Finite Group Databasebeta

← #29571775

Subgroups — #29571775

Order 15616.

782 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840472C211yesmaximal, characteristic
2#21445808C211yesmaximal, characteristic
3#21444505C211yesmaximal, characteristic, complemented
4#21444503C211yesmaximal, characteristic, complemented
5#21444248C211yesmaximal, characteristic, complemented
6#21444139C211yesmaximal, characteristic
7C61×#1487C211yesmaximal, characteristic, complemented
8#16840472—22no—
9#16840472—22no—
10#16840472—22no—
11#16840472—22no—
12C2×#14519777C2211yescharacteristic
13C2×#14519769—21no—
14C2×#14519755—22no—
15C2×#14519753C412yes—
16C2×C4×D244—21no—
17C2×C4×D244C2211yescharacteristic
18C2×C4⋊C4×D61C412yes—
19#16839815C2211yescharacteristic
20#16839786C2211yescharacteristic
21C2×#14519693—21no—
22#16839530—21no—
23#16839509—22no—
24#16839507—22no—
25Q8⋊#92418—22no—
26#16839485—22no—
27C2×C4×Q8×C61C2211yescharacteristic
28C61×#431C2211yescharacteristic
29C61×#423C2211yescharacteristic
30C61×Q8⋊C8—22no—
31C22×Dic122—21no—
32C22×D244D411yescharacteristic
33C22×C4×D61—22no—
34C22×C4×D61C2×C412yes—
35C2×#11758194—21no—
36#14519777—21no—
37#14519777—21no—
38#14519777D412yes—
39#14519777D412yes—
40#14519769—24no—
41#14519769—24no—
42#14519755—28no—
43#14519755—28no—
44#14519753—24no—
45#14519753—24no—
46C4×D244—24no—
47C4×D244—24no—
48C4×D244—21no—
49C4×D244—21no—
50C4×D244—21no—
51C4×D244—21no—
52C2×C4⋊Dic61—21no—
53C2×C4⋊Dic61C2×C412yes—
54C2×C4⋊Dic61D411yescharacteristic
55C2×#11758196—22no—
56C2×#11758196—22no—
57C4⋊C4×D61—24no—
58C4⋊C4×D61—24no—
59C2×#11758198—22no—
60C2×#11758198D412yes—
61C4⋊#92418—21no—
62C4⋊#92418—21no—
63C4⋊#92418—21no—
64#14519693—42no—
65C22⋊#92418—21no—
66C4×#92418—21no—
67C22×Q8×C61C2×C411yescharacteristic
68C2×M16×C61—21no—
69C4×Q8×C61—21no—
70C4×Q8×C61—21no—
71C4×Q8×C61D412yes—
72C4×Q8×C61D412yes—
73C2×C4⋊C4×C61—21no—
74C2×C4⋊C4×C61C2×C411yescharacteristic
75C2×C42×C61—21no—
76C2×C42×C61C2311yescharacteristic
77C4⋊C8×C61—21no—
78C4⋊C8×C61—21no—
79C4⋊C8×C61—21no—
80C22⋊C8×C61—21no—
81C4×C8×C61—21no—
82C23×D61C22⋊C412yes—
83C2×Q8×C61—21no—
84C2×Q8×C61—42no—
85C2×Q8×C61C22⋊C412yes—
86C22×C4×C61—21no—
87C22×C4×C61—21no—
88C22×C4×C61C22×C411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×Dic61—22no—
92C22×Dic61C22⋊C412yes—
93C2×D244—21no—
94C2×D244—21no—
95C2×D244—21no—
96C2×D244—21no—
97C2×D244SD1612yes—
98C2×D244Q1612yes—
99C2×C4×D61—22no—
100C2×C4×D61—22no—
101C2×C4×D61—28no—
102C2×C4×D61—44no—
103C2×C4×D61—84no—
104C2×Dic122—22no—
105C2×Dic122—22no—
106C2×Dic122—82no—
107M16×C61—41no—
108M16×C61—41no—
109C2×C8×C61—41no—
110C2×C8×C61—41no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61—22no—
113C4⋊C4×C61—22no—
114C4⋊C4×C61C22⋊C412yes—
115C42×C61—22no—
116C42×C61—22no—
117C42×C61C2×D411yescharacteristic
118C42×C61C2×D411yescharacteristic
119C42×C61C2×D411yescharacteristic
120C42×C61C2×D411yescharacteristic
121#11758198—28no—
122#11758198—22no—
123#11758198—22no—
124C4⋊Dic61—22no—
125C4⋊Dic61—22no—
126C4⋊Dic61—22no—
127C4⋊Dic61—21no—
128C4⋊Dic61—21no—
129C4⋊Dic61C22⋊C414yes—
130#11758196—28no—
131#11758196—28no—
132#11758194—41no—
