Finite Group Databasebeta

← #29571441

Subgroups — #29571441

Order 15616.

748 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840377C211yesmaximal, characteristic
2#21444215C211yesmaximal, characteristic, complemented
3#21444213C211yesmaximal, characteristic, complemented
4#21444210C211yesmaximal, characteristic, complemented
5#21444131C211yesmaximal, characteristic, complemented
6#21444131C211yesmaximal, characteristic, complemented
7C61×#1478C211yesmaximal, characteristic, complemented
8#16840377—22no—
9#16840377—22no—
10#16840377—22no—
11#16840377—22no—
12C2×#14519776C411yescharacteristic
13C2×#14519770—21no—
14C2×#14519764C411yescharacteristic
15C2×#14519763—21no—
16C2×#14519760—21no—
17C2×#14519757C411yescharacteristic
18C2×#14519756—21no—
19C2×#14519748C411yescharacteristic
20C2×C4×Dic122C2211yescharacteristic
21C2×#14519734C2211yescharacteristic
22#16839815C2211yescharacteristic
23#16839815C2211yescharacteristic
24#16839494—22no—
25#16839492—22no—
26D4⋊#92418—22no—
27#16839487—21no—
28#16839487—21no—
29#16839485—21no—
30#16839485—21no—
31C2×C4×D4×C61C2211yescharacteristic
32C61×#431C2211yescharacteristic
33C61×#431C2211yescharacteristic
34C61×D4⋊C8—22no—
35C22×Dic122—21no—
36C22×Dic122C2×C411yescharacteristic
37C22×C22⋊D61—21no—
38C22×C4×D61C2×C411yescharacteristic
39#14519776—22no—
40#14519776—22no—
41#14519770—24no—
42#14519770—24no—
43#14519764—22no—
44#14519764—22no—
45#14519763—24no—
46#14519763—24no—
47#14519760—24no—
48#14519760—24no—
49#14519757—22no—
50#14519757—22no—
51#14519756—24no—
52#14519756—24no—
53#14519748—22no—
54#14519748—22no—
55C4×Dic122—21no—
56C4×Dic122—21no—
57C4×Dic122D412yes—
58C4×Dic122D412yes—
59#14519734—21no—
60#14519734—21no—
61#14519734—21no—
62#14519734—21no—
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61C2×C411yescharacteristic
65C2×#11758196—21no—
66C2×#11758196—21no—
67C2×#11758196D411yescharacteristic
68C2×#11758196D411yescharacteristic
69C2×C22⋊Dic61—21no—
70C2×C22⋊Dic61—21no—
71C2×C22⋊Dic61—21no—
72C2×#11758198—21no—
73C2×#11758198D411yescharacteristic
74C2×#11758198D411yescharacteristic
75C2×C4×Dic61—21no—
76C2×C4×Dic61C2×C411yescharacteristic
77C4⋊#92418—21no—
78C4⋊#92418—21no—
79C22⋊#92418—21no—
80C22⋊#92418—21no—
81C4×#92418—21no—
82C4×#92418—21no—
83C22×D4×C61C2×C411yescharacteristic
84C23×C4×C61—21no—
85C4×D4×C61—21no—
86C4×D4×C61—21no—
87C4×D4×C61D412yes—
88C4×D4×C61D412yes—
89C2×C4⋊C4×C61C2×C411yescharacteristic
90C2×C22⋊C4×C61—21no—
91C2×C42×C61C2311yescharacteristic
92C4⋊C8×C61—21no—
93C4⋊C8×C61—21no—
94C22⋊C8×C61—21no—
95C22⋊C8×C61—21no—
96C4×C8×C61—21no—
97C4×C8×C61—21no—
98C24×C61—21no—
99C23×D61C22⋊C411yescharacteristic
100C2×D4×C61—21no—
101C2×D4×C61—22no—
