Finite Group Databasebeta

← #29709925

Subgroups — #29709925

Order 15616.

810 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448300C211yesmaximal, characteristic
2#21448224C211yesmaximal, characteristic
3#21447390C212yesmaximal, complemented
4#21447389C212yesmaximal, complemented
5#21447383C211yesmaximal, characteristic, complemented
6#21447382C211yesmaximal, characteristic, complemented
7#21447376C211yesmaximal, characteristic, complemented
8#21445534C212yesmaximal
9#21445534C212yesmaximal
10#336×D61C211yesmaximal, characteristic
11C61×#2099C211yesmaximal, characteristic, complemented
12C22×C8×D61C2212yes—
13C2×#14519735C2212yes—
14C2×#14519735C2211yescharacteristic
15C2×#14519735C2211yescharacteristic
16C2×C42×D61C2211yescharacteristic
17#16839661C2211yescharacteristic
18#16839660C2211yescharacteristic
19#16839658C2211yescharacteristic
20#16839636—21no—
21#16839633—21no—
22#16839632C2211yescharacteristic
23#16839627C2212yes—
24#16839619—21no—
25#16839619—21no—
26C4⋊C4×Dic61—21no—
27C4⋊C4×Dic61—21no—
28C4⋊C4×Dic61—21no—
29#16839613—21no—
30#16839525C2212yes—
31#16839525C2212yes—
32#16839524C2212yes—
33#16839524C2212yes—
34#16839524C2212yes—
35#16839524C2212yes—
36#16839517C2211yescharacteristic
37#16839516C2212yes—
38C61×#389C2211yescharacteristic
39C61×#384C2211yescharacteristic
40C61×#340C2212yes—
41C61×#340C2212yes—
42C61×#336C2211yescharacteristic
43C22×C4×D61D411yescharacteristic
44C22×C4×D61D411yescharacteristic
45C22×C4×D61C2311yescharacteristic
46C22×#92418C2312yes—
47C2×C8×D61—24no—
48C2×C8×D61—24no—
49C2×C8×D61—24no—
50#14519735—22no—
51#14519735—24no—
52#14519735—28no—
53#14519735Q814yes—
54C2×C4⋊Dic61—21no—
55C2×C4⋊Dic61—21no—
56C2×C4⋊Dic61—21no—
57C2×C4⋊Dic61C2312yes—
58C2×C4⋊Dic61C2311yescharacteristic
59C2×C4⋊Dic61C2311yescharacteristic
60C2×#11758196—21no—
61C2×#11758196—21no—
62C2×#11758198—21no—
63C2×#11758198—22no—
64C2×#11758198—21no—
65C2×C4×Dic61—21no—
66C2×C4×Dic61—21no—
67C2×C4×Dic61—22no—
68C2×C4×Dic61D411yescharacteristic
69C2×C4×Dic61D411yescharacteristic
70C2×C4×Dic61C2311yescharacteristic
71C42×D61—24no—
72#14519684—21no—
73#14519684—21no—
74#14519684—22no—
75#14519684—22no—
76#14519684—21no—
77C22×C8×C61C2312yes—
78C2×C4⋊C4×C61—21no—
79C2×C4⋊C4×C61—21no—
80C2×C4⋊C4×C61—21no—
81C2×C4⋊C4×C61C2312yes—
82C2×C4⋊C4×C61C2311yescharacteristic
83C2×C4⋊C4×C61C2311yescharacteristic
84C2×C42×C61C2311yescharacteristic
85#95×C61—21no—
86C23×D61C2×D411yescharacteristic
87C22×C4×C61—21no—
88C22×C4×C61—21no—
89C22×C4×C61—22no—
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2411yescharacteristic
93C22×Dic61—21no—
94C22×Dic61—21no—
95C22×Dic61—22no—
96C22×Dic61C2×D411yescharacteristic
97C22×Dic61C2×D411yescharacteristic
98C22×Dic61C2×D411yescharacteristic
99C2×C4×D61—22no—
100C2×C4×D61—22no—
101C2×C4×D61—22no—
102C2×C4×D61—22no—
103C2×C4×D61—41no—
104C2×C4×D61—41no—
105C2×C4×D61C2×Q812yes—
106C2×C4×D61#4114yes—
107C2×C4×D61#4114yes—
108C2×C4×D61#4112yes—
109C2×C8×C61—22no—
110C2×C8×C61—22no—
111C2×C8×C61—22no—
112C4⋊C4×C61—21no—
113C4⋊C4×C61—22no—
114C4⋊C4×C61—24no—
115C4⋊C4×C61—42no—
116C4⋊C4×C61—42no—
117C4⋊C4×C61—42no—
118C4⋊C4×C61C2×Q812yes—
119C42×C61—22no—
120#11758198—24no—
121#11758198—42no—
122#11758198—44no—
123C4⋊Dic61—21no—
124C4⋊Dic61—22no—
125C4⋊Dic61—24no—
126C4⋊Dic61—42no—
127C4⋊Dic61—42no—
128C4⋊Dic61—42no—
129C4⋊Dic61C2×Q812yes—
130#11758196—42no—
131#11758196—42no—
132C4×Dic61—22no—
133C4×Dic61—24no—
