Finite Group Databasebeta

← #29576279

Subgroups — #29576279

Order 15616.

724 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 115 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#21455820C211yesmaximal, characteristic
2C4×#14519739C211yesmaximal, characteristic, complemented
3#21446646C211yesmaximal, characteristic, complemented
4#21444313C211yesmaximal, characteristic, complemented
5#21444243C211yesmaximal, characteristic, complemented
6#21443651C211yesmaximal, characteristic, complemented
7C61×#1303C211yesmaximal, characteristic, complemented
8#16840312C2211yescharacteristic
9C2×C4×D244C2211yescharacteristic
10C2×#14519739—21no—
11C2×C42×D61—21no—
12#16840076—21no—
13#16840043C412yescomplemented
14#16839958C412yescomplemented
15#16839898—21no—
16C4×D488—22no—
17#16839815C2211yescharacteristic
18C2×#14519703—21no—
19C2×#14519703—21no—
20C4⋊C4×Dic61—21no—
21C4×#11758198—21no—
22#16839609—22no—
23C42×Dic61C2211yescharacteristic
24#16839495—22no—
25#16839489—22no—
26C61×#431C2211yescharacteristic
27C61×#423C2211yescharacteristic
28C4×C4⋊C4×C61C2211yescharacteristic
29C2×#11758222—21no—
30C22×D244D411yescharacteristic
31C22×C4×D61—22no—
32C22×C4×D61—21no—
33C2×D488—22no—
34#14519777C2×C411yescharacteristic, complemented
35#14519774C2×C411yescharacteristic, complemented
36#14519765—21no—
37#14519751—21no—
38#14519751—21no—
39C4×D244—21no—
40C4×D244—21no—
41C4×D244—21no—
42C4×D244—21no—
43C4×D244C2×C412yes—
44C4×D244D412yes—
45#14519739—28no—
46C2×C4⋊Dic61D411yescharacteristic
47C2×#11758198—22no—
48C2×#11758198—21no—
49C2×C4×Dic61—21no—
50C2×C4×Dic61—22no—
51C2×C4×Dic61—21no—
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54C42×D61—42no—
55C42×D61—42no—
56#14519711—22no—
57C4⋊#92418—21no—
58#14519703—42no—
59#14519703—42no—
60#14519699—22no—
61#14519699—22no—
62C22⋊#92418—21no—
63C4×#92418—21no—
64#14519684—22no—
65C2×M16×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C42×C61—21no—
68C2×C42×C61C2311yescharacteristic
69C4⋊C8×C61—21no—
70C4⋊C8×C61—21no—
71C4⋊C8×C61C2×C412yescomplemented
72C22⋊C8×C61—21no—
73C4×C8×C61—21no—
74#95×C61D412yes—
75C23×D61—21no—
76C22×C4×C61—22no—
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C2×C22⋊D61—41no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—21no—
84#11758222—41no—
85#11758222—41no—
86#11758222—41no—
87#11758222—41no—
88C2×D244—21no—
89C2×D244—24no—
90C2×D244—21no—
91C2×D244—21no—
92C2×D244—21no—
93C2×D244C22⋊C412yes—
94C2×C4×D61—28no—
95C2×C4×D61—22no—
96C2×C4×D61—22no—
97C2×C4×D61—44no—
98C2×C4×D61—44no—
99C2×C4×D61—41no—
100C2×C4×D61—41no—
101C2×C4×D61—41no—
102C2×C4×D61—41no—
103C2×C4×D61—41no—
104C2×Dic122—21no—
105M16×C61—41no—
106M16×C61—41no—
107C2×C8×C61—22no—
108C2×C8×C61—41no—
109C4⋊C4×C61—24no—
110C42×C61—41no—
111C42×C61—41no—
112C42×C61C22×C411yescharacteristic
113C42×C61C2×D411yescharacteristic
114C42×C61#4111yescharacteristic
115C42×C61#4111yescharacteristic
116#11758198—28no—
117#11758198—22no—
118#11758198—22no—
119#11758198—41no—
120#11758198—41no—
121C4⋊Dic61—21no—
122C4⋊Dic61—21no—
123C4⋊Dic61—21no—
124C4⋊Dic61C22⋊C412yes—
125C4×Dic61—24no—
126C4×Dic61—21no—
127C4×Dic61—21no—
128C4×Dic61—21no—
129C4×Dic61—44no—
130C4×Dic61—42no—
131C4×Dic61D812yescomplemented
132C2×#92418—41no—
133D488—44no—
134C23×C61#12011yescharacteristic
135C22×D61—24no—
136C22×D61—22no—
137C22×D61—42no—
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—41no—
