Finite Group Databasebeta

← #29581074

Subgroups — #29581074

Order 15616.

802 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840138C211yesmaximal, characteristic
2#21450818C211yesmaximal, characteristic, complemented
3#21446747C211yesmaximal, characteristic, complemented
4C2×#16839505C211yesmaximal, characteristic, complemented
5C2×Q8⋊#92418C211yesmaximal, characteristic, complemented
6#21443658C211yesmaximal, characteristic, complemented
7C2×C61×#460C211yesmaximal, characteristic, complemented
8C22×#11758199—22no—
9C2×#14519774C2211yescharacteristic
10C2×#14519766—21no—
11#16840138—22no—
12#16840138—22no—
13C2×C4⋊#92418C2211yescharacteristic
14C2×#14519698—22no—
15C2×C4×#92418C2211yescharacteristic
16#16839679—22no—
17#16839664—22no—
18#16839663—21no—
19C4×C4⋊Dic61C2211yescharacteristic
20#16839505—22no—
21Q8⋊#92418—22no—
22C22×SD16×C61—21no—
23C2×#127×C61C2211yescharacteristic
24C2×C4×Q8×C61C2211yescharacteristic
25C61×#460—22no—
26C61×#460—22no—
27C2×C4⋊C8×C61C2211yescharacteristic
28C2×#102×C61—21no—
29C22×D244—21no—
30C22×D244—21no—
31C22×D244D412yes—
32C2×#11758199—28no—
33C2×#11758199—48no—
34C22×#92418—21no—
35C22×#92418—21no—
36#14519774—21no—
37#14519774—21no—
38#14519774—21no—
39#14519774—21no—
40#14519766—42no—
41#14519766—42no—
42C2×C4⋊Dic61D412yes—
43C2×#11758198—24no—
44C2×#11758198—24no—
45C2×C4×Dic61—21no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48#14519698—44no—
49C4×#92418—21no—
50C4×#92418D412yes—
51#14519684—21no—
52C22×Q8×C61D411yescharacteristic
53C22×D4×C61—21no—
54C22×D4×C61—21no—
55C22×D4×C61—21no—
56C2×SD16×C61—24no—
57C2×SD16×C61—42no—
58C2×SD16×C61—42no—
59C22×C8×C61—21no—
60#127×C61—21no—
61#127×C61—21no—
62#127×C61—21no—
63#127×C61D412yes—
64C4×Q8×C61—21no—
65C4×Q8×C61—21no—
66C4×Q8×C61—21no—
67C4×Q8×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61D411yescharacteristic
70C2×C42×C61—21no—
71C2×C42×C61C2311yescharacteristic
72C4⋊C8×C61—21no—
73C4⋊C8×C61D412yes—
74#102×C61—24no—
75C24×C61—41no—
76C23×D61—22no—
77C2×Q8×C61—21no—
78C2×Q8×C61—21no—
79C2×Q8×C61—21no—
80C2×Q8×C61—21no—
81C2×Q8×C61—21no—
82C2×Q8×C61D812yescomplemented
83C2×D4×C61—22no—
84C2×D4×C61—22no—
85C2×D4×C61—22no—
86C2×D4×C61—44no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—42no—
93C2×D4×C61—41no—
94C2×D4×C61—41no—
95C2×D4×C61—42no—
96C22×C4×C61—21no—
97C22×C4×C61—21no—
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C22×Dic61—22no—
102C2×D244—22no—
103C2×D244—22no—
104C2×D244—44no—
105C2×D244—41no—
106C2×D244—41no—
107C2×D244—41no—
108C2×D244—41no—
109C2×D244—41no—
110C2×D244—41no—
111C2×D244—42no—
112C2×D244—41no—
113C2×D244—42no—
114C2×D244—41no—
115SD16×C61—48no—
116C2×C8×C61—22no—
117C2×C8×C61—41no—
118C2×C8×C61—41no—
119C4⋊C4×C61—21no—
120C4⋊C4×C61—21no—
121C4⋊C4×C61—41no—
122C4⋊C4×C61—41no—
123C42×C61—41no—
124C42×C61—41no—
125C42×C61C2×D411yescharacteristic
126C42×C61C2×D411yescharacteristic
127C42×C61C2×D411yescharacteristic
128C42×C61#4111yescharacteristic
129#11758199—416no—
130#11758198—48no—
131#11758198—84no—
132C4⋊Dic61—22no—
133C4⋊Dic61—22no—
134C4×Dic61—41no—
135C4×Dic61—41no—
136C2×#92418—24no—
137C2×#92418—22no—
138C2×#92418—41no—
139C2×#92418—42no—
140C23×C61—42no—
141C23×C61—81no—
142C23×C61—81no—
143C23×C61—82no—
144C23×C61—82no—
145C23×C61#12011yescharacteristic
146C22×D61—42no—
147C22×D61—42no—
148C22×D61—42no—
149C22×D61—44no—
150C22×D61—44no—
151Q8×C61—22no—
