Finite Group Databasebeta

← #29662427

Subgroups — #29662427

Order 15616.

628 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#21456144C211yesmaximal, characteristic
2#21455854C211yesmaximal, characteristic, complemented
3#21455851C211yesmaximal, characteristic
4C2×#16839886C211yesmaximal, characteristic, complemented
5#21445280C212yesmaximal, complemented
6#21445266C212yesmaximal, complemented
7#21445252C212yesmaximal, complemented
8#21445238C212yesmaximal, complemented
9#21444565C211yesmaximal, characteristic, complemented
10#21444469C211yesmaximal, characteristic
11C61×#1542C211yesmaximal, characteristic, complemented
12#16840312C2211yescharacteristic
13C2×C4×Dic122C2211yescharacteristic
14#16840119—21no—
15#16840119—21no—
16#16840114C2211yescharacteristic
17#16840114C2211yescharacteristic
18#16840110C2211yescharacteristic
19#16840110C2211yescharacteristic
20#16840095—21no—
21#16840081—21no—
22#16840054C2212yes—
23#16840048C2212yes—
24#16839969C2212yes—
25#16839963C2212yes—
26#16839917—21no—
27#16839903—21no—
28#16839886—21no—
29#16839886—21no—
30#16839886C2212yes—
31#16839886C2212yes—
32C4×#11758202—22no—
33C4×#11758190—22no—
34#16839815C2211yescharacteristic
35C2×#14519706—21no—
36#16839756—21no—
37#16839756—21no—
38C2×C4×#92418C2211yescharacteristic
39C2×C8×Dic61—21no—
40#16839514C2212yes—
41#16839512C2212yes—
42#16839509C2212yes—
43#16839505C2212yes—
44C61×#533C2211yescharacteristic
45C61×#431C2211yescharacteristic
46C2×C4⋊C8×C61C2211yescharacteristic
47C61×#333C2212yes—
48C61×#332C2212yes—
49C2×#11758222—21no—
50C22×Dic122D411yescharacteristic
51C2×#11758202—22no—
52C2×#11758190—22no—
53C22×#92418D411yescharacteristic
54C22×#92418D411yescharacteristic
55#14519777C2311yescharacteristic
56#14519774C2311yescharacteristic
57#14519765—21no—
58#14519751—21no—
59#14519751—21no—
60C4×Dic122—21no—
61C4×Dic122—21no—
62C4×Dic122D412yes—
63C4×Dic122C2312yes—
64C4×D244—21no—
65C4×D244—21no—
66C2×C4⋊Dic61D411yescharacteristic
67C2×#11758196—21no—
68C2×C4×Dic61—21no—
69#14519710—22no—
70#14519709—22no—
71C4⋊#92418C2312yes—
72#14519706—22no—
73#14519706—22no—
74#14519702—22no—
75#14519701—22no—
76#14519700—22no—
77#14519700—21no—
78#14519700—21no—
79#14519700—21no—
80#14519700—21no—
81#14519699—22no—
82#14519697—21no—
83#14519697—21no—
84#14519697—21no—
85#14519697—21no—
86C22⋊#92418—21no—
87C4×#92418—21no—
88C4×#92418D411yescharacteristic
89C4×#92418D411yescharacteristic
90C4×#92418C2311yescharacteristic
91C4×#92418C2311yescharacteristic
92C8×Dic61—22no—
93C8×Dic61—22no—
94C22×C8×C61—21no—
95C4⋊Q8×C61C2311yescharacteristic
96C4⋊Q8×C61C2311yescharacteristic
97#125×C61—21no—
98C22⋊Q8×C61—21no—
99C22⋊Q8×C61—21no—
100C4×Q8×C61—21no—
101C4×Q8×C61—21no—
102#117×C61—21no—
103C2×C42×C61C2311yescharacteristic
104C4⋊C8×C61—21no—
105C4⋊C8×C61C2312yes—
106C4⋊C8×C61C2312yes—
107C22⋊C8×C61—21no—
108C4×C8×C61—21no—
109C2×Q8×C61—21no—
110C2×Q8×C61—21no—
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61#4111yescharacteristic
114C2×C22⋊D61—41no—
115C22×Dic61—21no—
116C22×Dic61—21no—
117#11758222—42no—
118#11758222—42no—
119C2×D244—21no—
120C2×D244—21no—
121C2×D244—21no—
122C2×C4×D61—41no—
123C2×Dic122—21no—
124C2×Dic122—24no—
125C2×Dic122—21no—
126C2×Dic122C2×D412yes—
127C2×C8×C61—22no—
128C2×C8×C61—22no—
129C2×C8×C61—42no—
