Finite Group Databasebeta

← #30597734

Subgroups — #30597734

Order 15616.

816 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519834C211yesmaximal, characteristic, complemented
2C2×#16840613C212yesmaximal
3C4×(C2×#6923)⋊C4C211yesmaximal, characteristic, complemented
4#21460692C212yesmaximal, complemented
5#21448335C211yesmaximal, characteristic
6C22×C4×#6923—21no—
7C2×#14519834C2212yes—
8C2×C4×#92420—21no—
9C2×(C2×#6923)⋊C4—21no—
10C2×(C2×#6923)⋊C4C2212yes—
11#16840628—21no—
12#16840613C418yescomplemented
13C2×#14519748C2211yescharacteristic
14C2×D4×Dic61C411yescharacteristic, complemented
15C2×#14519737—21no—
16C2×C42×D61C2211yescharacteristic
17#16839660C411yescharacteristic, complemented
18#16839656—21no—
19#16839638—21no—
20#16839619C2211yescharacteristic
21C4⋊C4×Dic61C411yescharacteristic, complemented
22C22⋊C4×Dic61—21no—
23C61×#390C411yescharacteristic, complemented
24C23×#6923—22no—
25C22×#92420—22no—
26C2×C4×#6923—24no—
27C2×C4×#6923—42no—
28C2×C4×#6923—42no—
29#14519834—22no—
30#14519834C2×C414yescomplemented
31C4×#92420—42no—
32(C2×#6923)⋊C4—24no—
33(C2×#6923)⋊C4—22no—
34(C2×#6923)⋊C4C2×C414yescomplemented
35C22×C22⋊D61—21no—
36C23×Dic61—21no—
37C22×C4×D61D411yescharacteristic
38C22×C4×D61D411yescharacteristic
39C22×C4×D61C2311yescharacteristic
40#14519748—22no—
41#14519748C2×C414yes—
42D4×Dic61—42no—
43#14519737—42no—
44#14519737—42no—
45C2×C4⋊Dic61C2×C411yescharacteristic
46C2×C4⋊Dic61C2×C411yescharacteristic
47C2×#11758196—21no—
48C2×C22⋊Dic61—21no—
49C2×C22⋊Dic61—21no—
50C2×#11758198—21no—
51C2×C4×Dic61—21no—
52C2×C4×Dic61C2×C411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54C2×C4×Dic61D411yescharacteristic
55C42×D61—42no—
56#14519684—21no—
57#14519684—21no—
58#14519684—21no—
59C22×D4×C61C2×C411yescharacteristic
60C2×C4⋊C4×C61C2×C411yescharacteristic
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61—21no—
63C2×C42×C61C2×C411yescharacteristic
64C24×C61—21no—
65C23×D61C2×D411yescharacteristic
66C22×#6923—24no—
67C22×#6923—24no—
68C22×#6923—24no—
69C22×#6923—42no—
70C22×#6923—42no—
71C22×#6923—42no—
72C22×#6923—42no—
73C2×D4×C61—21no—
74C2×D4×C61—41no—
75C2×D4×C61—41no—
76C2×D4×C61C4212yescomplemented
77C22×C4×C61—21no—
78C22×C4×C61C22⋊C411yescharacteristic
79C22×C4×C61C22⋊C411yescharacteristic
80C22×C4×C61C22×C411yescharacteristic
81C2×C22⋊D61—24no—
82C2×C22⋊D61—41no—
83C2×C22⋊D61—41no—
84C2×C22⋊D61—42no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—42no—
88C22×Dic61—42no—
89C22×Dic61—42no—
90C22×Dic61C22⋊C411yescharacteristic
91C22×Dic61C22⋊C411yescharacteristic
92C22×Dic61C2×D411yescharacteristic
93C2×C4×D61—22no—
94C2×C4×D61—22no—
95C2×C4×D61—22no—
96C2×C4×D61—22no—
97C2×C4×D61—41no—
98C2×C4×D61—41no—
99C2×C4×D61—41no—
100C2×C4×D61D812yes—
101C2×C4×D61SD1612yes—
102C2×C4×D61C22×C412yes—
103C2×C4×D61#4112yes—
104C2×#92420—24no—
105C2×#92420—42no—
106C2×#92420—42no—
107C4×#6923—48no—
108C4⋊C4×C61—41no—
109C22⋊C4×C61—42no—
110C22⋊C4×C61—42no—
111C42×C61—41no—
112C22⋊Dic61—24no—
113C22⋊Dic61—42no—
114#11758198—41no—
115#11758198—41no—
116C4⋊Dic61—21no—
117C4⋊Dic61—41no—
118C4⋊Dic61C4212yescomplemented
119#11758196—42no—
120C4×Dic61—22no—
121C4×Dic61—22no—
122C4×Dic61—41no—
123C4×Dic61—42no—
124C23×C61—22no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61C2×C22⋊C411yescharacteristic
132C22×D61—21no—
133C22×D61—21no—
134C22×D61—21no—
135C22×D61—21no—
136C22×D61C4×D412yes—
137C22×D61C2×D811yescharacteristic
