Finite Group Databasebeta

← #30600393

Subgroups — #30600393

Order 15616.

612 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840765C211yesmaximal, characteristic
2#21461675C211yesmaximal, characteristic
3C2×#16840621C212yesmaximal, complemented
4#21460697C212yesmaximal, complemented
5#21454169C211yesmaximal, characteristic
6C22×#11758217—21no—
7#16840765—24no—
8C2×#14519844C2212yes—
9C2×#14519844C2212yes—
10C2×C4⋊#92420—21no—
11C2×C22⋊#92420—21no—
12#16840628—21no—
13#16840621—24no—
14C2×#14519776C2211yescharacteristic
15C2×#14519754—21no—
16C22×C4×Dic61C2211yescharacteristic
17#16839666—21no—
18#16839661C411yescharacteristic
19#16839659—21no—
20#16839658C411yescharacteristic
21#16839631C2211yescharacteristic
22#16839622C411yescharacteristic
23#16839620—21no—
24C61×#380C411yescharacteristic
25C2×#11758217—24no—
26C2×#11758217—42no—
27C2×#11758217—42no—
28C22×#92420—22no—
29C22×#92420—22no—
30#14519844—22no—
31#14519844—22no—
32#14519844—22no—
33#14519844D414yes—
34C4⋊#92420—24no—
35C22⋊#92420—42no—
36C22×Dic122—21no—
37C23×Dic61D411yescharacteristic
38C23×Dic61D411yescharacteristic
39#14519776—22no—
40#14519776—22no—
41#14519754—44no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×C4⋊Dic61C2×C411yescharacteristic
45C2×#11758196—21no—
46C2×#11758196—21no—
47C2×#11758196—21no—
48C2×#11758196—21no—
49C2×C22⋊Dic61—21no—
50C2×C4×Dic61—22no—
51C2×C4×Dic61—22no—
52C2×C4×Dic61C2×C411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54C2×C4×Dic61D411yescharacteristic
55C2×C4×Dic61C2311yescharacteristic
56#14519684—21no—
57#14519684—21no—
58#14519684—21no—
59C23×C4×C61C2×C411yescharacteristic
60C2×C4⋊C4×C61C2×C411yescharacteristic
61C2×C4⋊C4×C61C2×C411yescharacteristic
62C2×C22⋊C4×C61—21no—
63#95×C61—21no—
64C24×C61C22⋊C411yescharacteristic
65C22×C4×C61—22no—
66C22×C4×C61—22no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—41no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22×C411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—22no—
77C22×Dic61—21no—
78C22×Dic61—22no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61SD1612yes—
85C22×Dic61Q1612yes—
86C22×Dic61C2×D411yescharacteristic
87C22×Dic61C2×D411yescharacteristic
88C2×Dic122—42no—
89C2×Dic122—41no—
90C2×Dic122—42no—
91C2×Dic122—41no—
92#11758217—48no—
93C2×#92420—24no—
94C2×#92420—42no—
95C2×#92420—42no—
96C2×#92420—42no—
97C2×#92420—42no—
98C2×#92420—42no—
99C4⋊C4×C61—22no—
100C4⋊C4×C61—41no—
101C22⋊C4×C61—42no—
102C22⋊Dic61—42no—
103C4⋊Dic61—22no—
104C4⋊Dic61—42no—
105C4⋊Dic61—41no—
106#11758196—42no—
107#11758196—41no—
108#11758196—41no—
109#11758196—41no—
110#11758196—42no—
111#11758196—41no—
112C4×Dic61—22no—
113C4×Dic61—21no—
114C4×Dic61—22no—
115C4×Dic61—21no—
116C4×Dic61C2×D412yes—
117C4×Dic61#4112yes—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61#10312yes—
125C23×C61C2×C22⋊C411yescharacteristic
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—44no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61#10112yes—
138C2×C4×C61C4×D412yes—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—22no—
142C2×Dic61—22no—
143C2×Dic61—22no—
144C2×Dic61—22no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—42no—
149C2×Dic61—42no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61#10312yes—
157C2×Dic61#12011yescharacteristic
158C2×Dic61#12112yes—
159C2×Dic61#12311yescharacteristic
160C2×Dic61C2×SD1611yescharacteristic
161C2×Dic61C2×Q1611yescharacteristic
162C2×Dic61AGL(1,ℤ/8)11yescharacteristic
163C2×Dic61AGL(1,ℤ/8)12yes—
164C2×Dic61AGL(1,ℤ/8)11yescharacteristic
165C2×Dic61#13711yescharacteristic
166C2×Dic61#13711yescharacteristic
167Dic122—82no—
168Dic122—82no—
169#92420—44no—
170#92420—82no—
171#9137—611nomaximal, Sylow
172C22×C61—22no—
173C22×C61—22no—
174C22×C61—22no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61#38611yescharacteristic
180C22×C61C2×#10111yescharacteristic
181C22×C61#41311yescharacteristic
182C22×C61C2×#10311yescharacteristic
183C22×C61#41711yescharacteristic
184C22×C61#41711yescharacteristic
185C22×C61#41811yescharacteristic
186C4×C61—22no—
187C4×C61—22no—
188C4×C61—81no—
189C4×C61—81no—
190Dic61—22no—
191Dic61—41no—
192Dic61—81no—
193Dic61—81no—
194Dic61#45011yescharacteristic
195Dic61#45111yescharacteristic
196Dic61#46812yes—
