Finite Group Databasebeta

← #30600156

Subgroups — #30600156

Order 15616.

810 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×C4×D61⋊C8C211yesmaximal, characteristic, complemented
2#21461674C211yesmaximal, characteristic, complemented
3C2×#16840610C212yesmaximal, complemented
4#21460655C212yesmaximal, complemented
5#21448327C211yesmaximal, characteristic
6C22×D61⋊C8—21no—
7C2×C4⋊#92420C2212yes—
8C2×#14519834—21no—
9C4×D61⋊C8—24no—
10C2×C4×#92420—21no—
11C2×C4×#92420C2212yes—
12#16840628—21no—
13#16840610—24no—
14C2×#14519752C411yescharacteristic
15C2×#14519739—21no—
16C2×#14519739C2211yescharacteristic
17C2×C42×D61C2211yescharacteristic
18#16839664C411yescharacteristic
19#16839652—21no—
20#16839640—21no—
21#16839619C411yescharacteristic
22C4⋊C4×Dic61C2211yescharacteristic
23#16839609—21no—
24C61×#389C411yescharacteristic
25C2×D61⋊C8—24no—
26C2×D61⋊C8—24no—
27C2×D61⋊C8—24no—
28C22×#92420—22no—
29C22×#92420—22no—
30C4⋊#92420—22no—
31C4⋊#92420—22no—
32#14519834—42no—
33C4×#92420—24no—
34C4×#92420—22no—
35C4×#92420D414yescomplemented
36C22×D244—21no—
37C22×D244C2×C411yescharacteristic
38C22×C4×D61—21no—
39C22×C4×D61C2×C411yescharacteristic
40C22×C4×D61D411yescharacteristic
41C22×C4×D61D411yescharacteristic
42#14519752—22no—
43#14519752C814yescomplemented
44#14519739—22no—
45#14519739—22no—
46#14519739—42no—
47#14519739—42no—
48C2×C4⋊Dic61C2×C411yescharacteristic
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×#11758198—21no—
53C2×#11758198—21no—
54C2×C4×Dic61—21no—
55C2×C4×Dic61D411yescharacteristic
56C2×C4×Dic61D411yescharacteristic
57C2×C4×Dic61C2311yescharacteristic
58C42×D61—22no—
59C42×D61—22no—
60#14519684—21no—
61#14519684—21no—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61C2×C411yescharacteristic
64C2×C4⋊C4×C61C2×C411yescharacteristic
65C2×C42×C61C2×C411yescharacteristic
66#95×C61—21no—
67C23×D61—21no—
68C23×D61C22⋊C411yescharacteristic
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22×C411yescharacteristic
74C22×Dic61—21no—
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C2×D411yescharacteristic
77C22×Dic61C2×D411yescharacteristic
78C2×D244—22no—
79C2×D244—22no—
80C2×D244—24no—
81C2×D244—21no—
82C2×D244—42no—
83C2×D244—42no—
84C2×D244C2×C812yescomplemented
85C2×C4×D61—22no—
86C2×C4×D61—22no—
87C2×C4×D61—22no—
88C2×C4×D61—22no—
89C2×C4×D61—21no—
90C2×C4×D61—22no—
91C2×C4×D61—21no—
92C2×C4×D61—22no—
93C2×C4×D61—42no—
94C2×C4×D61—41no—
95C2×C4×D61—41no—
96C2×C4×D61—42no—
97C2×C4×D61C2×C812yes—
98C2×C4×D61M1612yes—
99C2×C4×D61D812yes—
100C2×C4×D61SD1612yes—
101C2×#92420—24no—
102C2×#92420—24no—
103C2×#92420—24no—
104C2×#92420—42no—
105C2×#92420—42no—
106C2×#92420—42no—
107D61⋊C8—216no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—22no—
110C4⋊C4×C61—42no—
111C4⋊C4×C61C2×C812yescomplemented
112C42×C61—22no—
113#11758198—24no—
114#11758198—42no—
115#11758198—42no—
116#11758198—42no—
117#11758198—41no—
118#11758198—41no—
119C4⋊Dic61—22no—
120C4×Dic61—21no—
121C4×Dic61—22no—
122C4×Dic61—21no—
123C4×Dic61—41no—
124C4×Dic61—41no—
125C4×Dic61C2×D412yes—
126C4×Dic61#4112yes—
127C23×C61C2×C22⋊C411yescharacteristic
128C22×D61—21no—
129C22×D61—21no—
130C22×D61—21no—
131C22×D61—21no—
132C22×D61—22no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61C22⋊C812yes—
140C22×D61#10212yes—
