Finite Group Databasebeta

← #29574534

Subgroups — #29574534

Order 15616.

684 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519756C211yesmaximal, characteristic
2C4×C22⋊#92418C211yesmaximal, characteristic
3C2×#16839492C212yesmaximal, complemented
4#21443658C212yesmaximal, complemented
5C22×C4⋊C8×C61C211yesmaximal, characteristic
6C2×#14519756C411yescharacteristic
7C2×C4×Dic122C2211yescharacteristic
8C2×C22⋊#92418—21no—
9C2×C4×#92418C2212yes—
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#16839492—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—
41C22⋊#92418—24no—
42C4×#92418—22no—
43C4×#92418—22no—
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—22no—
54C22×C8×C61—42no—
55C22×C8×C61—42no—
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—21no—
68C22×C4×C61—21no—
69C22×C4×C61—22no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—22no—
73C22×C4×C61—22no—
74C22×C4×C61—41no—
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22⋊C411yescharacteristic
77C22×C4×C61C22⋊C411yescharacteristic
78C22×C4×C61C2×C812yes—
79C22×C4×C61M1612yes—
80C22×C4×C61SD1612yes—
81C22×C4×C61Q1612yes—
82C22×C4×C61C22×C411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C2×Dic122—22no—
90C2×Dic122—22no—
91C2×Dic122—21no—
92C2×Dic122C2×C812yescomplemented
93C2×C8×C61—24no—
94C2×C8×C61—48no—
95C2×C8×C61—42no—
96C2×C8×C61—42no—
97C42×C61—22no—
98C42×C61—21no—
99C42×C61—22no—
100C42×C61—21no—
101C42×C61C2×D412yes—
102C42×C61#4112yes—
103C22⋊Dic61—24no—
104C22⋊Dic61—42no—
105C4⋊Dic61—21no—
106C4⋊Dic61—22no—
107C4⋊Dic61—22no—
108C4⋊Dic61C2×C812yescomplemented
109#11758196—24no—
110#11758196—42no—
111#11758196—42no—
112C4×Dic61—41no—
113C4×Dic61—41no—
114C4×Dic61—41no—
115C4×Dic61—41no—
116C2×#92418—24no—
117C2×#92418—42no—
118C2×#92418—42no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61C22⋊C812yes—
124C23×C61#10312yes—
125C23×C61#10412yes—
126C23×C61C2×C22⋊C411yescharacteristic
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—24no—
134C2×C4×C61—24no—
135C2×C4×C61—22no—
136C2×C4×C61—22no—
137C2×C4×C61—22no—
138C2×C4×C61—22no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—44no—
143C2×C4×C61C22⋊C812yes—
144C2×C4×C61#10312yes—
145C2×C4×C61C4×D412yes—
146C2×C4×C61#12011yescharacteristic
147C2×C4×C61#12112yes—
148C2×C4×C61#12311yescharacteristic
149C2×C4×C61C22×C811yescharacteristic
150C2×C4×C61C2×M1611yescharacteristic
151C2×C4×C61#13112yes—
152C2×C4×C61C2×SD1611yescharacteristic
153C2×C4×C61C2×Q1611yescharacteristic
154C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C61#13711yescharacteristic
156C2×Dic61—22no—
157C2×Dic61—22no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168Dic122—24no—
169Dic122—42no—
170C8×C61—44no—
171#92418—44no—
172#8937—611nomaximal, Sylow
173C22×C61—22no—
174C22×C61—22no—
175C22×C61—22no—
176C22×C61—22no—
177C22×C61—22no—
178C22×C61—22no—
179C22×C61Q8⋊C814yescomplemented
180C22×C61#38611yescharacteristic
181C22×C61C2×C22⋊C811yescharacteristic
182C22×C61#40811yescharacteristic
183C22×C61C2×#10311yescharacteristic
184C22×C61#41711yescharacteristic
185C22×C61C2×#10411yescharacteristic
186C22×C61#42111yescharacteristic
187C4×C61—22no—
188C4×C61—22no—
189C4×C61—22no—
190C4×C61—41no—
191C4×C61C8×D412yes—
192C4×C61#43512yes—
193C4×C61#45011yescharacteristic
194C4×C61#45111yescharacteristic
195C4×C61#48311yescharacteristic
196C4×C61#48411yescharacteristic
197Dic61—42no—
198Dic61—42no—
199Dic61—81no—
200Dic61—81no—
201C22×C4⋊C8D6111yescharacteristic
202C4×C22⋊Q8—611no—
203C4×C22⋊C8—611no—
204C2×Q8⋊C8—612no—
205#1279—612no—
206C2×C61—24no—
207C2×C61C2×Q8⋊C811yescharacteristic
208C2×C61#147711yescharacteristic
209C2×C61#148111yescharacteristic
210C2×C61#148311yescharacteristic
211C2×C61#186911yescharacteristic
212C2×C61#187111yescharacteristic
213C2×C61#187211yescharacteristic
214C23×C8—21no—
215C2×C22⋊Q8—611no—
216C2×C4×Q8—611no—
217C22×C42C2×D6111yescharacteristic
218C2×C4⋊C8—21no—
219C2×C4⋊C8—24no—
220C2×C4⋊C8C2×D6112yes—
221C2×C22⋊C8—1221no—
222C2×C4×C8—612no—
223#391—611no—
224#389—611no—
225#387—1221no—
226#385—1221no—
227#380—611no—
228C4×C4⋊C4—611no—
229C4×C4⋊C4—1221no—
230C4×C22⋊C4—1221no—