141C2×C4×C61—22no—
142C2×C4×C61—24no—
143C2×C4×C61—41no—
144C2×C4×C61—42no—
145C2×C4×C61—42no—
146C2×C4×C61C2×C22⋊C411yescharacteristic
147C2×C4×C61C4×D411yescharacteristic
148C2×C4×C61C4×D411yescharacteristic
149C2×C4×C61#12111yescharacteristic
150C2×C4×C61#12111yescharacteristic
151C2×C4×C61#12311yescharacteristic
152C2×C4×C61C2×D811yescharacteristic
153C2×C4×C61#13511yescharacteristic
154C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
156C22⋊D61—81no—
157C22⋊D61—81no—
158C2×Dic61—22no—
159C2×Dic61—22no—
160C2×Dic61—22no—
161C2×Dic61—22no—
162C2×Dic61—22no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168D244—24no—
169D244—22no—
170D244—42no—
171D244—41no—
172D244—41no—
173D244—81no—
174D244#10414yescomplemented
175C4×D61—416no—
176C4×D61—42no—
177C4×D61—42no—
178C4×D61—42no—
179C4×D61—42no—
180C4×D61—81no—
181C4×D61—81no—
182Dic122—41no—
183Dic122—41no—
184C8×C61—42no—
185C8×C61—81no—
186#92418—81no—
187#9233—611nomaximal, Sylow
188C22×C61—21no—
189C22×C61—21no—
190C22×C61#38611yescharacteristic
191C22×C61#44711yescharacteristic
192C22×C61#44911yescharacteristic
193C2×D61—24no—
194C2×D61—44no—
195C2×D61—44no—
196C2×D61—42no—
197C2×D61—42no—
198C2×D61—81no—
199C2×D61—81no—
200C2×D61—81no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—21no—
204C4×C61—44no—
205C4×C61C2×#10412yes—
206C4×C61C4×D811yescharacteristic
207C4×C61#44211yescharacteristic
208C4×C61#45911yescharacteristic
209C4×C61#46311yescharacteristic
210Dic61—24no—
211Dic61—42no—
212Dic61—42no—
213Dic61—81no—
214#3100—611no—
215C42×D4—611no—
216#1962—611no—
217#1502—611no—
218#1486—611no—
219#1303D6111yescharacteristic, complemented
220#1276—611no—
221C2×C61—21no—
222C2×C61—21no—
223C2×C61#187911yescharacteristic
224C2×C61#189611yescharacteristic
225C2×C61#190611yescharacteristic
226D61—44no—
227D61—161no—
228#532—611no—
229C2×C4×D4—611no—
230C2×C4×D4—1221no—
231C22×C42—1221no—
232#480—1221no—
233#474—612no—
234#459—612no—
235#447—1221no—
236C4×D8—1222no—
237#431—611no—
238#431C2×D6111yescharacteristic
239#423C2×D6111yescharacteristic
240C2×#104—1221no—
241C2×#104—1221no—
242C4×C4⋊C4—1221no—
243C4×C4⋊C4C2×D6111yescharacteristic
244C4×C22⋊C4—1221no—
245C4×C22⋊C4—1222no—
246C43—611no—
247#327—1222no—
248D4⋊C8—1222no—
249C61#923311yescharacteristic, complemented, Sylow
250C2×#41—1221no—
251C22×D4—611no—
252C23×C4—1222no—
253C23×C4—1221no—
254C2×D8—1222no—
255C2×M16—21no—
256C4⋊Q8—611no—
257#127—611no—
258#124—1221no—
259#121—1221no—
260#121—1221no—
261C4×D4—612no—
262C4×D4—612no—
263C4×D4—1228no—
264C4×D4—1221no—
265C4×D4—1221no—
266C4×D4—1221no—
267C4×D4—1221no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—611no—
270C2×C22⋊C4—1222no—
271C2×C22⋊C4—1221no—
272C2×C42—21no—
273C2×C42—611no—
274C2×C42—611no—
275C2×C42—1221no—
276C2×C42—1222no—
277C2×C42—1221no—
278C2×C42—2442no—
279C2×C42—2442no—
280C2×C42C22×D6111yescharacteristic
281#107—1222no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284C4⋊C8—1221no—
285C4⋊C8C4×D6112yescomplemented
286#104—2442no—
287#104—2442no—
288#102—1222no—
289#102—1222no—
290C22⋊C8—21no—
291C22⋊C8—1221no—
292C4×C8—21no—
293C4×C8—1221no—
294#95—1222no—
295#95D24412yes—
296C24—1221no—
297#41—2441no—
298#41—2441no—
299#41—2441no—
300#41—2441no—
301C2×Q8—1221no—
302C2×D4—612no—
303C2×D4—1224no—
304C2×D4—1221no—
305C2×D4—1221no—
306C2×D4—1221no—
307C2×D4—1221no—
308C2×D4—2441no—
309C22×C4—22no—
