Finite Group Databasebeta

← #29576110

Subgroups — #29576110

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#21445839C211yesmaximal, characteristic
3#21444319C211yesmaximal, characteristic, complemented
4#21444275C211yesmaximal, characteristic, complemented
5#21443715C211yesmaximal, characteristic, complemented
6#21443659C211yesmaximal, characteristic, complemented
7C61×#2965C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16840069—21no—
10#16840062—21no—
11#16840057C411yescharacteristic, complemented
12#16840052C411yescharacteristic, complemented
13#16840047C411yescharacteristic, complemented
14#16840042C411yescharacteristic, complemented
15#16839798—21no—
16#16839786C2211yescharacteristic
17C2×C4⋊#92418C2211yescharacteristic
18C2×#14519704—21no—
19#16839758—21no—
20C4×C4⋊Dic61C2211yescharacteristic
21#16839521—21no—
22#16839500—22no—
23#16839494—21no—
24#16839494—21no—
25C4×#41×C61C2211yescharacteristic
26C61×#446—21no—
27C61×#436—21no—
28C61×#435—22no—
29C61×#431—21no—
30C61×#431C2211yescharacteristic
31C4×M16×C61—21no—
32C2×C4×C8×C61C2211yescharacteristic
33C2×#11758194—21no—
34C22×#92418—21no—
35#14519777C2×C411yescharacteristic
36#14519777C2×C411yescharacteristic
37#14519769—21no—
38#14519756—21no—
39#14519756—21no—
40C4×Dic122—21no—
41C4×Dic122—21no—
42#14519736—21no—
43C2×C4⋊Dic61—21no—
44C2×C4×Dic61—21no—
45#14519710—21no—
46#14519710—21no—
47#14519708—21no—
48#14519708—21no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51C4⋊#92418—21no—
52C4⋊#92418C2×C411yescharacteristic
53C4⋊#92418C2×C411yescharacteristic
54#14519704—42no—
55#14519701—21no—
56#14519701—21no—
57#14519698—21no—
58#14519698—21no—
59#14519684—21no—
60C2×#41×C61D411yescharacteristic
61C2×M16×C61—22no—
62C22×C8×C61—21no—
63C4×Q8×C61C2×C411yescharacteristic
64C4×Q8×C61D411yescharacteristic
65C4×D4×C61—21no—
66C4×D4×C61—21no—
67C4×D4×C61C2×C411yescharacteristic
68C4×D4×C61D411yescharacteristic
69#117×C61—21no—
70#117×C61D411yescharacteristic
71C2×C42×C61—21no—
72C2×C42×C61C2311yescharacteristic
73C4⋊C8×C61—22no—
74C4⋊C8×C61—21no—
75C22⋊C8×C61—22no—
76C22⋊C8×C61D412yes—
77#97×C61—22no—
78C4×C8×C61—21no—
79C4×C8×C61—21no—
80C4×C8×C61D411yescharacteristic
81C4×C8×C61D411yescharacteristic
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×C61C2×D411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61#4111yescharacteristic
95C22×Dic61—41no—
96C2×Dic122—21no—
97C2×Dic122—21no—
98M16×C61—44no—
99C2×C8×C61—21no—
100C2×C8×C61—21no—
101C2×C8×C61—22no—
102C2×C8×C61—42no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
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×C61C22×C411yescharacteristic
114C42×C61C2×D411yescharacteristic
115C42×C61C2×D411yescharacteristic
116C42×C61#4111yescharacteristic
117C22⋊Dic61—41no—
118C4⋊Dic61—22no—
119C4⋊Dic61—21no—
120C4⋊Dic61—21no—
121C4⋊Dic61—21no—
122C4⋊Dic61—21no—
123C4⋊Dic61—41no—
124#11758196—41no—
125#11758196—41no—
126C4×Dic61—41no—
127C4×Dic61—41no—
128C4×Dic61—41no—
129#11758194—41no—
130#11758194—41no—
131C2×#92418—21no—
132C2×#92418—21no—
133C2×#92418—41no—
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×C61C2×C22⋊C411yescharacteristic
156C2×C4×C61C4×D411yescharacteristic
157C2×C4×C61C4×D411yescharacteristic
158C2×C4×C61#12011yescharacteristic
159C2×C4×C61#12111yescharacteristic
160C2×C4×C61#12311yescharacteristic
161C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C61#13711yescharacteristic
163C2×C4×C61#13711yescharacteristic
164C2×C4×C61#13711yescharacteristic
165C2×Dic61—42no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—81no—
169C2×Dic61—81no—
170Dic122—41no—
171Dic122—41no—
172Dic122—81no—
173C8×C61—22no—
174C8×C61—41no—
175C8×C61—42no—
176#92418—41no—
177#92418—41no—
178#92418—81no—
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#41711yescharacteristic
195C4×C61#41911yescharacteristic
196C4×C61#44311yescharacteristic
197C4×C61#44411yescharacteristic
198C4×C61#46811yescharacteristic
