Finite Group Databasebeta

← #29662694

Subgroups — #29662694

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#21455858C211yesmaximal, characteristic, complemented
3#21455850C211yesmaximal, characteristic
4#21445401C212yesmaximal, complemented
5#21445387C212yesmaximal, complemented
6#21445373C212yesmaximal, complemented
7#21445359C212yesmaximal, complemented
8#21444567C211yesmaximal, characteristic, complemented
9#21444477C211yesmaximal, characteristic, complemented
10#21444469C211yesmaximal, characteristic
11C2×C61×#446C211yesmaximal, characteristic, complemented
12#16840319C2211yescharacteristic
13#16840312C2211yescharacteristic
14#16840117—21no—
15#16840117—21no—
16#16840113C2211yescharacteristic
17#16840113C2211yescharacteristic
18#16840109C2211yescharacteristic
19#16840109C2211yescharacteristic
20#16840097—21no—
21#16840080—21no—
22#16840057C2212yes—
23#16840047C2212yes—
24#16839972C2212yes—
25#16839962C2212yes—
26#16839918—21no—
27#16839901—21no—
28C4×#11758202—22no—
29C4×#11758201—22no—
30#16839815C2211yescharacteristic
31#16839815C2211yescharacteristic
32#16839759—21no—
33#16839759—21no—
34#16839515C2212yes—
35#16839513C2212yes—
36#16839510C2212yes—
37#16839509C2212yes—
38#16839507C2212yes—
39#16839505C2212yes—
40C2×C4×Q8×C61C2211yescharacteristic
41C61×#446—21no—
42C61×#446—21no—
43C61×#446C2212yes—
44C61×#446C2212yes—
45C2×C4⋊C8×C61—21no—
46C2×C4⋊C8×C61C2211yescharacteristic
47C2×#97×C61—21no—
48C2×C4×C8×C61C2211yescharacteristic
49C2×#11758222—21no—
50C2×#11758202—22no—
51C2×#11758201—22no—
52#14519777C2311yescharacteristic
53#14519777C2311yescharacteristic
54#14519777C2311yescharacteristic
55#14519774C2311yescharacteristic
56#14519769—21no—
57#14519765—21no—
58#14519756—21no—
59#14519756—21no—
60#14519751—21no—
61#14519751—21no—
62C4×Dic122—21no—
63C4×Dic122—21no—
64C4×D244—21no—
65C4×D244—21no—
66#14519736—21no—
67#14519710—22no—
68#14519708—22no—
69C4⋊#92418C2312yes—
70C4⋊#92418C2312yes—
71#14519702—21no—
72#14519702—21no—
73#14519702—21no—
74#14519702—21no—
75#14519701—22no—
76#14519701—22no—
77#14519700—22no—
78#14519699—21no—
79#14519699—21no—
80#14519699—21no—
81#14519699—21no—
82#14519697—22no—
83C22⋊#92418—21no—
84C22⋊#92418—21no—
85C4×#92418—21no—
86C4×#92418—21no—
87C22×Q8×C61D411yescharacteristic
88C22×C8×C61—21no—
89C22×C8×C61D411yescharacteristic
90C22×C8×C61D411yescharacteristic
91C4×Q8×C61—21no—
92C4×Q8×C61—21no—
93C4×Q8×C61D412yes—
94C4×Q8×C61C2312yes—
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61D411yescharacteristic
97C2×C42×C61—21no—
98C2×C42×C61C2311yescharacteristic
99C4⋊C8×C61—22no—
100C4⋊C8×C61—22no—
101C4⋊C8×C61—21no—
102C4⋊C8×C61C2312yes—
103#97×C61—22no—
104#97×C61—22no—
105C4×C8×C61D411yescharacteristic
106C4×C8×C61D411yescharacteristic
107C4×C8×C61C2311yescharacteristic
108C4×C8×C61C2311yescharacteristic
109C2×Q8×C61—21no—
110C2×Q8×C61—42no—
111C2×Q8×C61C2×D412yes—
112C22×C4×C61—21no—
113C22×C4×C61—21no—
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61#4111yescharacteristic
117C2×C22⋊D61—41no—
118#11758222—42no—
119#11758222—42no—
120C2×D244—21no—
121C2×D244—21no—
122C2×D244—21no—
123C2×C4×D61—41no—
124C2×Dic122—21no—
125C2×Dic122—21no—
126C2×Dic122—21no—
127C2×C8×C61—22no—
128C2×C8×C61—22no—
129C2×C8×C61—22no—
