Finite Group Databasebeta

← #29575477

Subgroups — #29575477

Order 15616.

546 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454775C211yesmaximal, characteristic, complemented
2C4×#14519803C211yesmaximal, characteristic
3#21444207C211yesmaximal, characteristic, complemented
4C2×D4⋊#92418C211yesmaximal, characteristic, complemented
5#21443668C211yesmaximal, characteristic, complemented
6#21443655C211yesmaximal, characteristic, complemented
7C61×#1460C211yesmaximal, characteristic, complemented
8C2×#14519803C411yescharacteristic
9C4×#11758222C2211yescharacteristic
10#16839886—21no—
11#16839872—21no—
12#16839862—21no—
13C4×#11758200—21no—
14C4×#11758199—21no—
15#16839827—21no—
16#16839825—22no—
17#16839813—21no—
18#16839802C411yescharacteristic
19C2×C4⋊#92418C2211yescharacteristic
20#16839767C411yescharacteristic
21#16839761C411yescharacteristic
22C4×#11758194C2211yescharacteristic
23C2×C4×#92418C2211yescharacteristic
24C4×C8×D61—21no—
25#16839494—21no—
26#16839491—21no—
27D4⋊#92418—21no—
28D4⋊#92418—21no—
29C2×C4×D4×C61C2211yescharacteristic
30C61×#431C2211yescharacteristic
31C61×#431C2211yescharacteristic
32C61×#323—22no—
33C2×#11758222C2×C411yescharacteristic
34#14519803—22no—
35#14519803C814yescomplemented
36C2×#11758200—21no—
37C2×#11758199—21no—
38C2×#11758194C2×C411yescharacteristic
39C2×#11758194C2×C411yescharacteristic
40C22×#92418—21no—
41C22×#92418—21no—
42C2×C8×D61—22no—
43C4×Dic122D411yescharacteristic
44C4×Dic122D411yescharacteristic
45C4×D244D411yescharacteristic
46C4×D244D411yescharacteristic
47C4×C22⋊D61—21no—
48C4×C22⋊D61—21no—
49#14519736C2×C411yescharacteristic
50#14519734—21no—
51C42×D61—21no—
52#14519710—21no—
53#14519708—21no—
54C4⋊#92418—21no—
55C4⋊#92418—21no—
56#14519706—22no—
57#14519700—21no—
58#14519698—21no—
59#14519698—21no—
60#14519697—21no—
61#14519689—22no—
62#14519688—21no—
63C4×#92418—21no—
64C4×#92418—21no—
65C4×#92418D411yescharacteristic
66C4×#92418D411yescharacteristic
67C8×Dic61—22no—
68C22×D4×C61C2×C411yescharacteristic
69C23×C4×C61—21no—
70C4×D4×C61—21no—
71C4×D4×C61—21no—
72C4×D4×C61—21no—
73C4×D4×C61—21no—
74C2×C4⋊C4×C61C2×C411yescharacteristic
75C2×C22⋊C4×C61—21no—
76C2×C42×C61C2311yescharacteristic
77C4⋊C8×C61—21no—
78C4⋊C8×C61—21no—
79C22⋊C8×C61—21no—
80C22⋊C8×C61D412yes—
81C4×C8×C61—21no—
82C4×C8×C61—21no—
83C24×C61—21no—
84C2×D4×C61—21no—
85C2×D4×C61—21no—
86C2×D4×C61—21no—
87C2×D4×C61—21no—
88C2×D4×C61—21no—
89C2×D4×C61C2×C812yescomplemented
90C22×C4×C61—21no—
91C22×C4×C61—41no—
92C22×C4×C61—41no—
93C22×C4×C61—81no—
94C22×C4×C61—81no—
95C22×C4×C61C22×C411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61#4111yescharacteristic
98C2×C22⋊D61—21no—
99#11758222—21no—
100#11758222—21no—
101#11758222C2×C812yes—
102#11758222M1612yes—
103C2×D244C22⋊C411yescharacteristic
104C2×C4×D61—21no—
105C2×C4×D61—21no—
106C2×C4×D61—21no—
107C2×Dic122C22⋊C411yescharacteristic
108C2×C8×C61—22no—
109C2×C8×C61—41no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61—21no—
112C22⋊C4×C61—41no—
113C22⋊C4×C61—41no—
114C42×C61C2×D411yescharacteristic
115C42×C61C2×D411yescharacteristic
116C42×C61C2×D411yescharacteristic
117C42×C61#4111yescharacteristic
118C22⋊Dic61—21no—
119#11758200—24no—
120#11758199—24no—
121#11758198—21no—
122#11758198—21no—
123C4⋊Dic61C22⋊C411yescharacteristic
124C4⋊Dic61C22⋊C411yescharacteristic
125#11758196—21no—
126#11758196—21no—
127C4×Dic61—21no—
128C4×Dic61—21no—
129C4×Dic61—21no—
130#11758194—21no—
131#11758194—21no—
132#11758194—21no—
133#11758194C2×C812yescomplemented
134C2×#92418—21no—
