Finite Group Databasebeta

← #29573557

Subgroups — #29573557

Order 15616.

530 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448723C211yesmaximal, characteristic
2#21445804C211yesmaximal, characteristic
3#21444135C211yesmaximal, characteristic
4#21443699C211yesmaximal, characteristic, complemented
5#21443697C211yesmaximal, characteristic, complemented
6#21443686C211yesmaximal, characteristic, complemented
7C61×#1289C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D61C2211yescharacteristic
9C2×#14519737—21no—
10C2×#14519691—21no—
11C2×C22⋊#92418C2211yescharacteristic
12#16839657—21no—
13#16839634—21no—
14#16839633—21no—
15#16839626C411yescharacteristic, complemented
16#16839622C2211yescharacteristic
17#16839621C411yescharacteristic, complemented
18#16839613C411yescharacteristic, complemented
19C2×#14519684C2211yescharacteristic
20#95×D61C411yescharacteristic, complemented
21#16839528—21no—
22#16839487—21no—
23#16839485—21no—
24C2×C22⋊C8×C61C2211yescharacteristic
25C61×#380C2211yescharacteristic
26C61×#380C2211yescharacteristic
27C22×C22⋊D61D411yescharacteristic
28C23×Dic61—21no—
29C22×C4×D61—21no—
30C22×C4×D61C2×C411yescharacteristic
31C22×#92418—21no—
32C4×C22⋊D61—21no—
33C4×C22⋊D61—21no—
34C4×C22⋊D61—21no—
35C4×C22⋊D61—21no—
36#14519737—42no—
37#14519737—42no—
38C2×C4⋊Dic61—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196D411yescharacteristic
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61D411yescharacteristic
45C2×#11758198—21no—
46C2×#11758198D411yescharacteristic
47C2×C4×Dic61—21no—
48C2×C4×Dic61C2×C411yescharacteristic
49#14519691—42no—
50C22⋊#92418—21no—
51C22⋊#92418—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684C2×C411yescharacteristic
57#14519684C2×C411yescharacteristic
58C23×C4×C61C2311yescharacteristic
59C22×C8×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61—21no—
62C2×C22⋊C4×C61—21no—
63C2×C22⋊C4×C61—21no—
64C22⋊C8×C61—21no—
65C22⋊C8×C61—21no—
66#95×C61—21no—
67#95×C61C2×C411yescharacteristic
68#95×C61C2×C411yescharacteristic
69C24×C61C2×D411yescharacteristic
70C23×D61C22⋊C411yescharacteristic
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—41no—
74C22×C4×C61—81no—
75C22×C4×C61C22×C411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61#4111yescharacteristic
78C22×C4×C61#4111yescharacteristic
79C22×C4×C61#4111yescharacteristic
80C22×C4×C61#4111yescharacteristic
81C2×C22⋊D61—21no—
82C2×C22⋊D61—21no—
83C2×C22⋊D61—21no—
84C2×C22⋊D61—21no—
85C2×C22⋊D61D812yes—
86C2×C22⋊D61SD1612yes—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—42no—
90C22×Dic61—41no—
91C22×Dic61—41no—
92C22×Dic61—41no—
93C22×Dic61—81no—
94C22×Dic61C22⋊C411yescharacteristic
95C22×Dic61C22⋊C411yescharacteristic
96C22×Dic61C22⋊C411yescharacteristic
97C2×C4×D61—21no—
98C2×C4×D61—21no—
99C2×C4×D61—42no—
100C2×C4×D61—42no—
101C2×C4×D61—81no—
102C2×C4×D61—81no—
103C2×C8×C61—41no—
104C2×C8×C61—81no—
105C4⋊C4×C61—81no—
106C4⋊C4×C61—81no—
107C22⋊C4×C61—41no—
108C22⋊C4×C61—41no—
109C22⋊C4×C61—41no—
110C22⋊C4×C61—41no—
111C22⋊Dic61—21no—
112C22⋊Dic61—21no—
113C22⋊Dic61—41no—
114C22⋊Dic61—41no—
115#11758198—21no—
116#11758198—21no—
117#11758198—42no—
118C4⋊Dic61—81no—
119#11758196—21no—
120#11758196—21no—
121#11758196—42no—
122#11758196—42no—
123#11758196—81no—
124C4×Dic61—21no—
125C4×Dic61—21no—
126C4×Dic61—42no—
127C2×#92418—41no—
