Finite Group Databasebeta

← #30597512

Subgroups — #30597512

Order 15616.

568 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840794C211yesmaximal, characteristic
2#21461566C211yesmaximal, characteristic
3#21461558C211yesmaximal, characteristic, complemented
4#21461554C211yesmaximal, characteristic, complemented
5#21460660C211yesmaximal, characteristic, complemented
6#21460660C211yesmaximal, characteristic, complemented
7#21444134C211yesmaximal, characteristic
8C22×#11758217C411yescharacteristic, complemented
9C22×D61⋊C8C2211yescharacteristic
10#16840794—21no—
11#16840794—21no—
12#16840794—21no—
13#16840794—21no—
14C2×C4⋊#92420C411yescharacteristic, complemented
15C2×#14519835C412yes—
16C2×#14519834C2211yescharacteristic
17C2×C22⋊#92420C411yescharacteristic, complemented
18C2×#14519832C411yescharacteristic, complemented
19C2×#14519831—21no—
20C2×C8×#6923—21no—
21C4×C22⋊#6923C2211yescharacteristic
22C4×C22⋊#6923C2211yescharacteristic
23#16840640C412yes—
24(C2×#6923)⋊C8—21no—
25(C2×#6923)⋊C8—21no—
26C2×#14519737C2211yescharacteristic
27C22⋊C8×D61C2211yescharacteristic
28C22⋊C8×D61C2211yescharacteristic
29#16839487C411yescharacteristic, complemented
30#16839487C411yescharacteristic, complemented
31#16839486C411yescharacteristic, complemented
32C61×#323C411yescharacteristic, complemented
33C2×#11758217—21no—
34C2×#11758217—21no—
35C2×#11758217—42no—
36C2×D61⋊C8—42no—
37C2×D61⋊C8D411yescharacteristic
38C2×D61⋊C8D411yescharacteristic
39C2×D61⋊C8D411yescharacteristic
40C2×D61⋊C8D411yescharacteristic
41C22×#92420C2×C411yescharacteristic
42C22×#92420C2×C411yescharacteristic
43C22×#92420C2×C411yescharacteristic
44C22×#92420C2×C411yescharacteristic
45C2×C22⋊#6923C2×C412yes—
46C2×C22⋊#6923C2×C412yes—
47C2×C4×#6923—21no—
48C2×C4×#6923—21no—
49C4⋊#92420—21no—
50C4⋊#92420—21no—
51#14519835—24no—
52#14519834—21no—
53#14519834—21no—
54C22⋊#92420—21no—
55C22⋊#92420—21no—
56#14519832—21no—
57#14519832—21no—
58#14519831—42no—
59C8×#6923—42no—
60(C2×#6923)⋊C4—21no—
61(C2×#6923)⋊C4—21no—
62C22×C22⋊D61C2×C411yescharacteristic
63C23×Dic61C2×C411yescharacteristic
64C22×C4×D61C2311yescharacteristic
65C2×C8×D61—21no—
66C2×C8×D61—21no—
67#14519737—21no—
68#14519737—21no—
69#14519737—21no—
70#14519737—21no—
71C2×#11758196C2×C411yescharacteristic
72C2×#11758198C2×C411yescharacteristic
73C2×C4×Dic61C2×C411yescharacteristic
74C22⋊#92418C2×C411yescharacteristic
75C22⋊#92418C2×C411yescharacteristic
76#14519689—21no—
77#14519689—21no—
78C2×C22⋊C4×C61C2×C411yescharacteristic
79C22⋊C8×C61C2×C411yescharacteristic
80C22⋊C8×C61C2×C411yescharacteristic
81C24×C61C4211yescharacteristic
82C23×D61C22×C411yescharacteristic
83C22×#6923—22no—
84C22×#6923—22no—
85C22×C4×C61C4211yescharacteristic
