Finite Group Databasebeta

← #29598718

Subgroups — #29598718

Order 15616.

618 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519722C211yesmaximal, characteristic, complemented
2C2×#16840004C211yesmaximal, characteristic, complemented
3C2×#16839999C211yesmaximal, characteristic
4C2×#16839565C211yesmaximal, characteristic, complemented
5C2×#16839562C211yesmaximal, characteristic, complemented
6C2×#16839541C211yesmaximal, characteristic, complemented
7C61×#1380C211yesmaximal, characteristic, complemented
8C22×Dic244C2211yescharacteristic
9C22×D488C2211yescharacteristic
10C22×C8×D61C2211yescharacteristic
11C2×#14519757—21no—
12C2×#14519752—21no—
13C2×#14519722—22no—
14C2×#14519722—22no—
15C2×#14519722—22no—
16C22×#11758185C2211yescharacteristic
17#16840004—22no—
18#16840004—22no—
19#16839999—22no—
20#16839999—22no—
21C2×#14519700—21no—
22C2×#14519697—21no—
23#16839565—22no—
24#16839562—22no—
25#16839541—22no—
26C22×C16×C61C2211yescharacteristic
27C2×#107×C61C2211yescharacteristic
28C2×#107×C61C2211yescharacteristic
29C22×Dic122—21no—
30C22×D244—21no—
31C22×D244—41no—
32C22×C4×D61D411yescharacteristic
33C2×Dic244—21no—
34C2×Dic244—21no—
35C2×Dic244—21no—
36C2×Dic244—21no—
37C2×Dic244—21no—
38C2×Dic244D412yescomplemented
39C2×D488—21no—
40C2×D488—21no—
41C2×D488—21no—
42C2×D488—21no—
43C2×D488—21no—
44C2×D488D412yes—
45C22×#92418D411yescharacteristic
46C2×C8×D61—21no—
47C2×C8×D61—21no—
48C2×C8×D61—21no—
49C2×C8×D61—21no—
50C2×C8×D61—21no—
51C2×C8×D61—21no—
52#14519757—24no—
53#14519757—42no—
54#14519752—24no—
55#14519752—42no—
56C2×C4⋊Dic61—41no—
57C2×#11758198—41no—
58C2×#11758198—41no—
59#14519722—28no—
60C2×#11758185—21no—
61C2×#11758185—21no—
62C2×#11758185—21no—
63#14519700—24no—
64#14519697—24no—
65C22×C8×C61C2311yescharacteristic
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C16×C61—21no—
69C2×C16×C61—21no—
70C2×C16×C61D412yescomplemented
71#107×C61—21no—
72#107×C61—21no—
73#107×C61D412yes—
74#107×C61D412yescomplemented
75C23×D61—41no—
76C23×D61D811yescharacteristic
77C22×C4×C61—41no—
78C22×C4×C61—41no—
79C22×C4×C61C2×D411yescharacteristic
80C22×Dic61—41no—
81C22×Dic61D811yescharacteristic
82C2×D244—22no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244—41no—
86C2×D244—41no—
87C2×D244—44no—
88C2×D244—41no—
89C2×D244—82no—
90C2×D244—82no—
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61—21no—
94C2×C4×D61—21no—
95C2×C4×D61—21no—
96C2×C4×D61—21no—
97C2×Dic122—22no—
98C2×Dic122—41no—
99C2×Dic122—41no—
100C2×Dic122—41no—
101C2×Dic122—41no—
102C2×Dic122—41no—
103C2×C8×C61C2×D411yescharacteristic
104C2×C8×C61C2×D411yescharacteristic
105C2×C8×C61C2×D411yescharacteristic
106C2×C8×C61C2×D411yescharacteristic
107C2×C8×C61C2×D411yescharacteristic
108C2×C8×C61#4111yescharacteristic
109C4⋊C4×C61—22no—
110C4⋊C4×C61—22no—
111C4⋊C4×C61—41no—
112C4⋊C4×C61—41no—
113#11758198—44no—
114#11758198—44no—
115C4⋊Dic61—44no—
116C2×#92418—21no—
117C2×#92418—21no—
118C2×#92418—21no—
119Dic244—22no—
120Dic244—22no—
121Dic244—41no—
122Dic244—41no—
123D488—22no—
124D488—22no—
125D488—41no—
126D488—41no—
127C8×D61—41no—
128C8×D61—41no—
129C8×D61—41no—
130C8×D61—41no—
131C16×C61—22no—
132#11758185—41no—
133C23×C61C2×D811yescharacteristic
134C22×D61—21no—
135C22×D61—21no—
136C22×D61—21no—
137C22×D61—21no—
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—42no—
141C22×D61—81no—
142C22×D61—81no—
143C22×D61—81no—
144C22×D61—81no—
145C22×D61—81no—
146C22×D61—81no—
147C22×D61SD3212yescomplemented