128C2×#92418—81no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61C2×C22⋊C411yescharacteristic
132C23×C61#12311yescharacteristic
133C23×C61#12311yescharacteristic
134C23×C61C2×D811yescharacteristic
135C23×C61C2×SD1611yescharacteristic
136C23×C61#13711yescharacteristic
137C23×C61#13711yescharacteristic
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—41no—
141C22×D61—41no—
142C22×D61#10212yes—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—81no—
156C2×C4×C61—81no—
157C2×C4×C61—81no—
158C2×C4×C61#11711yescharacteristic
159C2×C4×C61#11711yescharacteristic
160C2×C4×C61#12311yescharacteristic
161C2×C4×C61#12311yescharacteristic
162C22⋊D61—22no—
163C22⋊D61—22no—
164C22⋊D61—22no—
165C22⋊D61—22no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—22no—
169C2×Dic61—21no—
170C2×Dic61—21no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—82no—
179C2×Dic61—82no—
180C2×Dic61—81no—
181C2×Dic61—81no—
182C2×Dic61—81no—
183C2×Dic61#10212yes—
184C4×D61—81no—
185C4×D61—81no—
186C4×D61—84no—
187C8×C61—81no—
188#92418—81no—
189#8760—611nomaximal, Sylow
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61—41no—
197C22×C61—41no—
198C22×C61—41no—
199C22×C61—41no—
200C22×C61#38111yescharacteristic
201C22×C61C2×#10211yescharacteristic
202C22×C61#41911yescharacteristic
203C22×C61#48011yescharacteristic
204C22×C61#48011yescharacteristic
205C22×C61#48311yescharacteristic
206C22×C61#48311yescharacteristic
207C2×D61—22no—
208C2×D61—42no—
209C2×D61—41no—
210C2×D61—41no—
211C2×D61—42no—
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—81no—
217C4×C61—81no—
218C4×C61—161no—
219Dic61—22no—
220Dic61—42no—
221Dic61—41no—
222Dic61—41no—
223Dic61—81no—
224Dic61—161no—
225#2349—611no—
226#1799—611no—
227#1459—611no—
228#1294—611no—
229#1294—611no—
230#1289—611no—
231#1289D6111yescharacteristic, complemented
232C2×C61—21no—
233C2×C61—21no—
234C2×C61—21no—
235C2×C61—21no—
236C2×C61—21no—
237C2×C61—21no—
238C2×C61#182311yescharacteristic
239C2×C61#182711yescharacteristic
240C2×C61#182811yescharacteristic
241D61—42no—
242C2×C4×D4—611no—
243C2×C4×D4—1221no—
244C2×#99—1221no—
245C2×C22⋊C8—611no—
246C2×C22⋊C8C2×D6111yescharacteristic
247#389—1221no—
248#385—1221no—
249#385—1221no—
250#382—611no—
251#380—611no—
252#380—611no—
253#380C2×D6111yescharacteristic
254#380C2×D6111yescharacteristic
255C4×C4⋊C4—611no—
256C2×#95—611no—
257C2×#95—611no—
258#342—1221no—
259#324—1221no—
260#323—1221no—
261C61#876011yescharacteristic, complemented, Sylow
262C22×D4—611no—
263C23×C4—611no—
264C23×C4—1221no—
265C23×C4—1221no—
266C23×C4C22×D6111yescharacteristic
267C22×C8—21no—
268C22×C8—1221no—
269C4×D4—1221no—
270C4×D4—1221no—
271C4×D4—1221no—
272C4×D4—1221no—
273C4×D4—2442no—
274C4×D4—2442no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—611no—
278C2×C4⋊C4—1221no—
279C2×C4⋊C4—1221no—
280C2×C4⋊C4—1221no—
281C2×C4⋊C4—1221no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—611no—
285C2×C22⋊C4—611no—
286C2×C22⋊C4—1221no—
287C2×C22⋊C4—1221no—
288C2×C42—611no—
289C2×C42—1221no—
290#99—2442no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293C22⋊C8—1221no—
294C22⋊C8—1221no—
295#95—21no—
296#95—611no—
297#95—611no—
298#95—1221no—
299#95—1221no—
300#95—1221no—
301#95—1221no—
302#95C4×D6111yescharacteristic
303#95C4×D6111yescharacteristic
304C24—611no—
305C24D4×D6111yescharacteristic
306C2×D4—612no—
307C2×D4—612no—
308C2×D4—1221no—
