Finite Group Databasebeta

← #29663517

Subgroups — #29663517

Order 15616.

652 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457136C211yesmaximal, characteristic
2#21456744C211yesmaximal, characteristic
3#21456361C211yesmaximal, characteristic, complemented
4#21454562C211yesmaximal, characteristic
5#21445331C212yesmaximal, complemented
6#21445317C212yesmaximal, complemented
7#21445207C212yesmaximal, complemented
8#21445193C212yesmaximal, complemented
9#21444569C211yesmaximal, characteristic, complemented
10#21444477C211yesmaximal, characteristic, complemented
11C2×C61×#332C211yesmaximal, characteristic, complemented
12C2×#14519783—21no—
13#16840319C2211yescharacteristic
14#16840312C2211yescharacteristic
15#16840168—22no—
16#16840165C2212yes—
17#16840158C2212yes—
18#16840136—21no—
19#16840112—21no—
20#16840053C2212yes—
21#16840048—21no—
22#16839991—22no—
23#16839968C2212yes—
24#16839964C2212yes—
25#16839964C2212yes—
26#16839963—21no—
27#16839901—22no—
28#16839839C2212yes—
29#16839832—22no—
30#16839827C2212yes—
31#16839815C2211yescharacteristic
32#16839802—21no—
33#16839802—21no—
34#16839728—21no—
35C4×#11758194C2211yescharacteristic
36#16839514C2212yes—
37#16839512C2212yes—
38#16839510C2211yescharacteristic
39#16839510C2211yescharacteristic
40#16839507C2211yescharacteristic
41#16839507C2211yescharacteristic
42C2×C4⋊Q8×C61C2211yescharacteristic
43C2×C4⋊C8×C61C2211yescharacteristic
44C2×C4⋊C8×C61C2211yescharacteristic
45C61×#332C2212yes—
46C61×#332C2212yes—
47C2×#11758222—21no—
48C2×#11758190—22no—
49C2×#11758201—22no—
50C2×#11758201—22no—
51#14519783—44no—
52C2×#11758194D411yescharacteristic
53C2×#11758194D411yescharacteristic
54C2×#11758189—22no—
55C2×C8×D61—22no—
56#14519777D411yescharacteristic
57#14519777C2311yescharacteristic
58#14519777C2311yescharacteristic
59#14519774D411yescharacteristic
60#14519769—21no—
61#14519765—21no—
62#14519756—21no—
63#14519756—21no—
64#14519751—21no—
65#14519751D412yes—
66C4×Dic122—21no—
67C4×Dic122—21no—
68C4×D244—21no—
69C4×D244C2312yes—
70#14519736—21no—
71#14519710—22no—
72#14519710—22no—
73#14519709—22no—
74#14519708—22no—
75#14519708—22no—
76C4⋊#92418C2311yescharacteristic
77C4⋊#92418C2311yescharacteristic
78#14519702—22no—
79#14519701—22no—
80#14519701—22no—
81#14519699—22no—
82C22⋊#92418—21no—
83#14519689—22no—
84#14519689—22no—
85#14519688D412yes—
86C4×#92418—21no—
87C4×#92418C2312yes—
88C22×Q8×C61—21no—
89C22×C8×C61—21no—
90C22×C8×C61—21no—
91C4⋊Q8×C61—21no—
92C4⋊Q8×C61—21no—
93C4⋊Q8×C61—21no—
94C4⋊Q8×C61C2312yes—
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61—21no—
97C2×C42×C61C2311yescharacteristic
98C4⋊C8×C61—21no—
99C4⋊C8×C61—21no—
100C4⋊C8×C61C2312yes—
101C4⋊C8×C61C2311yescharacteristic
102C4⋊C8×C61C2311yescharacteristic
103C2×Q8×C61—22no—
104C2×Q8×C61—41no—
105C2×Q8×C61—81no—
106C2×Q8×C61—81no—
107C22×C4×C61—41no—
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61#4111yescharacteristic
111C2×C22⋊D61—22no—
112#11758222—42no—
113#11758222—42no—
114C2×D244—21no—
115C2×D244—21no—
116C2×D244C2×D412yes—
117C2×C4×D61—22no—
118C2×Dic122—21no—
119C2×Dic122—21no—
120C2×Dic122—21no—
121C2×C8×C61—21no—
122C2×C8×C61—21no—
123C2×C8×C61—22no—
124C2×C8×C61—42no—
125C2×C8×C61—81no—
126C4⋊C4×C61—22no—
127C4⋊C4×C61—22no—
128C4⋊C4×C61—41no—
129C4⋊C4×C61—41no—
130C42×C61C2×D411yescharacteristic
131C42×C61C2×D411yescharacteristic
