Finite Group Databasebeta

← #29584241

Subgroups — #29584241

Order 15616.

506 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840110C211yesmaximal, characteristic
2#21446745C211yesmaximal, characteristic
3#21446743C211yesmaximal, characteristic, complemented
4#21446535C211yesmaximal, characteristic, complemented
5C2×#16839505C211yesmaximal, characteristic
6#21443653C211yesmaximal, characteristic, complemented
7C2×C61×#332C211yesmaximal, characteristic, complemented
8C2×#14519774C2211yescharacteristic
9#16840110—22no—
10#16840110—22no—
11C2×C4⋊#92418C2211yescharacteristic
12C2×#14519706—21no—
13C2×#14519701—21no—
14C2×#14519701—21no—
15C2×#14519699—21no—
16C2×#14519699—21no—
17C2×#14519697—21no—
18C2×#14519697—21no—
19C2×C4×#92418C2211yescharacteristic
20C4×C4⋊Dic61C2211yescharacteristic
21#16839516—21no—
22#16839505—22no—
23C2×C4⋊Q8×C61C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×C4⋊C8×C61C2211yescharacteristic
26C61×#332—22no—
27C22×D244—21no—
28C22×D244—21no—
29C22×D244—21no—
30C22×#92418—21no—
31C22×#92418D411yescharacteristic
32C22×#92418D411yescharacteristic
33#14519774—21no—
34#14519774—21no—
35#14519774—21no—
36#14519774D412yes—
37C2×C4⋊Dic61D411yescharacteristic
38C2×C4⋊Dic61D411yescharacteristic
39C2×C4×Dic61—21no—
40C4⋊#92418—21no—
41C4⋊#92418—21no—
42#14519706—42no—
43#14519701—42no—
44#14519701—42no—
45#14519699—42no—
46#14519699—42no—
47#14519697—24no—
48#14519697—24no—
49C4×#92418—21no—
50C4×#92418—21no—
51#14519684—21no—
52C22×Q8×C61—21no—
53C22×C8×C61—21no—
54C22×C8×C61—21no—
55C4⋊Q8×C61—21no—
56C4⋊Q8×C61—21no—
57C4⋊Q8×C61—21no—
58C4⋊Q8×C61D412yes—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C42×C61C2311yescharacteristic
62C4⋊C8×C61—21no—
63C4⋊C8×C61—21no—
64C4⋊C8×C61—21no—
65C4⋊C8×C61—21no—
66C23×D61—41no—
67C2×Q8×C61—22no—
68C2×Q8×C61—41no—
69C2×Q8×C61—41no—
70C2×Q8×C61—41no—
71C2×Q8×C61—41no—
72C2×Q8×C61—41no—
73C22×C4×C61—41no—
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61#4111yescharacteristic
77C22×Dic61—21no—
78C22×Dic61—21no—
79C2×D244—22no—
80C2×D244—22no—
81C2×D244—22no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244—41no—
86C2×D244—41no—
87C2×D244—41no—
88C2×D244—41no—
89C2×D244—41no—
90C2×D244—41no—
91C2×D244—41no—
92C2×D244—41no—
93C2×D244—81no—
94C2×D244—81no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C2×C8×C61—41no—
101C4⋊C4×C61—22no—
102C4⋊C4×C61—22no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C42×C61C2×D411yescharacteristic
106C42×C61C2×D411yescharacteristic
107C42×C61#4111yescharacteristic
108C42×C61#4111yescharacteristic
109C4⋊Dic61—21no—
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112C4⋊Dic61D812yes—
113C4×Dic61—41no—
114C4×Dic61—41no—
115C2×#92418—21no—
116C2×#92418—21no—
117C2×#92418—21no—
118C2×#92418—21no—
119C2×#92418—21no—
120C2×#92418—21no—
121C2×#92418—41no—
122C2×#92418—41no—
123C2×#92418—41no—
124C23×C61#12111yescharacteristic
125C22×D61—42no—
126C22×D61—81no—
127C22×D61—81no—
128C22×D61—81no—
129C22×D61—81no—
130C22×D61—81no—
131C22×D61—81no—
132Q8×C61—42no—
133Q8×C61—42no—
134Q8×C61—81no—
135Q8×C61—81no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—42no—
139C2×C4×C61—81no—
140C2×C4×C61—81no—
141C2×C4×C61#12011yescharacteristic
142C2×C4×C61#12111yescharacteristic