86C22×C4×C61C22×C411yescharacteristic
87C2×C22⋊D61—21no—
88C2×C22⋊D61—21no—
89C2×C22⋊D61—22no—
90C2×C22⋊D61—22no—
91C22×Dic61—21no—
92C22×Dic61—21no—
93C22×Dic61—41no—
94C22×Dic61—41no—
95C22×Dic61C4211yescharacteristic
96C22×Dic61C4211yescharacteristic
97C22×Dic61C22×C411yescharacteristic
98C2×C4×D61—41no—
99C2×C4×D61—41no—
100C2×C4×D61C2×D411yescharacteristic
101C2×C4×D61C2×D411yescharacteristic
102C2×C4×D61#4111yescharacteristic
103C2×C4×D61#4111yescharacteristic
104C22⋊#6923—22no—
105C22⋊#6923—22no—
106C22⋊#6923—22no—
107C22⋊#6923M1614yescomplemented
108#11758217—42no—
109#11758217—42no—
110C2×#92420—22no—
111C2×#92420—21no—
112C2×#92420—21no—
113C2×#92420—41no—
114C2×#92420—41no—
115C2×#92420—41no—
116C2×#92420C22⋊C411yescharacteristic
117C2×#92420C22⋊C411yescharacteristic
118C2×#92420C22⋊C411yescharacteristic
119C2×#92420C22⋊C411yescharacteristic
120C4×#6923—41no—
121C4×#6923—41no—
122C4×#6923—41no—
123C4×#6923—41no—
124D61⋊C8—22no—
125D61⋊C8—22no—
126D61⋊C8—41no—
127D61⋊C8—41no—
128C2×C8×C61—21no—
129C2×C8×C61—21no—
130C22⋊C4×C61—21no—
131C22⋊C4×C61—21no—
132#11758198—21no—
133#11758198—21no—
134#11758196—21no—
135#11758196—21no—
136C4×Dic61—21no—
137C4×Dic61—21no—
138C2×#92418—21no—
139C2×#92418—21no—
140C8×D61—41no—
141C8×D61—41no—
142C8×D61—41no—
143C8×D61—41no—
144C23×C61—21no—
145C23×C61—21no—
146C23×C61—21no—
147C23×C61—41no—
148C23×C61—41no—
149C23×C61C2×C4211yescharacteristic
150C22×D61—41no—
151C22×D61—41no—
152C22×D61C4×D411yescharacteristic
153C22×D61C4×D411yescharacteristic
154C22×D61C2×M1612yes—
155C22×D61#13112yes—
156C2×#6923—24no—
157C2×#6923—42no—
158C2×#6923—42no—
159C2×#6923—42no—
160C2×#6923—42no—
161C2×#6923—42no—
162C2×C4×C61—21no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61C4×D411yescharacteristic
166C2×C4×C61C4×D411yescharacteristic
167C22⋊D61—42no—
168C22⋊D61—42no—
169C2×Dic61—21no—
170C2×Dic61—21no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—21no—
175C2×Dic61—42no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61C2×C22⋊C411yescharacteristic
180C2×Dic61#11711yescharacteristic
181C4×D61—21no—
182C4×D61—21no—
183C4×D61—21no—
184C4×D61—21no—
185C4×D61—41no—
186C4×D61—41no—
187#92420—21no—
188#92420—21no—
189#92420—21no—
190#92420—41no—
191#92420—41no—
192#92420#9912yescomplemented
193C8×C61—41no—
194C8×C61—41no—
195#92418—41no—
196#92418—41no—
197#8161—611nomaximal, Sylow
198C22×C61—21no—
199C22×C61—21no—
200C22×C61—41no—
201C22×C61—41no—
202C22×C61—41no—
203C22×C61—81no—
204C22×C61—81no—
205C22×C61C4×C22⋊C411yescharacteristic
206C22×C61C4×M1611yescharacteristic
207C22×C61#40511yescharacteristic
208C2×D61—21no—
209C2×D61—21no—
210C2×D61—21no—
211C2×D61—21no—
212C2×D61—42no—
213C2×D61—42no—
214C2×D61#43512yes—
215C2×D61#43612yes—
