Finite Group Databasebeta

← #29579547

Subgroups — #29579547

Order 15616.

552 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×#16839991C211yesmaximal, characteristic
2#21446803C211yesmaximal, characteristic, complemented
3#21446654C211yesmaximal, characteristic
4#21445595C211yesmaximal, characteristic, complemented
5#21444390C211yesmaximal, characteristic, complemented
6#21444386C211yesmaximal, characteristic
7C61×#1808C211yesmaximal, characteristic, complemented
8C22×#11758190C411yescharacteristic, complemented
9C2×#14519756C2211yescharacteristic
10C2×#14519751C2211yescharacteristic
11#16839991—21no—
12#16839991—21no—
13#16839991—21no—
14#16839991—21no—
15C2×#14519709C411yescharacteristic, complemented
16C2×#14519702C411yescharacteristic, complemented
17C2×#14519699C411yescharacteristic, complemented
18C2×#14519691—22no—
19C2×C22⋊#92418C2211yescharacteristic
20C2×#14519687—21no—
21C4×C22⋊Dic61C2211yescharacteristic
22#16839528—22no—
23#16839516—21no—
24#16839498—22no—
25#16839495—22no—
26C23×C8×C61C2211yescharacteristic
27C2×#107×C61—21no—
28C61×#380C2211yescharacteristic
29C61×#380C2211yescharacteristic
30C61×#340—21no—
31C22×Dic122C2×C411yescharacteristic
32C22×D244C2×C411yescharacteristic
33C22×C22⋊D61—21no—
34C2×#11758190—21no—
35C2×#11758190—21no—
36C2×#11758190—42no—
37C22×#92418—21no—
38#14519756—21no—
39#14519756—21no—
40#14519756—21no—
41#14519756—21no—
42#14519751—21no—
43#14519751—21no—
44#14519751—21no—
45#14519751—21no—
46C2×C4⋊Dic61C2×C411yescharacteristic
47C2×C4⋊Dic61C2×C411yescharacteristic
48C2×#11758196—21no—
49C2×C22⋊Dic61—21no—
50C2×C22⋊Dic61D412yes—
51C2×#11758198—21no—
52C2×C4×Dic61—21no—
53#14519709—21no—
54#14519709—21no—
55#14519702—21no—
56#14519702—21no—
57#14519699—21no—
58#14519699—21no—
59#14519691—44no—
60C22⋊#92418—21no—
61C22⋊#92418D412yes—
62#14519687—42no—
63#14519684—21no—
64C23×C4×C61C2311yescharacteristic
65C22×C8×C61—42no—
66C22×C8×C61C2×C411yescharacteristic
67C22×C8×C61C2×C411yescharacteristic
68C22×C8×C61D411yescharacteristic
69C22×C8×C61D411yescharacteristic
70C22×C8×C61D411yescharacteristic
71C22×C8×C61D411yescharacteristic
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61—21no—
74C2×C22⋊C4×C61—21no—
75C2×C22⋊C4×C61—21no—
76#107×C61—42no—
77#95×C61—21no—
78#95×C61—21no—
79C24×C61C2×D411yescharacteristic
80C23×D61—21no—
81C22×C4×C61—41no—
82C22×C4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61—41no—
85C22×C4×C61C22×C411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61#4111yescharacteristic
90C22×C4×C61#4111yescharacteristic
91C2×C22⋊D61—41no—
92C2×C22⋊D61—41no—
93C2×C22⋊D61—42no—
94C2×C22⋊D61—42no—
95C22×Dic61—21no—
96C22×Dic61—22no—
97C22×Dic61—21no—
98C22×Dic61—21no—
99C2×D244—21no—
100C2×D244—21no—
101C2×D244—41no—
102C2×D244—41no—
103C2×Dic122—21no—
104C2×Dic122—21no—
105C2×Dic122—41no—
106C2×Dic122—41no—
107C2×C8×C61—22no—
108C2×C8×C61—22no—
109C2×C8×C61—22no—
110C2×C8×C61—41no—
111C2×C8×C61—41no—
112C2×C8×C61—41no—
113C2×C8×C61C22⋊C411yescharacteristic
114C2×C8×C61C22⋊C411yescharacteristic
115C2×C8×C61C22⋊C411yescharacteristic
116C2×C8×C61C22⋊C411yescharacteristic
117C4⋊C4×C61—41no—
118C4⋊C4×C61—41no—
119C4⋊C4×C61—41no—
120C4⋊C4×C61—41no—
121C22⋊C4×C61—42no—
122C22⋊C4×C61—42no—
123C22⋊Dic61—22no—
124C22⋊Dic61—22no—
125C22⋊Dic61—41no—
126C22⋊Dic61—41no—
127#11758198—41no—
128#11758198—41no—
129C4⋊Dic61—21no—
130C4⋊Dic61—21no—
131C4⋊Dic61—21no—
132C4⋊Dic61—21no—
133#11758196—41no—
134#11758196—41no—
