Finite Group Databasebeta

← #29576114

Subgroups — #29576114

Order 15616.

510 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455268C211yesmaximal, characteristic
2#21454780C211yesmaximal, characteristic, complemented
3#21445840C211yesmaximal, characteristic, complemented
4#21444270C211yesmaximal, characteristic, complemented
5#21443715C211yesmaximal, characteristic, complemented
6#21443660C211yesmaximal, characteristic, complemented
7C61×#1502C211yesmaximal, characteristic, complemented
8C2×#14519797—21no—
9C4×#11758222C2211yescharacteristic
10#16839981—21no—
11#16839974—21no—
12#16839969C411yescharacteristic, complemented
13#16839964C411yescharacteristic, complemented
14#16839959C411yescharacteristic, complemented
15#16839954C411yescharacteristic, complemented
16#16839889—21no—
17#16839839—21no—
18#16839830—22no—
19#16839813—21no—
20#16839786C2211yescharacteristic
21C2×C4⋊#92418C2211yescharacteristic
22C2×#14519705—21no—
23#16839758—21no—
24C4×#11758189—21no—
25C2×C4×#92418C2211yescharacteristic
26#16839522—21no—
27D4⋊#92418—21no—
28D4⋊#92418—21no—
29C61×#532C2211yescharacteristic
30C61×#431C2211yescharacteristic
31C4×C4⋊C4×C61C2211yescharacteristic
32C61×#327—22no—
33C2×#11758222D411yescharacteristic
34#14519797—42no—
35#14519797—42no—
36C2×#11758202—21no—
37C2×#11758200—21no—
38C2×#11758201—21no—
39C2×#11758199—21no—
40C2×#11758194—21no—
41C2×#11758189—22no—
42C22×#92418—21no—
43C22×#92418—21no—
44C4×Dic122C2×C411yescharacteristic
45C4×Dic122D411yescharacteristic
46C4×D244C2×C411yescharacteristic
47C4×D244D411yescharacteristic
48C4×C22⋊D61—21no—
49C4×C22⋊D61—21no—
50#14519736D411yescharacteristic
51#14519734—21no—
52C42×D61—21no—
53C4⋊#92418—21no—
54C4⋊#92418—21no—
55C4⋊#92418—21no—
56C4⋊#92418C2×C411yescharacteristic
57C4⋊#92418C2×C411yescharacteristic
58#14519706—22no—
59#14519705—42no—
60#14519701—21no—
61#14519701—21no—
62#14519698—21no—
63#14519698—21no—
64#14519689—22no—
65#14519687—22no—
66C4×#92418—21no—
67C4×#92418D411yescharacteristic
68C4×#92418D411yescharacteristic
69C2×#41×C61—21no—
70C4⋊Q8×C61C2×C411yescharacteristic
71#127×C61C2×C411yescharacteristic
72#124×C61—21no—
73#121×C61—21no—
74#121×C61—21no—
75C4×D4×C61—21no—
76C4×D4×C61—21no—
77C2×C4⋊C4×C61—21no—
78C2×C42×C61—21no—
79C2×C42×C61C2311yescharacteristic
80C4⋊C8×C61—21no—
81C22⋊C8×C61D412yes—
82C4×C8×C61—21no—
83#95×C61—21no—
84#41×C61—41no—
85#41×C61—41no—
86#41×C61—41no—
87#41×C61—41no—
88C2×Q8×C61—21no—
89C2×D4×C61—21no—
90C2×D4×C61—21no—
91C2×D4×C61—21no—
92C2×D4×C61—41no—
93C22×C4×C61—41no—
94C22×C4×C61—41no—
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61#4111yescharacteristic
98C2×C22⋊D61—21no—
99#11758222—21no—
100#11758222—21no—
101#11758222—21no—
102#11758222—21no—
103C2×D244C22⋊C411yescharacteristic
104C2×C4×D61—21no—
105C2×C4×D61—21no—
106C2×C4×D61—21no—
107C2×Dic122C22⋊C411yescharacteristic
108C2×C8×C61—22no—
109C4⋊C4×C61—22no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61—41no—
113C22⋊C4×C61—41no—
114C22⋊C4×C61—41no—
115C42×C61—41no—
116C42×C61—41no—
117C42×C61C22×C411yescharacteristic
118C42×C61C2×D411yescharacteristic
119C42×C61C2×D411yescharacteristic
120C42×C61#4111yescharacteristic
121C22⋊Dic61—21no—
122#11758202—42no—
123#11758201—42no—
124#11758200—42no—
125#11758199—42no—
126#11758198—21no—
127#11758198—21no—
128C4⋊Dic61C22⋊C411yescharacteristic
129C4⋊Dic61C22⋊C411yescharacteristic
130#11758196—21no—
131#11758196—21no—
132C4×Dic61—21no—
133C4×Dic61—21no—
