Finite Group Databasebeta

← #29590898

Subgroups — #29590898

Order 15616.

506 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450971C211yesmaximal, characteristic
2#21445892C211yesmaximal, characteristic
3#323×D61C211yesmaximal, characteristic
4#21443841C211yesmaximal, characteristic, complemented
5#21443839C211yesmaximal, characteristic, complemented
6#21443819C211yesmaximal, characteristic, complemented
7C61×#1344C211yesmaximal, characteristic, complemented
8C2×#14519757C411yescharacteristic, complemented
9C2×C22⋊C4×D61C2211yescharacteristic
10C22⋊C8×D61—21no—
11#16839688C411yescharacteristic, complemented
12#16839675C411yescharacteristic, complemented
13#16839674C2211yescharacteristic
14#16839655—21no—
15#16839654—21no—
16#16839624—21no—
17#16839617—21no—
18#16839617—21no—
19#16839609C411yescharacteristic, complemented
20#16839529C2211yescharacteristic
21#16839528—21no—
22#16839486C2211yescharacteristic
23#16839485—21no—
24C61×#397C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C24×D61D411yescharacteristic
28C22×Dic122C2×C411yescharacteristic
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C2×C8×D61—41no—
32#14519757—41no—
33#14519757—41no—
34C2×C4⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61D411yescharacteristic
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—41no—
43C2×#11758198—41no—
44C2×#11758198C2×C411yescharacteristic
45C2×#11758198D411yescharacteristic
46C22⋊C4×D61—41no—
47C22⋊C4×D61—41no—
48C2×C4×Dic61—21no—
49C22⋊#92418—21no—
50#14519689—41no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684C2×C411yescharacteristic
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61C2311yescharacteristic
59C22⋊C8×C61—21no—
60#95×C61—21no—
61#95×C61C2×C411yescharacteristic
62C24×C61C2×D411yescharacteristic
63C23×D61—21no—
64C23×D61—21no—
65C23×D61—21no—
66C23×D61—21no—
67C23×D61—41no—
68C23×D61—42no—
69C23×D61—81no—
70C23×D61C22⋊C411yescharacteristic
71C23×D61C22⋊C411yescharacteristic
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—41no—
75C22×C4×C61C22×C411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—41no—
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—42no—
87C2×C4×D61—81no—
88C2×Dic122—41no—
89C2×Dic122—81no—
90C2×C8×C61—41no—
91C4⋊C4×C61—41no—
92C22⋊C4×C61—41no—
93C22⋊C4×C61—41no—
94C22⋊C4×C61—41no—
95C22⋊C4×C61—41no—
96C22⋊C4×C61—41no—
97C22⋊Dic61—41no—
98C22⋊Dic61—41no—
99C22⋊Dic61—41no—
100C22⋊Dic61—81no—
101#11758198—41no—
102#11758198—41no—
103#11758198—42no—
104#11758198—42no—
105#11758198—41no—
106#11758198—41no—
107#11758198—81no—
108#11758198—82no—
109#11758198—82no—
110C4⋊Dic61—42no—
111C4×Dic61—81no—
112C2×#92418—41no—
113C8×D61—82no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61C2×C22⋊C411yescharacteristic
119C23×C61#13511yescharacteristic
120C23×C61#13511yescharacteristic
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—22no—
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—42no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—42no—
136C22×D61—81no—
137C22×D61—81no—
138C22×D61—84no—
139C22×D61—82no—
140C22×D61—82no—
141C22×D61#9911yescharacteristic
142C22×D61#9911yescharacteristic
143C2×C4×C61—21no—
144C2×C4×C61—21no—
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—81no—
154C2×C4×C61—81no—
155C2×C4×C61—81no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—81no—
167C2×Dic61—81no—
168C2×Dic61—81no—
169C4×D61—42no—
170C4×D61—81no—
171C4×D61—81no—
172C4×D61—81no—
173Dic122—82no—
174C8×C61—81no—
175#92418—81no—
176#11845—611nomaximal, Sylow
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61—81no—
186C22×C61C2×#9911yescharacteristic
187C22×C61#41611yescharacteristic
188C22×C61#42111yescharacteristic
189C2×D61—21no—
190C2×D61—21no—
191C2×D61—21no—
192C2×D61—21no—
193C2×D61—21no—
194C2×D61—42no—
195C2×D61—42no—
196C2×D61—42no—
197C2×D61—41no—
198C2×D61—41no—
199C2×D61—41no—
200C2×D61—82no—
201C2×D61—82no—
202C2×D61—82no—
203C2×D61—82no—
204C2×D61—81no—
205C2×D61#35412yes—
206C4×C61—41no—
207C4×C61—41no—
208C4×C61—81no—
209C4×C61—81no—
210C4×C61—161no—
211Dic61—41no—
212Dic61—41no—
213Dic61—81no—
214Dic61—81no—
215Dic61—161no—
216#2561—611no—
217#1819—611no—
218C2×#323—611no—
219#1351—611no—
220#1351—611no—
221#1344—611no—
222#1344D6111yescharacteristic, complemented
223C2×C61—21no—
224C2×C61—21no—
225C2×C61—41no—
226C2×C61—41no—
227C2×C61#151611yescharacteristic
228C2×C61#212111yescharacteristic