130C2×C8×C61—42no—
131C2×C8×C61C2×D411yescharacteristic
132C2×C8×C61C2×D411yescharacteristic
133C2×C8×C61C2×D411yescharacteristic
134C2×C8×C61C2×D411yescharacteristic
135C4⋊C4×C61—22no—
136C4⋊C4×C61—21no—
137C4⋊C4×C61—22no—
138C4⋊C4×C61C2×D412yes—
139C42×C61—22no—
140C42×C61—22no—
141C42×C61C2×D411yescharacteristic
142C42×C61C2×D411yescharacteristic
143C42×C61#4111yescharacteristic
144C42×C61C2411yescharacteristic
145C22⋊Dic61—41no—
146#11758202—44no—
147#11758201—44no—
148#11758198—41no—
149#11758198—41no—
150C4⋊Dic61—21no—
151C4⋊Dic61—21no—
152C4⋊Dic61—21no—
153C4⋊Dic61—21no—
154C4⋊Dic61—21no—
155C4⋊Dic61—21no—
156#11758196—41no—
157#11758196—41no—
158C4×Dic61—41no—
159C2×#92418—22no—
160C2×#92418—22no—
161C23×C61#12111yescharacteristic
162C22×D61—41no—
163Q8×C61—22no—
164Q8×C61—22no—
165Q8×C61—42no—
166C2×C4×C61—22no—
167C2×C4×C61—22no—
168C2×C4×C61—22no—
169C2×C4×C61—41no—
170C2×C4×C61—42no—
171C2×C4×C61—42no—
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61#12111yescharacteristic
174C2×C4×C61#12111yescharacteristic
175C2×C4×C61#13512yes—
176C2×C4×C61#13712yes—
177C2×C4×C61C22×D411yescharacteristic
178C2×C4×C61C22×D411yescharacteristic
179C2×C4×C61C2×#4111yescharacteristic
180C22⋊D61—82no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184D244—41no—
185D244—41no—
186D244—42no—
187D244—81no—
188C4×D61—82no—
189Dic122—41no—
190Dic122—41no—
191Dic122—42no—
192Dic122—81no—
193C8×C61—21no—
194C8×C61—21no—
195C8×C61—21no—
196C8×C61—21no—
197C8×C61—42no—
198#92418—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—42no—
212C4×C61—42no—
213C4×C61#46412yes—
214C4×C61C2×#13511yescharacteristic
215C4×C61C2×#13711yescharacteristic
216C4×C61#57512yes—
217Dic61—81no—
218Dic61—81no—
219Dic61—81no—
220#3131—611no—
221#3104—611no—
222#3103—611no—
223C2×#446D6111yescharacteristic, complemented
224#1704—612no—
225#1702—612no—
226#1700—612no—
227#1698—612no—
228#1564—611no—
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×Q8C2×D6111yescharacteristic
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—21no—
254#446—21no—
255#446C2×D6112yes—
256#446C2×D6112yes—
257C4×Q16—1222no—
258C4×SD16—1222no—
259#431—611no—
260#431—611no—
261C2×C4⋊C8—21no—
262C2×C4⋊C8C2×D6111yescharacteristic
263#416—1221no—
264#416—1221no—
265C2×#97—21no—
266C2×C4×C8C2×D6111yescharacteristic
267#335—612no—
268#334—612no—
269#333—612no—
270#332—612no—
271#332—612no—
272#331—612no—
273C61#1915511yescharacteristic, complemented, Sylow
274C2×#41—1221no—
275C22×Q8D24411yescharacteristic
276C2×Q16—1222no—
277C2×SD16—1222no—
278C22×C8—21no—
279C22×C8C22⋊D6111yescharacteristic
280C22×C8C22⋊D6111yescharacteristic
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—21no—
292C4×Q8—21no—
293C4×Q8—1221no—
294C4×Q8—1221no—
295C4×Q8D24412yes—
296C4×Q8C22×D6112yes—
297C4×D4—1221no—
298C4×D4—1221no—
299#117—1221no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4D24411yescharacteristic
302C2×C42—21no—
303C2×C42C22×D6111yescharacteristic
304#107—1222no—
305#106—1222no—
306C4⋊C8—22no—
307C4⋊C8—22no—
308C4⋊C8—21no—
309C4⋊C8—612no—
310C4⋊C8—612no—
311C4⋊C8C22×D6112yes—
312#103—1222no—
313#103—1222no—
314#103—1221no—
315#103—1221no—
316#103—1221no—
317#103—1221no—
318#103—1222no—
319#102—1221no—
320#102—1221no—
