Finite Group Databasebeta

← #29572725

Subgroups — #29572725

Order 15616.

548 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448280C211yesmaximal, characteristic
2#21445935C211yesmaximal, characteristic, complemented
3C4×#14519706C211yesmaximal, characteristic, complemented
4C2×#16839491C211yesmaximal, characteristic
5C2×#16839489C211yesmaximal, characteristic
6#21443660C211yesmaximal, characteristic, complemented
7C61×#1279C211yesmaximal, characteristic, complemented
8C2×C4×D244C2211yescharacteristic
9C2×#14519734—21no—
10C2×C4⋊#92418C2211yescharacteristic
11C2×#14519706—21no—
12C2×C4×#92418C2211yescharacteristic
13#16839663C411yescharacteristic
14#16839663C411yescharacteristic
15#16839658C411yescharacteristic
16#16839658C411yescharacteristic
17#16839651—21no—
18#16839651—21no—
19C4×#11758198—21no—
20C42×Dic61C2211yescharacteristic
21#16839516—21no—
22#16839516—21no—
23#16839516—21no—
24#16839491—22no—
25#16839489—22no—
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×C4×C8×C61C2211yescharacteristic
28C4×C4⋊C4×C61C2211yescharacteristic
29C22×D244C2×C411yescharacteristic
30C22×C4×D61—21no—
31C22×#92418—21no—
32C22×#92418—21no—
33C4×D244—21no—
34C4×D244—21no—
35C4×D244D412yes—
36C4×D244Q812yes—
37#14519734—42no—
38#14519734—42no—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×C4×Dic61C2×C411yescharacteristic
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C4⋊#92418—21no—
54C4⋊#92418—21no—
55#14519706—24no—
56C4×#92418—21no—
57C4×#92418—21no—
58#14519684—21no—
59#14519684—21no—
60C22×C8×C61—21no—
61C22×C8×C61—21no—
62C2×C4⋊C4×C61C2×C411yescharacteristic
63C2×C4⋊C4×C61C2×C411yescharacteristic
64C2×C42×C61—21no—
65C2×C42×C61C2311yescharacteristic
66C4⋊C8×C61—21no—
67C4⋊C8×C61—21no—
68C4×C8×C61—21no—
69C4×C8×C61—21no—
70#95×C61—21no—
71C23×D61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61C22×C411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×Dic61—21no—
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C2×D244—21no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244—21no—
87C2×D244C4⋊C412yes—
88C2×C4×D61—22no—
89C2×C4×D61—22no—
90C2×C4×D61—41no—
91C2×C4×D61—41no—
92C2×C4×D61—41no—
93C2×C4×D61—41no—
94C2×C8×C61—22no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—21no—
104C42×C61—41no—
105C42×C61—41no—
106C42×C61C2×D411yescharacteristic
107C42×C61C2×Q811yescharacteristic
108C42×C61#4111yescharacteristic
109C42×C61#4111yescharacteristic
110#11758198—22no—
111#11758198—22no—
112#11758198—42no—
113#11758198—42no—
114#11758198—42no—
115#11758198—42no—
116C4⋊Dic61—21no—
117C4⋊Dic61C4⋊C412yes—
118#11758196—42no—
119#11758196—42no—
120C4×Dic61—21no—
121C4×Dic61—21no—
122C4×Dic61—21no—
123C4×Dic61—21no—
124C4×Dic61—21no—
125C4×Dic61—21no—
126C4×Dic61—21no—
127C4×Dic61—21no—
128C4×Dic61—22no—
129C4×Dic61—41no—
130C2×#92418—22no—
131C2×#92418—41no—
132C2×#92418—41no—
133C2×#92418—41no—
134C2×#92418—41no—
135C2×#92418—41no—
136C23×C61C2×C22⋊C411yescharacteristic
137C22×D61—22no—
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—41no—
141C22×D61—41no—
142C22×D61—41no—
143C22×D61—41no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61C2×C4⋊C411yescharacteristic
153C2×C4×C61#11711yescharacteristic
154C2×C4×C61#12111yescharacteristic
155C2×C4×C61#12111yescharacteristic
156C2×C4×C61C22⋊Q811yescharacteristic
157C2×C4×C61C22⋊Q811yescharacteristic
158C2×C4×C61#13111yescharacteristic
159C2×C4×C61#13111yescharacteristic
