Finite Group Databasebeta

← #29597175

Subgroups — #29597175

Order 15616.

484 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458953C211yesmaximal, characteristic
2#21447554C211yesmaximal, characteristic, complemented
3#21447547C211yesmaximal, characteristic, complemented
4#21446707C211yesmaximal, characteristic, complemented
5#21443935C211yesmaximal, characteristic, complemented
6#21443901C211yesmaximal, characteristic, complemented
7C4×#135×C61C211yesmaximal, characteristic, complemented
8C2×#14519799C2211yescharacteristic
9#16840203—21no—
10#16840202C412yescomplemented
11#16840198—21no—
12#16840197C412yescomplemented
13#16840192—22no—
14C2×#14519717C2211yescharacteristic
15C2×#14519717C2211yescharacteristic
16C2×#14519713C2211yescharacteristic
17C2×#14519705—21no—
18#16839728—21no—
19#16839571—22no—
20#16839569—22no—
21C2×#135×C61C2211yescharacteristic
22C4×#41×C61—21no—
23C4×Q16×C61—21no—
24C4×SD16×C61—22no—
25C4×D8×C61—21no—
26C61×#427C2211yescharacteristic
27C61×#416—21no—
28C2×C4×C8×C61C2211yescharacteristic
29C2×#11758222—21no—
30#14519799—21no—
31#14519799—21no—
32#14519799—21no—
33#14519799—21no—
34C2×Dic244C2×C411yescharacteristic, complemented
35C2×#11758190—21no—
36C2×D488C2×C411yescharacteristic, complemented
37C2×#11758194—21no—
38#14519723—22no—
39#14519721—22no—
40#14519720—22no—
41#14519718—22no—
42#14519717—21no—
43#14519717—21no—
44#14519717—21no—
45#14519717C2×C412yescomplemented
46C2×#11758185—21no—
47C2×#11758185—21no—
48#14519713—21no—
49#14519713—21no—
50#14519705—41no—
51#14519705—41no—
52#14519689—42no—
53C2×#41×C61—21no—
54#135×C61—21no—
55#135×C61—21no—
56#135×C61C2×C412yes—
57#135×C61D412yes—
58C2×Q16×C61D411yescharacteristic
59C2×SD16×C61—21no—
60C2×D8×C61D411yescharacteristic
61C22×C8×C61D411yescharacteristic
62C22×C8×C61C2311yescharacteristic
63C4×Q8×C61—22no—
64C4×D4×C61—22no—
65C4×D4×C61—42no—
66#117×C61—21no—
67#117×C61—41no—
68C2×C42×C61—41no—
69C2×C42×C61D411yescharacteristic
70#107×C61—21no—
71#106×C61D412yes—
72#103×C61—22no—
73#102×C61—22no—
74C4×C8×C61—21no—
75C4×C8×C61—21no—
76#41×C61—22no—
77#41×C61—22no—
78#41×C61—41no—
79#41×C61—41no—
80C2×Q8×C61—21no—
81C2×D4×C61—21no—
82C2×D4×C61—41no—
83C22×C4×C61—21no—
84C22×C4×C61—42no—
85C22×C4×C61—41no—
86C22×C4×C61C2×D411yescharacteristic
87C2×C22⋊D61—41no—
88#11758222—41no—
89#11758222—41no—
90#11758222—41no—
91#11758222—41no—
92C2×D244—21no—
93C2×C4×D61—41no—
94C2×Dic122—21no—
95Q16×C61—21no—
96Q16×C61C22⋊C412yes—
97SD16×C61—22no—
98SD16×C61—22no—
99D8×C61—21no—
100D8×C61C22⋊C412yes—
101C2×C8×C61—21no—
102C2×C8×C61—21no—
103C2×C8×C61—21no—
104C2×C8×C61C22×C411yescharacteristic
105C2×C8×C61C2×D411yescharacteristic
106C2×C8×C61C2×D411yescharacteristic
107C2×C8×C61C2×D411yescharacteristic
108C2×C8×C61#4111yescharacteristic
109C2×C8×C61#4111yescharacteristic
110C4⋊C4×C61—22no—
111C4⋊C4×C61—42no—
112C22⋊C4×C61—42no—
113C22⋊C4×C61—41no—
114C42×C61—21no—
115C42×C61—42no—
116C42×C61—41no—
117C42×C61D811yescharacteristic
118C42×C61D811yescharacteristic
119#11758194—41no—
120#11758194—41no—
