Finite Group Databasebeta

← #29574770

Subgroups — #29574770

Order 15616.

592 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840049C211yesmaximal, characteristic
2#21448766C211yesmaximal, characteristic
3#21446622C211yesmaximal, characteristic, complemented
4C2×#16839489C211yesmaximal, characteristic
5#21443703C211yesmaximal, characteristic, complemented
6#21443660C211yesmaximal, characteristic, complemented
7C61×#1987C211yesmaximal, characteristic, complemented
8C2×C4×D244C2211yescharacteristic
9C2×#14519735—21no—
10#16840049—22no—
11#16840049C414yescomplemented
12C2×#14519708—21no—
13C2×C4⋊#92418C2211yescharacteristic
14C2×#14519701—22no—
15C2×#14519697—21no—
16C2×C4×#92418C2211yescharacteristic
17#16839664—21no—
18#16839654—22no—
19#16839632C2211yescharacteristic
20#16839619—21no—
21C4×C4⋊Dic61—21no—
22#16839489—22no—
23C2×C4⋊Q8×C61C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C4×C4⋊C4×C61C2211yescharacteristic
26C61×#340—21no—
27C61×#340—21no—
28C22×D244D411yescharacteristic
29C22×C4×D61—21no—
30C22×#92418—21no—
31C22×#92418—21no—
32C4×D244—21no—
33C4×D244—21no—
34C4×D244C2×C412yes—
35C4×D244D412yes—
36#14519735—42no—
37#14519735—42no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61D411yescharacteristic
41C2×C4⋊Dic61D412yes—
42C2×#11758198—21no—
43C2×#11758198—22no—
44C2×#11758198—22no—
45C2×C4×Dic61—22no—
46#14519708—24no—
47C4⋊#92418—21no—
48C4⋊#92418C2×C412yes—
49#14519701—44no—
50#14519697—24no—
51C4×#92418—21no—
52C4×#92418—21no—
53#14519684—22no—
54C22×Q8×C61—21no—
55C22×C8×C61—21no—
56C4⋊Q8×C61—21no—
57C4⋊Q8×C61—21no—
58C4⋊Q8×C61—21no—
59C4⋊Q8×C61C2×C412yes—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61D411yescharacteristic
63C2×C4⋊C4×C61D411yescharacteristic
64C2×C42×C61—21no—
65C2×C42×C61C2311yescharacteristic
66C4⋊C8×C61—21no—
67C4⋊C8×C61—21no—
68#95×C61—21no—
69C23×D61—21no—
70C2×Q8×C61—22no—
71C2×Q8×C61—42no—
72C2×Q8×C61—42no—
73C2×Q8×C61—41no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—41no—
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×Dic61—21no—
81C22×Dic61—22no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244—21no—
87C2×D244C22⋊C412yes—
88C2×C4×D61—22no—
89C2×C4×D61—22no—
90C2×C4×D61—41no—
91C2×C4×D61—41no—
92C2×C4×D61—41no—
93C2×C4×D61—41no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C4⋊C4×C61—21no—
98C4⋊C4×C61—22no—
99C4⋊C4×C61—22no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61SD1612yes—
105C42×C61—41no—
106C42×C61—41no—
107C42×C61C22×C411yescharacteristic
108C42×C61C2×D411yescharacteristic
109C42×C61#4111yescharacteristic
110C42×C61#4111yescharacteristic
111#11758198—22no—
112#11758198—22no—
113#11758198—44no—
114#11758198—82no—
115C4⋊Dic61—21no—
116C4⋊Dic61—41no—
117C4⋊Dic61—41no—
118C4⋊Dic61—41no—
119C4⋊Dic61—41no—
120C4⋊Dic61—42no—
121C4⋊Dic61C22⋊C412yes—
122C4×Dic61—44no—
123C2×#92418—22no—
124C2×#92418—22no—
125C2×#92418—41no—
126C2×#92418—41no—
127C2×#92418—41no—
128C2×#92418—41no—
129C23×C61#12011yescharacteristic
130C22×D61—22no—
131C22×D61—41no—
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—41no—
137Q8×C61—44no—
138Q8×C61—82no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—22no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—42no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—81no—
149C2×C4×C61—81no—
150C2×C4×C61C2×C22⋊C411yescharacteristic
151C2×C4×C61C4×D411yescharacteristic
152C2×C4×C61C4×D411yescharacteristic
