Finite Group Databasebeta

← #29581073

Subgroups — #29581073

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×#16839959C211yesmaximal, characteristic, complemented
2#21450822C211yesmaximal, characteristic, complemented
3#21446747C211yesmaximal, characteristic, complemented
4C2×#16839506C211yesmaximal, characteristic, complemented
5C2×#16839494C211yesmaximal, characteristic, complemented
6#21443659C211yesmaximal, characteristic, complemented
7C2×C61×#493C211yesmaximal, characteristic
8C22×#11758200—21no—
9C2×#14519764—21no—
10C2×C4×Dic122C2211yescharacteristic
11#16839959—22no—
12#16839959—22no—
13C2×C4⋊#92418C2211yescharacteristic
14C2×C4⋊#92418C2211yescharacteristic
15C2×#14519698—21no—
16C2×#14519698—22no—
17#16839676—22no—
18#16839665—21no—
19#16839665—22no—
20C4×C4⋊Dic61C2211yescharacteristic
21#16839506—22no—
22#16839494—22no—
23C22×D8×C61—22no—
24C2×#127×C61C2211yescharacteristic
25C2×#127×C61C2211yescharacteristic
26C61×#493—22no—
27C61×#493—22no—
28C2×C4×C8×C61C2211yescharacteristic
29C22×Dic122D411yescharacteristic
30C2×#11758200—24no—
31C2×#11758200—42no—
32C2×#11758200—42no—
33C22×#92418—21no—
34C22×#92418—21no—
35#14519764—42no—
36#14519764—42no—
37C4×Dic122—21no—
38C4×Dic122—21no—
39C4×Dic122—21no—
40C4×Dic122—21no—
41C2×C4⋊Dic61D411yescharacteristic
42C2×C4⋊Dic61D412yes—
43C2×#11758196—21no—
44C2×C22⋊Dic61—24no—
45C2×C22⋊Dic61—24no—
46C2×C4×Dic61—21no—
47C2×C4×Dic61—21no—
48C4⋊#92418—21no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51C4⋊#92418D412yes—
52#14519698—24no—
53#14519698—44no—
54#14519684—21no—
55C22×D4×C61—21no—
56C22×D4×C61—21no—
57C22×D4×C61—21no—
58C22×D4×C61—21no—
59C22×D4×C61—21no—
60C22×D4×C61D412yes—
61C2×D8×C61—28no—
62C2×D8×C61—48no—
63C22×C8×C61—21no—
64#127×C61—21no—
65#127×C61—21no—
66#127×C61—21no—
67#127×C61—21no—
68#127×C61—21no—
69#127×C61—21no—
70#127×C61—21no—
71#127×C61D412yes—
72C2×C42×C61C2311yescharacteristic
73C4×C8×C61—21no—
74C4×C8×C61D412yes—
75C24×C61—22no—
76C24×C61—41no—
77C2×D4×C61—22no—
78C2×D4×C61—22no—
79C2×D4×C61—22no—
80C2×D4×C61—22no—
81C2×D4×C61—22no—
82C2×D4×C61—44no—
83C2×D4×C61—44no—
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C2×D4×C61—41no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—41no—
93C2×D4×C61—41no—
94C2×D4×C61—42no—
95C2×D4×C61—41no—
96C2×D4×C61—42no—
97C2×D4×C61—41no—
98C2×D4×C61—42no—
99C2×D4×C61—41no—
100C2×D4×C61—41no—
101C2×D4×C61—42no—
102C2×D4×C61—41no—
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×Dic61—21no—
107C22×Dic61—22no—
108C22×Dic61—21no—
109C2×Dic122—21no—
110C2×Dic122—21no—
111C2×Dic122—21no—
112C2×Dic122—21no—
113C2×Dic122—21no—
114C2×Dic122D812yescomplemented
115D8×C61—416no—
116C2×C8×C61—24no—
117C2×C8×C61—22no—
118C42×C61C2×D411yescharacteristic
119C42×C61C2×D411yescharacteristic
120C42×C61C2×D411yescharacteristic
121C42×C61#4111yescharacteristic
122C22⋊Dic61—48no—
123C22⋊Dic61—84no—
124#11758200—48no—
125C4⋊Dic61—21no—
126C4⋊Dic61—21no—
127C4⋊Dic61—22no—
128C4⋊Dic61—22no—
129#11758196—41no—
130#11758196—41no—
131C4×Dic61—41no—
132C4×Dic61—41no—
133C4×Dic61—41no—
134C4×Dic61—41no—
135C2×#92418—22no—
136C2×#92418—41no—
137C2×#92418—41no—
138C2×#92418—41no—
139C2×#92418—42no—
140C23×C61—42no—
141C23×C61—42no—
142C23×C61—42no—
143C23×C61—42no—
144C23×C61—44no—