132C42×C61#4111yescharacteristic
133C42×C61C2411yescharacteristic
134C22⋊Dic61—41no—
135#11758201—82no—
136#11758201—82no—
137#11758198—22no—
138#11758198—22no—
139C4⋊Dic61—21no—
140C4⋊Dic61—21no—
141C4⋊Dic61—21no—
142C4⋊Dic61—21no—
143C4⋊Dic61—21no—
144C4⋊Dic61C2×D412yes—
145#11758196—41no—
146#11758196—41no—
147C4×Dic61—41no—
148#11758194—22no—
149#11758194SD1614yescomplemented
150C2×#92418—21no—
151C2×#92418—21no—
152C2×#92418C2×D412yes—
153C2×#92418C2×D412yes—
154#11758190—82no—
155#11758189—44no—
156C8×D61—44no—
157C23×C61#12111yescharacteristic
158C22×D61—22no—
159Q8×C61—42no—
160Q8×C61—42no—
161Q8×C61—82no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—41no—
165C2×C4×C61—42no—
166C2×C4×C61—82no—
167C2×C4×C61#12111yescharacteristic
168C2×C4×C61#12111yescharacteristic
169C2×C4×C61#12111yescharacteristic
170C2×C4×C61C2×SD1612yes—
171C2×C4×C61#13712yes—
172C2×C4×C61C22×D411yescharacteristic
173C2×C4×C61C22×D411yescharacteristic
174C2×C4×C61C2×#4111yescharacteristic
175C22⋊D61—44no—
176C2×Dic61—22no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179D244—22no—
180D244—22no—
181D244—42no—
182D244—81no—
183C4×D61—42no—
184C4×D61—42no—
185Dic122—42no—
186Dic122—41no—
187Dic122—41no—
188Dic122—81no—
189C8×C61—41no—
190C8×C61—41no—
191C8×C61—42no—
192#92418—22no—
193#92418—41no—
194#92418—41no—
195#92418C2×SD1614yes—
196#19232—611nomaximal, Sylow
197C22×C61—21no—
198C22×C61—21no—
199C22×C61#46112yes—
200C22×C61C2×#12111yescharacteristic
201C2×D61—42no—
202C2×D61—42no—
203C2×D61—42no—
204C4×C61—21no—
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—82no—
208C4×C61#46112yes—
209C4×C61C22×SD1611yescharacteristic
210C4×C61C2×#13711yescharacteristic
211C4×C61#57611yescharacteristic
212C4×C61#57711yescharacteristic
213Dic61—42no—
214Dic61—81no—
215Dic61—81no—
216#3246—611no—
217#3206—611no—
218#3165—611no—
219#2935—611no—
220#1693—612no—
221#1691—612no—
222#1673—612no—
223#1671—612no—
224#1565—611no—
225#1542—611no—
226C2×#332D6111yescharacteristic, complemented
227C2×C61—22no—
228C2×C61C2×#46111yescharacteristic
229C2×C61#306211yescharacteristic
230C2×C61#306911yescharacteristic
231D61—82no—
232C2×#131—1221no—
233#533—611no—
234#532—611no—
235C2×C4⋊Q8C2×D6111yescharacteristic
236#501—1222no—
237#500—612no—
238#498—612no—
239#492—1221no—
240#487—1221no—
241#476—612no—
242#475—1221no—
243#465—1222no—
244#461—612no—
245#461—612no—
246#461—612no—
247#460—1221no—
248#448—1222no—
249#436—612no—
250#435—1222no—
251C8×D4—612no—
252#431—611no—
253#428—1221no—
254#428—1221no—
255C2×C4⋊C8C2×D6111yescharacteristic
256C2×C4⋊C8C2×D6111yescharacteristic
257#408—1221no—
258C4×M16—611no—
259#335—612no—
260#334—612no—
261#333—611no—
262#333—611no—
263#332—611no—
264#332—611no—
265#332C2×D6112yes—
266#332C2×D6112yes—
267C61#1923211yescharacteristic, complemented, Sylow
268C2×#41—1221no—
269C22×Q8—21no—
270C2×SD16—1222no—
271C2×SD16—1222no—
272C2×SD16—1222no—
273#131—2444no—
274C2×M16—611no—
275C2×M16—611no—
276C2×M16—1222no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—1222no—
280C4⋊Q8—21no—
281C4⋊Q8—21no—
282C4⋊Q8—21no—
283C4⋊Q8—611no—
284C4⋊Q8—611no—
285C4⋊Q8—611no—
286C4⋊Q8C22×D6112yes—
287#127—611no—
288#125—1221no—
289#124—1221no—
290C22⋊Q8—1221no—
291C22⋊Q8—1221no—
292#121—612no—
293#121—1221no—
294C4×Q8—1221no—
295C4×Q8—1221no—
296C4×D4—612no—
297C4×D4—1221no—
