Finite Group Databasebeta

← #29579142

Subgroups — #29579142

Order 15616.

742 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454120C211yesmaximal, characteristic
2C2×#16839500C212yesmaximal, complemented
3C2×#16839497C212yesmaximal
4C4×#14519684C211yesmaximal, characteristic, complemented
5C61×#1797C211yesmaximal, characteristic, complemented
6C2×#14519765C411yescharacteristic, complemented
7C2×#14519756C2211yescharacteristic
8C2×#14519751C2211yescharacteristic
9C22×C4×Dic61—21no—
10#16839668C411yescharacteristic, complemented
11#16839664C411yescharacteristic, complemented
12#16839653—21no—
13#16839653—21no—
14#16839641—21no—
15#16839641—21no—
16#16839628C411yescharacteristic, complemented
17C2×#14519684—21no—
18C2×#14519684C2212yes—
19#16839500—24no—
20#16839497—24no—
21C22×C42×C61C2211yescharacteristic
22C2×C4⋊C8×C61—21no—
23C2×C22⋊C8×C61C2212yes—
24C61×#336—21no—
25C22×Dic122C2×C411yescharacteristic
26C22×D244C2×C411yescharacteristic
27C22×C22⋊D61—21no—
28C23×Dic61—22no—
29#14519765—42no—
30#14519756—22no—
31#14519756—22no—
32#14519751—22no—
33#14519751—22no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—21no—
37C2×C22⋊Dic61—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×C4×Dic61—24no—
44C2×C4×Dic61—42no—
45C2×C4×Dic61—42no—
46#14519684—24no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—22no—
52#14519684D414yes—
53C23×C4×C61D411yescharacteristic
54C23×C4×C61D411yescharacteristic
55C23×C4×C61C2311yescharacteristic
56C22×C8×C61—22no—
57C2×C42×C61—42no—
58C2×C42×C61C2×C411yescharacteristic
59C2×C42×C61C2×C411yescharacteristic
60C2×C42×C61D411yescharacteristic
61C2×C42×C61D411yescharacteristic
62C4⋊C8×C61—42no—
63C22⋊C8×C61—22no—
64C22⋊C8×C61—22no—
65C24×C61C2×D411yescharacteristic
66C23×D61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—22no—
70C22×C4×C61—22no—
71C22×C4×C61—22no—
72C22×C4×C61—22no—
73C22×C4×C61—41no—
74C22×C4×C61—41no—
75C22×C4×C61—41no—
76C22×C4×C61C22⋊C411yescharacteristic
77C22×C4×C61C22⋊C411yescharacteristic
78C22×C4×C61C22⋊C411yescharacteristic
79C22×C4×C61C22⋊C411yescharacteristic
80C22×C4×C61C22×C411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D412yes—
83C22×C4×C61#4112yes—
84C2×C22⋊D61—42no—
85C2×C22⋊D61—42no—
86C2×C22⋊D61—41no—
87C2×C22⋊D61—41no—
88C22×Dic61—24no—
89C22×Dic61—24no—
90C22×Dic61—24no—
91C22×Dic61—21no—
92C22×Dic61—21no—
93C22×Dic61—21no—
94C22×Dic61—42no—
95C22×Dic61—42no—
96C22×Dic61—42no—
97C22×Dic61—42no—
98C2×D244—22no—
99C2×D244—41no—
100C2×D244—41no—
101C2×Dic122—22no—
102C2×Dic122—41no—
103C2×Dic122—41no—
104C2×C8×C61—42no—
105C2×C8×C61—42no—
106C2×C8×C61—42no—
107C42×C61—22no—
108C42×C61—22no—
109C42×C61—41no—
110C42×C61—41no—
111C22⋊Dic61—42no—
112#11758198—42no—
113#11758198—42no—
114#11758198—42no—
115#11758198—42no—
116#11758198—41no—
117#11758198—41no—
118C4⋊Dic61—22no—
119C4⋊Dic61—22no—
120#11758196—41no—
121#11758196—41no—
122C4×Dic61—48no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61C2×C22⋊C411yescharacteristic
128C23×C61#12112yes—
129C23×C61#13512yes—
130C23×C61AGL(1,ℤ/8)11yescharacteristic
131C23×C61#13711yescharacteristic
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—41no—
