Finite Group Databasebeta

← #29575265

Subgroups — #29575265

Order 15616.

690 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840110C211yesmaximal, characteristic
2#21448883C211yesmaximal, characteristic
3#21446743C211yesmaximal, characteristic, complemented
4C2×#16839505C211yesmaximal, characteristic
5#21443660C211yesmaximal, characteristic, complemented
6#21443658C211yesmaximal, characteristic, complemented
7C61×#1988C211yesmaximal, characteristic, complemented
8C2×#14519774C2211yescharacteristic
9C2×C4×D244—21no—
10C2×#14519739—21no—
11#16840110—22no—
12#16840110C414yescomplemented
13C2×C4⋊#92418C2211yescharacteristic
14C2×#14519701—21no—
15C2×#14519701—21no—
16C2×#14519697—22no—
17C2×C4×#92418C2211yescharacteristic
18#16839664—21no—
19#16839663—21no—
20#16839640—22no—
21C4×C4⋊Dic61C2211yescharacteristic
22#16839505—22no—
23C2×C4⋊Q8×C61C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C4×C4⋊C4×C61C2211yescharacteristic
26C61×#340—21no—
27C61×#340—21no—
28C22×D244—21no—
29C22×D244—21no—
30C22×D244D412yes—
31C22×C4×D61—22no—
32C22×#92418—21no—
33C22×#92418—21no—
34#14519774—21no—
35#14519774—21no—
36#14519774C2×C412yes—
37#14519774D412yes—
38C4×D244—42no—
39C4×D244—42no—
40#14519739—42no—
41#14519739—42no—
42C2×C4⋊Dic61D411yescharacteristic
43C2×C4⋊Dic61D411yescharacteristic
44C2×#11758198—22no—
45C2×#11758198—22no—
46C2×#11758198—22no—
47C2×C4×Dic61—21no—
48C4⋊#92418—21no—
49C4⋊#92418—21no—
50#14519701—42no—
51#14519701—42no—
52#14519697—28no—
53C4×#92418—21no—
54C4×#92418C2×C412yescomplemented
55#14519684—21no—
56C22×Q8×C61—21no—
57C22×C8×C61—21no—
58C4⋊Q8×C61—21no—
59C4⋊Q8×C61—21no—
60C4⋊Q8×C61—21no—
61C4⋊Q8×C61C2×C412yescomplemented
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61D411yescharacteristic
65C2×C4⋊C4×C61D411yescharacteristic
66C2×C42×C61—21no—
67C2×C42×C61C2311yescharacteristic
68C4⋊C8×C61—21no—
69C4⋊C8×C61—21no—
70#95×C61—21no—
71C23×D61—22no—
72C2×Q8×C61—22no—
73C2×Q8×C61—41no—
74C2×Q8×C61—41no—
75C2×Q8×C61—41no—
76C2×Q8×C61—41no—
77C2×Q8×C61—41no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—41no—
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×Dic61—21no—
85C22×Dic61—21no—
86C2×D244—22no—
87C2×D244—22no—
88C2×D244—22no—
89C2×D244—22no—
90C2×D244—22no—
91C2×D244—41no—
92C2×D244—41no—
93C2×D244—41no—
94C2×D244—41no—
95C2×D244—41no—
96C2×D244—41no—
97C2×D244—41no—
98C2×D244—41no—
99C2×D244—42no—
100C2×D244—42no—
101C2×D244C22⋊C414yes—
102C2×C4×D61—44no—
103C2×C4×D61—44no—
104C2×C4×D61—82no—
105C2×C8×C61—41no—
106C2×C8×C61—41no—
107C2×C8×C61—41no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—22no—
110C4⋊C4×C61—22no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61—21no—
113C4⋊C4×C61—41no—
114C4⋊C4×C61—41no—
115C4⋊C4×C61SD1612yes—
116C42×C61—41no—
117C42×C61—41no—
118C42×C61C22×C411yescharacteristic
119C42×C61C2×D411yescharacteristic
120C42×C61#4111yescharacteristic
121C42×C61#4111yescharacteristic
122#11758198—44no—
123#11758198—44no—
124#11758198—82no—
125C4⋊Dic61—21no—
126C4⋊Dic61—21no—
127C4⋊Dic61—21no—
128C4⋊Dic61D812yes—
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×C61#12011yescharacteristic
138C22×D61—24no—
139C22×D61—42no—
140C22×D61—42no—
141C22×D61—42no—
142C22×D61—42no—
143C22×D61—42no—
144C22×D61—42no—
145Q8×C61—42no—
146Q8×C61—42no—
147Q8×C61—81no—
148Q8×C61—81no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—22no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—42no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—81no—
159C2×C4×C61—81no—