229C2×C61C2×#35411yescharacteristic
230D61—22no—
231D61—41no—
232D61—81no—
233C2×C22⋊Q8—611no—
234C22×C22⋊C4—611no—
235C2×C22⋊C8—1221no—
236#397—611no—
237#397C2×D6111yescharacteristic
238#393—611no—
239#393—611no—
240#388—1221no—
241#388—1221no—
242#381—1221no—
243#379—1221no—
244#379—1221no—
245C4×C22⋊C4—611no—
246#342—611no—
247#342—1221no—
248#342C2×D6111yescharacteristic
249#323—611no—
250#323—1221no—
251#323C2×D6111yescharacteristic
252C61#1184511yescharacteristic, complemented, Sylow
253C25—611no—
254C22×Q8—611no—
255C23×C4—611no—
256C23×C4—611no—
257C22×C8—2441no—
258C22⋊Q8—2441no—
259C22⋊Q8—2441no—
260C2×C4⋊C4—1221no—
261C2×C4⋊C4C4×D6111yescharacteristic
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—611no—
265C2×C22⋊C4—611no—
266C2×C22⋊C4—611no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4—1221no—
269C2×C22⋊C4—1221no—
270C2×C22⋊C4—1221no—
271C2×C22⋊C4—1221no—
272C2×C22⋊C4—1221no—
273C2×C22⋊C4—2441no—
274C2×C22⋊C4—2441no—
275C2×C22⋊C4—2441no—
276C2×C22⋊C4—2441no—
277C2×C22⋊C4C22×D6111yescharacteristic
278C2×C42—1221no—
279C22⋊C8—21no—
280C22⋊C8—1221no—
281C22⋊C8—2441no—
282#95—21no—
283#95—611no—
284#95—1221no—
285#95—1221no—
286#95—1221no—
287#95C4×D6111yescharacteristic
288C24—611no—
289C24—611no—
290C24—1221no—
291C24—1221no—
292C24—1221no—
293C24—1221no—
294C24—4881no—
295C24—2441no—
296C24—2442no—
297C24D4×D6111yescharacteristic
298C2×Q8—4881no—
299C2×Q8—2441no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—41no—
303C22×C4—611no—
304C22×C4—611no—
305C22×C4—1221no—
306C22×C4—1221no—
307C22×C4—1221no—
308C22×C4—1221no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4—4881no—
312C22×C4—2442no—
313C22×C4—2441no—
314C22×C4C2×C4×D6111yescharacteristic
315C22×C4D4×D6111yescharacteristic
316C2×C8—41no—
317C2×C8—4882no—
318C2×C8—2441no—
319C4⋊C4—41no—
320C4⋊C4—2442no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—4881no—
327C22⋊C4—4882no—
328C22⋊C4—4882no—
329C22⋊C4—4881no—
330C22⋊C4—2441no—
331C22⋊C4—2441no—
332C22⋊C4—2441no—
333C22⋊C4—2441no—
334C22⋊C4—2442no—
335C22⋊C4—2442no—
336C22⋊C4—2441no—
337C22⋊C4—2441no—
338C22⋊C4—2441no—
339C42—4881no—
340C23—21no—
341C23—21no—
342C23—41no—
343C23—41no—
344C23—611no—
345C23—611no—
346C23—1222no—
347C23—1221no—
348C23—1221no—
349C23—1221no—
350C23—1221no—
351C23—1221no—
352C23—4881no—
353C23—4881no—
354C23—4882no—
355C23—4882no—
356C23—4884no—
357C23—2441no—
358C23—2441no—
359C23—2441no—
360C23—2441no—
361C23—2441no—
362C23—2441no—
363C23—2441no—
364C23—2442no—
365C23—2442no—
366C23C22⋊C4×D6111yescharacteristic
367C23#1451979611yescharacteristic
368C23#1451979811yescharacteristic
369Q8—4882no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—1221no—
384C2×C4—1221no—
385C2×C4—4881no—
386C2×C4—4881no—
387C2×C4—4881no—
388C2×C4—4881no—
389C2×C4—4881no—
390C2×C4—4881no—
391C2×C4—2442no—
392C2×C4—2441no—
393C2×C4—2441no—
394C2×C4—2441no—
395C2×C4—2441no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2441no—
400C8—81no—
401C8—4881no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—81no—
411C22—612no—
412C22—1221no—
413C22—1221no—
414C22—1221no—
415C22—1221no—
416C22—1221no—
417C22—4881no—
418C22—4882no—
419C22—4882no—
420C22—4882no—
421C22—4882no—
422C22—2442no—
423C22—2442no—
424C22—2442no—
425C22—2441no—
426C22—2441no—
427C22—2441no—
428C22#99×D6111yescharacteristic
429C22#1683975511yescharacteristic
430C22#1683977711yescharacteristic
431C4—41no—
432C4—41no—
433C4—81no—
434C4—81no—
435C4—161no—
436C4—9761no—
437C4—4881no—
438C4—4881no—
439C4—2441no—
440C4—2441no—
441C2—21no—
442C2—21no—
443C2—41no—
444C2—41no—
445C2—1222no—
446C2—4881no—
447C2—2441no—
448C2#2144437211yescharacteristic
449C2#2144746411yescharacteristic
450C2#354×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1344C2
socleC22×C61C2×#99
prime radicalC24×D61D4
cosocleC2×C22⋊C4×C61C23
hypercenter#1344D61
hypocenterC61#11845
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1344

Complements

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

NH ≅ G/Ntype
4. #21443841C2semidirect
5. #21443839C2semidirect
6. #21443819C2semidirect
7. C61×#1344C2semidirect
8. C2×#14519757C4semidirect
11. #16839688C4semidirect
12. #16839675C4semidirect
19. #16839609C4semidirect
222. #1344D61semidirect
252. C61#11845semidirect

Maximal subgroups

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

subgroupindex
#214509712
#214458922
#323×D612
#214438412
#214438392
#214438192
C61×#13442
#1184561