148C2×C4×C61—42no—
149C2×C4×C61—42no—
150C2×C4×C61—81no—
151C2×C4×C61—81no—
152C2×C4×C61—81no—
153C2×C4×C61—81no—
154C2×C4×C61#12011yescharacteristic
155C2×C4×C61#12011yescharacteristic
156C2×C4×C61#12111yescharacteristic
157C2×C4×C61#13511yescharacteristic
158C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—42no—
164C2×Dic61—81no—
165C2×Dic61—81no—
166D244—42no—
167D244—42no—
168D244—88no—
169D244—81no—
170D244—81no—
171C4×D61—41no—
172C4×D61—41no—
173C4×D61—41no—
174C4×D61—41no—
175Dic122—42no—
176Dic122—42no—
177Dic122—81no—
178Dic122—81no—
179C8×C61#12011yescharacteristic
180C8×C61#12111yescharacteristic
181C8×C61#12111yescharacteristic
182C8×C61#12711yescharacteristic
183#92418—41no—
184#13305—611nomaximal, Sylow
185C22×C61#44711yescharacteristic
186C22×C61#44711yescharacteristic
187C22×C61#46611yescharacteristic
188C22×C61C2×SD3211yescharacteristic
189C22×C61#50811yescharacteristic
190C22×C61#50911yescharacteristic
191C22×C61#51011yescharacteristic
192C2×D61—22no—
193C2×D61—22no—
194C2×D61—22no—
195C2×D61—41no—
196C2×D61—41no—
197C2×D61—41no—
198C2×D61—41no—
199C2×D61—82no—
200C2×D61—82no—
201C2×D61—82no—
202C2×D61—161no—
203C2×D61—161no—
204C2×D61—161no—
205C2×D61—161no—
206C4×C61—82no—
207C4×C61—82no—
208C4×C61#39211yescharacteristic
209C4×C61#44911yescharacteristic
210C4×C61#44911yescharacteristic
211C4×C61#46911yescharacteristic
212Dic61—41no—
213Dic61—82no—
214C22×SD32—611no—
215C2×#467—611no—
216C2×#466—611no—
217C2×#358—611no—
218C2×#357—611no—
219C2×C22⋊C16—611no—
220#1380D6111yescharacteristic, complemented
221C2×C61#199911yescharacteristic
222C2×C61#218511yescharacteristic
223C2×C61#218611yescharacteristic
224C2×C61#218711yescharacteristic
225C2×C61#218911yescharacteristic
226C2×C61#221711yescharacteristic
227C2×C61#222011yescharacteristic
228D61—42no—
229D61—162no—
230C22×Q16—611no—
231C22×D8—611no—
232C23×C8—611no—
233C2×C22⋊Q8—1221no—
234C2×#121—1221no—
235C2×SD32—1222no—
236C2×SD32—1222no—
237C2×SD32—1222no—
238C22×C16—611no—
239C22×C16C2×D6111yescharacteristic
240#467—1222no—
241#467—1222no—
242#466—1222no—
243#466—1222no—
244C2×#107C2×D6111yescharacteristic
245C2×#107C2×D6111yescharacteristic
246C2×#103—1221no—
247C2×#102—1221no—
248#358—1222no—
249#357—1222no—
250C22⋊C16—1222no—
251C61#1330511yescharacteristic, complemented, Sylow
252C22×Q8—1221no—
253C22×D4—1221no—
254C22×D4—2441no—
255C23×C4—611no—
256C2×Q16—612no—
257C2×Q16—1221no—
258C2×Q16—1221no—
259C2×Q16—1221no—
260C2×Q16—1221no—
261C2×Q16—1221no—
262C2×D8—612no—
263C2×D8—1221no—
264C2×D8—1221no—
265C2×D8—1221no—
266C2×D8—1221no—
267C2×D8—1221no—
268C22×C8—611no—
269C22×C8—1221no—
270C22×C8—1221no—
271C22×C8—1221no—
272C22×C8—1221no—
273C22×C8—1221no—
274C22×C8—1221no—
275C22×C8C22×D6111yescharacteristic
276C22⋊Q8—1224no—
277C22⋊Q8—2442no—
278#121—1224no—
279#121—2442no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—2441no—
283C2×C22⋊C4—2441no—
284C2×C22⋊C4—2441no—
285SD32—1228no—
286C2×C16—21no—
287C2×C16—21no—
288C2×C16—1221no—
289C2×C16—1221no—
290C2×C16—1221no—
291C2×C16D24412yescomplemented
292#107—21no—
293#107—21no—
294#107D24412yes—
295#107D24412yescomplemented
296#103—1224no—
297#102—1224no—
298C24—611no—
299C24—2441no—
300C2×Q8—1222no—
301C2×Q8—2441no—
302C2×Q8—2441no—
303C2×Q8—2441no—
304C2×Q8—2441no—
305C2×Q8—2441no—
306C2×D4—1222no—
307C2×D4—4882no—
308C2×D4—4882no—
309C2×D4—2444no—
310C2×D4—2441no—
311C2×D4—2441no—
312C2×D4—2441no—
313C2×D4—2441no—