143C2×C4×C61#12111yescharacteristic
144C2×C4×C61#12311yescharacteristic
145C2×C4×C61#12311yescharacteristic
146C2×C4×C61#12411yescharacteristic
147C2×C4×C61C2×D811yescharacteristic
148C2×C4×C61#13511yescharacteristic
149C2×C4×C61#13511yescharacteristic
150C2×C4×C61#13511yescharacteristic
151C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C61#13711yescharacteristic
155C2×Dic61—22no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161D244—42no—
162D244—42no—
163D244—42no—
164D244—42no—
165D244—82no—
166D244—82no—
167D244—81no—
168D244—81no—
169D244—81no—
170D244—81no—
171C8×C61—81no—
172C8×C61—81no—
173#92418—41no—
174#92418—41no—
175#92418—81no—
176#10540—611nomaximal, Sylow
177C22×C61#39411yescharacteristic
178C22×C61#46311yescharacteristic
179C22×C61#46411yescharacteristic
180C22×C61#46611yescharacteristic
181C22×C61#46911yescharacteristic
182C22×C61#47111yescharacteristic
183C22×C61#47111yescharacteristic
184C2×D61—82no—
185C2×D61—82no—
186C2×D61—82no—
187C2×D61—161no—
188C2×D61—161no—
189C2×D61—161no—
190C2×D61—161no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—82no—
194C4×C61#44911yescharacteristic
195C4×C61#45211yescharacteristic
196C4×C61#45911yescharacteristic
197C4×C61#45911yescharacteristic
198C4×C61#46311yescharacteristic
199C4×C61#46311yescharacteristic
200C4×C61#48811yescharacteristic
201C4×C61#48911yescharacteristic
202Dic61—42no—
203Dic61—81no—
204C2×#486—611no—
205#1982—611no—
206#1981—611no—
207#1939—611no—
208C2×#332D6111yescharacteristic, complemented
209C2×#331—611no—
210#1277—611no—
211C2×C61#168111yescharacteristic
212C2×C61#168211yescharacteristic
213C2×C61#170111yescharacteristic
214C2×C61#170211yescharacteristic
215C2×C61#204211yescharacteristic
216C2×C61#204611yescharacteristic
217C2×C61#205411yescharacteristic
218D61—162no—
219C2×C4⋊Q8C2×D6111yescharacteristic
220C2×#127—611no—
221#486—1222no—
222#486—1222no—
223C2×C4⋊C8—611no—
224C2×C4⋊C8—1221no—
225C2×C4⋊C8C2×D6111yescharacteristic
226C2×C4⋊C8C2×D6111yescharacteristic
227C2×#103—1221no—
228C2×#103—1221no—
229C2×#102—1221no—
230C2×#102—1221no—
231C2×#102—1221no—
232C2×#102—1221no—
233C2×C4×C8—611no—
234C4×C4⋊C4—611no—
235#336—1221no—
236#332—22no—
237#331—1222no—
238C61#1054011yescharacteristic, complemented, Sylow
239C22×Q8—21no—
240C22×D4—1221no—
241C22×D4—1221no—
242C22×D4—1221no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—611no—
246C22×C8—611no—
247C22×C8—1221no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8C22⋊D6112yes—
252#127—612no—
253#127—1221no—
254#127—1221no—
255#127—1221no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—611no—
259C2×C4⋊C4—611no—
260C2×C42—1221no—
261C2×C42C22×D6111yescharacteristic
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—1221no—
267C4⋊C8—1221no—
268C4⋊C8—2442no—
269#103—2442no—
270#103—2442no—
271#102—1224no—
272#102—1224no—
273#102—2442no—
274#102—2442no—
275C4×C8—1221no—
276C4×C8—1221no—
277#95—1221no—
278C24—2441no—
279C2×Q8—22no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8—41no—
284C2×Q8—41no—
285C2×D4—1222no—
286C2×D4—1222no—
287C2×D4—1222no—
288C2×D4—4881no—
289C2×D4—4881no—
290C2×D4—2441no—
291C2×D4—2441no—
292C2×D4—2441no—
293C2×D4—2441no—
294C2×D4—2441no—
295C2×D4—2441no—
296C2×D4—2441no—