133#11758194—41no—
134C2×#92418—41no—
135C2×#92418—41no—
136C23×C61C2×C22⋊C411yescharacteristic
137C22×D61—22no—
138C22×D61—22no—
139C22×D61—42no—
140C22×D61—42no—
141C22×D61#10314yes—
142Q8×C61—24no—
143Q8×C61—42no—
144C2×C4×C61—22no—
145C2×C4×C61—22no—
146C2×C4×C61—22no—
147C2×C4×C61—41no—
148C2×C4×C61—42no—
149C2×C4×C61—42no—
150C2×C4×C61C2×C22⋊C411yescharacteristic
151C2×C4×C61C2×C22⋊C411yescharacteristic
152C2×C4×C61#12011yescharacteristic
153C2×C4×C61#12011yescharacteristic
154C2×C4×C61#12011yescharacteristic
155C2×C4×C61#12011yescharacteristic
156C2×C4×C61C2×SD1611yescharacteristic
157C2×C4×C61C2×Q1611yescharacteristic
158C2×C4×C61#13711yescharacteristic
159C2×C4×C61#13711yescharacteristic
160C2×Dic61—22no—
161C2×Dic61—24no—
162C2×Dic61—44no—
163C2×Dic61—42no—
164D244—22no—
165D244—22no—
166D244—22no—
167D244—22no—
168C4×D61—44no—
169C4×D61—44no—
170C4×D61—88no—
171Dic122—82no—
172Dic122—82no—
173C8×C61—81no—
174C8×C61—81no—
175#92418—81no—
176#92418—81no—
177#8395—611nomaximal, Sylow
178C22×C61—21no—
179C22×C61—21no—
180C22×C61#37911yescharacteristic
181C22×C61C2×#10311yescharacteristic
182C22×C61#41911yescharacteristic
183C2×D61—24no—
184C2×D61—44no—
185C2×D61—42no—
186C2×D61—42no—
187C2×D61—44no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—42no—
192C4×C61—42no—
193C4×C61#41312yes—
194C4×C61#44811yescharacteristic
195C4×C61#44811yescharacteristic
196C4×C61#45111yescharacteristic
197C4×C61#45111yescharacteristic
198Dic61—44no—
199Dic61—42no—
200C2×#554—611no—
201#1800—611no—
202#1549—611no—
203#1549—611no—
204#1487—611no—
205#1487D6111yescharacteristic, complemented
206#1460—611no—
207C2×C61—21no—
208C2×C61—21no—
209C2×C61#178511yescharacteristic
210C2×C61#178711yescharacteristic
211C2×C61#179511yescharacteristic
212D61—44no—
213#554—1222no—
214#554—1222no—
215#554—1222no—
216#554—1222no—
217C2×C4⋊Q8—611no—
218C2×#125—1221no—
219C2×C22⋊Q8—612no—
220C2×C22⋊Q8—1222no—
221C2×C4×Q8C2×D6111yescharacteristic
222C2×C4×D4—611no—
223C2×C4×D4—1221no—
224C22×C4⋊C4—612no—
225#431—611no—
226#431C2×D6111yescharacteristic
227#423—611no—
228#423C2×D6111yescharacteristic
229C2×#100—1221no—
230#343—1221no—
231#332—1222no—
232#332—1222no—
233Q8⋊C8—22no—
234Q8⋊C8—1222no—
235#323—1222no—
236C61#839511yescharacteristic, complemented, Sylow
237C22×Q8—1221no—
238C22×Q8C4×D6111yescharacteristic
239C22×D4—611no—
240C23×C4—612no—
241C23×C4—1222no—
242C2×M16—21no—
243C2×M16—1221no—
244C4⋊Q8—612no—
245C4⋊Q8—612no—
246C4⋊Q8—1221no—
247C4⋊Q8—1221no—
248#125—1224no—
249#125—1224no—
250C22⋊Q8—1228no—
251C22⋊Q8—1228no—
252C22⋊Q8—1224no—
253C22⋊Q8—1224no—
254C4×Q8—21no—
255C4×Q8—21no—
256C4×Q8D24412yes—
257C4×Q8C22⋊D6112yes—
258C4×D4—1224no—
259C4×D4—1224no—
260C4×D4—1221no—
261C4×D4—1221no—
262C4×D4—1221no—
263C4×D4—1221no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—612no—
266C2×C4⋊C4—611no—
267C2×C4⋊C4—1224no—
268C2×C4⋊C4—1222no—
269C2×C4⋊C4—1222no—
270C2×C4⋊C4—1221no—
271C2×C4⋊C4—1224no—
272C2×C4⋊C4C4×D6111yescharacteristic
273C2×C22⋊C4—612no—
274C2×C22⋊C4—1222no—
275C2×C42—21no—
276C2×C42C22×D6111yescharacteristic
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8—1221no—
