Finite Group Databasebeta

← #29583539

Subgroups — #29583539

Order 15616.

546 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450737C211yesmaximal, characteristic
2#21445978C211yesmaximal, characteristic, complemented
3#21445816C211yesmaximal, characteristic
4C2×Q8⋊#92418C211yesmaximal, characteristic, complemented
5C2×#16839489C211yesmaximal, characteristic
6#21443703C211yesmaximal, characteristic, complemented
7C61×#1803C211yesmaximal, characteristic, complemented
8C2×#14519753—21no—
9C2×C4×D244C2211yescharacteristic
10C2×#14519710—22no—
11C2×C4⋊#92418C2211yescharacteristic
12C2×#14519697—21no—
13C2×C4×#92418C2211yescharacteristic
14#16839684—22no—
15#16839664—21no—
16#16839660—21no—
17#16839632C2211yescharacteristic
18#16839619—21no—
19#16839524—21no—
20Q8⋊#92418—22no—
21#16839489—22no—
22C2×C4×Q8×C61C2211yescharacteristic
23C2×C4⋊C8×C61C2211yescharacteristic
24C2×#103×C61—21no—
25C61×#384C2211yescharacteristic
26C61×#340—21no—
27C22×D244D411yescharacteristic
28C22×C4×D61—21no—
29C22×#92418—21no—
30C22×#92418—21no—
31#14519753—42no—
32#14519753—42no—
33C4×D244—21no—
34C4×D244—21no—
35C4×D244—21no—
36C4×D244—21no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61D411yescharacteristic
40C2×C4⋊Dic61D412yes—
41C2×#11758196—22no—
42C2×#11758198—22no—
43C2×#11758198—21no—
44C2×#11758198—22no—
45#14519710—44no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48#14519697—42no—
49C4×#92418—21no—
50C4×#92418D412yes—
51#14519684—22no—
52C22×Q8×C61D411yescharacteristic
53C22×C8×C61—21no—
54C4×Q8×C61—21no—
55C4×Q8×C61—21no—
56C4×Q8×C61—21no—
57C4×Q8×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61D411yescharacteristic
63C2×C42×C61—21no—
64C2×C42×C61C2311yescharacteristic
65C4⋊C8×C61—21no—
66C4⋊C8×C61—21no—
67#103×C61—42no—
68C23×D61—21no—
69C2×Q8×C61—21no—
70C2×Q8×C61—21no—
71C2×Q8×C61—21no—
72C2×Q8×C61—21no—
73C2×Q8×C61—21no—
74C2×Q8×C61D812yes—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—41no—
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×Dic61—21no—
82C22×Dic61—22no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244—21no—
87C2×D244—21no—
88C2×D244Q1612yes—
89C2×C4×D61—41no—
90C2×C4×D61—41no—
91C2×C4×D61—41no—
92C2×C4×D61—41no—
93C2×C4×D61—41no—
94C2×C4×D61—41no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C4⋊C4×C61—21no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61—42no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—41no—
106C4⋊C4×C61—41no—
107C42×C61—41no—
108C42×C61—41no—
109C42×C61C2×D411yescharacteristic
110C42×C61#4111yescharacteristic
111C42×C61#4111yescharacteristic
112C42×C61#4111yescharacteristic
113#11758198—44no—
114#11758198—41no—
115#11758198—41no—
116#11758198—82no—
117C4⋊Dic61—21no—
118C4⋊Dic61—21no—
119C4⋊Dic61—41no—
120C4⋊Dic61—41no—
121C4⋊Dic61—41no—
122C4⋊Dic61—41no—
123C4⋊Dic61—42no—
124#11758196—44no—
125C2×#92418—22no—
126C2×#92418—22no—
127C2×#92418—22no—
128C2×#92418—41no—
129C2×#92418—41no—
130C2×#92418—41no—
131C23×C61#12011yescharacteristic
132C22×D61—22no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—41no—
138C22×D61—41no—
139Q8×C61—22no—
140Q8×C61—22no—
141Q8×C61—41no—
142Q8×C61—41no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—22no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—81no—
152C2×C4×C61—81no—
153C2×C4×C61—81no—
154C2×C4×C61#12111yescharacteristic
