Finite Group Databasebeta

← #30610174

Subgroups — #30610174

Order 15616.

1034 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462495C212yesmaximal, complemented
2#21461100C218yesmaximal, complemented
3#21461067C212yesmaximal, complemented
4#21461064C212yesmaximal
5C22×#14519770C211yesmaximal, characteristic
6#16840783C2214yescomplemented
7#16840782—22no—
8#16840779C2214yescomplemented
9#16840778—22no—
10#16840765—22no—
11#16840732C2214yes—
12C4×#11758217—22no—
13#16840607C2218yescomplemented
14#16840605C2218yes—
15C2×#14519770—22no—
16C2×#14519770—22no—
17C2×#14519770—22no—
18C2×#14519770—22no—
19C2×#14519770C414yes—
20C2×#14519770C2214yes—
21C22×C4⋊Dic61C2211yescharacteristic
22C22×#11758196C411yescharacteristic
23C22×#11758196C411yescharacteristic
24C22×C22⋊Dic61C411yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C4×Dic61C2211yescharacteristic
27C22×C22⋊C4×C61C411yescharacteristic
28C2×#11758217—24no—
29#14519844—24no—
30C4⋊#92420—24no—
31C22⋊#92420—24no—
32C22⋊#92420C2318yes—
33#14519832—24no—
34C4×#92420—24no—
35C23×Dic61C2×C411yescharacteristic
36C23×Dic61C2×C411yescharacteristic
37C23×Dic61C2×C411yescharacteristic
38C23×Dic61C2311yescharacteristic
39#14519770—24no—
40#14519770—24no—
41#14519770—24no—
42#14519770—24no—
43#14519770—24no—
44#14519770—24no—
45#14519770—24no—
46#14519770—24no—
47C2×C4⋊Dic61—22no—
48C2×C4⋊Dic61—22no—
49C2×C4⋊Dic61C2×C412yes—
50C2×C4⋊Dic61C2312yes—
51C2×#11758196—22no—
52C2×#11758196—21no—
53C2×#11758196—21no—
54C2×#11758196—22no—
55C2×#11758196—21no—
56C2×#11758196—21no—
57C2×#11758196C2×C414yes—
58C2×#11758196C2×C414yes—
59C2×C22⋊Dic61—21no—
60C2×C22⋊Dic61—21no—
61C2×C22⋊Dic61—22no—
62C2×C22⋊Dic61—22no—
63C2×C22⋊Dic61—22no—
64C2×C22⋊Dic61C2×C414yes—
65C2×C22⋊Dic61C2×C412yes—
66C2×C22⋊Dic61C2312yes—
67C2×C4×Dic61C2×C412yes—
68C2×C4×Dic61D412yes—
69C2×C4×Dic61D412yes—
70C2×C4×Dic61D412yes—
71C2×C4×Dic61D412yes—
72C2×C4×Dic61C2312yes—
73C25×C61C2×C411yescharacteristic
74C23×C4×C61C2×C411yescharacteristic
75C23×C4×C61C2×C411yescharacteristic
76C2×C22⋊C4×C61—22no—
77C2×C22⋊C4×C61—21no—
78C2×C22⋊C4×C61—21no—
79C2×C22⋊C4×C61C2×C414yes—
80C24×C61—21no—
81C24×C61—21no—
82C24×C61—42no—
83C24×C61—42no—
84C24×C61—42no—
85C24×C61C22×C411yescharacteristic
86C24×C61C22×C412yes—
87C22×C4×C61—21no—
88C22×C4×C61—21no—
89C22×C4×C61—42no—
90C22×C4×C61—42no—
91C22×C4×C61C22⋊C412yes—
92C22×C4×C61C22⋊C411yescharacteristic
93C22×C4×C61C22⋊C411yescharacteristic
94C22×C4×C61C22×C412yes—
95C22×C4×C61C22×C412yes—
96C22×Dic61—21no—
97C22×Dic61—21no—
98C22×Dic61—21no—
99C22×Dic61—21no—
100C22×Dic61—42no—
101C22×Dic61—42no—
102C22×Dic61—42no—
103C22×Dic61—42no—
104C22×Dic61C22⋊C412yes—
105C22×Dic61C22⋊C411yescharacteristic
106C22×Dic61C22⋊C411yescharacteristic
107C22×Dic61C22×C412yes—
108C22×Dic61C22×C412yes—
109C22×Dic61C22×C412yes—
110C22×Dic61C22×C411yescharacteristic
111C22×Dic61C2×D412yes—
112C22×Dic61C2×D412yes—
113C22×Dic61C2411yescharacteristic
114#11758217—48no—
115C2×#92420—28no—
116C22⋊C4×C61—24no—
117C22⋊C4×C61—24no—
118C22⋊Dic61—24no—
119C22⋊Dic61—24no—
120C22⋊Dic61—24no—
121C22⋊Dic61—24no—
122C4⋊Dic61—24no—
123C4⋊Dic61—24no—
