Finite Group Databasebeta

← #29571709

Subgroups — #29571709

Order 15616.

780 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C2×#16840452C211yesmaximal, characteristic
2#21445906C212yesmaximal, complemented
3#21445807C211yesmaximal, characteristic
4#21444392C212yesmaximal, complemented
5C61×#1459C211yesmaximal, characteristic
6#16840452—24no—
7#16840452—24no—
8C2×#14519770—21no—
9C2×#14519769C411yescharacteristic, complemented
10C2×#14519767—21no—
11C2×#14519758—21no—
12C2×#14519756C411yescharacteristic, complemented
13C2×#14519756C2211yescharacteristic
14C2×C4×Dic122C411yescharacteristic, complemented
15C2×#14519736C411yescharacteristic, complemented
16C2×#14519733—21no—
17C22×C4⋊Dic61C2211yescharacteristic
18C2×#14519692—21no—
19#16839622C2212yes—
20#16839529—21no—
21#16839525—24no—
22#16839500—24no—
23C2×C4×D4×C61C2211yescharacteristic
24C2×C22⋊C8×C61C2212yes—
25C61×#324—21no—
26C61×#323—21no—
27C22×Dic122C2×C411yescharacteristic
28C23×Dic61—21no—
29#14519770—28no—
30#14519769—22no—
31#14519769—22no—
32#14519767—28no—
33#14519758—28no—
34#14519756—22no—
35#14519756—22no—
36#14519756—22no—
37#14519756D414yes—
38C4×Dic122—22no—
39C4×Dic122—22no—
40#14519736—22no—
41#14519736—22no—
42#14519733—28no—
43C2×C4⋊Dic61—22no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61—22no—
46C2×C4⋊Dic61C2×C411yescharacteristic
47C2×C4⋊Dic61C2×C411yescharacteristic
48C2×C4⋊Dic61C2×C411yescharacteristic
49C2×C4⋊Dic61D414yes—
50C2×#11758196—21no—
51C2×#11758196—21no—
52C2×#11758196—21no—
53C2×#11758196—21no—
54C2×#11758196—21no—
55C2×C22⋊Dic61—21no—
56C2×C22⋊Dic61—21no—
57C2×C22⋊Dic61—21no—
58C2×C22⋊Dic61—22no—
59C2×C4×Dic61—21no—
60C2×C4×Dic61—21no—
61#14519692—42no—
62#14519684—22no—
63C22×D4×C61D411yescharacteristic
64C23×C4×C61C2×C411yescharacteristic
65C23×C4×C61C2311yescharacteristic
66C22×C8×C61—22no—
67C4×D4×C61—22no—
68C4×D4×C61—22no—
69C2×C4⋊C4×C61D411yescharacteristic
70C2×C22⋊C4×C61D411yescharacteristic
71C2×C22⋊C4×C61D411yescharacteristic
72C2×C42×C61C2×C411yescharacteristic
73C22⋊C8×C61—22no—
74C22⋊C8×C61—22no—
75C24×C61C22⋊C411yescharacteristic
76C24×C61C2×D411yescharacteristic
77C2×D4×C61—22no—
78C2×D4×C61—22no—
79C2×D4×C61—21no—
80C2×D4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—42no—
84C22×C4×C61—42no—
85C22×C4×C61C22⋊C411yescharacteristic
86C22×C4×C61C22⋊C411yescharacteristic
87C22×C4×C61C22⋊C411yescharacteristic
88C22×C4×C61C22×C411yescharacteristic
89C22×C4×C61C2×D412yes—
90C22×C4×C61C2×D412yes—
91C22×C4×C61C2×D411yescharacteristic
92C22×Dic61—21no—
93C22×Dic61—21no—
94C22×Dic61—21no—
95C22×Dic61—21no—
96C22×Dic61—24no—
97C22×Dic61—42no—
98C22×Dic61—41no—
99C22×Dic61—41no—
100C22×Dic61—42no—
101C2×Dic122—21no—
102C2×Dic122—42no—
103C2×Dic122C22⋊C412yes—
104C2×C8×C61—44no—
105C2×C8×C61—42no—
106C4⋊C4×C61—22no—
107C22⋊C4×C61—22no—
108C22⋊C4×C61—22no—
109C42×C61—21no—
110C42×C61—21no—
111C22⋊Dic61—24no—
112C22⋊Dic61—24no—
113C22⋊Dic61—24no—
114C22⋊Dic61—42no—
115C22⋊Dic61—42no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118C4⋊Dic61—21no—
119C4⋊Dic61—24no—
120C4⋊Dic61—44no—
121C4⋊Dic61C22⋊C412yes—
122C4⋊Dic61C22⋊C412yes—