309C2×D4—1221no—
310C2×D4—1221no—
311C2×D4—1221no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—41no—
315C22×C4—81no—
316C22×C4—611no—
317C22×C4—611no—
318C22×C4—611no—
319C22×C4—1221no—
320C22×C4—1221no—
321C22×C4—1221no—
322C22×C4—1221no—
323C22×C4—4881no—
324C22×C4—4881no—
325C22×C4—4881no—
326C22×C4—2442no—
327C22×C4—2442no—
328C22×C4—2442no—
329C22×C4—2441no—
330C22×C4—2441no—
331C22×C4—2441no—
332C22×C4C2×C4×D6111yescharacteristic
333C22×C4#1175822211yescharacteristic
334C22×C4#1175822211yescharacteristic
335C22×C4D4×D6111yescharacteristic
336C22×C4#1175822411yescharacteristic
337C22×C4#1175822611yescharacteristic
338C2×C8—41no—
339C2×C8—81no—
340C2×C8—4881no—
341C2×C8—2441no—
342C4⋊C4—81no—
343C4⋊C4—81no—
344C4⋊C4—1221no—
345C4⋊C4—1221no—
346C4⋊C4—4881no—
347C4⋊C4—4881no—
348C4⋊C4—2442no—
349C4⋊C4—2442no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—1221no—
355C22⋊C4—1221no—
356C22⋊C4—1221no—
357C22⋊C4—1221no—
358C22⋊C4—2442no—
359C22⋊C4—2441no—
360C22⋊C4—2441no—
361C42—1221no—
362C42—1221no—
363C42—2442no—
364C23—41no—
365C23—41no—
366C23—612no—
367C23—1221no—
368C23—1221no—
369C23—2441no—
370C23—2441no—
371C23C22⋊C4×D6111yescharacteristic
372C23#1451975911yescharacteristic
373C23#1451976211yescharacteristic
374C23D8×D6111yescharacteristic
375C23SD16×D6111yescharacteristic
376C23#1451980611yescharacteristic
377C23#1451980911yescharacteristic
378D4—1222no—
379D4—1222no—
380D4—1222no—
381D4—1222no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—612no—
398C2×C4—1221no—
399C2×C4—1221no—
400C2×C4—1222no—
401C2×C4—1221no—
402C2×C4—1221no—
403C2×C4—4881no—
404C2×C4—4881no—
405C2×C4—4884no—
406C2×C4—4881no—
407C2×C4—4881no—
408C2×C4—4881no—
409C2×C4—4882no—
410C2×C4—4882no—
411C2×C4—2441no—
412C2×C4—2441no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4#1451973411yescharacteristic
419C2×C4#1451973511yescharacteristic
420C2×C4#1451975911yescharacteristic
421C2×C4#1451976211yescharacteristic
422C8—81no—
423C8—4881no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—1222no—
435C22—2442no—
436C22—2442no—
437C22—2441no—
438C22—2441no—
439C22#1683962411yescharacteristic
440C22#102×D6111yescharacteristic
441C22#1683976911yescharacteristic
442C22#1684007411yescharacteristic
443C22#1684007711yescharacteristic
444C22#1684009111yescharacteristic
445C22#1684009411yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—81no—
451C4—81no—
452C4—161no—
453C4—1222no—
454C4—9761no—
455C4—4881no—
456C4—2442no—
457C4—2441no—
458C4—2441no—
459C2—21no—
460C2—21no—
461C2—21no—
462C2—21no—
463C2—21no—
464C2—21no—
465C2—2442no—
466C2#2144590411yescharacteristic
467C2#2144592111yescharacteristic
468C2#2144592611yescharacteristic
subgroupG/H
centerC22#16839624
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1289C2
socleC22×C61#381
prime radicalC22×C22⋊D61D4
cosocleC23×C4×C61C23
hypercenter#1289D61
hypocenterC61#8760
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
4. #21443699C2semidirect
5. #21443697C2semidirect
6. #21443686C2semidirect
7. C61×#1289C2semidirect
15. #16839626C4semidirect
17. #16839621C4semidirect
18. #16839613C4semidirect
20. #95×D61C4semidirect
231. #1289D61semidirect
261. C61#8760semidirect

Maximal subgroups

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

subgroupindex
#214487232
#214458042
#214441352
#214436992
#214436972
#214436862
C61×#12892
#876061