153C2×C4×C61#12111yescharacteristic
154C2×C4×C61#12111yescharacteristic
155C2×C4×C61#12311yescharacteristic
156C2×C4×C61C2×SD1611yescharacteristic
157C2×C4×C61#13511yescharacteristic
158C2×C4×C61#13511yescharacteristic
159C2×C4×C61#13511yescharacteristic
160C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C61#13711yescharacteristic
162C2×C4×C61#13711yescharacteristic
163C2×C4×C61#13711yescharacteristic
164C2×Dic61—22no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—42no—
168C2×Dic61—42no—
169C2×Dic61—42no—
170D244—22no—
171D244—22no—
172D244—41no—
173D244—41no—
174C4×D61—42no—
175C4×D61—42no—
176C4×D61—42no—
177C4×D61—42no—
178C8×C61—81no—
179#92418—42no—
180#92418—42no—
181#8976—611nomaximal, Sylow
182C22×C61#38611yescharacteristic
183C22×C61#45011yescharacteristic
184C22×C61#45211yescharacteristic
185C22×C61#45211yescharacteristic
186C22×C61#45211yescharacteristic
187C22×C61#45311yescharacteristic
188C22×C61#45411yescharacteristic
189C2×D61—42no—
190C2×D61—42no—
191C2×D61—42no—
192C2×D61—81no—
193C2×D61—81no—
194C2×D61—81no—
195C2×D61—81no—
196C4×C61—21no—
197C4×C61—21no—
198C4×C61—42no—
199C4×C61—82no—
200C4×C61—81no—
201C4×C61#41611yescharacteristic
202C4×C61#41911yescharacteristic
203C4×C61C4×SD1611yescharacteristic
204C4×C61#44011yescharacteristic
205C4×C61#46111yescharacteristic
206C4×C61#46311yescharacteristic
207C4×C61#48511yescharacteristic
208C4×C61#48511yescharacteristic
209Dic61—42no—
210Dic61—82no—
211C2×#476—611no—
212#2354—611no—
213#1987D6111yescharacteristic, complemented
214#1956—611no—
215C2×D4⋊C8—611no—
216#1296—611no—
217#1279—611no—
218C2×C61#163111yescharacteristic
219C2×C61#163411yescharacteristic
220C2×C61#163511yescharacteristic
221C2×C61#163811yescharacteristic
222C2×C61#187311yescharacteristic
223C2×C61#187711yescharacteristic
224C2×C61#188311yescharacteristic
225D61—82no—
226C2×C4⋊Q8C2×D6111yescharacteristic
227C2×C4×D4—611no—
228C2×#117—1221no—
229#476—614no—
230#476—1222no—
231C2×#106—1221no—
232C2×C4⋊C8—611no—
233C2×C4⋊C8C2×D6111yescharacteristic
234C2×#103—1222no—
235C2×#102—1221no—
236C2×C4×C8—611no—
237#390—1221no—
238#388—1222no—
239#384—611no—
240#380—1221no—
241C4×C4⋊C4—1221no—
242C4×C4⋊C4C2×D6111yescharacteristic
243#340—21no—
244#340—21no—
245D4⋊C8—1222no—
246C61#897611yescharacteristic, complemented, Sylow
247C22×Q8—21no—
248C22×D4—611no—
249C23×C4—1221no—
250C22×C8—21no—
251C22×C8—1221no—
252C22×C8—1221no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8C4×D6112yes—
257C4×D4—612no—
258C4×D4—612no—
259C4×D4—1221no—
260C4×D4—1221no—
261#117—2442no—
262#117—2442no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—611no—
266C2×C4⋊C4—612no—
267C2×C4⋊C4—1221no—
268C2×C4⋊C4—1221no—
269C2×C4⋊C4C22⋊D6111yescharacteristic
270C2×C4⋊C4C22⋊D6111yescharacteristic
271C2×C22⋊C4—1221no—
272C2×C22⋊C4—1222no—
273C2×C22⋊C4—1222no—
274C2×C42—21no—
275C2×C42—1222no—
276C2×C42C22×D6111yescharacteristic
277#106—1224no—
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8—612no—
281C4⋊C8—1221no—
282#103—2444no—
283#102—1224no—
284C4×C8—1221no—
285C4×C8—1221no—
286#95—21no—
287#95—1222no—
288C24—1221no—
289C2×Q8—22no—
290C2×Q8—42no—
291C2×Q8—42no—
292C2×Q8—41no—
293C2×D4—612no—
294C2×D4—1221no—
295C2×D4—1221no—
296C2×D4—1221no—
297C2×D4—1221no—
298C2×D4—1221no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—41no—
302C22×C4—1221no—
303C22×C4—1222no—
304C22×C4—1222no—
305C22×C4—1222no—