134C4×Dic61—21no—
135#11758194—41no—
136#11758194—41no—
137C2×#92418—21no—
138C2×#92418—21no—
139C2×#92418—21no—
140C2×#92418—21no—
141C2×#92418—42no—
142C2×#92418—41no—
143C2×#92418—41no—
144C2×#92418—41no—
145#11758189—44no—
146C23×C61—41no—
147C23×C61#12111yescharacteristic
148C22×D61—21no—
149Q8×C61—41no—
150Q8×C61—41no—
151D4×C61—41no—
152D4×C61—41no—
153D4×C61—41no—
154D4×C61—41no—
155D4×C61—81no—
156D4×C61—81no—
157D4×C61—81no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—41no—
161C2×C4×C61—42no—
162C2×C4×C61—41no—
163C2×C4×C61—81no—
164C2×C4×C61—81no—
165C2×C4×C61—81no—
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#12311yescharacteristic
173C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C61#13711yescharacteristic
177C22⋊D61—41no—
178C22⋊D61—41no—
179C2×Dic61—21no—
180C2×Dic61—21no—
181C2×Dic61—21no—
182D244—21no—
183D244—21no—
184C4×D61—42no—
185C4×D61—41no—
186C4×D61—41no—
187C4×D61—41no—
188C4×D61—41no—
189Dic122—21no—
190Dic122—21no—
191C8×C61—42no—
192#92418—22no—
193#92418—41no—
194#92418—41no—
195#92418—41no—
196#92418—81no—
197#9210—611nomaximal, Sylow
198C22×C61—21no—
199C22×C61—21no—
200C22×C61—81no—
201C22×C61—81no—
202C22×C61—81no—
203C22×C61#38611yescharacteristic
204C22×C61#46811yescharacteristic
205C22×C61#46911yescharacteristic
206C2×D61—41no—
207C2×D61—41no—
208C2×D61—41no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—82no—
213C4×C61—81no—
214C4×C61#41711yescharacteristic
215C4×C61#41811yescharacteristic
216C4×C61#44311yescharacteristic
217C4×C61#44411yescharacteristic
218C4×C61#46811yescharacteristic
219C4×C61#46911yescharacteristic
220Dic61—41no—
221Dic61—41no—
222Dic61—41no—
223#3035—611no—
224#2965—611no—
225#1806—611no—
226#1502D6111yescharacteristic, complemented
227#1492—611no—
228#1301—611no—
229#1279—611no—
230C2×C61—21no—
231C2×C61—21no—
232C2×C61—161no—
233C2×C61#187611yescharacteristic
234C2×C61#189511yescharacteristic
235C2×C61#190611yescharacteristic
236D61—81no—
237C2×#135—1221no—
238#532C2×D6111yescharacteristic
239C4×#41—611no—
240#464—1221no—
241#463—1221no—
242#462—611no—
243#461—611no—
244#460—611no—
245#459—611no—
246#446—1221no—
247#436—1221no—
248#435—1222no—
249#431—1221no—
250#431C2×D6111yescharacteristic
251#423—611no—
252C2×C4⋊C8—611no—
253C2×#104—1221no—
254#416—1221no—
255C4×M16—1221no—
256C2×C4×C8—611no—
257C4×C4⋊C4C2×D6111yescharacteristic
258#339—1221no—
259#327—22no—
260D4⋊C8—1221no—
261D4⋊C8—1221no—
262C61#921011yescharacteristic, complemented, Sylow
263C2×#41—21no—
264C2×#41—611no—
265#135—2442no—
266#135—2442no—
267C2×Q16—1221no—
268C2×SD16—1221no—
269C2×SD16—1221no—
270C2×D8—1221no—
271C2×M16—1222no—
272C2×M16—1221no—
273C22×C8—1221no—
274C22×C8—1221no—
275C4⋊Q8C4×D6111yescharacteristic
276#127C4×D6111yescharacteristic
277#124—21no—
278#121—21no—
279#121—21no—
280C4×Q8—611no—
281C4×Q8—611no—
282C4×D4—21no—
283C4×D4—21no—
284C4×D4—611no—
285C4×D4—611no—
286C4×D4—1221no—
287C4×D4—1221no—
288#117—611no—
289#117—1221no—
290C2×C4⋊C4—21no—
291C2×C42—21no—
292C2×C42—1221no—
293C2×C42C22×D6111yescharacteristic
294C4⋊C8—21no—
295C4⋊C8—611no—
296C4⋊C8—611no—
297C4⋊C8—1222no—
298C4⋊C8—1221no—
299C4⋊C8—1221no—
300C4⋊C8—1221no—
301#104—2442no—
302#103—1221no—
303#103—1221no—
304#102—1221no—
305#102—1221no—
306C22⋊C8—1222no—
307C22⋊C8C22⋊D6112yes—
308#97—1222no—
309C4×C8—21no—
310C4×C8—611no—
311C4×C8—611no—
312C4×C8—1221no—
313#95—21no—
314#41—41no—
315#41—41no—
316#41—41no—
317#41—41no—
