Finite Group Databasebeta

← #29579155

Subgroups — #29579155

Order 15616.

650 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454120C211yesmaximal, characteristic
2C2×#16839500C212yesmaximal, complemented
3C2×#16839497C212yesmaximal
4#21444046C211yesmaximal, characteristic, complemented
5C61×#1797C211yesmaximal, characteristic, complemented
6C2×#14519765C411yescharacteristic, complemented
7C2×#14519756C2211yescharacteristic
8C2×#14519751C2211yescharacteristic
9#16839668C411yescharacteristic, complemented
10#16839664C411yescharacteristic, complemented
11#16839653—21no—
12#16839653—21no—
13#16839641—21no—
14#16839641—21no—
15#16839628C411yescharacteristic, complemented
16C2×#14519684—21no—
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—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—22no—
48#14519684—42no—
49#14519684—42no—
50#14519684D414yes—
51C23×C4×C61D411yescharacteristic
52C23×C4×C61D411yescharacteristic
53C23×C4×C61C2311yescharacteristic
54C22×C8×C61—22no—
55C2×C42×C61—42no—
56C2×C42×C61C2×C411yescharacteristic
57C2×C42×C61C2×C411yescharacteristic
58C2×C42×C61D411yescharacteristic
59C2×C42×C61D411yescharacteristic
60C4⋊C8×C61—42no—
61C22⋊C8×C61—22no—
62C22⋊C8×C61—22no—
63C24×C61C2×D411yescharacteristic
64C23×D61—21no—
65C22×C4×C61—22no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—22no—
69C22×C4×C61—41no—
70C22×C4×C61—41no—
71C22×C4×C61—41no—
72C22×C4×C61—41no—
73C22×C4×C61—41no—
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22⋊C411yescharacteristic
77C22×C4×C61C22⋊C411yescharacteristic
78C22×C4×C61C22×C411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D412yes—
81C22×C4×C61#4112yes—
82C2×C22⋊D61—42no—
83C2×C22⋊D61—42no—
84C2×C22⋊D61—41no—
85C2×C22⋊D61—41no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—24no—
90C22×Dic61—42no—
91C22×Dic61—42no—
92C22×Dic61—42no—
93C22×Dic61—42no—
94C22×Dic61—42no—
95C22×Dic61—42no—
96C2×D244—22no—
97C2×D244—41no—
98C2×D244—41no—
99C2×Dic122—22no—
100C2×Dic122—41no—
101C2×Dic122—41no—
102C2×C8×C61—42no—
103C2×C8×C61—42no—
104C2×C8×C61—42no—
105C42×C61—22no—
106C42×C61—22no—
107C42×C61—41no—
108C42×C61—41no—
109C22⋊Dic61—42no—
110#11758198—42no—
111#11758198—42no—
112#11758198—42no—
113#11758198—42no—
114#11758198—41no—
115#11758198—41no—
116C4⋊Dic61—22no—
117C4⋊Dic61—22no—
118#11758196—41no—
119#11758196—41no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61C2×C22⋊C411yescharacteristic
125C23×C61#12112yes—
126C23×C61#13512yes—
127C23×C61AGL(1,ℤ/8)11yescharacteristic
128C23×C61#13711yescharacteristic
129C22×D61—41no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
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—42no—
152C2×C4×C61—42no—
153C2×C4×C61—44no—
154C2×C4×C61—42no—
155C2×C4×C61—42no—
156C2×C4×C61#9912yes—
157C2×C4×C61C4×D412yes—
158C2×C4×C61#12411yescharacteristic
159C2×C4×C61#12711yescharacteristic
160C22⋊D61—82no—
161C22⋊D61—82no—
162C2×Dic61—44no—
163C2×Dic61—44no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—44no—
174C2×Dic61—82no—
175C2×Dic61—82no—
176C2×Dic61—82no—
177C2×Dic61—82no—
178D244—82no—
179Dic122—82no—
180C8×C61—82no—
181#9716—611nomaximal, Sylow
182C22×C61—22no—
183C22×C61—22no—
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—22no—
189C22×C61—22no—
190C22×C61#39011yescharacteristic
191C22×C61C2×#9911yescharacteristic
192C22×C61#41011yescharacteristic
193C22×C61#41611yescharacteristic
194C22×C61#41711yescharacteristic
195C22×C61#42111yescharacteristic
196C22×C61#42111yescharacteristic
197C22×C61#46312yes—
198C22×C61#46412yes—
199C2×D61—81no—
200C2×D61—81no—
201C2×D61—81no—
202C2×D61—81no—
203C2×D61—81no—
204C2×D61—81no—
205C2×D61—81no—
206C4×C61—21no—
207C4×C61—22no—
208C4×C61—21no—
209C4×C61—22no—
210C4×C61—41no—
211C4×C61—41no—
212C4×C61—41no—
213Dic61—84no—
214Dic61—81no—
215Dic61—81no—
216Dic61—81no—
217#2850—611no—
218#1797D6111yescharacteristic, complemented
219C2×#328—612no—
220C2×#327—612no—
221#1434—611no—
222C2×C61—22no—
223C2×C61—22no—
224C2×C61#151211yescharacteristic
225C2×C61#151311yescharacteristic
226C2×C61#151611yescharacteristic
227C2×C61#152111yescharacteristic
228C2×C61#196311yescharacteristic
229C2×C61#196411yescharacteristic
230C2×C61#198311yescharacteristic