216#6923—44no—
217#6923—82no—
218C4×C61—21no—
219C4×C61—21no—
220C4×C61—41no—
221Dic61—21no—
222Dic61—41no—
223Dic61—41no—
224Dic61C2×#9911yescharacteristic
225Dic61#41011yescharacteristic
226C2×#435—611no—
227C4×#99—611no—
228#1752—611no—
229C8×C22⋊C4—611no—
230#1459—611no—
231#1282—611no—
232#1282—611no—
233C2×C61—21no—
234C2×C61—21no—
235C2×C61—81no—
236C2×C61#175311yescharacteristic
237C2×C61C4×#9911yescharacteristic
238C2×C61#175711yescharacteristic
239D61—22no—
240D61—22no—
241C22×M16—611no—
242C23×C8—611no—
243C2×C4×D4—611no—
244#435—1221no—
245#435—1221no—
246#435—1221no—
247#435—1221no—
248C2×C4⋊C8—611no—
249C2×#99—612no—
250C2×C22⋊C8—611no—
251C2×C22⋊C8—611no—
252C2×C22⋊C8—611no—
253C2×C22⋊C8—611no—
254C2×#97—611no—
255C2×#97—1221no—
256C2×C4×C8—1221no—
257C4×C22⋊C4—611no—
258C4×C22⋊C4—611no—
259#342—612no—
260#336—1221no—
261#336—1221no—
262#324—611no—
263#324—611no—
264#323—611no—
265#323#692311yescharacteristic, complemented
266C61#816111yescharacteristic, complemented, Sylow
267C22×D4—611no—
268C23×C4—611no—
269C23×C4—611no—
270C2×M16—1221no—
271C2×M16—1221no—
272C2×M16—2442no—
273C22×C8—611no—
274C22×C8—611no—
275C22×C8—611no—
276C22×C8—611no—
277C22×C8—611no—
278C22×C8—611no—
279C22×C8—611no—
280C22×C8—611no—
281C22×C8—1221no—
282C22×C8—1221no—
283C22×C8—2442no—
284C4×D4—1221no—
285C4×D4—1221no—
286C4×D4—1221no—
287C4×D4—1221no—
288C2×C4⋊C4—611no—
289C2×C22⋊C4—612no—
290C2×C22⋊C4—611no—
291C2×C22⋊C4—612no—
292C2×C22⋊C4C2×#692311yescharacteristic
293C2×C42—611no—
294C2×C42—1221no—
295C2×C42—1221no—
296C4⋊C8—1221no—
297C4⋊C8—1221no—
298#99—1224no—
299C22⋊C8—611no—
300C22⋊C8—611no—
301C22⋊C8—1221no—
302C22⋊C8—1221no—
303C22⋊C8—1221no—
304C22⋊C8—1221no—
305C22⋊C8—1221no—
306C22⋊C8—1221no—
307C22⋊C8C2×#692311yescharacteristic
308C22⋊C8C2×#692311yescharacteristic
309#97—1221no—
310#97—1221no—
311#97—2442no—
312C4×C8—2442no—
313#95—1221no—
314#95—1221no—
315C24—611no—
316C24C4×#692311yescharacteristic
317C2×D4—1222no—
318C2×D4—1221no—
319C2×D4—1221no—
320C2×D4—1222no—
321C22×C4—611no—
322C22×C4—611no—
323C22×C4—611no—
324C22×C4—611no—
325C22×C4—611no—
326C22×C4—611no—
327C22×C4—611no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4—1222no—
331C22×C4—1222no—
332C22×C4—2441no—
333C22×C4—2441no—
334C22×C4—2441no—
335C22×C4—2441no—
336C22×C4C4×#692311yescharacteristic
337C22×C4C22×#692311yescharacteristic
338M16—2442no—
339M16—2442no—
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—611no—
343C2×C8—611no—
344C2×C8—611no—
345C2×C8—611no—
346C2×C8—1222no—
347C2×C8—1222no—
348C2×C8—1222no—
349C2×C8—1221no—
350C2×C8—1221no—
351C2×C8—1221no—
352C2×C8—1221no—
353C2×C8—2441no—
354C2×C8—2441no—
355C2×C8—2441no—
356C2×C8—2441no—
357C2×C8—2441no—
