Finite Group Databasebeta

← #30597299

Subgroups — #30597299

Order 15616.

562 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462495C211yesmaximal, characteristic
2#21462495C211yesmaximal, characteristic
3#21460722C214yesmaximal
4#21448214C211yesmaximal, characteristic
5#16840783—21no—
6#16840783C412yescomplemented
7#16840782—21no—
8#16840782C412yescomplemented
9#16840779—21no—
10#16840779C412yescomplemented
11#16840778—21no—
12#16840778C412yescomplemented
13#16840765—21no—
14#16840765—21no—
15#16840732C2212yes—
16#16840732C2212yes—
17C4×#11758217—21no—
18C4×#11758217—21no—
19C22×C4×Dic61C2211yescharacteristic
20#16839629—21no—
21#16839627—21no—
22#16839623C2212yes—
23#16839622C411yescharacteristic
24C4⋊C4×Dic61—21no—
25C22⋊C4×Dic61C412yes—
26#16839607—21no—
27C61×#380C411yescharacteristic
28C2×#11758217—22no—
29C2×#11758217—22no—
30#14519844—22no—
31#14519844—22no—
32C4⋊#92420—22no—
33C4⋊#92420—22no—
34C22⋊#92420—22no—
35C22⋊#92420—22no—
36C22⋊#92420C2×C414yes—
37C22⋊#92420C2×C414yes—
38#14519832—22no—
39#14519832—22no—
40C4×#92420—22no—
41C4×#92420—22no—
42C23×Dic61C2×C411yescharacteristic
43C23×Dic61C2311yescharacteristic
44C2×C4⋊Dic61—21no—
45C2×C22⋊Dic61C2×C412yes—
46C2×C4×Dic61—22no—
47C2×C4×Dic61C2×C411yescharacteristic
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61C2×C411yescharacteristic
50C2×C4×Dic61C2×C411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54C2×C4×Dic61D411yescharacteristic
55C2×C4×Dic61D411yescharacteristic
56C2×C4×Dic61D411yescharacteristic
57C2×C4×Dic61Q811yescharacteristic
58C2×C4×Dic61Q811yescharacteristic
59#14519684—21no—
60#14519684—22no—
61#14519684—22no—
62#14519684—22no—
63C23×C4×C61C2×C411yescharacteristic
64C2×C4⋊C4×C61—21no—
65C2×C22⋊C4×C61C2×C412yes—
66#95×C61—21no—
67C24×C61C22×C411yescharacteristic
68C22×C4×C61—22no—
69C22×C4×C61—42no—
70C22×C4×C61C4211yescharacteristic
71C22×C4×C61C4211yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C4⋊C411yescharacteristic
75C22×C4×C61C4⋊C411yescharacteristic
76C22×Dic61—22no—
77C22×Dic61—42no—
78C22×Dic61—41no—
79C22×Dic61—41no—
80C22×Dic61C4211yescharacteristic
81C22×Dic61C4211yescharacteristic
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61C4⋊C411yescharacteristic
85C22×Dic61C4⋊C411yescharacteristic
86C22×Dic61C22×C411yescharacteristic
87C22×Dic61C22×C411yescharacteristic
88C22×Dic61C2×D411yescharacteristic
89C22×Dic61C2×D411yescharacteristic
90C22×Dic61C2×D411yescharacteristic
91C22×Dic61C2×Q811yescharacteristic
92#11758217—42no—
93#11758217—42no—
94#11758217—42no—
95#11758217—42no—
96C2×#92420—24no—
97C2×#92420—24no—
98C4⋊C4×C61—42no—
99C22⋊C4×C61—42no—
100C22⋊Dic61—42no—
101C4⋊Dic61—42no—
102C4×Dic61—44no—
103C4×Dic61C22⋊C411yescharacteristic
104C4×Dic61C22⋊C411yescharacteristic
105C4×Dic61C22⋊C411yescharacteristic
106C4×Dic61C22⋊C411yescharacteristic
107C4×Dic61C22⋊C411yescharacteristic
108C4×Dic61C22⋊C411yescharacteristic
109C4×Dic61C22⋊C411yescharacteristic
110C4×Dic61C22⋊C411yescharacteristic
111C4×Dic61C4⋊C411yescharacteristic
112C4×Dic61C4⋊C411yescharacteristic
113C4×Dic61C4⋊C411yescharacteristic
114C4×Dic61C4⋊C411yescharacteristic
115C4×Dic61C4⋊C411yescharacteristic
116C4×Dic61C4⋊C411yescharacteristic
117C4×Dic61C4⋊C411yescharacteristic
118C4×Dic61C4⋊C411yescharacteristic
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61C2×C4211yescharacteristic
124C23×C61C2×C22⋊C411yescharacteristic
125C23×C61C2×C4⋊C411yescharacteristic
126C2×C4×C61—22no—
127C2×C4×C61—22no—
128C2×C4×C61—22no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—42no—
133C2×C4×C61—42no—
134C2×C4×C61—42no—
135C2×C4×C61#9511yescharacteristic
136C2×C4×C61#9511yescharacteristic
137C2×C4×C61#9511yescharacteristic
138C2×C4×C61#9511yescharacteristic
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—22no—
144C2×Dic61—22no—
145C2×Dic61—22no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—42no—
154C2×Dic61—42no—
155C2×Dic61—42no—
156C2×Dic61#9511yescharacteristic
157C2×Dic61#9511yescharacteristic
158C2×Dic61#9511yescharacteristic
159C2×Dic61#9511yescharacteristic
160C2×Dic61C2×C22⋊C411yescharacteristic
161C2×Dic61C2×C22⋊C411yescharacteristic
162C2×Dic61C2×C4⋊C411yescharacteristic
163C2×Dic61C2×C4⋊C411yescharacteristic
164#92420—44no—
165#92420—44no—