124#11758196—24no—
125#11758196—24no—
126#11758196—24no—
127#11758196—24no—
128C4×Dic61C22⋊C412yes—
129C4×Dic61C22⋊C412yes—
130C4×Dic61C22⋊C412yes—
131C4×Dic61C22⋊C412yes—
132C4×Dic61C2×D412yes—
133C4×Dic61C2×D412yes—
134C4×Dic61C2×D412yes—
135C4×Dic61C2×D412yes—
136C23×C61—22no—
137C23×C61—22no—
138C23×C61—22no—
139C23×C61—22no—
140C23×C61—24no—
141C23×C61—42no—
142C23×C61—42no—
143C23×C61—42no—
144C23×C61—42no—
145C23×C61—42no—
146C23×C61—42no—
147C23×C61—42no—
148C23×C61—42no—
149C23×C61—88no—
150C23×C61C2×C22⋊C411yescharacteristic
151C23×C61C2×C22⋊C411yescharacteristic
152C23×C61C23×C411yescharacteristic
153C2×C4×C61—24no—
154C2×C4×C61—22no—
155C2×C4×C61—24no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—42no—
159C2×C4×C61—42no—
160C2×C4×C61—42no—
161C2×C4×C61C2×C22⋊C412yes—
162C2×C4×C61C2×C22⋊C412yes—
163C2×Dic61—24no—
164C2×Dic61—24no—
165C2×Dic61—22no—
166C2×Dic61—22no—
167C2×Dic61—42no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—42no—
172C2×Dic61—41no—
173C2×Dic61—42no—
174C2×Dic61—42no—
175C2×Dic61—42no—
176C2×Dic61—42no—
177C2×Dic61—42no—
178C2×Dic61—42no—
179C2×Dic61C2×C22⋊C412yes—
180C2×Dic61C2×C22⋊C412yes—
181C2×Dic61C2×C22⋊C412yes—
182C2×Dic61C22×D412yes—
183#92420—48no—
184#17398—611nomaximal, Sylow
185C22×C61—28no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—42no—
193C22×C61—42no—
194C22×C61—42no—
195C22×C61—84no—
196C22×C61—84no—
197C22×C61—84no—
198C22×C61#41012yes—
199C22×C61#41312yes—
200C22×C61C22×C22⋊C411yescharacteristic
201C22×C61#56812yes—
202C4×C61—22no—
203C4×C61—22no—
204C4×C61—42no—
205Dic61—22no—
206Dic61—22no—
207Dic61—22no—
208Dic61—22no—
209Dic61—42no—
210Dic61—42no—
211C22×#126—611no—
212#2920—612no—
213#1473—618no—
214#1463—612no—
215#1462—612no—
216C2×C61—22no—
217C2×C61—22no—
218C2×C61—22no—
219C2×C61—82no—
220C2×C61#287911yescharacteristic
221C2×C61C2×#41011yescharacteristic
222C2×C61C2×#41311yescharacteristic
223C2×#126—614no—
224C2×#126—614no—
225C2×#126—1222no—
226C2×#126—1222no—
227C2×#126—1222no—
228C2×#126—1222no—
229C22×C4⋊C4—611no—
230C22×C4⋊C4—611no—
231C22×C4⋊C4—611no—
232C22×C22⋊C4—611no—
233C22×C22⋊C4—611no—
234C22×C22⋊C4#692311yescharacteristic
235C22×C42—611no—
236#432—614no—
237#432—1222no—
238#431—614no—
239#431—1222no—
240#423—1222no—
241#407—614no—
242C4×M16—1222no—
243#324—618no—
244#323—618no—
245C61#1739811yescharacteristic, complemented, Sylow
246C25C2×#692311yescharacteristic
247C23×C4—611no—
248C23×C4—611no—
249C23×C4—611no—
250C23×C4—611no—
251C23×C4C2×#692311yescharacteristic
252C23×C4C2×#692311yescharacteristic
253C2×M16—1224no—
254#126—1224no—
255#126—1224no—
256#126—1224no—
257#126—1224no—
258#126—1224no—
259#126—1224no—
260#126—1224no—
261#126—1224no—
262C2×C4⋊C4—612no—
263C2×C4⋊C4—614no—
264C2×C4⋊C4—614no—
265C2×C4⋊C4—612no—
266C2×C4⋊C4—1222no—
267C2×C4⋊C4—1221no—
268C2×C4⋊C4—1221no—
269C2×C4⋊C4—1222no—
270C2×C4⋊C4—1222no—
271C2×C4⋊C4—1222no—
272C2×C4⋊C4—1221no—
273C2×C4⋊C4—1221no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—612no—
278C2×C22⋊C4—614no—
279C2×C22⋊C4—612no—
280C2×C22⋊C4—1222no—
281C2×C22⋊C4—1222no—
282C2×C22⋊C4—1222no—
283C2×C22⋊C4—1221no—
