Finite Group Databasebeta

← #30603267

Subgroups — #30603267

Order 15616.

934 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840760C212yesmaximal
2#21462299C211yesmaximal, characteristic, complemented
3#21461522C211yesmaximal, characteristic, complemented
4C2×#16840629C212yesmaximal, complemented
5#21448409C211yesmaximal, characteristic
6C2×D61⋊M16C2212yes—
7C2×#14519856C2212yes—
8#16840760—24no—
9#16840760—24no—
10C2×#14519841—24no—
11#16840713—24no—
12#16840704—22no—
13#16840642—22no—
14#16840629—24no—
15C22×#11758224C2211yescharacteristic
16C2×#14519734C2211yescharacteristic
17C2×C4⋊C4×D61C2211yescharacteristic
18#16839668C411yescharacteristic, complemented
19#16839667C411yescharacteristic, complemented
20#16839665C411yescharacteristic, complemented
21#16839638—22no—
22#16839620—22no—
23C61×#390C411yescharacteristic, complemented
24C2×#11758213—22no—
25D61⋊M16—22no—
26D61⋊M16—22no—
27D61⋊M16—22no—
28D61⋊M16D414yes—
29C2×#11758217—22no—
30C2×D61⋊C8—22no—
31#14519856—22no—
32#14519856—22no—
33#14519856—22no—
34#14519856—22no—
35C2×C4⋊#6923—22no—
36C2×C4⋊#6923—24no—
37C2×C22⋊#6923—22no—
38C2×C4×#6923D414yes—
39#14519841—216no—
40(C2×#6923)⋊C4—24no—
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×D61D412yes—
53C22×C4×D61C2311yescharacteristic
54#14519734—22no—
55#14519734—22no—
56C2×C4⋊Dic61C2×C411yescharacteristic
57C2×#11758196—21no—
58C2×#11758196D412yes—
59C4⋊C4×D61—22no—
60C4⋊C4×D61—22no—
61C2×C22⋊Dic61—22no—
62C2×#11758198—21no—
63C2×C4×Dic61C2×C411yescharacteristic
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—24no—
73C2×D4×C61—21no—
74C2×D4×C61—22no—
75C2×D4×C61—22no—
76C2×D4×C61C4⋊C412yescomplemented
77C22×C4×C61—21no—
78C22×C4×C61C22⋊C412yes—
79C22×C4×C61C22×C411yescharacteristic
80C2×C22⋊D61—22no—
81C2×C22⋊D61—22no—
82C2×C22⋊D61—41no—
83C2×C22⋊D61—41no—
84C2×C22⋊D61—41no—
85C2×C22⋊D61—41no—
86C22×Dic61—21no—
87C22×Dic61—22no—
88C22×Dic61—22no—
89C22×Dic61—21no—
90C22×Dic61—42no—
91C22×Dic61—42no—
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—22no—
103C2×C4×D61—22no—
104C2×C4×D61—82no—
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⋊C412yescomplemented
117C22⋊#6923—42no—
118C22⋊#6923—42no—
119#11758217—24no—
120#11758217—42no—
121C2×#92420—42no—
122C4⋊#6923—42no—
123C4⋊#6923—42no—
124C4⋊#6923—84no—
125C4×#6923—24no—
126C4×#6923—24no—
127#11758213—24no—
128#11758213—42no—
129D61⋊C8—24no—
130D61⋊C8—42no—
131C4⋊C4×C61—22no—
132C22⋊C4×C61—82no—
133C42×C61—22no—
134C22⋊Dic61—82no—
135#11758198—41no—
136#11758198—41no—
137C4⋊Dic61—22no—
138#11758196—24no—
139#11758196—42no—
140C4×Dic61—22no—
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#12011yescharacteristic
150C22×D61#12111yescharacteristic
151C22×D61C22⋊Q811yescharacteristic
152C22×D61#12311yescharacteristic
153C22×D61#12411yescharacteristic
154C22×D61#12711yescharacteristic
155C2×#6923—44no—
156C2×#6923—44no—
157C2×#6923—44no—
158D4×C61—24no—
159D4×C61—42no—
160C2×C4×C61—22no—
161C2×C4×C61—42no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61C2×C4⋊C411yescharacteristic
166C2×C4×C61#11711yescharacteristic
167C2×C4×C61C4×D412yes—
168C2×C4×C61C4×D412yes—
169C22⋊D61—42no—