134C4×Dic61—22no—
135C4×Dic61—22no—
136C4×Dic61—42no—
137C4×Dic61—44no—
138C2×#92418—22no—
139C2×#92418—22no—
140C2×#92418—22no—
141C8×D61—48no—
142C23×C61C22×D411yescharacteristic
143C22×D61—21no—
144C22×D61—21no—
145C22×D61—21no—
146C22×D61—21no—
147C22×D61C22⋊Q812yes—
148C22×D61#12312yes—
149C22×D61#12412yes—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—22no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—42no—
159C2×C4×C61—41no—
160C2×C4×C61—42no—
161C2×C4×C61—42no—
162C2×C4×C61—41no—
163C2×C4×C61#13512yes—
164C2×C4×C61#13512yes—
165C2×C4×C61C22×Q811yescharacteristic
166C2×C4×C61C2×#4112yes—
167C2×C4×C61C2×#4112yes—
168C2×C4×C61C2×#4111yescharacteristic
169C2×Dic61—22no—
170C2×Dic61—21no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—21no—
175C2×Dic61—21no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—42no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—42no—
183C2×Dic61—42no—
184C2×Dic61C22⋊Q812yes—
185C2×Dic61#12312yes—
186C2×Dic61#12412yes—
187C4×D61—44no—
188C4×D61—44no—
189C4×D61#12518yes—
190C4×D61#12618yes—
191C8×C61—42no—
192#92418—42no—
193#23744—611nomaximal, Sylow
194C22×C61C2×C22⋊Q811yescharacteristic
195C22×C61C2×#12311yescharacteristic
196C22×C61C2×#12411yescharacteristic
197C22×C61C2×#13511yescharacteristic
198C22×C61C2×#13511yescharacteristic
199C22×C61#57511yescharacteristic
200C22×C61#57511yescharacteristic
201C2×D61—22no—
202C2×D61—22no—
203C2×D61—22no—
204C2×D61—22no—
205C2×D61—22no—
206C2×D61—22no—
207C2×D61#40014yes—
208C4×C61—22no—
209C4×C61—22no—
210C4×C61—42no—
211C4×C61—81no—
212C4×C61—82no—
213C4×C61C2×#12512yes—
214C4×C61C2×#12612yes—
215Dic61—42no—
216Dic61—41no—
217Dic61—41no—
218Dic61—81no—
219Dic61—82no—
220Dic61#40014yes—
221#2296—611no—
222#2285—611no—
223#2101—612no—
224#2101—612no—
225#2100—611no—
226#2100—611no—
227#2099—611no—
228#2099D6111yescharacteristic, complemented
229#1735—612no—
230#1735—612no—
231C2×#336—611no—
232C2×C61C2×#40011yescharacteristic
233C2×C61#307611yescharacteristic
234C2×C61#307611yescharacteristic
235C2×C61#309111yescharacteristic
236C2×C61#309111yescharacteristic
237C2×C61#313111yescharacteristic
238C2×C61#313511yescharacteristic
239D61—24no—
240C23×C8—612no—
241C2×#117—611no—
242C2×#117—612no—
243C2×#117—611no—
244C22×C42—611no—
245#389—611no—
246#389—611no—
247#389—611no—
248#389C2×D6111yescharacteristic
249#385—1221no—
250#385—1221no—
251#384—611no—
252#384C2×D6111yescharacteristic
253#382—612no—
254#380—1221no—
255#380—1221no—
256C4×C4⋊C4—1221no—
257C4×C4⋊C4—1221no—
258C4×C4⋊C4—1221no—
259C4×C4⋊C4—1221no—
260#340—612no—
261#340—612no—
262#340—612no—
263#340—612no—
264#340—612no—
265#340—612no—
266#340C2×D6112yes—
267#340C2×D6112yes—
268#336—612no—
269#336—611no—
270#336C2×D6111yescharacteristic
271C61#2374411yescharacteristic, complemented, Sylow
272C23×C4—611no—
273C23×C4—611no—
274C23×C4—611no—
275C22×C8—612no—
276C22×C8—1224no—
277C22×C8—1224no—
278C22×C8—1224no—
279C22×C8C22×D6112yes—
280#117—614no—
281#117—1222no—
282#117—1224no—
283#117—1228no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—611no—
288C2×C4⋊C4—612no—
289C2×C4⋊C4—611no—
290C2×C4⋊C4—1221no—
291C2×C4⋊C4—1221no—
292C2×C4⋊C4—1221no—
293C2×C4⋊C4—1221no—
294C2×C4⋊C4—1221no—
295C2×C4⋊C4C22×D6112yes—
296C2×C4⋊C4C22×D6111yescharacteristic
297C2×C4⋊C4C22×D6111yescharacteristic
298C2×C22⋊C4—1221no—
299C2×C22⋊C4—1222no—
300C2×C22⋊C4—1221no—
301C2×C42—611no—
302C2×C42—611no—