231#336—1221no—
232Q8⋊C8—1224no—
233C61#893711yescharacteristic, complemented, Sylow
234C22×Q8—611no—
235C23×C4C4×D6111yescharacteristic
236C23×C4D24411yescharacteristic
237C23×C4C22⋊D6111yescharacteristic
238C22×C8—24no—
239C22×C8—22no—
240C22×C8—42no—
241C22×C8—42no—
242C22×C8—1222no—
243C22⋊Q8—614no—
244C22⋊Q8—1222no—
245C4×Q8—1222no—
246C4×Q8—1222no—
247C2×C4⋊C4—611no—
248C2×C4⋊C4—611no—
249C2×C4⋊C4—611no—
250C2×C4⋊C4—1221no—
251C2×C4⋊C4—1221no—
252C2×C4⋊C4—1221no—
253C2×C22⋊C4—1221no—
254C2×C22⋊C4—1221no—
255C2×C42—22no—
256C2×C42—22no—
257C2×C42—1221no—
258C2×C42—1221no—
259C2×C42C4×D6111yescharacteristic
260C2×C42D24411yescharacteristic
261C2×C42C22⋊D6111yescharacteristic
262C2×C42C22×D6111yescharacteristic
263C4⋊C8—24no—
264C4⋊C8—22no—
265C4⋊C8C22⋊D6114yes—
266C22⋊C8—1224no—
267C4×C8—1222no—
268C4×C8—1222no—
269#95—1221no—
270#95—1221no—
271#95—1221no—
272#95—1221no—
273#95—1221no—
274C24#1175819811yescharacteristic
275C2×Q8—612no—
276C2×Q8—1221no—
277C2×Q8—1222no—
278C2×Q8—1222no—
279C22×C4—21no—
280C22×C4—22no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—22no—
284C22×C4—21no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—41no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4C8×D6112yes—
293C22×C4#1175818912yes—
294C22×C4#1175819811yescharacteristic
295C22×C4#1175819811yescharacteristic
296C22×C4#1175819811yescharacteristic
297C22×C4#1175820012yes—
298C22×C4#1175820212yes—
299C22×C4C2×C4×D6111yescharacteristic
300C22×C4C2×D24411yescharacteristic
301C22×C4C2×C22⋊D6111yescharacteristic
302C2×C8—24no—
303C2×C8—48no—
304C2×C8—42no—
305C2×C8—42no—
306C2×C8—1224no—
307C2×C8—2442no—
308C2×C8—2442no—
309C4⋊C4—612no—
310C4⋊C4—1224no—
311C4⋊C4—1221no—
312C4⋊C4—1222no—
313C4⋊C4—1222no—
314C4⋊C4—2442no—
315C4⋊C4—2442no—
316C22⋊C4—1224no—
317C22⋊C4—2442no—
318C42—22no—
319C42—21no—
320C42—22no—
321C42—21no—
322C42—2441no—
323C42—2441no—
324C42—2441no—
325C42—2441no—
326C42#1175822212yes—
327C42C2×C22⋊D6112yes—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23#1451968912yes—
333C23#1451970012yes—
334C23#1451970312yes—
335C23C2×#1175819811yescharacteristic
336Q8—1224no—
337Q8—2442no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—44no—
354C2×C4—1222no—
355C2×C4—1222no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4#1451968912yes—
367C2×C4#1451970012yes—
368C2×C4C4×C22⋊D6112yes—
369C2×C4#1451974611yescharacteristic
370C2×C4#1451975112yes—
371C2×C4#1451976011yescharacteristic
372C2×C4C2×C8×D6111yescharacteristic
373C2×C4C2×#1175818911yescharacteristic
374C2×C4#1451978312yes—
375C2×C4C2×#1175820011yescharacteristic
376C2×C4C2×#1175820211yescharacteristic
377C2×C4#1451980311yescharacteristic
378C2×C4#1451980811yescharacteristic
379C8—44no—
380C8—2444no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22#1683949214yescomplemented
388C22#1683964111yescharacteristic
389C22C2×#1451968911yescharacteristic
390C22#1683972811yescharacteristic
391C22C2×#1451970011yescharacteristic
392C22#1683976111yescharacteristic
393C22C2×#1451970311yescharacteristic
394C22#1683977811yescharacteristic
395C4—22no—
396C4—22no—
397C4—22no—
398C4—41no—
399C4—4881no—
400C4—4881no—
401C4—2442no—
402C4—2442no—
403C4C8×C22⋊D6112yes—
404C4#1683983312yes—
405C4#1683991311yescharacteristic
406C4#1683991811yescharacteristic
407C4#1684009211yescharacteristic
408C4#1684009711yescharacteristic
409C2—24no—
410C2C2×#1683949211yescharacteristic
411C2#2144420411yescharacteristic
412C2#2144422111yescharacteristic
413C2#2144423011yescharacteristic
414C2#2144611111yescharacteristic
415C2#2144612111yescharacteristic
416C2#2144612611yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D61
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#8937
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×#16839492C2semidirect
4. #21443658C2semidirect
28. #14519756C8semidirect
92. C2×Dic122C2×C8semidirect
108. C4⋊Dic61C2×C8semidirect
179. C22×C61Q8⋊C8semidirect
233. C61#8937semidirect
387. C22#16839492semidirect

Maximal subgroups

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

subgroupindex
C4×#145197562
C4×C22⋊#924182
C2×#168394922
#214436582
C22×C4⋊C8×C612
#893761