Finite Group Databasebeta

← #29574898

Subgroups — #29574898

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#21455274C211yesmaximal, characteristic
2#21454387C211yesmaximal, characteristic, complemented
3#21444271C211yesmaximal, characteristic, complemented
4#21444219C211yesmaximal, characteristic, complemented
5#21443715C211yesmaximal, characteristic, complemented
6#21443654C211yesmaximal, characteristic, complemented
7C61×#1476C211yesmaximal, characteristic, complemented
8C2×#14519797—21no—
9C2×#14519784—21no—
10#16840312C2211yescharacteristic
11#16839984—21no—
12#16839977—21no—
13#16839972C411yescharacteristic
14#16839967C411yescharacteristic
15#16839962C411yescharacteristic
16#16839957C411yescharacteristic
17#16839789—22no—
18#16839789—21no—
19#16839786—21no—
20#16839786C2211yescharacteristic
21C2×C4⋊#92418—21no—
22C2×C4⋊#92418C2211yescharacteristic
23C2×C4⋊#92418C2211yescharacteristic
24#16839756—21no—
25#16839491—21no—
26#16839491—21no—
27#16839491—22no—
28C4×#41×C61C2211yescharacteristic
29C61×#431C2211yescharacteristic
30C2×C4×C8×C61C2211yescharacteristic
31C61×Q8⋊C8—21no—
32C61×D4⋊C8—21no—
33C2×#11758222—21no—
34#14519797—42no—
35#14519797—42no—
36C2×#11758202—21no—
37C2×#11758200—21no—
38C2×#11758201—21no—
39C2×#11758199—21no—
40#14519784—42no—
41#14519784—42no—
42C2×#11758194—22no—
43C2×#11758194—21no—
44C22×#92418—22no—
45C22×#92418—21no—
46C22×#92418—21no—
47#14519777C2×C411yescharacteristic
48#14519774C2×C411yescharacteristic
49#14519765—21no—
50#14519751—21no—
51#14519751—21no—
52C4×D244—21no—
53C4×D244—21no—
54C4⋊#92418—22no—
55C4⋊#92418—22no—
56C4⋊#92418—21no—
57C4⋊#92418—21no—
58C4⋊#92418—21no—
59C4⋊#92418C2×C411yescharacteristic
60C4⋊#92418C2×C411yescharacteristic
61C4⋊#92418D411yescharacteristic
62C4⋊#92418D411yescharacteristic
63C4⋊#92418D412yes—
64#14519700—21no—
65#14519700—21no—
66#14519697—21no—
67#14519697—21no—
68C2×#41×C61D411yescharacteristic
69C22×C8×C61—21no—
70C4×Q8×C61C2×C411yescharacteristic
71C4×Q8×C61D411yescharacteristic
72C4×D4×C61—21no—
73C4×D4×C61—21no—
74C4×D4×C61C2×C411yescharacteristic
75C4×D4×C61D411yescharacteristic
76#117×C61—21no—
77#117×C61D411yescharacteristic
78C2×C42×C61—21no—
79C2×C42×C61C2311yescharacteristic
80C4⋊C8×C61—21no—
81C22⋊C8×C61—21no—
82C4×C8×C61—21no—
83C4×C8×C61—21no—
84C4×C8×C61—21no—
85#41×C61—21no—
86#41×C61—21no—
87#41×C61D812yes—
88#41×C61SD1612yes—
89C2×Q8×C61C22⋊C411yescharacteristic
90C2×D4×C61—21no—
91C2×D4×C61C22⋊C411yescharacteristic
92C22×C4×C61—21no—
93C22×C4×C61—21no—
94C22×C4×C61—21no—
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61#4111yescharacteristic
97C22×C4×C61#4111yescharacteristic
98C2×C22⋊D61—41no—
99#11758222—41no—
100#11758222—41no—
101#11758222—41no—
102#11758222—41no—
103C2×D244—21no—
104C2×D244—21no—
105C2×D244—21no—
106C2×C4×D61—41no—
107C2×Dic122—21no—
108C2×C8×C61—22no—
109C2×C8×C61—41no—
110C2×C8×C61—41no—
111C2×C8×C61—41no—
112C4⋊C4×C61—21no—
113C4⋊C4×C61—21no—
114C4⋊C4×C61C22⋊C411yescharacteristic
115C4⋊C4×C61C22⋊C411yescharacteristic
116C22⋊C4×C61—21no—
117C22⋊C4×C61—21no—
118C22⋊C4×C61—21no—
119C42×C61—21no—
120C42×C61—21no—
121C42×C61—21no—
122C42×C61C22×C411yescharacteristic
123C42×C61C2×D411yescharacteristic
124C42×C61C2×D411yescharacteristic
125C42×C61C2×D411yescharacteristic
126#11758202—42no—
127#11758201—42no—
128#11758200—42no—
129#11758199—42no—
130#11758198—41no—
131#11758198—41no—
132C4⋊Dic61—21no—
133C4⋊Dic61—21no—
134#11758194—44no—