298#117—1221no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C42C22×D6111yescharacteristic
302#107—1222no—
303#107—1222no—
304#106—1222no—
305#106—1222no—
306#106—1222no—
307C4⋊C8—21no—
308C4⋊C8—21no—
309C4⋊C8—611no—
310C4⋊C8—611no—
311C4⋊C8C22×D6111yescharacteristic
312C4⋊C8C22×D6111yescharacteristic
313C4⋊C8C22×D6112yes—
314#103—1222no—
315#103—1222no—
316#103—1222no—
317#102—1222no—
318C22⋊C8—1222no—
319C22⋊C8—1222no—
320C22⋊C8—1221no—
321#97—612no—
322C4×C8—612no—
323C4×C8—1221no—
324#41—2442no—
325#41—2442no—
326C2×Q8—22no—
327C2×Q8—41no—
328C2×Q8—81no—
329C2×Q8—81no—
330C2×Q8—1221no—
331C2×Q8—1221no—
332C2×Q8—1221no—
333C2×D4—612no—
334C2×D4—1222no—
335C2×D4—1221no—
336C2×D4—1221no—
337C22×C4—41no—
338C22×C4—1222no—
339C22×C4#1175822211yescharacteristic
340C22×C4D4×D6111yescharacteristic
341C22×C4D4×D6111yescharacteristic
342SD16—4882no—
343SD16—4882no—
344SD16—4882no—
345M16—614no—
346M16—1222no—
347M16—2444no—
348C2×C8—21no—
349C2×C8—21no—
350C2×C8—22no—
351C2×C8—42no—
352C2×C8—81no—
353C2×C8—612no—
354C2×C8—612no—
355C2×C8—1221no—
356C2×C8—1221no—
357C2×C8—2444no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4—612no—
363C4⋊C4—1221no—
364C4⋊C4—1221no—
365C4⋊C4—1221no—
366C4⋊C4—1221no—
367C4⋊C4—1221no—
368C4⋊C4—2441no—
369C4⋊C4—2441no—
370C22⋊C4—1222no—
371C22⋊C4—1222no—
372C22⋊C4—2441no—
373C42—2441no—
374C42#1175822211yescharacteristic
375C42D4×D6111yescharacteristic
376C42D4×D6111yescharacteristic
377C42C23×D6111yescharacteristic
378C23—1222no—
379C23#1451975011yescharacteristic
380Q8—42no—
381Q8—42no—
382Q8—82no—
383Q8—4881no—
384Q8—2441no—
385Q8—2441no—
386Q8—2442no—
387D4—1222no—
388D4—1222no—
389D4—4881no—
390D4—2444no—
391D4—2442no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—82no—
397C2×C4—1222no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2442no—
401C2×C4—2442no—
402C2×C4#1451975011yescharacteristic
403C2×C4#1451975011yescharacteristic
404C2×C4#1451975011yescharacteristic
405C2×C4SD16×D6112yes—
406C2×C4#1451980912yes—
407C2×C4C2×D4×D6111yescharacteristic
408C2×C4C2×D4×D6111yescharacteristic
409C2×C4C2×#1175822211yescharacteristic
410C8—41no—
411C8—41no—
412C8—42no—
413C8—614no—
414C8—1222no—
415C8—2441no—
416C8—2441no—
417C22—21no—
418C22—21no—
419C22—2442no—
420C22—2442no—
421C22—2442no—
422C22#1683996612yes—
423C22C2×#1451975011yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—82no—
428C4—4881no—
429C4—4881no—
430C4—2442no—
431C4#1683996612yes—
432C4C2×SD16×D6111yescharacteristic
433C4C2×#1451980911yescharacteristic
434C4#1684056311yescharacteristic
435C4#1684056811yescharacteristic
436C2—22no—
437C2—4882no—
438C2C2×#1683996611yescharacteristic
439C2#2145549711yescharacteristic
440C2#2145555511yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#332C2
socleC22×C61C2×#121
prime radical#16840312C22
hypercenterC2×#332D61
hypocenterC61#19232
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
3. #21456361C2semidirect
5. #21445331C2semidirect
6. #21445317C2semidirect
7. #21445207C2semidirect
8. #21445193C2semidirect
9. #21444569C2semidirect
10. #21444477C2semidirect
11. C2×C61×#332C2semidirect
149. #11758194SD16semidirect
226. C2×#332D61semidirect
267. C61#19232semidirect

Maximal subgroups

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

subgroupindex
#214571362
#214567442
#214563612
#214545622
#214453312
#214453172
#214452072
#214451932
#214445692
#214444772
C2×C61×#3322
#1923261