297C2×D4—2441no—
298C2×D4—2441no—
299C2×D4—2441no—
300C2×D4—2441no—
301C22×C4—41no—
302C22×C4—1221no—
303C22×C4—1221no—
304C22×C4#1175822211yescharacteristic
305C22×C4D4×D6111yescharacteristic
306C22×C4D4×D6111yescharacteristic
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—1221no—
314C2×C8—1221no—
315C2×C8—1221no—
316C2×C8—1221no—
317C2×C8—1221no—
318C2×C8—1221no—
319C2×C8—2441no—
320C2×C8—2441no—
321C2×C8—2441no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—612no—
327C4⋊C4—1221no—
328C4⋊C4—1221no—
329C4⋊C4—1221no—
330C42—2441no—
331C42—2441no—
332C42#1175822211yescharacteristic
333C42D4×D6111yescharacteristic
334C42#1175822411yescharacteristic
335C42C2×C22⋊D6111yescharacteristic
336C23—4881no—
337C23—4881no—
338C23—4881no—
339C23—4881no—
340C23—4881no—
341C23—4881no—
342C23—2442no—
343C23#1451975011yescharacteristic
344Q8—42no—
345Q8—42no—
346Q8—81no—
347Q8—81no—
348D4—4882no—
349D4—4882no—
350D4—4881no—
351D4—4881no—
352D4—4881no—
353D4—4881no—
354D4—2442no—
355D4—2442no—
356D4—2442no—
357D4—2442no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—1222no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4#1451974511yescharacteristic
370C2×C4#1451974911yescharacteristic
371C2×C4#1451975011yescharacteristic
372C2×C4#1451975911yescharacteristic
373C2×C4#1451976011yescharacteristic
374C2×C4#1451976311yescharacteristic
375C2×C4D8×D6111yescharacteristic
376C2×C4#1451979811yescharacteristic
377C2×C4#1451979811yescharacteristic
378C2×C4#1451980011yescharacteristic
379C2×C4#1451980111yescharacteristic
380C2×C4#1451980411yescharacteristic
381C2×C4#1451980411yescharacteristic
382C2×C4#1451980911yescharacteristic
383C8—81no—
384C8—81no—
385C8—4881no—
386C8—2441no—
387C8—2441no—
388C22—9761no—
389C22—9761no—
390C22—9761no—
391C22—9761no—
392C22—4882no—
393C22—4882no—
394C22—4882no—
395C22#1683967711yescharacteristic
396C22#1683998011yescharacteristic
397C22#1683998711yescharacteristic
398C22#1683999711yescharacteristic
399C22#1684001411yescharacteristic
400C22#1684002811yescharacteristic
401C22#1684002811yescharacteristic
402C4—21no—
403C4—21no—
404C4—82no—
405C4—4881no—
406C4—2442no—
407C4#1683990611yescharacteristic
408C4#1683992311yescharacteristic
409C4#1683995511yescharacteristic
410C4#1683995611yescharacteristic
411C4#1683997611yescharacteristic
412C4#1683997911yescharacteristic
413C4#1684011811yescharacteristic
414C4#1684012311yescharacteristic
415C2—9762no—
416C2#2144525911yescharacteristic
417C2#2144526611yescharacteristic
418C2#2144538311yescharacteristic
419C2#2144539011yescharacteristic
420C2#2144705611yescharacteristic
421C2#2144707811yescharacteristic
422C2#2144712811yescharacteristic
subgroupG/H
centerC23#14519750
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC2×C61×#332C2
socleC23×C61#121
prime radicalC2×#14519774C22
hypercenterC2×#332D61
hypocenterC61#10540
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
3. #21446743C2semidirect
4. #21446535C2semidirect
6. #21443653C2semidirect
7. C2×C61×#332C2semidirect
208. C2×#332D61semidirect
238. C61#10540semidirect

Maximal subgroups

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

subgroupindex
C2×#168401102
#214467452
#214467432
#214465352
C2×#168395052
#214436532
C2×C61×#3322
#1054061