160C2×C4×C61#13111yescharacteristic
161C2×C4×C61#13111yescharacteristic
162C2×C4×C61#13511yescharacteristic
163C2×C4×C61#13511yescharacteristic
164C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—22no—
169C2×Dic61—21no—
170C2×Dic61—21no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—21no—
175C2×Dic61—21no—
176C2×Dic61—21no—
177C2×Dic61—21no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61#10412yes—
181D244—22no—
182D244—22no—
183D244—41no—
184D244—41no—
185C4×D61—42no—
186C4×D61—42no—
187C4×D61—42no—
188C4×D61—42no—
189C8×C61—42no—
190C8×C61—81no—
191#92418—42no—
192#92418—81no—
193#8569—611nomaximal, Sylow
194C22×C61#38011yescharacteristic
195C22×C61#40811yescharacteristic
196C22×C61#40811yescharacteristic
197C22×C61#41611yescharacteristic
198C22×C61#41811yescharacteristic
199C22×C61C2×#10411yescharacteristic
200C22×C61#42111yescharacteristic
201C2×D61—42no—
202C2×D61—42no—
203C2×D61—42no—
204C2×D61—81no—
205C2×D61—81no—
206C2×D61—81no—
207C2×D61—81no—
208C4×C61—21no—
209C4×C61—21no—
210C4×C61—81no—
211C4×C61—81no—
212C4×C61#42411yescharacteristic
213C4×C61#42411yescharacteristic
214C4×C61#43311yescharacteristic
215C4×C61#43311yescharacteristic
216C4×C61#46311yescharacteristic
217C4×C61#46311yescharacteristic
218C4×C61#47811yescharacteristic
219C4×C61#47811yescharacteristic
220Dic61—22no—
221Dic61—42no—
222Dic61—41no—
223Dic61—41no—
224Dic61—41no—
225#2293—611no—
226#1831—611no—
227C4×C4⋊C8—611no—
228C2×D4⋊C8—611no—
229C2×D4⋊C8—611no—
230#1279—611no—
231#1279D6111yescharacteristic, complemented
232C2×C61#148211yescharacteristic
233C2×C61#148411yescharacteristic
234C2×C61#149411yescharacteristic
235C2×C61#149611yescharacteristic
236C2×C61#179811yescharacteristic
237C2×C61#180411yescharacteristic
238C2×C61#180611yescharacteristic
239D61—82no—
240C2×C4×D4—611no—
241C2×#117—1221no—
242C2×C4⋊C8—611no—
243C2×C4⋊C8—1221no—
244C2×C4⋊C8C2×D6111yescharacteristic
245C2×C4×C8—611no—
246C2×C4×C8C2×D6111yescharacteristic
247#390—611no—
248#390—611no—
249#389—611no—
250#389—611no—
251#388—1221no—
252#388—1221no—
253C4×C4⋊C4C2×D6111yescharacteristic
254C4×C22⋊C4—1221no—
255C43—611no—
256#336—1221no—
257#336—1221no—
258#336—1221no—
259D4⋊C8—1222no—
260D4⋊C8—1222no—
261C61#856911yescharacteristic, complemented, Sylow
262C22×D4—611no—
263C23×C4—1221no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—1221no—
267C22×C8—1221no—
268C4×D4—612no—
269C4×D4—612no—
270C4×D4—1221no—
271C4×D4—1221no—
272#117—2442no—
273#117—2442no—
274C2×C4⋊C4—611no—
275C2×C4⋊C4—1221no—
276C2×C4⋊C4—1221no—
277C2×C4⋊C4C4×D6111yescharacteristic
278C2×C4⋊C4C4×D6111yescharacteristic
279C2×C22⋊C4—1221no—
280C2×C22⋊C4—1221no—
281C2×C22⋊C4—1221no—
282C2×C22⋊C4—1221no—
283C2×C22⋊C4—1221no—
284C2×C42—21no—
285C2×C42—611no—
286C2×C42—611no—
287C2×C42—611no—
288C2×C42—611no—
289C2×C42—611no—
290C2×C42—611no—
291C2×C42C22×D6111yescharacteristic
292C4⋊C8—21no—
293C4⋊C8—21no—
294C4⋊C8—1224no—
295C4⋊C8—1221no—
296C4⋊C8—1221no—
297C4×C8—21no—
298C4×C8—21no—
299C4×C8—1221no—
300C4×C8—1221no—
301#95—21no—
302#95—1221no—
303#95—1221no—
304C24—1221no—
305C2×D4—612no—
306C2×D4—1221no—
307C2×D4—1221no—
308C2×D4—1221no—
309C2×D4—1221no—
310C2×D4—1221no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—611no—
314C22×C4—611no—
315C22×C4—611no—
316C22×C4—611no—
317C22×C4—1221no—
318C22×C4—1222no—
319C22×C4—1222no—
320C22×C4—2441no—
321C22×C4—2441no—
322C22×C4—2441no—
323C22×C4—2441no—
324C22×C4C2×C4×D6111yescharacteristic
