Finite Group Databasebeta

← #29576307

Subgroups — #29576307

Order 15616.

588 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 111 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
2#21448280C211yesmaximal, 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×#14519734—21no—
11#16840076—21no—
12#16840043C412yescomplemented
13#16839958C412yescomplemented
14#16839898—21no—
15C4×D488—22no—
16#16839815C2211yescharacteristic
17C2×#14519703—21no—
18C2×#14519703—21no—
19#16839663—21no—
20#16839658—21no—
21#16839651—22no—
22C4×#11758198—21no—
23C42×Dic61C2211yescharacteristic
24#16839495—22no—
25#16839489—22no—
26C61×#431C2211yescharacteristic
27C61×#423C2211yescharacteristic
28C4×C4⋊C4×C61C2211yescharacteristic
29C2×#11758222—21no—
30C22×D244D411yescharacteristic
31C22×C4×D61—21no—
32C2×D488—22no—
33#14519777C2×C411yescharacteristic
34#14519774C2×C411yescharacteristic
35#14519765—21no—
36#14519751—21no—
37#14519751—21no—
38C4×D244—21no—
39C4×D244—21no—
40C4×D244—21no—
41C4×D244—21no—
42C4×D244C2×C412yes—
43C4×D244D412yes—
44#14519734—42no—
45#14519734—42no—
46C2×C4⋊Dic61D411yescharacteristic
47C2×#11758196—22no—
48C2×#11758198—21no—
49C2×#11758198—22no—
50C2×#11758198—22no—
51C2×C4×Dic61—21no—
52C2×C4×Dic61—21no—
53C2×C4×Dic61D411yescharacteristic
54C2×C4×Dic61D411yescharacteristic
55#14519711—22no—
56C4⋊#92418—21no—
57#14519703—42no—
58#14519703—42no—
59#14519699—22no—
60#14519699—22no—
61C22⋊#92418—21no—
62C4×#92418—21no—
63#14519684—22no—
64C2×M16×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C42×C61—21no—
67C2×C42×C61C2311yescharacteristic
68C4⋊C8×C61—21no—
69C4⋊C8×C61—21no—
70C4⋊C8×C61C2×C412yes—
71C22⋊C8×C61—21no—
72C4×C8×C61—21no—
73#95×C61D412yes—
74C23×D61—21no—
75C22×C4×C61—22no—
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C2×C22⋊D61—41no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83#11758222—41no—
84#11758222—41no—
85#11758222—41no—
86#11758222—41no—
87C2×D244—21no—
88C2×D244—21no—
89C2×D244—21no—
90C2×D244—21no—
91C2×D244—42no—
92C2×D244C22⋊C412yes—
93C2×C4×D61—22no—
94C2×C4×D61—22no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97C2×C4×D61—41no—
98C2×C4×D61—41no—
99C2×C4×D61—41no—
100C2×Dic122—21no—
101M16×C61—41no—
102M16×C61—41no—
103C2×C8×C61—22no—
104C2×C8×C61—41no—
105C4⋊C4×C61—42no—
106C42×C61—41no—
107C42×C61—41no—
108C42×C61C22×C411yescharacteristic
109C42×C61C2×D411yescharacteristic
110C42×C61#4111yescharacteristic
111C42×C61#4111yescharacteristic
112#11758198—22no—
113#11758198—22no—
114#11758198—44no—
115#11758198—44no—
116#11758198—41no—
117#11758198—41no—
118C4⋊Dic61—21no—
119C4⋊Dic61—21no—
120C4⋊Dic61—21no—
121C4⋊Dic61C22⋊C412yes—
122#11758196—44no—
123C4×Dic61—21no—
124C4×Dic61—21no—
125C4×Dic61—21no—
126C4×Dic61—42no—
127C4×Dic61—42no—
128C4×Dic61D812yescomplemented
129C2×#92418—41no—
130D488—44no—
131C23×C61#12011yescharacteristic
132C22×D61—22no—
133C22×D61—42no—
134C22×D61—42no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—41no—
138C2×C4×C61—22no—
139C2×C4×C61—41no—
140C2×C4×C61—42no—
141C2×C4×C61—42no—
142C2×C4×C61—42no—