303C2×C42—611no—
304C2×C42—1224no—
305C2×C42—1221no—
306C2×C42—1221no—
307C2×C42—1222no—
308C2×C42C22×D6111yescharacteristic
309#95—21no—
310#95—1222no—
311#95—1222no—
312#95—1221no—
313#95—1221no—
314#95—1221no—
315C24—611no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—22no—
319C22×C4—611no—
320C22×C4—612no—
321C22×C4—614no—
322C22×C4—614no—
323C22×C4—612no—
324C22×C4—611no—
325C22×C4—611no—
326C22×C4—1222no—
327C22×C4—1222no—
328C22×C4—1221no—
329C22×C4—1222no—
330C22×C4—1222no—
331C22×C4—1221no—
332C22×C4—1222no—
333C22×C4—2441no—
334C22×C4—2441no—
335C22×C4D4×D6111yescharacteristic
336C22×C4D4×D6111yescharacteristic
337C22×C4C23×D6111yescharacteristic
338C2×C8—22no—
339C2×C8—22no—
340C2×C8—22no—
341C2×C8—1222no—
342C2×C8—1222no—
343C2×C8—1222no—
344C2×C8—2448no—
345C4⋊C4—21no—
346C4⋊C4—22no—
347C4⋊C4—24no—
348C4⋊C4—42no—
349C4⋊C4—42no—
350C4⋊C4—42no—
351C4⋊C4—612no—
352C4⋊C4—1221no—
353C4⋊C4—1222no—
354C4⋊C4—1224no—
355C4⋊C4—2442no—
356C4⋊C4—2442no—
357C4⋊C4—2442no—
358C4⋊C4—2442no—
359C4⋊C4—2442no—
360C4⋊C4Q8×D6112yes—
361C22⋊C4—1224no—
362C22⋊C4—2442no—
363C22⋊C4—2444no—
364C42—22no—
365C42—1222no—
366C42—1222no—
367C42—1224no—
368C42—1222no—
369C42—2442no—
370C42—2444no—
371C23—612no—
372C23—612no—
373C23—612no—
374C23—1221no—
375C23—1221no—
376C23—1221no—
377C23—1221no—
378C23C2×D4×D6111yescharacteristic
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—612no—
393C2×C4—612no—
394C2×C4—612no—
395C2×C4—618no—
396C2×C4—618no—
397C2×C4—1222no—
398C2×C4—1221no—
399C2×C4—1221no—
400C2×C4—1221no—
401C2×C4—1221no—
402C2×C4—1221no—
403C2×C4—1221no—
404C2×C4—2444no—
405C2×C4—2444no—
406C2×C4—2441no—
407C2×C4—2442no—
408C2×C4—2441no—
409C2×C4—2442no—
410C2×C4—2442no—
411C2×C4—2441no—
412C2×C4—2441no—
413C2×C4—2441no—
414C2×C4#1451979612yes—
415C2×C4#1451979812yes—
416C2×C4C2×Q8×D6111yescharacteristic
417C2×C4#41×D6112yes—
418C2×C4#41×D6112yes—
419C2×C4#41×D6111yescharacteristic
420C8—42no—
421C8—2442no—
422C22—614no—
423C22—1222no—
424C22—1222no—
425C22—1222no—
426C22—1222no—
427C22—1222no—
428C22—1222no—
429C22C22⋊Q8×D6111yescharacteristic
430C22#123×D6111yescharacteristic
431C22#124×D6111yescharacteristic
432C22C2×#1451979611yescharacteristic
433C22C2×#1451979811yescharacteristic
434C22#1684056111yescharacteristic
435C22#1684056111yescharacteristic
436C4—22no—
437C4—22no—
438C4—42no—
439C4—82no—
440C4—81no—
441C4—614no—
442C4—4882no—
443C4—4881no—
444C4—2441no—
445C4—2441no—
446C4—2442no—
447C4#125×D6112yes—
448C4#126×D6112yes—
449C2—1224no—
450C2#400×D6111yescharacteristic
451C2#2145560011yescharacteristic
452C2#2145560211yescharacteristic
453C2#2145572711yescharacteristic
454C2#2145573311yescharacteristic
455C2#2145613811yescharacteristic
456C2#2145616611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2099C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
hypercenter#2099D61
hypocenterC61#23744
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2099

Complements

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

NH ≅ G/Ntype
3. #21447390C2semidirect
4. #21447389C2semidirect
5. #21447383C2semidirect
6. #21447382C2semidirect
7. #21447376C2semidirect
11. C61×#2099C2semidirect
228. #2099D61semidirect
271. C61#23744semidirect

Maximal subgroups

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

subgroupindex
#214483002
#214482242
#214473902
#214473892
#214473832
#214473822
#214473762
#214455342
#336×D612
C61×#20992
#2374461