Finite Group Databasebeta

← #29574899

Subgroups — #29574899

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#21455276C211yesmaximal, characteristic
2#21454384C211yesmaximal, characteristic, complemented
3#21444271C211yesmaximal, characteristic, complemented
4#21444217C211yesmaximal, characteristic, complemented
5#21444202C211yesmaximal, characteristic, complemented
6#21443716C211yesmaximal, characteristic, complemented
7C61×#1277C211yesmaximal, characteristic, complemented
8C2×#14519799—21no—
9C2×#14519783—21no—
10#16840312C2211yescharacteristic
11C4×#11758222C2211yescharacteristic
12#16839985—21no—
13#16839978—21no—
14#16839973C411yescharacteristic
15#16839968C411yescharacteristic
16#16839963C411yescharacteristic
17#16839958C411yescharacteristic
18#16839815C2211yescharacteristic
19#16839788—21no—
20#16839787—22no—
21#16839786C2211yescharacteristic
22#16839784—21no—
23C4⋊C8×D61—21no—
24#16839759—21no—
25#16839494—21no—
26#16839491—21no—
27#16839491—22no—
28#16839489—21no—
29#16839489—21no—
30C2×C4⋊C8×C61C2211yescharacteristic
31C2×C4⋊C8×C61C2211yescharacteristic
32C2×C4×C8×C61C2211yescharacteristic
33C2×#11758222—21no—
34C2×#11758222D411yescharacteristic
35#14519799—42no—
36#14519799—42no—
37C2×Dic244—21no—
38C2×#11758190—21no—
39C2×#11758190—21no—
40C2×D488—21no—
41#14519783—42no—
42#14519783—42no—
43C2×#11758194—21no—
44C2×#11758189—22no—
45C2×C8×D61—22no—
46#14519777C2×C411yescharacteristic
47#14519774C2×C411yescharacteristic
48#14519765—21no—
49#14519751—21no—
50#14519751—21no—
51C4×Dic122C2×C411yescharacteristic
52C4×Dic122D411yescharacteristic
53C4×D244—21no—
54C4×D244—21no—
55C4×D244C2×C411yescharacteristic
56C4×D244D411yescharacteristic
57C4×C22⋊D61—21no—
58C4×C22⋊D61—21no—
59#14519736D411yescharacteristic
60#14519734—21no—
61C42×D61—21no—
62C4⋊#92418—21no—
63C4⋊#92418—21no—
64C4⋊#92418D412yes—
65#14519706—22no—
66#14519706—22no—
67#14519702—21no—
68#14519702—21no—
69#14519699—21no—
70#14519699—21no—
71C22⋊#92418—21no—
72C4×#92418—21no—
73C22×C8×C61—21no—
74C22×C8×C61—21no—
75C22×C8×C61—21no—
76C2×C42×C61C2311yescharacteristic
77C4⋊C8×C61—21no—
78C4⋊C8×C61—21no—
79C4⋊C8×C61C2×C411yescharacteristic
80C4⋊C8×C61C2×C411yescharacteristic
81C4⋊C8×C61D411yescharacteristic
82C4⋊C8×C61D411yescharacteristic
83C4×C8×C61—21no—
84C4×C8×C61—21no—
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61#4111yescharacteristic
87C22×C4×C61#4111yescharacteristic
88C2×C22⋊D61—21no—
89C2×C22⋊D61—41no—
90#11758222—21no—
91#11758222—21no—
92#11758222—41no—
93#11758222—41no—
94#11758222—41no—
95#11758222—41no—
96#11758222D812yes—
97#11758222SD1612yes—
98C2×D244—21no—
99C2×D244—21no—
100C2×D244—21no—
101C2×D244C22⋊C411yescharacteristic
102C2×C4×D61—21no—
103C2×C4×D61—21no—
104C2×C4×D61—21no—
105C2×C4×D61—41no—
106C2×Dic122—21no—
107C2×Dic122C22⋊C411yescharacteristic
108C2×C8×C61—22no—
109C2×C8×C61—21no—
110C2×C8×C61—21no—
111C2×C8×C61—21no—
112C2×C8×C61—21no—
113C2×C8×C61—41no—
114C2×C8×C61—41no—
115C2×C8×C61—41no—
116C2×C8×C61—41no—
117C2×C8×C61—41no—
118C2×C8×C61—41no—
119C42×C61C22×C411yescharacteristic
120C42×C61C2×D411yescharacteristic
121C42×C61C2×D411yescharacteristic
122C42×C61C2×D411yescharacteristic
123C22⋊Dic61—21no—
124#11758198—21no—
125#11758198—21no—
126#11758198—41no—
127#11758198—41no—
128C4⋊Dic61—21no—
129C4⋊Dic61—21no—
130C4⋊Dic61C22⋊C411yescharacteristic
131C4⋊Dic61C22⋊C411yescharacteristic
