Finite Group Databasebeta

← #29590791

Subgroups — #29590791

Order 15616.

464 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 69 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#21451708C211yesmaximal, characteristic
2#21445806C211yesmaximal, characteristic, complemented
3#21444158C211yesmaximal, characteristic, complemented
4#21443844C211yesmaximal, characteristic, complemented
5#21443842C211yesmaximal, characteristic, complemented
6#21443816C211yesmaximal, characteristic, complemented
7C61×#1343C211yesmaximal, characteristic, complemented
8C2×#14519748C411yescharacteristic, complemented
9C2×#14519737C2211yescharacteristic
10#16839816—21no—
11C2×#14519691—21no—
12#16839702C411yescharacteristic, complemented
13#16839698C2211yescharacteristic
14#16839677—21no—
15#16839676C411yescharacteristic, complemented
16#16839670—21no—
17#16839656—21no—
18#16839642—21no—
19#16839624C411yescharacteristic, complemented
20#16839620—21no—
21#16839529C2211yescharacteristic
22#16839486C2211yescharacteristic
23#16839485—21no—
24C61×#392C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C22×C22⋊D61—21no—
28C22×C22⋊D61D411yescharacteristic
29C23×Dic61D411yescharacteristic
30C22×C4×D61C2×C411yescharacteristic
31#14519748—41no—
32#14519748—41no—
33#14519737—41no—
34#14519737—41no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—41no—
38C2×#11758196C2×C411yescharacteristic
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×#11758198—21no—
45C2×#11758198D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47#14519706—41no—
48#14519691—42no—
49C22⋊#92418—21no—
50#14519687—41no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—41no—
55#14519684C2×C411yescharacteristic
56C22×D4×C61—21no—
57C22×D4×C61C2×C411yescharacteristic
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61C2311yescharacteristic
61C22⋊C8×C61—21no—
62#95×C61C2×C411yescharacteristic
63C24×C61—21no—
64C24×C61C2×D411yescharacteristic
65C23×D61C22⋊C411yescharacteristic
66C2×D4×C61—41no—
67C2×D4×C61—41no—
68C2×D4×C61—41no—
69C2×D4×C61—81no—
70C2×D4×C61—81no—
71C2×D4×C61—81no—
72C22×C4×C61—21no—
73C22×C4×C61—41no—
74C22×C4×C61C22×C411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C2×C22⋊D61—21no—
77C2×C22⋊D61—21no—
78C2×C22⋊D61—41no—
79C2×C22⋊D61—41no—
80C2×C22⋊D61—42no—
81C2×C22⋊D61—81no—
82C2×C22⋊D61—81no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—41no—
88C22×Dic61—81no—
89C22×Dic61C22⋊C411yescharacteristic
90C22×Dic61C22⋊C411yescharacteristic
91C22×Dic61C22⋊C411yescharacteristic
92C2×C4×D61—21no—
93C2×C4×D61—21no—
94C2×C4×D61—81no—
95C2×C8×C61—41no—
96C22⋊C4×C61—41no—
97C22⋊C4×C61—41no—
98C22⋊C4×C61—41no—
99C22⋊C4×C61—81no—
100C22⋊Dic61—42no—
101C22⋊Dic61—41no—
102C22⋊Dic61—41no—
103C22⋊Dic61—41no—
104C22⋊Dic61—41no—
105C22⋊Dic61—81no—
106C22⋊Dic61—81no—
107#11758198—41no—
108#11758198—81no—
109C4⋊Dic61—41no—
110#11758196—41no—
111#11758196—81no—
112#11758196—82no—
113C4×Dic61—21no—
114C4×Dic61—21no—
115C2×#92418—41no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61C2×C22⋊C411yescharacteristic
128C23×C61AGL(1,ℤ/8)11yescharacteristic
129C23×C61#13711yescharacteristic
130C22×D61—21no—
131C22×D61—21no—
132C22×D61—21no—
133C22×D61—41no—
134C22×D61—41no—
135D4×C61—82no—
136D4×C61—82no—
137D4×C61—82no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—81no—
146C2×C4×C61—81no—
147C2×C4×C61—81no—
148C22⋊D61—42no—
149C22⋊D61—42no—
150C22⋊D61—84no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—41no—
156C2×Dic61—42no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—81no—
165C2×Dic61—81no—
166C2×Dic61—81no—
167C2×Dic61—81no—
168C2×Dic61#9911yescharacteristic
169C2×Dic61#9911yescharacteristic
170C4×D61—81no—
171C4×D61—81no—
172C8×C61—81no—
173#92418—81no—
174#11824—611nomaximal, Sylow
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—81no—
184C22×C61—81no—
185C22×C61—81no—
186C22×C61—81no—
187C22×C61—81no—
188C22×C61—81no—
189C22×C61—81no—
190C22×C61—81no—
191C22×C61C2×#9911yescharacteristic
192C22×C61#41711yescharacteristic
193C22×C61#42111yescharacteristic
194C2×D61—41no—
195C2×D61—41no—
196C2×D61—41no—
197C2×D61—81no—
198C2×D61—81no—
199C4×C61—41no—
200C4×C61—41no—
201C4×C61—81no—
202C4×C61—161no—
203Dic61—21no—
204Dic61—21no—
205Dic61—41no—
206Dic61—41no—
207Dic61—81no—
208Dic61—81no—
209Dic61—161no—
210#2635—611no—
211#1799—611no—
212#1466—611no—
213#1352—611no—
214#1352—611no—