102C2×D4×C61—22no—
103C2×D4×C61C22⋊C412yes—
104C22×C4×C61—21no—
105C22×C4×C61—22no—
106C22×C4×C61—22no—
107C22×C4×C61—82no—
108C22×C4×C61C22×C411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C2×C22⋊D61—24no—
112C2×C22⋊D61—82no—
113C22×Dic61—21no—
114C22×Dic61—21no—
115C22×Dic61C22⋊C411yescharacteristic
116C22×Dic61C22⋊C411yescharacteristic
117C22×Dic61C22⋊C411yescharacteristic
118C2×C4×D61—21no—
119C2×C4×D61—21no—
120C2×C4×D61—22no—
121C2×C4×D61—22no—
122C2×Dic122—22no—
123C2×Dic122—22no—
124C2×Dic122—21no—
125C2×Dic122—24no—
126C2×Dic122—82no—
127C2×Dic122C22⋊C412yes—
128C2×C8×C61—41no—
129C2×C8×C61—41no—
130C4⋊C4×C61—21no—
131C4⋊C4×C61C22⋊C412yes—
132C22⋊C4×C61—22no—
133C22⋊C4×C61—22no—
134C42×C61C2×D411yescharacteristic
135C42×C61C2×D411yescharacteristic
136C42×C61C2×D411yescharacteristic
137C42×C61C2×D411yescharacteristic
138C22⋊Dic61—24no—
139C22⋊Dic61—24no—
140C22⋊Dic61—24no—
141#11758198—24no—
142#11758198—21no—
143#11758198—21no—
144#11758198—21no—
145#11758198—21no—
146C4⋊Dic61—24no—
147C4⋊Dic61—21no—
148C4⋊Dic61C22⋊C412yes—
149#11758196—24no—
150#11758196—22no—
151#11758196—22no—
152#11758196—21no—
153#11758196—21no—
154#11758196—21no—
155#11758196—21no—
156C4×Dic61—21no—
157C4×Dic61—21no—
158C4×Dic61—22no—
159C4×Dic61—22no—
160C2×#92418—41no—
161C2×#92418—41no—
162C23×C61—22no—
163C23×C61—42no—
164C23×C61—42no—
165C23×C61—42no—
166C23×C61C2×C22⋊C411yescharacteristic
167C22×D61—21no—
168C22×D61—22no—
169C22×D61—41no—
170C22×D61—41no—
171D4×C61—22no—
172D4×C61—22no—
173D4×C61—42no—
174C2×C4×C61—22no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—42no—
178C2×C4×C61—82no—
179C2×C4×C61—82no—
180C2×C4×C61C2×C22⋊C411yescharacteristic
181C2×C4×C61C2×C22⋊C411yescharacteristic
182C2×C4×C61#12011yescharacteristic
183C2×C4×C61#12011yescharacteristic
184C2×C4×C61#12011yescharacteristic
185C2×C4×C61#12011yescharacteristic
186C2×C4×C61#13112yes—
187C2×C4×C61#13112yes—
188C22⋊D61—84no—
189C2×Dic61—21no—
190C2×Dic61—22no—
191C2×Dic61—22no—
192C2×Dic61—21no—
193C2×Dic61—21no—
194C2×Dic61—22no—
195C2×Dic61—42no—
196C2×Dic61—42no—
197C2×Dic61—41no—
198C2×Dic61—41no—
199C4×D61—42no—
200C4×D61—41no—
201C4×D61—41no—
202Dic122—24no—
203Dic122—41no—
204Dic122—41no—
205Dic122—84no—
206C8×C61—81no—
207C8×C61—81no—
208#92418—81no—
209#92418—81no—
210#8325—611nomaximal, Sylow
211C22×C61—21no—
212C22×C61—21no—
213C22×C61—42no—
214C22×C61—42no—
215C22×C61—42no—
216C22×C61—84no—
217C22×C61#37911yescharacteristic
218C22×C61#40812yes—
219C2×D61—41no—
220C2×D61—41no—
221C2×D61—41no—
222C2×D61—82no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—21no—
226C4×C61—21no—
227C4×C61—42no—
228C4×C61#40812yes—
229C4×C61#40811yescharacteristic