160C2×C4×C61C2×C22⋊C411yescharacteristic
161C2×C4×C61C4×D411yescharacteristic
162C2×C4×C61C4×D411yescharacteristic
163C2×C4×C61#12111yescharacteristic
164C2×C4×C61#12111yescharacteristic
165C2×C4×C61#12311yescharacteristic
166C2×C4×C61C2×D811yescharacteristic
167C2×C4×C61C2×SD1611yescharacteristic
168C2×C4×C61#13511yescharacteristic
169C2×C4×C61#13511yescharacteristic
170C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C61#13711yescharacteristic
174C2×Dic61—22no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180D244—44no—
181D244—42no—
182D244—42no—
183D244—42no—
184D244—42no—
185D244—42no—
186D244—42no—
187D244—42no—
188D244—42no—
189D244—82no—
190C4×D61—88no—
191C8×C61—81no—
192#92418—42no—
193#92418—81no—
194#9057—611nomaximal, Sylow
195C22×C61#38611yescharacteristic
196C22×C61#44711yescharacteristic
197C22×C61#44911yescharacteristic
198C22×C61#45011yescharacteristic
199C22×C61#45211yescharacteristic
200C22×C61#45511yescharacteristic
201C22×C61#45511yescharacteristic
202C2×D61—44no—
203C2×D61—44no—
204C2×D61—44no—
205C2×D61—82no—
206C2×D61—82no—
207C2×D61—82no—
208C2×D61—82no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—42no—
212C4×C61—82no—
213C4×C61—81no—
214C4×C61C4×D811yescharacteristic
215C4×C61C4×SD1611yescharacteristic
216C4×C61#44011yescharacteristic
217C4×C61#44211yescharacteristic
218C4×C61#45911yescharacteristic
219C4×C61#46111yescharacteristic
220C4×C61#46311yescharacteristic
221C4×C61#46311yescharacteristic
222Dic61—42no—
223Dic61—81no—
224C2×#486—611no—
225#2366—611no—
226#1988D6111yescharacteristic, complemented
227#1981—611no—
228C2×#331—611no—
229#1279—611no—
230#1279—611no—
231C2×C61#163911yescharacteristic
232C2×C61#164011yescharacteristic
233C2×C61#164111yescharacteristic
234C2×C61#164211yescharacteristic
235C2×C61#187711yescharacteristic
236C2×C61#187911yescharacteristic
237C2×C61#188511yescharacteristic
238D61—84no—
239C2×C4⋊Q8C2×D6111yescharacteristic
240C2×#127—611no—
241C2×C4×D4—1221no—
242C2×C4×D4—1221no—
243#486—614no—
244#486—1222no—
245C2×C4⋊C8—611no—
246C2×C4⋊C8C2×D6111yescharacteristic
247C2×#103—1221no—
248C2×#103—1221no—
249C2×#102—1222no—
250C2×C4×C8—611no—
251#390—1221no—
252#390—1221no—
253#386—1222no—
254C4×C4⋊C4—611no—
255C4×C4⋊C4C2×D6111yescharacteristic
256#340—21no—
257#340—21no—
258#331—1222no—
259C61#905711yescharacteristic, complemented, Sylow
260C22×Q8—21no—
261C22×D4—612no—
262C22×D4—1221no—
263C22×D4—1221no—
264C23×C4—1222no—
265C22×C8—21no—
266C22×C8—1221no—
267C22×C8—1221no—
268C4⋊Q8—21no—
269C4⋊Q8—21no—
270C4⋊Q8—21no—
271C4⋊Q8C4×D6112yescomplemented
272#127—612no—
273#127—612no—
274#127—1221no—
275#127—1221no—
276C4×D4—2442no—
277C4×D4—2442no—
278C4×D4—2442no—
279C4×D4—2442no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—611no—
283C2×C4⋊C4—611no—
284C2×C4⋊C4C22⋊D6111yescharacteristic
285C2×C4⋊C4C22⋊D6111yescharacteristic
286C2×C22⋊C4—1222no—
287C2×C22⋊C4—1222no—
288C2×C22⋊C4—1222no—
289C2×C42—21no—
290C2×C42—1221no—
291C2×C42C22×D6111yescharacteristic
292C4⋊C8—21no—
293C4⋊C8—21no—
294C4⋊C8—1221no—
295C4⋊C8—1221no—
296#103—2442no—
297#103—2442no—
298#102—1228no—
299C4×C8—612no—
300C4×C8—1221no—
301#95—21no—
302#95—1221no—
303C24—1222no—
304C2×Q8—22no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×Q8—41no—
309C2×Q8—41no—
310C2×D4—614no—
311C2×D4—1222no—
312C2×D4—1222no—
313C2×D4—1222no—
314C2×D4—1222no—
315C2×D4—1222no—
316C2×D4—2442no—
317C2×D4—2442no—
318C2×D4—2441no—
319C2×D4—2441no—
320C2×D4—2441no—
321C2×D4—2441no—
322C2×D4—2441no—
323C2×D4—2441no—
324C2×D4—2441no—