130C4⋊C4×C61—21no—
131C4⋊C4×C61—21no—
132C4⋊C4×C61—21no—
133C4⋊C4×C61—21no—
134C4⋊C4×C61—41no—
135C4⋊C4×C61—41no—
136C22⋊C4×C61—41no—
137C42×C61—41no—
138C42×C61C2×D411yescharacteristic
139C42×C61C2×D411yescharacteristic
140C42×C61#4111yescharacteristic
141C42×C61C2411yescharacteristic
142#11758202—44no—
143#11758198—41no—
144#11758198—41no—
145C4⋊Dic61—21no—
146C4⋊Dic61—21no—
147C4⋊Dic61—21no—
148C4⋊Dic61C2×D412yes—
149#11758196—22no—
150#11758196—22no—
151C4×Dic61—22no—
152C4×Dic61—22no—
153C2×#92418—22no—
154C2×#92418—22no—
155C2×#92418—22no—
156C2×#92418C2×D411yescharacteristic
157C2×#92418C2×D411yescharacteristic
158C2×#92418C2×D411yescharacteristic
159C2×#92418C2×D411yescharacteristic
160#11758190—44no—
161C23×C61#12111yescharacteristic
162C22×D61—41no—
163Q8×C61—42no—
164Q8×C61—81no—
165C2×C4×C61—22no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61#12111yescharacteristic
170C2×C4×C61#12111yescharacteristic
171C2×C4×C61#12111yescharacteristic
172C2×C4×C61#13512yes—
173C2×C4×C61#13712yes—
174C2×C4×C61C22×D411yescharacteristic
175C2×C4×C61C22×D411yescharacteristic
176C2×C4×C61C2×#4111yescharacteristic
177C22⋊D61—82no—
178C2×Dic61—24no—
179C2×Dic61—22no—
180C2×Dic61—22no—
181C2×Dic61—42no—
182C2×Dic61—41no—
183D244—42no—
184D244—41no—
185D244—41no—
186D244—81no—
187C4×D61—82no—
188Dic122—24no—
189Dic122—22no—
190Dic122—41no—
191Dic122—41no—
192Dic122#13514yes—
193C8×C61—42no—
194C8×C61—42no—
195#92418—21no—
196#92418—21no—
197#92418—21no—
198#92418—21no—
199#92418—42no—
200#19123—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—81no—
212C4×C61—81no—
213C4×C61#46412yes—
214C4×C61C2×#13512yes—
215C4×C61C2×#13511yescharacteristic
216C4×C61C2×#13711yescharacteristic
217Dic61—24no—
218Dic61—42no—
219Dic61—81no—
220#3131—611no—
221#3104—611no—
222#3103—611no—
223C2×C8×Q8—611no—
224#1684—612no—
225#1682—612no—
226#1680—612no—
227#1678—612no—
228#1564—611no—
229#1542D6111yescharacteristic, complemented
230#1540—611no—
231C2×C61—22no—
232C2×C61C2×#46411yescharacteristic
233C2×C61#305011yescharacteristic
234C2×C61#306711yescharacteristic
235D61—161no—
236#533C2×D6111yescharacteristic
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—
253C8×Q8—612no—
254C8×Q8—612no—
255C8×Q8—1221no—
256C8×Q8—1221no—
257C4×Q16—1222no—
258C4×SD16—1222no—
259#431—611no—
260#431C2×D6111yescharacteristic
261C2×C4⋊C8—1221no—
262C2×C4⋊C8C2×D6111yescharacteristic
263#416—1221no—
264#416—1221no—
265C2×C4×C8—611no—
266C2×C4×C8—1221no—
267#335—612no—
268#334—612no—
269#333C2×D6112yes—
270#332—612no—
271#332C2×D6112yes—
272#331—612no—
273C61#1912311yescharacteristic, complemented, Sylow
274C2×#41—1221no—
275C22×Q8—611no—
276C2×Q16—1222no—
277C2×SD16—1222no—
278C22×C8—21no—
279C22×C8—611no—
280C22×C8—611no—
281C4⋊Q8—611no—
282C4⋊Q8C22×D6111yescharacteristic
283C4⋊Q8C22×D6111yescharacteristic
284#127—611no—
285#125—21no—
286#124—1221no—
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289#121—1221no—
290#121—1221no—
291C4×Q8—21no—
292C4×Q8—21no—
293C4×Q8—612no—
294C4×Q8—612no—
295C4×Q8—1221no—
296C4×Q8—1221no—
297C4×D4—1221no—
298C4×D4—1221no—
299#117—21no—
300C2×C4⋊C4—611no—
301C2×C4⋊C4—1221no—
302C2×C42—1221no—
303C2×C42C22×D6111yescharacteristic
304#107—1222no—
305#106—1222no—
306C4⋊C8—21no—
307C4⋊C8—612no—
308C4⋊C8—1222no—