123C4⋊Dic61C22⋊C412yes—
124#11758196—24no—
125#11758196—24no—
126#11758196—24no—
127#11758196—24no—
128#11758196—24no—
129C4×Dic61—24no—
130C4×Dic61—24no—
131C23×C61—21no—
132C23×C61—21no—
133C23×C61—21no—
134C23×C61—41no—
135C23×C61—41no—
136C23×C61—41no—
137C23×C61—41no—
138C23×C61C2×C22⋊C411yescharacteristic
139C23×C61#12012yes—
140C23×C61#13512yes—
141C23×C61AGL(1,ℤ/8)11yescharacteristic
142C23×C61#13711yescharacteristic
143D4×C61—42no—
144D4×C61—42no—
145C2×C4×C61—24no—
146C2×C4×C61—22no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—41no—
153C2×C4×C61—42no—
154C2×C4×C61—42no—
155C2×C4×C61—42no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61C2×C22⋊C411yescharacteristic
159C2×C4×C61C2×C22⋊C411yescharacteristic
160C2×C4×C61#12012yes—
161C2×Dic61—22no—
162C2×Dic61—22no—
163C2×Dic61—22no—
164C2×Dic61—22no—
165C2×Dic61—42no—
166C2×Dic61—42no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—44no—
172C2×Dic61—44no—
173C2×Dic61—82no—
174C2×Dic61—82no—
175C2×Dic61—82no—
176Dic122—42no—
177Dic122—42no—
178C8×C61—82no—
179#8382—611nomaximal, Sylow
180C22×C61—21no—
181C22×C61—22no—
182C22×C61—21no—
183C22×C61—22no—
184C22×C61—42no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—41no—
188C22×C61—41no—
189C22×C61—41no—
190C22×C61—81no—
191C22×C61—81no—
192C22×C61#37911yescharacteristic
193C22×C61#41611yescharacteristic
194C22×C61#41711yescharacteristic
195C22×C61#44912yes—
196C22×C61#45212yes—
197C4×C61—22no—
198C4×C61—21no—
199C4×C61—41no—
200C4×C61—41no—
201C4×C61—41no—
202C4×C61#41012yes—
203Dic61—42no—
204Dic61—42no—
205Dic61—42no—
206Dic61—42no—
207Dic61—162no—
208C2×#552—611no—
209#1823—612no—
210#1799—611no—
211#1520—612no—
212#1459D6111yescharacteristic
213C2×C61—22no—
214C2×C61—21no—
215C2×C61—21no—
216C2×C61—22no—
217C2×C61—81no—
218C2×C61#178211yescharacteristic
219C2×C61#178811yescharacteristic
220C2×C61#179611yescharacteristic
221#552—1224no—
222#552—1224no—
223C2×#126—1221no—
224C2×#125—611no—
225C2×#125—1221no—
226C2×#123—1221no—
227C2×C22⋊Q8—611no—
228C2×C22⋊Q8—611no—
229C2×C4×Q8—611no—
230C2×C4×D4C2×D6111yescharacteristic
231C2×#117—611no—
232C2×#117—1221no—
233C22×C4⋊C4—611no—
234C2×#99—1221no—
235C2×C22⋊C8C2×D6112yes—
236#380—612no—
237#342—1221no—
238#340—1224no—
239#328—1224no—
240#324—21no—
241#323—21no—
242C61#838211yescharacteristic, complemented, Sylow
243C22×Q8—611no—
244C22×D4D24411yescharacteristic
245C23×C4—1221no—
246C23×C4C4×D6111yescharacteristic
247C23×C4C22×D6111yescharacteristic
248C22×C8—22no—
249#126—1228no—
250#125—1222no—
251#125—1222no—
252#125—1228no—
253#123—1228no—
254C22⋊Q8—614no—
255C22⋊Q8—1222no—
256C22⋊Q8—1222no—
257C22⋊Q8—1222no—
258C4×Q8—1222no—
259C4×Q8—1222no—
260C4×D4—22no—
261C4×D4—22no—
262#117—1228no—
263#117—1222no—
264#117—1222no—
265C2×C4⋊C4—611no—
266C2×C4⋊C4—611no—
267C2×C4⋊C4—611no—
268C2×C4⋊C4—614no—
269C2×C4⋊C4—1221no—
270C2×C4⋊C4—1221no—
271C2×C4⋊C4—1221no—
272C2×C4⋊C4—1221no—
273C2×C4⋊C4—1222no—
274C2×C4⋊C4—1221no—
275C2×C4⋊C4—1221no—
276C2×C4⋊C4—1222no—
277C2×C4⋊C4C22⋊D6111yescharacteristic
278C2×C22⋊C4—1221no—
279C2×C22⋊C4—1221no—
280C2×C22⋊C4—1221no—
281C2×C22⋊C4—1222no—