230C4×C61#40811yescharacteristic
231Dic61—41no—
232Dic61—42no—
233Dic61—41no—
234Dic61—42no—
235Dic61—41no—
236C2×#542—611no—
237#1479—611no—
238#1479—611no—
239#1478—611no—
240#1478D6111yescharacteristic, complemented
241#1458—611no—
242#1458—611no—
243C2×C61—22no—
244C2×C61—82no—
245C2×C61#178011yescharacteristic
246C2×C61#179511yescharacteristic
247C2×C61#179611yescharacteristic
248D61—81no—
249#542—1222no—
250#542—1222no—
251#542—1222no—
252#542—1222no—
253C2×C4⋊Q8—611no—
254C2×#126—1221no—
255C2×#124—611no—
256C2×#124—1221no—
257C2×#123—1221no—
258C2×C22⋊Q8—611no—
259C2×C22⋊Q8—1221no—
260C2×#121—611no—
261C2×C4×Q8—611no—
262C2×C4×D4C2×D6111yescharacteristic
263C2×#117—611no—
264#431—611no—
265#431—611no—
266#431C2×D6111yescharacteristic
267#431C2×D6111yescharacteristic
268Q8⋊C8—1222no—
269Q8⋊C8—1222no—
270D4⋊C8—22no—
271D4⋊C8—1222no—
272#324—1221no—
273#324—1221no—
274#323—1221no—
275#323—1221no—
276C61#832511yescharacteristic, complemented, Sylow
277C22×Q8—611no—
278C22×Q8—1221no—
279C22×D4—1221no—
280C22×D4C4×D6111yescharacteristic
281C23×C4—21no—
282C23×C4—611no—
283C4⋊Q8—1222no—
284C4⋊Q8—1222no—
285#126—1224no—
286#126—1224no—
287#124—1224no—
288#124—1224no—
289#124—1222no—
290#124—1222no—
291#123—1224no—
292#123—1224no—
293C22⋊Q8—1222no—
294C22⋊Q8—1224no—
295C22⋊Q8—1224no—
296C22⋊Q8—1222no—
297#121—1222no—
298#121—1222no—
299C4×Q8—612no—
300C4×Q8—612no—
301C4×Q8—1221no—
302C4×Q8—1221no—
303C4×D4—21no—
304C4×D4—21no—
305C4×D4D24412yes—
306C4×D4C22⋊D6112yes—
307#117—1221no—
308#117—1221no—
309#117—1221no—
310#117—1221no—
311C2×C4⋊C4—611no—
312C2×C4⋊C4—611no—
313C2×C4⋊C4—611no—
314C2×C4⋊C4—1221no—
315C2×C4⋊C4—1221no—
316C2×C4⋊C4—1221no—
317C2×C4⋊C4C4×D6111yescharacteristic
318C2×C22⋊C4—21no—
319C2×C22⋊C4—611no—
320C2×C22⋊C4—611no—
321C2×C22⋊C4—1221no—
322C2×C22⋊C4—1221no—
323C2×C22⋊C4—1221no—
324C2×C22⋊C4—1221no—
325C2×C42—611no—
326C2×C42—1221no—
327C2×C42C22×D6111yescharacteristic
328C4⋊C8—21no—
329C4⋊C8—21no—
330C4⋊C8—1221no—
331C4⋊C8—1221no—
332C22⋊C8—21no—
333C22⋊C8—21no—
334C22⋊C8—1221no—
335C22⋊C8—1221no—
336C4×C8—21no—
337C4×C8—21no—
338C4×C8—1221no—
339C4×C8—1221no—
340C24—21no—
341C24—611no—
342C2×Q8—612no—
343C2×Q8—1224no—
344C2×Q8—1221no—
345C2×Q8—1222no—
346C2×Q8—1222no—
347C2×Q8—4882no—
348C2×D4—21no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—1224no—
352C2×D4—4882no—
353C2×D4#1175819812yes—
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—82no—
358C22×C4—611no—
359C22×C4—611no—
360C22×C4—611no—
361C22×C4—1221no—
362C22×C4—1221no—
363C22×C4—1221no—
364C22×C4—1221no—
365C22×C4—1222no—
366C22×C4—1222no—
367C22×C4C2×C4×D6111yescharacteristic
368C22×C4D4×D6111yescharacteristic
369C22×C4D4×D6111yescharacteristic
370C2×C8—41no—
