Finite Group Databasebeta

← #29575344

Subgroups — #29575344

Order 15616.

726 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519756C211yesmaximal, characteristic
2#21445799C211yesmaximal, characteristic
3C2×#16839494C212yesmaximal, complemented
4#21443659C212yesmaximal, complemented
5C22×C4×C8×C61C211yesmaximal, characteristic
6C2×#14519756C411yescharacteristic
7C2×C4×Dic122C2211yescharacteristic
8C2×C4⋊#92418C2212yes—
9C2×C22⋊#92418—21no—
10#16839668C411yescharacteristic
11#16839660C411yescharacteristic
12#16839646—21no—
13#16839635—21no—
14#16839622C411yescharacteristic
15C4×#11758196—21no—
16C4×C4⋊Dic61C2211yescharacteristic
17C4×C22⋊Dic61—21no—
18#16839517—21no—
19#16839494—24no—
20C23×C8×C61—21no—
21C22×C42×C61C2211yescharacteristic
22C2×C4×C8×C61—21no—
23C2×C4×C8×C61—24no—
24C2×C4×C8×C61C2212yes—
25C22×Dic122C2×C411yescharacteristic
26C22×#92418—22no—
27#14519756—22no—
28#14519756C814yescomplemented
29C4×Dic122—22no—
30C4×Dic122—22no—
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C4×Dic61—21no—
40C2×C4×Dic61—21no—
41C4⋊#92418—22no—
42C4⋊#92418—22no—
43C22⋊#92418—42no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49C23×C4×C61C2×C411yescharacteristic
50C23×C4×C61D411yescharacteristic
51C23×C4×C61D411yescharacteristic
52C22×C8×C61—24no—
53C22×C8×C61—24no—
54C22×C8×C61—24no—
55C22×C8×C61—22no—
56C2×C42×C61—22no—
57C2×C42×C61—22no—
58C2×C42×C61C2×C411yescharacteristic
59C2×C42×C61D411yescharacteristic
60C2×C42×C61D411yescharacteristic
61C2×C42×C61C2311yescharacteristic
62C4×C8×C61—24no—
63C4×C8×C61—22no—
64C4×C8×C61D414yes—
65C24×C61C22⋊C411yescharacteristic
66C22×C4×C61—22no—
67C22×C4×C61—22no—
68C22×C4×C61—22no—
69C22×C4×C61—21no—
70C22×C4×C61—22no—
71C22×C4×C61—21no—
72C22×C4×C61—22no—
73C22×C4×C61—22no—
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22⋊C411yescharacteristic
77C22×C4×C61C2×C812yes—
78C22×C4×C61M1612yes—
79C22×C4×C61SD1612yes—
80C22×C4×C61Q1612yes—
81C22×C4×C61C22×C411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C2×Dic122—22no—
89C2×Dic122—22no—
90C2×Dic122—21no—
91C2×Dic122C2×C812yescomplemented
92C2×C8×C61—216no—
93C2×C8×C61—24no—
94C2×C8×C61—24no—
95C2×C8×C61—24no—
96C42×C61—22no—
97C42×C61—21no—
98C42×C61—22no—
99C42×C61—21no—
100C42×C61C2×D412yes—
101C42×C61#4112yes—
102C22⋊Dic61—24no—
103C22⋊Dic61—42no—
104C4⋊Dic61—21no—
105C4⋊Dic61—22no—
106C4⋊Dic61—22no—
107C4⋊Dic61C2×C812yescomplemented
108#11758196—24no—
109#11758196—42no—
110#11758196—41no—
111#11758196—41no—
112C4×Dic61—42no—
113C4×Dic61—42no—
114C2×#92418—42no—
115C2×#92418—42no—
116C2×#92418—42no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61C22⋊C812yes—
122C23×C61#10312yes—
123C23×C61#10412yes—
124C23×C61C2×C22⋊C411yescharacteristic
125C2×C4×C61—24no—
126C2×C4×C61—24no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—24no—
136C2×C4×C61—24no—
137C2×C4×C61—24no—
138C2×C4×C61—24no—
139C2×C4×C61C22⋊C812yes—
140C2×C4×C61#10312yes—
141C2×C4×C61#10412yes—
