Finite Group Databasebeta

← #29583054

Subgroups — #29583054

Order 15616.

536 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
1#21446746C211yesmaximal, characteristic
2#21446746C211yesmaximal, characteristic
3#21446624C211yesmaximal, characteristic
4#21443702C211yesmaximal, characteristic, complemented
5#21443660C211yesmaximal, characteristic, complemented
6#21443660C211yesmaximal, characteristic, complemented
7C61×#2552C211yesmaximal, characteristic, complemented
8C2×#14519774C2211yescharacteristic
9C2×C4⋊#92418C2211yescharacteristic
10C2×C4⋊#92418C2211yescharacteristic
11C2×#14519697—21no—
12C2×#14519697—21no—
13C2×#14519697—21no—
14C2×#14519697—21no—
15C2×#14519697—22no—
16C2×C4×#92418C2211yescharacteristic
17C2×#125×C61—21no—
18C61×#398—22no—
19C61×#389—21no—
20C61×#389—21no—
21C61×#384—21no—
22C61×#384C2211yescharacteristic
23C4×C4⋊C4×C61C2211yescharacteristic
24C4×C4⋊C4×C61C2211yescharacteristic
25C22×D244—21no—
26C22×D244—21no—
27C22×D244—21no—
28C22×#92418—21no—
29C22×#92418—21no—
30C22×#92418—21no—
31#14519774—21no—
32#14519774—21no—
33#14519774—21no—
34#14519774Q812yes—
35C4⋊#92418—21no—
36C4⋊#92418—21no—
37C4⋊#92418—21no—
38C4⋊#92418—21no—
39#14519697—44no—
40#14519697—42no—
41#14519697—42no—
42#14519697—42no—
43#14519697—42no—
44C4×#92418—21no—
45C4×#92418—21no—
46#125×C61—42no—
47#125×C61—42no—
48C2×C4⋊C4×C61—22no—
49C2×C4⋊C4×C61—22no—
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61—22no—
53C2×C4⋊C4×C61D411yescharacteristic
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C4⋊C4×C61D411yescharacteristic
56C2×C4⋊C4×C61D411yescharacteristic
57C2×C4⋊C4×C61D412yes—
58C2×C42×C61—21no—
59C2×C42×C61—21no—
60C2×C42×C61C2311yescharacteristic
61#95×C61—22no—
62#95×C61—21no—
63#95×C61—21no—
64C23×D61—41no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—22no—
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C2×D244—22no—
74C2×D244—22no—
75C2×D244—22no—
76C2×D244—42no—
77C2×D244—42no—
78C2×D244—41no—
79C2×D244—41no—
80C2×D244—41no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244—41no—
86C2×D244—41no—
87C2×D244—41no—
88C2×D244—41no—
89C4⋊C4×C61—21no—
90C4⋊C4×C61—21no—
91C4⋊C4×C61—21no—
92C4⋊C4×C61—21no—
93C4⋊C4×C61—21no—
94C4⋊C4×C61—21no—
95C4⋊C4×C61—44no—
96C4⋊C4×C61—44no—
97C4⋊C4×C61—42no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—82no—
103C4⋊C4×C61D812yes—
104C4⋊C4×C61SD1612yes—
105C42×C61—41no—
106C42×C61—41no—
107C42×C61—41no—
108C42×C61—41no—
109C42×C61C2×Q811yescharacteristic
110C42×C61#4111yescharacteristic
111C42×C61#4111yescharacteristic
112C42×C61#4111yescharacteristic
113C2×#92418—22no—
114C2×#92418—41no—
115C2×#92418—41no—
116C2×#92418—41no—
117C2×#92418—41no—
118C2×#92418—41no—
119C2×#92418—41no—
120C2×#92418—41no—
121C2×#92418—41no—
122C23×C61#12011yescharacteristic
123C22×D61—42no—
124C22×D61—81no—
125C22×D61—81no—
126C22×D61—81no—
127C22×D61—81no—
128C22×D61—81no—
129C22×D61—81no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—22no—
133C2×C4×C61—22no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—42no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—42no—
144C2×C4×C61—42no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61C22⋊Q811yescharacteristic