132#11758196—21no—
133#11758196—21no—
134C4×Dic61—21no—
135C4×Dic61—21no—
136C4×Dic61—21no—
137#11758194—41no—
138#11758194—41no—
139C2×#92418—22no—
140C2×#92418—41no—
141Dic244—42no—
142D488—42no—
143#11758190—42no—
144#11758190—42no—
145#11758189—44no—
146C8×D61—44no—
147C23×C61#12311yescharacteristic
148C22×D61—21no—
149C22×D61—41no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—41no—
153C2×C4×C61C2×C22⋊C411yescharacteristic
154C2×C4×C61C4×D411yescharacteristic
155C2×C4×C61C4×D411yescharacteristic
156C2×C4×C61#12011yescharacteristic
157C2×C4×C61#12111yescharacteristic
158C2×C4×C61#12111yescharacteristic
159C2×C4×C61C2×D811yescharacteristic
160C2×C4×C61C2×SD1611yescharacteristic
161C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C61#13711yescharacteristic
163C22⋊D61—22no—
164C22⋊D61—22no—
165C22⋊D61—81no—
166C22⋊D61—81no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—41no—
171D244—21no—
172D244—42no—
173D244—41no—
174D244—41no—
175D244—41no—
176D244—41no—
177D244#10212yes—
178C4×D61—22no—
179C4×D61—22no—
180C4×D61—41no—
181C4×D61—41no—
182C4×D61—81no—
183C4×D61—81no—
184C4×D61—81no—
185Dic122—21no—
186Dic122—41no—
187Dic122—41no—
188Dic122#10212yes—
189C8×C61—42no—
190C8×C61—41no—
191C8×C61—41no—
192C8×C61—41no—
193C8×C61—41no—
194#92418—42no—
195#92418—81no—
196#8995—611nomaximal, Sylow
197C22×C61—21no—
198C22×C61—21no—
199C22×C61#38611yescharacteristic
200C22×C61#48011yescharacteristic
201C22×C61#48111yescharacteristic
202C2×D61—22no—
203C2×D61—41no—
204C2×D61—41no—
205C2×D61—81no—
206C2×D61—81no—
207C2×D61—81no—
208C4×C61—21no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61C2×#10211yescharacteristic
212C4×C61#41711yescharacteristic
213C4×C61#44311yescharacteristic
214C4×C61#44411yescharacteristic
215C4×C61#44711yescharacteristic
216C4×C61#44811yescharacteristic
217Dic61—22no—
218Dic61—41no—
219Dic61—41no—
220Dic61—81no—
221#3035—611no—
222#2906—611no—
223#1492—611no—
224#1480—611no—
225#1476—611no—
226#1301—611no—
227#1277D6111yescharacteristic, complemented
228C2×C61—21no—
229C2×C61—21no—
230C2×C61#187411yescharacteristic
231C2×C61#187611yescharacteristic
232C2×C61#188111yescharacteristic
233D61—42no—
234D61—161no—
235C2×#135—1221no—
236C2×#131—1221no—
237#532—611no—
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—1222no—
247#424—1221no—
248#423—611no—
249#423—1221no—
250C2×C4⋊C8—1221no—
251C2×C4⋊C8C2×D6111yescharacteristic
252C2×C4⋊C8C2×D6111yescharacteristic
253#416—1221no—
254C2×C4×C8C2×D6111yescharacteristic
255Q8⋊C8—1221no—
256D4⋊C8—1222no—
257D4⋊C8—1221no—
258D4⋊C8—1221no—
259D4⋊C8—1221no—
260C61#899511yescharacteristic, complemented, Sylow
261C2×#41—611no—
262C2×#41—1221no—
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—1222no—
272C2×M16—1221no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—1222no—
277C4⋊Q8—611no—
278#127—611no—
279#124—1221no—
280#121—1221no—
281#121—1221no—
282C4×Q8—611no—
283C4×Q8—611no—
284C4×D4—611no—
285C4×D4—611no—
286C4×D4—1221no—
287C4×D4—1221no—
288C4×D4—1221no—
289C4×D4—1221no—
290#117—611no—
291#117—1221no—
292C2×C42—1221no—
293C2×C42C22×D6111yescharacteristic
294C4⋊C8—21no—
295C4⋊C8—21no—
296C4⋊C8—612no—
297C4⋊C8—1222no—
298C4⋊C8—1222no—
299C4⋊C8—1221no—
300C4⋊C8—1221no—
301C4⋊C8C4×D6111yescharacteristic
302C4⋊C8C4×D6111yescharacteristic
303C4⋊C8D24411yescharacteristic
304C4⋊C8D24411yescharacteristic