135C2×#92418—21no—
136C2×#92418—21no—
137C2×#92418—21no—
138C2×#92418—42no—
139C2×#92418—41no—
140C2×#92418—81no—
141C8×D61—44no—
142C23×C61—22no—
143C23×C61—41no—
144C23×C61—41no—
145C23×C61—81no—
146C23×C61—81no—
147C23×C61C4×D411yescharacteristic
148C22×D61—21no—
149D4×C61—22no—
150D4×C61—22no—
151D4×C61—41no—
152D4×C61—41no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—82no—
158C2×C4×C61—81no—
159C2×C4×C61—81no—
160C2×C4×C61—81no—
161C2×C4×C61C2×C22⋊C411yescharacteristic
162C2×C4×C61C4×D411yescharacteristic
163C2×C4×C61#12011yescharacteristic
164C2×C4×C61#12111yescharacteristic
165C2×C4×C61#12111yescharacteristic
166C2×C4×C61#12311yescharacteristic
167C2×C4×C61C22×C811yescharacteristic
168C2×C4×C61C2×M1611yescharacteristic
169C2×C4×C61#13111yescharacteristic
170C2×C4×C61#13111yescharacteristic
171C22⋊D61—22no—
172C22⋊D61—22no—
173C2×Dic61—21no—
174C2×Dic61—21no—
175C2×Dic61—21no—
176D244—21no—
177D244C22⋊C812yes—
178C4×D61—22no—
179C4×D61—22no—
180C4×D61—42no—
181C4×D61—41no—
182C4×D61—41no—
183Dic122—21no—
184Dic122C22⋊C812yes—
185C8×C61—42no—
186C8×C61—81no—
187#92418—22no—
188#92418—22no—
189#92418—41no—
190#92418—41no—
191#92418—81no—
192#9095—611nomaximal, Sylow
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—42no—
196C22×C61—82no—
197C22×C61—82no—
198C22×C61—81no—
199C22×C61—81no—
200C22×C61#38611yescharacteristic
201C22×C61C8×D411yescharacteristic
202C22×C61#43511yescharacteristic
203C2×D61—22no—
204C2×D61—41no—
205C2×D61—41no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—81no—
210C4×C61C2×C22⋊C811yescharacteristic
211C4×C61#40811yescharacteristic
212C4×C61C8×D411yescharacteristic
213C4×C61#43511yescharacteristic
214C4×C61#47111yescharacteristic
215C4×C61#47211yescharacteristic
216Dic61—22no—
217Dic61—41no—
218Dic61—41no—
219C8×#41—611no—
220C4×AGL(1,ℤ/8)—611no—
221#1477—611no—
222C2×D4⋊C8—611no—
223#1460D6111yescharacteristic, complemented
224#1283—611no—
225#1278—611no—
226C2×C61—21no—
227C2×C61—21no—
228C2×C61—82no—
229C2×C61#186911yescharacteristic
230C2×C61#190611yescharacteristic
231C2×C61#190711yescharacteristic
232D61—42no—
233C2×AGL(1,ℤ/8)—611no—
234C4×#41—611no—
235C2×C4×D4C2×D6111yescharacteristic
236C8×Q8—1221no—
237#442—1221no—
238#440—1221no—
239C4×SD16—1221no—
240C4×D8—1221no—
241C8×D4—1221no—
242C8×D4—1222no—
243#431—1221no—
244#431C2×D6111yescharacteristic
245#431C2×D6111yescharacteristic
246#428—611no—
247C2×C4⋊C8—611no—
248#418—611no—
249#417—611no—
250C4×M16—611no—
251C2×C4×C8—611no—
252C2×C4×C8—1221no—
253Q8⋊C8—1221no—
254D4⋊C8—1221no—
255D4⋊C8—1221no—
256D4⋊C8—1221no—
257#323—22no—
258C61#909511yescharacteristic, complemented, Sylow
259C2×#41—611no—
260C22×D4C4×D6111yescharacteristic
261C23×C4—21no—
262AGL(1,ℤ/8)—614no—
263AGL(1,ℤ/8)—1222no—
264C2×SD16—1221no—
265C2×D8—1221no—
266C2×M16—611no—
267C2×M16—611no—
268C22×C8—1222no—
269C22×C8—1221no—
270C22×C8—1221no—
271C4×Q8—611no—
272C4×Q8—611no—
273C4×D4—21no—
274C4×D4—21no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—611no—
278C4×D4—611no—
279C4×D4—1221no—
280C4×D4—1221no—
281#117—611no—
282#117—1221no—
283C2×C4⋊C4C4×D6111yescharacteristic
284C2×C22⋊C4—21no—
285C2×C42—1221no—
286C2×C42C22×D6111yescharacteristic
287#107—1221no—
288#106—1221no—
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8—1222no—
292C4⋊C8—1221no—
293C4⋊C8—1221no—
294#103—1221no—
295#102—1221no—
296#102—1221no—
297#102—1221no—
298C22⋊C8—21no—
299C22⋊C8—1222no—
300C22⋊C8C22⋊D6112yes—
301#97—1221no—
302C4×C8—21no—
303C4×C8—21no—
304C4×C8—611no—
305C4×C8—611no—
306C4×C8—1222no—