282C2×C22⋊C4D24411yescharacteristic
283C2×C22⋊C4C22⋊D6111yescharacteristic
284C2×C42—1221no—
285C2×C42—1221no—
286C2×C42C4×D6111yescharacteristic
287#99—2442no—
288C22⋊C8—22no—
289C22⋊C8—22no—
290#95—1222no—
291C24#1175819811yescharacteristic
292C24C2×D24411yescharacteristic
293C2×Q8—612no—
294C2×Q8—1221no—
295C2×Q8—2442no—
296C2×D4—21no—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4—1221no—
307C22×C4—1221no—
308C22×C4—1224no—
309C22×C4—2442no—
310C22×C4—2441no—
311C22×C4—2442no—
312C22×C4—2441no—
313C22×C4#1175819811yescharacteristic
314C22×C4#1175819811yescharacteristic
315C22×C4#1175819811yescharacteristic
316C22×C4C2×C4×D6111yescharacteristic
317C22×C4D4×D6112yes—
318C22×C4D4×D6112yes—
319C22×C4C2×C22⋊D6111yescharacteristic
320C2×C8—44no—
321C2×C8—42no—
322C4⋊C4—22no—
323C4⋊C4—612no—
324C4⋊C4—612no—
325C4⋊C4—612no—
326C4⋊C4—1224no—
327C4⋊C4—1224no—
328C4⋊C4—1224no—
329C4⋊C4—1224no—
330C4⋊C4—1221no—
331C4⋊C4—1221no—
332C4⋊C4—1221no—
333C4⋊C4—1224no—
334C4⋊C4—1224no—
335C4⋊C4—2444no—
336C22⋊C4—22no—
337C22⋊C4—22no—
338C22⋊C4—1224no—
339C22⋊C4—1224no—
340C22⋊C4—1224no—
341C22⋊C4—2442no—
342C22⋊C4—2442no—
343C42—21no—
344C42—21no—
345C42—1224no—
346C42—1224no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23C2×#1175819811yescharacteristic
355C23#1451974712yes—
356C23#1451979912yes—
357C23#1451980511yescharacteristic
358C23#1451981011yescharacteristic
359Q8—2442no—
360Q8—2442no—
361D4—42no—
362D4—42no—
363C2×C4—24no—
364C2×C4—22no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—1222no—
377C2×C4—1222no—
378C2×C4—1222no—
379C2×C4—1222no—
380C2×C4—4882no—
381C2×C4—4882no—
382C2×C4—4882no—
383C2×C4—2442no—
384C2×C4—2442no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4—2441no—
388C2×C4—2441no—
389C2×C4—2444no—
390C2×C4—2444no—
391C2×C4C22⋊C4×D6111yescharacteristic
392C2×C4C22⋊C4×D6111yescharacteristic
393C2×C4#1451974512yes—
394C8—82no—
395C22—21no—
396C22—22no—
397C22—21no—
398C22—22no—
399C22—41no—
400C22—42no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—81no—
406C22—81no—
407C22#1683961711yescharacteristic
408C22#1683975911yescharacteristic
409C22#1683976411yescharacteristic
410C22#1683990912yes—
411C22#1683992612yes—
412C4—22no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—41no—
417C4—9762no—
418C4—2442no—
419C4—2442no—
420C4—2442no—
421C4—2442no—
422C4#1683973412yes—
423C2—22no—
424C2—21no—
425C2—21no—
426C2—22no—
427C2—81no—
428C2#2144573511yescharacteristic
429C2#2144576011yescharacteristic
430C2#2144579511yescharacteristic
subgroupG/H
centerC22#16839617
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1459C2
socleC22×C61#379
prime radicalC22×D4×C61D4
cosocleC23×C4×C61C23
hypercenter#1459D61
hypocenterC61#8382
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
2. #21445906C2semidirect
4. #21444392C2semidirect
9. C2×#14519769C4semidirect
12. C2×#14519756C4semidirect
14. C2×C4×Dic122C4semidirect
15. C2×#14519736C4semidirect
242. C61#8382semidirect

Maximal subgroups

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

subgroupindex
C2×#168404522
#214459062
#214458072
#214443922
C61×#14592
#838261