138C22×D61C2×SD1611yescharacteristic
139C22×D61#13512yes—
140C2×#6923—28no—
141C2×#6923—44no—
142C2×#6923—44no—
143C2×#6923—44no—
144C2×#6923—44no—
145C2×#6923—44no—
146C2×#6923—44no—
147D4×C61—42no—
148D4×C61—42no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61#10212yes—
159C2×C4×C61#10412yes—
160C2×C4×C61C2×C4211yescharacteristic
161C2×C4×C61#11711yescharacteristic
162C22⋊D61—44no—
163C22⋊D61—44no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—22no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—84no—
176C2×Dic61#9912yes—
177C2×Dic61#10212yes—
178C2×Dic61#10412yes—
179C2×Dic61C4×D412yes—
180C4×D61—24no—
181C4×D61—24no—
182C4×D61—42no—
183C4×D61—42no—
184C4×D61—44no—
185#92420—44no—
186C4×#327—611nomaximal, Sylow
187C22×C61—42no—
188C22×C61—42no—
189C22×C61—42no—
190C22×C61—81no—
191C22×C61—81no—
192C22×C61—81no—
193C22×C61—81no—
194C22×C61C4×C22⋊C411yescharacteristic
195C22×C61C2×#9911yescharacteristic
196C22×C61#41011yescharacteristic
197C22×C61C2×#10211yescharacteristic
198C22×C61#41611yescharacteristic
199C22×C61C2×#10411yescharacteristic
200C22×C61C2×#10411yescharacteristic
201C2×D61—21no—
202C2×D61—21no—
203C2×D61—22no—
204C2×D61—22no—
205C2×D61—22no—
206C2×D61—21no—
207C2×D61—21no—
208C2×D61—22no—
209C2×D61C4×D812yes—
210C2×D61C4×SD1612yes—
211#6923—48no—
212C4×C61—22no—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—22no—
216C4×C61—81no—
217Dic61—22no—
218Dic61—41no—
219Dic61—42no—
220Dic61—81no—
221Dic61#32714yescomplemented
222C4×#121—611no—
223C4×C22⋊C8—611no—
224C2×#327—612no—
225C4×#95—611no—
226#1294—612no—
227C2×C61—82no—
228C2×C61C2×#32711yescharacteristic
229C2×C61#150011yescharacteristic
230C2×C61#150111yescharacteristic
231C2×C61#150211yescharacteristic
232C2×C61C4×#9911yescharacteristic
233C2×C61C4×#10411yescharacteristic
234C2×C61C4×#10211yescharacteristic
235D61—22no—
236D61—22no—
237C2×#121—611no—
238C2×C4×D4—611no—
239C2×C4×D4—1221no—
240C22×C42—611no—
241C22×C42—1221no—
242C2×C22⋊C8—612no—
243C2×C4×C8—1221no—
244#390#692311yescharacteristic, complemented
245#389—611no—
246#388—1221no—
247#386—1221no—
248#380—611no—
249C4×C4⋊C4—611no—
250C4×C22⋊C4—1221no—
251C2×#95—612no—
252C2×#95—1221no—
253#336—1221no—
254#327—618no—
255C61C4×#32711yescharacteristic, complemented, Sylow
256C22×D4—1221no—
257C22×D4C2×#692311yescharacteristic
258C23×C4—611no—
259C23×C4—611no—
260C23×C4—611no—
261C23×C4—1221no—
262C23×C4—1222no—
263C22×C8—1222no—
264#121—614no—
265#121—1222no—
266C4×D4—2442no—
267C4×D4—2442no—
268C4×D4—2442no—
269C2×C4⋊C4—611no—
270C2×C4⋊C4—611no—
271C2×C4⋊C4—1221no—
272C2×C4⋊C4C2×#692311yescharacteristic
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—1221no—
276C2×C22⋊C4—1221no—
277C2×C22⋊C4—1221no—
278C2×C42—611no—
279C2×C42—611no—
280C2×C42—611no—
281C2×C42—1221no—
282C2×C42—1224no—
283C2×C42—2442no—
284C2×C42—2442no—
285C2×C42—2442no—
286C2×C42C2×#692311yescharacteristic
287C22⋊C8—614no—
288C22⋊C8—1222no—
289C4×C8—2442no—
290#95—614no—
291#95—1221no—
292#95—1221no—
293#95—1222no—
294#95—1224no—
295#95—1221no—
296C24—21no—
297C24—611no—
298C2×D4—21no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—1224no—
302C2×D4—2441no—
303C2×D4—2441no—
304C2×D4—2442no—
305C2×D4C4×#692312yescomplemented
306C22×C4—21no—
307C22×C4—611no—
308C22×C4—611no—
309C22×C4—612no—
310C22×C4—612no—
311C22×C4—612no—
312C22×C4—612no—
313C22×C4—611no—
314C22×C4—1222no—
315C22×C4—1222no—
316C22×C4—1222no—
