Finite Group Databasebeta

← #29732130

Subgroups — #29732130

Order 15616.

664 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456366C211yesmaximal, characteristic, complemented
2#21455612C211yesmaximal, characteristic
3C2×#16840053C211yesmaximal, characteristic
4#21447329C212yesmaximal, complemented
5#21447178C212yesmaximal
6#21446808C211yesmaximal, characteristic, complemented
7#21446599C212yesmaximal, complemented
8#21446595C211yesmaximal, characteristic, complemented
9#21446481C212yesmaximal
10C4×#14519693C211yesmaximal, characteristic
11C61×#2962C211yesmaximal, characteristic, complemented
12C2×#14519777C2211yescharacteristic
13C2×C4×D244C2211yescharacteristic
14#16840172—22no—
15#16840165—21no—
16#16840158—21no—
17#16840059—22no—
18#16840053—21no—
19#16840053—21no—
20#16840053—22no—
21#16840049—21no—
22#16840039—21no—
23C2×#14519713C2212yes—
24#16839805C2212yes—
25#16839805C2212yes—
26#16839805C2212yes—
27C2×#14519709C2212yes—
28#16839786C2211yescharacteristic
29#16839766C2212yes—
30C2×#14519699C2212yes—
31C2×#14519693C2211yescharacteristic
32C2×#14519693C2211yescharacteristic
33C4×#11758194C2211yescharacteristic
34#16839530C2212yes—
35#16839530C2212yes—
36#16839530C2211yescharacteristic
37#16839530C2211yescharacteristic
38#16839527C2212yes—
39C61×#533C2211yescharacteristic
40C61×#446—22no—
41C61×#446—21no—
42C8×Q8×C61—21no—
43C61×#424C2212yes—
44C2×C4⋊C8×C61C2211yescharacteristic
45C61×#405C2212yes—
46C4×M16×C61C2211yescharacteristic
47C22×Dic122—21no—
48C22×D244C2311yescharacteristic
49C22×C4×D61—21no—
50C2×#11758194C2312yes—
51C2×#11758194C2311yescharacteristic
52C2×#11758194C2311yescharacteristic
53#14519777—21no—
54#14519777—21no—
55#14519777—21no—
56#14519777—21no—
57C4×D244—21no—
58C4×D244—21no—
59C4×D244—21no—
60C4×D244—21no—
61C2×C4⋊Dic61—21no—
62C2×C4⋊Dic61C2311yescharacteristic
63C2×C4⋊Dic61C2312yes—
64C2×#11758198—21no—
65#14519713—24no—
66#14519710—22no—
67#14519710—22no—
68#14519710—22no—
69#14519709—22no—
70#14519709—22no—
71#14519708—22no—
72#14519708—22no—
73#14519708—22no—
74C4⋊#92418—21no—
75C4⋊#92418—21no—
76#14519699—22no—
77#14519699—22no—
78#14519697—22no—
79#14519697—22no—
80#14519693—22no—
81#14519693Q814yescomplemented
82#14519688—21no—
83C4×#92418—21no—
84C2×M16×C61C2311yescharacteristic
85C2×M16×C61C2311yescharacteristic
86C22×C8×C61C2312yes—
87C4⋊Q8×C61D411yescharacteristic
88C4⋊Q8×C61D411yescharacteristic
89#125×C61D412yes—
90C22⋊Q8×C61—21no—
91C22⋊Q8×C61—21no—
92C4×Q8×C61—21no—
93C4×Q8×C61—21no—
94#117×C61C2312yes—
95C2×C42×C61C2311yescharacteristic
96C4⋊C8×C61—22no—
97C4⋊C8×C61—22no—
98C4⋊C8×C61D411yescharacteristic
99C4⋊C8×C61D411yescharacteristic
100C4⋊C8×C61D412yes—
101#97×C61—22no—
102#97×C61—21no—
