Finite Group Databasebeta

← #29573372

Subgroups — #29573372

Order 15616.

540 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448223C211yesmaximal, characteristic
2#21445796C211yesmaximal, characteristic
3C4×#14519689C211yesmaximal, characteristic
4#21443660C211yesmaximal, characteristic, complemented
5#21443659C211yesmaximal, characteristic, complemented
6#21443658C211yesmaximal, characteristic, complemented
7C61×#1279C211yesmaximal, characteristic, complemented
8C2×#14519734—21no—
9C2×C42×D61C2211yescharacteristic
10C2×C4⋊#92418C2211yescharacteristic
11C2×#14519689—21no—
12C2×#14519689—21no—
13C2×C4×#92418C2211yescharacteristic
14#16839631C411yescharacteristic
15#16839631C411yescharacteristic
16#16839626—21no—
17#16839621—21no—
18#16839619C411yescharacteristic
19#16839619C411yescharacteristic
20C4×#11758196—21no—
21C4×C4⋊Dic61C2211yescharacteristic
22#16839516—21no—
23#16839516—21no—
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×C4×C8×C61C2211yescharacteristic
26C4×C4⋊C4×C61C2211yescharacteristic
27C22×C4×D61C2×C411yescharacteristic
28C22×C4×D61D411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C22×#92418—21no—
31C22×#92418—21no—
32#14519734—42no—
33#14519734—42no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×C4×Dic61—21no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C42×D61—21no—
47C42×D61—21no—
48C42×D61—21no—
49C42×D61—21no—
50C4⋊#92418—21no—
51C4⋊#92418—21no—
52#14519689—24no—
53#14519689—42no—
54C4×#92418—21no—
55C4×#92418—21no—
56#14519684—21no—
57#14519684—21no—
58#14519684—21no—
59C22×C8×C61—21no—
60C22×C8×C61—21no—
61C2×C4⋊C4×C61C2×C411yescharacteristic
62C2×C4⋊C4×C61C2×C411yescharacteristic
63C2×C42×C61—21no—
64C2×C42×C61C2311yescharacteristic
65C4⋊C8×C61—21no—
66C4⋊C8×C61—21no—
67C4×C8×C61—21no—
68C4×C8×C61—21no—
69#95×C61—21no—
70C23×D61C22⋊C411yescharacteristic
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61C22×C411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C22⋊C411yescharacteristic
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61—22no—
94C2×C4×D61—41no—
95C2×C4×D61D812yes—
96C2×C4×D61SD1612yes—
97C2×C8×C61—22no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C2×C8×C61—41no—
101C2×C8×C61—41no—
102C2×C8×C61—41no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—21no—
107C42×C61—41no—
108C42×C61—41no—
109C42×C61#4111yescharacteristic
110C42×C61#4111yescharacteristic
111C42×C61#4111yescharacteristic
112C42×C61#4111yescharacteristic
113#11758198—42no—
114#11758198—42no—
115C4⋊Dic61—21no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118C4⋊Dic61—21no—
119#11758196—42no—
120#11758196—42no—
121#11758196—42no—
122#11758196—42no—
123C4×Dic61—21no—
124C4×Dic61—21no—
125C4×Dic61—21no—
126C4×Dic61—21no—
127C4×Dic61—21no—
128C4×Dic61—21no—
129C4×Dic61—41no—
130C4×Dic61—41no—
131C2×#92418—22no—
132C2×#92418—41no—
133C2×#92418—41no—
134C2×#92418—41no—
135C2×#92418—41no—
136C2×#92418—41no—
137C23×C61C2×C22⋊C411yescharacteristic
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—21no—
143C22×D61—21no—
144C22×D61#10212yes—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61#11711yescharacteristic
154C2×C4×C61#11711yescharacteristic
155C2×C4×C61#12311yescharacteristic
156C2×C4×C61#12311yescharacteristic
157C2×C4×C61#12311yescharacteristic
158C2×C4×C61#12311yescharacteristic
159C2×C4×C61#13111yescharacteristic
160C2×C4×C61#13111yescharacteristic
161C2×C4×C61#13111yescharacteristic
