Finite Group Databasebeta

← #29580298

Subgroups — #29580298

Order 15616.

654 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840090C211yesmaximal, characteristic
2C2×#16839692C211yesmaximal, characteristic
3#21445903C211yesmaximal, characteristic
4C2×#16839499C211yesmaximal, characteristic
5C2×#16839488C211yesmaximal, characteristic
6#21443697C211yesmaximal, characteristic
7C61×#2627C211yesmaximal, characteristic
8C22×C4⋊Dic61C2211yescharacteristic
9C22×#11758196—21no—
10#16840090—22no—
11#16840090—22no—
12C2×#14519708—21no—
13C2×#14519701—21no—
14C2×C22⋊#92418C2211yescharacteristic
15C2×C22⋊#92418C2211yescharacteristic
16#16839692—22no—
17#16839692—22no—
18C2×#14519684—21no—
19C2×#14519684C2211yescharacteristic
20#16839524—22no—
21#16839499—22no—
22#16839488—22no—
23C2×C22⋊Q8×C61C2211yescharacteristic
24C22×C4⋊C4×C61C2211yescharacteristic
25C61×#400—21no—
26C61×#398—22no—
27C61×#395—21no—
28C61×#385—21no—
29C61×#381—21no—
30C61×#380C2211yescharacteristic
31C23×Dic61—21no—
32C23×Dic61—21no—
33C22×#92418—21no—
34C22×#92418—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61D412yes—
41C2×#11758196—24no—
42C2×#11758196—42no—
43C2×#11758196—42no—
44#14519708—24no—
45#14519701—24no—
46C22⋊#92418—21no—
47C22⋊#92418—21no—
48C22⋊#92418—21no—
49C22⋊#92418D412yes—
50#14519684—24no—
51#14519684—21no—
52#14519684D412yes—
53C22×Q8×C61D411yescharacteristic
54C23×C4×C61D411yescharacteristic
55C23×C4×C61D411yescharacteristic
56C23×C4×C61C2311yescharacteristic
57C22⋊Q8×C61—21no—
58C22⋊Q8×C61—21no—
59C22⋊Q8×C61—21no—
60C22⋊Q8×C61—21no—
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61—22no—
69C2×C4⋊C4×C61D411yescharacteristic
70C2×C4⋊C4×C61D412yes—
71C2×C22⋊C4×C61—21no—
72C2×C22⋊C4×C61—21no—
73#95×C61—22no—
74#95×C61—22no—
75#95×C61—22no—
76#95×C61—21no—
77C24×C61C2×D411yescharacteristic
78C2×Q8×C61—21no—
79C2×Q8×C61—21no—
80C2×Q8×C61—42no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61—21no—
87C22×C4×C61—21no—
88C22×C4×C61—22no—
89C22×C4×C61—21no—
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—21no—
93C22×C4×C61—42no—
94C22×C4×C61—42no—
95C22×C4×C61SD1612yes—
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61#4111yescharacteristic
102C22×Dic61—24no—
103C22×Dic61—22no—
104C22×Dic61—22no—
105C22×Dic61—42no—
106C22×Dic61—41no—
107C22×Dic61—41no—
108C22×Dic61—41no—
109C22×Dic61—41no—
110C22×Dic61—41no—
111C22×Dic61—41no—
112C22×Dic61—41no—
113C22×Dic61—41no—
114C4⋊C4×C61—21no—
115C4⋊C4×C61—21no—
116C4⋊C4×C61—42no—
117C4⋊C4×C61—41no—
118C4⋊C4×C61—41no—
119C4⋊C4×C61—41no—
120C4⋊C4×C61—41no—
121C4⋊C4×C61—41no—
122C4⋊C4×C61—41no—
123C4⋊C4×C61—82no—
124C22⋊C4×C61—41no—
125C22⋊C4×C61—41no—
126C22⋊C4×C61—41no—
127C22⋊C4×C61—41no—
128C4⋊Dic61—22no—
129C4⋊Dic61—22no—
130C4⋊Dic61—41no—
131C4⋊Dic61—41no—
132#11758196—48no—
133C2×#92418—22no—
134C2×#92418—42no—
135C2×#92418—42no—
136C2×#92418—41no—
137C23×C61—22no—
138C23×C61—22no—
139C23×C61#12011yescharacteristic
140C23×C61#12011yescharacteristic
141C23×C61#12111yescharacteristic