170C22⋊D61—42no—
171C22⋊D61—42no—
172C22⋊D61—42no—
173C2×Dic61—22no—
174C2×Dic61—22no—
175C2×Dic61—41no—
176C2×Dic61—41no—
177C2×Dic61—44no—
178C2×Dic61—44no—
179C2×Dic61—42no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61#12111yescharacteristic
184C2×Dic61#12112yes—
185C2×Dic61#12112yes—
186C2×Dic61C22⋊Q811yescharacteristic
187C4×D61—44no—
188C4×D61—82no—
189C4×D61#12012yes—
190C4×D61#12112yes—
191C4×D61C22⋊Q812yes—
192C4×D61C22⋊Q812yes—
193C4×D61#12312yes—
194C4×D61#12312yes—
195C4×D61#12412yes—
196C4×D61#12612yes—
197Dic122—24no—
198Dic122—42no—
199#92420—44no—
200#11072—611nomaximal, Sylow
201C22×C61—21no—
202C22×C61—21no—
203C22×C61—44no—
204C22×C61—42no—
205C22×C61—82no—
206C22×C61—81no—
207C22×C61—81no—
208C22×C61#38011yescharacteristic
209C22×C61#38611yescharacteristic
210C22×C61#39011yescharacteristic
211C2×D61—21no—
212C2×D61—21no—
213C2×D61—21no—
214C2×D61—21no—
215C2×D61—41no—
216C2×D61—41no—
217C2×D61—41no—
218C2×D61—41no—
219C2×D61#39211yescharacteristic
220C2×D61#39311yescharacteristic
221C2×D61#39711yescharacteristic
222C2×D61#39911yescharacteristic
223#6923—84no—
224C4×C61—42no—
225C4×C61—81no—
226C4×C61#38512yes—
227C4×C61#38812yes—
228Dic61—42no—
229Dic61—42no—
230Dic61—81no—
231Dic61#39412yes—
232Dic61#39612yes—
233C2×#421—612no—
234#2316—611no—
235#2311—611no—
236C2×#343—611no—
237C2×H(3,ℤ/4)—612no—
238C2×C61—21no—
239C2×C61—21no—
240C2×C61—82no—
241C2×C61#143911yescharacteristic
242C2×C61#191111yescharacteristic
243C2×C61#191211yescharacteristic
244D61—21no—
245D61—21no—
246D61—21no—
247D61—21no—
248C22×#41—611no—
249C22×M16—612no—
250C2×#117—612no—
251C2×#117—611no—
252C22×C4⋊C4—611no—
253#421—1224no—
254#421—1224no—
255C2×#104—1224no—
256#391—611no—
257#391—611no—
258#390—611no—
259#390#692311yescharacteristic, complemented
260#389—1224no—
261#386—1222no—
262#380—1222no—
263#380—1222no—
264#343—1222no—
265H(3,ℤ/4)—1224no—
266C61#1107211yescharacteristic, complemented, Sylow
267C2×#41—612no—
268C2×#41—612no—
269C2×#41—1221no—
270C2×#41—1221no—
271C2×#41—1222no—
272C2×#41—1222no—
273C2×#41—1222no—
274C2×#41—1222no—
275C22×Q8—611no—
276C22×D4—1221no—
277C22×D4C2×#692311yescharacteristic
278C23×C4—611no—
279C23×C4—612no—
280C23×C4—1221no—
281C2×M16—614no—
282C2×M16—1222no—
283C2×M16—1222no—
284C2×M16—1222no—
285C2×M16—1222no—
286C2×M16—1222no—
287C22×C8—1222no—
288#117—1222no—
289#117—1222no—
290#117—1222no—
291#117—1222no—
292#117—1222no—
293#117—1222no—
294C2×C4⋊C4—612no—
295C2×C4⋊C4—611no—
296C2×C4⋊C4—1222no—
297C2×C4⋊C4—1222no—
298C2×C4⋊C4—1224no—
299C2×C4⋊C4—1221no—
300C2×C4⋊C4—1222no—
301C2×C4⋊C4C2×#692311yescharacteristic
302C2×C22⋊C4—22no—
303C2×C22⋊C4—1222no—
304C2×C22⋊C4—1221no—
305C2×C22⋊C4—1222no—
306C2×C42—614no—
307C2×C42—611no—
308C2×C42C2×#692311yescharacteristic
309#104—12216no—
310#95—1222no—
311#95—1224no—
312#95—1222no—
313C24—21no—
314C24—611no—
315#41—1224no—
316#41—1224no—
317#41—1224no—
318#41—1224no—
319#41—2442no—
320#41—2442no—
321#41—2442no—
322#41—2442no—
323C2×Q8—612no—
324C2×Q8—1221no—
325C2×Q8—1222no—
326C2×Q8—1222no—
327C2×D4—21no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4—1222no—
331C2×D4—1222no—