148C2×C4×C61C22⋊Q811yescharacteristic
149C2×C4×C61C22⋊Q811yescharacteristic
150C2×C4×C61#12411yescharacteristic
151C2×C4×C61#12411yescharacteristic
152C2×C4×C61#12411yescharacteristic
153C2×C4×C61C2×D811yescharacteristic
154C2×C4×C61C2×SD1611yescharacteristic
155C2×C4×C61#13511yescharacteristic
156C2×C4×C61#13511yescharacteristic
157C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C61#13711yescharacteristic
161D244—44no—
162D244—42no—
163D244—42no—
164D244—42no—
165D244—42no—
166D244—82no—
167D244—81no—
168D244—81no—
169D244—81no—
170D244—81no—
171#92418—42no—
172#92418—81no—
173#92418—81no—
174#10354—611nomaximal, Sylow
175C22×C61#39311yescharacteristic
176C22×C61#44711yescharacteristic
177C22×C61#44811yescharacteristic
178C22×C61#44911yescharacteristic
179C22×C61#44911yescharacteristic
180C22×C61#45311yescharacteristic
181C22×C61#45411yescharacteristic
182C2×D61—82no—
183C2×D61—82no—
184C2×D61—82no—
185C2×D61—161no—
186C2×D61—161no—
187C2×D61—161no—
188C2×D61—161no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—42no—
192C4×C61—42no—
193C4×C61—81no—
194C4×C61—82no—
195C4×C61—81no—
196C4×C61#47411yescharacteristic
197C4×C61#47611yescharacteristic
198C4×C61#47811yescharacteristic
199C4×C61#47811yescharacteristic
200C4×C61#48611yescharacteristic
201C4×C61#48811yescharacteristic
202C4×C61#48911yescharacteristic
203C4×C61#49011yescharacteristic
204#2552D6111yescharacteristic, complemented
205#1982—611no—
206#1982—611no—
207#1957—611no—
208#1296—611no—
209#1279—611no—
210#1279—611no—
211C2×C61#162111yescharacteristic
212C2×C61#162211yescharacteristic
213C2×C61#162511yescharacteristic
214C2×C61#162611yescharacteristic
215C2×C61#202311yescharacteristic
216C2×C61#202511yescharacteristic
217C2×C61#202711yescharacteristic
218D61—162no—
219C2×#127—611no—
220C2×#125—21no—
221C2×C4⋊C8—611no—
222C2×C4⋊C8—611no—
223C2×#102—1222no—
224C2×#102—1221no—
225C2×#102—1221no—
226C2×#102—1221no—
227C2×#102—1221no—
228C2×C4×C8—611no—
229#398—22no—
230#389—21no—
231#389—21no—
232#384—21no—
233#384C2×D6111yescharacteristic
234C4×C4⋊C4C2×D6111yescharacteristic
235C4×C4⋊C4C2×D6111yescharacteristic
236C61#1035411yescharacteristic, complemented, Sylow
237C22×D4—1221no—
238C22×D4—1221no—
239C22×D4—1221no—
240C22×C8—1221no—
241C22×C8—1221no—
242C22×C8—1221no—
243#127—612no—
244#127—1221no—
245#127—1221no—
246#127—1221no—
247#125—42no—
248#125—42no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4C22⋊D6111yescharacteristic
255C2×C4⋊C4C22⋊D6111yescharacteristic
256C2×C4⋊C4C22⋊D6111yescharacteristic
257C2×C4⋊C4C22⋊D6111yescharacteristic
258C2×C4⋊C4C22⋊D6112yes—
259C2×C42—21no—
260C2×C42—21no—
261C2×C42C22×D6111yescharacteristic
262C4⋊C8—1221no—
263C4⋊C8—1221no—
264C4⋊C8—1221no—
265C4⋊C8—1221no—
266#102—2442no—
267#102—2442no—
268#102—2444no—
269#102—2442no—
270#102—2442no—
271C4×C8—1221no—
272C4×C8—1221no—
273#95—22no—
274#95—21no—
275#95—21no—
276C24—2441no—
277C2×D4—1222no—
278C2×D4—1222no—
279C2×D4—1222no—
280C2×D4—2442no—
281C2×D4—2442no—
282C2×D4—2441no—
283C2×D4—2441no—
284C2×D4—2441no—
285C2×D4—2441no—
286C2×D4—2441no—
287C2×D4—2441no—
288C2×D4—2441no—
289C2×D4—2441no—
290C2×D4—2441no—