135#11758194—41no—
136#11758194—41no—
137C2×#92418—21no—
138C2×#92418—21no—
139C2×#92418—21no—
140C2×#92418—22no—
141C2×#92418—21no—
142C2×#92418—44no—
143C2×#92418—41no—
144C2×#92418—41no—
145C2×#92418—41no—
146C2×#92418—41no—
147C23×C61—21no—
148C23×C61#12311yescharacteristic
149C22×D61—41no—
150Q8×C61—21no—
151Q8×C61#10212yes—
152D4×C61—22no—
153D4×C61—22no—
154D4×C61—21no—
155D4×C61#10212yes—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—22no—
160C2×C4×C61—22no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—81no—
167C2×C4×C61C2×C22⋊C411yescharacteristic
168C2×C4×C61C4×D411yescharacteristic
169C2×C4×C61C4×D411yescharacteristic
170C2×C4×C61#12011yescharacteristic
171C2×C4×C61#12111yescharacteristic
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61C2×D811yescharacteristic
174C2×C4×C61C2×SD1611yescharacteristic
175C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C61#13711yescharacteristic
177C22⋊D61—81no—
178C22⋊D61—81no—
179C2×Dic61—41no—
180D244—42no—
181D244—41no—
182D244—41no—
183D244—41no—
184D244—41no—
185C4×D61—81no—
186C4×D61—81no—
187Dic122—41no—
188Dic122—41no—
189C8×C61—42no—
190C8×C61—81no—
191#92418—41no—
192#92418—41no—
193#92418—41no—
194#92418—42no—
195#92418—41no—
196#8995—611nomaximal, Sylow
197C22×C61—21no—
198C22×C61—21no—
199C22×C61—22no—
200C22×C61—41no—
201C22×C61—41no—
202C22×C61#38611yescharacteristic
203C22×C61#48011yescharacteristic
204C22×C61#48111yescharacteristic
205C2×D61—81no—
206C2×D61—81no—
207C2×D61—81no—
208C4×C61—22no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—41no—
213C4×C61—41no—
214C4×C61C2×#10211yescharacteristic
215C4×C61#41711yescharacteristic
216C4×C61#44311yescharacteristic
217C4×C61#44411yescharacteristic
218C4×C61#44711yescharacteristic
219C4×C61#44811yescharacteristic
220Dic61—81no—
221#3035—611no—
222#2906—611no—
223#1492—611no—
224#1480—611no—
225#1476D6111yescharacteristic, complemented
226#1301—611no—
227#1277—611no—
228C2×C61—21no—
229C2×C61—21no—
230C2×C61—42no—
231C2×C61#187411yescharacteristic
232C2×C61#187611yescharacteristic
233C2×C61#188111yescharacteristic
234D61—161no—
235C2×#135—1221no—
236C2×#131—1221no—
237#532—611no—
238C4×#41C2×D6111yescharacteristic
239#464—1221no—
240#463—1221no—
241#462—611no—
242#461—611no—
243#460—611no—
244#459—611no—
245#431C2×D6111yescharacteristic
246#424—1222no—
247#424—1221no—
248#423—611no—
249#423—1221no—
250C2×C4⋊C8—611no—
251C2×C4⋊C8—611no—
252C2×C4⋊C8—1221no—
253#416—1221no—
254C2×C4×C8C2×D6111yescharacteristic
255Q8⋊C8—21no—
256D4⋊C8—21no—
257D4⋊C8—1221no—
258D4⋊C8—1221no—
259D4⋊C8—1222no—
260C61#899511yescharacteristic, complemented, Sylow
261C2×#41—1221no—
262C2×#41D24411yescharacteristic
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—1222no—
275C22×C8—1221no—
276C22×C8—1221no—
277C4⋊Q8—611no—
278#127—611no—
279#124—1221no—
280#121—1221no—
281#121—1221no—
282C4×Q8C4×D6111yescharacteristic
283C4×Q8C22⋊D6111yescharacteristic
284C4×D4—21no—
285C4×D4—21no—
286C4×D4—1221no—
287C4×D4—1221no—
288C4×D4C4×D6111yescharacteristic
289C4×D4C22⋊D6111yescharacteristic
290#117—21no—
291#117D24411yescharacteristic
292C2×C42—21no—
293C2×C42C22×D6111yescharacteristic
294C4⋊C8—21no—
295C4⋊C8—611no—
296C4⋊C8—611no—
297C4⋊C8—611no—
298C4⋊C8—611no—
299C4⋊C8—612no—
300C4⋊C8—1222no—
301C4⋊C8—1222no—
302C4⋊C8—1221no—
303C4⋊C8—1221no—
304C4⋊C8—1221no—
305#103—1221no—
306#103—1221no—
307#102—1221no—
308#102—1221no—
309C22⋊C8—21no—
310C4×C8—21no—