231D61—161no—
232C2×#124—611no—
233C2×C22⋊Q8—611no—
234C2×#121—611no—
235C22×C42C2×D6111yescharacteristic
236C2×C4⋊C8—21no—
237C2×C22⋊C8C2×D6112yes—
238#391—611no—
239#390—611no—
240#388—1221no—
241#388—1221no—
242#386—1221no—
243#386—1221no—
244#382—611no—
245C2×#95—612no—
246C2×#95—1221no—
247C2×#95—1221no—
248#336—21no—
249#328—1224no—
250#327—1224no—
251C61#971611yescharacteristic, complemented, Sylow
252C22×Q8—611no—
253C22×D4—611no—
254C22×D4—1221no—
255C23×C4—1222no—
256C23×C4D24411yescharacteristic
257C23×C4D24411yescharacteristic
258C23×C4C22×D6111yescharacteristic
259C22×C8—22no—
260#124—2442no—
261C22⋊Q8—1222no—
262C22⋊Q8—1222no—
263#121—1222no—
264#121—1222no—
265C2×C4⋊C4—611no—
266C2×C4⋊C4—611no—
267C2×C4⋊C4—1221no—
268C2×C22⋊C4—1221no—
269C2×C22⋊C4—1221no—
270C2×C22⋊C4—1221no—
271C2×C22⋊C4—1221no—
272C2×C22⋊C4—1221no—
273C2×C22⋊C4—1221no—
274C2×C42—42no—
275C2×C42C4×D6111yescharacteristic
276C2×C42C4×D6111yescharacteristic
277C2×C42C22⋊D6111yescharacteristic
278C2×C42C22⋊D6111yescharacteristic
279C4⋊C8—42no—
280C22⋊C8—22no—
281C22⋊C8—22no—
282#95—614no—
283#95—1221no—
284#95—1221no—
285#95—1221no—
286#95—1221no—
287#95—1222no—
288#95—2442no—
289#95—2442no—
290C24—1221no—
291C24C2×D24411yescharacteristic
292C2×Q8—1222no—
293C2×Q8—2441no—
294C2×Q8—2441no—
295C2×D4—1222no—
296C2×D4—2441no—
297C2×D4—2441no—
298C2×D4—2441no—
299C2×D4—2442no—
300C2×D4—2442no—
301C2×D4—2441no—
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4—1221no—
314C22×C4—1224no—
315C22×C4—2442no—
316C22×C4—2442no—
317C22×C4—2442no—
318C22×C4—2442no—
319C22×C4—2442no—
320C22×C4—2442no—
321C22×C4#1175819811yescharacteristic
322C22×C4#1175819811yescharacteristic
323C22×C4#1175819811yescharacteristic
324C22×C4#1175819811yescharacteristic
325C22×C4C2×C4×D6111yescharacteristic
326C22×C4D4×D6112yes—
327C22×C4#1175822612yes—
328C22×C4C2×C22⋊D6111yescharacteristic
329C2×C8—42no—
330C2×C8—42no—
331C2×C8—42no—
332C4⋊C4—1222no—
333C4⋊C4—1222no—
334C4⋊C4—2441no—
335C4⋊C4—2441no—
336C22⋊C4—2442no—
337C22⋊C4—2442no—
338C22⋊C4—2442no—
339C22⋊C4—2442no—
340C22⋊C4—2442no—
341C22⋊C4—2441no—
342C22⋊C4—2441no—
343C42—22no—
344C42—22no—
345C42—41no—
346C42—41no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—2441no—
352C23—2441no—
353C23—2441no—
354C23—2441no—
355C23—2441no—
356C23—2441no—
357C23—2441no—
358C23C2×#1175819811yescharacteristic
359C23#1451975212yes—
360C23#1451979912yes—
361C23#1451980511yescharacteristic
362C23#1451981011yescharacteristic
363Q8—4882no—
364D4—4882no—
365D4—4882no—
366D4—4882no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—44no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—4882no—
388C2×C4—4882no—
389C2×C4—4882no—
390C2×C4—4882no—
391C2×C4—2444no—
392C2×C4—2444no—
393C2×C4—2444no—
394C2×C4—2441no—
395C2×C4—2441no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4#1451969112yes—
404C2×C4#1451973912yes—
405C2×C4#1451976611yescharacteristic
406C2×C4#1451977311yescharacteristic
407C8—82no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—22no—
416C22—4881no—
417C22—4881no—
418C22—4881no—
419C22—4881no—
420C22—4881no—
421C22—4881no—
422C22—4881no—
423C22#1683966311yescharacteristic
424C22C2×#1451969111yescharacteristic
425C22#1683973511yescharacteristic
426C22#1683975911yescharacteristic
427C22#1683976411yescharacteristic
428C22#1683977811yescharacteristic
429C22#1683977811yescharacteristic
430C22#1683997812yes—
431C22#1683998512yes—
432C4—22no—
433C4—21no—
434C4—22no—
435C4—21no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—4884no—
440C4—4881no—
441C4—4881no—
442C4—4881no—
443C2—22no—
444C2—22no—
445C2—9761no—
446C2#2144435811yescharacteristic
447C2#2144436311yescharacteristic
448C2#2144437611yescharacteristic
449C2#2144439711yescharacteristic
450C2#2144665011yescharacteristic
451C2#2144665411yescharacteristic
452C2#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#9716
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. #21444046C2semidirect
5. C61×#1797C2semidirect
6. C2×#14519765C4semidirect
9. #16839668C4semidirect
10. #16839664C4semidirect
15. #16839628C4semidirect
218. #1797D61semidirect
251. C61#9716semidirect

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
#214440462
C61×#17972
#971661