Finite Group Databasebeta

← #29571434

Subgroups — #29571434

Order 15616.

930 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840239C211yesmaximal, characteristic
2#21444215C212yesmaximal, complemented
3#21444213C212yesmaximal, complemented
4#21444133C211yesmaximal, characteristic
5C61×#1458C211yesmaximal, characteristic
6C23×Dic122C411yescharacteristic
7#16840239—24no—
8#16840239—24no—
9C2×C4×Dic122C411yescharacteristic
10C2×C4×Dic122C411yescharacteristic
11C2×C4×Dic122C2211yescharacteristic
12C2×C4×Dic122C2211yescharacteristic
13C2×#14519742—21no—
14C2×#14519742—21no—
15C2×#14519736C411yescharacteristic
16C2×#14519733—21no—
17C2×#14519733—21no—
18#16839815C2212yes—
19#16839494—24no—
20#16839492—24no—
21#16839488—21no—
22#16839486—21no—
23C2×#117×C61C2211yescharacteristic
24C61×#431C2212yes—
25C61×#324—21no—
26C61×#323—21no—
27C22×Dic122—21no—
28C22×Dic122—22no—
29C22×Dic122—22no—
30C22×Dic122—22no—
31C22×Dic122—22no—
32C22×Dic122—22no—
33C22×Dic122C814yescomplemented
34C22×Dic122C2×C411yescharacteristic
35C22×Dic122C2×C411yescharacteristic
36C23×Dic61—21no—
37C4×Dic122—22no—
38C4×Dic122—22no—
39C4×Dic122—22no—
40C4×Dic122—22no—
41C4×Dic122—22no—
42C4×Dic122—22no—
43C4×Dic122D414yes—
44C4×Dic122D414yes—
45#14519742—28no—
46#14519742—28no—
47#14519736—22no—
48#14519736—22no—
49#14519733—28no—
50#14519733—28no—
51C2×C4⋊Dic61C2×C411yescharacteristic
52C2×C4⋊Dic61C2×C411yescharacteristic
53C2×#11758196—21no—
54C2×#11758196—21no—
55C2×#11758196—21no—
56C2×#11758196—21no—
57C2×C22⋊Dic61—21no—
58C2×C4×Dic61—21no—
59C2×C4×Dic61—21no—
60C2×C4×Dic61—21no—
61C2×C4×Dic61—21no—
62C2×C4×Dic61—21no—
63C4⋊#92418—22no—
64C22⋊#92418—22no—
65C4×#92418—22no—
66C23×C4×C61C2×C411yescharacteristic
67#117×C61—22no—
68#117×C61—22no—
69C2×C4⋊C4×C61D411yescharacteristic
70C2×C4⋊C4×C61D411yescharacteristic
71C2×C22⋊C4×C61D411yescharacteristic
72C2×C22⋊C4×C61D411yescharacteristic
73C2×C42×C61C2×C411yescharacteristic
74C2×C42×C61C2311yescharacteristic
75C4⋊C8×C61—22no—
76C22⋊C8×C61—22no—
77C4×C8×C61—22no—
78C24×C61C22⋊C411yescharacteristic
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61C22⋊C411yescharacteristic
84C22×C4×C61C22⋊C411yescharacteristic
85C22×C4×C61C22⋊C411yescharacteristic
86C22×C4×C61C2×C812yes—
87C22×C4×C61M1612yes—
88C22×C4×C61C22×C411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×Dic61—24no—
92C22×Dic61—24no—
93C22×Dic61—24no—
94C22×Dic61—21no—
95C22×Dic61—21no—
96C22×Dic61—21no—
97C22×Dic61—21no—
98C2×Dic122—24no—
99C2×Dic122—28no—
100C2×Dic122—28no—
101C2×Dic122—24no—
102C2×Dic122—24no—
103C2×Dic122—21no—
104C2×Dic122—21no—
105C2×Dic122—21no—
106C2×Dic122—21no—
107C2×Dic122—21no—
108C2×Dic122—21no—
109C2×Dic122—28no—
110C2×Dic122—28no—
111C2×Dic122C22⋊C412yes—
112C2×Dic122C22⋊C412yes—
113C2×Dic122C2×C812yes—
114C2×Dic122C2×C812yes—
115C2×Dic122M1612yes—
116C2×Dic122M1612yes—
117C2×C8×C61—42no—
118C4⋊C4×C61—22no—
119C4⋊C4×C61—22no—
120C22⋊C4×C61—22no—
121C22⋊C4×C61—22no—
122C42×C61—21no—
123C42×C61—21no—
124C42×C61C2×D412yes—
125C42×C61C2×D412yes—
126C22⋊Dic61—24no—
127C4⋊Dic61—21no—
128C4⋊Dic61—21no—
129C4⋊Dic61C22⋊C412yes—
130C4⋊Dic61C22⋊C412yes—
131#11758196—24no—
132#11758196—24no—
133#11758196—24no—
134#11758196—24no—