121C2×#92418—41no—
122Dic244—21no—
123Dic244—21no—
124D488—21no—
125D488—21no—
126#11758190—41no—
127#11758190—41no—
128#11758185—22no—
129#11758185—41no—
130C23×C61—41no—
131C23×C61AGL(1,ℤ/8)11yescharacteristic
132C22×D61—41no—
133Q8×C61—22no—
134Q8×C61—41no—
135D4×C61—22no—
136D4×C61—42no—
137D4×C61—42no—
138D4×C61—41no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—42no—
142C2×C4×C61—41no—
143C2×C4×C61—42no—
144C2×C4×C61—42no—
145C2×C4×C61—42no—
146C2×C4×C61—84no—
147C2×C4×C61C4×D411yescharacteristic
148C2×C4×C61#12011yescharacteristic
149C2×C4×C61#12111yescharacteristic
150C2×C4×C61C2×D811yescharacteristic
151C2×C4×C61#13511yescharacteristic
152C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
153C22⋊D61—81no—
154C22⋊D61—81no—
155C2×Dic61—41no—
156D244—41no—
157D244—41no—
158C4×D61—81no—
159C4×D61—81no—
160Dic122—41no—
161Dic122—41no—
162C8×C61—41no—
163C8×C61C2×C22⋊C411yescharacteristic
164C8×C61C4×D411yescharacteristic
165C8×C61#12111yescharacteristic
166C8×C61#12311yescharacteristic
167#92418—81no—
168#13027—611nomaximal, Sylow
169C22×C61—41no—
170C22×C61—42no—
171C22×C61—82no—
172C22×C61#44211yescharacteristic
173C22×C61#44711yescharacteristic
174C22×C61#46311yescharacteristic
175C2×D61—82no—
176C2×D61—81no—
177C4×C61—22no—
178C4×C61—41no—
179C4×C61—42no—
180C4×C61—82no—
181C4×C61#38611yescharacteristic
182C4×C61C4×D811yescharacteristic
183C4×C61#44911yescharacteristic
184C4×C61#45911yescharacteristic
185Dic61—81no—
186#3414—611no—
187C4×#135D6111yescharacteristic, complemented
188#2145—611no—
189#2143—611no—
190#1974—611no—
191#1389—611no—
192#1376—611no—
193C2×C61—21no—
194C2×C61—21no—
195C2×C61—21no—
196C2×C61—82no—
197C2×C61#187911yescharacteristic
198D61—161no—
199C2×#135—611no—
200C2×#135C2×D6111yescharacteristic
201C4×#41—21no—
202#510—612no—
203#510—1221no—
204#509—612no—
205#509—1221no—
206#508—1222no—
207C2×M32—611no—
208C2×M32—611no—
209C4×Q16—21no—
210C4×SD16—22no—
211C4×D8—21no—
212C2×#108—611no—
213#427C2×D6111yescharacteristic
214C2×#104—1221no—
215#416—21no—
216#408—1221no—
217C2×C4×C8C2×D6111yescharacteristic
218#360—1222no—
219#359—1222no—
220C61#1302711yescharacteristic, complemented, Sylow
221C2×#41—21no—
222C2×#41—1221no—
223#135—21no—
224#135—21no—
225#135—1221no—
226#135—1221no—
227#135—1221no—
228#135—1221no—
229#135C4×D6112yes—
230#135D24412yes—
231C2×Q16—611no—
232C2×Q16C22⋊D6111yescharacteristic
233C2×SD16—21no—
234C2×SD16—1221no—
235C2×D8—611no—
236C2×D8C22⋊D6111yescharacteristic
237C2×M16—1221no—
238C22×C8C22⋊D6111yescharacteristic
239C22×C8C22×D6111yescharacteristic
240C4×Q8—22no—
241C4×D4—22no—
242C4×D4—42no—
243#117—21no—
244#117—41no—
245C2×C42—41no—
246C2×C42C22⋊D6111yescharacteristic
247Q32—1222no—
248SD32—1222no—
249SD32—1222no—
250D16—1222no—
251M32—612no—
252M32—1221no—
253M32—1221no—
254M32—1221no—
255C2×C16—1221no—
256C2×C16—1221no—
257#108—1221no—
258#108—1221no—
259#107—21no—
260#106C22⋊D6112yes—
261#104—2441no—
262#104—2441no—
263#103—22no—
264#102—22no—
265C22⋊C8—2442no—
266C4×C8—21no—
267C4×C8—21no—
268#41—22no—