321#102—1221no—
322#102—1221no—
323#102—1222no—
324C22⋊C8—1221no—
325C22⋊C8—1221no—
326#97—22no—
327#97—22no—
328C4×C8—1221no—
329C4×C8—1221no—
330C4×C8C22⋊D6111yescharacteristic
331C4×C8C22⋊D6111yescharacteristic
332C4×C8C22×D6111yescharacteristic
333C4×C8C22×D6111yescharacteristic
334#41—2442no—
335#41—2442no—
336C2×Q8—21no—
337C2×Q8—42no—
338C2×Q8—1221no—
339C2×Q8—1221no—
340C2×Q8—1221no—
341C2×Q8C2×D24412yes—
342C2×D4—1221no—
343C2×D4—1221no—
344C2×D4—1221no—
345C2×D4—2441no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—2441no—
349C22×C4C2×D24411yescharacteristic
350C22×C4#1175822211yescharacteristic
351C22×C4C2×C22⋊D6111yescharacteristic
352Q16—2444no—
353SD16—2444no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—42no—
358C2×C8—1222no—
359C2×C8—1222no—
360C2×C8C2×C22⋊D6111yescharacteristic
361C2×C8C2×C22⋊D6111yescharacteristic
362C2×C8C2×C22⋊D6111yescharacteristic
363C2×C8C2×C22⋊D6111yescharacteristic
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—21no—
367C4⋊C4—1221no—
368C4⋊C4—1221no—
369C4⋊C4—1221no—
370C4⋊C4—1221no—
371C4⋊C4—1221no—
372C4⋊C4—1221no—
373C4⋊C4—2441no—
374C4⋊C4—2441no—
375C4⋊C4C2×D24412yes—
376C22⋊C4—2441no—
377C22⋊C4—2441no—
378C22⋊C4—2441no—
379C42—22no—
380C42—22no—
381C42—2441no—
382C42C2×D24411yescharacteristic
383C42#1175822211yescharacteristic
384C42C2×C22⋊D6111yescharacteristic
385C42C23×D6111yescharacteristic
386C23—2441no—
387C23#1451975111yescharacteristic
388Q8—22no—
389Q8—22no—
390Q8—42no—
391Q8—4881no—
392Q8—2441no—
393Q8—2441no—
394Q8—2442no—
395D4—4881no—
396D4—4882no—
397D4—2441no—
398D4—2441no—
399D4—2442no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—4882no—
407C2×C4—2441no—
408C2×C4—2441no—
409C2×C4—2441no—
410C2×C4#1451975111yescharacteristic
411C2×C4#1451975111yescharacteristic
412C2×C4#1451975111yescharacteristic
413C2×C4#1451979712yes—
414C2×C4#1451980812yes—
415C2×C4C22×C22⋊D6111yescharacteristic
416C2×C4C22×D24411yescharacteristic
417C2×C4C2×#1175822211yescharacteristic
418C8—21no—
419C8—21no—
420C8—21no—
421C8—21no—
422C8—42no—
423C8—2442no—
424C8—2442no—
425C22—21no—
426C22—21no—
427C22—4881no—
428C22—4881no—
429C22—4881no—
430C22#1683998412yes—
431C22C2×#1451975111yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—42no—
436C4—42no—
437C4—4881no—
438C4—4881no—
439C4—4881no—
440C4#1683998412yes—
441C4C2×#1451979711yescharacteristic
442C4C2×#1451980811yescharacteristic
443C4#1684056212yes—
444C2—22no—
445C2—9761no—
446C2C2×#1683998411yescharacteristic
447C2#2145542811yescharacteristic
448C2#2145553911yescharacteristic
subgroupG/H
centerC2×C4#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#446C2
socleC22×C61C2×#121
prime radical#16840312C22
hypercenterC2×#446D61
hypocenterC61#19155
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #21455858C2semidirect
4. #21445401C2semidirect
5. #21445387C2semidirect
6. #21445373C2semidirect
7. #21445359C2semidirect
8. #21444567C2semidirect
9. #21444477C2semidirect
11. C2×C61×#446C2semidirect
223. C2×#446D61semidirect
273. C61#19155semidirect

Maximal subgroups

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

subgroupindex
#214561422
#214558582
#214558502
#214454012
#214453872
#214453732
#214453592
#214445672
#214444772
#214444692
C2×C61×#4462
#1915561