141C22×D61#10412yes—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—22no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61#10212yes—
153C2×C4×C61#10412yes—
154C2×C4×C61C4×D412yes—
155C2×C4×C61C22×C811yescharacteristic
156C2×C4×C61C2×M1611yescharacteristic
157C2×C4×C61#13112yes—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61C22⋊C812yes—
166C2×Dic61#12011yescharacteristic
167C2×Dic61#12112yes—
168C2×Dic61#12311yescharacteristic
169C2×Dic61C2×D811yescharacteristic
170C2×Dic61C2×SD1611yescharacteristic
171C2×Dic61#13512yes—
172D244—24no—
173D244—48no—
174D244—42no—
175C4×D61—24no—
176C4×D61—24no—
177C4×D61—24no—
178C4×D61—24no—
179C4×D61—24no—
180C4×D61—24no—
181C4×D61—82no—
182C4×D61—82no—
183#92420—28no—
184#92420—82no—
185#9072—611nomaximal, Sylow
186C22×C61#38611yescharacteristic
187C22×C61C2×C22⋊C811yescharacteristic
188C22×C61#40811yescharacteristic
189C22×C61C2×#10211yescharacteristic
190C22×C61#41611yescharacteristic
191C22×C61C2×#10411yescharacteristic
192C22×C61C2×#10411yescharacteristic
193C2×D61—22no—
194C2×D61—22no—
195C2×D61—22no—
196C2×D61—22no—
197C2×D61—22no—
198C2×D61—22no—
199C2×D61—42no—
200C2×D61—42no—
201C2×D61—42no—
202C2×D61—81no—
203C2×D61—81no—
204C2×D61—81no—
205C2×D61—81no—
206C2×D61D4⋊C814yescomplemented
207C4×C61—22no—
208C4×C61—22no—
209C4×C61—42no—
210C4×C61—81no—
211C4×C61C8×D412yes—
212C4×C61#43512yes—
213Dic61—22no—
214Dic61—21no—
215Dic61—21no—
216Dic61—81no—
217Dic61#46512yes—
218Dic61#46612yes—
219C22×C4×C8—611no—
220C4×#121—611no—
221#1797—611no—
222C2×D4⋊C8—612no—
223#1279—612no—
224C2×C61C2×D4⋊C811yescharacteristic
225C2×C61#147611yescharacteristic
226C2×C61#149211yescharacteristic
227C2×C61#149411yescharacteristic
228C2×C61#186911yescharacteristic
229C2×C61#189311yescharacteristic
230C2×C61#189611yescharacteristic
231D61—24no—
232D61—82no—
233C23×C8—1221no—
234C2×#121—611no—
235C2×C4×D4—611no—
236C2×C4×D4—1221no—
237C22×C42—611no—
238C2×C4⋊C8—612no—
239C2×C22⋊C8—1221no—
240C2×C4×C8—612no—
241C2×C4×C8—1224no—
242C2×C4×C8—1221no—
243#390—611no—
244#389#692311yescharacteristic
245#388—1221no—
246#386—1221no—
247#380—611no—
248C4×C4⋊C4—611no—
249C4×C22⋊C4—1221no—
250#336—1221no—
251D4⋊C8—1224no—
252C61#907211yescharacteristic, complemented, Sylow
253C22×D4—611no—
254C22×D4—1221no—
255C23×C4—611no—
256C23×C4—611no—
257C23×C4—611no—
258C23×C4—1221no—
259C22×C8—1222no—
260C22×C8—1224no—
261C22×C8—1224no—
262C22×C8—1224no—
263C22×C8—1222no—
264#121—614no—
265#121—1222no—
266C4×D4—1222no—
267C4×D4—1222no—
268C4×D4—2442no—
269C4×D4—2442no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—611no—
272C2×C4⋊C4C2×#692311yescharacteristic
273C2×C4⋊C4C2×#692311yescharacteristic
274C2×C22⋊C4—1221no—
275C2×C22⋊C4—1221no—
276C2×C22⋊C4—1221no—
277C2×C22⋊C4—1221no—
278C2×C22⋊C4—1221no—
279C2×C42—611no—
280C2×C42—611no—
281C2×C42—611no—
282C2×C42—1222no—
283C2×C42—1222no—
284C2×C42—1221no—
285C2×C42C2×#692311yescharacteristic
286C4⋊C8—1222no—
287C4⋊C8—1222no—
288C22⋊C8—2442no—
289C4×C8—614no—
290C4×C8—1222no—
291C4×C8—1224no—
292#95—21no—
293#95—1221no—
294#95—1221no—
295C24—611no—
296C24—1221no—
297C2×D4—612no—
298C2×D4—1224no—
299C2×D4—1222no—
300C2×D4—1221no—
301C2×D4—1222no—
302C2×D4—2442no—
303C2×D4—2442no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—611no—
307C22×C4—611no—