162C2×C4×C61#13111yescharacteristic
163C2×C4×C61C2×D811yescharacteristic
164C2×C4×C61C2×SD1611yescharacteristic
165C2×C4×C61#13711yescharacteristic
166C2×C4×C61#13711yescharacteristic
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—21no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61#10212yes—
181C2×Dic61#10412yes—
182C4×D61—22no—
183C4×D61—22no—
184C4×D61—22no—
185C4×D61—22no—
186C4×D61—42no—
187C4×D61—42no—
188C4×D61—41no—
189C4×D61—41no—
190C4×D61—41no—
191C4×D61—41no—
192C8×C61—42no—
193C8×C61—81no—
194#92418—42no—
195#92418—81no—
196#8709—611nomaximal, Sylow
197C22×C61#38111yescharacteristic
198C22×C61#40811yescharacteristic
199C22×C61#40811yescharacteristic
200C22×C61C2×#10211yescharacteristic
201C22×C61#41911yescharacteristic
202C22×C61C2×#10411yescharacteristic
203C22×C61#42111yescharacteristic
204C2×D61—22no—
205C2×D61—22no—
206C2×D61—22no—
207C2×D61—41no—
208C2×D61—41no—
209C2×D61—41no—
210C2×D61—41no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—81no—
214C4×C61—81no—
215C4×C61#43311yescharacteristic
216C4×C61#43311yescharacteristic
217C4×C61#43311yescharacteristic
218C4×C61#43311yescharacteristic
219C4×C61#48011yescharacteristic
220C4×C61#48011yescharacteristic
221C4×C61#48311yescharacteristic
222C4×C61#48311yescharacteristic
223Dic61—22no—
224Dic61—22no—
225Dic61—41no—
226Dic61—81no—
227Dic61—81no—
228#2285—611no—
229#1797—611no—
230C4×C22⋊C8—611no—
231#1279—611no—
232#1279—611no—
233#1279—611no—
234#1279D6111yescharacteristic, complemented
235C2×C61#148011yescharacteristic
236C2×C61#148511yescharacteristic
237C2×C61#149211yescharacteristic
238C2×C61#149711yescharacteristic
239C2×C61#181811yescharacteristic
240C2×C61#182311yescharacteristic
241C2×C61#182611yescharacteristic
242D61—42no—
243C2×#117—1221no—
244C22×C42—611no—
245C2×C4⋊C8—611no—
246C2×C4⋊C8C2×D6111yescharacteristic
247C2×C22⋊C8—1221no—
248C2×C22⋊C8—1221no—
249C2×C4×C8—611no—
250C2×C4×C8C2×D6111yescharacteristic
251#384—611no—
252#384—611no—
253#382—1221no—
254#380—611no—
255#380—611no—
256#380—1221no—
257C4×C4⋊C4—611no—
258C4×C4⋊C4—1221no—
259C4×C4⋊C4C2×D6111yescharacteristic
260#336—1221no—
261#336—1221no—
262C61#870911yescharacteristic, complemented, Sylow
263C23×C4—611no—
264C23×C4—611no—
265C23×C4—611no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—1221no—
269C22×C8—1221no—
270#117—2442no—
271#117—2442no—
272C2×C4⋊C4—611no—
273C2×C4⋊C4—611no—
274C2×C4⋊C4—1221no—
275C2×C4⋊C4—1221no—
276C2×C4⋊C4—1221no—
277C2×C4⋊C4—1221no—
278C2×C4⋊C4C4×D6111yescharacteristic
279C2×C4⋊C4C4×D6111yescharacteristic
280C2×C22⋊C4—1221no—
281C2×C22⋊C4—1221no—
282C2×C42—21no—
283C2×C42—611no—
284C2×C42—611no—
285C2×C42—611no—
286C2×C42—1221no—
287C2×C42—1221no—
288C2×C42—1221no—
289C2×C42—1221no—
290C2×C42—1221no—
291C2×C42C22×D6111yescharacteristic
292C4⋊C8—21no—
293C4⋊C8—21no—
294C4⋊C8—1221no—
295C4⋊C8—1221no—
296C22⋊C8—1224no—
297C22⋊C8—2442no—
298C4×C8—21no—
299C4×C8—21no—
300C4×C8—1221no—
301C4×C8—1221no—
302#95—21no—
303#95—1221no—
304#95—1221no—
305#95—1221no—
306C24—611no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—611no—
310C22×C4—611no—
311C22×C4—612no—
312C22×C4—612no—
313C22×C4—611no—
314C22×C4—1222no—
315C22×C4—1221no—
316C22×C4—1221no—
317C22×C4—1221no—
318C22×C4—1221no—
319C22×C4—1221no—
320C22×C4—1221no—
321C22×C4—1221no—
322C22×C4—1221no—
323C22×C4—1221no—
324C22×C4—1221no—
325C22×C4—1221no—
326C22×C4—1221no—
327C22×C4—1221no—
328C22×C4—1221no—
329C22×C4—2441no—
