Finite Group Databasebeta

← #29663958

Subgroups — #29663958

Order 15616.

608 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456333C211yesmaximal, characteristic, complemented
2#21455981C212yesmaximal
3#21445223C211yesmaximal, characteristic, complemented
4#21445218C211yesmaximal, characteristic, complemented
5#21445213C211yesmaximal, characteristic, complemented
6#21445208C211yesmaximal, characteristic, complemented
7#21445201C212yesmaximal, complemented
8#21445194C212yesmaximal, complemented
9#21444582C211yesmaximal, characteristic, complemented
10#21444527C212yesmaximal, complemented
11C8×#41×C61C211yesmaximal, characteristic
12#16840319C2212yes—
13#16840167C2211yescharacteristic
14#16840167C2211yescharacteristic
15#16840164—21no—
16#16840164—21no—
17#16840160C2212yes—
18#16840103—22no—
19#16840057C2212yes—
20#16840052C2212yes—
21#16839972C2212yes—
22#16839967C2212yes—
23#16839924—22no—
24#16839867—22no—
25#16839862—22no—
26#16839819C2212yes—
27#16839800—21no—
28#16839800—21no—
29#16839515C2211yescharacteristic
30#16839515C2211yescharacteristic
31#16839513C2212yes—
32#16839510C2212yes—
33#16839510C2212yes—
34#16839507C2212yes—
35#16839507C2212yes—
36C4×#41×C61C2211yescharacteristic
37C8×Q8×C61C2211yescharacteristic
38C8×Q8×C61C2211yescharacteristic
39C8×D4×C61—21no—
40C8×D4×C61—21no—
41C8×D4×C61C2211yescharacteristic
42C8×D4×C61C2211yescharacteristic
43C61×#431—21no—
44C61×#431C2211yescharacteristic
45C2×C4×C8×C61—21no—
46C2×C4×C8×C61C2211yescharacteristic
47C2×#11758202—22no—
48C2×#11758200—22no—
49#14519777C2312yes—
50#14519777C2312yes—
51#14519769—22no—
52#14519756—22no—
53#14519756—22no—
54C4×Dic122—22no—
55C4×Dic122—22no—
56#14519736—22no—
57#14519711—21no—
58#14519711—21no—
59#14519711—21no—
60#14519711—21no—
61#14519710—22no—
62#14519709—22no—
63#14519709—22no—
64#14519708—22no—
65C4⋊#92418C2312yes—
66C4⋊#92418C2312yes—
67#14519701—22no—
68#14519700—22no—
69#14519700—22no—
70#14519698—22no—
71C22⋊#92418—22no—
72#14519688—22no—
73C2×#41×C61D411yescharacteristic
74C22×C8×C61—21no—
75C22×C8×C61—21no—
76C22×C8×C61D411yescharacteristic
77C22×C8×C61D411yescharacteristic
78C4×Q8×C61D411yescharacteristic
79C4×Q8×C61C2311yescharacteristic
80C4×D4×C61—21no—
81C4×D4×C61—21no—
82C4×D4×C61D411yescharacteristic
83C4×D4×C61C2311yescharacteristic
84#117×C61—21no—
85#117×C61D411yescharacteristic
86C2×C42×C61—21no—
87C2×C42×C61C2311yescharacteristic
88C4⋊C8×C61—21no—
89C4⋊C8×C61—21no—
90C4⋊C8×C61C2311yescharacteristic
91C4⋊C8×C61C2311yescharacteristic
92C22⋊C8×C61—21no—
93C22⋊C8×C61—21no—
94C22⋊C8×C61—21no—
95C4×C8×C61—21no—
96C4×C8×C61—21no—
97C4×C8×C61—21no—
98C4×C8×C61D411yescharacteristic
99C4×C8×C61D411yescharacteristic
100C4×C8×C61C2311yescharacteristic
101C4×C8×C61C2311yescharacteristic
102#41×C61—22no—
103#41×C61—22no—
104C2×Q8×C61C2×D411yescharacteristic
105C2×D4×C61—21no—
106C2×D4×C61C2×D411yescharacteristic
107C22×C4×C61—21no—
108C22×C4×C61—21no—
109C22×C4×C61—21no—
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61#4111yescharacteristic
113C2×Dic122—22no—
114C2×Dic122—22no—
115C2×C8×C61—22no—
116C2×C8×C61—22no—
117C2×C8×C61—21no—
118C2×C8×C61—21no—
119C2×C8×C61—42no—
120C2×C8×C61—42no—
121C2×C8×C61C2×D411yescharacteristic
122C2×C8×C61C2×D411yescharacteristic
123C2×C8×C61C2×D411yescharacteristic
124C2×C8×C61C2×D411yescharacteristic
125C4⋊C4×C61—21no—
126C4⋊C4×C61—21no—
127C4⋊C4×C61C2×D411yescharacteristic
