Finite Group Databasebeta

← #29573849

Subgroups — #29573849

Order 15616.

500 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839814C211yesmaximal, characteristic
2#21445796C211yesmaximal, characteristic
3C4×#14519689C211yesmaximal, characteristic
4C2×#16839512C211yesmaximal, characteristic, complemented
5#21443654C211yesmaximal, characteristic, complemented
6#21443653C211yesmaximal, characteristic, complemented
7C2×C61×#335C211yesmaximal, characteristic, complemented
8C2×C42×D61C2211yescharacteristic
9#16839814—22no—
10#16839814—22no—
11C2×C4⋊#92418C2211yescharacteristic
12C2×C4⋊#92418C2211yescharacteristic
13C2×#14519689—21no—
14C2×#14519689—21no—
15C2×#14519689C411yescharacteristic
16C2×#14519689C411yescharacteristic
17C2×C4×#92418C2211yescharacteristic
18C2×C8×Dic61—21no—
19#16839516—21no—
20#16839516C411yescharacteristic
21#16839516C411yescharacteristic
22#16839512—22no—
23C2×C4⋊C8×C61C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×C4×C8×C61C2211yescharacteristic
26C61×#335—22no—
27C22×C4×D61C2×C411yescharacteristic
28C22×C4×D61D411yescharacteristic
29C22×C4×D61Q811yescharacteristic
30C22×#92418—21no—
31C22×#92418—21no—
32C22×#92418C2×C411yescharacteristic
33C22×#92418C2×C411yescharacteristic
34C2×C4×Dic61C2×C411yescharacteristic
35C2×C4×Dic61D411yescharacteristic
36C2×C4×Dic61Q811yescharacteristic
37C42×D61—21no—
38C42×D61—21no—
39C42×D61—21no—
40C42×D61—21no—
41C4⋊#92418—21no—
42C4⋊#92418—21no—
43C4⋊#92418—21no—
44C4⋊#92418D412yes—
45#14519689—24no—
46#14519689—22no—
47#14519689—42no—
48#14519689C814yescomplemented
49C4×#92418—21no—
50C4×#92418—21no—
51C8×Dic61—24no—
52C22×C8×C61—21no—
53C22×C8×C61—21no—
54C22×C8×C61C2×C411yescharacteristic
55C22×C8×C61C2×C411yescharacteristic
56C2×C42×C61C2311yescharacteristic
57C4⋊C8×C61—21no—
58C4⋊C8×C61—21no—
59C4⋊C8×C61—21no—
60C4⋊C8×C61D412yes—
61C4×C8×C61—21no—
62C4×C8×C61—21no—
63C23×D61C4⋊C411yescharacteristic
64C22×C4×C61C22×C411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61C2×Q811yescharacteristic
67C22×Dic61C4⋊C411yescharacteristic
68C22×Dic61C4⋊C411yescharacteristic
69C22×Dic61C4⋊C411yescharacteristic
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—22no—
83C2×C4×D61—41no—
84C2×C4×D61C2×C812yes—
85C2×C4×D61M1612yes—
86C2×C8×C61—21no—
87C2×C8×C61—21no—
88C2×C8×C61—21no—
89C2×C8×C61—22no—
90C2×C8×C61—21no—
91C2×C8×C61—21no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61C2×C812yes—
98C42×C61C2×D411yescharacteristic
99C42×C61C2×D411yescharacteristic
100C42×C61#4111yescharacteristic
101C42×C61#4111yescharacteristic
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C2×#92418—21no—
109C2×#92418—21no—
110C2×#92418—21no—
111C2×#92418—22no—
112C2×#92418—21no—
113C2×#92418—21no—
114C2×#92418—41no—
115C2×#92418—41no—
116C2×#92418—41no—
117C2×#92418—41no—
118C2×#92418—41no—
119C2×#92418C2×C812yes—
120C23×C61C2×C4⋊C411yescharacteristic
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61C4⋊C812yes—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61C4×D411yescharacteristic
131C2×C4×C61C4×D411yescharacteristic
132C2×C4×C61#12011yescharacteristic
133C2×C4×C61C22⋊Q811yescharacteristic
134C2×C4×C61C22⋊Q811yescharacteristic
135C2×C4×C61#12311yescharacteristic