310C22×C4—1228no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4—1221no—
314C22×C4—1222no—
315C22×C4—1222no—
316C22×C4—2444no—
317C22×C4—2444no—
318C22×C4—2441no—
319C22×C4—2441no—
320C22×C4—2441no—
321C22×C4—2441no—
322C22×C4—2441no—
323C22×C4C2×D24411yescharacteristic
324C22×C4D4×D6111yescharacteristic
325C22×C4D4×D6111yescharacteristic
326D8—2444no—
327M16—41no—
328M16—41no—
329C2×C8—22no—
330C2×C8—41no—
331C2×C8—2441no—
332C4⋊C4—24no—
333C4⋊C4—612no—
334C4⋊C4—1221no—
335C4⋊C4—1221no—
336C4⋊C4—1221no—
337C22⋊C4—1228no—
338C22⋊C4—1222no—
339C22⋊C4—1222no—
340C22⋊C4—2441no—
341C22⋊C4—2441no—
342C42—41no—
343C42—41no—
344C42—612no—
345C42—1224no—
346C42—1221no—
347C42—1221no—
348C42—1221no—
349C42—2444no—
350C42—2442no—
351C42C2×C4×D6111yescharacteristic
352C42#1175822211yescharacteristic
353C42D4×D6111yescharacteristic
354C42#1175822611yescharacteristic
355C23—1224no—
356C23—1222no—
357C23—2442no—
358C23—2441no—
359C23—2441no—
360C23—2441no—
361C23#1451974711yescharacteristic
362Q8—2441no—
363Q8—2441no—
364D4—614no—
365D4—1224no—
366D4—1222no—
367D4—4881no—
368D4—4881no—
369D4—4881no—
370D4—2442no—
371D4—2441no—
372D4—2441no—
373C2×C4—22no—
374C2×C4—24no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—1222no—
379C2×C4—1222no—
380C2×C4—1222no—
381C2×C4—1222no—
382C2×C4—1222no—
383C2×C4—4881no—
384C2×C4—4881no—
385C2×C4—24416no—
386C2×C4—2441no—
387C2×C4—2441no—
388C2×C4—2441no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4—2442no—
392C2×C4—2442no—
393C2×C4—2442no—
394C2×C4—2442no—
395C2×C4C22⋊C4×D6111yescharacteristic
396C2×C4#1451973911yescharacteristic
397C2×C4C4×D24411yescharacteristic
398C2×C4#1451975011yescharacteristic
399C2×C4#1451975211yescharacteristic
400C2×C4#1451976211yescharacteristic
401C2×C4D8×D6111yescharacteristic
402C2×C4#1451980011yescharacteristic
403C2×C4#1451980411yescharacteristic
404C2×C4#1451980411yescharacteristic
405C8—42no—
406C8—81no—
407C8—4881no—
408C22—21no—
409C22—21no—
410C22—1224no—
411C22—4881no—
412C22—4881no—
413C22—4881no—
414C22—2444no—
415C22—2444no—
416C22—2442no—
417C22—2442no—
418C22#1683964011yescharacteristic
419C22#1683989711yescharacteristic
420C22#1683991011yescharacteristic
421C4—21no—
422C4—21no—
423C4—21no—
424C4—44no—
425C4—1224no—
426C4—4881no—
427C4—2442no—
428C4—2442no—
429C4#104×D6112yes—
430C4#1683984411yescharacteristic
431C4#1683987311yescharacteristic
432C4#1683995611yescharacteristic
433C4#1683998011yescharacteristic
434C2—21no—
435C2—21no—
436C2—9761no—
437C2—2444no—
438C2#2144616811yescharacteristic
439C2#2144626111yescharacteristic
440C2#2144632111yescharacteristic
subgroupG/H
centerC2×C4#14519750
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1303C2
socleC22×C61#386
prime radical#21455820C2
cosocleC2×C42×C61C23
hypercenter#1303D61
hypocenterC61#9233
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
2. C4×#14519739C2semidirect
3. #21446646C2semidirect
4. #21444313C2semidirect
5. #21444243C2semidirect
6. #21443651C2semidirect
7. C61×#1303C2semidirect
13. #16840043C4semidirect
14. #16839958C4semidirect
34. #14519777C2×C4semidirect
35. #14519774C2×C4semidirect
71. C4⋊C8×C61C2×C4semidirect
131. C4×Dic61D8semidirect
174. D244#104semidirect
219. #1303D61semidirect
249. C61#9233semidirect
285. C4⋊C8C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214558202
C4×#145197392
#214466462
#214443132
#214442432
#214436512
C61×#13032
#923361