318#41—1221no—
319#41—1221no—
320#41—1221no—
321#41—1221no—
322C2×Q8—21no—
323C2×Q8—611no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—41no—
328C2×D4—611no—
329C2×D4—1221no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—1221no—
333C22×C4—1221no—
334C22×C4—1221no—
335C22×C4D4×D6111yescharacteristic
336C22×C4#1175822411yescharacteristic
337C22×C4C2×C22⋊D6111yescharacteristic
338Q16—2442no—
339SD16—2442no—
340SD16—2442no—
341D8—2442no—
342M16—2444no—
343M16—2441no—
344M16—2441no—
345C2×C8—22no—
346C2×C8—1221no—
347C2×C8—1221no—
348C2×C8—1221no—
349C2×C8—1221no—
350C2×C8—2442no—
351C2×C8—2441no—
352C2×C8—2441no—
353C2×C8—2441no—
354C4⋊C4—22no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—41no—
358C4⋊C4—611no—
359C4⋊C4—611no—
360C4⋊C4—1221no—
361C4⋊C4—1221no—
362C22⋊C4—41no—
363C22⋊C4—41no—
364C22⋊C4—1221no—
365C22⋊C4—1221no—
366C22⋊C4—1221no—
367C42—41no—
368C42—41no—
369C42—1221no—
370C42—1221no—
371C42—1221no—
372C42C2×C4×D6111yescharacteristic
373C42#1175822211yescharacteristic
374C42D4×D6111yescharacteristic
375C42D4×D6111yescharacteristic
376C23—41no—
377C23—1221no—
378C23#1451974811yescharacteristic
379Q8—41no—
380Q8—41no—
381Q8—1221no—
382Q8—1221no—
383D4—41no—
384D4—41no—
385D4—41no—
386D4—41no—
387D4—81no—
388D4—81no—
389D4—81no—
390D4—1221no—
391D4—1221no—
392D4—2441no—
393D4—2441no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—1221no—
406C2×C4—2442no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4—2441no—
410C2×C4—2441no—
411C2×C4C22⋊C4×D6111yescharacteristic
412C2×C4#1451973711yescharacteristic
413C2×C4C4×C22⋊D6111yescharacteristic
414C2×C4#1451974511yescharacteristic
415C2×C4#1451975011yescharacteristic
416C2×C4#1451975911yescharacteristic
417C2×C4#1451980111yescharacteristic
418C2×C4#1451980111yescharacteristic
419C2×C4#1451980411yescharacteristic
420C2×C4#1451980611yescharacteristic
421C8—42no—
422C8—1222no—
423C8—4881no—
424C8—2441no—
425C8—2441no—
426C8—2441no—
427C22—21no—
428C22—21no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22—2441no—
433C22—2441no—
434C22—2441no—
435C22#1683963811yescharacteristic
436C22#1684000511yescharacteristic
437C22#1684001211yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—82no—
442C4—81no—
443C4—2441no—
444C4—2441no—
445C4—2441no—
446C4#1683976011yescharacteristic
447C4#1683976511yescharacteristic
448C4#1683987611yescharacteristic
449C4#1683988111yescharacteristic
450C4#1684000711yescharacteristic
451C4#1684001411yescharacteristic
452C2—21no—
453C2—21no—
454C2—161no—
455C2—4881no—
456C2#2144614311yescharacteristic
457C2#2144625411yescharacteristic
458C2#2144631711yescharacteristic
subgroupG/H
centerC2×C4#14519750
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1502C2
socleC22×C61#386
prime radical#21455268C2
cosocleC2×C42×C61C23
hypercenter#1502D61
hypocenterC61#9210
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1502

Complements

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

NH ≅ G/Ntype
2. #21454780C2semidirect
3. #21445840C2semidirect
4. #21444270C2semidirect
5. #21443715C2semidirect
6. #21443660C2semidirect
7. C61×#1502C2semidirect
12. #16839969C4semidirect
13. #16839964C4semidirect
14. #16839959C4semidirect
15. #16839954C4semidirect
226. #1502D61semidirect
262. C61#9210semidirect

Maximal subgroups

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

subgroupindex
#214552682
#214547802
#214458402
#214442702
#214437152
#214436602
C61×#15022
#921061