145C23×C61—44no—
146C23×C61—81no—
147C23×C61—81no—
148C23×C61—82no—
149C23×C61—82no—
150C23×C61#12011yescharacteristic
151D4×C61—44no—
152D4×C61—44no—
153D4×C61—42no—
154D4×C61—42no—
155D4×C61—44no—
156D4×C61—82no—
157D4×C61—82no—
158D4×C61—81no—
159D4×C61—81no—
160D4×C61—82no—
161D4×C61—81no—
162D4×C61—81no—
163D4×C61—81no—
164D4×C61—81no—
165D4×C61—81no—
166D4×C61—81no—
167D4×C61—81no—
168D4×C61—81no—
169C2×C4×C61—22no—
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—22no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—42no—
187C2×Dic61—42no—
188C2×Dic61—42no—
189C2×Dic61—42no—
190Dic122—22no—
191Dic122—22no—
192Dic122—41no—
193Dic122—41no—
194C8×C61—24no—
195#92418—42no—
196#92418—81no—
197#10047—611nomaximal, Sylow
198C22×C61—84no—
199C22×C61—84no—
200C22×C61—82no—
201C22×C61—82no—
202C22×C61—82no—
203C22×C61—82no—
204C22×C61—82no—
205C22×C61—82no—
206C22×C61—162no—
207C22×C61—162no—
208C22×C61#39211yescharacteristic
209C22×C61#44711yescharacteristic
210C22×C61#44911yescharacteristic
211C22×C61#44912yes—
212C22×C61#45312yes—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61#44711yescharacteristic
216C4×C61#44911yescharacteristic
217C4×C61#46312yes—
218C4×C61#46611yescharacteristic
219C4×C61#46911yescharacteristic
220C4×C61#49511yescharacteristic
221C4×C61#49611yescharacteristic
222Dic61—42no—
223Dic61—82no—
224Dic61—81no—
225C2×#493D6111yescharacteristic
226C2×#460—611no—
227#2548—611no—
228#1982—611no—
229C2×#331—611no—
230C2×Q8⋊C8—611no—
231#1279—611no—
232C2×C61—162no—
233C2×C61—162no—
234C2×C61#162012yes—
235C2×C61#162112yes—
236C2×C61#199911yescharacteristic
237C2×C61#200211yescharacteristic
238C2×C61#201211yescharacteristic
239C22×SD16—1221no—
240C22×D8—22no—
241C2×#127C2×D6111yescharacteristic
242C2×#127C2×D6111yescharacteristic
243C2×#124—1221no—
244C2×C4×Q8—611no—
245#493—22no—
246#493—22no—
247#460—1222no—
248#460—1222no—
249C2×C4⋊C8—611no—
250C2×C4⋊C8—611no—
251C2×#102—1221no—
252C2×#102—1222no—
253C2×C4×C8C2×D6111yescharacteristic
254#394—1222no—
255#390—1222no—
256#390—1221no—
257C4×C4⋊C4—611no—
258#331—1222no—
259Q8⋊C8—1222no—
260C61#1004711yescharacteristic, complemented, Sylow
261C22×Q8—611no—
262C22×D4—21no—
263C22×D4—21no—
264C22×D4—21no—
265C22×D4—21no—
266C22×D4—21no—
267C22×D4C22⋊D6112yes—
268C2×SD16—1224no—
269C2×SD16—2442no—
270C2×SD16—2442no—
271C2×D8—28no—
272C2×D8—48no—
273C22×C8—21no—
274C22×C8—1221no—
275C22×C8—1221no—
276#127—21no—
277#127—21no—
278#127—21no—
279#127—21no—
280#127—21no—
281#127—21no—
282#127—21no—
283#127C22⋊D6112yes—
284#124—2442no—
285#124—2442no—
286C4×Q8—1221no—
287C4×Q8—1221no—
288C4×Q8—1221no—
289C4×Q8—1221no—
290C2×C4⋊C4—611no—
291C2×C4⋊C4—612no—
292C2×C4⋊C4—1221no—
293C2×C22⋊C4—1224no—
294C2×C22⋊C4—1224no—
295C2×C42—1221no—
296C2×C42—1221no—
297C2×C42C22×D6111yescharacteristic
298C4⋊C8—612no—
299C4⋊C8—1221no—
300C4⋊C8—1221no—
301C4⋊C8—1221no—
302#102—1224no—
303#102—2444no—
304C4×C8—21no—
305C4×C8C22⋊D6112yes—
306#95—1221no—
307C24—22no—
308C24—41no—
309C2×Q8—612no—
310C2×Q8—1221no—
311C2×Q8—1221no—
312C2×Q8—1221no—
313C2×Q8—1221no—
314C2×Q8—1221no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—22no—
320C2×D4—44no—
321C2×D4—44no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—41no—
328C2×D4—41no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—42no—
