Finite Group Databasebeta

← #29571948

Subgroups — #29571948

Order 15616.

734 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459631C211yesmaximal, characteristic
2#21446767C211yesmaximal, characteristic, complemented
3#21445840C211yesmaximal, characteristic
4#21444509C211yesmaximal, characteristic, complemented
5#21444503C211yesmaximal, characteristic, complemented
6#21444207C211yesmaximal, characteristic
7C61×#1503C211yesmaximal, characteristic, complemented
8Q8×Dic122—21no—
9#16840490C412yescomplemented
10#16840472—21no—
11#16840470—22no—
12Q8×D244C412yescomplemented
13#16840425—22no—
14#16840392—22no—
15#16840390—21no—
16#16840317—21no—
17C2×#14519777C2211yescharacteristic
18C4⋊Q8×D61—21no—
19#16840242—21no—
20C4×#11758222C2211yescharacteristic
21#16839786C2211yescharacteristic
22C2×C4⋊#92418C2211yescharacteristic
23C2×#14519705—21no—
24#16839524—22no—
25#16839522—21no—
26#16839511—21no—
27#16839509—22no—
28#16839508—21no—
29#16839494—21no—
30#16839491—21no—
31C61×#533C2211yescharacteristic
32C61×#431C2211yescharacteristic
33C4×C4⋊C4×C61C2211yescharacteristic
34C61×#328—22no—
35C2×#11758222D411yescharacteristic
36C22×Dic122—21no—
37C2×Q8×D61—22no—
38C2×#11758194—21no—
39C22×#92418—21no—
40#14519777—21no—
41#14519777—21no—
42#14519777—22no—
43#14519777C2×C412yes—
44#14519777D412yes—
45#14519776—22no—
46#14519776—24no—
47#14519776—22no—
48#14519775—22no—
49#14519769—22no—
50#14519768—22no—
51#14519767—24no—
52#14519757—22no—
53#14519757—24no—
54#14519755—24no—
55#14519754—24no—
56#14519753—22no—
57Q8×Dic61—22no—
58C4×Dic122—22no—
59C4×Dic122C2×C411yescharacteristic
60C4×Dic122D411yescharacteristic
61#14519742—22no—
62C4×D244—22no—
63C4×D244C2×C411yescharacteristic
64C4×D244D411yescharacteristic
65C4×C22⋊D61—21no—
66C4×C22⋊D61—21no—
67#14519737—24no—
68#14519736D411yescharacteristic
69#14519735—22no—
70#14519734—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61D412yes—
73C4⋊C4×D61—22no—
74C4⋊C4×D61—22no—
75C42×D61—21no—
76C4⋊#92418—21no—
77C4⋊#92418—21no—
78C4⋊#92418—21no—
79C4⋊#92418—21no—
80#14519705—42no—
81C4⋊Q8×C61D411yescharacteristic
82C4⋊Q8×C61D411yescharacteristic
83#125×C61—21no—
84C22⋊Q8×C61—21no—
85C22⋊Q8×C61D412yes—
86C4×Q8×C61—21no—
87C4×Q8×C61C2×C412yes—
88#117×C61—21no—
89C2×C4⋊C4×C61—21no—
90C2×C42×C61—21no—
91C2×C42×C61C2311yescharacteristic
92C4⋊C8×C61—21no—
93C22⋊C8×C61—21no—
94C4×C8×C61—21no—
95#95×C61—21no—
96C2×Q8×C61—21no—
97C2×Q8×C61C22⋊C412yes—
98C22×C4×C61—41no—
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C2×C22⋊D61—21no—
103C22×Dic61—22no—
104Q8×D61—84no—
105#11758222—21no—
106#11758222—21no—
107#11758222SD1612yes—
108#11758222Q1612yes—
