Finite Group Databasebeta

← #29598709

Subgroups — #29598709

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×#16839999C211yesmaximal, characteristic, complemented
3C2×#16839995C211yesmaximal, characteristic, complemented
4C2×#16839564C211yesmaximal, characteristic, complemented
5C2×#16839541C211yesmaximal, characteristic, complemented
6#21443910C211yesmaximal, characteristic, complemented
7C2×C61×#357C211yesmaximal, characteristic, complemented
8C22×D488C2211yescharacteristic
9C22×C8×D61C2211yescharacteristic
10C2×#14519752—21no—
11C2×#14519748—21no—
12C2×#14519718—22no—
13C2×#14519718—22no—
14C2×#14519718—22no—
15C22×#11758185C2211yescharacteristic
16#16839999—22no—
17#16839999—22no—
18#16839995—22no—
19#16839995—22no—
20C2×#14519711C2211yescharacteristic
21C2×#14519698—21no—
22C2×#14519697—21no—
23#16839564—22no—
24#16839541—22no—
25C22×D8×C61C2211yescharacteristic
26C22×C16×C61C2211yescharacteristic
27C2×#107×C61C2211yescharacteristic
28C61×#357—22no—
29C22×D244—21no—
30C22×D244—41no—
31C22×C22⋊D61—41no—
32C22×C4×D61D411yescharacteristic
33C2×D488—21no—
34C2×D488—21no—
35C2×D488—21no—
36C2×D488—21no—
37C2×D488—21no—
38C2×D488D412yescomplemented
39C22×#92418D411yescharacteristic
40C2×C8×D61—21no—
41C2×C8×D61—21no—
42C2×C8×D61—21no—
43C2×C8×D61—21no—
44C2×C8×D61—21no—
45C2×C8×D61—21no—
46#14519752—24no—
47#14519752—42no—
48#14519748—24no—
49#14519748—42no—
50C2×C4⋊Dic61—21no—
51C2×C22⋊Dic61—41no—
52C2×#11758198—41no—
53#14519718—28no—
54C2×#11758185—21no—
55C2×#11758185—21no—
56C2×#11758185D412yescomplemented
57#14519711—21no—
58#14519711D412yescomplemented
59#14519698—24no—
60#14519697—24no—
61C22×D4×C61—21no—
62C2×D8×C61—21no—
63C2×D8×C61—21no—
64C2×D8×C61—21no—
65C2×D8×C61—21no—
66C2×D8×C61—21no—
67C2×D8×C61D412yescomplemented
68C22×C8×C61C2311yescharacteristic
69C2×C4⋊C4×C61—21no—
70C2×C16×C61—21no—
71C2×C16×C61—21no—
72C2×C16×C61—21no—
73#107×C61—21no—
74#107×C61D412yescomplemented
75C24×C61—41no—
76C23×D61—41no—
77C23×D61D811yescharacteristic
78C2×D4×C61—22no—
79C2×D4×C61—41no—
80C2×D4×C61—41no—
81C2×D4×C61—41no—
82C2×D4×C61—41no—
83C2×D4×C61—41no—
84C22×C4×C61—41no—
85C22×C4×C61C2×D411yescharacteristic
86C2×C22⋊D61—44no—
87C2×C22⋊D61—82no—
88C2×C22⋊D61—82no—
89C22×Dic61—41no—
90C22×Dic61D811yescharacteristic
91C2×D244—22no—
92C2×D244—41no—
93C2×D244—41no—
94C2×D244—41no—
95C2×D244—41no—
96C2×D244—44no—
97C2×D244—41no—
98C2×D244—82no—
99C2×D244—82no—
100C2×C4×D61—21no—
101C2×C4×D61—21no—
102C2×C4×D61—21no—
103C2×C4×D61—21no—
104C2×C4×D61—21no—
105C2×C4×D61—21no—
106D8×C61—22no—
107D8×C61—22no—
108D8×C61—41no—
109D8×C61—41no—
110C2×C8×C61C2×D411yescharacteristic
111C2×C8×C61C2×D411yescharacteristic
112C2×C8×C61C2×D411yescharacteristic
113C2×C8×C61C2×D411yescharacteristic
114C2×C8×C61C2×D411yescharacteristic
115C2×C8×C61#4111yescharacteristic
116C4⋊C4×C61—22no—
117C4⋊C4×C61—41no—
118C22⋊Dic61—44no—
119#11758198—44no—
120C4⋊Dic61—22no—
121C4⋊Dic61—41no—
122C2×#92418—21no—
123C2×#92418—21no—
124C2×#92418—21no—
125D488—22no—
126D488—22no—
127D488—41no—
128D488—41no—
129C8×D61—41no—
130C8×D61—41no—
131C8×D61—41no—
132C8×D61—41no—
133C16×C61—41no—
134#11758185—22no—
135C23×C61—42no—
136C23×C61—81no—
137C23×C61—81no—
138C23×C61—81no—
139C23×C61—81no—
140C23×C61—81no—
141C23×C61—81no—
142C23×C61C2×D811yescharacteristic
143C22×D61—21no—
144C22×D61—21no—
145C22×D61—21no—
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—21no—
149C22×D61—42no—
150C22×D61—81no—
151C22×D61—81no—
152C22×D61—81no—
153C22×D61—81no—
154C22×D61—81no—
155C22×D61—81no—
156C22×D61D1612yescomplemented