281C4⋊C8—1221no—
282C4⋊C8—1221no—
283#100—2442no—
284C22⋊C8—21no—
285C22⋊C8—1221no—
286C4×C8—21no—
287C4×C8—1221no—
288C24—612no—
289C2×Q8—21no—
290C2×Q8—42no—
291C2×Q8—1222no—
292C2×Q8—1222no—
293C2×Q8—4882no—
294C2×Q8#1175819812yes—
295C2×D4—612no—
296C2×D4—612no—
297C2×D4—1221no—
298C2×D4—1221no—
299C2×D4—1221no—
300C2×D4—1221no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—612no—
304C22×C4—1228no—
305C22×C4—1222no—
306C22×C4—1222no—
307C22×C4—1222no—
308C22×C4—4884no—
309C22×C4—2444no—
310C22×C4C2×C4×D6111yescharacteristic
311C22×C4D4×D6111yescharacteristic
312C22×C4D4×D6111yescharacteristic
313M16—41no—
314M16—41no—
315M16—2441no—
316M16—2441no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—2441no—
320C2×C8—2441no—
321C4⋊C4—21no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—614no—
325C4⋊C4—1228no—
326C4⋊C4—1228no—
327C4⋊C4—1222no—
328C4⋊C4—1221no—
329C4⋊C4—1222no—
330C4⋊C4—1221no—
331C4⋊C4—1222no—
332C4⋊C4#1175819812yes—
333C22⋊C4—1228no—
334C22⋊C4—1222no—
335C22⋊C4—1222no—
336C42—22no—
337C42—22no—
338C42C2×D24411yescharacteristic
339C42D4×D6111yescharacteristic
340C42D4×D6111yescharacteristic
341C42C2×C22⋊D6111yescharacteristic
342C23—614no—
343C23—1222no—
344C23—1222no—
345C23—2442no—
346C23—2442no—
347C23C22⋊C4×D6111yescharacteristic
348Q8—24no—
349Q8—42no—
350Q8—4882no—
351Q8—4882no—
352D4—1222no—
353D4—1222no—
354D4—1222no—
355D4—1222no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—1224no—
363C2×C4—1222no—
364C2×C4—4888no—
365C2×C4—2444no—
366C2×C4—2444no—
367C2×C4—2444no—
368C2×C4—2442no—
369C2×C4C22⋊C4×D6111yescharacteristic
370C2×C4C2×#1175819811yescharacteristic
371C2×C4#1451974511yescharacteristic
372C2×C4#1451974511yescharacteristic
373C2×C4#1451974711yescharacteristic
374C2×C4#1451974711yescharacteristic
375C2×C4SD16×D6111yescharacteristic
376C2×C4Q16×D6111yescharacteristic
377C2×C4#1451980611yescharacteristic
378C2×C4#1451980911yescharacteristic
379C8—81no—
380C8—81no—
381C8—4881no—
382C8—4881no—
383C22—21no—
384C22—21no—
385C22—1224no—
386C22—2444no—
387C22—2444no—
388C22—2442no—
389C22—2442no—
390C22#1683961711yescharacteristic
391C22#103×D6111yescharacteristic
392C22#1683976911yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—42no—
397C4—42no—
398C4—2442no—
399C4—2444no—
400C4#1683974412yes—
401C4#1683989911yescharacteristic
402C4#1683990211yescharacteristic
403C4#1683991611yescharacteristic
404C4#1683991911yescharacteristic
405C2—21no—
406C2—21no—
407C2—2444no—
408C2#2144574511yescharacteristic
409C2#2144575211yescharacteristic
410C2#2144578811yescharacteristic
subgroupG/H
centerC22#16839617
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1487C2
socleC22×C61#379
prime radicalC22×D244D4
cosocleC2×C42×C61C23
hypercenter#1487D61
hypocenterC61#8395
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
3. #21444505C2semidirect
4. #21444503C2semidirect
5. #21444248C2semidirect
7. C61×#1487C2semidirect
205. #1487D61semidirect
236. C61#8395semidirect

Maximal subgroups

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

subgroupindex
C2×#168404722
#214458082
#214445052
#214445032
#214442482
#214441392
C61×#14872
#839561