Finite Group Databasebeta

← #29576113

Subgroups — #29576113

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#21455601C211yesmaximal, characteristic
2#21454785C211yesmaximal, characteristic
3#21445836C211yesmaximal, characteristic
4#21444318C211yesmaximal, characteristic, complemented
5#21443714C211yesmaximal, characteristic, complemented
6#21443659C211yesmaximal, characteristic, complemented
7C61×#1493C211yesmaximal, characteristic, complemented
8C4×#11758222C2211yescharacteristic
9#16840066—21no—
10#16840059—21no—
11#16840054C411yescharacteristic, complemented
12#16840049C411yescharacteristic, complemented
13#16840044C411yescharacteristic, complemented
14#16840039C411yescharacteristic, complemented
15#16839892—21no—
16#16839841—21no—
17#16839833—22no—
18#16839815C2211yescharacteristic
19#16839813—21no—
20#16839798—21no—
21C2×C4⋊#92418C2211yescharacteristic
22C2×#14519703—21no—
23#16839756—21no—
24C4×#11758189—21no—
25C4×C4⋊Dic61C2211yescharacteristic
26#16839523—21no—
27#16839499—22no—
28C61×#533C2211yescharacteristic
29C61×#423C2211yescharacteristic
30C2×C4×C8×C61C2211yescharacteristic
31C61×Q8⋊C8—21no—
32C61×Q8⋊C8—21no—
33C2×#11758222D411yescharacteristic
34C2×#11758189—22no—
35C22×#92418—21no—
36C4×Dic122C2×C411yescharacteristic
37C4×Dic122D411yescharacteristic
38C4×D244C2×C411yescharacteristic
39C4×D244D411yescharacteristic
40C4×C22⋊D61—21no—
41C4×C22⋊D61—21no—
42#14519736D411yescharacteristic
43#14519734—21no—
44C2×C4⋊Dic61—21no—
45C2×C4×Dic61—21no—
46C42×D61—21no—
47#14519710—21no—
48#14519710—21no—
49#14519708—21no—
50#14519708—21no—
51C4⋊#92418—21no—
52C4⋊#92418—21no—
53C4⋊#92418C2×C411yescharacteristic
54C4⋊#92418C2×C411yescharacteristic
55#14519706—22no—
56#14519703—42no—
57#14519700—21no—
58#14519700—21no—
59#14519697—21no—
60#14519697—21no—
61C22⋊#92418D412yes—
62#14519689—22no—
63#14519687—22no—
64C4×#92418—21no—
65#14519684—21no—
66C2×M16×C61—21no—
67C22×C8×C61—21no—
68C4⋊Q8×C61C2×C411yescharacteristic
69C4⋊Q8×C61C2×C411yescharacteristic
70#125×C61—21no—
71C22⋊Q8×C61—21no—
72C22⋊Q8×C61—21no—
73C4×Q8×C61—21no—
74C4×Q8×C61—21no—
75#117×C61—21no—
76C2×C42×C61C2311yescharacteristic
77C4⋊C8×C61—21no—
78C4⋊C8×C61—21no—
79C4×C8×C61—21no—
80C4×C8×C61D411yescharacteristic
81C4×C8×C61D411yescharacteristic
82C2×Q8×C61—21no—
83C2×Q8×C61—21no—
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61#4111yescharacteristic
87C2×C22⋊D61—21no—
88C22×Dic61—41no—
89#11758222—21no—
90#11758222—21no—
91#11758222—21no—
92#11758222—21no—
93C2×D244C22⋊C411yescharacteristic
94C2×C4×D61—21no—
95C2×C4×D61—21no—
96C2×C4×D61—21no—
97C2×Dic122C22⋊C411yescharacteristic
98M16×C61—41no—
99M16×C61—41no—
100C2×C8×C61—21no—
101C2×C8×C61—21no—
102C2×C8×C61—42no—
103C2×C8×C61—41no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—21no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—41no—
109C4⋊C4×C61—41no—
110C22⋊C4×C61—41no—
111C42×C61—41no—
112C42×C61C22×C411yescharacteristic
113C42×C61C2×D411yescharacteristic
114C42×C61C2×D411yescharacteristic
115C42×C61#4111yescharacteristic
116C22⋊Dic61—21no—
117#11758198—21no—
118#11758198—21no—
