Finite Group Databasebeta

← #29574897

Subgroups — #29574897

Order 15616.

530 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455268C211yesmaximal, characteristic
2#21454388C211yesmaximal, characteristic, complemented
3#21444218C211yesmaximal, characteristic, complemented
4#21444202C211yesmaximal, characteristic, complemented
5#21443714C211yesmaximal, characteristic, complemented
6#21443654C211yesmaximal, characteristic, complemented
7C61×#1492C211yesmaximal, characteristic, complemented
8C2×#14519797—21no—
9C2×#14519785—21no—
10C4×#11758222C2211yescharacteristic
11#16839981—21no—
12#16839974—21no—
13#16839969C411yescharacteristic
14#16839964C411yescharacteristic
15#16839959C411yescharacteristic
16#16839954C411yescharacteristic
17#16839815C2211yescharacteristic
18#16839790—21no—
19#16839787—22no—
20#16839784—21no—
21C2×C4⋊#92418C2211yescharacteristic
22C2×C4⋊#92418C2211yescharacteristic
23C4⋊C8×D61—21no—
24#16839758—21no—
25#16839494—21no—
26#16839491—21no—
27D4⋊#92418—21no—
28D4⋊#92418—21no—
29C61×#532C2211yescharacteristic
30C61×#423C2211yescharacteristic
31C2×C4×C8×C61C2211yescharacteristic
32C61×D4⋊C8—22no—
33C2×#11758222D411yescharacteristic
34#14519797—42no—
35#14519797—42no—
36C2×#11758202—21no—
37C2×#11758200—21no—
38C2×#11758201—21no—
39C2×#11758199—21no—
40#14519785—42no—
41#14519785—42no—
42C2×#11758189—22no—
43C22×#92418—21no—
44C22×#92418—21no—
45C2×C8×D61—22no—
46C4×Dic122C2×C411yescharacteristic
47C4×Dic122D411yescharacteristic
48C4×D244C2×C411yescharacteristic
49C4×D244D411yescharacteristic
50C4×C22⋊D61—21no—
51C4×C22⋊D61—21no—
52#14519736D411yescharacteristic
53#14519734—21no—
54C42×D61—21no—
55C4⋊#92418—21no—
56C4⋊#92418—21no—
57C4⋊#92418—21no—
58C4⋊#92418C2×C411yescharacteristic
59C4⋊#92418C2×C411yescharacteristic
60C4⋊#92418D411yescharacteristic
61C4⋊#92418D411yescharacteristic
62#14519706—22no—
63#14519706—22no—
64#14519701—21no—
65#14519701—21no—
66#14519698—21no—
67#14519698—21no—
68C22⋊#92418—21no—
69C4×#92418—21no—
70C2×#41×C61—21no—
71C2×M16×C61—21no—
72C22×C8×C61—21no—
73C4⋊Q8×C61C2×C411yescharacteristic
74#127×C61C2×C411yescharacteristic
75#124×C61—21no—
76#121×C61—21no—
77#121×C61—21no—
78C4×D4×C61—21no—
79C4×D4×C61—21no—
80C2×C42×C61C2311yescharacteristic
81C4⋊C8×C61—21no—
82C4⋊C8×C61D412yes—
83C4×C8×C61—21no—
84C4×C8×C61—21no—
85#41×C61—41no—
86#41×C61—41no—
87#41×C61—41no—
88#41×C61—41no—
89C2×Q8×C61—21no—
90C2×D4×C61—21no—
91C2×D4×C61—21no—
92C2×D4×C61—21no—
93C2×D4×C61—41no—
94C22×C4×C61—41no—
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61#4111yescharacteristic
97C22×C4×C61#4111yescharacteristic
98C2×C22⋊D61—21no—
99#11758222—21no—
100#11758222—21no—
101#11758222D812yes—
102#11758222SD1612yes—
103C2×D244C22⋊C411yescharacteristic
104C2×C4×D61—21no—
105C2×C4×D61—21no—
106C2×C4×D61—21no—
107C2×Dic122C22⋊C411yescharacteristic
108M16×C61—41no—
109M16×C61—41no—
110C2×C8×C61—22no—
111C2×C8×C61—22no—
112C2×C8×C61—41no—
113C2×C8×C61—41no—
114C4⋊C4×C61—21no—
115C4⋊C4×C61—21no—
116C22⋊C4×C61—41no—
117C22⋊C4×C61—41no—
118C42×C61C22×C411yescharacteristic
119C42×C61C2×D411yescharacteristic
120C42×C61C2×D411yescharacteristic
121C42×C61C2×D411yescharacteristic
122C22⋊Dic61—21no—
123#11758202—42no—
124#11758201—42no—
125#11758200—42no—
126#11758199—42no—
127#11758198—21no—
128#11758198—21no—
129C4⋊Dic61C22⋊C411yescharacteristic
130C4⋊Dic61C22⋊C411yescharacteristic
131#11758196—21no—
132#11758196—21no—
133C4×Dic61—21no—
134C4×Dic61—21no—
