Finite Group Databasebeta

← #29576108

Subgroups — #29576108

Order 15616.

456 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455607C211yesmaximal, characteristic
2#21454786C211yesmaximal, characteristic
3#21444317C211yesmaximal, characteristic, complemented
4#21444273C211yesmaximal, characteristic, complemented
5#21443714C211yesmaximal, characteristic, complemented
6#21443660C211yesmaximal, characteristic, complemented
7C61×#1806C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16840069—21no—
10#16840062—21no—
11#16840057C411yescharacteristic, complemented
12#16840052C411yescharacteristic, complemented
13#16840047C411yescharacteristic, complemented
14#16840042C411yescharacteristic, complemented
15#16839893—21no—
16#16839840—21no—
17#16839834—22no—
18#16839815—21no—
19#16839815C2211yescharacteristic
20#16839798—21no—
21C2×C4⋊#92418C2211yescharacteristic
22#16839758—21no—
23C4×#11758194—21no—
24C2×C4×#92418C2211yescharacteristic
25#16839498—22no—
26#16839492—21no—
27#16839492—21no—
28C4×#41×C61C2211yescharacteristic
29C61×#423C2211yescharacteristic
30C2×#104×C61—21no—
31C4×C4⋊C4×C61C2211yescharacteristic
32C61×#339—21no—
33C2×#11758194—22no—
34C22×#92418—21no—
35C22×#92418—21no—
36#14519777C2×C411yescharacteristic
37#14519777C2×C411yescharacteristic
38#14519769—21no—
39#14519756—21no—
40#14519756—21no—
41C4×Dic122—21no—
42C4×Dic122—21no—
43#14519736—21no—
44#14519710—21no—
45#14519710—21no—
46#14519708—21no—
47#14519708—21no—
48C4⋊#92418—22no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51C4⋊#92418C2×C411yescharacteristic
52C4⋊#92418C2×C411yescharacteristic
53#14519701—21no—
54#14519701—21no—
55#14519698—21no—
56#14519698—21no—
57C22⋊#92418—22no—
58C22⋊#92418D412yes—
59#14519688—22no—
60C4×#92418—21no—
61C4×#92418—21no—
62C4×#92418D411yescharacteristic
63C4×#92418D411yescharacteristic
64C2×#41×C61D411yescharacteristic
65C2×M16×C61—21no—
66C4×Q8×C61C2×C411yescharacteristic
67C4×Q8×C61D411yescharacteristic
68C4×D4×C61—21no—
69C4×D4×C61—21no—
70C4×D4×C61C2×C411yescharacteristic
71C4×D4×C61D411yescharacteristic
72#117×C61—21no—
73#117×C61D411yescharacteristic
74C2×C4⋊C4×C61—21no—
75C2×C42×C61—21no—
76C2×C42×C61—21no—
77C2×C42×C61C2311yescharacteristic
78C4⋊C8×C61—21no—
79C4⋊C8×C61—21no—
80#104×C61—42no—
81#95×C61—21no—
82#41×C61—21no—
83#41×C61—21no—
84#41×C61—21no—
85#41×C61—21no—
86C2×Q8×C61C22⋊C411yescharacteristic
87C2×D4×C61—21no—
88C2×D4×C61C22⋊C411yescharacteristic
89C22×C4×C61—21no—
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—41no—
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61#4111yescharacteristic
96C2×Dic122—21no—
97C2×Dic122—21no—
98M16×C61—41no—
99M16×C61—41no—
100C2×C8×C61—41no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—22no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61C22⋊C411yescharacteristic
106C4⋊C4×C61C22⋊C411yescharacteristic
107C22⋊C4×C61—21no—
108C22⋊C4×C61—21no—
109C22⋊C4×C61—21no—
110C42×C61—21no—
111C42×C61—21no—
112C42×C61—21no—
113C42×C61—41no—
114C42×C61—41no—
115C42×C61C22×C411yescharacteristic
116C42×C61C2×D411yescharacteristic
117C42×C61C2×D411yescharacteristic
118C42×C61#4111yescharacteristic
119C22⋊Dic61—41no—
120C4⋊Dic61—21no—
