Finite Group Databasebeta

← #29598708

Subgroups — #29598708

Order 15616.

670 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519718C211yesmaximal, characteristic, complemented
2C2×#16839998C211yesmaximal, characteristic, complemented
3C2×#16839563C211yesmaximal, characteristic, complemented
4C2×#16839562C211yesmaximal, characteristic, complemented
5C2×C22⋊#11758185C211yesmaximal, characteristic, complemented
6#21443910C211yesmaximal, characteristic, complemented
7C2×C61×#466C211yesmaximal, characteristic, complemented
8C22×D488C2211yescharacteristic
9C2×#14519751—21no—
10C2×#14519718—22no—
11C2×#14519718—22no—
12C2×#14519718—22no—
13C22×#11758185C2211yescharacteristic
14C22×#11758185C2211yescharacteristic
15#16839998—22no—
16#16839998—22no—
17C2×#14519711C2211yescharacteristic
18C2×#14519699—21no—
19#16839563—22no—
20#16839562—22no—
21C22⋊#11758185—22no—
22C22×D8×C61C2211yescharacteristic
23C23×C8×C61C2211yescharacteristic
24C2×#121×C61—21no—
25C61×#466—22no—
26C61×#466—22no—
27C2×#107×C61C2211yescharacteristic
28C2×#102×C61—21no—
29C22×D244—21no—
30C22×C22⋊D61—41no—
31C2×D488—21no—
32C2×D488—21no—
33C2×D488—21no—
34C2×D488—21no—
35C2×D488—21no—
36C2×D488D412yescomplemented
37#14519751—24no—
38#14519751—42no—
39C2×C4⋊Dic61—21no—
40C2×#11758198—41no—
41#14519718—28no—
42C2×#11758185—21no—
43C2×#11758185—21no—
44C2×#11758185—21no—
45C2×#11758185—21no—
46C2×#11758185—21no—
47C2×#11758185D412yescomplemented
48#14519711—21no—
49#14519711D412yescomplemented
50#14519699—24no—
51C22×D4×C61—21no—
52C22×D4×C61—41no—
53C23×C4×C61D411yescharacteristic
54C2×D8×C61—21no—
55C2×D8×C61—21no—
56C2×D8×C61—21no—
57C2×D8×C61—21no—
58C2×D8×C61—21no—
59C2×D8×C61D412yescomplemented
60C22×C8×C61—21no—
61C22×C8×C61—21no—
62C22×C8×C61—21no—
63C22×C8×C61—21no—
64C22×C8×C61—21no—
65C22×C8×C61—21no—
66C22×C8×C61D411yescharacteristic
67C22×C8×C61C2311yescharacteristic
68#121×C61—24no—
69#121×C61—42no—
70C2×C4⋊C4×C61—21no—
71C2×C22⋊C4×C61—41no—
72#107×C61—21no—
73#107×C61D412yescomplemented
74#102×C61—24no—
75C24×C61—41no—
76C24×C61D811yescharacteristic
77C23×D61—41no—
78C2×D4×C61—22no—
79C2×D4×C61—44no—
80C2×D4×C61—41no—
81C2×D4×C61—41no—
82C2×D4×C61—41no—
83C2×D4×C61—41no—
84C2×D4×C61—41no—
85C2×D4×C61—82no—
86C2×D4×C61—82no—
87C22×C4×C61—21no—
88C22×C4×C61—21no—
89C22×C4×C61—21no—
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—21no—
93C22×C4×C61—41no—
94C22×C4×C61D811yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C2×C22⋊D61—44no—
97C2×C22⋊D61—82no—
98C2×C22⋊D61—82no—
99C22×Dic61—41no—
100C2×D244—22no—
101C2×D244—41no—
102C2×D244—41no—
103C2×D244—41no—
104C2×D244—41no—
105C2×D244—41no—
106D8×C61—22no—
107D8×C61—22no—
108D8×C61—41no—
109D8×C61—41no—
110C2×C8×C61—21no—
111C2×C8×C61—21no—
112C2×C8×C61—21no—
113C2×C8×C61—41no—
114C2×C8×C61—41no—
115C2×C8×C61—41no—
116C2×C8×C61—41no—
117C2×C8×C61C2×D411yescharacteristic
118C2×C8×C61C2×D411yescharacteristic
119C2×C8×C61C2×D411yescharacteristic
120C2×C8×C61C2×D411yescharacteristic
121C2×C8×C61C2×D411yescharacteristic
122C2×C8×C61#4111yescharacteristic
123C4⋊C4×C61—22no—
124C4⋊C4×C61—41no—
125C22⋊C4×C61—44no—
126#11758198—44no—
127C4⋊Dic61—22no—
128C4⋊Dic61—41no—
129D488—22no—
130D488—22no—
131D488—41no—
132D488—41no—
133#11758185—22no—
134#11758185—41no—
135C23×C61—21no—
136C23×C61—21no—
137C23×C61—21no—
138C23×C61—21no—
139C23×C61—21no—
140C23×C61—21no—
141C23×C61—42no—
142C23×C61—81no—
143C23×C61—81no—
144C23×C61—81no—
145C23×C61—81no—
146C23×C61—81no—
147C23×C61—81no—
148C23×C61D1612yescomplemented
149C23×C61C2×D811yescharacteristic
150C22×D61—42no—
