Finite Group Databasebeta

← #29662696

Subgroups — #29662696

Order 15616.

608 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456142C211yesmaximal, characteristic
2#21455859C211yesmaximal, characteristic, complemented
3#21455851C211yesmaximal, characteristic
4C2×#16839892C211yesmaximal, characteristic, complemented
5#21445402C212yesmaximal, complemented
6#21445388C212yesmaximal, complemented
7#21445374C212yesmaximal, complemented
8#21445360C212yesmaximal, complemented
9#21444474C211yesmaximal, characteristic, complemented
10#21444466C211yesmaximal, characteristic
11C61×#1564C211yesmaximal, characteristic, complemented
12#16840319C2211yescharacteristic
13#16840312C2211yescharacteristic
14C2×C4×Dic122C2211yescharacteristic
15#16840117—21no—
16#16840117—21no—
17#16840113C2211yescharacteristic
18#16840113C2211yescharacteristic
19#16840109C2211yescharacteristic
20#16840109C2211yescharacteristic
21#16840098—21no—
22#16840081—21no—
23#16840058C2212yes—
24#16840048C2212yes—
25#16839973C2212yes—
26#16839963C2212yes—
27#16839920—21no—
28#16839903—21no—
29#16839892—21no—
30#16839892—21no—
31#16839892C2212yes—
32#16839892C2212yes—
33C4×Dic244—22no—
34C4×#11758190—22no—
35C2×C4⋊#92418C2211yescharacteristic
36C2×#14519706—21no—
37#16839759—21no—
38#16839759—21no—
39C2×#14519687—21no—
40#16839510C2212yes—
41#16839509C2212yes—
42#16839507C2212yes—
43#16839505C2212yes—
44C61×#431C2211yescharacteristic
45C61×#431C2211yescharacteristic
46C2×C4×C8×C61C2211yescharacteristic
47C61×#335C2212yes—
48C61×#334C2212yes—
49C2×#11758222—21no—
50C22×Dic122D411yescharacteristic
51C2×Dic244—22no—
52C2×#11758190—22no—
53C22×#92418—21no—
54#14519777C2311yescharacteristic
55#14519777C2311yescharacteristic
56#14519777C2311yescharacteristic
57#14519774C2311yescharacteristic
58#14519769—21no—
59#14519765—21no—
60#14519756—21no—
61#14519756—21no—
62#14519751—21no—
63#14519751—21no—
64C4×Dic122—21no—
65C4×Dic122—21no—
66C4×Dic122—21no—
67C4×Dic122—21no—
68C4×Dic122D412yes—
69C4×Dic122C2312yes—
70C4×D244—21no—
71C4×D244—21no—
72#14519736—21no—
73C2×C4⋊Dic61D411yescharacteristic
74C2×#11758196—21no—
75C2×C4×Dic61—21no—
76#14519711—22no—
77#14519709—22no—
78C4⋊#92418—21no—
79C4⋊#92418C2312yes—
80#14519706—22no—
81#14519706—22no—
82#14519702—22no—
83#14519702—22no—
84#14519702—21no—
85#14519702—21no—
86#14519702—21no—
87#14519702—21no—
88#14519702—22no—
89#14519699—21no—
90#14519699—21no—
91#14519699—21no—
92#14519699—21no—
93#14519699—22no—
94#14519687—22no—
95#14519687—22no—
96C22×C8×C61D411yescharacteristic
97C22×C8×C61D411yescharacteristic
98C2×C42×C61C2311yescharacteristic
99C4⋊C8×C61C2312yes—
100C4⋊C8×C61C2312yes—
101C22⋊C8×C61—21no—
102C22⋊C8×C61—21no—
103C4×C8×C61—21no—
104C4×C8×C61—21no—
105C4×C8×C61D411yescharacteristic
106C4×C8×C61D411yescharacteristic
107C4×C8×C61C2311yescharacteristic
108C4×C8×C61C2311yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61#4111yescharacteristic
112C2×C22⋊D61—41no—
113C22×Dic61—21no—
114C22×Dic61—21no—
115#11758222—42no—
116#11758222—42no—
117C2×D244—21no—
118C2×D244—21no—
119C2×D244—21no—
120C2×C4×D61—41no—
121C2×Dic122—21no—
122C2×Dic122—21no—
123C2×Dic122—21no—
124C2×Dic122—21no—
125C2×Dic122—42no—
126C2×Dic122C2×D412yes—
127C2×C8×C61—22no—
128C2×C8×C61—22no—
129C2×C8×C61—22no—
130C2×C8×C61—22no—
131C2×C8×C61C2×D411yescharacteristic
132C2×C8×C61C2×D411yescharacteristic
133C2×C8×C61C2×D411yescharacteristic
134C2×C8×C61C2×D411yescharacteristic
135C42×C61C2×D411yescharacteristic