155C2×C4×C61#12111yescharacteristic
156C2×C4×C61#12111yescharacteristic
157C2×C4×C61#12311yescharacteristic
158C2×C4×C61#12311yescharacteristic
159C2×C4×C61#12411yescharacteristic
160C2×C4×C61C2×D811yescharacteristic
161C2×C4×C61C2×Q1611yescharacteristic
162C2×C4×C61#13511yescharacteristic
163C2×C4×C61#13511yescharacteristic
164C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C61#13711yescharacteristic
167C2×C4×C61#13711yescharacteristic
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—42no—
171C2×Dic61—42no—
172C2×Dic61—41no—
173C2×Dic61—42no—
174D244—22no—
175D244—22no—
176D244—41no—
177D244—41no—
178C4×D61—81no—
179C4×D61—81no—
180C4×D61—81no—
181C4×D61—81no—
182C8×C61—81no—
183#92418—24no—
184#92418—81no—
185#10434—611nomaximal, Sylow
186C22×C61#39411yescharacteristic
187C22×C61#44711yescharacteristic
188C22×C61#44911yescharacteristic
189C22×C61#45111yescharacteristic
190C22×C61#45211yescharacteristic
191C22×C61#45311yescharacteristic
192C22×C61#45611yescharacteristic
193C2×D61—42no—
194C2×D61—42no—
195C2×D61—42no—
196C2×D61—81no—
197C2×D61—81no—
198C2×D61—81no—
199C2×D61—81no—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—42no—
203C4×C61—81no—
204C4×C61—161no—
205C4×C61#46611yescharacteristic
206C4×C61#46711yescharacteristic
207C4×C61#46811yescharacteristic
208C4×C61#46811yescharacteristic
209C4×C61#48011yescharacteristic
210C4×C61#48211yescharacteristic
211C4×C61#48411yescharacteristic
212C4×C61#48511yescharacteristic
213Dic61—82no—
214Dic61—81no—
215#2538—611no—
216#1845—611no—
217#1803D6111yescharacteristic, complemented
218#1802—611no—
219C2×Q8⋊C8—611no—
220C2×D4⋊C8—611no—
221#1296—611no—
222C2×C61#162111yescharacteristic
223C2×C61#163211yescharacteristic
224C2×C61#164911yescharacteristic
225C2×C61#165011yescharacteristic
226C2×C61#203311yescharacteristic
227C2×C61#203611yescharacteristic
228C2×C61#203911yescharacteristic
229D61—82no—
230C2×C22⋊Q8—1221no—
231C2×C4×Q8C2×D6111yescharacteristic
232C2×C4×D4—611no—
233C2×#107—1222no—
234C2×C4⋊C8—611no—
235C2×C4⋊C8C2×D6111yescharacteristic
236C2×#103—21no—
237C2×#102—1221no—
238C2×C4×C8—611no—
239#396—1222no—
240#390—1221no—
241#389—1221no—
242#384—611no—
243#384C2×D6111yescharacteristic
244#380—1221no—
245#340—21no—
246#340—1221no—
247Q8⋊C8—1222no—
248D4⋊C8—1222no—
249C61#1043411yescharacteristic, complemented, Sylow
250C22×Q8C22⋊D6111yescharacteristic
251C22×D4—611no—
252C23×C4—1221no—
253C22×C8—21no—
254C22×C8—1221no—
255C22×C8—1221no—
256C22⋊Q8—2442no—
257C22⋊Q8—2442no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×D4—1221no—
263C4×D4—1221no—
264C4×D4—1221no—
265C4×D4—1221no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—611no—
271C2×C4⋊C4—612no—
272C2×C4⋊C4—1222no—
273C2×C4⋊C4—1221no—
274C2×C4⋊C4—1221no—
275C2×C4⋊C4C22⋊D6111yescharacteristic
276C2×C22⋊C4—1222no—
277C2×C22⋊C4—1222no—
278C2×C22⋊C4—1221no—
279C2×C42—21no—
280C2×C42C22×D6111yescharacteristic
281#107—2444no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284C4⋊C8—1221no—
285C4⋊C8—1221no—
286#103—42no—
287#102—2442no—
288C4×C8—612no—
289C4×C8—1221no—
290#95—1222no—
291C24—1221no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8#1175819912yes—
298C2×D4—612no—
299C2×D4—1221no—
300C2×D4—1221no—
301C2×D4—1221no—
302C2×D4—1221no—
303C2×D4—1221no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—41no—
307C22×C4—1221no—