151C22×D61—81no—
152C22×D61—81no—
153C22×D61—81no—
154C22×D61—81no—
155C22×D61—81no—
156C22×D61—81no—
157D4×C61—42no—
158D4×C61—42no—
159D4×C61—88no—
160D4×C61—81no—
161D4×C61—81no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—42no—
170C2×C4×C61—81no—
171C2×C4×C61—81no—
172C2×C4×C61#12011yescharacteristic
173C2×C4×C61#12011yescharacteristic
174C2×C4×C61#12111yescharacteristic
175C2×C4×C61#13511yescharacteristic
176C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
178C22⋊D61—88no—
179C2×Dic61—42no—
180C2×Dic61—81no—
181C2×Dic61—81no—
182D244—42no—
183D244—42no—
184D244—81no—
185D244—81no—
186C8×C61—41no—
187C8×C61#12011yescharacteristic
188C8×C61#12111yescharacteristic
189C8×C61#12111yescharacteristic
190C8×C61#12711yescharacteristic
191#13304—611nomaximal, Sylow
192C22×C61—22no—
193C22×C61—22no—
194C22×C61—22no—
195C22×C61—41no—
196C22×C61—41no—
197C22×C61—41no—
198C22×C61—41no—
199C22×C61—82no—
200C22×C61—82no—
201C22×C61—82no—
202C22×C61—161no—
203C22×C61—161no—
204C22×C61—161no—
205C22×C61—161no—
206C22×C61#44711yescharacteristic
207C22×C61#44711yescharacteristic
208C22×C61#46611yescharacteristic
209C22×C61C2×D1611yescharacteristic
210C22×C61#50811yescharacteristic
211C22×C61#50911yescharacteristic
212C22×C61#50911yescharacteristic
213C2×D61—82no—
214C2×D61—82no—
215C2×D61—82no—
216C2×D61—161no—
217C2×D61—161no—
218C2×D61—161no—
219C2×D61—161no—
220C4×C61—41no—
221C4×C61—82no—
222C4×C61#39211yescharacteristic
223C4×C61#44911yescharacteristic
224C4×C61#44911yescharacteristic
225C4×C61#46911yescharacteristic
226Dic61—82no—
227C22×D16—611no—
228C2×#466—611no—
229C2×#466D6111yescharacteristic, complemented
230C2×#357—611no—
231C2×#357—611no—
232C2×C22⋊C16—611no—
233#1380—611no—
234C2×C61—42no—
235C2×C61—162no—
236C2×C61#199911yescharacteristic
237C2×C61#218411yescharacteristic
238C2×C61#218411yescharacteristic
239C2×C61#218611yescharacteristic
240C2×C61#218611yescharacteristic
241C2×C61#221511yescharacteristic
242C2×C61#221811yescharacteristic
243D61—162no—
244C22×D8—611no—
245C22×D8C2×D6111yescharacteristic
246C23×C8C2×D6111yescharacteristic
247C2×#121—21no—
248C2×#121—1221no—
249C2×D16—1222no—
250C2×D16—1222no—
251C2×D16—1222no—
252C22×C16—611no—
253C22×C16—611no—
254#466—22no—
255#466—22no—
256#466—1222no—
257#466—1222no—
258C2×#107—611no—
259C2×#107C2×D6111yescharacteristic
260C2×#102—21no—
261C2×#102—1221no—
262#357—1222no—
263#357—1222no—
264C22⋊C16—1222no—
265C61#1330411yescharacteristic, complemented, Sylow
266C22×D4—21no—
267C22×D4—41no—
268C22×D4—1221no—
269C22×D4—2441no—
270C23×C4C22⋊D6111yescharacteristic
271C2×D8—21no—
272C2×D8—21no—
273C2×D8—21no—
274C2×D8—21no—
275C2×D8—21no—
276C2×D8—612no—
277C2×D8—1221no—
278C2×D8—1221no—
279C2×D8—1221no—
280C2×D8—1221no—
281C2×D8—1221no—
282C2×D8C22⋊D6112yescomplemented
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8C22⋊D6111yescharacteristic
290C22×C8C22×D6111yescharacteristic
291#121—24no—
292#121—42no—
293#121—1224no—
294#121—2442no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—1221no—
297C2×C22⋊C4—41no—
298C2×C22⋊C4—2441no—
299D16—1228no—
300C2×C16—612no—
301C2×C16—1221no—
302C2×C16—1221no—
303C2×C16—1221no—
304C2×C16—1221no—
305C2×C16—1221no—
306#107—21no—
307#107—612no—
308#107—1221no—
309#107C22⋊D6112yescomplemented
310#102—24no—
311#102—1224no—
312C24—41no—
313C24—2441no—
314C24#1175819911yescharacteristic
315C2×D4—22no—
316C2×D4—44no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—82no—
323C2×D4—82no—
324C2×D4—1222no—
325C2×D4—4882no—
326C2×D4—4882no—
327C2×D4—2444no—
328C2×D4—2441no—
329C2×D4—2441no—