166#8113—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—42no—
176C22×C61—42no—
177C22×C61C2×#9511yescharacteristic
178C22×C61#41011yescharacteristic
179C22×C61#41011yescharacteristic
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—82no—
184C4×C61#34412yes—
185Dic61—21no—
186Dic61—21no—
187Dic61—21no—
188Dic61—21no—
189Dic61—21no—
190Dic61—21no—
191Dic61—21no—
192Dic61—82no—
193Dic61#34412yes—
194#2920—611no—
195#2920—611no—
196#2283—611no—
197#1306—614no—
198C2×C61—21no—
199C2×C61—21no—
200C2×C61—41no—
201C2×C61—41no—
202C2×C61#174011yescharacteristic
203C2×C61C2×#34411yescharacteristic
204C2×C61C2×#34411yescharacteristic
205C22×C42—611no—
206#432—612no—
207#432—612no—
208#432—1221no—
209#432—1221no—
210#431—612no—
211#431—612no—
212#431—1221no—
213#431—1221no—
214#423—1221no—
215#423—1221no—
216#407—612no—
217#407—612no—
218C4×M16—1221no—
219C4×M16—1221no—
220#383—1221no—
221#382—1221no—
222#381—612no—
223#380—611no—
224#380#692311yescharacteristic
225C4×C4⋊C4—1221no—
226C4×C22⋊C4—612no—
227#376—1221no—
228C61#811311yescharacteristic, complemented, Sylow
229C23×C4—611no—
230C23×C4—611no—
231C23×C4C2×#692311yescharacteristic
232C2×M16—1222no—
233C2×M16—1222no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—1221no—
236C2×C22⋊C4—612no—
237C2×C22⋊C4C2×#692312yes—
238C2×C42—611no—
239C2×C42—611no—
240C2×C42—611no—
241C2×C42—611no—
242C2×C42—611no—
243C2×C42—611no—
244C2×C42—611no—
245C2×C42—611no—
246C2×C42—611no—
247C2×C42—611no—
248C2×C42—611no—
249C2×C42—611no—
250C2×C42—1222no—
251C4⋊C8—1222no—
252C4⋊C8—1222no—
253C4⋊C8—1222no—
254C4⋊C8—1222no—
255C22⋊C8—614no—
256C22⋊C8—614no—
257C22⋊C8—1222no—
258C22⋊C8—1222no—
259#97—1222no—
260#97—1222no—
261C4×C8—1222no—
262C4×C8—1222no—
263#95—21no—
264#95—1222no—
265#95—1222no—
266#95—1222no—
267#95—1221no—
268C24C22×#692311yescharacteristic
269C22×C4—22no—
270C22×C4—42no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—1222no—
284C22×C4—2442no—
285C22×C4—2441no—
286C22×C4—2441no—
287C22×C4C4×#692311yescharacteristic
288C22×C4C4×#692311yescharacteristic
289C22×C4C4⋊#692311yescharacteristic
290C22×C4C4⋊#692311yescharacteristic
291C22×C4C22⋊#692311yescharacteristic
292C22×C4C22⋊#692311yescharacteristic
293M16—2442no—
294M16—2442no—
295M16—2442no—
296M16—2442no—
297C2×C8—1224no—
298C2×C8—1224no—
299C4⋊C4—42no—
300C4⋊C4—2442no—
301C22⋊C4—42no—
302C22⋊C4—2442no—
303C42—611no—
304C42—611no—
305C42—611no—
306C42—611no—
307C42—611no—
308C42—611no—
309C42—611no—
310C42—611no—
311C42—611no—
312C42—611no—
313C42—611no—
314C42—611no—
315C42—611no—
316C42—611no—
317C42—611no—
318C42—611no—
319C42—2444no—
320C23—21no—
321C23—21no—
322C23—41no—
323C23—41no—
324C23C2×C4×#692311yescharacteristic
325C23C2×C22⋊#692311yescharacteristic
326C23C2×C4⋊#692311yescharacteristic
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—611no—
337C2×C4—611no—
338C2×C4—611no—
339C2×C4—611no—
340C2×C4—611no—
341C2×C4—611no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—1222no—
345C2×C4—1222no—
346C2×C4—1222no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2442no—
359C2×C4—2442no—
360C2×C4—2442no—
361C2×C4(C2×#6923)⋊C411yescharacteristic
362C2×C4(C2×#6923)⋊C411yescharacteristic
363C2×C4(C2×#6923)⋊C411yescharacteristic
364C2×C4(C2×#6923)⋊C411yescharacteristic
365C8—2444no—
366C8—2444no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—42no—
376C22—42no—
377C22C2×(C2×#6923)⋊C411yescharacteristic
378C22#1684074211yescharacteristic
379C22#1684074311yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—82no—
384C4—612no—
385C4—1221no—
386C4—1221no—
387C4—1221no—
388C4—1221no—
389C4—1221no—
390C4—1221no—
391C4—1221no—
392C4—4882no—
393C4#1684064312yes—
394C2—21no—
395C2—21no—
396C2—41no—
397C2—41no—
398C2#2146151911yescharacteristic
399C2C2×#1684064311yescharacteristic
400C2#2146152711yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC61×#380C4
socleC22×C61C2×#95
prime radicalC24×C61C22×C4
cosocleC23×Dic61C23
hypercenter#380#6923
hypocenterC61#8113
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
6. #16840783C4semidirect
8. #16840782C4semidirect
10. #16840779C4semidirect
12. #16840778C4semidirect
228. C61#8113semidirect

Maximal subgroups

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

subgroupindex
#214624952
#214607222
#214482142
#811361