332C2×D4—41no—
333C2×D4—42no—
334C2×D4—41no—
335C2×D4—42no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—42no—
340C2×D4—41no—
341C22×C4—1221no—
342C22×C4—1222no—
343C22×C4—1221no—
344C22×C4D4×D6111yescharacteristic
345C22×C4D4×D6111yescharacteristic
346C22×C4C2×C22⋊D6111yescharacteristic
347SD16—2448no—
348D8—416no—
349C2×C8—24no—
350C2×C8—22no—
351C2×C8—1222no—
352C2×C8—2441no—
353C2×C8—2442no—
354C2×C8—2441no—
355C2×C8—2441no—
356C4⋊C4—1221no—
357C4⋊C4—1221no—
358C4⋊C4—1222no—
359C4⋊C4—1222no—
360C4⋊C4—2441no—
361C4⋊C4—2441no—
362C22⋊C4—4884no—
363C22⋊C4—2448no—
364C42—2441no—
365C42—2441no—
366C42—2441no—
367C42—2441no—
368C42D4×D6111yescharacteristic
369C42#1175822411yescharacteristic
370C42C2×C22⋊D6111yescharacteristic
371C42C2×C22⋊D6111yescharacteristic
372C23—42no—
373C23—42no—
374C23—44no—
375C23—42no—
376C23—42no—
377C23—44no—
378C23—81no—
379C23—81no—
380C23—82no—
381C23—82no—
382C23#1451974511yescharacteristic
383Q8—1222no—
384Q8—1222no—
385Q8—2441no—
386Q8—2441no—
387D4—44no—
388D4—44no—
389D4—44no—
390D4—42no—
391D4—42no—
392D4—82no—
393D4—82no—
394D4—82no—
395D4—81no—
396D4—81no—
397D4—81no—
398D4—81no—
399D4—81no—
400D4—81no—
401D4—81no—
402D4—81no—
403D4—81no—
404D4—81no—
405C2×C4—22no—
406C2×C4—1222no—
407C2×C4—2442no—
408C2×C4—2442no—
409C2×C4—2441no—
410C2×C4—2442no—
411C2×C4—2442no—
412C2×C4—2441no—
413C2×C4—2441no—
414C2×C4#1451974511yescharacteristic
415C2×C4#1451974611yescharacteristic
416C2×C4#1451974811yescharacteristic
417C2×C4#1451974911yescharacteristic
418C2×C4#1451974911yescharacteristic
419C2×C4#1451977311yescharacteristic
420C2×C4D8×D6111yescharacteristic
421C2×C4#1451979612yes—
422C2×C4#1451979611yescharacteristic
423C2×C4#1451980112yes—
424C2×C4#1451980111yescharacteristic
425C2×C4#1451980111yescharacteristic
426C8—24no—
427C8—4881no—
428C8—2442no—
429C22—84no—
430C22—84no—
431C22—82no—
432C22—82no—
433C22—82no—
434C22—82no—
435C22—82no—
436C22—82no—
437C22—162no—
438C22—162no—
439C22#1683967011yescharacteristic
440C22#1683989411yescharacteristic
441C22#1683990411yescharacteristic
442C22#1683990412yes—
443C22#1683992912yes—
444C4—21no—
445C4—21no—
446C4—4882no—
447C4—4881no—
448C4—2442no—
449C4#1683989411yescharacteristic
450C4#1683990411yescharacteristic
451C4#1683997512yes—
452C4#1683999511yescharacteristic
453C4#1684001211yescharacteristic
454C4#1684014511yescharacteristic
455C4#1684015011yescharacteristic
456C2—162no—
457C2—162no—
458C2#2144487612yes—
459C2#2144488112yes—
460C2#2144681411yescharacteristic
461C2#2144683411yescharacteristic
462C2#2144689411yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
Fitting, prime radicalC2×C61×#493C2
socleC23×C61#120
hypercenterC2×#493D61
hypocenterC61#10047
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#493

Complements

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

NH ≅ G/Ntype
1. C2×#16839959C2semidirect
2. #21450822C2semidirect
3. #21446747C2semidirect
4. C2×#16839506C2semidirect
5. C2×#16839494C2semidirect
6. #21443659C2semidirect
114. C2×Dic122D8semidirect
260. C61#10047semidirect

Maximal subgroups

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

subgroupindex
C2×#168399592
#214508222
#214467472
C2×#168395062
C2×#168394942
#214436592
C2×C61×#4932
#1004761