138C22×D61—41no—
139C2×C4×C61—24no—
140C2×C4×C61—24no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—42no—
155C2×C4×C61—42no—
156C2×C4×C61—44no—
157C2×C4×C61#9912yes—
158C2×C4×C61#10412yes—
159C2×C4×C61#10412yes—
160C2×C4×C61C4×D412yes—
161C2×C4×C61#12411yescharacteristic
162C2×C4×C61#12711yescharacteristic
163C22⋊D61—82no—
164C22⋊D61—82no—
165C2×Dic61—28no—
166C2×Dic61—44no—
167C2×Dic61—44no—
168C2×Dic61—44no—
169C2×Dic61—44no—
170C2×Dic61—44no—
171C2×Dic61—44no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181D244—82no—
182Dic122—82no—
183C8×C61—82no—
184#9713—611nomaximal, Sylow
185C22×C61—22no—
186C22×C61—22no—
187C22×C61—22no—
188C22×C61—22no—
189C22×C61—21no—
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—21no—
193C22×C61#39011yescharacteristic
194C22×C61C2×#9911yescharacteristic
195C22×C61#41011yescharacteristic
196C22×C61#41611yescharacteristic
197C22×C61#41711yescharacteristic
198C22×C61C2×#10411yescharacteristic
199C22×C61C2×#10411yescharacteristic
200C22×C61#46312yes—
201C22×C61#46412yes—
202C2×D61—81no—
203C2×D61—81no—
204C2×D61—81no—
205C2×D61—81no—
206C2×D61—81no—
207C2×D61—81no—
208C2×D61—81no—
209C4×C61—21no—
210C4×C61—22no—
211C4×C61—21no—
212C4×C61—22no—
213C4×C61—22no—
214C4×C61—22no—
215C4×C61—41no—
216Dic61—48no—
217Dic61—81no—
218Dic61—81no—
219Dic61—81no—
220#2850—611no—
221#1797D6111yescharacteristic, complemented
222C2×#328—612no—
223C2×#327—612no—
224C4×#95—611no—
225C2×C61—22no—
226C2×C61—22no—
227C2×C61#150011yescharacteristic
228C2×C61#150111yescharacteristic
229C2×C61#150411yescharacteristic
230C2×C61#150911yescharacteristic
231C2×C61#196211yescharacteristic
232C2×C61#196411yescharacteristic
233C2×C61#198311yescharacteristic
234D61—161no—
235C2×#124—611no—
236C2×C22⋊Q8—611no—
237C2×#121—611no—
238C22×C42—1221no—
239C22×C42C2×D6111yescharacteristic
240C2×C4⋊C8—21no—
241C2×C22⋊C8C2×D6112yes—
242#391—611no—
243#390—611no—
244#388—1221no—
245#388—1221no—
246#386—1221no—
247#386—1221no—
248#382—611no—
249C2×#95—612no—
250C2×#95—1221no—
251#336—21no—
252#328—1224no—
253#327—1224no—
254C61#971311yescharacteristic, complemented, Sylow
255C22×Q8—611no—
256C22×D4—611no—
257C22×D4—1221no—
258C23×C4—1222no—
259C23×C4D24411yescharacteristic
260C23×C4D24411yescharacteristic
261C23×C4C22×D6111yescharacteristic
262C22×C8—22no—
263#124—2442no—
264C22⋊Q8—1222no—
265C22⋊Q8—1222no—
266#121—1222no—
267#121—1222no—
268C2×C4⋊C4—611no—
269C2×C4⋊C4—611no—
270C2×C4⋊C4—1221no—
271C2×C22⋊C4—1221no—
272C2×C22⋊C4—1221no—
273C2×C22⋊C4—1221no—
274C2×C22⋊C4—1221no—
275C2×C22⋊C4—1221no—
276C2×C22⋊C4—1221no—
277C2×C42—42no—
278C2×C42—1224no—
279C2×C42—2442no—
280C2×C42—2442no—
281C2×C42C4×D6111yescharacteristic
282C2×C42C4×D6111yescharacteristic
283C2×C42C22⋊D6111yescharacteristic
284C2×C42C22⋊D6111yescharacteristic
285C4⋊C8—42no—
286C22⋊C8—22no—
287C22⋊C8—22no—
288#95—614no—
289#95—1224no—
290#95—1221no—
291#95—1221no—
292#95—1221no—
293#95—1221no—
294#95—1222no—
295C24—1221no—
296C24C2×D24411yescharacteristic
297C2×Q8—1222no—
298C2×Q8—2441no—
299C2×Q8—2441no—
300C2×D4—1222no—
301C2×D4—2441no—
302C2×D4—2441no—
303C2×D4—2441no—
304C2×D4—2442no—
305C2×D4—2442no—
