Finite Group Databasebeta

← #29574780

Subgroups — #29574780

Order 15616.

616 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839963C211yesmaximal, characteristic
2#21448774C211yesmaximal, characteristic, complemented
3#21446746C211yesmaximal, characteristic
4#21446625C211yesmaximal, characteristic
5C2×#16839494C211yesmaximal, characteristic, complemented
6#21443703C211yesmaximal, characteristic, complemented
7C61×#1279C211yesmaximal, characteristic, complemented
8C22×#11758190—21no—
9C2×#14519774C2211yescharacteristic
10C2×C4×Dic122C2211yescharacteristic
11#16839963—22no—
12#16839963C414yescomplemented
13C2×C4⋊#92418C2211yescharacteristic
14C2×#14519699—21no—
15C2×#14519699—22no—
16C2×#14519697—21no—
17C2×#14519697—21no—
18#16839668—21no—
19#16839649—22no—
20#16839632C2211yescharacteristic
21#16839627—21no—
22C4⋊C4×Dic61—21no—
23C4×C4⋊Dic61—21no—
24#16839494—22no—
25C2×C4⋊C8×C61C2211yescharacteristic
26C2×C4×C8×C61C2211yescharacteristic
27C4×C4⋊C4×C61C2211yescharacteristic
28C22×Dic122D411yescharacteristic
29C22×D244—21no—
30C22×D244—21no—
31C22×D244—21no—
32C2×#11758190—24no—
33C2×#11758190—42no—
34C2×#11758190—42no—
35C22×#92418—21no—
36#14519774—21no—
37#14519774—21no—
38#14519774—21no—
39#14519774C2×C412yes—
40C4×Dic122—21no—
41C4×Dic122—21no—
42C4×Dic122C2×C412yes—
43C4×Dic122D412yes—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61—21no—
46C2×C4⋊Dic61D411yescharacteristic
47C2×C4⋊Dic61D412yes—
48C2×#11758196—21no—
49C2×C4×Dic61—21no—
50C2×C4×Dic61—22no—
51C4⋊#92418—21no—
52C4⋊#92418—21no—
53#14519699—24no—
54#14519699—44no—
55#14519697—42no—
56#14519697—42no—
57#14519684—22no—
58#14519684—22no—
59#14519684—22no—
60C22×C8×C61—21no—
61C22×C8×C61—21no—
62C2×C4⋊C4×C61D411yescharacteristic
63C2×C4⋊C4×C61D411yescharacteristic
64C2×C42×C61—21no—
65C2×C42×C61C2311yescharacteristic
66C4⋊C8×C61—21no—
67C4⋊C8×C61C2×C412yes—
68C4×C8×C61—21no—
69C4×C8×C61—21no—
70#95×C61—21no—
71C23×D61—41no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—22no—
80C2×D244—22no—
81C2×D244—22no—
82C2×D244—22no—
83C2×D244—42no—
84C2×D244—42no—
85C2×D244—41no—
86C2×D244—41no—
87C2×D244—41no—
88C2×D244—41no—
89C2×D244—41no—
90C2×D244—41no—
91C2×D244—41no—
92C2×D244—41no—
93C2×D244—41no—
94C2×D244—41no—
95C2×D244—41no—
96C2×Dic122—21no—
97C2×Dic122—21no—
98C2×Dic122—21no—
99C2×Dic122—21no—
100C2×Dic122—21no—
101C2×Dic122C22⋊C412yes—
102C2×C8×C61—22no—
103C2×C8×C61—22no—
104C2×C8×C61—41no—
105C2×C8×C61—41no—
106C2×C8×C61—41no—
107C2×C8×C61—41no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61SD1612yescomplemented
112C42×C61—41no—
113C42×C61—41no—
114C42×C61C22×C411yescharacteristic
115C42×C61C2×D411yescharacteristic
116C42×C61#4111yescharacteristic
117C42×C61#4111yescharacteristic
118C4⋊Dic61—21no—
119C4⋊Dic61—41no—
120C4⋊Dic61—41no—
121C4⋊Dic61—41no—
122C4⋊Dic61—41no—
123C4⋊Dic61—42no—
124C4⋊Dic61C22⋊C412yes—
125#11758196—22no—
126#11758196—22no—
127C4×Dic61—22no—
128C4×Dic61—22no—
129C4×Dic61—82no—
130C2×#92418—41no—
131C2×#92418—41no—
132C2×#92418—41no—
133#11758190—48no—
134C23×C61#12011yescharacteristic
135C22×D61—42no—
136C22×D61—81no—
137C22×D61—81no—
138C22×D61—81no—
139C22×D61—81no—
140C22×D61—81no—
141C22×D61—81no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—22no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61C2×C22⋊C411yescharacteristic
151C2×C4×C61C4×D411yescharacteristic
152C2×C4×C61C4×D411yescharacteristic
153C2×C4×C61#12111yescharacteristic
154C2×C4×C61#12111yescharacteristic
155C2×C4×C61#12311yescharacteristic
