Finite Group Databasebeta

← #29570565

Subgroups — #29570565

Order 15616.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839830C211yesmaximal, characteristic
2C4×#14519691C211yesmaximal, characteristic
3#21445597C211yesmaximal, characteristic, complemented
4#21445593C211yesmaximal, characteristic, complemented
5#21444135C211yesmaximal, characteristic
6#21443666C211yesmaximal, characteristic, complemented
7C61×#1282C211yesmaximal, characteristic, complemented
8C22×#11758189C411yescharacteristic, complemented
9C23×#92418C2211yescharacteristic
10C2×C4×C22⋊D61C2211yescharacteristic
11#16839830—21no—
12#16839830—21no—
13#16839830—21no—
14#16839830—21no—
15C2×#14519706C411yescharacteristic, complemented
16C2×#14519691C412yes—
17C2×C22⋊#92418C2211yescharacteristic
18C2×#14519689C411yescharacteristic, complemented
19C2×#14519688—21no—
20C2×#14519687C411yescharacteristic, complemented
21C2×C8×Dic61—21no—
22C4×C22⋊Dic61C2211yescharacteristic
23#16839528C412yes—
24#16839517—21no—
25#16839516—21no—
26#16839487C412yescomplemented
27#16839485C412yescomplemented
28C2×C22⋊C8×C61C2211yescharacteristic
29C2×C22⋊C8×C61C2211yescharacteristic
30C4×C22⋊C4×C61C2211yescharacteristic
31C22×C22⋊D61C2×C411yescharacteristic
32C22×C4×D61C2×C411yescharacteristic
33C2×#11758189—21no—
34C2×#11758189—21no—
35C2×#11758189—42no—
36C22×#92418—21no—
37C22×#92418—42no—
38C22×#92418C2×C411yescharacteristic
39C22×#92418C2×C411yescharacteristic
40C22×#92418D411yescharacteristic
41C22×#92418D411yescharacteristic
42C22×#92418D411yescharacteristic
43C22×#92418D411yescharacteristic
44C4×C22⋊D61—21no—
45C4×C22⋊D61—21no—
46C4×C22⋊D61—21no—
47C4×C22⋊D61—21no—
48C2×#11758196C2×C411yescharacteristic
49C2×C22⋊Dic61C2×C411yescharacteristic
50C2×C22⋊Dic61C2×C412yes—
51C2×#11758198C2×C411yescharacteristic
52C2×C4×Dic61—21no—
53C2×C4×Dic61C2×C411yescharacteristic
54#14519706—21no—
55#14519706—21no—
56#14519691—24no—
57C22⋊#92418—21no—
58C22⋊#92418C2×C412yes—
59#14519689—21no—
60#14519689—21no—
61#14519688—42no—
62#14519687—21no—
63#14519687—21no—
64C8×Dic61—42no—
65#14519684—21no—
66C23×C4×C61C2311yescharacteristic
67C22×C8×C61—21no—
68C22×C8×C61C2×C411yescharacteristic
69C22×C8×C61C2×C411yescharacteristic
70C2×C22⋊C4×C61C2×C412yes—
71C2×C42×C61—21no—
72C22⋊C8×C61—21no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61—21no—
75C22⋊C8×C61C2×C412yes—
76#95×C61—21no—
77C24×C61C22×C411yescharacteristic
78C23×D61C4211yescharacteristic
79C22×C4×C61—22no—
80C22×C4×C61—41no—
81C22×C4×C61—41no—
82C22×C4×C61C22×C411yescharacteristic
83C22×C4×C61C22×C411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61#4111yescharacteristic
87C22×C4×C61#4111yescharacteristic
88C2×C22⋊D61—21no—
89C2×C22⋊D61—21no—
90C2×C22⋊D61—22no—
91C2×C22⋊D61—22no—
92C22×Dic61—22no—
93C22×Dic61C4211yescharacteristic
94C22×Dic61C4211yescharacteristic
95C22×Dic61C4211yescharacteristic
96C2×C4×D61—21no—
97C2×C4×D61—21no—
98C2×C4×D61—41no—
99C2×C4×D61—41no—
100C2×C8×C61—21no—
101C2×C8×C61—21no—
102C2×C8×C61—22no—
103C2×C8×C61—41no—
104C2×C8×C61—41no—
105C2×C8×C61—41no—
106C2×C8×C61—41no—
107C22⋊C4×C61—22no—
108C22⋊C4×C61—22no—
109C42×C61—41no—
110C42×C61—41no—
111C22⋊Dic61—21no—
112C22⋊Dic61—21no—
113C22⋊Dic61—22no—
114C22⋊Dic61M1614yescomplemented
115#11758198—21no—
116#11758198—21no—
117#11758196—21no—
118#11758196—21no—
119C4×Dic61—21no—
120C4×Dic61—21no—
121C4×Dic61—41no—
122C4×Dic61—41no—
123C2×#92418—22no—
124C2×#92418—22no—
125C2×#92418—22no—
126C2×#92418—22no—
127C2×#92418—41no—