325C2×D4—2441no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—41no—
329C22×C4—1221no—
330C22×C4—1221no—
331C22×C4—4882no—
332C22×C4—2444no—
333C22×C4—2444no—
334C22×C4D4×D6111yescharacteristic
335C22×C4D4×D6111yescharacteristic
336C22×C4C2×C22⋊D6111yescharacteristic
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—1222no—
341C2×C8—2441no—
342C2×C8—2441no—
343C2×C8—2441no—
344C2×C8—2441no—
345C2×C8—2441no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—21no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—612no—
354C4⋊C4—1221no—
355C4⋊C4—1221no—
356C4⋊C4—1221no—
357C4⋊C4#1175820112yes—
358C22⋊C4—4882no—
359C22⋊C4—2444no—
360C22⋊C4—2444no—
361C42—41no—
362C42—41no—
363C42—2441no—
364C42—2441no—
365C42C2×C4×D6111yescharacteristic
366C42#1175822211yescharacteristic
367C42D4×D6111yescharacteristic
368C42#1175822411yescharacteristic
369C23—1224no—
370C23—2442no—
371C23—2442no—
372C23—2442no—
373C23—2442no—
374C23—2442no—
375C23—2442no—
376C23#1451974511yescharacteristic
377Q8—42no—
378Q8—42no—
379Q8—81no—
380Q8—81no—
381D4—4882no—
382D4—2444no—
383D4—2442no—
384D4—2442no—
385D4—2442no—
386D4—2442no—
387D4—2442no—
388D4—2442no—
389D4—2442no—
390D4—2442no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—22no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—1222no—
403C2×C4—4888no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4C22⋊C4×D6111yescharacteristic
410C2×C4#1451973711yescharacteristic
411C2×C4C4×C22⋊D6111yescharacteristic
412C2×C4#1451974811yescharacteristic
413C2×C4#1451975011yescharacteristic
414C2×C4#1451975911yescharacteristic
415C2×C4D8×D6111yescharacteristic
416C2×C4C2×#1175820111yescharacteristic
417C2×C4#1451979711yescharacteristic
418C2×C4#1451979811yescharacteristic
419C2×C4#1451980111yescharacteristic
420C2×C4#1451980211yescharacteristic
421C2×C4#1451980411yescharacteristic
422C2×C4#1451980811yescharacteristic
423C8—81no—
424C8—4881no—
425C8—2442no—
426C22—4882no—
427C22—4882no—
428C22—4882no—
429C22—4882no—
430C22—2444no—
431C22—2444no—
432C22—2444no—
433C22#1683963811yescharacteristic
434C22#1683989411yescharacteristic
435C22#1683990611yescharacteristic
436C22#1683991211yescharacteristic
437C22#1683992211yescharacteristic
438C22#1683993811yescharacteristic
439C22#1683993811yescharacteristic
440C4—21no—
441C4—21no—
442C4—42no—
443C4—82no—
444C4—81no—
445C4—4881no—
446C4—2442no—
447C4#1683984211yescharacteristic
448C4C4×#1175820111yescharacteristic
449C4#1683986011yescharacteristic
450C4#1683987111yescharacteristic
451C4#1683995611yescharacteristic
452C4#1683996411yescharacteristic
453C4#1683997411yescharacteristic
454C4#1683997611yescharacteristic
455C2—4884no—
456C2#2144499711yescharacteristic
457C2#2144500411yescharacteristic
458C2#2144501111yescharacteristic
459C2#2144501811yescharacteristic
460C2#2144615611yescharacteristic
461C2#2144616411yescharacteristic
462C2#2144620411yescharacteristic
subgroupG/H
centerC23#14519745
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1988C2
socleC23×C61#120
prime radicalC2×#14519774C22
cosocleC2×C42×C61C23
hypercenter#1988D61
hypocenterC61#9057
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
3. #21446743C2semidirect
5. #21443660C2semidirect
6. #21443658C2semidirect
7. C61×#1988C2semidirect
12. #16840110C4semidirect
54. C4×#92418C2×C4semidirect
61. C4⋊Q8×C61C2×C4semidirect
226. #1988D61semidirect
259. C61#9057semidirect
271. C4⋊Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168401102
#214488832
#214467432
C2×#168395052
#214436602
#214436582
C61×#19882
#905761