—611no—
241C22×C22⋊C4C2×D6111yescharacteristic
242#397—1222no—
243#388—1222no—
244#388—1222no—
245#385—612no—
246#385—1221no—
247#381—612no—
248#381—1221no—
249#380—1221no—
250#379—611no—
251#379—611no—
252#379—611no—
253#379C2×D6111yescharacteristic
254#379C2×D6111yescharacteristic
255C4×C22⋊C4—1221no—
256#342—22no—
257#342—1222no—
258#342—1222no—
259C61#950211yescharacteristic, complemented, Sylow
260C25C22×D6111yescharacteristic
261C23×C4—611no—
262C23×C4—611no—
263C23×C4C4×D6111yescharacteristic
264C23×C4C4×D6111yescharacteristic
265C2×C4⋊C4—1222no—
266C2×C4⋊C4—1222no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—612no—
279C2×C22⋊C4—612no—
280C2×C22⋊C4—612no—
281C2×C22⋊C4—612no—
282C2×C22⋊C4—1221no—
283C2×C22⋊C4—1221no—
284C2×C22⋊C4—1221no—
285C2×C22⋊C4—1221no—
286C2×C22⋊C4—1221no—
287C2×C22⋊C4—1221no—
288C2×C22⋊C4—1221no—
289C2×C22⋊C4—1221no—
290C2×C22⋊C4—1221no—
291C2×C22⋊C4—1221no—
292C2×C22⋊C4—1221no—
293C2×C22⋊C4C22⋊D6112yes—
294C2×C42—1222no—
295#95—1222no—
296#95—1222no—
297#95—1222no—
298#95—1222no—
299#95—1222no—
300C24—42no—
301C24—42no—
302C24—81no—
303C24C2×C4×D6111yescharacteristic
304C24#1175822211yescharacteristic
305C24D4×D6111yescharacteristic
306C24D4×D6111yescharacteristic
307C24D4×D6111yescharacteristic
308C24#1175822411yescharacteristic
309C24C2×C22⋊D6111yescharacteristic
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—42no—
318C22×C4—41no—
319C22×C4—81no—
320C22×C4—612no—
321C22×C4—612no—
322C22×C4—1221no—
323C22×C4—1221no—
324C22×C4—1221no—
325C22×C4—1221no—
326C22×C4—1222no—
327C22×C4—1222no—
328C22×C4—4881no—
329C22×C4—2441no—
330C22×C4—2442no—
331C4⋊C4—4882no—
332C4⋊C4—4882no—
333C22⋊C4—42no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—42no—
339C22⋊C4—42no—
340C22⋊C4—42no—
341C22⋊C4—81no—
342C22⋊C4—81no—
343C22⋊C4—1222no—
344C22⋊C4—1222no—
345C22⋊C4—1222no—
346C22⋊C4—1222no—
347C22⋊C4—4881no—
348C22⋊C4—4881no—
349C22⋊C4—4881no—
350C22⋊C4—2442no—
351C22⋊C4—2442no—
352C22⋊C4—2442no—
353C22⋊C4—2442no—
354C22⋊C4—2442no—
355C22⋊C4—2442no—
356C42—4882no—
357C23—22no—
358C23—22no—
359C23—22no—
360C23—22no—
361C23—22no—
362C23—22no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—88no—
379C23C22⋊C4×D6111yescharacteristic
380C23#1451973711yescharacteristic
381C23C4×C22⋊D6111yescharacteristic
382C23#1451974511yescharacteristic
383C23#1451974811yescharacteristic
384C23#1451975011yescharacteristic
385C23#1451975911yescharacteristic
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—1222no—
401C2×C4—1222no—
402C2×C4—4881no—
403C2×C4—4881no—
404C2×C4—4881no—
405C2×C4—4881no—
406C2×C4—4881no—
407C2×C4—2442no—
408C2×C4—2442no—
409C2×C4—2442no—
410C2×C4—2442no—
411C2×C4—2442no—
412C2×C4—2442no—
413C2×C4—2442no—
414C2×C4—2442no—
415C2×C4—2442no—
416C2×C4—2442no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—44no—
437C22—44no—
438C22—82no—
439C22—82no—
440C22—82no—
441C22—82no—
442C22—82no—
443C22#1683963811yescharacteristic
444C22#1683973412yes—
445C22#1683995112yes—
446C4—82no—
447C4—81no—
448C4—81no—
449C4—161no—
450C4—9761no—
451C4—4882no—
452C4—4882no—
453C4—2442no—
454C4—2442no—
455C2—22no—
456C2—22no—
457C2—41no—
458C2—41no—
459C2—41no—
460C2—41no—
461C2—41no—
462C2#2144622911yescharacteristic
463C2#2144627411yescharacteristic
464C2#2144635811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC24×C61C22×C4
FrattiniC25C22×D61
FittingC61×#1819C2
socleC22×C61#386
prime radical, cosocleC25×C61C23
hypercenter#1819D61
hypocenterC61#9502
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C25 ◁ #1819

Complements

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

NH ≅ G/Ntype
12. #16839635C4semidirect
14. #16839625C4semidirect
259. C61#9502semidirect

Maximal subgroups

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

subgroupindex
#214500972
#214484152
#214458932
#214458912
#214437232
C61×#18192
#950261