330C22×C4C2×C4×D6111yescharacteristic
331C22×C4D4×D6111yescharacteristic
332C22×C4D4×D6111yescharacteristic
333C2×C8—22no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—1222no—
340C2×C8—2441no—
341C2×C8—2441no—
342C2×C8—2441no—
343C2×C8—2441no—
344C2×C8—2441no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—1221no—
350C4⋊C4—1221no—
351C4⋊C4—1221no—
352C4⋊C4—1221no—
353C4⋊C4—2442no—
354C4⋊C4—2442no—
355C4⋊C4—2442no—
356C4⋊C4—2442no—
357C22⋊C4—2442no—
358C22⋊C4—2442no—
359C42—41no—
360C42—41no—
361C42—1221no—
362C42—1221no—
363C42—1221no—
364C42—1221no—
365C42—1221no—
366C42—1221no—
367C42—2441no—
368C42—2441no—
369C42#1175822211yescharacteristic
370C42#1175822211yescharacteristic
371C42#1175822411yescharacteristic
372C42#1175822611yescharacteristic
373C23—612no—
374C23—1221no—
375C23—1221no—
376C23—1221no—
377C23—1221no—
378C23—1221no—
379C23—1221no—
380C23C22⋊C4×D6111yescharacteristic
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—612no—
390C2×C4—612no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—1221no—
394C2×C4—1221no—
395C2×C4—1222no—
396C2×C4—1222no—
397C2×C4—1222no—
398C2×C4—1222no—
399C2×C4—1221no—
400C2×C4—1221no—
401C2×C4—1221no—
402C2×C4—2442no—
403C2×C4—2442no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4—2441no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4—2441no—
413C2×C4—2441no—
414C2×C4#1451973411yescharacteristic
415C2×C4#1451973511yescharacteristic
416C2×C4#1451975911yescharacteristic
417C2×C4#1451975911yescharacteristic
418C2×C4#1451976211yescharacteristic
419C2×C4#1451976211yescharacteristic
420C2×C4#1451978311yescharacteristic
421C2×C4#1451978311yescharacteristic
422C2×C4#1451978511yescharacteristic
423C2×C4#1451978511yescharacteristic
424C2×C4D8×D6111yescharacteristic
425C2×C4SD16×D6111yescharacteristic
426C2×C4#1451980611yescharacteristic
427C2×C4#1451980911yescharacteristic
428C8—42no—
429C8—81no—
430C8—4881no—
431C8—2442no—
432C22—1222no—
433C22—1222no—
434C22—1222no—
435C22—2441no—
436C22—2441no—
437C22—2441no—
438C22—2441no—
439C22#1683962411yescharacteristic
440C22#1683972711yescharacteristic
441C22#1683972711yescharacteristic
442C22#102×D6111yescharacteristic
443C22#1683976911yescharacteristic
444C22#104×D6111yescharacteristic
445C22#1683977711yescharacteristic
446C4—21no—
447C4—21no—
448C4—81no—
449C4—81no—
450C4—1222no—
451C4—1222no—
452C4—4881no—
453C4—4881no—
454C4—2441no—
455C4#1683982111yescharacteristic
456C4#1683982211yescharacteristic
457C4#1683982211yescharacteristic
458C4#1683982411yescharacteristic
459C4#1684007411yescharacteristic
460C4#1684007711yescharacteristic
461C4#1684009111yescharacteristic
462C4#1684009411yescharacteristic
463C2—2442no—
464C2#2144421611yescharacteristic
465C2#2144423811yescharacteristic
466C2#2144426811yescharacteristic
467C2#2144429011yescharacteristic
468C2#2144588911yescharacteristic
469C2#2144590411yescharacteristic
470C2#2144591711yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1279C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1279D61
hypocenterC61#8709
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
4. #21443660C2semidirect
5. #21443659C2semidirect
6. #21443658C2semidirect
7. C61×#1279C2semidirect
234. #1279D61semidirect
262. C61#8709semidirect

Maximal subgroups

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

subgroupindex
#214482232
#214457962
C4×#145196892
#214436602
#214436592
#214436582
C61×#12792
#870961