Finite Group Databasebeta

← #30603245

Subgroups — #30603245

Order 15616.

942 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462463C211yesmaximal, characteristic, complemented
2C2×#16840760C212yesmaximal
3#21461519C211yesmaximal, characteristic, complemented
4C2×#16840633C212yesmaximal, complemented
5#21448306C211yesmaximal, characteristic
6C2×D61⋊M16C2212yes—
7C2×#14519856C2212yes—
8#16840769—24no—
9#16840765—22no—
10#16840760—24no—
11#16840760—24no—
12C2×#14519841—24no—
13#16840640—22no—
14#16840633—24no—
15C22×#11758224C2211yescharacteristic
16C2×#14519735C2211yescharacteristic
17C2×C42×D61C2211yescharacteristic
18#16839668C411yescharacteristic, complemented
19#16839667C411yescharacteristic, complemented
20#16839665C411yescharacteristic, complemented
21#16839638—22no—
22C22⋊C4×Dic61—22no—
23C61×#390C411yescharacteristic, complemented
24C2×#11758213D414yes—
25D61⋊M16—22no—
26D61⋊M16—22no—
27D61⋊M16—22no—
28D61⋊M16—22no—
29C2×#11758217—22no—
30C2×D61⋊C8—22no—
31#14519856—22no—
32#14519856—22no—
33#14519856—22no—
34#14519856D414yes—
35C2×C4⋊#6923—22no—
36C2×C22⋊#6923—22no—
37C2×C4×#6923—22no—
38#14519844—24no—
39C4⋊#92420—24no—
40#14519841—216no—
41C2×#11758224—22no—
42C2×#11758224—22no—
43C2×#11758224—22no—
44C2×#11758224—22no—
45C2×#11758224—21no—
46C2×#11758224—21no—
47C2×#11758224D412yes—
48C2×#11758224Q812yes—
49C22×Dic122C2×C411yescharacteristic
50C22×C22⋊D61—21no—
51C23×Dic61—21no—
52C22×C4×D61—21no—
53C22×C4×D61C2311yescharacteristic
54#14519735—22no—
55#14519735—22no—
56C2×C4⋊Dic61C2×C411yescharacteristic
57C2×C22⋊Dic61—22no—
58C2×#11758198D412yes—
59C2×C4×Dic61—21no—
60C2×C4×Dic61C2×C411yescharacteristic
61C2×C4×Dic61D412yes—
62C42×D61—22no—
63C42×D61—22no—
64#14519684—22no—
65#14519684—22no—
66C22×D4×C61C2×C411yescharacteristic
67C2×C4⋊C4×C61C2×C411yescharacteristic
68C2×C22⋊C4×C61—22no—
69C2×C42×C61C2×C411yescharacteristic
70C24×C61—21no—
71C23×D61C2×D411yescharacteristic
72C22×#6923—42no—
73C2×D4×C61—21no—
74C2×D4×C61—22no—
75C2×D4×C61—22no—
76C2×D4×C61C4⋊C412yes—
77C22×C4×C61—21no—
78C22×C4×C61C22⋊C412yes—
79C22×C4×C61C22×C411yescharacteristic
80C2×C22⋊D61—22no—
81C2×C22⋊D61—22no—
82C2×C22⋊D61—42no—
83C2×C22⋊D61—42no—
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—22no—
87C22×Dic61—22no—
88C22×Dic61—41no—
89C22×Dic61—41no—
90C22×Dic61—41no—
91C22×Dic61—41no—
92C22×Dic61C22⋊C412yes—
93C22×Dic61C2×D411yescharacteristic
94#11758224—24no—
95#11758224—24no—
96#11758224—24no—
97#11758224—24no—
98#11758224—42no—
99#11758224—42no—
100#11758224—42no—
101#11758224—42no—
102C2×C4×D61—42no—
103C2×C4×D61—42no—
104C2×C4×D61—42no—
105C2×C4×D61C2×D411yescharacteristic
106C2×C4×D61C2×D412yes—
107C2×C4×D61C2×D412yes—
108C2×C4×D61C2×Q811yescharacteristic
109C2×C4×D61#4111yescharacteristic
110C2×C4×D61#4112yes—
111C2×C4×D61#4112yes—
112C2×C4×D61#4111yescharacteristic
113C2×Dic122—22no—
114C2×Dic122—22no—
115C2×Dic122—21no—
116C2×Dic122C4⋊C412yes—
117C22⋊#6923—24no—
118C22⋊#6923—42no—
119#11758217—42no—
120#11758217—42no—
121C2×#92420—24no—
122C4⋊#6923—24no—
123C4⋊#6923—42no—
124C4×#6923—24no—
125C4×#6923—42no—
126#11758213—24no—
127#11758213—24no—
128D61⋊C8—42no—
129D61⋊C8—42no—
130C4⋊C4×C61—22no—
131C22⋊C4×C61—44no—
132C42×C61—22no—
133C22⋊Dic61—44no—
134#11758198—24no—
135C4⋊Dic61—22no—
136C4×Dic61—22no—
137C4×Dic61—22no—
138C4×Dic61—22no—
139C4×Dic61—41no—
140C4×Dic61—41no—
141C23×C61—22no—