325C22×C4D4×D6111yescharacteristic
326C22×C4D4×D6111yescharacteristic
327C2×C8—22no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—1222no—
334C2×C8—2441no—
335C2×C8—2441no—
336C2×C8—2441no—
337C2×C8—2441no—
338C2×C8—2441no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—612no—
344C4⋊C4—1221no—
345C4⋊C4—2442no—
346C4⋊C4—2442no—
347C22⋊C4—1222no—
348C22⋊C4—1222no—
349C22⋊C4—2442no—
350C22⋊C4—2442no—
351C22⋊C4—2442no—
352C22⋊C4—2442no—
353C42—41no—
354C42—41no—
355C42—1222no—
356C42—1221no—
357C42—1221no—
358C42—1221no—
359C42—1221no—
360C42—1221no—
361C42—1221no—
362C42—1221no—
363C42—1221no—
364C42—2441no—
365C42#1175822211yescharacteristic
366C42#1175822211yescharacteristic
367C42D4×D6111yescharacteristic
368C42Q8×D6111yescharacteristic
369C23—1222no—
370C23—2441no—
371C23—2441no—
372C23—2441no—
373C23—2441no—
374C23—2441no—
375C23—2441no—
376C23C22⋊C4×D6111yescharacteristic
377D4—1222no—
378D4—1222no—
379D4—2441no—
380D4—2441no—
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—1221no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—1221no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—1221no—
397C2×C4—1221no—
398C2×C4—1221no—
399C2×C4—1221no—
400C2×C4—1221no—
401C2×C4—1222no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4—2442no—
405C2×C4—2442no—
406C2×C4—2442no—
407C2×C4—2442no—
408C2×C4C4⋊C4×D6111yescharacteristic
409C2×C4#1451973411yescharacteristic
410C2×C4#1451975011yescharacteristic
411C2×C4#1451975011yescharacteristic
412C2×C4#1451975511yescharacteristic
413C2×C4#1451975511yescharacteristic
414C2×C4#1451978311yescharacteristic
415C2×C4#1451978311yescharacteristic
416C2×C4#1451978511yescharacteristic
417C2×C4#1451978511yescharacteristic
418C2×C4#1451979811yescharacteristic
419C2×C4#1451980011yescharacteristic
420C2×C4#1451980111yescharacteristic
421C2×C4#1451980411yescharacteristic
422C8—42no—
423C8—81no—
424C8—4881no—
425C8—2442no—
426C22—4881no—
427C22—4881no—
428C22—4881no—
429C22—4881no—
430C22—2442no—
431C22—2442no—
432C22—2442no—
433C22#1683962111yescharacteristic
434C22#1683972711yescharacteristic
435C22#1683972711yescharacteristic
436C22#1683975711yescharacteristic
437C22#1683976511yescharacteristic
438C22#104×D6111yescharacteristic
439C22#1683977711yescharacteristic
440C4—21no—
441C4—21no—
442C4—81no—
443C4—81no—
444C4—1222no—
445C4—2441no—
446C4—2441no—
447C4—2441no—
448C4—2442no—
449C4#1683978711yescharacteristic
450C4#1683978711yescharacteristic
451C4#1683982111yescharacteristic
452C4#1683982411yescharacteristic
453C4#1683997611yescharacteristic
454C4#1683998011yescharacteristic
455C4#1684006111yescharacteristic
456C4#1684006511yescharacteristic
457C2—4882no—
458C2#2144422611yescharacteristic
459C2#2144423411yescharacteristic
460C2#2144427811yescharacteristic
461C2#2144428611yescharacteristic
462C2#2144580211yescharacteristic
463C2#2144582811yescharacteristic
464C2#2144583811yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1279C2
socleC23×C61C2×C22⋊C4
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1279D61
hypocenterC61#8569
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
2. #21445935C2semidirect
3. C4×#14519706C2semidirect
6. #21443660C2semidirect
7. C61×#1279C2semidirect
231. #1279D61semidirect
261. C61#8569semidirect

Maximal subgroups

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

subgroupindex
#214482802
#214459352
C4×#145197062
C2×#168394912
C2×#168394892
#214436602
C61×#12792
#856961