142C2×C4×C61C4×D412yes—
143C2×C4×C61#12011yescharacteristic
144C2×C4×C61#12112yes—
145C2×C4×C61#12311yescharacteristic
146C2×C4×C61C22×C811yescharacteristic
147C2×C4×C61C2×M1611yescharacteristic
148C2×C4×C61#13112yes—
149C2×C4×C61C2×SD1611yescharacteristic
150C2×C4×C61C2×Q1611yescharacteristic
151C2×C4×C61#13512yes—
152C2×Dic61—22no—
153C2×Dic61—22no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164Dic122—24no—
165Dic122—42no—
166C8×C61—28no—
167#92418—82no—
168#9071—611nomaximal, Sylow
169C22×C61—22no—
170C22×C61—22no—
171C22×C61—22no—
172C22×C61—22no—
173C22×C61—22no—
174C22×C61—22no—
175C22×C61Q8⋊C814yescomplemented
176C22×C61#38611yescharacteristic
177C22×C61C2×C22⋊C811yescharacteristic
178C22×C61#40811yescharacteristic
179C22×C61C2×#10311yescharacteristic
180C22×C61#41611yescharacteristic
181C22×C61C2×#10411yescharacteristic
182C22×C61C2×#10411yescharacteristic
183C4×C61—22no—
184C4×C61—22no—
185C4×C61—21no—
186C4×C61—22no—
187C4×C61—21no—
188C4×C61C8×D412yes—
189C4×C61#43512yes—
190C4×C61#46512yes—
191C4×C61#46712yes—
192Dic61—42no—
193Dic61—42no—
194Dic61—81no—
195Dic61—81no—
196C22×C4×C8D6111yescharacteristic
197C4×C22⋊Q8—611no—
198#1797—611no—
199C2×Q8⋊C8—612no—
200#1279—612no—
201C2×C61—24no—
202C2×C61C2×Q8⋊C811yescharacteristic
203C2×C61#147611yescharacteristic
204C2×C61#149311yescharacteristic
205C2×C61#149411yescharacteristic
206C2×C61#186911yescharacteristic
207C2×C61#189211yescharacteristic
208C2×C61#189611yescharacteristic
209C23×C8—21no—
210C2×C22⋊Q8—611no—
211C2×C4×Q8—611no—
212C22×C42C2×D6111yescharacteristic
213C2×C4⋊C8—612no—
214C2×C22⋊C8—1221no—
215C2×C4×C8—21no—
216C2×C4×C8—24no—
217C2×C4×C8C2×D6112yes—
218#391—611no—
219#389—611no—
220#387—1221no—
221#385—1221no—
222#380—611no—
223C4×C4⋊C4—611no—
224C4×C4⋊C4—1221no—
225C4×C22⋊C4—1221no—
226#336—1221no—
227Q8⋊C8—1224no—
228C61#907111yescharacteristic, complemented, Sylow
229C22×Q8—611no—
230C23×C4C4×D6111yescharacteristic
231C23×C4D24411yescharacteristic
232C23×C4C22⋊D6111yescharacteristic
233C22×C8—24no—
234C22×C8—24no—
235C22×C8—24no—
236C22×C8—22no—
237C22×C8—1222no—
238C22⋊Q8—614no—
239C22⋊Q8—1222no—
240C4×Q8—1222no—
241C4×Q8—1222no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4—611no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4—1221no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1221no—
250C2×C42—22no—
251C2×C42—22no—
252C2×C42—1221no—
253C2×C42—1221no—
254C2×C42C4×D6111yescharacteristic
255C2×C42D24411yescharacteristic
256C2×C42C22⋊D6111yescharacteristic
257C2×C42C22×D6111yescharacteristic
258C4⋊C8—1222no—
259C4⋊C8—1222no—
260C22⋊C8—2442no—
261C4×C8—24no—
262C4×C8—22no—
263C4×C8C22⋊D6114yes—
264#95—1221no—
265#95—1221no—
266#95—1221no—
267#95—1221no—
268#95—1221no—
269C24#1175819811yescharacteristic
270C2×Q8—612no—
271C2×Q8—1221no—
272C2×Q8—1222no—
273C2×Q8—1222no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—21no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4C8×D6112yes—