308C22×C4—1222no—
309C22×C4—2441no—
310C22×C4—2441no—
311C22×C4—2441no—
312C22×C4—2441no—
313C22×C4—2441no—
314C22×C4—2441no—
315C22×C4D4×D6111yescharacteristic
316C22×C4D4×D6111yescharacteristic
317C22×C4C2×C22⋊D6111yescharacteristic
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—1222no—
322C2×C8—1222no—
323C2×C8—1222no—
324C2×C8—2441no—
325C2×C8—2441no—
326C2×C8—2441no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—42no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—1221no—
337C4⋊C4—1221no—
338C4⋊C4—2442no—
339C4⋊C4—2444no—
340C4⋊C4—2441no—
341C4⋊C4—2441no—
342C4⋊C4—2441no—
343C4⋊C4—2441no—
344C22⋊C4—4882no—
345C22⋊C4—2444no—
346C22⋊C4—2441no—
347C22⋊C4—2441no—
348C42—41no—
349C42—41no—
350C42#1175822211yescharacteristic
351C42#1175822211yescharacteristic
352C42D4×D6111yescharacteristic
353C42#1175822411yescharacteristic
354C23—1222no—
355C23—2441no—
356C23—2441no—
357C23—2441no—
358C23—2441no—
359C23—2441no—
360C23—2441no—
361C23#1451974511yescharacteristic
362Q8—22no—
363Q8—22no—
364Q8—41no—
365Q8—41no—
366D4—1222no—
367D4—1222no—
368D4—2441no—
369D4—2441no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—4881no—
382C2×C4—4881no—
383C2×C4—4881no—
384C2×C4—4881no—
385C2×C4—2442no—
386C2×C4—2441no—
387C2×C4—2442no—
388C2×C4—2441no—
389C2×C4—2442no—
390C2×C4—2441no—
391C2×C4#1451974911yescharacteristic
392C2×C4#1451975011yescharacteristic
393C2×C4#1451975011yescharacteristic
394C2×C4#1451975911yescharacteristic
395C2×C4#1451976011yescharacteristic
396C2×C4#1451976311yescharacteristic
397C2×C4C2×#1175819911yescharacteristic
398C2×C4Q16×D6111yescharacteristic
399C2×C4#1451979711yescharacteristic
400C2×C4#1451979811yescharacteristic
401C2×C4#1451980211yescharacteristic
402C2×C4#1451980411yescharacteristic
403C2×C4#1451980811yescharacteristic
404C2×C4#1451980911yescharacteristic
405C8—81no—
406C8—1224no—
407C8—4881no—
408C22—4881no—
409C22—4881no—
410C22—4881no—
411C22—4881no—
412C22—2442no—
413C22—2442no—
414C22—2442no—
415C22#1683967711yescharacteristic
416C22#1683989511yescharacteristic
417C22#1683990611yescharacteristic
418C22#1683991611yescharacteristic
419C22#1683992211yescharacteristic
420C22#1683992811yescharacteristic
421C22#1683994311yescharacteristic
422C4—21no—
423C4—21no—
424C4—42no—
425C4—81no—
426C4—161no—
427C4—4882no—
428C4—4881no—
429C4#1683999611yescharacteristic
430C4#1684000211yescharacteristic
431C4#1684001011yescharacteristic
432C4#1684001111yescharacteristic
433C4#1684007511yescharacteristic
434C4#1684008611yescharacteristic
435C4#1684009611yescharacteristic
436C4#1684010111yescharacteristic
437C2—4882no—
438C2#2144488211yescharacteristic
439C2#2144495211yescharacteristic
440C2#2144506611yescharacteristic
441C2#2144507411yescharacteristic
442C2#2144700111yescharacteristic
443C2#2144702011yescharacteristic
444C2#2144704111yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1803C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#1803D61
hypocenterC61#10434
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
2. #21445978C2semidirect
4. C2×Q8⋊#92418C2semidirect
6. #21443703C2semidirect
7. C61×#1803C2semidirect
217. #1803D61semidirect
249. C61#10434semidirect

Maximal subgroups

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

subgroupindex
#214507372
#214459782
#214458162
C2×Q8⋊#924182
C2×#168394892
#214437032
C61×#18032
#1043461