143C2×C4×C61C2×C22⋊C411yescharacteristic
144C2×C4×C61C4×D411yescharacteristic
145C2×C4×C61C4×D411yescharacteristic
146C2×C4×C61#12111yescharacteristic
147C2×C4×C61#12111yescharacteristic
148C2×C4×C61#12311yescharacteristic
149C2×C4×C61C2×D811yescharacteristic
150C2×C4×C61#13511yescharacteristic
151C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
153C22⋊D61—81no—
154C22⋊D61—81no—
155C2×Dic61—22no—
156C2×Dic61—22no—
157C2×Dic61—22no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165D244—22no—
166D244—22no—
167D244—42no—
168D244—42no—
169D244—41no—
170D244—41no—
171D244—81no—
172C4×D61—42no—
173C4×D61—42no—
174C4×D61—42no—
175C4×D61—42no—
176C4×D61—81no—
177C4×D61—81no—
178Dic122—41no—
179Dic122—41no—
180C8×C61—42no—
181C8×C61—81no—
182#92418—81no—
183#9237—611nomaximal, Sylow
184C22×C61—21no—
185C22×C61—21no—
186C22×C61#38611yescharacteristic
187C22×C61#44711yescharacteristic
188C22×C61#44911yescharacteristic
189C2×D61—42no—
190C2×D61—42no—
191C2×D61—42no—
192C2×D61—82no—
193C2×D61—82no—
194C2×D61—81no—
195C2×D61—81no—
196C2×D61—81no—
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—82no—
201C4×C61#42112yes—
202C4×C61C4×D811yescharacteristic
203C4×C61#44211yescharacteristic
204C4×C61#45911yescharacteristic
205C4×C61#46311yescharacteristic
206Dic61—42no—
207Dic61—42no—
208Dic61—42no—
209Dic61—81no—
210#3100—611no—
211#2293—611no—
212#1962—611no—
213#1502—611no—
214#1486—611no—
215#1303D6111yescharacteristic, complemented
216#1276—611no—
217C2×C61—21no—
218C2×C61—21no—
219C2×C61#187911yescharacteristic
220C2×C61#189711yescharacteristic
221C2×C61#190611yescharacteristic
222D61—82no—
223D61—161no—
224#532—611no—
225C2×C4×D4—611no—
226C2×#117—1221no—
227#480—1221no—
228#474—612no—
229#459—612no—
230#447—1221no—
231C4×D8—1222no—
232#431—611no—
233#431C2×D6111yescharacteristic
234#423C2×D6111yescharacteristic
235C2×#104—1221no—
236C2×#104—1221no—
237#390—1221no—
238#389—1221no—
239#388—1222no—
240C4×C4⋊C4C2×D6111yescharacteristic
241C4×C22⋊C4—1221no—
242C43—611no—
243#327—1222no—
244D4⋊C8—1222no—
245C61#923711yescharacteristic, complemented, Sylow
246C2×#41—1221no—
247C22×D4—611no—
248C23×C4—1221no—
249C2×D8—1222no—
250C2×M16—21no—
251C4⋊Q8—611no—
252#127—611no—
253#124—1221no—
254#121—1221no—
255#121—1221no—
256C4×D4—612no—
257C4×D4—612no—
258C4×D4—1221no—
259C4×D4—1221no—
260C4×D4—1221no—
261C4×D4—1221no—
262#117—2442no—
263#117—2442no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—611no—
266C2×C4⋊C4—1222no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4—1222no—
269C2×C22⋊C4—1222no—
270C2×C42—21no—
271C2×C42—611no—
272C2×C42—611no—
273C2×C42—1221no—
274C2×C42—1221no—
275C2×C42C22×D6111yescharacteristic
276#107—1222no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8—1221no—
280C4⋊C8C4×D6112yes—
281#104—2442no—
282#104—2442no—
283#102—1222no—
284#102—1222no—
285C22⋊C8—21no—
286C22⋊C8—1221no—
287C4×C8—21no—
288C4×C8—1221no—
289#95—1222no—
290#95D24412yes—
291C24—1221no—
292#41—2441no—
293#41—2441no—
294#41—2441no—
295#41—2441no—
296C2×Q8—1221no—
297C2×D4—612no—
298C2×D4—1221no—