215#1343—611no—
216#1343D6111yescharacteristic, complemented
217C2×C61—21no—
218C2×C61—21no—
219C2×C61—41no—
220C2×C61—41no—
221C2×C61—161no—
222C2×C61#151311yescharacteristic
223C2×C61#212111yescharacteristic
224C2×C61#212811yescharacteristic
225D61—81no—
226C2×#121—611no—
227C2×C4×D4—611no—
228#432—1221no—
229C2×#99—1221no—
230#400—611no—
231#399—611no—
232#394—611no—
233#394—1221no—
234#392—1221no—
235#392C2×D6111yescharacteristic
236#388—1221no—
237#386—1221no—
238#381—611no—
239#380—1221no—
240#342—611no—
241#342C2×D6111yescharacteristic
242#323—611no—
243#323—1221no—
244#323C2×D6111yescharacteristic
245C61#1182411yescharacteristic, complemented, Sylow
246C22×D4—21no—
247C22×D4—611no—
248C22×D4—1221no—
249C22×D4C4×D6111yescharacteristic
250C23×C4—611no—
251C23×C4—611no—
252#121—2441no—
253#121—2441no—
254C4×D4—2441no—
255C4×D4—2441no—
256C2×C4⋊C4—611no—
257C2×C4⋊C4—611no—
258C2×C4⋊C4—1221no—
259C2×C4⋊C4—2441no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—611no—
263C2×C22⋊C4—1221no—
264C2×C22⋊C4—1221no—
265C2×C22⋊C4—1221no—
266C2×C22⋊C4—1221no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4—1221no—
269C2×C22⋊C4C22×D6111yescharacteristic
270C2×C42—611no—
271C4⋊C8—2441no—
272#99—2442no—
273C22⋊C8—21no—
274C22⋊C8—1221no—
275#97—2441no—
276#95—611no—
277#95—1221no—
278#95—1221no—
279#95—1221no—
280#95—2441no—
281#95C4×D6111yescharacteristic
282C24—21no—
283C24—611no—
284C24D4×D6111yescharacteristic
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—81no—
289C2×D4—81no—
290C2×D4—81no—
291C2×D4—1221no—
292C2×D4—1221no—
293C2×D4—4881no—
294C2×D4—4881no—
295C2×D4—2441no—
296C2×D4—2441no—
297C2×D4—2442no—
298C22×C4—21no—
299C22×C4—41no—
300C22×C4—611no—
301C22×C4—611no—
302C22×C4—611no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4—1221no—
307C22×C4—1221no—
308C22×C4—1221no—
309C22×C4—4881no—
310C22×C4—4881no—
311C22×C4—2441no—
312C22×C4C2×C4×D6111yescharacteristic
313C22×C4D4×D6111yescharacteristic
314C2×C8—41no—
315C2×C8—2441no—
316C4⋊C4—4881no—
317C4⋊C4—4882no—
318C4⋊C4—2441no—
319C4⋊C4—2441no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—81no—
324C22⋊C4—4881no—
325C22⋊C4—4881no—
326C22⋊C4—4881no—
327C22⋊C4—2441no—
328C22⋊C4—2441no—
329C22⋊C4—2441no—
330C22⋊C4—2442no—
331C22⋊C4—2441no—
332C22⋊C4—2441no—
333C42—1221no—
334C42—1221no—
335C23—21no—
336C23—21no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—1221no—
347C23—1221no—
348C23—1221no—
349C23—2441no—
350C23—2441no—
351C23C22⋊C4×D6111yescharacteristic
352C23#1451980111yescharacteristic
353C23#1451980611yescharacteristic
354D4—82no—
355D4—82no—
356D4—82no—
357D4—4884no—
358D4—2442no—
359D4—2442no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—611no—
371C2×C4—611no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—4881no—
377C2×C4—4881no—
378C2×C4—4881no—
379C2×C4—4881no—
380C2×C4—4881no—
381C2×C4—4881no—
382C2×C4—2441no—
383C2×C4—2442no—
384C2×C4—2441no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4—2441no—
388C2×C4—2441no—
389C2×C4—2441no—
390C2×C4—2441no—
391C8—81no—
392C8—4881no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—4881no—
410C22—4881no—
411C22—2441no—
412C22—2441no—
413C22—2441no—
414C22#99×D6111yescharacteristic
415C22#1683976011yescharacteristic
416C22#1683977711yescharacteristic
417C4—41no—
418C4—41no—
419C4—81no—
420C4—161no—
421C4—1221no—
422C4—1221no—
423C4—9761no—
424C4—4881no—
425C4—4881no—
426C4—2441no—
427C4—2441no—
428C2—21no—
429C2—21no—
430C2—41no—
431C2—41no—
432C2—161no—
433C2—4881no—
434C2#2144435911yescharacteristic
435C2#2144746211yescharacteristic
436C2#2144748911yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1343C2
socleC22×C61C2×#99
prime radical#21451708C2
cosocleC2×C22⋊C4×C61C23
hypercenter#1343D61
hypocenterC61#11824
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1343

Complements

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

NH ≅ G/Ntype
2. #21445806C2semidirect
3. #21444158C2semidirect
4. #21443844C2semidirect
5. #21443842C2semidirect
6. #21443816C2semidirect
7. C61×#1343C2semidirect
8. C2×#14519748C4semidirect
12. #16839702C4semidirect
15. #16839676C4semidirect
19. #16839624C4semidirect
216. #1343D61semidirect
245. C61#11824semidirect

Maximal subgroups

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

subgroupindex
#214517082
#214458062
#214441582
#214438442
#214438422
#214438162
C61×#13432
#1182461