152Q8×C61—22no—
153Q8×C61—41no—
154Q8×C61—41no—
155D4×C61—44no—
156D4×C61—42no—
157D4×C61—42no—
158D4×C61—44no—
159D4×C61—82no—
160D4×C61—81no—
161D4×C61—81no—
162D4×C61—81no—
163D4×C61—81no—
164C2×C4×C61—22no—
165C2×C4×C61—22no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—42no—
170C2×C4×C61#12011yescharacteristic
171C2×C4×C61#12011yescharacteristic
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61#12111yescharacteristic
174C2×C4×C61#12111yescharacteristic
175C2×C4×C61#12711yescharacteristic
176C2×C4×C61C2×D811yescharacteristic
177C2×C4×C61#13511yescharacteristic
178C2×C4×C61#13512yes—
179C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C61AGL(1,ℤ/8)12yes—
182C2×Dic61—42no—
183C2×Dic61—42no—
184C2×Dic61—42no—
185D244—44no—
186D244—82no—
187D244—81no—
188D244—81no—
189D244—82no—
190D244—81no—
191D244—81no—
192D244—81no—
193D244—81no—
194C8×C61—42no—
195#92418—24no—
196#92418—81no—
197#10047—611nomaximal, Sylow
198C22×C61—82no—
199C22×C61—82no—
200C22×C61—82no—
201C22×C61—162no—
202C22×C61—162no—
203C22×C61#39211yescharacteristic
204C22×C61#44711yescharacteristic
205C22×C61#44911yescharacteristic
206C22×C61#44912yes—
207C22×C61#45312yes—
208C2×D61—84no—
209C2×D61—84no—
210C2×D61—82no—
211C2×D61—82no—
212C2×D61—82no—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—42no—
216C4×C61—81no—
217C4×C61#44711yescharacteristic
218C4×C61#44911yescharacteristic
219C4×C61#46312yes—
220C4×C61#46611yescharacteristic
221C4×C61#46911yescharacteristic
222C4×C61#49511yescharacteristic
223C4×C61#49611yescharacteristic
224Dic61—82no—
225C2×#493—611no—
226C2×#460D6111yescharacteristic, complemented
227#2548—611no—
228#1982—611no—
229C2×#331—611no—
230C2×Q8⋊C8—611no—
231#1279—611no—
232C2×C61—162no—
233C2×C61#162012yes—
234C2×C61#162112yes—
235C2×C61#199911yescharacteristic
236C2×C61#200211yescharacteristic
237C2×C61#201211yescharacteristic
238D61—162no—
239C22×SD16—21no—
240C22×D8—1222no—
241C2×#127—611no—
242C2×#127C2×D6111yescharacteristic
243C2×#124—1221no—
244C2×C4×Q8C2×D6111yescharacteristic
245#493—1222no—
246#493—1222no—
247#460—22no—
248#460—22no—
249C2×C4⋊C8—611no—
250C2×C4⋊C8C2×D6111yescharacteristic
251C2×#102—21no—
252C2×#102—1222no—
253C2×C4×C8—611no—
254#394—1222no—
255#390—1222no—
256#390—1221no—
257C4×C4⋊C4—611no—
258#331—1222no—
259Q8⋊C8—1222no—
260C61#1004711yescharacteristic, complemented, Sylow
261C22×Q8C22⋊D6111yescharacteristic
262C22×D4—21no—
263C22×D4—21no—
264C22×D4—21no—
265C22×D4—612no—
266C22×D4—1221no—
267C22×D4—1221no—
268C2×SD16—24no—
269C2×SD16—42no—
270C2×SD16—42no—
271C2×D8—1228no—
272C2×D8—2448no—
273C22×C8—21no—
274C22×C8—1221no—
275C22×C8—1221no—
276#127—21no—
277#127—21no—
278#127—21no—
279#127—1221no—
280#127—1221no—
281#127—1221no—
282#127—1221no—
283#127C22⋊D6112yes—
284#124—2442no—
285#124—2442no—
286C4×Q8—21no—
287C4×Q8—21no—
288C4×Q8—21no—
289C4×Q8—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—612no—
292C2×C4⋊C4C22⋊D6111yescharacteristic
293C2×C22⋊C4—1224no—
294C2×C22⋊C4—1224no—
295C2×C42—21no—
296C2×C42—1221no—
297C2×C42C22×D6111yescharacteristic
298C4⋊C8—21no—
299C4⋊C8—1221no—
300C4⋊C8—1221no—
301C4⋊C8C22⋊D6112yes—
302#102—24no—
303#102—2444no—
304C4×C8—612no—
305C4×C8—1221no—
306#95—1221no—
307C24—41no—
308C24—1222no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8#1175819912yescomplemented
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—22no—