109C2×D244C22⋊C411yescharacteristic
110C2×C4×D61—21no—
111C2×C4×D61—21no—
112C2×C4×D61—21no—
113C2×C4×D61—24no—
114C2×Dic122—22no—
115C2×Dic122—24no—
116C2×Dic122—22no—
117C2×Dic122—82no—
118C2×Dic122C22⋊C411yescharacteristic
119C2×C8×C61—41no—
120C4⋊C4×C61—22no—
121C4⋊C4×C61—21no—
122C4⋊C4×C61—21no—
123C4⋊C4×C61—21no—
124C4⋊C4×C61—22no—
125C4⋊C4×C61—22no—
126C4⋊C4×C61—41no—
127C4⋊C4×C61C22⋊C412yes—
128C22⋊C4×C61—22no—
129C42×C61—22no—
130C42×C61—41no—
131C42×C61—41no—
132C42×C61C22×C411yescharacteristic
133C42×C61C2×D411yescharacteristic
134C42×C61C2×D411yescharacteristic
135C42×C61C2×D411yescharacteristic
136C22⋊Dic61—21no—
137#11758198—24no—
138#11758198—21no—
139#11758198—21no—
140C4⋊Dic61—24no—
141C4⋊Dic61—22no—
142C4⋊Dic61—22no—
143C4⋊Dic61—22no—
144C4⋊Dic61C22⋊C414yes—
145C4⋊Dic61C22⋊C411yescharacteristic
146C4⋊Dic61C22⋊C411yescharacteristic
147#11758196—24no—
148#11758196—24no—
149#11758196—24no—
150#11758196—21no—
151#11758196—21no—
152C4×Dic61—24no—
153C4×Dic61—21no—
154C4×Dic61—21no—
155C4×Dic61—21no—
156#11758194—41no—
157#11758194—41no—
158C2×#92418—42no—
159C2×#92418—41no—
160C2×#92418—41no—
161C23×C61#12011yescharacteristic
162C22×D61—21no—
163Q8×C61—42no—
164Q8×C61—41no—
165Q8×C61—41no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—22no—
169C2×C4×C61—22no—
170C2×C4×C61—41no—
171C2×C4×C61—42no—
172C2×C4×C61—81no—
173C2×C4×C61—81no—
174C2×C4×C61C2×C22⋊C411yescharacteristic
175C2×C4×C61C2×C22⋊C411yescharacteristic
176C2×C4×C61C2×C22⋊C411yescharacteristic
177C2×C4×C61#12011yescharacteristic
178C2×C4×C61#12011yescharacteristic
179C2×C4×C61#12011yescharacteristic
180C2×C4×C61C2×SD1611yescharacteristic
181C2×C4×C61C2×Q1611yescharacteristic
182C2×C4×C61#13711yescharacteristic
183C2×C4×C61#13711yescharacteristic
184C22⋊D61—22no—
185C22⋊D61—22no—
186C2×Dic61—21no—
187C2×Dic61—21no—
188C2×Dic61—21no—
189C2×Dic61—24no—
190C2×Dic61—82no—
191D244—21no—
192D244#10312yes—
193C4×D61—22no—
194C4×D61—22no—
195C4×D61—42no—
196C4×D61—41no—
197C4×D61—41no—
198C4×D61—84no—
199Dic122—21no—
200Dic122—44no—
201Dic122—82no—
202Dic122—84no—
203Dic122#10312yes—
204C8×C61—81no—
205#92418—81no—
206#92418—81no—
207#8424—611nomaximal, Sylow
208C22×C61—21no—
209C22×C61—21no—
210C22×C61#37911yescharacteristic
211C22×C61#44811yescharacteristic
212C22×C61#45111yescharacteristic
213C2×D61—22no—
214C2×D61—41no—
215C2×D61—41no—
216C4×C61—21no—
217C4×C61—21no—
218C4×C61—21no—
219C4×C61—42no—
220C4×C61—42no—
221C4×C61—82no—
222C4×C61C2×#10311yescharacteristic
223C4×C61#41911yescharacteristic
224C4×C61#44811yescharacteristic
225C4×C61#45111yescharacteristic
226C4×C61#45411yescharacteristic
227C4×C61#45611yescharacteristic