330C2×D4—2441no—
331C2×D4—2441no—
332C2×D4—2441no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—41no—
340C22×C4—2441no—
341C22×C4#1175819911yescharacteristic
342C22×C4C2×C22⋊D6111yescharacteristic
343D8—22no—
344D8—22no—
345D8—41no—
346D8—41no—
347D8—1222no—
348D8—1222no—
349D8—2441no—
350D8—2441no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8—41no—
355C2×C8—41no—
356C2×C8—41no—
357C2×C8—41no—
358C2×C8D4×D6111yescharacteristic
359C2×C8D4×D6111yescharacteristic
360C2×C8D4×D6111yescharacteristic
361C2×C8#1175822411yescharacteristic
362C2×C8C2×C22⋊D6111yescharacteristic
363C2×C8C2×C22⋊D6111yescharacteristic
364C4⋊C4—22no—
365C4⋊C4—41no—
366C4⋊C4—1222no—
367C4⋊C4—2441no—
368C22⋊C4—44no—
369C22⋊C4—2444no—
370C16—1222no—
371C16—2441no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—42no—
379C23—81no—
380C23—81no—
381C23—81no—
382C23—81no—
383C23—81no—
384C23—81no—
385C23—4881no—
386C23—4881no—
387C23—4881no—
388C23—4881no—
389C23—4881no—
390C23—4881no—
391C23—2442no—
392C23#1451971812yescomplemented
393C23C2×#1175819911yescharacteristic
394D4—42no—
395D4—42no—
396D4—88no—
397D4—81no—
398D4—81no—
399D4—4888no—
400D4—4881no—
401D4—4881no—
402D4—2442no—
403D4—2442no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—81no—
413C2×C4—81no—
414C2×C4—4881no—
415C2×C4—4881no—
416C2×C4—2442no—
417C2×C4#1451974511yescharacteristic
418C2×C4#1451974611yescharacteristic
419C2×C4#1451974911yescharacteristic
420C2×C4#1451979711yescharacteristic
421C2×C4#1451980211yescharacteristic
422C2×C4#1451980311yescharacteristic
423C8—41no—
424C8#1451974511yescharacteristic
425C8#1451974811yescharacteristic
426C8#1451974911yescharacteristic
427C8#1451977311yescharacteristic
428C22—22no—
429C22—22no—
430C22—22no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—82no—
436C22—82no—
437C22—82no—
438C22—161no—
439C22—161no—
440C22—161no—
441C22—161no—
442C22—9761no—
443C22—9761no—
444C22—9761no—
445C22—9761no—
446C22—4882no—
447C22—4882no—
448C22—4882no—
449C22#1683989511yescharacteristic
450C22#1683989611yescharacteristic
451C22#1683999611yescharacteristic
452C22C2×#1451971811yescharacteristic
453C22#1684019211yescharacteristic
454C22#1684019711yescharacteristic
455C22#1684019811yescharacteristic
456C4—41no—
457C4—82no—
458C4—4882no—
459C4#1683967011yescharacteristic
460C4#1683990511yescharacteristic
461C4#1683990711yescharacteristic
462C4#1684001311yescharacteristic
463C2—42no—
464C2—162no—
465C2—9762no—
466C2#2144681511yescharacteristic
467C2#2144773011yescharacteristic
468C2#2144773111yescharacteristic
469C2#2144774011yescharacteristic
470C2#2144774211yescharacteristic
471C2#2144790311yescharacteristic
472C2#2144792011yescharacteristic
subgroupG/H
centerC23C2×#11758199
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC2×C61×#466C2
socleC23×C61C2×D8
hypercenterC2×#466D61
hypocenterC61#13304
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C22×#14519718C2semidirect
2. C2×#16839998C2semidirect
3. C2×#16839563C2semidirect
4. C2×#16839562C2semidirect
5. C2×C22⋊#11758185C2semidirect
6. #21443910C2semidirect
7. C2×C61×#466C2semidirect
36. C2×D488D4semidirect
47. C2×#11758185D4semidirect
49. #14519711D4semidirect
59. C2×D8×C61D4semidirect
73. #107×C61D4semidirect
148. C23×C61D16semidirect
229. C2×#466D61semidirect
265. C61#13304semidirect
282. C2×D8C22⋊D61semidirect
309. #107C22⋊D61semidirect
392. C23#14519718semidirect

Maximal subgroups

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

subgroupindex
C22×#145197182
C2×#168399982
C2×#168395632
C2×#168395622
C2×C22⋊#117581852
#214439102
C2×C61×#4662
#1330461