119C4⋊Dic61—22no—
120C4⋊Dic61—41no—
121C4⋊Dic61C22⋊C411yescharacteristic
122C4⋊Dic61C22⋊C411yescharacteristic
123#11758196—21no—
124#11758196—21no—
125C4×Dic61—21no—
126C4×Dic61—21no—
127C4×Dic61—21no—
128C4×Dic61—41no—
129C4×Dic61—41no—
130C2×#92418—21no—
131C2×#92418—21no—
132C2×#92418—22no—
133C2×#92418—41no—
134C2×#92418—41no—
135#11758189—44no—
136C23×C61#12111yescharacteristic
137C22×D61—21no—
138Q8×C61—41no—
139Q8×C61—41no—
140Q8×C61—81no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61C2×C22⋊C411yescharacteristic
147C2×C4×C61C4×D411yescharacteristic
148C2×C4×C61C4×D411yescharacteristic
149C2×C4×C61#12011yescharacteristic
150C2×C4×C61#12111yescharacteristic
151C2×C4×C61#12311yescharacteristic
152C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C61#13711yescharacteristic
154C2×C4×C61#13711yescharacteristic
155C2×C4×C61#13711yescharacteristic
156C22⋊D61—41no—
157C22⋊D61—41no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—42no—
162C2×Dic61—81no—
163C2×Dic61—81no—
164D244—21no—
165D244—21no—
166C4×D61—42no—
167C4×D61—41no—
168C4×D61—41no—
169C4×D61—41no—
170C4×D61—41no—
171Dic122—21no—
172Dic122—21no—
173C8×C61—22no—
174C8×C61—41no—
175C8×C61—81no—
176#92418—42no—
177#92418—41no—
178#92418—41no—
179#9209—611nomaximal, Sylow
180C22×C61—21no—
181C22×C61—21no—
182C22×C61#38611yescharacteristic
183C22×C61#46811yescharacteristic
184C22×C61#47011yescharacteristic
185C2×D61—41no—
186C2×D61—41no—
187C2×D61—41no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—81no—
192C4×C61—81no—
193C4×C61#41711yescharacteristic
194C4×C61#41911yescharacteristic
195C4×C61#44311yescharacteristic
196C4×C61#44411yescharacteristic
197C4×C61#46811yescharacteristic
198C4×C61#47011yescharacteristic
199Dic61—41no—
200Dic61—41no—
201Dic61—41no—
202Dic61—82no—
203#3076—611no—
204#2965—611no—
205#1806—611no—
206#1503—611no—
207#1493D6111yescharacteristic, complemented
208#1301—611no—
209#1279—611no—
210C2×C61—21no—
211C2×C61—21no—
212C2×C61#187611yescharacteristic
213C2×C61#189411yescharacteristic
214C2×C61#190611yescharacteristic
215D61—81no—
216#533C2×D6111yescharacteristic
217C4×#41—611no—
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—1221no—
233#416—1221no—
234C4×M16—1221no—
235C2×C4×C8C2×D6111yescharacteristic
236C4×C4⋊C4—611no—
237#339—1221no—
238#328—1222no—
239Q8⋊C8—21no—
240Q8⋊C8—21no—
241C61#920911yescharacteristic, complemented, Sylow
242C2×#41—611no—
243C2×M16—21no—
244C2×M16—1222no—
245C22×C8—21no—
246C22×C8—1221no—
247C4⋊Q8C4×D6111yescharacteristic
248C4⋊Q8C4×D6111yescharacteristic
249#125—21no—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252C4×Q8—21no—
253C4×Q8—21no—
254C4×Q8—611no—
255C4×Q8—611no—
256C4×D4—611no—
257C4×D4—611no—
258C4×D4—1221no—
259C4×D4—1221no—
260#117—21no—
261#117—611no—
262#117—1221no—
263C2×C4⋊C4—1221no—
264C2×C42—1221no—
265C2×C42—1221no—
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—2442no—
279#103—1221no—
280#103—1221no—
281#102—1221no—
282#102—1221no—
283C22⋊C8—612no—
284C22⋊C8—1222no—
285#97—1222no—
286C4×C8—21no—
287C4×C8—1221no—
288C4×C8C22⋊D6111yescharacteristic