314C2×D4—2441no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—611no—
318C22×C4—1221no—
319C22×C4—1221no—
320C22×C4—1221no—
321C22×C4—1221no—
322C22×C4—1221no—
323C22×C4—1221no—
324C22×C4—2441no—
325C22×C4D4×D6111yescharacteristic
326Q16—1222no—
327Q16—1222no—
328Q16—2441no—
329Q16—2441no—
330D8—1222no—
331D8—1222no—
332D8—2441no—
333D8—2441no—
334C2×C8—1221no—
335C2×C8—1221no—
336C2×C8—1221no—
337C2×C8—2441no—
338C2×C8—2441no—
339C2×C8—2441no—
340C2×C8—2441no—
341C2×C8C2×D24411yescharacteristic
342C2×C8C2×D24411yescharacteristic
343C2×C8C2×D24411yescharacteristic
344C2×C8D4×D6111yescharacteristic
345C2×C8D4×D6111yescharacteristic
346C2×C8#1175822611yescharacteristic
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—2444no—
352C22⋊C4—2444no—
353C22⋊C4—2444no—
354C16—22no—
355C16—2441no—
356C23—612no—
357C23—1221no—
358C23—1221no—
359C23—1221no—
360C23—1221no—
361C23—1221no—
362C23—1221no—
363C23—4881no—
364C23—4881no—
365C23—4881no—
366C23—4881no—
367C23—4881no—
368C23—4881no—
369C23—2442no—
370C23D8×D6111yescharacteristic
371Q8—4881no—
372Q8—4881no—
373Q8—2442no—
374Q8—2442no—
375D4—4888no—
376D4—4881no—
377D4—4881no—
378D4—2442no—
379D4—2442no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—1221no—
387C2×C4—1221no—
388C2×C4—1221no—
389C2×C4—4881no—
390C2×C4—4881no—
391C2×C4—2442no—
392C2×C4—2441no—
393C2×C4—2441no—
394C2×C4—2441no—
395C2×C4—2441no—
396C2×C4#1451974711yescharacteristic
397C2×C4#1451974711yescharacteristic
398C2×C4#1451975211yescharacteristic
399C2×C4#1451980011yescharacteristic
400C2×C4#1451980411yescharacteristic
401C2×C4#1451980411yescharacteristic
402C8—2441no—
403C8#1451974711yescharacteristic
404C8#1451975211yescharacteristic
405C8#1451975211yescharacteristic
406C8#1451977411yescharacteristic
407C22—1222no—
408C22—1222no—
409C22—1222no—
410C22—9761no—
411C22—9761no—
412C22—9761no—
413C22—9761no—
414C22—4882no—
415C22—4882no—
416C22—4882no—
417C22—2441no—
418C22—2441no—
419C22—2441no—
420C22—2441no—
421C22#1683989711yescharacteristic
422C22#1683989711yescharacteristic
423C22#1683999911yescharacteristic
424C22SD32×D6111yescharacteristic
425C22#1684019311yescharacteristic
426C22#1684019611yescharacteristic
427C22#1684020411yescharacteristic
428C4—82no—
429C4—82no—
430C4—4882no—
431C4—2441no—
432C4#1683967211yescharacteristic
433C4#1683991011yescharacteristic
434C4#1683991011yescharacteristic
435C4#1684001611yescharacteristic
436C2—9762no—
437C2—2442no—
438C2#2144681811yescharacteristic
439C2#2144773711yescharacteristic
440C2#2144774311yescharacteristic
441C2#2144774911yescharacteristic
442C2#2144776211yescharacteristic
443C2#2144791611yescharacteristic
444C2#2144793311yescharacteristic
subgroupG/H
centerC23D8×D61
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#1380C2
socleC23×C61C2×D8
prime radicalC2×#16839999C2
hypercenter#1380D61
hypocenterC61#13305
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
1. C22×#14519722C2semidirect
2. C2×#16840004C2semidirect
4. C2×#16839565C2semidirect
5. C2×#16839562C2semidirect
6. C2×#16839541C2semidirect
7. C61×#1380C2semidirect
38. C2×Dic244D4semidirect
70. C2×C16×C61D4semidirect
74. #107×C61D4semidirect
147. C22×D61SD32semidirect
220. #1380D61semidirect
251. C61#13305semidirect
291. C2×C16D244semidirect
295. #107D244semidirect

Maximal subgroups

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

subgroupindex
C22×#145197222
C2×#168400042
C2×#168399992
C2×#168395652
C2×#168395622
C2×#168395412
C61×#13802
#1330561