157D4×C61—42no—
158D4×C61—42no—
159D4×C61—81no—
160D4×C61—81no—
161C2×C4×C61—42no—
162C2×C4×C61—81no—
163C2×C4×C61—81no—
164C2×C4×C61#12011yescharacteristic
165C2×C4×C61#12011yescharacteristic
166C2×C4×C61#12111yescharacteristic
167C2×C4×C61#13511yescharacteristic
168C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
170C22⋊D61—88no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—42no—
175C2×Dic61—81no—
176C2×Dic61—81no—
177D244—42no—
178D244—42no—
179D244—88no—
180D244—81no—
181D244—81no—
182C4×D61—41no—
183C4×D61—41no—
184C4×D61—41no—
185C4×D61—41no—
186C8×C61#12011yescharacteristic
187C8×C61#12111yescharacteristic
188C8×C61#12111yescharacteristic
189C8×C61#12711yescharacteristic
190#92418—41no—
191#13304—611nomaximal, Sylow
192C22×C61—82no—
193C22×C61—82no—
194C22×C61—82no—
195C22×C61—161no—
196C22×C61—161no—
197C22×C61—161no—
198C22×C61—161no—
199C22×C61#44711yescharacteristic
200C22×C61#44711yescharacteristic
201C22×C61#46611yescharacteristic
202C22×C61C2×D1611yescharacteristic
203C22×C61#50811yescharacteristic
204C22×C61#50911yescharacteristic
205C22×C61#50911yescharacteristic
206C2×D61—22no—
207C2×D61—22no—
208C2×D61—22no—
209C2×D61—41no—
210C2×D61—41no—
211C2×D61—41no—
212C2×D61—41no—
213C2×D61—82no—
214C2×D61—82no—
215C2×D61—82no—
216C2×D61—161no—
217C2×D61—161no—
218C2×D61—161no—
219C2×D61—161no—
220C4×C61—82no—
221C4×C61#39211yescharacteristic
222C4×C61#44911yescharacteristic
223C4×C61#44911yescharacteristic
224C4×C61#46911yescharacteristic
225Dic61—41no—
226Dic61—82no—
227C22×D16—611no—
228C2×#466—611no—
229C2×#466—611no—
230C2×#357—611no—
231C2×#357D6111yescharacteristic, complemented
232C2×C22⋊C16—611no—
233#1380—611no—
234C2×C61—162no—
235C2×C61#199911yescharacteristic
236C2×C61#218411yescharacteristic
237C2×C61#218411yescharacteristic
238C2×C61#218611yescharacteristic
239C2×C61#218611yescharacteristic
240C2×C61#221511yescharacteristic
241C2×C61#221811yescharacteristic
242D61—42no—
243D61—162no—
244C22×D8—611no—
245C22×D8C2×D6111yescharacteristic
246C23×C8—611no—
247C2×#121—1221no—
248C2×#121—1221no—
249C2×D16—1222no—
250C2×D16—1222no—
251C2×D16—1222no—
252C22×C16—611no—
253C22×C16C2×D6111yescharacteristic
254#466—1222no—
255#466—1222no—
256#466—1222no—
257#466—1222no—
258C2×#107—611no—
259C2×#107C2×D6111yescharacteristic
260C2×#102—1221no—
261C2×#102—1221no—
262#357—22no—
263#357—1222no—
264C22⋊C16—1222no—
265C61#1330411yescharacteristic, complemented, Sylow
266C22×D4—21no—
267C22×D4—1221no—
268C22×D4—2441no—
269C22×D4—2441no—
270C23×C4—611no—
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×D8D24412yescomplemented
283C22×C8—611no—
284C22×C8—1221no—
285C22×C8—1221no—
286C22×C8—1221no—
287C22×C8—1221no—
288C22×C8—1221no—
289C22×C8—1221no—
290C22×C8C22×D6111yescharacteristic
291#121—1224no—
292#121—1224no—
293#121—2442no—
294#121—2442no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—1221no—
297C2×C22⋊C4—2441no—
298C2×C22⋊C4—2441no—
299D16—1228no—
300C2×C16—21no—
301C2×C16—21no—
302C2×C16—21no—
303C2×C16—612no—
304C2×C16—1221no—
305C2×C16—1221no—
306#107—21no—
307#107—612no—
308#107—1221no—
309#107C22⋊D6112yescomplemented
310#102—1224no—
311#102—1224no—
312C24—41no—
313C24—611no—
314C24—2441no—
315C2×D4—22no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—1222no—
322C2×D4—4882no—
323C2×D4—4882no—
324C2×D4—4882no—
325C2×D4—4882no—
326C2×D4—2444no—
327C2×D4—2444no—
328C2×D4—2441no—
329C2×D4—2441no—
330C2×D4—2441no—
331C2×D4—2441no—
332C2×D4—2441no—
333C22×C4—41no—
334C22×C4—611no—
335C22×C4—1221no—
336C22×C4—1221no—