136C2×C4×C61C22×C811yescharacteristic
137C2×C4×C61C2×M1611yescharacteristic
138C2×C4×C61#13111yescharacteristic
139C2×C4×C61#13111yescharacteristic
140C2×C4×C61#13511yescharacteristic
141C2×C4×C61#13511yescharacteristic
142C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C61#13711yescharacteristic
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61C4⋊C812yes—
152C2×Dic61#10812yes—
153C4×D61—22no—
154C4×D61—22no—
155C4×D61—22no—
156C4×D61—22no—
157C4×D61—42no—
158C4×D61—42no—
159C4×D61—41no—
160C4×D61—41no—
161C4×D61—41no—
162C4×D61—41no—
163C8×C61—22no—
164C8×C61—41no—
165C8×C61—42no—
166C8×C61—81no—
167#92418—22no—
168#92418—41no—
169#92418—42no—
170#92418—81no—
171#8831—611nomaximal, Sylow
172C22×C61#38511yescharacteristic
173C22×C61C2×C4⋊C811yescharacteristic
174C22×C61#42411yescharacteristic
175C22×C61#42711yescharacteristic
176C22×C61#42811yescharacteristic
177C22×C61C2×#10811yescharacteristic
178C22×C61#43011yescharacteristic
179C2×D61—22no—
180C2×D61—22no—
181C2×D61—22no—
182C2×D61—41no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—41no—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61C8×D411yescharacteristic
189C4×C61C8×D411yescharacteristic
190C4×C61#43511yescharacteristic
191C4×C61#43511yescharacteristic
192C4×C61#44911yescharacteristic
193C4×C61#45211yescharacteristic
194C4×C61#48211yescharacteristic
195C4×C61#48511yescharacteristic
196Dic61—22no—
197Dic61—22no—
198Dic61—41no—
199C2×#431—611no—
200#1797—611no—
201C4×C22⋊C8—611no—
202C2×#335D6111yescharacteristic, complemented
203C2×#334—611no—
204#1277—611no—
205#1277—611no—
206C2×C61#156411yescharacteristic
207C2×C61#156511yescharacteristic
208C2×C61#157211yescharacteristic
209C2×C61#157411yescharacteristic
210C2×C61#185011yescharacteristic
211C2×C61#185411yescharacteristic
212C2×C61#185511yescharacteristic
213D61—42no—
214C22×C42—611no—
215#431—1222no—
216#431—1222no—
217C2×C4⋊C8—611no—
218C2×C4⋊C8—611no—
219C2×C4⋊C8C2×D6111yescharacteristic
220C2×C4⋊C8C2×D6111yescharacteristic
221C2×C22⋊C8—611no—
222C2×C22⋊C8—611no—
223C2×C22⋊C8—1221no—
224C2×C22⋊C8—1221no—
225C2×C4×C8—611no—
226C2×C4×C8—1221no—
227C2×C4×C8C2×D6111yescharacteristic
228#336—611no—
229#336—611no—
230#336—1221no—
231#335—22no—
232#334—1222no—
233C61#883111yescharacteristic, complemented, Sylow
234C23×C4—611no—
235C23×C4—611no—
236C23×C4—611no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—611no—
240C22×C8—611no—
241C22×C8—1221no—
242C22×C8—1221no—
243C22×C8C4×D6111yescharacteristic
244C22×C8C4×D6111yescharacteristic
245C2×C42—611no—
246C2×C42—611no—
247C2×C42—611no—
248C2×C42—1221no—
249C2×C42—1221no—
250C2×C42—1221no—
251C2×C42—1221no—
252C2×C42C22×D6111yescharacteristic
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—612no—
257C4⋊C8—1221no—
258C4⋊C8—1221no—
259C4⋊C8—1221no—
260C4⋊C8C22⋊D6112yes—
261C22⋊C8—614no—
262C22⋊C8—1222no—
263C22⋊C8—1224no—
264C22⋊C8—2442no—
265C4×C8—21no—
266C4×C8—21no—
267C4×C8—1224no—
268C4×C8—1221no—
269C4×C8—1221no—
270C24—611no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—612no—
274C22×C4—612no—
275C22×C4—611no—
276C22×C4—1222no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—2441no—
290C22×C4C2×C4×D6111yescharacteristic