142C23×C61—42no—
143C23×C61—42no—
144C23×C61—41no—
145C23×C61—41no—
146C23×C61C2×C22⋊C411yescharacteristic
147C22×D61—41no—
148C22×D61—41no—
149C22×D61#12112yes—
150C22×D61#12111yescharacteristic
151C22×D61#12112yes—
152C22×D61C22⋊Q811yescharacteristic
153C2×#6923—44no—
154C2×#6923—82no—
155C2×#6923—82no—
156D4×C61—24no—
157D4×C61—42no—
158C2×C4×C61—22no—
159C2×C4×C61—22no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—42no—
163C2×C4×C61C2×C4⋊C411yescharacteristic
164C2×C4×C61#11711yescharacteristic
165C2×C4×C61C4×D412yes—
166C2×C4×C61C4×D412yes—
167C22⋊D61—44no—
168C22⋊D61—44no—
169C2×Dic61—22no—
170C2×Dic61—22no—
171C2×Dic61—22no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—42no—
177C2×Dic61—42no—
178C2×Dic61—42no—
179C2×Dic61—42no—
180C2×Dic61—42no—
181C2×Dic61#12011yescharacteristic
182C2×Dic61#12111yescharacteristic
183C2×Dic61C22⋊Q811yescharacteristic
184C2×Dic61#12311yescharacteristic
185C2×Dic61#12411yescharacteristic
186C2×Dic61#12711yescharacteristic
187C4×D61—48no—
188C4×D61#12012yes—
189C4×D61#12112yes—
190C4×D61C22⋊Q812yes—
191C4×D61C22⋊Q812yes—
192C4×D61#12312yes—
193C4×D61#12312yes—
194C4×D61#12412yes—
195C4×D61#12612yes—
196Dic122—24no—
197Dic122—42no—
198#92420—44no—
199#11056—611nomaximal, Sylow
200C22×C61—21no—
201C22×C61—21no—
202C22×C61—44no—
203C22×C61—42no—
204C22×C61—82no—
205C22×C61—81no—
206C22×C61—81no—
207C22×C61#38011yescharacteristic
208C22×C61#38611yescharacteristic
209C22×C61#39011yescharacteristic
210C2×D61—22no—
211C2×D61—22no—
212C2×D61—42no—
213C2×D61—41no—
214C2×D61—41no—
215C2×D61#39412yes—
216C2×D61#39612yes—
217#6923—84no—
218C4×C61—42no—
219C4×C61—42no—
220C4×C61#38512yes—
221C4×C61#38812yes—
222Dic61—42no—
223Dic61—42no—
224Dic61—42no—
225Dic61#39211yescharacteristic
226Dic61#39311yescharacteristic
227Dic61#39711yescharacteristic
228Dic61#39911yescharacteristic
229#2905—611no—
230C2×#421—612no—
231#2297—611no—
232#1740—611no—
233C2×#339—612no—
234C2×C61—21no—
235C2×C61—21no—
236C2×C61—82no—
237C2×C61#143911yescharacteristic
238C2×C61#188411yescharacteristic
239C2×C61#188411yescharacteristic
240D61—22no—
241D61—22no—
242C22×#41—611no—
243C22×M16—612no—
244C2×#117—611no—
245C2×#117—612no—
246C22×C42—611no—
247#424—1224no—
248#423—1222no—
249#421—1224no—
250#421—1224no—
251C2×#104—1224no—
252#391—611no—
253#391—611no—
254#390—611no—
255#390#692311yescharacteristic, complemented
256#386—1222no—
257C4×C22⋊C4—1222no—
258#342—1222no—
259#339—1224no—
260C61#1105611yescharacteristic, complemented, Sylow
261C2×#41—612no—
262C2×#41—612no—
263C2×#41—1221no—
264C2×#41—1221no—
265C2×#41—1222no—
266C2×#41—1222no—
267C2×#41—1222no—
268C2×#41—1222no—
269C22×Q8—611no—
270C22×D4—1221no—
271C22×D4C2×#692311yescharacteristic
272C23×C4—611no—
273C23×C4—1221no—
274C23×C4—1221no—
275C2×M16—614no—
276C2×M16—1222no—
277C2×M16—1222no—
278C2×M16—1222no—
279C2×M16—1222no—
280C2×M16—1222no—
281C22×C8—1222no—
282#117—614no—
283#117—1222no—
284#117—1222no—
285#117—1222no—
286#117—1222no—
287#117—1222no—
288C2×C4⋊C4—611no—
289C2×C4⋊C4—1222no—
290C2×C4⋊C4C2×#692311yescharacteristic
291C2×C22⋊C4—22no—
292C2×C22⋊C4—612no—
293C2×C22⋊C4—1222no—
294C2×C22⋊C4—1222no—
295C2×C42—612no—
296C2×C42—611no—
297C2×C42—1222no—
298C2×C42—1222no—
299C2×C42—1222no—
300C2×C42—1221no—
301C2×C42C2×#692311yescharacteristic
302C4⋊C8—1224no—
303C4⋊C8—1224no—
304#104—12216no—
305#95—1222no—
306#95—1222no—
307C24—21no—