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—612no—
314#41—612no—
315#41—1221no—
316#41—1221no—
317#41—2441no—
318#41—2441no—
319#41—2441no—
320#41—2441no—
321C2×Q8—611no—
322C2×Q8—1221no—
323C2×D4—611no—
324C2×D4—1221no—
325C2×D4—1221no—
326C2×D4—1221no—
327C2×D4—1221no—
328C2×D4—2441no—
329C22×C4—1221no—
330C22×C4—1221no—
331C22×C4—1221no—
332C22×C4—2441no—
333C22×C4#1175822211yescharacteristic
334C22×C4D4×D6111yescharacteristic
335C22×C4#1175822611yescharacteristic
336Q16—2442no—
337SD16—2442no—
338SD16—2442no—
339D8—2442no—
340M16—2444no—
341M16—2441no—
342M16—2441no—
343C2×C8—22no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8—41no—
351C2×C8—41no—
352C2×C8—41no—
353C2×C8—41no—
354C2×C8—1222no—
355C2×C8—2444no—
356C2×C8—2441no—
357C4⋊C4—611no—
358C4⋊C4—611no—
359C4⋊C4—1221no—
360C4⋊C4—1221no—
361C4⋊C4—1221no—
362C4⋊C4—1221no—
363C22⋊C4—1221no—
364C22⋊C4—1221no—
365C22⋊C4—1221no—
366C22⋊C4—2441no—
367C22⋊C4—2441no—
368C42—1221no—
369C42—1221no—
370C42—1221no—
371C42C2×C4×D6111yescharacteristic
372C42C2×D24411yescharacteristic
373C42D4×D6111yescharacteristic
374C42D4×D6111yescharacteristic
375C23—1221no—
376C23—2441no—
377C23#1451976211yescharacteristic
378Q8—612no—
379Q8—1221no—
380Q8—2441no—
381Q8—2441no—
382D4—612no—
383D4—1222no—
384D4—1222no—
385D4—1221no—
386D4—4881no—
387D4—4881no—
388D4—2442no—
389D4—2441no—
390D4—2441no—
391D4—2441no—
392D4—2441no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—41no—
396C2×C4—1221no—
397C2×C4—1222no—
398C2×C4—1222no—
399C2×C4—1221no—
400C2×C4—1221no—
401C2×C4—4881no—
402C2×C4—4881no—
403C2×C4—4881no—
404C2×C4—2441no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4C22⋊C4×D6111yescharacteristic
408C2×C4#1451973911yescharacteristic
409C2×C4C4×D24411yescharacteristic
410C2×C4#1451974711yescharacteristic
411C2×C4#1451975011yescharacteristic
412C2×C4#1451975211yescharacteristic
413C2×C4D8×D6111yescharacteristic
414C2×C4SD16×D6111yescharacteristic
415C2×C4#1451980411yescharacteristic
416C2×C4#1451980911yescharacteristic
417C8—42no—
418C8—41no—
419C8—41no—
420C8—41no—
421C8—41no—
422C8—4881no—
423C8—2442no—
424C22—21no—
425C22—21no—
426C22—1222no—
427C22—4881no—
428C22—4881no—
429C22—4881no—
430C22—2441no—
431C22—2441no—
432C22#1683964011yescharacteristic
433C22#1684007711yescharacteristic
434C22#1684008211yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—1222no—
439C4—4881no—
440C4—2441no—
441C4—2441no—
442C4#102×D6111yescharacteristic
443C4#1683976211yescharacteristic
444C4#1683988011yescharacteristic
445C4#1683988511yescharacteristic
446C4#1683989711yescharacteristic
447C4#1683990211yescharacteristic
448C2—21no—
449C2—21no—
450C2—9761no—
451C2—2442no—
452C2#2144613511yescharacteristic
453C2#2144614511yescharacteristic
454C2#2144618211yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1277C2
socleC22×C61#386
prime radical#21455276C2
cosocleC2×C42×C61C23
hypercenter#1277D61
hypocenterC61#8995
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
2. #21454384C2semidirect
3. #21444271C2semidirect
4. #21444217C2semidirect
5. #21444202C2semidirect
6. #21443716C2semidirect
7. C61×#1277C2semidirect
227. #1277D61semidirect
260. C61#8995semidirect

Maximal subgroups

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

subgroupindex
#214552762
#214543842
#214442712
#214442172
#214442022
#214437162
C61×#12772
#899561