156C2×C4×C61C2×SD1611yescharacteristic
157C2×C4×C61#13511yescharacteristic
158C2×C4×C61#13511yescharacteristic
159C2×C4×C61#13511yescharacteristic
160C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C61#13711yescharacteristic
164C2×Dic61—22no—
165C2×Dic61—22no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—42no—
171C2×Dic61—42no—
172C2×Dic61—42no—
173D244—44no—
174D244—42no—
175D244—42no—
176D244—42no—
177D244—42no—
178D244—82no—
179D244—81no—
180D244—81no—
181D244—81no—
182D244—81no—
183Dic122—22no—
184Dic122—22no—
185Dic122—41no—
186Dic122—41no—
187C8×C61—42no—
188C8×C61—42no—
189#92418—81no—
190#8978—611nomaximal, Sylow
191C22×C61#38611yescharacteristic
192C22×C61#44811yescharacteristic
193C22×C61#44911yescharacteristic
194C22×C61#44911yescharacteristic
195C22×C61#44911yescharacteristic
196C22×C61#45311yescharacteristic
197C22×C61#45411yescharacteristic
198C2×D61—82no—
199C2×D61—82no—
200C2×D61—82no—
201C2×D61—161no—
202C2×D61—161no—
203C2×D61—161no—
204C2×D61—161no—
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—42no—
208C4×C61—81no—
209C4×C61#41611yescharacteristic
210C4×C61#41811yescharacteristic
211C4×C61C4×SD1611yescharacteristic
212C4×C61#44011yescharacteristic
213C4×C61#46011yescharacteristic
214C4×C61#46411yescharacteristic
215C4×C61#48211yescharacteristic
216C4×C61#48211yescharacteristic
217Dic61—42no—
218Dic61—42no—
219Dic61—82no—
220C2×#460—611no—
221#2355—611no—
222#1982—611no—
223#1957—611no—
224C2×Q8⋊C8—611no—
225#1296—611no—
226#1279D6111yescharacteristic, complemented
227C2×C61#162011yescharacteristic
228C2×C61#162211yescharacteristic
229C2×C61#162611yescharacteristic
230C2×C61#162811yescharacteristic
231C2×C61#187511yescharacteristic
232C2×C61#188011yescharacteristic
233C2×C61#188311yescharacteristic
234D61—162no—
235C22×SD16—1221no—
236C2×#127—611no—
237C2×C4×Q8—611no—
238#460—614no—
239#460—1222no—
240C2×C4⋊C8—611no—
241C2×C4⋊C8C2×D6111yescharacteristic
242C2×#102—1221no—
243C2×#102—1222no—
244C2×#102—1221no—
245C2×#102—1221no—
246C2×C4×C8C2×D6111yescharacteristic
247#391—1221no—
248#387—1222no—
249#384—611no—
250#382—1221no—
251C4×C4⋊C4—1221no—
252C4×C4⋊C4—1221no—
253C4×C4⋊C4C2×D6111yescharacteristic
254Q8⋊C8—1222no—
255C61#897811yescharacteristic, complemented, Sylow
256C22×Q8—611no—
257C22×D4—1221no—
258C22×D4—1221no—
259C22×D4—1221no—
260C2×SD16—1224no—
261C2×SD16—2442no—
262C2×SD16—2442no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—1221no—
266#127—612no—
267#127—1221no—
268#127—1221no—
269#127—1221no—
270C4×Q8—612no—
271C4×Q8—612no—
272C4×Q8—1221no—
273C4×Q8—1221no—
274C2×C4⋊C4—611no—
275C2×C4⋊C4—612no—
276C2×C4⋊C4—1221no—
277C2×C4⋊C4—1221no—
278C2×C4⋊C4—1221no—
279C2×C4⋊C4D24411yescharacteristic
280C2×C4⋊C4D24411yescharacteristic
281C2×C42—21no—
282C2×C42—1221no—
283C2×C42—1222no—
284C2×C42C22×D6111yescharacteristic
285C4⋊C8—21no—
286C4⋊C8—1221no—
287C4⋊C8—1221no—
288C4⋊C8C4×D6112yes—
289#102—1224no—
290#102—2442no—
291#102—2444no—
292#102—2442no—
293C4×C8—21no—
294C4×C8—21no—
295#95—21no—
296#95—1222no—
297#95—1222no—
298#95—1222no—
299C24—2441no—
300C2×Q8—612no—
301C2×Q8—1221no—
302C2×Q8—1221no—
303C2×Q8—1221no—
304C2×Q8—1221no—
305C2×Q8—1221no—
306C2×D4—1222no—
307C2×D4—1222no—
308C2×D4—1222no—
309C2×D4—2442no—
310C2×D4—2442no—
311C2×D4—2441no—
312C2×D4—2441no—
313C2×D4—2441no—
314C2×D4—2441no—
315C2×D4—2441no—
316C2×D4—2441no—
317C2×D4—2441no—
318C2×D4—2441no—
319C2×D4—2441no—
320C2×D4—2441no—
321C2×D4—2441no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—1221no—