199C4×C61#47011yescharacteristic
200Dic61—82no—
201Dic61—81no—
202Dic61—81no—
203#3076—611no—
204#2965D6111yescharacteristic
205#1806—611no—
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—21no—
225#436—21no—
226#435—22no—
227#431—21no—
228#431C2×D6111yescharacteristic
229#427—1221no—
230#423—611no—
231C2×C4⋊C8—611no—
232C2×#104—1221no—
233#416—1221no—
234C4×M16—21no—
235C2×C4×C8C2×D6111yescharacteristic
236C4×C4⋊C4—611no—
237#339—1221no—
238#328—1222no—
239Q8⋊C8—1221no—
240Q8⋊C8—1221no—
241C61#920911yescharacteristic, complemented, Sylow
242C2×#41D24411yescharacteristic
243C2×M16—22no—
244C2×M16—1221no—
245C22×C8—21no—
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×Q8C22⋊D6111yescharacteristic
256C4×D4—21no—
257C4×D4—21no—
258C4×D4C4×D6111yescharacteristic
259C4×D4C22⋊D6111yescharacteristic
260#117—21no—
261#117—1221no—
262#117D24411yescharacteristic
263C2×C4⋊C4—1221no—
264C2×C42—21no—
265C2×C42—1221no—
266C2×C42C22×D6111yescharacteristic
267#107—1221no—
268#107—1221no—
269#106—1221no—
270#106—1221no—
271C4⋊C8—22no—
272C4⋊C8—21no—
273C4⋊C8—611no—
274C4⋊C8—611no—
275C4⋊C8—1221no—
276C4⋊C8—1221no—
277C4⋊C8—1221no—
278#104—2442no—
279#103—1221no—
280#103—1221no—
281#102—1221no—
282#102—1221no—
283C22⋊C8—22no—
284C22⋊C8C22⋊D6112yes—
285#97—22no—
286C4×C8—21no—
287C4×C8—21no—
288C4×C8C22⋊D6111yescharacteristic
289C4×C8C22⋊D6111yescharacteristic
290#95—1221no—
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—2441no—
304C22×C4C2×D24411yescharacteristic
305C22×C4#1175822211yescharacteristic
306C22×C4C2×C22⋊D6111yescharacteristic
307M16—44no—
308M16—2441no—
309M16—2441no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—22no—
313C2×C8—42no—
314C2×C8—1221no—
315C2×C8—1221no—
316C2×C8—2441no—
317C2×C8—2441no—
318C2×C8—2441no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—1222no—
322C4⋊C4—1221no—
323C4⋊C4—1221no—
324C4⋊C4—1221no—
325C4⋊C4—1221no—
326C4⋊C4—2441no—
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—2441no—
339C42—2441no—
340C42—2441no—
341C42C2×C4×D6111yescharacteristic
342C42#1175822211yescharacteristic
343C42C2×C22⋊D6111yescharacteristic
344C42C2×C22⋊D6111yescharacteristic
345C23—21no—
346C23#1451975111yescharacteristic
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—4881no—
368C2×C4—4881no—
369C2×C4—2442no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4C2×#1175819811yescharacteristic
373C2×C4C4×C22⋊D6111yescharacteristic
374C2×C4C4×C22⋊D6111yescharacteristic
375C2×C4#1451974611yescharacteristic
376C2×C4#1451975111yescharacteristic
377C2×C4#1451976011yescharacteristic
378C2×C4#1451980511yescharacteristic
379C2×C4#1451981011yescharacteristic
380C2×C4#1451981011yescharacteristic
381C2×C4#1451981011yescharacteristic
382C8—22no—
383C8—41no—
384C8—42no—
385C8—4881no—
386C8—2441no—
387C8—2441no—
388C22—21no—
389C22—21no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22#1683964111yescharacteristic
394C22#1684000811yescharacteristic
395C22#1684002011yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—4882no—
403C4—4881no—
404C4—4881no—
405C4#1683976411yescharacteristic
406C4#1683977211yescharacteristic
407C4#1683987711yescharacteristic
408C4#1683988211yescharacteristic
409C4#1684000811yescharacteristic
410C4#1684002011yescharacteristic
411C2—21no—
412C2—21no—
413C2—81no—
414C2#2144614611yescharacteristic
415C2#2144625211yescharacteristic
416C2#2144632011yescharacteristic
subgroupG/H
centerC2×C4#14519751
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2965C2
socleC22×C61#386
prime radicalC2×#41×C61D4
cosocleC2×C42×C61C23
hypercenter#2965D61
hypocenterC61#9209
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2965

Complements

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

NH ≅ G/Ntype
3. #21444319C2semidirect
4. #21444275C2semidirect
5. #21443715C2semidirect
6. #21443659C2semidirect
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
#214458392
#214443192
#214442752
#214437152
#214436592
C61×#29652
#920961