291C2×D4—2441no—
292C2×D4—2441no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—22no—
298C22×C4C2×C22⋊D6111yescharacteristic
299C22×C4C2×C22⋊D6111yescharacteristic
300C22×C4C2×C22⋊D6111yescharacteristic
301C2×C8—1222no—
302C2×C8—2441no—
303C2×C8—2441no—
304C2×C8—2441no—
305C2×C8—2441no—
306C2×C8—2441no—
307C2×C8—2441no—
308C2×C8—2441no—
309C2×C8—2441no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—42no—
317C4⋊C4—44no—
318C4⋊C4—44no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—82no—
324C4⋊C4#1175819912yes—
325C4⋊C4#1175820112yes—
326C42—41no—
327C42—41no—
328C42—41no—
329C42—41no—
330C42Q8×D6111yescharacteristic
331C42#1175822611yescharacteristic
332C42#1175822611yescharacteristic
333C42#1175822611yescharacteristic
334C23—4881no—
335C23—4881no—
336C23—4881no—
337C23—4881no—
338C23—4881no—
339C23—4881no—
340C23—2442no—
341C23#1451974611yescharacteristic
342D4—4882no—
343D4—4881no—
344D4—4881no—
345D4—4881no—
346D4—4881no—
347D4—2444no—
348D4—2442no—
349D4—2442no—
350D4—2442no—
351D4—2442no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4#1451975311yescharacteristic
370C2×C4#1451975311yescharacteristic
371C2×C4#1451975311yescharacteristic
372C2×C4#1451976611yescharacteristic
373C2×C4#1451976611yescharacteristic
374C2×C4#1451976611yescharacteristic
375C2×C4C2×#1175819911yescharacteristic
376C2×C4C2×#1175820111yescharacteristic
377C2×C4#1451979711yescharacteristic
378C2×C4#1451979711yescharacteristic
379C2×C4#1451980211yescharacteristic
380C2×C4#1451980211yescharacteristic
381C2×C4#1451980311yescharacteristic
382C2×C4#1451980811yescharacteristic
383C8—4881no—
384C8—4881no—
385C8—2442no—
386C22—9761no—
387C22—9761no—
388C22—9761no—
389C22—9761no—
390C22—4882no—
391C22—4882no—
392C22—4882no—
393C22#1683967311yescharacteristic
394C22#1683989611yescharacteristic
395C22#1683990111yescharacteristic
396C22#1683990711yescharacteristic
397C22#1683990711yescharacteristic
398C22#1683993011yescharacteristic
399C22#1683993511yescharacteristic
400C4—21no—
401C4—21no—
402C4—42no—
403C4—42no—
404C4—81no—
405C4—82no—
406C4—81no—
407C4#1684003911yescharacteristic
408C4#1684004911yescharacteristic
409C4#1684005911yescharacteristic
410C4#1684005911yescharacteristic
411C4#1684011011yescharacteristic
412C4#1684011911yescharacteristic
413C4#1684012411yescharacteristic
414C4#1684012811yescharacteristic
415C2—9762no—
416C2#2144488411yescharacteristic
417C2#2144489111yescharacteristic
418C2#2144490811yescharacteristic
419C2#2144491511yescharacteristic
420C2#2144695211yescharacteristic
421C2#2144696211yescharacteristic
422C2#2144697211yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2552C2
socleC23×C61#120
prime radicalC2×#14519774C22
hypercenter#2552D61
hypocenterC61#10354
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2552

Complements

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

NH ≅ G/Ntype
4. #21443702C2semidirect
5. #21443660C2semidirect
6. #21443660C2semidirect
7. C61×#2552C2semidirect
204. #2552D61semidirect
236. C61#10354semidirect

Maximal subgroups

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

subgroupindex
#214467462
#214466242
#214437022
#214436602
C61×#25522
#1035461