128C4⋊C4×C61C2×D411yescharacteristic
129C22⋊C4×C61—21no—
130C22⋊C4×C61—21no—
131C22⋊C4×C61—21no—
132C42×C61—21no—
133C42×C61—21no—
134C42×C61—21no—
135C42×C61C2×D411yescharacteristic
136C42×C61C2×D411yescharacteristic
137C42×C61#4111yescharacteristic
138C42×C61C2411yescharacteristic
139C22⋊Dic61—42no—
140#11758202—44no—
141#11758200—44no—
142C4⋊Dic61—22no—
143C4⋊Dic61—22no—
144C4⋊Dic61—22no—
145C4⋊Dic61—22no—
146#11758196—42no—
147#11758196—42no—
148C4×Dic61—42no—
149C2×#92418—22no—
150C2×#92418—22no—
151C23×C61—21no—
152C23×C61#12111yescharacteristic
153Q8×C61—21no—
154Q8×C61#13512yes—
155D4×C61—24no—
156D4×C61—21no—
157D4×C61#13512yes—
158C2×C4×C61—24no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—41no—
167C2×C4×C61—42no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61#12111yescharacteristic
171C2×C4×C61#12111yescharacteristic
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61C22×D411yescharacteristic
174C2×C4×C61C22×D411yescharacteristic
175C2×C4×C61C2×#4111yescharacteristic
176C2×Dic61—42no—
177C2×Dic61—42no—
178Dic122—42no—
179Dic122—42no—
180Dic122—82no—
181C8×C61—21no—
182C8×C61—21no—
183C8×C61—41no—
184C8×C61—41no—
185C8×C61#13712yes—
186C8×C61#13712yes—
187#92418—42no—
188#92418—42no—
189#19273—611nomaximal, Sylow
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—22no—
193C22×C61—21no—
194C22×C61—41no—
195C22×C61—41no—
196C22×C61C2×#12111yescharacteristic
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—22no—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—41no—
203C4×C61—41no—
204C4×C61C2×#13511yescharacteristic
205C4×C61C2×#13511yescharacteristic
206C4×C61C2×#13711yescharacteristic
207C4×C61C2×#13711yescharacteristic
208Dic61—82no—
209Dic61—82no—
210#3160—611no—
211#3116—612no—
212C8×#41D6111yescharacteristic
213#1676—611no—
214#1675—611no—
215#1674—611no—
216#1673—611no—
217#1672—612no—
218#1671—612no—
219#1568—611no—
220#1554—612no—
221C2×C61—41no—
222C2×C61—42no—
223C2×C61#303911yescharacteristic
224C2×C61#305011yescharacteristic
225C2×C61#306711yescharacteristic
226#533—612no—
227C4×#41C2×D6111yescharacteristic
228#500—611no—
229#500—611no—
230#499—1221no—
231#499—1221no—
232#498—612no—
233#485—1222no—
234#477—612no—
235#476—612no—
236#462—612no—
237#461—612no—
238#452—1222no—
239C8×Q8C2×D6111yescharacteristic
240C8×Q8C2×D6111yescharacteristic
241#441—1222no—
242#440—1222no—
243C8×D4—21no—
244C8×D4—21no—
245C8×D4C2×D6111yescharacteristic
246C8×D4C2×D6111yescharacteristic
247#432—612no—
248#431—21no—
249#431C2×D6111yescharacteristic
250#427—1221no—
251#427—1221no—
252C2×C4×C8—21no—
253C2×C4×C8C2×D6111yescharacteristic
254#335—611no—
255#335—611no—
256#334—612no—
257#333—612no—
258#333—612no—
259#332—612no—
260#332—612no—
261C61#1927311yescharacteristic, complemented, Sylow
262C2×#41D24411yescharacteristic
263C2×Q16—1222no—
264C2×SD16—1222no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8C22⋊D6111yescharacteristic
268C22×C8C22⋊D6111yescharacteristic
269C4⋊Q8—612no—
270C4⋊Q8—612no—
271#125—1222no—
272C22⋊Q8—1222no—
273C22⋊Q8—1222no—
274C4×Q8—1222no—
275C4×Q8—1222no—
276C4×Q8D24411yescharacteristic
277C4×Q8C22×D6111yescharacteristic
278C4×D4—21no—
279C4×D4—21no—
280C4×D4D24411yescharacteristic
281C4×D4C22×D6111yescharacteristic
282#117—21no—
283#117—1222no—
284#117D24411yescharacteristic
285C2×C42—21no—
286C2×C42C22×D6111yescharacteristic
287#107—1221no—
288#107—1221no—
289#107—1221no—
290#107—1221no—