103C4×C8×C61—22no—
104C4×C8×C61—21no—
105C23×D61—21no—
106C2×Q8×C61—21no—
107C2×Q8×C61—21no—
108C22×C4×C61#4111yescharacteristic
109C22×C4×C61#4111yescharacteristic
110C22×C4×C61C2411yescharacteristic
111C22×Dic61—21no—
112C22×Dic61—22no—
113C2×D244—21no—
114C2×D244—21no—
115C2×D244—21no—
116C2×D244—21no—
117C2×D244—21no—
118C2×D244C2×Q812yes—
119C2×C4×D61—41no—
120C2×C4×D61—41no—
121C2×C4×D61—82no—
122C2×Dic122—41no—
123C2×Dic122—41no—
124C2×Dic122—82no—
125M16×C61—21no—
126M16×C61—21no—
127M16×C61—21no—
128M16×C61C2×Q812yes—
129C2×C8×C61—21no—
130C2×C8×C61—22no—
131C2×C8×C61—22no—
132C2×C8×C61—21no—
133C2×C8×C61C2×D412yes—
134C2×C8×C61C2×D412yes—
135C4⋊C4×C61—22no—
136C4⋊C4×C61—22no—
137C4⋊C4×C61—21no—
138C4⋊C4×C61—21no—
139C4⋊C4×C61C2×D412yes—
140C4⋊C4×C61C2×D412yes—
141C22⋊C4×C61—22no—
142C42×C61—22no—
143C42×C61C2×D411yescharacteristic
144C42×C61C2×D411yescharacteristic
145C42×C61C2×D411yescharacteristic
146C42×C61C2×D411yescharacteristic
147#11758198—41no—
148#11758198—41no—
149C4⋊Dic61—22no—
150C4⋊Dic61—21no—
151C4⋊Dic61—22no—
152C4⋊Dic61—21no—
153C4⋊Dic61—41no—
154C4⋊Dic61—41no—
155#11758194—21no—
156#11758194—21no—
157#11758194—22no—
158#11758194—22no—
159#11758194C2×Q812yes—
160#11758194#4112yes—
161C2×#92418—21no—
162C2×#92418—21no—
163C2×#92418—22no—
164C23×C61C2×#4111yescharacteristic
165C22×D61—22no—
166C22×D61—41no—
167C22×D61—41no—
168C22×D61—81no—
169C22×D61—81no—
170Q8×C61—42no—
171Q8×C61—81no—
172C2×C4×C61—22no—
173C2×C4×C61—22no—
174C2×C4×C61—22no—
175C2×C4×C61—41no—
176C2×C4×C61#12111yescharacteristic
177C2×C4×C61#12111yescharacteristic
178C2×C4×C61#12111yescharacteristic
179C2×C4×C61#12111yescharacteristic
180C2×C4×C61C22×D411yescharacteristic
181C2×C4×C61C22×D411yescharacteristic
182C2×C4×C61C22×Q811yescharacteristic
183C2×C4×C61C2×#4111yescharacteristic
184C2×C4×C612−1+411yescharacteristic
185C2×C4×C612−1+411yescharacteristic
186C2×Dic61—42no—
187C2×Dic61—41no—
188C2×Dic61—82no—
189C2×Dic61—81no—
190D244—22no—
191D244—22no—
192D244—41no—
193D244—41no—
194C4×D61—82no—
195C4×D61—82no—
196Dic122—82no—
197Dic122—82no—
198C8×C61—22no—
199C8×C61—22no—
200C8×C61—22no—
201C8×C61—41no—
202#92418—22no—
203#92418—22no—
204#92418—42no—
205#25490—611nomaximal, Sylow
206C22×C61—21no—
207C22×C61—21no—
208C22×C61C2×#12111yescharacteristic
209C22×C61#53311yescharacteristic
210C22×C61#54111yescharacteristic
211C2×D61—42no—
212C2×D61—82no—
213C2×D61—81no—
214C2×D61—81no—
215C2×D61—82no—
216C4×C61—21no—
217C4×C61—21no—
218C4×C61—21no—
219C4×C61—42no—
220C4×C61—42no—
221C4×C61#47112yes—
222C4×C61#54711yescharacteristic
223C4×C61#54811yescharacteristic
224C4×C61D4×Q811yescharacteristic
225C4×C61D4×Q811yescharacteristic
226Dic61—81no—
227Dic61—82no—