306C22×C4—2441no—
307C22×C4—2441no—
308C22×C4—2441no—
309C22×C4—2441no—
310C22×C4D4×D6111yescharacteristic
311C22×C4D4×D6111yescharacteristic
312C22×C4C2×C22⋊D6111yescharacteristic
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—1222no—
317C2×C8—1222no—
318C2×C8—2441no—
319C2×C8—2441no—
320C2×C8—2441no—
321C2×C8—2441no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—21no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—612no—
330C4⋊C4—1221no—
331C4⋊C4—2442no—
332C4⋊C4—2441no—
333C4⋊C4—2441no—
334C4⋊C4—2441no—
335C4⋊C4—2441no—
336C4⋊C4#1175820112yes—
337C22⋊C4—1222no—
338C22⋊C4—1222no—
339C22⋊C4—4882no—
340C22⋊C4—2444no—
341C42—41no—
342C42—41no—
343C42—2444no—
344C42C2×C4×D6111yescharacteristic
345C42#1175822211yescharacteristic
346C42D4×D6111yescharacteristic
347C42#1175822411yescharacteristic
348C23—1222no—
349C23—2441no—
350C23—2441no—
351C23—2441no—
352C23—2441no—
353C23—2441no—
354C23—2441no—
355C23#1451974511yescharacteristic
356Q8—44no—
357Q8—82no—
358D4—1222no—
359D4—1222no—
360D4—2441no—
361D4—2441no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—1222no—
374C2×C4—2442no—
375C2×C4—2442no—
376C2×C4—2442no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2442no—
380C2×C4—2442no—
381C2×C4—2442no—
382C2×C4—2442no—
383C2×C4C22⋊C4×D6111yescharacteristic
384C2×C4#1451973711yescharacteristic
385C2×C4C4×C22⋊D6111yescharacteristic
386C2×C4#1451974811yescharacteristic
387C2×C4#1451975011yescharacteristic
388C2×C4#1451975911yescharacteristic
389C2×C4C2×#1175820111yescharacteristic
390C2×C4#1451979711yescharacteristic
391C2×C4#1451979811yescharacteristic
392C2×C4#1451980011yescharacteristic
393C2×C4#1451980211yescharacteristic
394C2×C4#1451980611yescharacteristic
395C2×C4#1451980811yescharacteristic
396C2×C4#1451980911yescharacteristic
397C8—81no—
398C8—2442no—
399C8—2442no—
400C22—4881no—
401C22—4881no—
402C22—4881no—
403C22—4881no—
404C22—2442no—
405C22—2442no—
406C22—2442no—
407C22#1683963811yescharacteristic
408C22#1683991211yescharacteristic
409C22#1683992111yescharacteristic
410C22#1683992211yescharacteristic
411C22#1683992311yescharacteristic
412C22#1683992811yescharacteristic
413C22#1683993311yescharacteristic
414C4—21no—
415C4—21no—
416C4—42no—
417C4—82no—
418C4—81no—
419C4—4882no—
420C4—2442no—
421C4#1683975711yescharacteristic
422C4#1683976911yescharacteristic
423C4C4×#1175820111yescharacteristic
424C4#1683986011yescharacteristic
425C4#1683996411yescharacteristic
426C4#1683997411yescharacteristic
427C4#1684010111yescharacteristic
428C4#1684010211yescharacteristic
429C2—4882no—
430C2#2144494411yescharacteristic
431C2#2144496311yescharacteristic
432C2#2144496811yescharacteristic
433C2#2144499011yescharacteristic
434C2#2144612811yescharacteristic
435C2#2144615611yescharacteristic
436C2#2144619211yescharacteristic
subgroupG/H
centerC23#14519745
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1987C2
socleC23×C61#120
prime radicalC22×D244D4
cosocleC2×C42×C61C23
hypercenter#1987D61
hypocenterC61#8976
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
3. #21446622C2semidirect
5. #21443703C2semidirect
6. #21443660C2semidirect
7. C61×#1987C2semidirect
11. #16840049C4semidirect
213. #1987D61semidirect
246. C61#8976semidirect

Maximal subgroups

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

subgroupindex
C2×#168400492
#214487662
#214466222
C2×#168394892
#214437032
#214436602
C61×#19872
#897661