228Dic61—22no—
229Dic61—41no—
230Dic61—44no—
231Dic61—41no—
232#3503—611no—
233#1987—611no—
234#1806—611no—
235#1550—611no—
236#1549—611no—
237#1503D6111yescharacteristic, complemented
238#1477—611no—
239C2×C61—21no—
240C2×C61—21no—
241C2×C61#178711yescharacteristic
242C2×C61#179311yescharacteristic
243C2×C61#179511yescharacteristic
244D61—42no—
245Q82—1221no—
246#557—612no—
247#554—1222no—
248#554—1221no—
249D4×Q8—612no—
250D4×Q8—1222no—
251#544—1221no—
252#544—1222no—
253#533—1221no—
254#533C2×D6111yescharacteristic
255C2×C4⋊Q8—611no—
256C2×C4⋊Q8—1221no—
257#520—1221no—
258C4×#41—611no—
259#431C2×D6111yescharacteristic
260#423—611no—
261C2×C4⋊C8—611no—
262C2×#104—1221no—
263C4×C4⋊C4C2×D6111yescharacteristic
264#340—1222no—
265#339—1221no—
266#333—1221no—
267#332—1222no—
268#332—1221no—
269#328—22no—
270Q8⋊C8—1221no—
271D4⋊C8—1221no—
272C61#842411yescharacteristic, complemented, Sylow
273C2×#41—611no—
274C22×Q8—1222no—
275C22×Q8—1221no—
276C2×M16—1221no—
277C22×C8—1221no—
278C4⋊Q8—612no—
279C4⋊Q8—612no—
280C4⋊Q8—1222no—
281C4⋊Q8—1222no—
282C4⋊Q8—1222no—
283C4⋊Q8—1224no—
284C4⋊Q8—1222no—
285C4⋊Q8—1221no—
286C4⋊Q8—1221no—
287C4⋊Q8D24411yescharacteristic
288C4⋊Q8D24411yescharacteristic
289#125—21no—
290#125—1222no—
291#125—1224no—
292#125—1222no—
293C22⋊Q8—21no—
294C22⋊Q8—1224no—
295C22⋊Q8—1224no—
296C22⋊Q8—1224no—
297C22⋊Q8—1222no—
298C22⋊Q8—1222no—
299C22⋊Q8C22⋊D6112yes—
300C4×Q8—21no—
301C4×Q8—611no—
302C4×Q8—611no—
303C4×Q8—1222no—
304C4×Q8—1222no—
305C4×Q8—1222no—
306C4×Q8C4×D6112yes—
307C4×D4—611no—
308C4×D4—611no—
309C4×D4—1222no—
310C4×D4—1224no—
311C4×D4—1221no—
312C4×D4—1221no—
313#117—21no—
314#117—611no—
315#117—1222no—
316#117—1221no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—612no—
319C2×C4⋊C4—1222no—
320C2×C4⋊C4—1222no—
321C2×C4⋊C4—1221no—
322C2×C42—21no—
323C2×C42—1221no—
324C2×C42C22×D6111yescharacteristic
325C4⋊C8—21no—
326C4⋊C8—1221no—
327C4⋊C8—1221no—
328C4⋊C8—1221no—
329C4⋊C8—1221no—
330#104—2442no—
331C22⋊C8—21no—
332C4×C8—21no—
333#95—21no—
334#41—612no—
335#41—612no—
336#41—1221no—
337#41—1221no—
338C2×Q8—21no—
339C2×Q8—611no—
340C2×Q8—1224no—
341C2×Q8—1222no—
342C2×Q8—1222no—
343C2×Q8—4882no—
344C2×Q8—4884no—
345C2×Q8#1175819812yes—
346C2×D4—611no—
347C2×D4—1221no—
348C22×C4—41no—
349C22×C4—1224no—
350C22×C4—1221no—
351C22×C4—1222no—
352C22×C4—1221no—
353C22×C4—1221no—
354C22×C4D4×D6111yescharacteristic
355C22×C4D4×D6111yescharacteristic
356C22×C4C2×C22⋊D6111yescharacteristic
357M16—2441no—
358M16—2441no—
359C2×C8—41no—
360C2×C8—2442no—
361C2×C8—2441no—
362C2×C8—2441no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—41no—
370C4⋊C4—614no—