358C2×C8—2441no—
359C2×C8—2441no—
360C2×C8—2441no—
361C2×C8—2441no—
362C4⋊C4—1221no—
363C4⋊C4—1221no—
364C22⋊C4—21no—
365C22⋊C4—21no—
366C22⋊C4—614no—
367C22⋊C4—1221no—
368C22⋊C4—1221no—
369C22⋊C4—1222no—
370C22⋊C4—1222no—
371C22⋊C4—1222no—
372C42—1221no—
373C42—1221no—
374C42—2441no—
375C42—2441no—
376C42—2441no—
377C42—2441no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—41no—
382C23—41no—
383C23—611no—
384C23—611no—
385C23—612no—
386C23—612no—
387C23—2441no—
388C23—2441no—
389C23C2×C4×#692311yescharacteristic
390D4—2442no—
391D4—2442no—
392C2×C4—21no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—611no—
396C2×C4—611no—
397C2×C4—1221no—
398C2×C4—1221no—
399C2×C4—1221no—
400C2×C4—1221no—
401C2×C4—1221no—
402C2×C4—1221no—
403C2×C4—1224no—
404C2×C4—1221no—
405C2×C4—1221no—
406C2×C4—1221no—
407C2×C4—1221no—
408C2×C4—2441no—
409C2×C4—2441no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4—2442no—
413C2×C4—2442no—
414C2×C4—2442no—
415C2×C4—2442no—
416C2×C4—2442no—
417C2×C4—2442no—
418C2×C4—2441no—
419C2×C4D4×#692311yescharacteristic
420C2×C4D4×#692311yescharacteristic
421C8—41no—
422C8—41no—
423C8—612no—
424C8—1221no—
425C8—1221no—
426C8—1221no—
427C8—2441no—
428C8—2441no—
429C8—2441no—
430C8—2441no—
431C22—21no—
432C22—21no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—81no—
437C22—81no—
438C22—612no—
439C22—612no—
440C22—1221no—
441C22—1221no—
442C22—1221no—
443C22—1221no—
444C22—2442no—
445C22—2442no—
446C22C22⋊C4×#692311yescharacteristic
447C22M16×#692311yescharacteristic
448C22#1684072511yescharacteristic
449C4—21no—
450C4—21no—
451C4—41no—
452C4—611no—
453C4—611no—
454C4—1221no—
455C4—4882no—
456C4—2444no—
457C4—2441no—
458C4—2441no—
459C2—21no—
460C2—21no—
461C2—81no—
462C2—1222no—
463C2—1222no—
464C2#2146156211yescharacteristic
465C2#99×#692311yescharacteristic
466C2#2146157611yescharacteristic
subgroupG/H
centerC22C22⋊C4×#6923
commutatorC23×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#323C4
socleC22×C61C4×C22⋊C4
prime radicalC22×C22⋊D61C2×C4
cosocleC22×C4×D61C23
hypercenter#323#6923
hypocenterC61#8161
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
3. #21461558C2semidirect
4. #21461554C2semidirect
5. #21460660C2semidirect
6. #21460660C2semidirect
8. C22×#11758217C4semidirect
14. C2×C4⋊#92420C4semidirect
17. C2×C22⋊#92420C4semidirect
18. C2×#14519832C4semidirect
29. #16839487C4semidirect
30. #16839487C4semidirect
31. #16839486C4semidirect
32. C61×#323C4semidirect
107. C22⋊#6923M16semidirect
192. #92420#99semidirect
265. #323#6923semidirect
266. C61#8161semidirect

Maximal subgroups

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

subgroupindex
C2×#168407942
#214615662
#214615582
#214615542
#214606602
#214441342
#816161