299C2×D4—1221no—
300C2×D4—1221no—
301C2×D4—1221no—
302C2×D4—2442no—
303C2×D4—2441no—
304C22×C4—22no—
305C22×C4—1221no—
306C22×C4—1221no—
307C22×C4—1221no—
308C22×C4—1222no—
309C22×C4—1222no—
310C22×C4—2441no—
311C22×C4—2441no—
312C22×C4—2441no—
313C22×C4—2441no—
314C22×C4—2441no—
315C22×C4C2×D24411yescharacteristic
316C22×C4D4×D6111yescharacteristic
317C22×C4D4×D6111yescharacteristic
318D8—2444no—
319M16—41no—
320M16—41no—
321C2×C8—22no—
322C2×C8—41no—
323C2×C8—2441no—
324C4⋊C4—42no—
325C4⋊C4—612no—
326C4⋊C4—1221no—
327C4⋊C4—1221no—
328C4⋊C4—1221no—
329C4⋊C4—2444no—
330C22⋊C4—1222no—
331C22⋊C4—1222no—
332C22⋊C4—2444no—
333C22⋊C4—2444no—
334C22⋊C4—2441no—
335C22⋊C4—2441no—
336C42—41no—
337C42—41no—
338C42—612no—
339C42—1221no—
340C42—1221no—
341C42—1221no—
342C42—2442no—
343C42—2442no—
344C42C2×C4×D6111yescharacteristic
345C42#1175822211yescharacteristic
346C42D4×D6111yescharacteristic
347C42#1175822611yescharacteristic
348C23—1222no—
349C23—2442no—
350C23—2442no—
351C23—2441no—
352C23—2441no—
353C23—2441no—
354C23#1451974711yescharacteristic
355Q8—2441no—
356Q8—2441no—
357D4—1222no—
358D4—1222no—
359D4—4881no—
360D4—4881no—
361D4—4881no—
362D4—2442no—
363D4—2442no—
364D4—2441no—
365D4—2441no—
366C2×C4—22no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—1222no—
372C2×C4—1222no—
373C2×C4—1222no—
374C2×C4—4881no—
375C2×C4—4881no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4—2442no—
384C2×C4—2442no—
385C2×C4—2442no—
386C2×C4—2442no—
387C2×C4C22⋊C4×D6111yescharacteristic
388C2×C4#1451973911yescharacteristic
389C2×C4C4×D24411yescharacteristic
390C2×C4#1451975011yescharacteristic
391C2×C4#1451975211yescharacteristic
392C2×C4#1451976211yescharacteristic
393C2×C4D8×D6111yescharacteristic
394C2×C4#1451980011yescharacteristic
395C2×C4#1451980411yescharacteristic
396C2×C4#1451980411yescharacteristic
397C8—42no—
398C8—81no—
399C8—4881no—
400C22—21no—
401C22—21no—
402C22—4882no—
403C22—4882no—
404C22—4881no—
405C22—4881no—
406C22—4881no—
407C22—2442no—
408C22—2442no—
409C22—2442no—
410C22#1683964011yescharacteristic
411C22#1683989711yescharacteristic
412C22#1683991011yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—82no—
417C4—4881no—
418C4—2442no—
419C4—2442no—
420C4—2442no—
421C4#1683977712yes—
422C4#1683984411yescharacteristic
423C4#1683987311yescharacteristic
424C4#1683995611yescharacteristic
425C4#1683998011yescharacteristic
426C2—21no—
427C2—21no—
428C2—9761no—
429C2—4882no—
430C2#2144616811yescharacteristic
431C2#2144626611yescharacteristic
432C2#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#9237
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. #21448280C2semidirect
3. #21446646C2semidirect
4. #21444313C2semidirect
5. #21444243C2semidirect
6. #21443651C2semidirect
7. C61×#1303C2semidirect
12. #16840043C4semidirect
13. #16839958C4semidirect
128. C4×Dic61D8semidirect
215. #1303D61semidirect
245. C61#9237semidirect

Maximal subgroups

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

subgroupindex
#214558202
#214482802
#214466462
#214443132
#214442432
#214436512
C61×#13032
#923761