308C22×C4—611no—
309C22×C4—612no—
310C22×C4—612no—
311C22×C4—612no—
312C22×C4—612no—
313C22×C4—1221no—
314C22×C4—1222no—
315C22×C4—1221no—
316C22×C4—1222no—
317C22×C4—1222no—
318C22×C4—1222no—
319C22×C4—1222no—
320C22×C4—1222no—
321C22×C4—1221no—
322C22×C4—2442no—
323C22×C4—2441no—
324C22×C4—2441no—
325C22×C4—2442no—
326C22×C4C22⋊#692311yescharacteristic
327C22×C4C22⋊#692311yescharacteristic
328C22×C4C22×#692311yescharacteristic
329C2×C8—1224no—
330C2×C8—12216no—
331C2×C8—1224no—
332C2×C8—1224no—
333C2×C8—2442no—
334C2×C8—2442no—
335C2×C8—2442no—
336C4⋊C4—21no—
337C4⋊C4—22no—
338C4⋊C4—42no—
339C4⋊C4—1222no—
340C4⋊C4D61⋊C812yescomplemented
341C22⋊C4—1224no—
342C22⋊C4—2441no—
343C22⋊C4—2441no—
344C22⋊C4—2442no—
345C22⋊C4—2442no—
346C22⋊C4—2442no—
347C42—22no—
348C42—612no—
349C42—612no—
350C42—1221no—
351C42—1222no—
352C42—1221no—
353C42—2441no—
354C42—2441no—
355C23—612no—
356C23—612no—
357C23—612no—
358C23—1221no—
359C23—1221no—
360C23—1221no—
361C23—1221no—
362C23—1222no—
363C23—2441no—
364C23—2441no—
365C23—2441no—
366C23—2441no—
367C23—2441no—
368C23—2441no—
369C23C2×C22⋊#692311yescharacteristic
370D4—1224no—
371D4—2448no—
372D4—2442no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—22no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—612no—
384C2×C4—611no—
385C2×C4—611no—
386C2×C4—612no—
387C2×C4—611no—
388C2×C4—611no—
389C2×C4—612no—
390C2×C4—1224no—
391C2×C4—1224no—
392C2×C4—1224no—
393C2×C4—1224no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—1221no—
397C2×C4—1221no—
398C2×C4—1224no—
399C2×C4—1224no—
400C2×C4—4882no—
401C2×C4—4882no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4—2441no—
405C2×C4#1451983912yes—
406C2×C4#1451984212yes—
407C2×C4D4×#692312yes—
408C2×C4C2×D61⋊C811yescharacteristic
409C2×C4D61⋊M1611yescharacteristic
410C2×C4#1451986512yes—
411C8—1228no—
412C8—4882no—
413C22—614no—
414C22—1222no—
415C22—1222no—
416C22—1222no—
417C22—1222no—
418C22—1222no—
419C22—1222no—
420C22—4881no—
421C22—4881no—
422C22—4881no—
423C22—4881no—
424C22—2442no—
425C22—2442no—
426C22—2442no—
427C22#1684071011yescharacteristic
428C22D61⋊(C22⋊C8)11yescharacteristic
429C22#1684073711yescharacteristic
430C22C2×#1451983911yescharacteristic
431C22#1684075211yescharacteristic
432C22D61⋊#10411yescharacteristic
433C22C2×#1451984211yescharacteristic
434C4—22no—
435C4—22no—
436C4—42no—
437C4—81no—
438C4—612no—
439C4—612no—
440C4—1222no—
441C4—1221no—
442C4—1221no—
443C4—4881no—
444C4#1684079012yes—
445C4#1684079212yes—
446C2—1224no—
447C2—4882no—
448C2D61⋊(D4⋊C8)11yescharacteristic
449C2#2146111311yescharacteristic
450C2#2146116611yescharacteristic
451C2#2146117311yescharacteristic
452C2#2146179511yescharacteristic
453C2#2146183311yescharacteristic
454C2#2146183611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519752C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#9072
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×C4×D61⋊C8C2semidirect
2. #21461674C2semidirect
3. C2×#16840610C2semidirect
4. #21460655C2semidirect
35. C4×#92420D4semidirect
43. #14519752C8semidirect
84. C2×D244C2×C8semidirect
111. C4⋊C4×C61C2×C8semidirect
206. C2×D61D4⋊C8semidirect
252. C61#9072semidirect
340. C4⋊C4D61⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D61⋊C82
#214616742
C2×#168406102
#214606552
#214483272
#907261