317C22×C4—1224no—
318C22×C4—1224no—
319C22×C4—1224no—
320C22×C4—1221no—
321C22×C4—1222no—
322C22×C4—1221no—
323C22×C4—2441no—
324C22×C4—2441no—
325C22×C4—2441no—
326C22×C4—2442no—
327C22×C4—2442no—
328C22×C4—2442no—
329C22×C4—2442no—
330C22×C4—2442no—
331C22×C4—2442no—
332C22×C4—2442no—
333C22×C4C22⋊#692311yescharacteristic
334C22×C4C22⋊#692311yescharacteristic
335C22×C4C22×#692311yescharacteristic
336C2×C8—1224no—
337C2×C8—2442no—
338C2×C8—2442no—
339C4⋊C4—41no—
340C4⋊C4—612no—
341C4⋊C4—1221no—
342C4⋊C4—2441no—
343C4⋊C4—2442no—
344C22⋊C4—42no—
345C22⋊C4—42no—
346C22⋊C4—1224no—
347C22⋊C4—2441no—
348C22⋊C4—2441no—
349C22⋊C4—2442no—
350C42—41no—
351C42—1222no—
352C42—1222no—
353C42—2441no—
354C42—2442no—
355C42—2448no—
356C23—22no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—611no—
364C23—611no—
365C23—612no—
366C23—612no—
367C23—1221no—
368C23—1221no—
369C23—1221no—
370C23—1221no—
371C23C2×C22⋊#692311yescharacteristic
372D4—42no—
373D4—42no—
374D4—2444no—
375D4—2444no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—612no—
386C2×C4—612no—
387C2×C4—612no—
388C2×C4—612no—
389C2×C4—1224no—
390C2×C4—1224no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—1228no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—1221no—
397C2×C4—1222no—
398C2×C4—4884no—
399C2×C4—2442no—
400C2×C4—2442no—
401C2×C4—2444no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4—2441no—
405C2×C4—2444no—
406C2×C4—2444no—
407C2×C4—2444no—
408C2×C4—2444no—
409C2×C4—2444no—
410C2×C4—2444no—
411C2×C4—2441no—
412C2×C4—2441no—
413C2×C4#1451983912yes—
414C2×C4#1451984112yes—
415C2×C4C2×C4×#692311yescharacteristic
416C2×C4#1451985611yescharacteristic
417C8—2444no—
418C22—42no—
419C22—42no—
420C22—42no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—612no—
426C22—612no—
427C22—1222no—
428C22—1222no—
429C22—1221no—
430C22—1221no—
431C22—1222no—
432C22—1222no—
433C22—1221no—
434C22—1221no—
435C22C4×C22⋊#692311yescharacteristic
436C22D61⋊#9911yescharacteristic
437C22#1684074211yescharacteristic
438C22C2×#1451983911yescharacteristic
439C22#1684075211yescharacteristic
440C22C2×#1451984111yescharacteristic
441C22D61⋊#10411yescharacteristic
442C4—21no—
443C4—21no—
444C4—22no—
445C4—22no—
446C4—81no—
447C4—614no—
448C4—1222no—
449C4—4881no—
450C4—2448no—
451C4—2442no—
452C4—2441no—
453C2—82no—
454C2—1222no—
455C2—1222no—
456C2D61⋊#32711yescharacteristic
457C2#2146119111yescharacteristic
458C2#2146119511yescharacteristic
459C2#2146119911yescharacteristic
460C2#2146156611yescharacteristic
461C2C4×#1451984111yescharacteristic
462C2C4×#1451983911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#390C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519748C22
cosocleC22×C4×D61C23
hypercenter#390#6923
hypocenterC61C4×#327
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C4×#14519834C2semidirect
3. C4×(C2×#6923)⋊C4C2semidirect
4. #21460692C2semidirect
12. #16840613C4semidirect
14. C2×D4×Dic61C4semidirect
17. #16839660C4semidirect
21. C4⋊C4×Dic61C4semidirect
23. C61×#390C4semidirect
30. #14519834C2×C4semidirect
34. (C2×#6923)⋊C4C2×C4semidirect
76. C2×D4×C61C42semidirect
118. C4⋊Dic61C42semidirect
221. Dic61#327semidirect
244. #390#6923semidirect
255. C61C4×#327semidirect
305. C2×D4C4×#6923semidirect

Maximal subgroups

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

subgroupindex
C4×#145198342
C2×#168406132
C4×(C2×#6923)⋊C42
#214606922
#214483352
C4×#32761