197Dic61#46912yes—
198Dic61#48311yescharacteristic
199Dic61#48411yescharacteristic
200C2×#423—611no—
201#2857—611no—
202#1797—611no—
203C2×#332—612no—
204#1296—612no—
205C2×C61—42no—
206C2×C61#154911yescharacteristic
207C2×C61#155011yescharacteristic
208C2×C61#155711yescharacteristic
209C2×C61#156111yescharacteristic
210C2×C61#187211yescharacteristic
211C2×C61#189511yescharacteristic
212C2×C61#190111yescharacteristic
213C22×M16—1221no—
214C2×C4⋊Q8—611no—
215C2×C22⋊Q8—1221no—
216C22×C42—611no—
217#423—1224no—
218C2×C4⋊C8—612no—
219C2×C4⋊C8—612no—
220C2×C4⋊C8—1221no—
221C2×C22⋊C8—1221no—
222#391—1221no—
223#389—611no—
224#389—611no—
225#389—1221no—
226#384—611no—
227#380—611no—
228#380—1221no—
229#380#692311yescharacteristic
230#336—1221no—
231#332—1224no—
232C61#913711yescharacteristic, complemented, Sylow
233C22×Q8—1221no—
234C23×C4—611no—
235C23×C4—611no—
236C23×C4C2×#692311yescharacteristic
237C2×M16—1224no—
238C2×M16—2442no—
239C2×M16—2442no—
240C22×C8—1222no—
241C22×C8—1222no—
242C4⋊Q8—1222no—
243C4⋊Q8—1222no—
244C22⋊Q8—2444no—
245C2×C4⋊C4—611no—
246C2×C4⋊C4—611no—
247C2×C4⋊C4—1221no—
248C2×C4⋊C4—1221no—
249C2×C4⋊C4—1221no—
250C2×C4⋊C4—1221no—
251C2×C4⋊C4—1221no—
252C2×C4⋊C4C2×#692311yescharacteristic
253C2×C4⋊C4C2×#692311yescharacteristic
254C2×C22⋊C4—21no—
255C2×C22⋊C4—1221no—
256C2×C42—611no—
257C2×C42—611no—
258C2×C42—611no—
259C2×C42—611no—
260C2×C42—1222no—
261C2×C42—1222no—
262C4⋊C8—614no—
263C4⋊C8—1222no—
264C4⋊C8—1222no—
265C4⋊C8—1222no—
266C4⋊C8—1224no—
267C22⋊C8—2442no—
268#95—21no—
269#95—1221no—
270#95—1221no—
271#95—1221no—
272C24C22⋊#692311yescharacteristic
273C2×Q8—2442no—
274C2×Q8—2442no—
275C2×Q8—2441no—
276C2×Q8—2441no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—41no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—612no—
285C22×C4—612no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4—1222no—
294C22×C4—1222no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4C22⋊#692311yescharacteristic
299C22×C4C22×#692311yescharacteristic
300M16—2448no—
301C2×C8—1224no—
302C2×C8—2442no—
303C2×C8—2442no—
304C2×C8—2442no—
305C2×C8—2442no—
306C2×C8—2442no—
307C4⋊C4—22no—
308C4⋊C4—41no—
309C4⋊C4—1222no—
310C4⋊C4—2441no—
311C4⋊C4—2441no—
312C4⋊C4—2441no—
313C4⋊C4—2442no—
314C4⋊C4—2441no—
315C4⋊C4—2441no—
316C4⋊C4—2442no—
317C4⋊C4—2442no—
318C22⋊C4—42no—
319C22⋊C4—2442no—
320C42—612no—
321C42—612no—
322C42—1221no—
323C42—1222no—
324C42—1221no—
325C42—1222no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23#1451984012yes—
333C23C2×C22⋊#692311yescharacteristic
334Q8—4882no—
335Q8—4882no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—44no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—611no—
348C2×C4—612no—
349C2×C4—611no—
350C2×C4—611no—
351C2×C4—611no—
352C2×C4—611no—
353C2×C4—611no—
354C2×C4—611no—
355C2×C4—611no—
356C2×C4—612no—
357C2×C4—612no—
358C2×C4—1222no—
359C2×C4—1222no—
360C2×C4—1222no—
361C2×C4—1222no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—2442no—
368C2×C4—2442no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4#1451983812yes—
376C2×C4D4×#692312yes—
377C8—4882no—
378C8—2444no—
379C22—22no—
380C22—22no—
381C22—22no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22#1684071011yescharacteristic
387C22C2×#1451983811yescharacteristic
388C22#1684074911yescharacteristic
389C22C2×#1451984011yescharacteristic
390C22#1684075311yescharacteristic
391C22#1684075311yescharacteristic
392C22#1684075411yescharacteristic
393C4—22no—
394C4—22no—
395C4—81no—
396C4—81no—
397C4—611no—
398C4—611no—
399C4—611no—
400C4—611no—
401C4—612no—
402C4—612no—
403C4—1222no—
404C4—4881no—
405C4—4881no—
406C4—2441no—
407C2—42no—
408C2#2146133411yescharacteristic
409C2#2146133711yescharacteristic
410C2#2146135111yescharacteristic
411C2#2146135811yescharacteristic
412C2#2146180411yescharacteristic
413C2#2146183511yescharacteristic
414C2#2146184611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#380#6923
hypocenterC61#9137
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. C2×#16840621C2semidirect
4. #21460697C2semidirect
232. C61#9137semidirect

Maximal subgroups

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

subgroupindex
C2×#168407652
#214616752
C2×#168406212
#214606972
#214541692
#913761