332C2×D4—2441no—
333C2×D4—2441no—
334C2×D4—2441no—
335C2×D4—2441no—
336C2×D4C4⋊#692312yescomplemented
337C22×C4—21no—
338C22×C4—611no—
339C22×C4—611no—
340C22×C4—611no—
341C22×C4—611no—
342C22×C4—611no—
343C22×C4—612no—
344C22×C4—612no—
345C22×C4—612no—
346C22×C4—612no—
347C22×C4—612no—
348C22×C4—1222no—
349C22×C4—1222no—
350C22×C4—1222no—
351C22×C4—1222no—
352C22×C4—1221no—
353C22×C4—1224no—
354C22×C4—1221no—
355C22×C4—4882no—
356C22×C4—2442no—
357C22×C4—2442no—
358C22×C4C22⋊#692312yes—
359C22×C4C22×#692311yescharacteristic
360M16—1224no—
361M16—1224no—
362M16—2442no—
363M16—2442no—
364C2×C8—1224no—
365C2×C8—2442no—
366C2×C8—2442no—
367C4⋊C4—22no—
368C4⋊C4—1224no—
369C4⋊C4—1222no—
370C4⋊C4—4884no—
371C4⋊C4—2442no—
372C4⋊C4—2442no—
373C4⋊C4—2442no—
374C22⋊C4—82no—
375C22⋊C4—4882no—
376C22⋊C4—2441no—
377C22⋊C4—2441no—
378C22⋊C4—2442no—
379C22⋊C4—2442no—
380C42—22no—
381C42—1224no—
382C42—1224no—
383C42—1222no—
384C23—22no—
385C23—42no—
386C23—42no—
387C23—41no—
388C23—41no—
389C23—611no—
390C23—611no—
391C23—611no—
392C23—611no—
393C23—611no—
394C23—611no—
395C23—2441no—
396C23—2441no—
397C23C2×C22⋊#692311yescharacteristic
398Q8—1224no—
399Q8—2442no—
400D4—24no—
401D4—42no—
402D4—2442no—
403D4—2442no—
404D4—2442no—
405D4—2442no—
406C2×C4—22no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—611no—
412C2×C4—611no—
413C2×C4—612no—
414C2×C4—612no—
415C2×C4—612no—
416C2×C4—612no—
417C2×C4—612no—
418C2×C4—612no—
419C2×C4—612no—
420C2×C4—612no—
421C2×C4—612no—
422C2×C4—612no—
423C2×C4—1222no—
424C2×C4—1222no—
425C2×C4—4882no—
426C2×C4—2444no—
427C2×C4—2444no—
428C2×C4—2444no—
429C2×C4—2441no—
430C2×C4—2441no—
431C2×C4—2444no—
432C2×C4—2444no—
433C2×C4—2444no—
434C2×C4—2441no—
435C2×C4—2441no—
436C2×C4—2441no—
437C2×C4—2442no—
438C2×C4C2×C4⋊#692311yescharacteristic
439C2×C4#1451985611yescharacteristic
440C2×C4D4×#692312yes—
441C2×C4D4×#692312yes—
442C8—2444no—
443C22—21no—
444C22—21no—
445C22—44no—
446C22—42no—
447C22—82no—
448C22—81no—
449C22—81no—
450C22—611no—
451C22—611no—
452C22—611no—
453C22—611no—
454C22—1221no—
455C22—1221no—
456C22—1221no—
457C22—1221no—
458C22—2441no—
459C22—2441no—
460C22—2441no—
461C22—2441no—
462C22#1684070411yescharacteristic
463C22#1684071011yescharacteristic
464C22#1684071411yescharacteristic
465C4—42no—
466C4—81no—
467C4—612no—
468C4—612no—
469C4—4881no—
470C4—4884no—
471C4—2442no—
472C4—2442no—
473C4#1684070912yes—
474C4#1684071212yes—
475C2—21no—
476C2—21no—
477C2—82no—
478C2—1221no—
479C2—1221no—
480C2—1221no—
481C2—1221no—
482C2#2146100211yescharacteristic
483C2#2146186511yescharacteristic
484C2#2146186711yescharacteristic
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#11072
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
2. #21462299C2semidirect
3. #21461522C2semidirect
4. C2×#16840629C2semidirect
18. #16839668C4semidirect
19. #16839667C4semidirect
20. #16839665C4semidirect
23. C61×#390C4semidirect
76. C2×D4×C61C4⋊C4semidirect
116. C2×Dic122C4⋊C4semidirect
259. #390#6923semidirect
266. C61#11072semidirect
336. C2×D4C4⋊#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407602
#214622992
#214615222
C2×#168406292
#214484092
#1107261