128C2×#92418—41no—
129C2×#92418—41no—
130C2×#92418—41no—
131C2×#92418—41no—
132C2×#92418C22⋊C411yescharacteristic
133C2×#92418C22⋊C411yescharacteristic
134C2×#92418C22⋊C411yescharacteristic
135C2×#92418C22⋊C411yescharacteristic
136#11758189—42no—
137#11758189—42no—
138C23×C61—41no—
139C23×C61—41no—
140C23×C61C2×C4211yescharacteristic
141C23×C61C4×D411yescharacteristic
142C23×C61C4×D411yescharacteristic
143C23×C61C2×M1612yes—
144C23×C61#13112yes—
145C22×D61—21no—
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—41no—
149C22×D61—41no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—42no—
160C2×C4×C61—42no—
161C2×C4×C61—42no—
162C2×C4×C61C2×C22⋊C411yescharacteristic
163C2×C4×C61#11711yescharacteristic
164C2×C4×C61C4×D411yescharacteristic
165C2×C4×C61C4×D411yescharacteristic
166C22⋊D61—42no—
167C22⋊D61—42no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—21no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—24no—
174C2×Dic61—42no—
175C2×Dic61—42no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C4×D61—42no—
179C4×D61—41no—
180C4×D61—41no—
181C8×C61—42no—
182C8×C61—41no—
183C8×C61—41no—
184#92418—21no—
185#92418—21no—
186#92418—21no—
187#92418—42no—
188#92418#9912yescomplemented
189#8161—611nomaximal, Sylow
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61—42no—
197C22×C61—42no—
198C22×C61C4×C22⋊C411yescharacteristic
199C22×C61C4×M1611yescharacteristic
200C22×C61#40511yescharacteristic
201C22×C61#43512yes—
202C22×C61#43612yes—
203C2×D61—41no—
204C2×D61—41no—
205C2×D61—41no—
206C2×D61—81no—
207C2×D61—81no—
208C4×C61—21no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—82no—
212C4×C61C2×#9911yescharacteristic
213C4×C61#41011yescharacteristic
214Dic61—44no—
215Dic61—41no—
216Dic61—41no—
217Dic61—41no—
218C2×#435—611no—
219C4×#99—611no—
220#1752—611no—
221C8×C22⋊C4—611no—
222#1459—611no—
223#1282—611no—
224#1282D6111yescharacteristic, complemented
225C2×C61—22no—
226C2×C61—22no—
227C2×C61—21no—
228C2×C61—21no—
229C2×C61#175311yescharacteristic
230C2×C61C4×#9911yescharacteristic
231C2×C61#175711yescharacteristic
232D61—81no—
233C22×M16—611no—
234C23×C8—611no—
235C2×C4×D4—611no—
236#435—1221no—
237#435—1221no—
238#435—1221no—
239#435—1221no—
240C2×C4⋊C8—611no—
241C2×#99—612no—
242C2×C22⋊C8—611no—
243C2×C22⋊C8—611no—
244C2×C22⋊C8C2×D6111yescharacteristic
245C2×C22⋊C8C2×D6111yescharacteristic
246C2×#97—611no—
247C2×#97—1221no—
248C2×C4×C8—1221no—
249C4×C22⋊C4—611no—
250C4×C22⋊C4C2×D6111yescharacteristic
251#342—612no—
252#336—1221no—
253#336—1221no—
254#324—612no—
255#323—612no—
256C61#816111yescharacteristic, complemented, Sylow
257C22×D4—611no—
258C23×C4—611no—
259C23×C4C22×D6111yescharacteristic
260C2×M16—1221no—
261C2×M16—1221no—
262C2×M16—2442no—
263C22×C8—21no—
264C22×C8—611no—
265C22×C8—611no—
266C22×C8—611no—
267C22×C8—611no—
268C22×C8—611no—
269C22×C8—611no—
270C22×C8—1221no—
271C22×C8—2442no—
272C22×C8C4×D6111yescharacteristic
273C22×C8C4×D6111yescharacteristic
274C4×D4—1221no—
275C4×D4—1221no—
276C4×D4—1221no—
277C4×D4—1221no—
278C2×C4⋊C4—611no—
279C2×C22⋊C4—612no—
280C2×C22⋊C4—611no—
281C2×C22⋊C4—611no—
282C2×C22⋊C4C4×D6112yes—
283C2×C42—21no—
284C2×C42—611no—
285C2×C42—1221no—
286C4⋊C8—1221no—
287C4⋊C8—1221no—
288#99—1224no—
289C22⋊C8—21no—
290C22⋊C8—21no—
291C22⋊C8—21no—
292C22⋊C8—612no—
293C22⋊C8—1221no—
294C22⋊C8—1221no—
295C22⋊C8—1221no—
296C22⋊C8C4×D6112yes—
297#97—1221no—
298#97—1221no—
299#97—2442no—
300C4×C8—2442no—
301#95—21no—
302#95—1221no—