291#107—1222no—
292#106—1222no—
293#106—1222no—
294#106—1222no—
295C4⋊C8—21no—
296C4⋊C8—21no—
297C4⋊C8—612no—
298C4⋊C8—612no—
299C4⋊C8C22×D6111yescharacteristic
300C4⋊C8C22×D6111yescharacteristic
301#103—1222no—
302#103—1222no—
303#103—1222no—
304#102—1222no—
305C22⋊C8—21no—
306C22⋊C8—21no—
307C22⋊C8—21no—
308C22⋊C8—1222no—
309#97—1222no—
310C4×C8—21no—
311C4×C8—21no—
312C4×C8—21no—
313C4×C8C22⋊D6111yescharacteristic
314C4×C8C22⋊D6111yescharacteristic
315C4×C8C22×D6111yescharacteristic
316C4×C8C22×D6111yescharacteristic
317#41—22no—
318#41—22no—
319C2×Q8—1222no—
320C2×Q8—1222no—
321C2×Q8C2×D24411yescharacteristic
322C2×D4—21no—
323C2×D4C2×D24411yescharacteristic
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4C2×D24411yescharacteristic
328C22×C4#1175822211yescharacteristic
329C22×C4C2×C22⋊D6111yescharacteristic
330Q16—2444no—
331SD16—2444no—
332C2×C8—22no—
333C2×C8—22no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—42no—
337C2×C8—42no—
338C2×C8—1222no—
339C2×C8—1222no—
340C2×C8C2×C22⋊D6111yescharacteristic
341C2×C8C2×C22⋊D6111yescharacteristic
342C2×C8C2×C22⋊D6111yescharacteristic
343C2×C8C2×C22⋊D6111yescharacteristic
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—1222no—
347C4⋊C4—1222no—
348C4⋊C4—1222no—
349C4⋊C4—1222no—
350C4⋊C4—2442no—
351C4⋊C4—2442no—
352C4⋊C4C2×D24411yescharacteristic
353C4⋊C4C2×D24411yescharacteristic
354C22⋊C4—21no—
355C22⋊C4—21no—
356C22⋊C4—21no—
357C22⋊C4—2442no—
358C42—21no—
359C42—21no—
360C42—21no—
361C42—2442no—
362C42C2×D24411yescharacteristic
363C42#1175822211yescharacteristic
364C42C2×C22⋊D6111yescharacteristic
365C42C23×D6111yescharacteristic
366C23—21no—
367C23#1451975111yescharacteristic
368Q8—21no—
369Q8—4882no—
370Q8—2442no—
371Q8—2442no—
372Q8#1451979912yes—
373D4—24no—
374D4—21no—
375D4#1451979912yes—
376C2×C4—24no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—2442no—
389C2×C4—2442no—
390C2×C4#1451975111yescharacteristic
391C2×C4#1451975111yescharacteristic
392C2×C4#1451975111yescharacteristic
393C2×C4C22×C22⋊D6111yescharacteristic
394C2×C4C22×D24411yescharacteristic
395C2×C4C2×#1175822211yescharacteristic
396C8—21no—
397C8—21no—
398C8—41no—
399C8—41no—
400C8—2442no—
401C8—2442no—
402C8#1451980712yes—
403C8#1451980712yes—
404C22—21no—
405C22—22no—
406C22—21no—
407C22—21no—
408C22—41no—
409C22—41no—
410C22C2×#1451975111yescharacteristic
411C4—21no—
412C4—22no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—41no—
417C4—41no—
418C4—4882no—
419C4—4882no—
420C4C2×#1451979911yescharacteristic
421C4C2×#1451979911yescharacteristic
422C4C2×#1451980711yescharacteristic
423C4C2×#1451980711yescharacteristic
424C2—41no—
425C2—42no—
426C2#2145530611yescharacteristic
427C2#2145540011yescharacteristic
428C2#2145553911yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC8×#41×C61C2
socleC22×C61C2×#121
prime radicalC2×#41×C61D4
hypercenterC8×#41D61
hypocenterC61#19273
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
1. #21456333C2semidirect
3. #21445223C2semidirect
4. #21445218C2semidirect
5. #21445213C2semidirect
6. #21445208C2semidirect
7. #21445201C2semidirect
8. #21445194C2semidirect
9. #21444582C2semidirect
10. #21444527C2semidirect
261. C61#19273semidirect

Maximal subgroups

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

subgroupindex
#214563332
#214559812
#214452232
#214452182
#214452132
#214452082
#214452012
#214451942
#214445822
#214445272
C8×#41×C612
#1927361