228#3165—611no—
229#3077—611no—
230C2×#476—611no—
231#2962D6111yescharacteristic, complemented
232#2090—612no—
233#2063—612no—
234#1997—611no—
235#1951—612no—
236#1950—611no—
237#1931—612no—
238C4×#100—611no—
239C2×C61—21no—
240C2×C61—21no—
241C2×C61#242911yescharacteristic
242C2×C61C2×#47111yescharacteristic
243C2×C61#306811yescharacteristic
244D61—82no—
245#533C2×D6111yescharacteristic
246C2×C4⋊Q8—611no—
247C2×C4×D4—611no—
248#501—1222no—
249#500—1221no—
250#498—1221no—
251#478—1222no—
252#476—1221no—
253#476—1221no—
254#476—1222no—
255#476—1221no—
256#474—1221no—
257#446—22no—
258#446—21no—
259C8×Q8—21no—
260C2×#108—612no—
261#428—612no—
262#428—612no—
263#428—612no—
264C2×#106—612no—
265#424C2×D6112yes—
266#423—611no—
267C2×C4⋊C8C2×D6111yescharacteristic
268#418—612no—
269C2×#102—612no—
270C2×#100—611no—
271C2×#100—611no—
272#405C2×D6112yes—
273C4×M16—611no—
274C4×M16C2×D6111yescharacteristic
275#343—612no—
276#343—611no—
277#343—612no—
278#343—611no—
279#341—612no—
280C61#2549011yescharacteristic, complemented, Sylow
281C22×Q8—1221no—
282C22×D4—611no—
283C23×C4—1221no—
284C2×M16—611no—
285C2×M16—611no—
286C2×M16—612no—
287C2×M16C22×D6111yescharacteristic
288C2×M16C22×D6111yescharacteristic
289C22×C8C22×D6112yes—
290C4⋊Q8—1221no—
291C4⋊Q8—1221no—
292C4⋊Q8—1221no—
293C4⋊Q8—1221no—
294C4⋊Q8D24411yescharacteristic
295C4⋊Q8D24411yescharacteristic
296#125D24412yes—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×D4—1221no—
302C4×D4—1221no—
303C4×D4—1221no—
304C4×D4—1221no—
305#117C22×D6112yes—
306C2×C4⋊C4—611no—
307C2×C4⋊C4—612no—
308C2×C4⋊C4—1221no—
309C2×C22⋊C4—1221no—
310C2×C42C22×D6111yescharacteristic
311#108—1224no—
312#107—1222no—
313#107—1222no—
314#107—1222no—
315#106—1222no—
316#106—1222no—
317#106—1222no—
318#106—1222no—
319#106—1222no—
320C4⋊C8—22no—
321C4⋊C8—22no—
322C4⋊C8—1221no—
323C4⋊C8—1221no—
324C4⋊C8C22⋊D6111yescharacteristic
325C4⋊C8C22⋊D6111yescharacteristic
326C4⋊C8C22⋊D6112yes—
327#102—1222no—
328#102—1222no—
329#102—1222no—
330#102—1222no—
331#100—614no—
332#100—1222no—
333#97—22no—
334#97—21no—
335#97—1221no—
336C4×C8—22no—
337C4×C8—21no—
338C4×C8—1221no—
339C24—1221no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—4882no—
343C2×Q8—2441no—
344C2×Q8—2441no—
345C2×D4—612no—
346C2×D4—1221no—
347C2×D4—1221no—
348C2×D4—1221no—
349C2×D4—1221no—
350C2×D4—1221no—
351C22×C4—1221no—
352C22×C4—1222no—
353C22×C4—4882no—
354C22×C4—2441no—
355C22×C4—2441no—
356C22×C4#1175822211yescharacteristic
357C22×C4#1175822211yescharacteristic
358C22×C4C23×D6111yescharacteristic
359M16—21no—
360M16—21no—
361M16—21no—
362M16—612no—
363M16—612no—
364M16—1221no—
365M16—1221no—
366M16—1222no—
367M16—1222no—
368M16Q8×D6112yes—
369C2×C8—21no—