135C4×Dic61—24no—
136C4×Dic61—24no—
137C4×Dic61—24no—
138C4×Dic61—24no—
139C4×Dic61—24no—
140C2×#92418—42no—
141C23×C61—21no—
142C23×C61—21no—
143C23×C61—41no—
144C23×C61—41no—
145C23×C61C22⋊C812yes—
146C23×C61C2×C22⋊C411yescharacteristic
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—22no—
150C2×C4×C61—22no—
151C2×C4×C61—22no—
152C2×C4×C61—22no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61C22⋊C812yes—
160C2×C4×C61C2×C22⋊C411yescharacteristic
161C2×C4×C61C2×C22⋊C411yescharacteristic
162C2×C4×C61#12012yes—
163C2×C4×C61#12012yes—
164C2×C4×C61C22×C811yescharacteristic
165C2×C4×C61C2×M1611yescharacteristic
166C2×C4×C61C2×M1611yescharacteristic
167C2×C4×C61C2×M1611yescharacteristic
168C2×Dic61—216no—
169C2×Dic61—22no—
170C2×Dic61—22no—
171C2×Dic61—22no—
172C2×Dic61—22no—
173C2×Dic61—22no—
174C2×Dic61—22no—
175C2×Dic61—22no—
176C2×Dic61—22no—
177C2×Dic61—42no—
178C2×Dic61—42no—
179Dic122—216no—
180Dic122—22no—
181Dic122—22no—
182Dic122—22no—
183Dic122—22no—
184Dic122—22no—
185Dic122—22no—
186Dic122C22⋊C814yes—
187Dic122C22⋊C814yes—
188C8×C61—82no—
189#92418—82no—
190#8323—611nomaximal, Sylow
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—22no—
194C22×C61—42no—
195C22×C61—42no—
196C22×C61—41no—
197C22×C61—41no—
198C22×C61#37911yescharacteristic
199C22×C61C2×C22⋊C811yescharacteristic
200C22×C61#40711yescharacteristic
201C4×C61—22no—
202C4×C61—22no—
203C4×C61—22no—
204C4×C61—41no—
205C4×C61—41no—
206C4×C61C2×C22⋊C811yescharacteristic
207C4×C61C2×C22⋊C811yescharacteristic
208C4×C61#40711yescharacteristic
209C4×C61#40711yescharacteristic
210Dic61—24no—
211Dic61—24no—
212Dic61—42no—
213Dic61—42no—
214C2×#519—611no—
215#1479—612no—
216#1479—612no—
217#1458—611no—
218#1458D6111yescharacteristic
219C2×C61—21no—
220C2×C61—21no—
221C2×C61—42no—
222C2×C61#177911yescharacteristic
223C2×C61#179611yescharacteristic
224C2×C61#179611yescharacteristic
225C23×Q8—611no—
226#519—1224no—
227#519—1224no—
228C2×C4×Q8—611no—
229C2×C4×Q8—611no—
230C2×C4×Q8—611no—
231C2×C4×Q8—611no—
232C2×C4×Q8—1221no—
233C2×C4×Q8—1221no—
234C2×#117—611no—
235C2×#117—1221no—
236C2×#117—1221no—
237C2×#117C2×D6111yescharacteristic
238#431—612no—
239#431C2×D6112yes—
240Q8⋊C8—1224no—
241Q8⋊C8—1224no—
242#324—21no—
243#324—1221no—
244#323—21no—
245#323—1221no—
246C61#832311yescharacteristic, complemented, Sylow
247C22×Q8—614no—
248C22×Q8—611no—
249C22×Q8—611no—
250C22×Q8—1222no—
251C22×Q8—1222no—
252C22×Q8—1222no—
253C22×Q8—1222no—
254C22×Q8—1222no—
255C22×Q8—1221no—
256C23×C4—1221no—
257C23×C4C4×D6111yescharacteristic
258C4×Q8—614no—
259C4×Q8—614no—
260C4×Q8—1222no—
261C4×Q8—1222no—
262C4×Q8—1222no—
263C4×Q8—1222no—
264C4×Q8—1228no—
265C4×Q8—1228no—
266C4×Q8—1222no—
267C4×Q8—1222no—
268#117—22no—
269#117—22no—
270#117—1228no—
271#117—1228no—
272#117—1222no—
273#117—1222no—
274C2×C4⋊C4—611no—
275C2×C4⋊C4—611no—
276C2×C4⋊C4—1221no—
277C2×C4⋊C4—1221no—
278C2×C4⋊C4—1221no—
279C2×C4⋊C4—1221no—
280C2×C4⋊C4D24411yescharacteristic
281C2×C4⋊C4C22⋊D6111yescharacteristic
282C2×C22⋊C4—1221no—
283C2×C22⋊C4D24411yescharacteristic
284C2×C22⋊C4C22⋊D6111yescharacteristic
285C2×C42—1221no—
286C2×C42—1221no—
287C2×C42—1221no—
288C2×C42—1221no—
289C2×C42—1221no—
290C2×C42C4×D6111yescharacteristic