136C42×C61C2×D411yescharacteristic
137C42×C61#4111yescharacteristic
138C42×C61C2411yescharacteristic
139C22⋊Dic61—41no—
140#11758198—41no—
141#11758198—41no—
142C4⋊Dic61—21no—
143C4⋊Dic61—21no—
144C4⋊Dic61—21no—
145C4⋊Dic61—21no—
146C4⋊Dic61—21no—
147C4⋊Dic61—21no—
148C4⋊Dic61—21no—
149C4⋊Dic61C2×D412yes—
150#11758196—22no—
151#11758196—22no—
152#11758196—41no—
153#11758196—41no—
154C4×Dic61—22no—
155C4×Dic61—22no—
156C4×Dic61—41no—
157C2×#92418—22no—
158C2×#92418—42no—
159Dic244—44no—
160#11758190—44no—
161C23×C61#12111yescharacteristic
162C22×D61—41no—
163C2×C4×C61—22no—
164C2×C4×C61—41no—
165C2×C4×C61#12111yescharacteristic
166C2×C4×C61#12111yescharacteristic
167C2×C4×C61#12111yescharacteristic
168C2×C4×C61#13512yes—
169C2×C4×C61#13712yes—
170C2×C4×C61C22×D411yescharacteristic
171C2×C4×C61C22×D411yescharacteristic
172C2×C4×C61C2×#4111yescharacteristic
173C22⋊D61—82no—
174C2×Dic61—22no—
175C2×Dic61—22no—
176C2×Dic61—42no—
177C2×Dic61—42no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181D244—41no—
182D244—41no—
183D244—42no—
184D244—81no—
185C4×D61—82no—
186Dic122—22no—
187Dic122—22no—
188Dic122—42no—
189Dic122—41no—
190Dic122—41no—
191Dic122—42no—
192Dic122—81no—
193C8×C61—21no—
194C8×C61—21no—
195C8×C61—21no—
196C8×C61—21no—
197C8×C61—42no—
198C8×C61—42no—
199#92418—42no—
200#19155—611nomaximal, Sylow
201C22×C61—21no—
202C22×C61—21no—
203C22×C61#46412yes—
204C22×C61C2×#12111yescharacteristic
205C2×D61—81no—
206C2×D61—81no—
207C2×D61—81no—
208C4×C61—21no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61#46412yes—
212C4×C61C2×#13511yescharacteristic
213C4×C61C2×#13711yescharacteristic
214C4×C61#57512yes—
215Dic61—42no—
216Dic61—42no—
217Dic61—81no—
218Dic61—81no—
219Dic61—81no—
220#3131—611no—
221#3104—611no—
222#3103—611no—
223C2×#446—611no—
224#1704—612no—
225#1702—612no—
226#1700—612no—
227#1698—612no—
228#1564D6111yescharacteristic, complemented
229#1542—611no—
230#1540—611no—
231C2×C61—22no—
232C2×C61C2×#46411yescharacteristic
233C2×C61#305411yescharacteristic
234C2×C61#306711yescharacteristic
235D61—161no—
236#533—611no—
237#532—611no—
238C2×C4×Q8—611no—
239#488—1221no—
240#488—1221no—
241#487—611no—
242#487—611no—
243#486—611no—
244#486—611no—
245#484—1221no—
246#481—1221no—
247#477—612no—
248#475—612no—
249#462—612no—
250#460—612no—
251#451—1221no—
252#448—1221no—
253#446—612no—
254#446—612no—
255#446—1221no—
256#446—1221no—
257C4×Q16—1222no—
258C4×SD16—1222no—
259#431C2×D6111yescharacteristic
260#431C2×D6111yescharacteristic
261C2×C4⋊C8—611no—
262C2×C4⋊C8—1221no—
263#416—1221no—
264#416—1221no—
265C2×#97—1221no—
266C2×C4×C8C2×D6111yescharacteristic
267#335C2×D6112yes—
268#334C2×D6112yes—
269#333—612no—
270#332—612no—
271#332—612no—
272#331—612no—
273C61#1915511yescharacteristic, complemented, Sylow
274C2×#41—1221no—
275C22×Q8—611no—
276C2×Q16—1222no—
277C2×SD16—1222no—
278C22×C8—1221no—
279C22×C8D24411yescharacteristic
280C22×C8D24411yescharacteristic
281C4⋊Q8—611no—
282C4⋊Q8—611no—
283C4⋊Q8—611no—
284#127—611no—
285#125—1221no—
286#124—1221no—
287C22⋊Q8—1221no—
288C22⋊Q8—1221no—
289#121—1221no—
290#121—1221no—
291C4×Q8—612no—
292C4×Q8—612no—
293C4×Q8—1221no—
294C4×Q8—1221no—
295C4×Q8—1221no—
296C4×Q8—1221no—
297C4×D4—1221no—
298C4×D4—1221no—
299#117—1221no—
300C2×C4⋊C4—611no—
301C2×C4⋊C4—1221no—
302C2×C42—1221no—
303C2×C42C22×D6111yescharacteristic
304#107—1222no—
305#106—1222no—
306C4⋊C8—612no—
307C4⋊C8—1222no—
308C4⋊C8—1222no—
309C4⋊C8—1221no—
310C4⋊C8C22×D6112yes—
311C4⋊C8C22×D6112yes—
312#103—1222no—