135C4×Dic61—41no—
136C4×Dic61—41no—
137C2×#92418—22no—
138C2×#92418—41no—
139C2×#92418—41no—
140#11758190—42no—
141#11758190—42no—
142C23×C61—41no—
143C23×C61—41no—
144C23×C61C4×D411yescharacteristic
145C23×C61#12111yescharacteristic
146C23×C61#12711yescharacteristic
147C23×C61AGL(1,ℤ/8)12yes—
148C23×C61#13712yes—
149C22×D61—41no—
150C22×D61—42no—
151C22×D61—81no—
152C22×D61—81no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—81no—
163C2×C4×C61—81no—
164C2×C4×C61—81no—
165C2×C4×C61—81no—
166C2×C4×C61—81no—
167C2×C4×C61—81no—
168C2×C4×C61C2×C22⋊C411yescharacteristic
169C2×C4×C61C4×D411yescharacteristic
170C2×C4×C61#12111yescharacteristic
171C2×C4×C61#12411yescharacteristic
172C22⋊D61—82no—
173C22⋊D61—81no—
174C22⋊D61—81no—
175C2×Dic61—42no—
176C2×Dic61—42no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—42no—
181C2×Dic61—42no—
182C2×Dic61—81no—
183C2×Dic61—81no—
184D244—41no—
185D244—41no—
186D244—81no—
187Dic122—41no—
188Dic122—41no—
189Dic122—81no—
190C8×C61—21no—
191C8×C61—21no—
192C8×C61—21no—
193C8×C61#9912yescomplemented
194#92418—42no—
195#9786—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#39011yescharacteristic
205C22×C61#44012yes—
206C22×C61#46812yes—
207C22×C61#49611yescharacteristic
208C22×C61#49711yescharacteristic
209C2×D61—81no—
210C2×D61—81no—
211C2×D61—81no—
212C2×D61—162no—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—161no—
217C4×C61—161no—
218C4×C61C2×#9911yescharacteristic
219C4×C61#41011yescharacteristic
220Dic61—82no—
221Dic61—81no—
222Dic61—81no—
223Dic61—81no—
224C2×#465—611no—
225#1996—611no—
226#1964—611no—
227#1808D6111yescharacteristic, complemented
228#1752—611no—
229#1520—611no—
230#1519—611no—
231C2×C61—22no—
232C2×C61—21no—
233C2×C61—22no—
234C2×C61—21no—
235C2×C61#196411yescharacteristic
236C2×C61#197311yescharacteristic
237C2×C61#197611yescharacteristic
238D61—161no—
239C22×SD16—611no—
240C23×C8C2×D6111yescharacteristic
241C2×C22⋊Q8—611no—
242C2×#121—611no—
243#465—1221no—
244#465—1221no—
245#465—1221no—
246#465—1221no—
247C2×#107—21no—
248C2×#106—611no—
249C2×#103—611no—
250C2×#102—611no—
251C2×#99—1222no—
252C2×C22⋊C8—611no—
253C2×#97—1221no—
254#380C2×D6111yescharacteristic
255#380C2×D6111yescharacteristic
256C4×C22⋊C4—611no—
257#342—1222no—
258#340—21no—
259#336—1221no—
260#328—1222no—
261#327—1222no—
262C61#978611yescharacteristic, complemented, Sylow
263C22×Q8—611no—
264C22×D4—611no—
265C22×D4—1221no—
266C23×C4C22×D6111yescharacteristic
267C2×SD16—1221no—
268C2×SD16—1221no—
269C2×SD16—2442no—
270C22×C8—42no—
271C22×C8—1221no—
272C22×C8C4×D6111yescharacteristic
273C22×C8C4×D6111yescharacteristic
274C22×C8D24411yescharacteristic
275C22×C8D24411yescharacteristic
276C22×C8C22⋊D6111yescharacteristic
277C22×C8C22⋊D6111yescharacteristic
278C22⋊Q8—1221no—
279C22⋊Q8—1221no—
280C22⋊Q8—1221no—
281C22⋊Q8—1221no—
282#121—1221no—
283#121—1221no—
284#121—1221no—
285#121—1221no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—611no—
289C2×C4⋊C4—611no—
290C2×C4⋊C4—1221no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—612no—
294C2×C22⋊C4—1221no—
295C2×C22⋊C4—1221no—
296C2×C42—1221no—
297#107—42no—
298#106—1221no—
299#106—1221no—
300#103—1221no—
301#103—1221no—
302#102—1221no—
303#102—1221no—
304#99—2444no—
305C22⋊C8—612no—
306C22⋊C8—1221no—
307#97—2442no—
308#95—21no—
309#95—21no—
310#95—1221no—
311C24—1221no—
312C24D4×D6111yescharacteristic
313C2×Q8—1221no—
314C2×Q8—1221no—
315C2×Q8—2441no—
316C2×Q8—2441no—