371C4⋊C4—611no—
372C4⋊C4—611no—
373C4⋊C4—1224no—
374C4⋊C4—1224no—
375C4⋊C4—1224no—
376C4⋊C4—1224no—
377C4⋊C4—1222no—
378C4⋊C4—1221no—
379C4⋊C4—1221no—
380C4⋊C4—1222no—
381C4⋊C4—1222no—
382C4⋊C4#1175819812yes—
383C22⋊C4—22no—
384C22⋊C4—1224no—
385C22⋊C4—1221no—
386C22⋊C4—1221no—
387C22⋊C4—1221no—
388C42—22no—
389C42—41no—
390C42—41no—
391C42—1224no—
392C42—1221no—
393C42—1221no—
394C42—1221no—
395C42C2×C4×D6111yescharacteristic
396C42C2×D24411yescharacteristic
397C42D4×D6111yescharacteristic
398C42D4×D6111yescharacteristic
399C23—1221no—
400C23#1451974511yescharacteristic
401Q8—42no—
402Q8—41no—
403Q8—41no—
404Q8—612no—
405Q8—1221no—
406Q8—4882no—
407Q8—4884no—
408Q8—2444no—
409D4—612no—
410D4—1222no—
411D4—1222no—
412D4—1221no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4—1221no—
422C2×C4—1222no—
423C2×C4—1222no—
424C2×C4—1221no—
425C2×C4—1221no—
426C2×C4—1224no—
427C2×C4—4884no—
428C2×C4—4882no—
429C2×C4—2442no—
430C2×C4—2441no—
431C2×C4—2441no—
432C2×C4C22⋊C4×D6111yescharacteristic
433C2×C4C22⋊C4×D6111yescharacteristic
434C2×C4C2×#1175819811yescharacteristic
435C2×C4#1451974511yescharacteristic
436C2×C4#1451974711yescharacteristic
437C2×C4#1451974711yescharacteristic
438C2×C4SD16×D6111yescharacteristic
439C2×C4Q16×D6111yescharacteristic
440C2×C4#1451980611yescharacteristic
441C2×C4#1451980911yescharacteristic
442C8—81no—
443C8—4881no—
444C8—4881no—
445C22—21no—
446C22—21no—
447C22—1222no—
448C22—2441no—
449C22—2441no—
450C22#1683961711yescharacteristic
451C22#1683989911yescharacteristic
452C22#1683991611yescharacteristic
453C4—21no—
454C4—21no—
455C4—21no—
456C4—42no—
457C4—42no—
458C4—82no—
459C4—1222no—
460C4—2441no—
461C4—2444no—
462C4—2441no—
463C4#103×D6111yescharacteristic
464C4#1683976911yescharacteristic
465C4#1683990211yescharacteristic
466C4#1683991911yescharacteristic
467C4#1683993611yescharacteristic
468C4#1683994611yescharacteristic
469C2—21no—
470C2—21no—
471C2—2442no—
472C2#2144575211yescharacteristic
473C2#2144577911yescharacteristic
474C2#2144578711yescharacteristic
subgroupG/H
centerC22#16839617
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1503C2
socleC22×C61#379
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenter#1503D61
hypocenterC61#8424
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
2. #21446767C2semidirect
4. #21444509C2semidirect
5. #21444503C2semidirect
7. C61×#1503C2semidirect
9. #16840490C4semidirect
12. Q8×D244C4semidirect
237. #1503D61semidirect
272. C61#8424semidirect

Maximal subgroups

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

subgroupindex
#214596312
#214467672
#214458402
#214445092
#214445032
#214442072
C61×#15032
#842461