121C4⋊Dic61—21no—
122C4⋊Dic61—21no—
123C4⋊Dic61—21no—
124#11758196—41no—
125#11758196—41no—
126C4×Dic61—41no—
127#11758194—44no—
128C2×#92418—21no—
129C2×#92418—21no—
130C2×#92418—21no—
131C2×#92418—21no—
132C2×#92418—22no—
133C2×#92418—42no—
134C2×#92418—41no—
135C2×#92418—41no—
136C23×C61—21no—
137C23×C61#12111yescharacteristic
138Q8×C61—21no—
139Q8×C61—21no—
140D4×C61—21no—
141D4×C61—21no—
142D4×C61—41no—
143D4×C61—41no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—41no—
150C2×C4×C61—42no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—42no—
156C2×C4×C61—81no—
157C2×C4×C61—81no—
158C2×C4×C61C2×C22⋊C411yescharacteristic
159C2×C4×C61C4×D411yescharacteristic
160C2×C4×C61C4×D411yescharacteristic
161C2×C4×C61#12011yescharacteristic
162C2×C4×C61#12111yescharacteristic
163C2×C4×C61#12311yescharacteristic
164C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C61#13711yescharacteristic
166C2×C4×C61#13711yescharacteristic
167C2×C4×C61#13711yescharacteristic
168C2×Dic61—41no—
169C2×Dic61—41no—
170Dic122—41no—
171Dic122—41no—
172Dic122—81no—
173C8×C61—81no—
174#92418—22no—
175#92418—41no—
176#92418—42no—
177#92418—41no—
178#92418—41no—
179#9209—611nomaximal, Sylow
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61#38611yescharacteristic
186C22×C61#46811yescharacteristic
187C22×C61#47011yescharacteristic
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—41no—
192C4×C61—41no—
193C4×C61—41no—
194C4×C61—82no—
195C4×C61#41711yescharacteristic
196C4×C61#41911yescharacteristic
197C4×C61#44311yescharacteristic
198C4×C61#44411yescharacteristic
199C4×C61#46811yescharacteristic
200C4×C61#47011yescharacteristic
201Dic61—81no—
202Dic61—81no—
203#3076—611no—
204#2965—611no—
205#1806D6111yescharacteristic
206#1503—611no—
207#1493—611no—
208#1301—611no—
209#1279—611no—
210C2×C61—21no—
211C2×C61—21no—
212C2×C61—81no—
213C2×C61#187611yescharacteristic
214C2×C61#189411yescharacteristic
215C2×C61#190611yescharacteristic
216#533—611no—
217C4×#41C2×D6111yescharacteristic
218#479—1221no—
219#478—1221no—
220#477—611no—
221#476—611no—
222#475—611no—
223#474—611no—
224#446—1221no—
225#436—1221no—
226#435—1222no—
227#431—611no—
228#431—1221no—
229#427—1221no—
230#423C2×D6111yescharacteristic
231C2×C4⋊C8—611no—
232C2×#104—21no—
233#416—1221no—
234C4×M16—1221no—
235C2×C4×C8—611no—
236C4×C4⋊C4C2×D6111yescharacteristic
237#339—21no—
238#328—1222no—
239Q8⋊C8—1221no—
240Q8⋊C8—1221no—
241C61#920911yescharacteristic, complemented, Sylow
242C2×#41C22⋊D6111yescharacteristic
243C2×M16—21no—
244C2×M16—1222no—
245C22×C8—1221no—
246C22×C8—1221no—
247C4⋊Q8—611no—
248C4⋊Q8—611no—
249#125—1221no—
250C22⋊Q8—1221no—
251C22⋊Q8—1221no—
252C4×Q8—1221no—
253C4×Q8—1221no—
254C4×Q8C4×D6111yescharacteristic
255C4×Q8D24411yescharacteristic
256C4×D4—21no—
257C4×D4—21no—
258C4×D4C4×D6111yescharacteristic
259C4×D4D24411yescharacteristic
260#117—21no—
261#117—1221no—
262#117C22⋊D6111yescharacteristic
263C2×C4⋊C4—21no—
264C2×C42—21no—
265C2×C42—21no—
266C2×C42C22×D6111yescharacteristic
267#107—1221no—
268#107—1221no—
269#106—1221no—
270#106—1221no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—611no—
274C4⋊C8—611no—
275C4⋊C8—1222no—
276C4⋊C8—1221no—
277C4⋊C8—1221no—