309C4⋊C8—1222no—
310C4⋊C8C22×D6112yes—
311C4⋊C8C22×D6112yes—
312#103—1221no—
313#103—1221no—
314#103—1221no—
315#103—1221no—
316#103—1222no—
317#103—1222no—
318#103—1222no—
319#102—1221no—
320#102—1221no—
321#102—1221no—
322#102—1221no—
323#102—1222no—
324C22⋊C8—21no—
325C22⋊C8—1221no—
326C4×C8—21no—
327C4×C8—611no—
328C4×C8—611no—
329C4×C8—611no—
330C4×C8—611no—
331C4×C8—1222no—
332C4×C8—1222no—
333C4×C8—1221no—
334#41—2442no—
335#41—2442no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—612no—
339C2×Q8—1224no—
340C2×Q8—1221no—
341C2×Q8—1221no—
342C2×D4—1221no—
343C2×D4—1221no—
344C2×D4—1221no—
345C2×D4—2441no—
346C22×C4—1221no—
347C22×C4—1221no—
348C22×C4—2441no—
349C22×C4#1175822211yescharacteristic
350C22×C4D4×D6111yescharacteristic
351C22×C4D4×D6111yescharacteristic
352Q16—2444no—
353SD16—2444no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—42no—
357C2×C8—611no—
358C2×C8—611no—
359C2×C8—611no—
360C2×C8—611no—
361C2×C8—1222no—
362C2×C8—1222no—
363C2×C8—1222no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—612no—
371C4⋊C4—1222no—
372C4⋊C4—1221no—
373C4⋊C4—1222no—
374C4⋊C4—1221no—
375C4⋊C4—1221no—
376C22⋊C4—41no—
377C22⋊C4—2441no—
378C22⋊C4—2441no—
379C42—41no—
380C42—1222no—
381C42—1222no—
382C42#1175822211yescharacteristic
383C42D4×D6111yescharacteristic
384C42D4×D6111yescharacteristic
385C42C23×D6111yescharacteristic
386C23—2441no—
387C23#1451975011yescharacteristic
388Q8—42no—
389Q8—81no—
390Q8—614no—
391Q8—1224no—
392Q8—1222no—
393Q8—2441no—
394Q8—2441no—
395D4—4881no—
396D4—4882no—
397D4—2442no—
398D4—2441no—
399D4—2441no—
400C2×C4—22no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—1224no—
405C2×C4—1222no—
406C2×C4—1222no—
407C2×C4—4882no—
408C2×C4—2441no—
409C2×C4—2442no—
410C2×C4#1451975011yescharacteristic
411C2×C4#1451975011yescharacteristic
412C2×C4#1451975011yescharacteristic
413C2×C4#1451979812yes—
414C2×C4#1451980912yes—
415C2×C4C2×D4×D6111yescharacteristic
416C2×C4C2×D4×D6111yescharacteristic
417C2×C4C2×#1175822211yescharacteristic
418C8—42no—
419C8—42no—
420C8—1221no—
421C8—1221no—
422C8—1221no—
423C8—1221no—
424C8—2442no—
425C22—21no—
426C22—21no—
427C22—4881no—
428C22—4881no—
429C22—4881no—
430C22#1683998712yes—
431C22C2×#1451975011yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—81no—
436C4—81no—
437C4—1224no—
438C4—4881no—
439C4—2442no—
440C4#1683998712yes—
441C4#135×D6112yes—
442C4C2×#1451979811yescharacteristic
443C4C2×#1451980911yescharacteristic
444C2—22no—
445C2—9761no—
446C2C2×#1683998711yescharacteristic
447C2#2145539911yescharacteristic
448C2#2145553811yescharacteristic
subgroupG/H
centerC2×C4#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1542C2
socleC22×C61C2×#121
prime radical#16840312C22
hypercenter#1542D61
hypocenterC61#19123
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
2. #21455854C2semidirect
4. C2×#16839886C2semidirect
5. #21445280C2semidirect
6. #21445266C2semidirect
7. #21445252C2semidirect
8. #21445238C2semidirect
9. #21444565C2semidirect
11. C61×#1542C2semidirect
229. #1542D61semidirect
273. C61#19123semidirect

Maximal subgroups

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

subgroupindex
#214561442
#214558542
#214558512
C2×#168398862
#214452802
#214452662
#214452522
#214452382
#214445652
#214444692
C61×#15422
#1912361