142C23×C61C2×SD1611yescharacteristic
143C23×C61#13511yescharacteristic
144C23×C61AGL(1,ℤ/8)11yescharacteristic
145C23×C61#13711yescharacteristic
146Q8×C61—42no—
147Q8×C61—81no—
148C2×C4×C61—22no—
149C2×C4×C61—22no—
150C2×C4×C61—22no—
151C2×C4×C61—22no—
152C2×C4×C61—22no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—42no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—42no—
166C2×C4×C61—42no—
167C2×C4×C61—42no—
168C2×C4×C61—42no—
169C2×C4×C61—42no—
170C2×C4×C61—42no—
171C2×C4×C61—81no—
172C2×C4×C61#12011yescharacteristic
173C2×C4×C61#12111yescharacteristic
174C2×C4×C61#12111yescharacteristic
175C2×C4×C61#12711yescharacteristic
176C2×Dic61—24no—
177C2×Dic61—44no—
178C2×Dic61—44no—
179C2×Dic61—42no—
180C2×Dic61—42no—
181C2×Dic61—42no—
182C2×Dic61—42no—
183C2×Dic61—42no—
184C2×Dic61—81no—
185C2×Dic61—81no—
186C2×Dic61—81no—
187C2×Dic61—81no—
188#92418—42no—
189#92418—81no—
190#9927—611nomaximal, Sylow
191C22×C61—22no—
192C22×C61—22no—
193C22×C61—22no—
194C22×C61—22no—
195C22×C61—21no—
196C22×C61—21no—
197C22×C61—21no—
198C22×C61—21no—
199C22×C61#39211yescharacteristic
200C22×C61#44811yescharacteristic
201C22×C61#44911yescharacteristic
202C22×C61#45011yescharacteristic
203C22×C61#45211yescharacteristic
204C22×C61#45612yes—
205C22×C61#45812yes—
206C22×C61#46511yescharacteristic
207C22×C61#46811yescharacteristic
208C4×C61—21no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—42no—
213C4×C61—82no—
214C4×C61—81no—
215C4×C61—81no—
216C4×C61—81no—
217Dic61—44no—
218Dic61—82no—
219C2×#483—611no—
220#2627D6111yescharacteristic
221C2×#398—611no—
222#1823—611no—
223C2×#328—611no—
224C2×#324—611no—
225#1294—611no—
226C2×C61—21no—
227C2×C61—21no—
228C2×C61—21no—
229C2×C61—21no—
230C2×C61#160912yes—
231C2×C61#161112yes—
232C2×C61#200011yescharacteristic
233C2×C61#200511yescharacteristic
234C2×C61#202211yescharacteristic
235C2×C22⋊Q8C2×D6111yescharacteristic
236C22×C4⋊C4—611no—
237C22×C4⋊C4—1221no—
238C22×C4⋊C4C2×D6111yescharacteristic
239#483—1222no—
240#483—1222no—
241C2×#106—1221no—
242C2×#103—1221no—
243C2×C22⋊C8—611no—
244C2×C22⋊C8—611no—
245#400—21no—
246#398—22no—
247#398—1222no—
248#398—1222no—
249#395—21no—
250#385—21no—
251#381—21no—
252#380C2×D6111yescharacteristic
253C2×#95—611no—
254C2×#95—1221no—
255#340—1222no—
256#328—1222no—
257#324—1222no—
258C61#992711yescharacteristic, complemented, Sylow
259C22×Q8C22⋊D6111yescharacteristic
260C23×C4—1221no—
261C23×C4—1221no—
262C23×C4C22⋊D6111yescharacteristic
263C23×C4C22⋊D6111yescharacteristic
264C23×C4C22×D6111yescharacteristic
265C22×C8—1221no—
266C22×C8—1221no—
267C22⋊Q8—21no—
268C22⋊Q8—21no—
269C22⋊Q8—21no—
270C22⋊Q8—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—612no—
280C2×C4⋊C4—1221no—
281C2×C4⋊C4—1221no—
282C2×C4⋊C4—1221no—
283C2×C4⋊C4—1221no—
284C2×C4⋊C4—1224no—
285C2×C4⋊C4—1221no—
286C2×C4⋊C4—2442no—
287C2×C4⋊C4—2442no—
288C2×C4⋊C4C22⋊D6111yescharacteristic
289C2×C4⋊C4C22⋊D6112yes—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292#106—1224no—
293#103—1224no—
294C22⋊C8—612no—