303C24—611no—
304C24C2×C4×D6111yescharacteristic
305C2×D4—1221no—
306C2×D4—1221no—
307C2×D4—1222no—
308C2×D4—1222no—
309C22×C4—22no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—611no—
313C22×C4—611no—
314C22×C4—611no—
315C22×C4—1222no—
316C22×C4—1221no—
317C22×C4—1221no—
318C22×C4—2441no—
319C22×C4—2441no—
320C22×C4C2×C4×D6111yescharacteristic
321C22×C4C2×C4×D6111yescharacteristic
322C22×C4D4×D6111yescharacteristic
323C22×C4D4×D6111yescharacteristic
324C22×C4#1175822411yescharacteristic
325C22×C4#1175822611yescharacteristic
326M16—2442no—
327M16—2442no—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—22no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—611no—
336C2×C8—611no—
337C2×C8—611no—
338C2×C8—611no—
339C2×C8—1222no—
340C2×C8—1222no—
341C2×C8—1222no—
342C2×C8—1222no—
343C2×C8—2441no—
344C2×C8—2441no—
345C2×C8—2441no—
346C2×C8—2441no—
347C2×C8—2441no—
348C4⋊C4—1221no—
349C4⋊C4—1221no—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—614no—
353C22⋊C4—1221no—
354C22⋊C4—1221no—
355C22⋊C4—1222no—
356C22⋊C4—1221no—
357C22⋊C4—1221no—
358C42—41no—
359C42—41no—
360C42—1221no—
361C42—1221no—
362C42—2441no—
363C42—2441no—
364C23—41no—
365C23—41no—
366C23—1221no—
367C23—1221no—
368C23—1221no—
369C23—2441no—
370C23—2441no—
371C23C42×D6111yescharacteristic
372C23#1451973711yescharacteristic
373C23#1451973911yescharacteristic
374C23M16×D6112yes—
375C23#1451978312yes—
376D4—2442no—
377D4—2442no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—1221no—
391C2×C4—1221no—
392C2×C4—1224no—
393C2×C4—1221no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—2442no—
397C2×C4—2442no—
398C2×C4—2442no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4C22⋊C4×D6111yescharacteristic
404C2×C4#1451973511yescharacteristic
405C2×C4#1451973711yescharacteristic
406C2×C4#1451973911yescharacteristic
407C8—42no—
408C8—41no—
409C8—41no—
410C8—612no—
411C8—1221no—
412C8—1221no—
413C8—1221no—
414C8—2442no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—42no—
422C22—42no—
423C22—4881no—
424C22—4881no—
425C22—2441no—
426C22—2441no—
427C22—2441no—
428C22#1683960911yescharacteristic
429C22#1683971411yescharacteristic
430C22#1683971611yescharacteristic
431C22#1683983212yes—
432C22#1683983712yes—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—82no—
437C4—2444no—
438C4—2441no—
439C4—2441no—
440C4—2441no—
441C4#99×D6111yescharacteristic
442C4#1683973411yescharacteristic
443C2—22no—
444C2—22no—
445C2—21no—
446C2—21no—
447C2—4881no—
448C2#2144560111yescharacteristic
449C2#2144560611yescharacteristic
450C2#2144561811yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC23×C61C2×C42
FrattiniC23×C4C22×D61
FittingC61×#1282C2
socleC22×C61C4×C22⋊C4
prime radicalC22×C22⋊D61C2×C4
cosocleC23×C4×C61C23
hypercenter#1282D61
hypocenterC61#8161
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1282

Complements

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

NH ≅ G/Ntype
3. #21445597C2semidirect
4. #21445593C2semidirect
6. #21443666C2semidirect
7. C61×#1282C2semidirect
8. C22×#11758189C4semidirect
15. C2×#14519706C4semidirect
18. C2×#14519689C4semidirect
20. C2×#14519687C4semidirect
26. #16839487C4semidirect
27. #16839485C4semidirect
114. C22⋊Dic61M16semidirect
188. #92418#99semidirect
224. #1282D61semidirect
256. C61#8161semidirect

Maximal subgroups

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

subgroupindex
C2×#168398302
C4×#145196912
#214455972
#214455932
#214441352
#214436662
C61×#12822
#816161