306C2×D4—2441no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—1224no—
317C22×C4—1224no—
318C22×C4—1224no—
319C22×C4—1221no—
320C22×C4—1221no—
321C22×C4—1221no—
322C22×C4—2442no—
323C22×C4—2442no—
324C22×C4—2442no—
325C22×C4—2442no—
326C22×C4#1175819811yescharacteristic
327C22×C4#1175819811yescharacteristic
328C22×C4#1175819811yescharacteristic
329C22×C4#1175819811yescharacteristic
330C22×C4C2×C4×D6111yescharacteristic
331C22×C4D4×D6112yes—
332C22×C4#1175822612yes—
333C22×C4C2×C22⋊D6111yescharacteristic
334C2×C8—42no—
335C2×C8—42no—
336C2×C8—42no—
337C4⋊C4—1222no—
338C4⋊C4—1222no—
339C4⋊C4—2441no—
340C4⋊C4—2441no—
341C22⋊C4—2442no—
342C22⋊C4—2442no—
343C22⋊C4—2442no—
344C22⋊C4—2442no—
345C22⋊C4—2442no—
346C22⋊C4—2441no—
347C22⋊C4—2441no—
348C42—22no—
349C42—22no—
350C42—41no—
351C42—41no—
352C42—2448no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—2441no—
358C23—2441no—
359C23—2441no—
360C23—2441no—
361C23—2441no—
362C23—2441no—
363C23—2441no—
364C23C2×#1175819811yescharacteristic
365C23#1451975212yes—
366C23#1451979912yes—
367C23#1451980511yescharacteristic
368C23#1451981011yescharacteristic
369Q8—4882no—
370D4—4882no—
371D4—4882no—
372D4—4882no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—44no—
391C2×C4—1228no—
392C2×C4—2441no—
393C2×C4—2441no—
394C2×C4—2441no—
395C2×C4—2441no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4—2444no—
402C2×C4—2444no—
403C2×C4—2444no—
404C2×C4—2444no—
405C2×C4—2444no—
406C2×C4—2444no—
407C2×C4#1451969112yes—
408C2×C4#1451970312yes—
409C2×C4#1451970312yes—
410C2×C4#1451973912yes—
411C2×C4#1451976611yescharacteristic
412C2×C4#1451977311yescharacteristic
413C8—82no—
414C22—22no—
415C22—22no—
416C22—21no—
417C22—21no—
418C22—22no—
419C22—21no—
420C22—21no—
421C22—22no—
422C22—4881no—
423C22—4881no—
424C22—4881no—
425C22—4881no—
426C22—4881no—
427C22—4881no—
428C22—4881no—
429C22#1683966311yescharacteristic
430C22C2×#1451969111yescharacteristic
431C22#1683973511yescharacteristic
432C22#1683975911yescharacteristic
433C22#1683976411yescharacteristic
434C22C2×#1451970311yescharacteristic
435C22C2×#1451970311yescharacteristic
436C22#1683997812yes—
437C22#1683998512yes—
438C4—22no—
439C4—22no—
440C4—22no—
441C4—21no—
442C4—22no—
443C4—21no—
444C4—41no—
445C4—4881no—
446C4—4881no—
447C4—4881no—
448C4—2448no—
449C2—22no—
450C2—22no—
451C2—9761no—
452C2#2144430611yescharacteristic
453C2#2144431111yescharacteristic
454C2#2144432411yescharacteristic
455C2#2144434511yescharacteristic
456C2#2144664611yescharacteristic
457C2#2144665411yescharacteristic
458C2#2144674911yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1797C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519751C22
cosocleC23×C4×C61C23
hypercenter#1797D61
hypocenterC61#9713
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. C2×#16839500C2semidirect
4. C4×#14519684C2semidirect
5. C61×#1797C2semidirect
6. C2×#14519765C4semidirect
10. #16839668C4semidirect
11. #16839664C4semidirect
16. #16839628C4semidirect
221. #1797D61semidirect
254. C61#9713semidirect

Maximal subgroups

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

subgroupindex
#214541202
C2×#168395002
C2×#168394972
C4×#145196842
C61×#17972
#971361