291C22×C4D4×D6111yescharacteristic
292C22×C4Q8×D6111yescharacteristic
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—22no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—612no—
305C2×C8—1221no—
306C2×C8—1221no—
307C2×C8—1221no—
308C2×C8—1222no—
309C2×C8—1221no—
310C2×C8—1221no—
311C2×C8—2441no—
312C2×C8—2441no—
313C2×C8—2441no—
314C2×C8—2441no—
315C2×C8—2441no—
316C2×C8C8×D6112yes—
317C42—1221no—
318C42—1221no—
319C42—1221no—
320C42—1221no—
321C42—1221no—
322C42—1221no—
323C42#1175822211yescharacteristic
324C42D4×D6111yescharacteristic
325C42#1175822611yescharacteristic
326C42C2×C22⋊D6111yescharacteristic
327C23—612no—
328C23—1221no—
329C23—1221no—
330C23—1221no—
331C23—1221no—
332C23—1221no—
333C23—1221no—
334C23C4⋊C4×D6111yescharacteristic
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—612no—
338C2×C4—612no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1222no—
344C2×C4—1222no—
345C2×C4—1222no—
346C2×C4—1222no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—2442no—
351C2×C4—2442no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4C4×C22⋊D6111yescharacteristic
357C2×C4#1451973911yescharacteristic
358C2×C4#1451974511yescharacteristic
359C2×C4#1451975311yescharacteristic
360C2×C4#1451975511yescharacteristic
361C2×C4#1451976211yescharacteristic
362C2×C4C2×C8×D6111yescharacteristic
363C2×C4M16×D6111yescharacteristic
364C2×C4#1451978311yescharacteristic
365C2×C4#1451978511yescharacteristic
366C2×C4#1451979611yescharacteristic
367C2×C4#1451980011yescharacteristic
368C2×C4#1451980111yescharacteristic
369C2×C4#1451980911yescharacteristic
370C8—22no—
371C8—41no—
372C8—42no—
373C8—81no—
374C8—1222no—
375C8—4881no—
376C8—2441no—
377C8—2442no—
378C22—1222no—
379C22—1222no—
380C22—1222no—
381C22—2441no—
382C22—2441no—
383C22—2441no—
384C22—2441no—
385C22#1683963311yescharacteristic
386C22C4⋊C8×D6111yescharacteristic
387C22#1683978711yescharacteristic
388C22#1683979911yescharacteristic
389C22#1683980311yescharacteristic
390C22#108×D6111yescharacteristic
391C22#1683980911yescharacteristic
392C4—21no—
393C4—21no—
394C4—1222no—
395C4—1222no—
396C4—2441no—
397C4C8×C22⋊D6111yescharacteristic
398C4#1683982711yescharacteristic
399C4#1683983111yescharacteristic
400C4#1683983211yescharacteristic
401C4#1683990411yescharacteristic
402C4#1683992311yescharacteristic
403C4#1684008911yescharacteristic
404C4#1684010511yescharacteristic
405C2—2442no—
406C2#2144456611yescharacteristic
407C2#2144457011yescharacteristic
408C2#2144459811yescharacteristic
409C2#2144460911yescharacteristic
410C2#2144599511yescharacteristic
411C2#2144601511yescharacteristic
412C2#2144602211yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC2×C61×#335C2
socleC23×C61C2×C4⋊C4
prime radicalC23×D61C4⋊C4
cosocleC2×C42×C61C23
hypercenterC2×#335D61
hypocenterC61#8831
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
4. C2×#16839512C2semidirect
5. #21443654C2semidirect
6. #21443653C2semidirect
7. C2×C61×#335C2semidirect
48. #14519689C8semidirect
202. C2×#335D61semidirect
233. C61#8831semidirect

Maximal subgroups

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

subgroupindex
C2×#168398142
#214457962
C4×#145196892
C2×#168395122
#214436542
#214436532
C2×C61×#3352
#883161