289C4×C8C22⋊D6111yescharacteristic
290#95—1221no—
291#41—1221no—
292#41—1221no—
293#41—1221no—
294#41—1221no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—611no—
298C2×D4—611no—
299C2×D4—1221no—
300C22×C4—1221no—
301C22×C4—1221no—
302C22×C4—1221no—
303C22×C4—2441no—
304C22×C4#1175822211yescharacteristic
305C22×C4D4×D6111yescharacteristic
306C22×C4D4×D6111yescharacteristic
307M16—41no—
308M16—41no—
309M16—2444no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—42no—
313C2×C8—41no—
314C2×C8—1221no—
315C2×C8—1221no—
316C2×C8—1222no—
317C2×C8—2441no—
318C2×C8—2441no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—611no—
326C4⋊C4—611no—
327C4⋊C4—1222no—
328C4⋊C4—1221no—
329C4⋊C4—1221no—
330C4⋊C4—2441no—
331C22⋊C4—41no—
332C22⋊C4—1221no—
333C22⋊C4—1221no—
334C22⋊C4—1221no—
335C42—41no—
336C42—1221no—
337C42—1221no—
338C42—1221no—
339C42—2441no—
340C42—2441no—
341C42C2×C4×D6111yescharacteristic
342C42D4×D6111yescharacteristic
343C42#1175822411yescharacteristic
344C42C2×C22⋊D6111yescharacteristic
345C23—1221no—
346C23#1451975011yescharacteristic
347Q8—41no—
348Q8—41no—
349Q8—81no—
350Q8—1221no—
351Q8—1221no—
352D4—1221no—
353D4—1221no—
354D4—2441no—
355D4—2441no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—4881no—
365C2×C4—4881no—
366C2×C4—2442no—
367C2×C4—2442no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4C22⋊C4×D6111yescharacteristic
373C2×C4#1451973711yescharacteristic
374C2×C4C4×C22⋊D6111yescharacteristic
375C2×C4#1451974511yescharacteristic
376C2×C4#1451974811yescharacteristic
377C2×C4#1451975911yescharacteristic
378C2×C4#1451980411yescharacteristic
379C2×C4#1451980611yescharacteristic
380C2×C4#1451980911yescharacteristic
381C2×C4#1451980911yescharacteristic
382C8—22no—
383C8—41no—
384C8—81no—
385C8—2442no—
386C8—2441no—
387C8—2441no—
388C22—21no—
389C22—21no—
390C22—2441no—
391C22—2441no—
392C22—2441no—
393C22#1683963811yescharacteristic
394C22#1684001111yescharacteristic
395C22#1684001911yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—81no—
400C4—81no—
401C4—4882no—
402C4—2441no—
403C4—2441no—
404C4—2441no—
405C4#1683976211yescharacteristic
406C4#1683976911yescharacteristic
407C4#1683987711yescharacteristic
408C4#1683988211yescharacteristic
409C4#1684000511yescharacteristic
410C4#1684001711yescharacteristic
411C2—21no—
412C2—21no—
413C2—4881no—
414C2#2144614911yescharacteristic
415C2#2144624911yescharacteristic
416C2#2144632311yescharacteristic
subgroupG/H
centerC2×C4#14519748
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1493C2
socleC22×C61#386
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenter#1493D61
hypocenterC61#9209
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
4. #21444318C2semidirect
5. #21443714C2semidirect
6. #21443659C2semidirect
7. C61×#1493C2semidirect
11. #16840054C4semidirect
12. #16840049C4semidirect
13. #16840044C4semidirect
14. #16840039C4semidirect
207. #1493D61semidirect
241. C61#9209semidirect

Maximal subgroups

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

subgroupindex
#214556012
#214547852
#214458362
#214443182
#214437142
#214436592
C61×#14932
#920961