325C22×C4—1221no—
326C22×C4—1222no—
327C22×C4C2×D24411yescharacteristic
328C22×C4D4×D6111yescharacteristic
329C22×C4D4×D6111yescharacteristic
330SD16—2448no—
331C2×C8—22no—
332C2×C8—22no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—2441no—
338C2×C8—2441no—
339C2×C8—2441no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—612no—
344C4⋊C4—1222no—
345C4⋊C4—1222no—
346C4⋊C4—1221no—
347C4⋊C4—2442no—
348C4⋊C4—2441no—
349C4⋊C4—2441no—
350C4⋊C4—2441no—
351C4⋊C4—2441no—
352C4⋊C4#1175819012yescomplemented
353C42—41no—
354C42—41no—
355C42—1222no—
356C42—1222no—
357C42—4882no—
358C42C2×C4×D6111yescharacteristic
359C42#1175822211yescharacteristic
360C42D4×D6111yescharacteristic
361C42#1175822611yescharacteristic
362C23—4881no—
363C23—4881no—
364C23—4881no—
365C23—4881no—
366C23—4881no—
367C23—4881no—
368C23—2442no—
369C23#1451974711yescharacteristic
370Q8—1222no—
371Q8—1222no—
372Q8—2441no—
373Q8—2441no—
374D4—4882no—
375D4—4881no—
376D4—4881no—
377D4—4881no—
378D4—4881no—
379D4—2444no—
380D4—2442no—
381D4—2442no—
382D4—2442no—
383D4—2442no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—22no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—1222no—
393C2×C4—1222no—
394C2×C4—2442no—
395C2×C4—2442no—
396C2×C4—2442no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4C22⋊C4×D6111yescharacteristic
402C2×C4#1451973911yescharacteristic
403C2×C4C4×D24411yescharacteristic
404C2×C4#1451975011yescharacteristic
405C2×C4#1451975211yescharacteristic
406C2×C4#1451976211yescharacteristic
407C2×C4C2×#1175819011yescharacteristic
408C2×C4#1451979811yescharacteristic
409C2×C4#1451979911yescharacteristic
410C2×C4#1451980011yescharacteristic
411C2×C4#1451980111yescharacteristic
412C2×C4#1451980411yescharacteristic
413C2×C4#1451980511yescharacteristic
414C2×C4#1451981011yescharacteristic
415C8—42no—
416C8—42no—
417C8—4881no—
418C22—9761no—
419C22—9761no—
420C22—9761no—
421C22—9761no—
422C22—4882no—
423C22—4882no—
424C22—4882no—
425C22#1683964011yescharacteristic
426C22#1683990311yescharacteristic
427C22#1683990811yescharacteristic
428C22#1683990911yescharacteristic
429C22#1683991011yescharacteristic
430C22#1683993111yescharacteristic
431C22#1683993611yescharacteristic
432C4—21no—
433C4—21no—
434C4—42no—
435C4—81no—
436C4—4882no—
437C4—2442no—
438C4—2442no—
439C4#1683975711yescharacteristic
440C4#1683976511yescharacteristic
441C4C4×#1175819011yescharacteristic
442C4#1683986411yescharacteristic
443C4#1683996311yescharacteristic
444C4#1683998511yescharacteristic
445C4#1684008811yescharacteristic
446C4#1684008911yescharacteristic
447C2—9762no—
448C2#2144488011yescharacteristic
449C2#2144489311yescharacteristic
450C2#2144491811yescharacteristic
451C2#2144493111yescharacteristic
452C2#2144614011yescharacteristic
453C2#2144617311yescharacteristic
454C2#2144619611yescharacteristic
subgroupG/H
centerC23#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1279C2
socleC23×C61#120
prime radicalC2×#14519774C22
cosocleC2×C42×C61C23
hypercenter#1279D61
hypocenterC61#8978
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
2. #21448774C2semidirect
5. C2×#16839494C2semidirect
6. #21443703C2semidirect
7. C61×#1279C2semidirect
12. #16839963C4semidirect
111. C4⋊C4×C61SD16semidirect
226. #1279D61semidirect
255. C61#8978semidirect
352. C4⋊C4#11758190semidirect

Maximal subgroups

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

subgroupindex
C2×#168399632
#214487742
#214467462
#214466252
C2×#168394942
#214437032
C61×#12792
#897861