287C22×C4#1175818912yes—
288C22×C4#1175819012yes—
289C22×C4Dic24412yes—
290C22×C4#1175819811yescharacteristic
291C22×C4#1175819811yescharacteristic
292C22×C4#1175819811yescharacteristic
293C22×C4C2×C4×D6111yescharacteristic
294C22×C4C2×D24411yescharacteristic
295C22×C4C2×C22⋊D6111yescharacteristic
296C2×C8—216no—
297C2×C8—24no—
298C2×C8—24no—
299C2×C8—24no—
300C2×C8—2442no—
301C2×C8—2442no—
302C2×C8—2442no—
303C4⋊C4—612no—
304C4⋊C4—1224no—
305C4⋊C4—1221no—
306C4⋊C4—1222no—
307C4⋊C4—1222no—
308C4⋊C4—2442no—
309C4⋊C4—2441no—
310C4⋊C4—2441no—
311C22⋊C4—1224no—
312C22⋊C4—2442no—
313C42—22no—
314C42—21no—
315C42—22no—
316C42—21no—
317C42—2442no—
318C42—2442no—
319C42#1175822212yes—
320C42C2×C22⋊D6112yes—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23#1451968912yes—
326C23#1451970212yes—
327C23#1451970512yes—
328C23C2×#1175819811yescharacteristic
329Q8—1224no—
330Q8—2442no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—1222no—
346C2×C4—1222no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4#1451968912yes—
358C2×C4#1451970212yes—
359C2×C4#1451970512yes—
360C2×C4C4×C22⋊D6112yes—
361C2×C4#1451974611yescharacteristic
362C2×C4#1451975112yes—
363C2×C4#1451976011yescharacteristic
364C2×C4C2×C8×D6111yescharacteristic
365C2×C4C2×#1175818911yescharacteristic
366C2×C4#1451978312yes—
367C2×C4C2×#1175819011yescharacteristic
368C2×C4C2×Dic24411yescharacteristic
369C2×C4#1451979912yes—
370C8—28no—
371C8—4882no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22#1683949414yescomplemented
379C22#1683964111yescharacteristic
380C22C2×#1451968911yescharacteristic
381C22#1683972811yescharacteristic
382C22C2×#1451970211yescharacteristic
383C22#1683975911yescharacteristic
384C22C2×#1451970511yescharacteristic
385C22C2×#1451970511yescharacteristic
386C4—22no—
387C4—21no—
388C4—22no—
389C4—21no—
390C4—22no—
391C4—4881no—
392C4—4881no—
393C4—2442no—
394C4—2442no—
395C4C8×C22⋊D6112yes—
396C4#1683983312yes—
397C4#1683999112yes—
398C4#1684000312yes—
399C2—24no—
400C2C2×#1683949411yescharacteristic
401C2#2144420211yescharacteristic
402C2#2144427511yescharacteristic
403C2#2144428011yescharacteristic
404C2#2144611111yescharacteristic
405C2#2144624211yescharacteristic
406C2#2144626211yescharacteristic
subgroupG/H
centerC22×C4C2×D244
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC22×C4×C8×C61C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenterC22×C4×C8D61
hypocenterC61#9071
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4×C8

Complements

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

NH ≅ G/Ntype
3. C2×#16839494C2semidirect
4. #21443659C2semidirect
28. #14519756C8semidirect
91. C2×Dic122C2×C8semidirect
107. C4⋊Dic61C2×C8semidirect
175. C22×C61Q8⋊C8semidirect
228. C61#9071semidirect
378. C22#16839494semidirect

Maximal subgroups

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

subgroupindex
C4×#145197562
#214457992
C2×#168394942
#214436592
C22×C4×C8×C612
#907161