337C22×C4—1221no—
338C22×C4—1221no—
339C22×C4—1221no—
340C22×C4—1221no—
341C22×C4—2441no—
342C22×C4D4×D6111yescharacteristic
343D8—22no—
344D8—22no—
345D8—41no—
346D8—41no—
347D8—1222no—
348D8—1222no—
349D8—2441no—
350D8—2441no—
351C2×C8—1221no—
352C2×C8—1221no—
353C2×C8—1221no—
354C2×C8—2441no—
355C2×C8—2441no—
356C2×C8—2441no—
357C2×C8—2441no—
358C2×C8C2×D24411yescharacteristic
359C2×C8#1175822211yescharacteristic
360C2×C8D4×D6111yescharacteristic
361C2×C8D4×D6111yescharacteristic
362C2×C8D4×D6111yescharacteristic
363C2×C8C2×C22⋊D6111yescharacteristic
364C4⋊C4—22no—
365C4⋊C4—41no—
366C4⋊C4—1222no—
367C4⋊C4—2441no—
368C22⋊C4—2444no—
369C22⋊C4—2444no—
370C16—41no—
371C16—1222no—
372C23—42no—
373C23—81no—
374C23—81no—
375C23—81no—
376C23—81no—
377C23—81no—
378C23—81no—
379C23—612no—
380C23—1221no—
381C23—1221no—
382C23—1221no—
383C23—1221no—
384C23—1221no—
385C23—1221no—
386C23—4881no—
387C23—4881no—
388C23—4881no—
389C23—4881no—
390C23—4881no—
391C23—4881no—
392C23—2442no—
393C23D8×D6111yescharacteristic
394D4—42no—
395D4—42no—
396D4—81no—
397D4—81no—
398D4—4888no—
399D4—4888no—
400D4—4881no—
401D4—4881no—
402D4—2442no—
403D4—2442no—
404C2×C4—42no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—1221no—
408C2×C4—1221no—
409C2×C4—1221no—
410C2×C4—4881no—
411C2×C4—4881no—
412C2×C4—2442no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4—2441no—
417C2×C4#1451974511yescharacteristic
418C2×C4#1451974711yescharacteristic
419C2×C4#1451975011yescharacteristic
420C2×C4#1451979811yescharacteristic
421C2×C4#1451980111yescharacteristic
422C2×C4#1451980411yescharacteristic
423C8—2441no—
424C8#1451974711yescharacteristic
425C8#1451975011yescharacteristic
426C8#1451975111yescharacteristic
427C8#1451977311yescharacteristic
428C22—82no—
429C22—82no—
430C22—82no—
431C22—161no—
432C22—161no—
433C22—161no—
434C22—161no—
435C22—1222no—
436C22—1222no—
437C22—1222no—
438C22—9761no—
439C22—9761no—
440C22—9761no—
441C22—9761no—
442C22—4882no—
443C22—4882no—
444C22—4882no—
445C22—2441no—
446C22—2441no—
447C22—2441no—
448C22—2441no—
449C22#1683989411yescharacteristic
450C22#1683989711yescharacteristic
451C22#1683999711yescharacteristic
452C22D16×D6111yescharacteristic
453C22#1684019311yescharacteristic
454C22#1684019611yescharacteristic
455C22#1684019911yescharacteristic
456C4—82no—
457C4—4882no—
458C4—2441no—
459C4#1683967111yescharacteristic
460C4#1683990611yescharacteristic
461C4#1683990811yescharacteristic
462C4#1684001411yescharacteristic
463C2—162no—
464C2—9762no—
465C2—2442no—
466C2#2144681611yescharacteristic
467C2#2144772911yescharacteristic
468C2#2144773211yescharacteristic
469C2#2144774111yescharacteristic
470C2#2144774311yescharacteristic
471C2#2144790411yescharacteristic
472C2#2144792111yescharacteristic
subgroupG/H
centerC23D8×D61
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC2×C61×#357C2
socleC23×C61C2×D8
hypercenterC2×#357D61
hypocenterC61#13304
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
1. C22×#14519718C2semidirect
2. C2×#16839999C2semidirect
3. C2×#16839995C2semidirect
4. C2×#16839564C2semidirect
5. C2×#16839541C2semidirect
6. #21443910C2semidirect
7. C2×C61×#357C2semidirect
38. C2×D488D4semidirect
56. C2×#11758185D4semidirect
58. #14519711D4semidirect
67. C2×D8×C61D4semidirect
74. #107×C61D4semidirect
156. C22×D61D16semidirect
231. C2×#357D61semidirect
265. C61#13304semidirect
282. C2×D8D244semidirect
309. #107C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145197182
C2×#168399992
C2×#168399952
C2×#168395642
C2×#168395412
#214439102
C2×C61×#3572
#1330461