313#103—1222no—
314#103—1222no—
315#103—1221no—
316#103—1221no—
317#103—1221no—
318#103—1221no—
319#102—1222no—
320#102—1221no—
321#102—1221no—
322#102—1221no—
323#102—1221no—
324C22⋊C8—21no—
325C22⋊C8—21no—
326#97—1222no—
327#97—1222no—
328C4×C8—21no—
329C4×C8—21no—
330C4×C8D24411yescharacteristic
331C4×C8D24411yescharacteristic
332C4×C8C22×D6111yescharacteristic
333C4×C8C22×D6111yescharacteristic
334#41—2442no—
335#41—2442no—
336C2×Q8—612no—
337C2×Q8—1221no—
338C2×Q8—1221no—
339C2×Q8—1221no—
340C2×Q8—1221no—
341C2×Q8—2442no—
342C2×D4—1221no—
343C2×D4—1221no—
344C2×D4—1221no—
345C2×D4—2441no—
346C22×C4—1221no—
347C22×C4—1221no—
348C22×C4—2441no—
349C22×C4C2×D24411yescharacteristic
350C22×C4D4×D6111yescharacteristic
351C22×C4#1175822611yescharacteristic
352Q16—2444no—
353SD16—2444no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—1222no—
359C2×C8—2442no—
360C2×C8C2×D24411yescharacteristic
361C2×C8C2×D24411yescharacteristic
362C2×C8C2×D24411yescharacteristic
363C2×C8C2×D24411yescharacteristic
364C4⋊C4—612no—
365C4⋊C4—1222no—
366C4⋊C4—1221no—
367C4⋊C4—1222no—
368C4⋊C4—1221no—
369C4⋊C4—1221no—
370C4⋊C4—1221no—
371C4⋊C4—1221no—
372C4⋊C4—1221no—
373C4⋊C4—1221no—
374C4⋊C4—2441no—
375C4⋊C4—2441no—
376C22⋊C4—2441no—
377C22⋊C4—2441no—
378C22⋊C4—2441no—
379C42—1222no—
380C42—1222no—
381C42—2441no—
382C42C2×D24411yescharacteristic
383C42D4×D6111yescharacteristic
384C42#1175822611yescharacteristic
385C42C23×D6111yescharacteristic
386C23—2441no—
387C23#1451975211yescharacteristic
388Q8—1222no—
389Q8—1222no—
390Q8—4881no—
391Q8—2442no—
392Q8—2441no—
393Q8—2441no—
394Q8—2442no—
395D4—4881no—
396D4—4882no—
397D4—2441no—
398D4—2441no—
399D4—2442no—
400C2×C4—22no—
401C2×C4—41no—
402C2×C4—1222no—
403C2×C4—1222no—
404C2×C4—4882no—
405C2×C4—2441no—
406C2×C4—2441no—
407C2×C4—2441no—
408C2×C4—2442no—
409C2×C4—2442no—
410C2×C4#1451975211yescharacteristic
411C2×C4#1451975211yescharacteristic
412C2×C4#1451975211yescharacteristic
413C2×C4#1451979912yes—
414C2×C4#1451981012yes—
415C2×C4C2×D4×D6111yescharacteristic
416C2×C4C22×D24411yescharacteristic
417C2×C4C2×#1175822611yescharacteristic
418C8—21no—
419C8—21no—
420C8—21no—
421C8—21no—
422C8—42no—
423C8—42no—
424C8—2442no—
425C22—21no—
426C22—21no—
427C22—4881no—
428C22—4881no—
429C22—4881no—
430C22#1683998512yes—
431C22C2×#1451975211yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—4881no—
436C4—4881no—
437C4—4881no—
438C4—2442no—
439C4—2442no—
440C4#1683998512yes—
441C4C2×#1451979911yescharacteristic
442C4C2×#1451981011yescharacteristic
443C4#1684055912yes—
444C2—22no—
445C2—9761no—
446C2C2×#1683998511yescharacteristic
447C2#2145542911yescharacteristic
448C2#2145554011yescharacteristic
subgroupG/H
centerC2×C4#14519752
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1564C2
socleC22×C61C2×#121
prime radical#16840312C22
hypercenter#1564D61
hypocenterC61#19155
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1564

Complements

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

NH ≅ G/Ntype
2. #21455859C2semidirect
4. C2×#16839892C2semidirect
5. #21445402C2semidirect
6. #21445388C2semidirect
7. #21445374C2semidirect
8. #21445360C2semidirect
9. #21444474C2semidirect
11. C61×#1564C2semidirect
228. #1564D61semidirect
273. C61#19155semidirect

Maximal subgroups

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

subgroupindex
#214561422
#214558592
#214558512
C2×#168398922
#214454022
#214453882
#214453742
#214453602
#214444742
#214444662
C61×#15642
#1915561