278#104—42no—
279#103—1221no—
280#103—1221no—
281#102—1221no—
282#102—1221no—
283C22⋊C8—612no—
284C22⋊C8—1222no—
285#97—1222no—
286C4×C8—611no—
287C4×C8—611no—
288C4×C8—1221no—
289C4×C8—1221no—
290#95—21no—
291#41—21no—
292#41—21no—
293#41—21no—
294#41—21no—
295C2×Q8—1221no—
296C2×Q8—1221no—
297C2×Q8#1175819811yescharacteristic
298C2×D4—21no—
299C2×D4#1175819811yescharacteristic
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4D4×D6111yescharacteristic
305C22×C4#1175822411yescharacteristic
306C22×C4C2×C22⋊D6111yescharacteristic
307M16—41no—
308M16—41no—
309M16—2444no—
310C2×C8—41no—
311C2×C8—1221no—
312C2×C8—1221no—
313C2×C8—1221no—
314C2×C8—1221no—
315C2×C8—1222no—
316C2×C8—2442no—
317C2×C8—2441no—
318C2×C8—2441no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—22no—
322C4⋊C4—41no—
323C4⋊C4—1221no—
324C4⋊C4—1221no—
325C4⋊C4—1221no—
326C4⋊C4—1221no—
327C4⋊C4—2441no—
328C4⋊C4—2441no—
329C4⋊C4#1175819811yescharacteristic
330C4⋊C4#1175819811yescharacteristic
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—2441no—
335C42—21no—
336C42—21no—
337C42—21no—
338C42—41no—
339C42—41no—
340C42—2441no—
341C42C2×C4×D6111yescharacteristic
342C42C2×D24411yescharacteristic
343C42D4×D6111yescharacteristic
344C42#1175822411yescharacteristic
345C23—21no—
346C23#1451974911yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—4881no—
350Q8—2441no—
351Q8—2441no—
352D4—21no—
353D4—21no—
354D4—41no—
355D4—41no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4C2×#1175819811yescharacteristic
373C2×C4#1451973711yescharacteristic
374C2×C4#1451973711yescharacteristic
375C2×C4#1451974711yescharacteristic
376C2×C4#1451974911yescharacteristic
377C2×C4#1451976111yescharacteristic
378C2×C4#1451980311yescharacteristic
379C2×C4#1451980711yescharacteristic
380C2×C4#1451980711yescharacteristic
381C2×C4#1451980811yescharacteristic
382C8—81no—
383C8—1222no—
384C8—2441no—
385C8—2442no—
386C8—2441no—
387C8—2441no—
388C22—21no—
389C22—21no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22#1683963911yescharacteristic
394C22#1684000611yescharacteristic
395C22#1684001811yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—82no—
403C4—4881no—
404C4—4881no—
405C4#1683976111yescharacteristic
406C4#1683977011yescharacteristic
407C4#1683987611yescharacteristic
408C4#1683988111yescharacteristic
409C4#1684000611yescharacteristic
410C4#1684001811yescharacteristic
411C2—21no—
412C2—21no—
413C2—81no—
414C2#2144614411yescharacteristic
415C2#2144625011yescharacteristic
416C2#2144631811yescharacteristic
subgroupG/H
centerC2×C4#14519749
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1806C2
socleC22×C61#386
prime radicalC2×#41×C61D4
cosocleC2×C42×C61C23
hypercenter#1806D61
hypocenterC61#9209
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
3. #21444317C2semidirect
4. #21444273C2semidirect
5. #21443714C2semidirect
6. #21443660C2semidirect
11. #16840057C4semidirect
12. #16840052C4semidirect
13. #16840047C4semidirect
14. #16840042C4semidirect
241. C61#9209semidirect

Maximal subgroups

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

subgroupindex
#214556072
#214547862
#214443172
#214442732
#214437142
#214436602
C61×#18062
#920961