371C2×C8—41no—
372C2×C8—2441no—
373C2×C8—2441no—
374C4⋊C4—21no—
375C4⋊C4—612no—
376C4⋊C4—1224no—
377C4⋊C4—1224no—
378C4⋊C4—1221no—
379C4⋊C4—1221no—
380C4⋊C4—1221no—
381C4⋊C4—1222no—
382C4⋊C4—1221no—
383C4⋊C4—1221no—
384C4⋊C4—1222no—
385C4⋊C4#1175819812yes—
386C22⋊C4—22no—
387C22⋊C4—22no—
388C22⋊C4—1224no—
389C22⋊C4—1224no—
390C22⋊C4—1224no—
391C22⋊C4—1224no—
392C22⋊C4—1221no—
393C22⋊C4—1221no—
394C22⋊C4—1221no—
395C22⋊C4—1221no—
396C42—1221no—
397C42—1221no—
398C42—1222no—
399C42—1222no—
400C42C2×D24411yescharacteristic
401C42D4×D6111yescharacteristic
402C42D4×D6111yescharacteristic
403C42C2×C22⋊D6111yescharacteristic
404C23—22no—
405C23—42no—
406C23—42no—
407C23—42no—
408C23—1222no—
409C23—1221no—
410C23—2441no—
411C23—2441no—
412C23C22⋊C4×D6111yescharacteristic
413Q8—1224no—
414Q8—4884no—
415Q8—2441no—
416Q8—2441no—
417D4—22no—
418D4—22no—
419D4—42no—
420D4—4884no—
421C2×C4—22no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—82no—
426C2×C4—82no—
427C2×C4—1222no—
428C2×C4—1221no—
429C2×C4—1222no—
430C2×C4—1221no—
431C2×C4—1222no—
432C2×C4—1221no—
433C2×C4—2442no—
434C2×C4—2442no—
435C2×C4—2442no—
436C2×C4—2441no—
437C2×C4—2441no—
438C2×C4—2441no—
439C2×C4—2441no—
440C2×C4C22⋊C4×D6111yescharacteristic
441C2×C4C2×#1175819811yescharacteristic
442C2×C4#1451974511yescharacteristic
443C2×C4#1451974511yescharacteristic
444C2×C4#1451974711yescharacteristic
445C2×C4#1451974711yescharacteristic
446C2×C4#1451978312yes—
447C2×C4#1451978512yes—
448C8—81no—
449C8—81no—
450C8—4881no—
451C8—4881no—
452C22—21no—
453C22—21no—
454C22—42no—
455C22—42no—
456C22—42no—
457C22—84no—
458C22—4882no—
459C22—2441no—
460C22—2441no—
461C22—2441no—
462C22#1683961711yescharacteristic
463C22#1683972712yes—
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—42no—
469C4—2441no—
470C4—2442no—
471C4—2442no—
472C4—2441no—
473C4—2441no—
474C4#1683972712yes—
475C4#1683972811yescharacteristic
476C4#1683973011yescharacteristic
477C2—22no—
478C2—82no—
479C2—4881no—
480C2#2144573011yescharacteristic
481C2#2144578611yescharacteristic
482C2#2144579311yescharacteristic
subgroupG/H
centerC22#16839617
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1478C2
socleC22×C61#379
prime radicalC2×#14519748C4
cosocleC2×C42×C61C23
hypercenter#1478D61
hypocenterC61#8325
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
2. #21444215C2semidirect
3. #21444213C2semidirect
4. #21444210C2semidirect
5. #21444131C2semidirect
6. #21444131C2semidirect
7. C61×#1478C2semidirect
240. #1478D61semidirect
276. C61#8325semidirect

Maximal subgroups

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

subgroupindex
C2×#168403772
#214442152
#214442132
#214442102
#214441312
C61×#14782
#832561