135C4×Dic61—21no—
136C2×#92418—21no—
137C2×#92418—21no—
138C2×#92418—21no—
139C2×#92418—21no—
140C2×#92418—41no—
141C2×#92418—41no—
142C2×#92418—41no—
143C2×#92418—41no—
144C2×#92418—41no—
145#11758189—44no—
146C8×D61—44no—
147C23×C61—41no—
148C23×C61#12311yescharacteristic
149C22×D61—21no—
150Q8×C61—41no—
151Q8×C61—41no—
152D4×C61—42no—
153D4×C61—41no—
154D4×C61—41no—
155D4×C61—41no—
156D4×C61—41no—
157D4×C61—81no—
158D4×C61—81no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—81no—
164C2×C4×C61—81no—
165C2×C4×C61C2×C22⋊C411yescharacteristic
166C2×C4×C61C4×D411yescharacteristic
167C2×C4×C61C4×D411yescharacteristic
168C2×C4×C61#12011yescharacteristic
169C2×C4×C61#12111yescharacteristic
170C2×C4×C61#12111yescharacteristic
171C2×C4×C61C2×D811yescharacteristic
172C2×C4×C61C2×SD1611yescharacteristic
173C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C61#13711yescharacteristic
175C22⋊D61—22no—
176C22⋊D61—22no—
177C2×Dic61—21no—
178C2×Dic61—21no—
179C2×Dic61—21no—
180D244—21no—
181D244#10212yes—
182C4×D61—22no—
183C4×D61—22no—
184C4×D61—41no—
185C4×D61—41no—
186C4×D61—81no—
187Dic122—21no—
188Dic122#10212yes—
189C8×C61—42no—
190C8×C61—42no—
191#92418—41no—
192#92418—41no—
193#92418—41no—
194#92418—41no—
195#92418—81no—
196#8995—611nomaximal, Sylow
197C22×C61—21no—
198C22×C61—21no—
199C22×C61—81no—
200C22×C61—81no—
201C22×C61—81no—
202C22×C61#38611yescharacteristic
203C22×C61#48011yescharacteristic
204C22×C61#48111yescharacteristic
205C2×D61—22no—
206C2×D61—41no—
207C2×D61—41no—
208C4×C61—21no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—81no—
212C4×C61C2×#10211yescharacteristic
213C4×C61#41711yescharacteristic
214C4×C61#44311yescharacteristic
215C4×C61#44411yescharacteristic
216C4×C61#44711yescharacteristic
217C4×C61#44811yescharacteristic
218Dic61—22no—
219Dic61—41no—
220Dic61—41no—
221#3035—611no—
222#2906—611no—
223#1492D6111yescharacteristic, complemented
224#1480—611no—
225#1476—611no—
226#1301—611no—
227#1277—611no—
228C2×C61—21no—
229C2×C61—21no—
230C2×C61—161no—
231C2×C61#187411yescharacteristic
232C2×C61#187611yescharacteristic
233C2×C61#188111yescharacteristic
234D61—42no—
235C2×#135—1221no—
236C2×#131—1221no—
237#532C2×D6111yescharacteristic
238C4×#41—611no—
239#464—1221no—
240#463—1221no—
241#462—611no—
242#461—611no—
243#460—611no—
244#459—611no—
245#431—611no—
246#424—1221no—
247#424—1222no—
248#423—1221no—
249#423C2×D6111yescharacteristic
250C2×C4⋊C8—611no—
251C2×C4⋊C8—611no—
252C2×C4⋊C8—1221no—
253#416—1221no—
254C2×C4×C8C2×D6111yescharacteristic
255Q8⋊C8—1221no—
256D4⋊C8—22no—
257D4⋊C8—1221no—
258D4⋊C8—1221no—
259D4⋊C8—1221no—
260C61#899511yescharacteristic, complemented, Sylow
261C2×#41—21no—
262C2×#41—611no—
263#135—2442no—
264#135—2442no—
265C2×Q16—1221no—
266C2×SD16—1221no—
267C2×SD16—1221no—
268C2×D8—1221no—
269#131—2442no—
270#131—2442no—
271C2×M16—21no—
272C2×M16—1222no—
273C22×C8—21no—
274C22×C8—1222no—
275C22×C8—1221no—
276C22×C8—1221no—
277C4⋊Q8C4×D6111yescharacteristic
278#127C4×D6111yescharacteristic
279#124—21no—
280#121—21no—
281#121—21no—
282C4×Q8—611no—
283C4×Q8—611no—
284C4×D4—21no—
285C4×D4—21no—
286C4×D4—611no—
287C4×D4—611no—
288C4×D4—1221no—
289C4×D4—1221no—
290#117—611no—
291#117—1221no—
292C2×C42—1221no—
293C2×C42C22×D6111yescharacteristic
294C4⋊C8—21no—
295C4⋊C8—611no—
296C4⋊C8—611no—
297C4⋊C8—611no—
298C4⋊C8—611no—
299C4⋊C8—1222no—
300C4⋊C8—1222no—
301C4⋊C8—1221no—
302C4⋊C8—1221no—
303C4⋊C8—1221no—