317C2×D4—1221no—
318C2×D4—1221no—
319C2×D4—2441no—
320C2×D4—2441no—
321C2×D4—2442no—
322C2×D4—2441no—
323C2×D4—2441no—
324C2×D4—2442no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—1221no—
330C22×C4—1221no—
331C22×C4—1221no—
332C22×C4—1222no—
333C22×C4C2×C4×D6111yescharacteristic
334C22×C4C2×D24411yescharacteristic
335C22×C4D4×D6111yescharacteristic
336C22×C4#1175822611yescharacteristic
337C22×C4#1175822611yescharacteristic
338C22×C4C2×C22⋊D6111yescharacteristic
339SD16—2442no—
340SD16—2442no—
341C2×C8—22no—
342C2×C8—22no—
343C2×C8—22no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8—1222no—
348C2×C8—2441no—
349C2×C8—2441no—
350C2×C8#1175819811yescharacteristic
351C2×C8#1175819811yescharacteristic
352C2×C8#1175819811yescharacteristic
353C2×C8#1175819811yescharacteristic
354C4⋊C4—41no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—1221no—
359C4⋊C4—1221no—
360C4⋊C4—1221no—
361C4⋊C4—1221no—
362C4⋊C4—2441no—
363C4⋊C4—2441no—
364C22⋊C4—42no—
365C22⋊C4—42no—
366C22⋊C4—1222no—
367C22⋊C4—1222no—
368C22⋊C4—2441no—
369C22⋊C4—2441no—
370C22⋊C4—2441no—
371C22⋊C4—2441no—
372C42—2441no—
373C42—2441no—
374C23—41no—
375C23—41no—
376C23—4881no—
377C23—4881no—
378C23—2442no—
379C23—2441no—
380C23#1451973911yescharacteristic
381C23#1451975211yescharacteristic
382C23#1451977311yescharacteristic
383C23#1451980112yes—
384C23#1451980912yes—
385Q8—4881no—
386Q8—2441no—
387Q8—2441no—
388D4—4881no—
389D4—4882no—
390D4—4881no—
391D4—4881no—
392D4—2441no—
393D4—2441no—
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—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4—4881no—
410C2×C4—4881no—
411C2×C4—2442no—
412C2×C4—2442no—
413C2×C4—2442no—
414C2×C4—2442no—
415C2×C4—2441no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4C2×#1175819811yescharacteristic
419C2×C4#1451973911yescharacteristic
420C2×C4#1451975211yescharacteristic
421C2×C4#1451976611yescharacteristic
422C8—21no—
423C8—21no—
424C8—21no—
425C8—2442no—
426C8#1451969112yescomplemented
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—42no—
434C22—42no—
435C22—9762no—
436C22—4881no—
437C22—4881no—
438C22—4881no—
439C22#1683966311yescharacteristic
440C22#1683986112yes—
441C22#1684000912yes—
442C22#1684015011yescharacteristic
443C22#1684015511yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—161no—
448C4—161no—
449C4—4882no—
450C4—4881no—
451C4—4881no—
452C4—4881no—
453C4C2×#1451969111yescharacteristic
454C4#1683973511yescharacteristic
455C2—21no—
456C2—22no—
457C2—22no—
458C2—21no—
459C2—9761no—
460C2#2144665411yescharacteristic
461C2#2144669811yescharacteristic
462C2#2144671511yescharacteristic
subgroupG/H
centerC22#16839663
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1808C2
socleC22×C61#390
prime radicalC2×#14519751C22
cosocleC23×C4×C61C23
hypercenter#1808D61
hypocenterC61#9786
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1808

Complements

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

NH ≅ G/Ntype
2. #21446803C2semidirect
4. #21445595C2semidirect
5. #21444390C2semidirect
7. C61×#1808C2semidirect
8. C22×#11758190C4semidirect
15. C2×#14519709C4semidirect
16. C2×#14519702C4semidirect
17. C2×#14519699C4semidirect
193. C8×C61#99semidirect
227. #1808D61semidirect
262. C61#9786semidirect
426. C8#14519691semidirect

Maximal subgroups

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

subgroupindex
C2×#168399912
#214468032
#214466542
#214455952
#214443902
#214443862
C61×#18082
#978661