Finite Group Databasebeta

← #29579523

Subgroups — #29579523

Order 15616.

564 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×#16839989C211yesmaximal, characteristic
2#21446803C211yesmaximal, characteristic, complemented
3#21446656C211yesmaximal, characteristic
4#21445842C211yesmaximal, characteristic, complemented
5#21445593C211yesmaximal, characteristic, complemented
6#21444392C211yesmaximal, characteristic, complemented
7C61×#1519C211yesmaximal, characteristic
8C22×#11758200C411yescharacteristic, complemented
9C23×#92418C2211yescharacteristic
10C2×#14519756C2211yescharacteristic
11#16839989—21no—
12#16839989—21no—
13#16839989—21no—
14#16839989—21no—
15C2×#14519708—21no—
16C2×#14519708C411yescharacteristic, complemented
17C2×#14519700C411yescharacteristic, complemented
18C2×#14519698C411yescharacteristic, complemented
19C2×#14519692—22no—
20C2×C8×Dic61—21no—
21#16839622C2211yescharacteristic
22C4×C22⋊Dic61C2211yescharacteristic
23#16839528—22no—
24#16839524—21no—
25#16839516—21no—
26#16839500—22no—
27C2×#121×C61C2211yescharacteristic
28C2×C22⋊C8×C61C2211yescharacteristic
29C61×#380C2211yescharacteristic
30C61×#327—22no—
31C22×Dic122C2×C411yescharacteristic
32C2×#11758200—21no—
33C2×#11758200—21no—
34C2×#11758200—42no—
35C22×#92418—42no—
36C22×#92418C2×C411yescharacteristic
37C22×#92418C2×C411yescharacteristic
38C22×#92418D411yescharacteristic
39C22×#92418D411yescharacteristic
40C22×#92418D411yescharacteristic
41C22×#92418D411yescharacteristic
42#14519756—21no—
43#14519756—21no—
44#14519756—21no—
45#14519756—21no—
46C2×C4⋊Dic61—21no—
47C2×C4⋊Dic61C2×C411yescharacteristic
48C2×#11758196—21no—
49C2×C22⋊Dic61—21no—
50C2×C22⋊Dic61—21no—
51C2×C22⋊Dic61D412yes—
52C2×C4×Dic61—21no—
53#14519708—21no—
54#14519708—21no—
55#14519708—42no—
56#14519700—21no—
57#14519700—21no—
58#14519698—21no—
59#14519698—21no—
60#14519692—44no—
61C8×Dic61—42no—
62#14519684—21no—
63#14519684—21no—
64C22×D4×C61—21no—
65C22×D4×C61C2×C411yescharacteristic
66C23×C4×C61C2311yescharacteristic
67C22×C8×C61—21no—
68#121×C61—21no—
69#121×C61—21no—
70#121×C61—21no—
71#121×C61—21no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61C2×C411yescharacteristic
74C2×C22⋊C4×C61—21no—
75C2×C22⋊C4×C61—21no—
76C22⋊C8×C61—21no—
77C22⋊C8×C61D412yes—
78#95×C61—21no—
79C24×C61—21no—
80C24×C61C2×D411yescharacteristic
81C2×D4×C61—21no—
82C2×D4×C61—21no—
83C2×D4×C61—41no—
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C2×D4×C61—41no—
87C2×D4×C61—42no—
88C2×D4×C61—42no—
89C22×C4×C61—21no—
90C22×C4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61—41no—
93C22×C4×C61C22×C411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61#4111yescharacteristic
98C22×C4×C61#4111yescharacteristic
99C22×Dic61—22no—
100C22×Dic61—21no—
101C22×Dic61—21no—
102C22×Dic61—41no—
103C2×Dic122—21no—
104C2×Dic122—21no—
105C2×Dic122—41no—
106C2×Dic122—41no—
107C2×C8×C61—22no—
108C2×C8×C61—41no—
109C2×C8×C61—41no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61—41no—
113C4⋊C4×C61—41no—
114C22⋊C4×C61—41no—
115C22⋊C4×C61—41no—
116C22⋊C4×C61—42no—
117C22⋊Dic61—22no—
118C22⋊Dic61—41no—
119C22⋊Dic61—41no—
120C22⋊Dic61—42no—
121C22⋊Dic61SD1614yescomplemented
122#11758200—42no—
123#11758200—42no—
124C4⋊Dic61—21no—
125C4⋊Dic61—21no—
126C4⋊Dic61—41no—
127C4⋊Dic61—41no—
128#11758196—41no—
129#11758196—41no—
130C4×Dic61—41no—
131C4×Dic61—41no—
132C2×#92418—22no—