307C4×C8—1221no—
308C4×C8—1221no—
309C24—21no—
310#41—612no—
311#41—612no—
312#41—1221no—
313#41—1221no—
314C2×Q8—611no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—611no—
321C2×D4—1221no—
322C2×D4C8×D6112yescomplemented
323C22×C4—21no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—81no—
327C22×C4—81no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4—1221no—
331C22×C4C2×C4×D6111yescharacteristic
332C22×C4#1175822211yescharacteristic
333C22×C4C2×C22⋊D6111yescharacteristic
334SD16—1224no—
335D8—1224no—
336M16—612no—
337M16—1221no—
338M16—1221no—
339M16—1221no—
340C2×C8—22no—
341C2×C8—41no—
342C2×C8—1221no—
343C2×C8—1221no—
344C2×C8—1221no—
345C2×C8—1221no—
346C2×C8—4881no—
347C2×C8—2444no—
348C2×C8—2442no—
349C2×C8—2441no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—611no—
353C4⋊C4—611no—
354C4⋊C4—1221no—
355C4⋊C4—1221no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—1221no—
359C22⋊C4—1221no—
360C22⋊C4—1221no—
361C42—1221no—
362C42—1221no—
363C42—1221no—
364C42D4×D6111yescharacteristic
365C42D4×D6111yescharacteristic
366C42D4×D6111yescharacteristic
367C42#1175822411yescharacteristic
368C23—22no—
369C23—41no—
370C23—41no—
371C23—81no—
372C23—81no—
373C23—1221no—
374C23C4×C22⋊D6111yescharacteristic
375Q8—612no—
376Q8—1221no—
377D4—22no—
378D4—22no—
379D4—41no—
380D4—41no—
381D4—612no—
382D4—1222no—
383D4—1222no—
384D4—1221no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—82no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—1221no—
394C2×C4—1222no—
395C2×C4—1222no—
396C2×C4—1221no—
397C2×C4—1221no—
398C2×C4—2442no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4C22⋊C4×D6111yescharacteristic
402C2×C4#1451973711yescharacteristic
403C2×C4#1451974511yescharacteristic
404C2×C4#1451974811yescharacteristic
405C2×C4#1451975011yescharacteristic
406C2×C4#1451975911yescharacteristic
407C2×C4C2×C8×D6111yescharacteristic
408C2×C4M16×D6111yescharacteristic
409C2×C4#1451978311yescharacteristic
410C2×C4#1451978511yescharacteristic
411C8—42no—
412C8—81no—
413C8—1222no—
414C8—1222no—
415C8—4881no—
416C8—2441no—
417C8—2441no—
418C22—21no—
419C22—21no—
420C22—42no—
421C22—82no—
422C22—82no—
423C22—81no—
424C22—81no—
425C22—1222no—
426C22—2441no—
427C22—2441no—
428C22#1683963811yescharacteristic
429C22C8×C22⋊D6111yescharacteristic
430C22#1683983111yescharacteristic
431C4—21no—
432C4—21no—
433C4—21no—
434C4—81no—
435C4—1222no—
436C4—2441no—
437C4—2441no—
438C4C22⋊C8×D6111yescharacteristic
439C4#1683972711yescharacteristic
440C4#1683982511yescharacteristic
441C4#1683983611yescharacteristic
442C4#1684002411yescharacteristic
443C4#1684003111yescharacteristic
444C2—21no—
445C2—21no—
446C2—82no—
447C2—2442no—
448C2#2144610811yescharacteristic
449C2#2144631711yescharacteristic
450C2#2144632411yescharacteristic
subgroupG/H
centerC2×C4#14519750
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1460C2
socleC22×C61#386
prime radicalC2×#14519803C4
cosocleC2×C42×C61C23
hypercenter#1460D61
hypocenterC61#9095
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
1. #21454775C2semidirect
3. #21444207C2semidirect
4. C2×D4⋊#92418C2semidirect
5. #21443668C2semidirect
6. #21443655C2semidirect
7. C61×#1460C2semidirect
35. #14519803C8semidirect
89. C2×D4×C61C2×C8semidirect
133. #11758194C2×C8semidirect
223. #1460D61semidirect
258. C61#9095semidirect
322. C2×D4C8×D61semidirect

Maximal subgroups

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

subgroupindex
#214547752
C4×#145198032
#214442072
C2×D4⋊#924182
#214436682
#214436552
C61×#14602
#909561