Finite Group Databasebeta

← #29574552

Subgroups — #29574552

Order 15616.

604 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839819C211yesmaximal, characteristic
2C4×#14519756C211yesmaximal, characteristic
3C2×#16839494C212yesmaximal, complemented
4#21443659C212yesmaximal, complemented
5C4×C22⋊C8×C61C211yesmaximal, characteristic
6C2×#14519756C411yescharacteristic
7C2×C4×Dic122C2211yescharacteristic
8#16839819—24no—
9C2×C4⋊#92418C2212yes—
10C2×C22⋊#92418—21no—
11C2×#14519688—21no—
12#16839668C411yescharacteristic
13#16839660C411yescharacteristic
14#16839646—21no—
15#16839635—21no—
16#16839622C411yescharacteristic
17C4×#11758196—21no—
18C4×C4⋊Dic61C2211yescharacteristic
19C4×C22⋊Dic61—21no—
20#16839494—24no—
21C22×C42×C61C2211yescharacteristic
22C2×C22⋊C8×C61—21no—
23C2×C4×C8×C61C2212yes—
24C61×#336—21no—
25C22×Dic122C2×C411yescharacteristic
26C22×#92418—22no—
27#14519756—22no—
28#14519756—22no—
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⋊#92418D414yes—
43C22⋊#92418—24no—
44#14519688—24no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50C23×C4×C61C2×C411yescharacteristic
51C23×C4×C61D411yescharacteristic
52C23×C4×C61D411yescharacteristic
53C22×C8×C61—22no—
54C2×C42×C61—22no—
55C2×C42×C61—22no—
56C2×C42×C61C2×C411yescharacteristic
57C2×C42×C61D411yescharacteristic
58C2×C42×C61D411yescharacteristic
59C2×C42×C61C2311yescharacteristic
60C22⋊C8×C61—24no—
61C4×C8×C61—22no—
62C4×C8×C61—22no—
63C24×C61C22⋊C411yescharacteristic
64C22×C4×C61—22no—
65C22×C4×C61—22no—
66C22×C4×C61—21no—
67C22×C4×C61—22no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—22no—
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×C61C22×C411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C2×Dic122—22no—
86C2×Dic122—22no—
87C2×Dic122—21no—
88C2×Dic122M1612yes—
89C2×C8×C61—24no—
90C2×C8×C61—42no—
91C2×C8×C61—42no—
92C42×C61—22no—
93C42×C61—21no—
94C42×C61—22no—
95C42×C61—21no—
96C42×C61C2×D412yes—
97C42×C61#4112yes—
98C22⋊Dic61—24no—
99C22⋊Dic61—42no—
100C4⋊Dic61—21no—
101C4⋊Dic61—22no—
102C4⋊Dic61—22no—
103C4⋊Dic61M1612yes—
104#11758196—24no—
105#11758196—42no—
106#11758196—42no—
107C4×Dic61—41no—
108C4×Dic61—41no—
109C4×Dic61—42no—
110C2×#92418—24no—
111C2×#92418—42no—
112C2×#92418—42no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61#10412yes—
120C23×C61C2×C22⋊C411yescharacteristic
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—44no—
133C2×C4×C61—42no—
134C2×C4×C61—42no—
135C2×C4×C61—42no—
136C2×C4×C61—42no—
137C2×C4×C61C4×D412yes—
138C2×C4×C61#12011yescharacteristic
139C2×C4×C61#12112yes—
140C2×C4×C61#12311yescharacteristic
141C2×C4×C61C2×M1611yescharacteristic
142C2×C4×C61C2×M1611yescharacteristic
143C2×C4×C61#13112yes—
144C2×C4×C61#13512yes—
145C2×C4×C61#13712yes—
146C2×Dic61—22no—
147C2×Dic61—22no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158Dic122—24no—
159Dic122—42no—
160C8×C61—44no—
161#92418—44no—
162#8941—611nomaximal, Sylow
163C22×C61—22no—
164C22×C61—22no—
165C22×C61—22no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61#38611yescharacteristic
171C22×C61#40711yescharacteristic
172C22×C61#40811yescharacteristic
173C22×C61#41611yescharacteristic
174C22×C61#41911yescharacteristic
175C22×C61C2×#10411yescharacteristic
176C22×C61#42111yescharacteristic
177C4×C61—22no—
178C4×C61—41no—
179C4×C61—41no—
180C4×C61—41no—
181C4×C61#43512yes—
182C4×C61#43612yes—
183C4×C61#45212yes—
184C4×C61#48512yes—
185Dic61—42no—
186Dic61—42no—
187Dic61—81no—
188Dic61—81no—
189C2×#432—611no—
190C4×C22⋊Q8—611no—
191C4×C22⋊C8D6111yescharacteristic
192C2×Q8⋊C8—612no—
193#1279—612no—
194C2×C61—42no—
195C2×C61#148811yescharacteristic
196C2×C61#149111yescharacteristic
197C2×C61#149411yescharacteristic
198C2×C61#149711yescharacteristic
199C2×C61#187011yescharacteristic
200C2×C61#187111yescharacteristic
201C2×C61#187311yescharacteristic