295C22⋊C8—1221no—
296C22⋊C8—1221no—
297C22⋊C8—1221no—
298#95—22no—
299#95—22no—
300#95—22no—
301#95—21no—
302#95—612no—
303#95—1224no—
304#95—1221no—
305C24C2×C22⋊D6111yescharacteristic
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—42no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—1224no—
324C22×C4—1222no—
325C22×C4—1222no—
326C22×C4—2441no—
327C22×C4—2441no—
328C22×C4—2441no—
329C22×C4—2441no—
330C22×C4—2441no—
331C22×C4—2441no—
332C22×C4—2442no—
333C22×C4—2441no—
334C22×C4—2441no—
335C22×C4#1175820112yes—
336C22×C4D4×D6111yescharacteristic
337C22×C4D4×D6111yescharacteristic
338C22×C4D4×D6111yescharacteristic
339C22×C4#1175822411yescharacteristic
340C22×C4C2×C22⋊D6111yescharacteristic
341C22×C4C2×C22⋊D6111yescharacteristic
342C2×C8—1222no—
343C2×C8—2442no—
344C2×C8—2441no—
345C2×C8—2442no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—42no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4—82no—
356C4⋊C4—1222no—
357C4⋊C4—1222no—
358C4⋊C4—2448no—
359C4⋊C4—2441no—
360C4⋊C4—2441no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C23—22no—
366C23—22no—
367C23#1451974511yescharacteristic
368C23#1451974611yescharacteristic
369C23#1451974911yescharacteristic
370C23C2×#1175820111yescharacteristic
371C23#1451979711yescharacteristic
372C23#1451980211yescharacteristic
373C23#1451980811yescharacteristic
374Q8—42no—
375Q8—81no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—81no—
400C2×C4—1224no—
401C2×C4—4881no—
402C2×C4—4881no—
403C2×C4—4881no—
404C2×C4—4881no—
405C2×C4—2442no—
406C2×C4—2442no—
407C2×C4—2442no—
408C2×C4—2442no—
409C2×C4—2444no—
410C2×C4—2444no—
411C2×C4—2442no—
412C2×C4#1451974511yescharacteristic
413C2×C4#1451974811yescharacteristic
414C2×C4#1451974911yescharacteristic
415C2×C4#1451977311yescharacteristic
416C8—4881no—
417C8—2442no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—22no—
423C22—22no—
424C22—22no—
425C22—22no—
426C22#1683967011yescharacteristic
427C22#1683990111yescharacteristic
428C22#1683990711yescharacteristic
429C22#1683991211yescharacteristic
430C22#1683992211yescharacteristic
431C22#1683994512yes—
432C22#1683995212yes—
433C22#1683999311yescharacteristic
434C22#1684001011yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—42no—
440C4—81no—
441C4—81no—
442C4—81no—
443C4—82no—
444C4—4882no—
445C4—2444no—
446C2—21no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2#2144481612yes—
451C2#2144482712yes—
452C2#2144682011yescharacteristic
453C2#2144685311yescharacteristic
454C2#2144694811yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#2627C2
socleC23×C61#120
prime radicalC24×C61C2×D4
hypercenter#2627D61
hypocenterC61#9927
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2627

Complements

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

NH ≅ G/Ntype
258. C61#9927semidirect

Maximal subgroups

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

subgroupindex
C2×#168400902
C2×#168396922
#214459032
C2×#168394992
C2×#168394882
#214436972
C61×#26272
#992761