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—21no—
373C2×C8—1221no—
374C2×C8—1221no—
375C2×C8—1222no—
376C2×C8C2×C22⋊D6112yes—
377C2×C8C2×C22⋊D6112yes—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—1222no—
383C4⋊C4—1221no—
384C4⋊C4—1221no—
385C4⋊C4—1222no—
386C4⋊C4—2441no—
387C4⋊C4—2441no—
388C4⋊C4C2×D24412yes—
389C4⋊C4C2×D24412yes—
390C22⋊C4—22no—
391C22⋊C4—2441no—
392C22⋊C4—2441no—
393C42—22no—
394C42C2×D24411yescharacteristic
395C42C2×D24411yescharacteristic
396C42C2×C22⋊D6111yescharacteristic
397C42C2×C22⋊D6111yescharacteristic
398C23—1222no—
399C23—4881no—
400C23—4881no—
401C23—2441no—
402C23—2441no—
403C23C2×#1175822211yescharacteristic
404Q8—42no—
405Q8—81no—
406Q8—4882no—
407Q8—4882no—
408D4—1222no—
409D4—1222no—
410D4—2441no—
411D4—2441no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—41no—
416C2×C4—4882no—
417C2×C4—4882no—
418C2×C4—4881no—
419C2×C4—4882no—
420C2×C4—2441no—
421C2×C4—2442no—
422C2×C4#1451975111yescharacteristic
423C2×C4#1451975111yescharacteristic
424C2×C4#1451975111yescharacteristic
425C2×C4#1451975111yescharacteristic
426C2×C4C22×C22⋊D6111yescharacteristic
427C2×C4C22×D24411yescharacteristic
428C2×C4C2×Q8×D6111yescharacteristic
429C2×C4#41×D6111yescharacteristic
430C2×C4#1451982411yescharacteristic
431C2×C4#1451982511yescharacteristic
432C8—22no—
433C8—22no—
434C8—22no—
435C8—41no—
436C8—1222no—
437C8—1222no—
438C8—2442no—
439C22—21no—
440C22—21no—
441C22—4882no—
442C22—4882no—
443C22—4881no—
444C22—4881no—
445C22—2442no—
446C22C2×#1451975111yescharacteristic
447C22#1684031611yescharacteristic
448C22#1684037011yescharacteristic
449C4—21no—
450C4—21no—
451C4—21no—
452C4—42no—
453C4—42no—
454C4—4881no—
455C4—4882no—
456C4#1684002512yes—
457C4#1684041111yescharacteristic
458C4#1684042411yescharacteristic
459C4Q8×C22⋊D6111yescharacteristic
460C4Q8×D24411yescharacteristic
461C2—21no—
462C2—21no—
463C2—4882no—
464C2#2144941211yescharacteristic
465C2C2×#1684002511yescharacteristic
466C2#2145554711yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2962C2
socleC22×C61C2×#121
prime radicalC22×D244C23
hypercenter#2962D61
hypocenterC61#25490
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2962

Complements

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

NH ≅ G/Ntype
1. #21456366C2semidirect
4. #21447329C2semidirect
6. #21446808C2semidirect
7. #21446599C2semidirect
8. #21446595C2semidirect
11. C61×#2962C2semidirect
81. #14519693Q8semidirect
231. #2962D61semidirect
280. C61#25490semidirect

Maximal subgroups

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

subgroupindex
#214563662
#214556122
C2×#168400532
#214473292
#214471782
#214468082
#214465992
#214465952
#214464812
C4×#145196932
C61×#29622
#2549061