291C2×C42C22×D6111yescharacteristic
292C4⋊C8—22no—
293C4⋊C8—1222no—
294C22⋊C8—22no—
295C22⋊C8—1222no—
296C4×C8—22no—
297C4×C8—1222no—
298C24#1175819811yescharacteristic
299C2×Q8—612no—
300C2×Q8—612no—
301C2×Q8—612no—
302C2×Q8—612no—
303C2×Q8—612no—
304C2×Q8—612no—
305C2×Q8—1228no—
306C2×Q8—1228no—
307C2×Q8—1224no—
308C2×Q8—1224no—
309C2×Q8—1228no—
310C2×Q8—1228no—
311C2×Q8—1224no—
312C2×Q8—1221no—
313C2×Q8—1221no—
314C2×Q8—1221no—
315C2×Q8—1221no—
316C2×Q8—1221no—
317C2×Q8—1221no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—1224no—
323C22×C4—1224no—
324C22×C4—1224no—
325C22×C4—1221no—
326C22×C4—1221no—
327C22×C4—1221no—
328C22×C4—1221no—
329C22×C4C8×D6112yes—
330C22×C4#1175818912yes—
331C22×C4#1175819811yescharacteristic
332C22×C4#1175819811yescharacteristic
333C22×C4#1175819811yescharacteristic
334C22×C4C2×C4×D6111yescharacteristic
335C22×C4C2×D24411yescharacteristic
336C22×C4C2×C22⋊D6111yescharacteristic
337C2×C8—42no—
338C2×C8—2442no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—612no—
342C4⋊C4—612no—
343C4⋊C4—1224no—
344C4⋊C4—1224no—
345C4⋊C4—1221no—
346C4⋊C4—1221no—
347C4⋊C4—1224no—
348C4⋊C4—1224no—
349C22⋊C4—22no—
350C22⋊C4—22no—
351C22⋊C4—1224no—
352C42—21no—
353C42—21no—
354C42—1224no—
355C42—1224no—
356C42—1224no—
357C42—1224no—
358C42—1224no—
359C42D4×D6112yes—
360C42D4×D6112yes—
361C23—21no—
362C23—21no—
363C23—41no—
364C23—41no—
365C23#1451968912yes—
366C23C2×#1175819811yescharacteristic
367Q8—614no—
368Q8—614no—
369Q8—12216no—
370Q8—1222no—
371Q8—1222no—
372Q8—1222no—
373Q8—1222no—
374Q8—1222no—
375Q8—1222no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—12216no—
389C2×C4—1222no—
390C2×C4—1222no—
391C2×C4—1222no—
392C2×C4—1222no—
393C2×C4—1222no—
394C2×C4—1222no—
395C2×C4—1222no—
396C2×C4—1222no—
397C2×C4—2442no—
398C2×C4—2442no—
399C2×C4#1451968912yes—
400C2×C4C22⋊C4×D6111yescharacteristic
401C2×C4C22⋊C4×D6111yescharacteristic
402C2×C4#1451974512yes—
403C2×C4#1451974712yes—
404C2×C4C2×C8×D6111yescharacteristic
405C2×C4M16×D6111yescharacteristic
406C2×C4M16×D6111yescharacteristic
407C2×C4C2×#1175818911yescharacteristic
408C8—82no—
409C8—4882no—
410C22—21no—
411C22—21no—
412C22—22no—
413C22—42no—
414C22—42no—
415C22—41no—
416C22—41no—
417C22#1683961711yescharacteristic
418C22C2×#1451968911yescharacteristic
419C22#1683972511yescharacteristic
420C4—22no—
421C4—22no—
422C4—22no—
423C4—41no—
424C4—41no—
425C4—1224no—
426C4—1224no—
427C4—2442no—
428C4—2442no—
429C4C22⋊C8×D6111yescharacteristic
430C4C22⋊C8×D6111yescharacteristic
431C4#1683972411yescharacteristic
432C4#1683972411yescharacteristic
433C2—21no—
434C2—21no—
435C2—42no—
436C2#2144572811yescharacteristic
437C2#2144579211yescharacteristic
438C2#2144579511yescharacteristic
subgroupG/H
centerC22#16839617
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1458C2
socleC22×C61#379
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1458D61
hypocenterC61#8323
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
2. #21444215C2semidirect
3. #21444213C2semidirect
33. C22×Dic122C8semidirect
246. C61#8323semidirect

Maximal subgroups

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

subgroupindex
C2×#168402392
#214442152
#214442132
#214441332
C61×#14582
#832361