311C4×C8—21no—
312C4×C8—21no—
313#41—21no—
314#41—21no—
315#41—2441no—
316#41—2441no—
317#41—2441no—
318#41—2441no—
319#41#1175819012yes—
320#41D48812yes—
321C2×Q8—1221no—
322C2×Q8#1175819811yescharacteristic
323C2×D4—21no—
324C2×D4—1221no—
325C2×D4—1221no—
326C2×D4—1221no—
327C2×D4—2441no—
328C2×D4#1175819811yescharacteristic
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—2441no—
333C22×C4C2×D24411yescharacteristic
334C22×C4#1175822411yescharacteristic
335C22×C4#1175822411yescharacteristic
336Q16—2442no—
337SD16—2442no—
338SD16—2442no—
339D8—2442no—
340M16—2444no—
341M16—2441no—
342M16—2441no—
343C2×C8—22no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8—1221no—
348C2×C8—1221no—
349C2×C8—1221no—
350C2×C8—1221no—
351C2×C8—1222no—
352C2×C8—2444no—
353C2×C8—2441no—
354C2×C8—2441no—
355C2×C8—2441no—
356C2×C8—2441no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—1221no—
360C4⋊C4—1221no—
361C4⋊C4#1175819811yescharacteristic
362C4⋊C4#1175819811yescharacteristic
363C22⋊C4—21no—
364C22⋊C4—21no—
365C22⋊C4—21no—
366C22⋊C4—2441no—
367C22⋊C4—2441no—
368C42—21no—
369C42—21no—
370C42—21no—
371C42C2×C4×D6111yescharacteristic
372C42D4×D6111yescharacteristic
373C42D4×D6111yescharacteristic
374C42C2×C22⋊D6111yescharacteristic
375C23—21no—
376C23—2441no—
377C23#1451976111yescharacteristic
378Q8—21no—
379Q8—2441no—
380Q8—2441no—
381Q8#1451969912yes—
382D4—22no—
383D4—22no—
384D4—21no—
385D4—4881no—
386D4—4881no—
387D4—2442no—
388D4—2441no—
389D4—2441no—
390D4—2441no—
391D4—2441no—
392D4#1451969912yes—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—81no—
404C2×C4—4881no—
405C2×C4—4881no—
406C2×C4—2441no—
407C2×C4C2×#1175819811yescharacteristic
408C2×C4#1451973711yescharacteristic
409C2×C4#1451973711yescharacteristic
410C2×C4#1451974711yescharacteristic
411C2×C4#1451974911yescharacteristic
412C2×C4#1451974911yescharacteristic
413C2×C4C2×D48811yescharacteristic
414C2×C4C2×#1175819011yescharacteristic
415C2×C4#1451980511yescharacteristic
416C2×C4#1451981011yescharacteristic
417C8—42no—
418C8—81no—
419C8—2441no—
420C8—2441no—
421C8—2441no—
422C8—2442no—
423C8—2441no—
424C22—21no—
425C22—21no—
426C22—22no—
427C22—41no—
428C22—41no—
429C22—4881no—
430C22—4881no—
431C22—4881no—
432C22#1683963911yescharacteristic
433C22#1684007611yescharacteristic
434C22#1684008111yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—22no—
439C4—41no—
440C4—41no—
441C4—4881no—
442C4C2×#1451969911yescharacteristic
443C4#1683976411yescharacteristic
444C4#1683987611yescharacteristic
445C4#1683988111yescharacteristic
446C4#1683989811yescharacteristic
447C4#1683990311yescharacteristic
448C2—21no—
449C2—21no—
450C2—42no—
451C2—9761no—
452C2#2144613411yescharacteristic
453C2#2144614411yescharacteristic
454C2#2144617911yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1476C2
socleC22×C61#386
prime radical#21455274C2
cosocleC2×C42×C61C23
hypercenter#1476D61
hypocenterC61#8995
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1476

Complements

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

NH ≅ G/Ntype
2. #21454387C2semidirect
3. #21444271C2semidirect
4. #21444219C2semidirect
5. #21443715C2semidirect
6. #21443654C2semidirect
7. C61×#1476C2semidirect
225. #1476D61semidirect
260. C61#8995semidirect

Maximal subgroups

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

subgroupindex
#214552742
#214543872
#214442712
#214442192
#214437152
#214436542
C61×#14762
#899561