304C4⋊C8C22⋊D6112yes—
305#103—1221no—
306#103—1221no—
307#102—1221no—
308#102—1221no—
309C22⋊C8—1221no—
310C4×C8—21no—
311C4×C8—21no—
312C4×C8—1221no—
313#41—41no—
314#41—41no—
315#41—41no—
316#41—41no—
317#41—612no—
318#41—612no—
319#41—1221no—
320#41—1221no—
321C2×Q8—21no—
322C2×Q8—611no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—41no—
327C2×D4—611no—
328C2×D4—1221no—
329C22×C4—41no—
330C22×C4—1221no—
331C22×C4—1221no—
332C22×C4—1221no—
333C22×C4#1175822211yescharacteristic
334C22×C4D4×D6111yescharacteristic
335C22×C4#1175822411yescharacteristic
336Q16—2442no—
337SD16—2442no—
338SD16—2442no—
339D8—2442no—
340M16—41no—
341M16—41no—
342M16—2444no—
343C2×C8—22no—
344C2×C8—22no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8—1221no—
348C2×C8—1221no—
349C2×C8—1221no—
350C2×C8—1221no—
351C2×C8—2444no—
352C2×C8—2441no—
353C2×C8—2441no—
354C2×C8—2441no—
355C2×C8—2441no—
356C2×C8—2441no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—611no—
360C4⋊C4—611no—
361C4⋊C4—1221no—
362C4⋊C4—1221no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—1221no—
366C22⋊C4—1221no—
367C22⋊C4—1221no—
368C42—1221no—
369C42—1221no—
370C42—1221no—
371C42C2×C4×D6111yescharacteristic
372C42D4×D6111yescharacteristic
373C42D4×D6111yescharacteristic
374C42C2×C22⋊D6111yescharacteristic
375C23—41no—
376C23—1221no—
377C23#1451975911yescharacteristic
378Q8—41no—
379Q8—41no—
380Q8—612no—
381Q8—1221no—
382D4—42no—
383D4—41no—
384D4—41no—
385D4—41no—
386D4—41no—
387D4—81no—
388D4—81no—
389D4—612no—
390D4—1222no—
391D4—1222no—
392D4—1221no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—1221no—
400C2×C4—1222no—
401C2×C4—1222no—
402C2×C4—1221no—
403C2×C4—1221no—
404C2×C4—4881no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4C22⋊C4×D6111yescharacteristic
408C2×C4#1451973711yescharacteristic
409C2×C4C4×C22⋊D6111yescharacteristic
410C2×C4#1451974511yescharacteristic
411C2×C4#1451974811yescharacteristic
412C2×C4#1451975011yescharacteristic
413C2×C4D8×D6111yescharacteristic
414C2×C4SD16×D6111yescharacteristic
415C2×C4#1451980111yescharacteristic
416C2×C4#1451980611yescharacteristic
417C8—42no—
418C8—42no—
419C8—4881no—
420C8—2441no—
421C8—2441no—
422C8—2441no—
423C8—2441no—
424C22—21no—
425C22—21no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22—1222no—
430C22—2441no—
431C22—2441no—
432C22#1683963811yescharacteristic
433C22#1684007411yescharacteristic
434C22#1684007911yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—81no—
439C4—1222no—
440C4—2441no—
441C4—2441no—
442C4#102×D6111yescharacteristic
443C4#1683976011yescharacteristic
444C4#1683987611yescharacteristic
445C4#1683988111yescharacteristic
446C4#1683989411yescharacteristic
447C4#1683989911yescharacteristic
448C2—21no—
449C2—21no—
450C2—161no—
451C2—2442no—
452C2#2144613311yescharacteristic
453C2#2144614311yescharacteristic
454C2#2144618411yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1492C2
socleC22×C61#386
prime radical#21455268C2
cosocleC2×C42×C61C23
hypercenter#1492D61
hypocenterC61#8995
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
2. #21454388C2semidirect
3. #21444218C2semidirect
4. #21444202C2semidirect
5. #21443714C2semidirect
6. #21443654C2semidirect
7. C61×#1492C2semidirect
223. #1492D61semidirect
260. C61#8995semidirect

Maximal subgroups

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

subgroupindex
#214552682
#214543882
#214442182
#214442022
#214437142
#214436542
C61×#14922
#899561