269#41—22no—
270#41—41no—
271#41—41no—
272#41—2441no—
273#41—2441no—
274#41—2441no—
275#41—2441no—
276C2×Q8—21no—
277C2×Q8—1221no—
278C2×D4—21no—
279C2×D4—41no—
280C2×D4—1221no—
281C2×D4—2441no—
282C22×C4—21no—
283C22×C4—42no—
284C22×C4—41no—
285C22×C4—2441no—
286C22×C4C2×C22⋊D6111yescharacteristic
287Q16—21no—
288Q16—1221no—
289Q16—1221no—
290Q16#1175819812yes—
291SD16—22no—
292SD16—22no—
293SD16—2441no—
294SD16—2441no—
295D8—21no—
296D8—1221no—
297D8—1221no—
298D8#1175819812yes—
299M16—2441no—
300M16—2441no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—2441no—
305C2×C8C2×C4×D6111yescharacteristic
306C2×C8C2×D24411yescharacteristic
307C2×C8#1175822211yescharacteristic
308C2×C8#1175822211yescharacteristic
309C2×C8C2×C22⋊D6111yescharacteristic
310C2×C8C2×C22⋊D6111yescharacteristic
311C4⋊C4—22no—
312C4⋊C4—42no—
313C22⋊C4—42no—
314C22⋊C4—41no—
315C42—21no—
316C42—42no—
317C42—41no—
318C42#1175819911yescharacteristic
319C42#1175819911yescharacteristic
320C16—1222no—
321C16—2441no—
322C23—41no—
323C23—2441no—
324C23#1451980311yescharacteristic
325Q8—22no—
326Q8—41no—
327Q8—2441no—
328Q8—2441no—
329D4—22no—
330D4—42no—
331D4—42no—
332D4—41no—
333D4—4881no—
334D4—4881no—
335D4—2441no—
336D4—2441no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—84no—
345C2×C4—4881no—
346C2×C4—4881no—
347C2×C4—2441no—
348C2×C4C4×C22⋊D6111yescharacteristic
349C2×C4#1451974611yescharacteristic
350C2×C4#1451975111yescharacteristic
351C2×C4C2×#1175819911yescharacteristic
352C2×C4#1451979711yescharacteristic
353C2×C4#1451980211yescharacteristic
354C8—41no—
355C8—4881no—
356C8C2×#1175819811yescharacteristic
357C8C4×C22⋊D6111yescharacteristic
358C8#1451975111yescharacteristic
359C8#1451976011yescharacteristic
360C22—41no—
361C22—42no—
362C22—82no—
363C22—4882no—
364C22—4881no—
365C22#1683987211yescharacteristic
366C22#1683989611yescharacteristic
367C22#1683997711yescharacteristic
368C4—22no—
369C4—41no—
370C4—42no—
371C4—82no—
372C4—4881no—
373C4#1683964111yescharacteristic
374C4C4×#1175819911yescharacteristic
375C4#1683990711yescharacteristic
376C4#1683995711yescharacteristic
377C2—21no—
378C2—21no—
379C2—21no—
380C2—82no—
381C2—9761no—
382C2#2144616711yescharacteristic
subgroupG/H
centerC4#16839957
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC4×#135×C61C2
socleC2×C61#1879
prime radical#21458953C2
cosocleC22×C8×C61C23
hypercenterC4×#135D61
hypocenterC61#13027
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×C4×C8 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
2. #21447554C2semidirect
3. #21447547C2semidirect
4. #21446707C2semidirect
5. #21443935C2semidirect
6. #21443901C2semidirect
7. C4×#135×C61C2semidirect
10. #16840202C4semidirect
12. #16840197C4semidirect
34. C2×Dic244C2×C4semidirect
36. C2×D488C2×C4semidirect
45. #14519717C2×C4semidirect
187. C4×#135D61semidirect
220. C61#13027semidirect

Maximal subgroups

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

subgroupindex
#214589532
#214475542
#214475472
#214467072
#214439352
#214439012
C4×#135×C612
#1302761