284C2×C22⋊C4—1221no—
285C2×C22⋊C4C2×#692314yes—
286C2×C42—612no—
287C2×C42—612no—
288C2×C42—612no—
289C2×C42—612no—
290C2×C42—612no—
291C2×C42—612no—
292C4⋊C8—1224no—
293C4⋊C8—1224no—
294C22⋊C8—618no—
295C22⋊C8—1224no—
296#97—1224no—
297C4×C8—1224no—
298C24—21no—
299C24—21no—
300C24—42no—
301C24—42no—
302C24—42no—
303C24C22×#692311yescharacteristic
304C24C22×#692312yes—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—612no—
310C22×C4—612no—
311C22×C4—612no—
312C22×C4—612no—
313C22×C4—611no—
314C22×C4—611no—
315C22×C4—611no—
316C22×C4—611no—
317C22×C4—612no—
318C22×C4—612no—
319C22×C4—1221no—
320C22×C4—1221no—
321C22×C4—1221no—
322C22×C4—1221no—
323C22×C4—2442no—
324C22×C4—2442no—
325C22×C4—2442no—
326C22×C4—2442no—
327C22×C4C22⋊#692312yes—
328C22×C4C22⋊#692311yescharacteristic
329C22×C4C22⋊#692311yescharacteristic
330C22×C4C22×#692312yes—
331C22×C4C22×#692312yes—
332M16—2448no—
333C2×C8—1228no—
334C4⋊C4—1224no—
335C4⋊C4—1224no—
336C4⋊C4—1224no—
337C4⋊C4—1224no—
338C4⋊C4—1224no—
339C4⋊C4—1224no—
340C22⋊C4—24no—
341C22⋊C4—24no—
342C22⋊C4—1224no—
343C22⋊C4—1224no—
344C22⋊C4—1224no—
345C22⋊C4—1224no—
346C42—612no—
347C42—612no—
348C42—612no—
349C42—612no—
350C42—612no—
351C42—612no—
352C42—612no—
353C42—612no—
354C23—22no—
355C23—22no—
356C23—22no—
357C23—22no—
358C23—24no—
359C23—42no—
360C23—42no—
361C23—42no—
362C23—42no—
363C23—42no—
364C23—42no—
365C23—42no—
366C23—42no—
367C23—88no—
368C23C2×C22⋊#692311yescharacteristic
369C23C2×C22⋊#692311yescharacteristic
370C23C23×#692311yescharacteristic
371C2×C4—24no—
372C2×C4—22no—
373C2×C4—24no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—612no—
380C2×C4—612no—
381C2×C4—612no—
382C2×C4—612no—
383C2×C4—1224no—
384C2×C4—1224no—
385C2×C4—1222no—
386C2×C4—1222no—
387C2×C4—2442no—
388C2×C4—2441no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4—2442no—
392C2×C4—2441no—
393C2×C4—2442no—
394C2×C4—2442no—
395C2×C4—2442no—
396C2×C4—2442no—
397C2×C4—2442no—
398C2×C4—2442no—
399C2×C4C2×C22⋊#692312yes—
400C2×C4C2×C22⋊#692312yes—
401C8—2448no—
402C22—28no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—42no—
410C22—42no—
411C22—42no—
412C22—84no—
413C22—84no—
414C22—84no—
415C22#1684074112yes—
416C22#1684074912yes—
417C22C22×C22⋊#692311yescharacteristic
418C22#1684084012yes—
419C4—22no—
420C4—22no—
421C4—42no—
422C4—1222no—
423C4—1222no—
424C4—1222no—
425C4—1222no—
426C4—2442no—
427C4—2442no—
428C2—22no—
429C2—22no—
430C2—22no—
431C2—82no—
432C2#2146240511yescharacteristic
433C2C2×#1684074111yescharacteristic
434C2C2×#1684074911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C22⋊C4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC25×C61C2×C4
cosocleC22×Dic61C24
hypercenterC22×C22⋊C4#6923
hypocenterC61#17398
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #21462495C2semidirect
2. #21461100C2semidirect
3. #21461067C2semidirect
6. #16840783C22semidirect
8. #16840779C22semidirect
13. #16840607C22semidirect
245. C61#17398semidirect

Maximal subgroups

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

subgroupindex
#214624952
#214611002
#214610672
#214610642
C22×#145197702
#1739861