133C2×#92418—22no—
134C2×#92418—22no—
135C2×#92418—41no—
136C2×#92418—41no—
137C2×#92418—41no—
138C2×#92418C22⋊C411yescharacteristic
139C2×#92418C22⋊C411yescharacteristic
140C2×#92418C22⋊C411yescharacteristic
141C2×#92418C22⋊C411yescharacteristic
142C23×C61—41no—
143C23×C61—41no—
144C23×C61—41no—
145C23×C61—42no—
146C23×C61—81no—
147C23×C61—81no—
148C23×C61C4×D411yescharacteristic
149C23×C61#12111yescharacteristic
150C23×C61#12711yescharacteristic
151C23×C61C2×SD1612yes—
152C23×C61#13512yes—
153D4×C61—41no—
154D4×C61—41no—
155D4×C61—81no—
156D4×C61—82no—
157D4×C61—81no—
158D4×C61—81no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—42no—
170C2×C4×C61—81no—
171C2×C4×C61—81no—
172C2×C4×C61—81no—
173C2×C4×C61C2×C22⋊C411yescharacteristic
174C2×C4×C61C4×D411yescharacteristic
175C2×C4×C61#12111yescharacteristic
176C2×C4×C61#12411yescharacteristic
177C2×Dic61—24no—
178C2×Dic61—42no—
179C2×Dic61—42no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—81no—
183C2×Dic61—81no—
184C2×Dic61—81no—
185C2×Dic61—81no—
186C2×Dic61—81no—
187Dic122—41no—
188Dic122—41no—
189Dic122—81no—
190C8×C61—42no—
191#92418—21no—
192#92418—21no—
193#92418—21no—
194#92418#9912yescomplemented
195#9781—611nomaximal, Sylow
196C22×C61—21no—
197C22×C61—21no—
198C22×C61—21no—
199C22×C61—21no—
200C22×C61—21no—
201C22×C61—21no—
202C22×C61—42no—
203C22×C61—42no—
204C22×C61—81no—
205C22×C61—81no—
206C22×C61—81no—
207C22×C61—162no—
208C22×C61#39011yescharacteristic
209C22×C61C4×SD1612yes—
210C22×C61#46512yes—
211C22×C61#49211yescharacteristic
212C22×C61#49511yescharacteristic
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—81no—
217C4×C61—161no—
218C4×C61C2×#9911yescharacteristic
219C4×C61#41011yescharacteristic
220Dic61—44no—
221Dic61—81no—
222Dic61—81no—
223Dic61—161no—
224C2×#465—611no—
225#1996—611no—
226#1964—611no—
227#1807—611no—
228C8×C22⋊C4—611no—
229#1520—611no—
230#1519D6111yescharacteristic
231C2×C61—22no—
232C2×C61—21no—
233C2×C61—21no—
234C2×C61—22no—
235C2×C61—161no—
236C2×C61#196411yescharacteristic
237C2×C61#196811yescharacteristic
238C2×C61#197611yescharacteristic
239C22×SD16—611no—
240C23×C8—611no—
241C2×C22⋊Q8—611no—
242C2×#121C2×D6111yescharacteristic
243#465—1221no—
244#465—1221no—
245#465—1221no—
246#465—1221no—
247C2×#106—611no—
248C2×#106—1221no—
249C2×#103—611no—
250C2×#102—611no—
251C2×#99—1222no—
252C2×C22⋊C8C2×D6111yescharacteristic
253C2×C4×C8—1221no—
254#380—611no—
255#380C2×D6111yescharacteristic
256C4×C22⋊C4—611no—
257#342—1222no—
258#340—1221no—
259#336—1221no—
260#328—1222no—
261#327—22no—
262C61#978111yescharacteristic, complemented, Sylow
263C22×Q8—611no—
264C22×D4—21no—
265C22×D4C4×D6111yescharacteristic
266C23×C4C22×D6111yescharacteristic
267C2×SD16—1221no—
268C2×SD16—1221no—
269C2×SD16—2442no—
270C22×C8—21no—
271C22×C8—611no—
272C22×C8—611no—
273C22×C8—611no—
274C22×C8—611no—
275C22×C8—611no—
276C22×C8—611no—
277C22×C8—2442no—
278C22⋊Q8—1221no—
279C22⋊Q8—1221no—
280C22⋊Q8—1221no—
281C22⋊Q8—1221no—
282#121—21no—
283#121—21no—
284#121—21no—
285#121—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—611no—
288C2×C4⋊C4—1221no—
289C2×C4⋊C4—1221no—
290C2×C4⋊C4C4×D6111yescharacteristic
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—612no—
294C2×C22⋊C4—1221no—
295C2×C22⋊C4—1221no—
296C2×C42—1221no—
297#106—1221no—
298#106—1221no—
299#106—2442no—
300#103—1221no—
301#103—1221no—
302#102—1221no—
303#102—1221no—