318C2×D4—44no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—42no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—42no—
328C2×D4—1222no—
329C2×D4—1222no—
330C2×D4—2444no—
331C2×D4—2441no—
332C2×D4—2441no—
333C2×D4—2441no—
334C2×D4—2441no—
335C2×D4—2441no—
336C2×D4—2441no—
337C2×D4—2442no—
338C2×D4—2441no—
339C2×D4—2441no—
340C2×D4—2442no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—1222no—
344C22×C4D4×D6111yescharacteristic
345C22×C4D4×D6111yescharacteristic
346C22×C4C2×C22⋊D6111yescharacteristic
347SD16—48no—
348D8—24416no—
349C2×C8—22no—
350C2×C8—41no—
351C2×C8—41no—
352C2×C8—1224no—
353C2×C8—1222no—
354C2×C8—2441no—
355C2×C8—2442no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—1222no—
361C4⋊C4—1222no—
362C22⋊C4—4884no—
363C22⋊C4—2448no—
364C42—41no—
365C42—41no—
366C42—2441no—
367C42—2441no—
368C42D4×D6111yescharacteristic
369C42#1175822411yescharacteristic
370C42C2×C22⋊D6111yescharacteristic
371C42C2×C22⋊D6111yescharacteristic
372C23—42no—
373C23—81no—
374C23—81no—
375C23—82no—
376C23—82no—
377C23—2442no—
378C23—2442no—
379C23—2444no—
380C23—2442no—
381C23—2444no—
382C23#1451974511yescharacteristic
383Q8—22no—
384Q8—22no—
385Q8—41no—
386Q8—41no—
387D4—44no—
388D4—44no—
389D4—42no—
390D4—42no—
391D4—82no—
392D4—81no—
393D4—81no—
394D4—81no—
395D4—81no—
396D4—4882no—
397D4—4882no—
398D4—4881no—
399D4—4881no—
400D4—4881no—
401D4—4881no—
402D4—4881no—
403D4—4881no—
404D4—2444no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—2442no—
412C2×C4—2442no—
413C2×C4—2442no—
414C2×C4#1451974511yescharacteristic
415C2×C4#1451974611yescharacteristic
416C2×C4#1451974811yescharacteristic
417C2×C4#1451974911yescharacteristic
418C2×C4#1451974911yescharacteristic
419C2×C4#1451977311yescharacteristic
420C2×C4C2×#1175819911yescharacteristic
421C2×C4#1451979711yescharacteristic
422C2×C4#1451979812yes—
423C2×C4#1451980211yescharacteristic
424C2×C4#1451980311yescharacteristic
425C2×C4#1451980412yes—
426C8—42no—
427C8—1224no—
428C8—4881no—
429C22—82no—
430C22—82no—
431C22—82no—
432C22—162no—
433C22—162no—
434C22—4884no—
435C22—4884no—
436C22—4882no—
437C22—4882no—
438C22—4882no—
439C22#1683967011yescharacteristic
440C22#1683989511yescharacteristic
441C22#1683990511yescharacteristic
442C22#1683990612yes—
443C22#1683992812yes—
444C4—21no—
445C4—21no—
446C4—42no—
447C4—81no—
448C4—4882no—
449C4#1683989611yescharacteristic
450C4#1683990711yescharacteristic
451C4#1683997912yes—
452C4#1683999611yescharacteristic
453C4#1684001311yescharacteristic
454C4#1684014311yescharacteristic
455C4#1684014811yescharacteristic
456C2—162no—
457C2—9762no—
458C2#2144487712yes—
459C2#2144488212yes—
460C2#2144681511yescharacteristic
461C2#2144683111yescharacteristic
462C2#2144689311yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC2×C61×#460C2
socleC23×C61#120
prime radicalC2×#16840138C2
hypercenterC2×#460D61
hypocenterC61#10047
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
2. #21450818C2semidirect
3. #21446747C2semidirect
4. C2×#16839505C2semidirect
5. C2×Q8⋊#92418C2semidirect
6. #21443658C2semidirect
7. C2×C61×#460C2semidirect
82. C2×Q8×C61D8semidirect
226. C2×#460D61semidirect
260. C61#10047semidirect
314. C2×Q8#11758199semidirect

Maximal subgroups

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

subgroupindex
C2×#168401382
#214508182
#214467472
C2×#168395052
C2×Q8⋊#924182
#214436582
C2×C61×#4602
#1004761