308C24—611no—
309#41—1224no—
310#41—1224no—
311#41—1224no—
312#41—1224no—
313#41—2442no—
314#41—2442no—
315#41—2442no—
316#41—2442no—
317C2×Q8—612no—
318C2×Q8—1221no—
319C2×Q8—1222no—
320C2×Q8—1222no—
321C2×D4—21no—
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—1222no—
325C2×D4—1222no—
326C2×D4—2442no—
327C2×D4—2442no—
328C2×D4C4⋊#692312yes—
329C22×C4—21no—
330C22×C4—611no—
331C22×C4—611no—
332C22×C4—611no—
333C22×C4—611no—
334C22×C4—611no—
335C22×C4—612no—
336C22×C4—612no—
337C22×C4—612no—
338C22×C4—612no—
339C22×C4—612no—
340C22×C4—1222no—
341C22×C4—1222no—
342C22×C4—1221no—
343C22×C4—1221no—
344C22×C4—2442no—
345C22×C4—2442no—
346C22×C4—2442no—
347C22×C4—2441no—
348C22×C4—2441no—
349C22×C4—2441no—
350C22×C4—2441no—
351C22×C4—2442no—
352C22×C4C22⋊#692312yes—
353C22×C4C22×#692311yescharacteristic
354M16—1224no—
355M16—1224no—
356M16—2442no—
357M16—2442no—
358C2×C8—1224no—
359C2×C8—2442no—
360C2×C8—2442no—
361C4⋊C4—22no—
362C4⋊C4—1224no—
363C4⋊C4—1222no—
364C4⋊C4—2442no—
365C22⋊C4—44no—
366C22⋊C4—1224no—
367C22⋊C4—1224no—
368C22⋊C4—2444no—
369C22⋊C4—2442no—
370C42—22no—
371C42—1222no—
372C42—1222no—
373C42—1224no—
374C42—1222no—
375C42—2441no—
376C42—2441no—
377C42—2442no—
378C23—22no—
379C23—42no—
380C23—42no—
381C23—41no—
382C23—41no—
383C23—612no—
384C23—611no—
385C23—611no—
386C23—612no—
387C23—2441no—
388C23—2441no—
389C23C2×C22⋊#692311yescharacteristic
390Q8—1224no—
391Q8—2442no—
392D4—24no—
393D4—42no—
394D4—2444no—
395D4—2444no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—611no—
402C2×C4—611no—
403C2×C4—611no—
404C2×C4—611no—
405C2×C4—611no—
406C2×C4—611no—
407C2×C4—612no—
408C2×C4—612no—
409C2×C4—612no—
410C2×C4—612no—
411C2×C4—612no—
412C2×C4—612no—
413C2×C4—612no—
414C2×C4—612no—
415C2×C4—1222no—
416C2×C4—1222no—
417C2×C4—1222no—
418C2×C4—4882no—
419C2×C4—4882no—
420C2×C4—2448no—
421C2×C4—2442no—
422C2×C4—2442no—
423C2×C4—2442no—
424C2×C4—2442no—
425C2×C4—2444no—
426C2×C4—2441no—
427C2×C4—2441no—
428C2×C4—2441no—
429C2×C4—2441no—
430C2×C4—2442no—
431C2×C4C2×C4⋊#692311yescharacteristic
432C2×C4#1451985611yescharacteristic
433C2×C4D4×#692312yes—
434C2×C4D4×#692312yes—
435C8—2444no—
436C22—21no—
437C22—21no—
438C22—44no—
439C22—42no—
440C22—82no—
441C22—81no—
442C22—81no—
443C22—612no—
444C22—612no—
445C22—1222no—
446C22—1222no—
447C22—2442no—
448C22—2441no—
449C22—2441no—
450C22#1684070411yescharacteristic
451C22#1684071011yescharacteristic
452C22#1684071411yescharacteristic
453C4—42no—
454C4—42no—
455C4—611no—
456C4—611no—
457C4—611no—
458C4—611no—
459C4—4884no—
460C4—2442no—
461C4—2442no—
462C4—2442no—
463C4#1684070912yes—
464C4#1684071212yes—
465C2—21no—
466C2—21no—
467C2—82no—
468C2—1222no—
469C2—1222no—
470C2#2146100211yescharacteristic
471C2#2146182211yescharacteristic
472C2#2146182311yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#390C4
socleC22×C61#386
prime radicalC22×#11758224C22
cosocleC22×C4×D61C23
hypercenter#390#6923
hypocenterC61#11056
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #21462463C2semidirect
3. #21461519C2semidirect
4. C2×#16840633C2semidirect
18. #16839668C4semidirect
19. #16839667C4semidirect
20. #16839665C4semidirect
23. C61×#390C4semidirect
255. #390#6923semidirect
260. C61#11056semidirect

Maximal subgroups

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

subgroupindex
#214624632
C2×#168407602
#214615192
C2×#168406332
#214483062
#1105661