304#99—2444no—
305C22⋊C8—21no—
306C22⋊C8C22⋊D6112yes—
307C4×C8—2442no—
308#95—21no—
309#95—1221no—
310#95—1221no—
311C24—21no—
312C24D4×D6111yescharacteristic
313C2×Q8—1221no—
314C2×Q8—1221no—
315C2×Q8—2441no—
316C2×Q8—2441no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—42no—
324C2×D4—42no—
325C22×C4—21no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—1222no—
330C22×C4—1221no—
331C22×C4—1221no—
332C22×C4—2441no—
333C22×C4C2×C4×D6111yescharacteristic
334C22×C4#1175822211yescharacteristic
335C22×C4D4×D6111yescharacteristic
336C22×C4D4×D6111yescharacteristic
337C22×C4#1175822411yescharacteristic
338C22×C4C2×C22⋊D6111yescharacteristic
339SD16—2442no—
340SD16—2442no—
341C2×C8—22no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—611no—
345C2×C8—611no—
346C2×C8—611no—
347C2×C8—611no—
348C2×C8—1222no—
349C2×C8—1222no—
350C2×C8—1222no—
351C2×C8—2441no—
352C2×C8—2441no—
353C2×C8—2441no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—1221no—
359C4⋊C4—1221no—
360C4⋊C4—2441no—
361C4⋊C4—2441no—
362C4⋊C4—2441no—
363C4⋊C4—2441no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—42no—
367C22⋊C4—614no—
368C22⋊C4—1222no—
369C22⋊C4—2442no—
370C22⋊C4—2441no—
371C22⋊C4—2441no—
372C42—2441no—
373C42—2441no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—42no—
378C23—81no—
379C23—81no—
380C23#1451973711yescharacteristic
381C23#1451975011yescharacteristic
382C23#1451977311yescharacteristic
383C23SD16×D6112yes—
384C23#1451979612yes—
385Q8—4881no—
386Q8—2441no—
387Q8—2441no—
388D4—41no—
389D4—41no—
390D4—81no—
391D4—82no—
392D4—81no—
393D4—81no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—1224no—
409C2×C4—4881no—
410C2×C4—4881no—
411C2×C4—4881no—
412C2×C4—4881no—
413C2×C4—4881no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4—2442no—
417C2×C4—2442no—
418C2×C4C22⋊C4×D6111yescharacteristic
419C2×C4C4×C22⋊D6111yescharacteristic
420C2×C4#1451974911yescharacteristic
421C2×C4#1451976311yescharacteristic
422C8—42no—
423C8—612no—
424C8—1221no—
425C8—1221no—
426C8—1221no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—42no—
434C22—42no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22—162no—
439C22#1683966211yescharacteristic
440C22#1683985312yes—
441C22#1683999012yes—
442C22#1684013311yescharacteristic
443C22#1684014511yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—81no—
448C4—161no—
449C4—9761no—
450C4—4881no—
451C4—4881no—
452C4—2444no—
453C4#99×D6111yescharacteristic
454C4#1683973411yescharacteristic
455C2—21no—
456C2—21no—
457C2—22no—
458C2—22no—
459C2—161no—
460C2#2144665311yescharacteristic
461C2#2144667411yescharacteristic
462C2#2144671611yescharacteristic
subgroupG/H
centerC22#16839662
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1519C2
socleC22×C61#390
prime radicalC2×#121×C61C22
cosocleC23×C4×C61C23
hypercenter#1519D61
hypocenterC61#9781
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
2. #21446803C2semidirect
4. #21445842C2semidirect
5. #21445593C2semidirect
6. #21444392C2semidirect
8. C22×#11758200C4semidirect
16. C2×#14519708C4semidirect
17. C2×#14519700C4semidirect
18. C2×#14519698C4semidirect
121. C22⋊Dic61SD16semidirect
194. #92418#99semidirect
262. C61#9781semidirect

Maximal subgroups

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

subgroupindex
C2×#168399892
#214468032
#214466562
#214458422
#214455932
#214443922
C61×#15192
#978161