202C2×C22⋊Q8—611no—
203C2×C4×Q8—611no—
204C22×C42C2×D6111yescharacteristic
205#432—1224no—
206C2×C4⋊C8—612no—
207C2×C22⋊C8—21no—
208C2×C22⋊C8—1221no—
209C2×#97—1221no—
210C2×C4×C8C2×D6112yes—
211#391—611no—
212#389—611no—
213#387—1221no—
214#385—1221no—
215#380—611no—
216C4×C4⋊C4—611no—
217C4×C4⋊C4—1221no—
218C4×C22⋊C4—1221no—
219#336—21no—
220Q8⋊C8—1224no—
221C61#894111yescharacteristic, complemented, Sylow
222C22×Q8—611no—
223C23×C4C4×D6111yescharacteristic
224C23×C4D24411yescharacteristic
225C23×C4C22⋊D6111yescharacteristic
226C22×C8—22no—
227C22×C8—1222no—
228C22⋊Q8—1222no—
229C22⋊Q8—1222no—
230C4×Q8—1222no—
231C4×Q8—1222no—
232C2×C4⋊C4—611no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—1221no—
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—1221no—
240C2×C42—22no—
241C2×C42—22no—
242C2×C42—1221no—
243C2×C42—1221no—
244C2×C42C4×D6111yescharacteristic
245C2×C42D24411yescharacteristic
246C2×C42C22⋊D6111yescharacteristic
247C2×C42C22×D6111yescharacteristic
248C4⋊C8—614no—
249C4⋊C8—1222no—
250C22⋊C8—24no—
251C22⋊C8—1224no—
252#97—1224no—
253C4×C8—22no—
254C4×C8—22no—
255#95—1221no—
256#95—1221no—
257#95—1221no—
258#95—1221no—
259#95—1221no—
260C24#1175819811yescharacteristic
261C2×Q8—612no—
262C2×Q8—1221no—
263C2×Q8—1222no—
264C2×Q8—1222no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—41no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4#1175819811yescharacteristic
281C22×C4#1175819811yescharacteristic
282C22×C4#1175819811yescharacteristic
283C22×C4C2×C4×D6111yescharacteristic
284C22×C4C2×D24411yescharacteristic
285C22×C4C2×C22⋊D6111yescharacteristic
286C2×C8—24no—
287C2×C8—42no—
288C2×C8—42no—
289C2×C8—1224no—
290C2×C8—2442no—
291C2×C8—2442no—
292C4⋊C4—612no—
293C4⋊C4—1224no—
294C4⋊C4—1221no—
295C4⋊C4—1222no—
296C4⋊C4—1222no—
297C4⋊C4—2442no—
298C4⋊C4—2442no—
299C22⋊C4—1224no—
300C22⋊C4—2442no—
301C42—22no—
302C42—21no—
303C42—22no—
304C42—21no—
305C42—2441no—
306C42—2441no—
307C42—2442no—
308C42D4×D6112yes—
309C42#1175822412yes—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23#1451970512yes—
317C23C2×#1175819811yescharacteristic
318Q8—1224no—
319Q8—2442no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—44no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—1222no—
337C2×C4—1222no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4#1451973712yes—
349C2×C4#1451974711yescharacteristic
350C2×C4#1451974912yes—
351C2×C4#1451976111yescharacteristic
352C2×C4M16×D6111yescharacteristic
353C2×C4M16×D6111yescharacteristic
354C2×C4#1451978312yes—
355C2×C4#1451979912yes—
356C2×C4#1451981012yes—
357C8—44no—
358C8—2444no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22#1683963911yescharacteristic
367C22#1683972511yescharacteristic
368C22#1683972811yescharacteristic
369C22#1683975911yescharacteristic
370C22#1683977211yescharacteristic
371C22C2×#1451970511yescharacteristic
372C22#1683978011yescharacteristic
373C4—22no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—4881no—
378C4—4881no—
379C4—2442no—
380C4—2442no—
381C4#1683983612yes—
382C4#1683983712yes—
383C4#1683992612yes—
384C4#1684010412yes—
385C2—42no—
386C2#2144425411yescharacteristic
387C2#2144426711yescharacteristic
388C2#2144428011yescharacteristic
389C2#2144429311yescharacteristic
390C2#2144611411yescharacteristic
391C2#2144611911yescharacteristic
392C2#2144612911yescharacteristic
subgroupG/H
centerC22×C4C2×D244
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC4×C22⋊C8×C61C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenterC4×C22⋊C8D61
hypocenterC61#8941
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. C2×#16839494C2semidirect
4. #21443659C2semidirect
221. C61#8941semidirect

Maximal subgroups

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

subgroupindex
C2×#168398192
C4×#145197562
C2×#168394942
#214436592
C4×C22⋊C8×C612
#894161