Finite Group Databasebeta

← #30603307

Subgroups — #30603307

Order 15616.

866 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519847C211yesmaximal, characteristic, complemented
2C2×#16840759C212yesmaximal
3C2×#16840645C212yesmaximal, complemented
4#21461505C211yesmaximal, characteristic, complemented
5#408×D61C211yesmaximal, characteristic
6C22×#11758213C2212yes—
7C2×#14519856C2212yes—
8C2×#14519847—22no—
9C2×#14519847—24no—
10#16840759—24no—
11#16840759—24no—
12C2×#14519842—22no—
13C2×#14519841—22no—
14#16840645—24no—
15#16840636—22no—
16C2×#41×D61C2211yescharacteristic
17C2×M16×D61C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16839730C411yescharacteristic, complemented
20#16839729C411yescharacteristic, complemented
21#16839728C411yescharacteristic, complemented
22#16839727—22no—
23C22⋊C8×D61—22no—
24C61×#408C411yescharacteristic, complemented
25C2×#11758213—22no—
26C2×#11758213—22no—
27C2×#11758213—22no—
28C2×#11758213—22no—
29C2×#11758213—22no—
30C2×#11758213D414yes—
31C22×#92420—22no—
32#14519856—22no—
33#14519856—22no—
34#14519856—22no—
35#14519856D414yes—
36C2×C4⋊#6923—22no—
37C2×C22⋊#6923—22no—
38C2×C4×#6923—22no—
39#14519847—28no—
40#14519842—28no—
41#14519841—28no—
42C2×#11758226D411yescharacteristic
43C2×#11758222—21no—
44C2×#11758222C2×C411yescharacteristic
45C2×#11758224—21no—
46C2×#11758224D411yescharacteristic
47#41×D61—22no—
48#41×D61—22no—
49#41×D61—22no—
50#41×D61—22no—
51C2×Q8×D61Q811yescharacteristic
52C2×D4×D61—21no—
53C2×D4×D61Q811yescharacteristic
54C22×C4×D61—21no—
55C22×C4×D61C2311yescharacteristic
56C2×#11758194C2×C411yescharacteristic
57C2×#11758189—21no—
58M16×D61—22no—
59M16×D61—22no—
60C22×#92418C2×C411yescharacteristic
61C2×C8×D61—22no—
62C2×C8×D61—22no—
63C2×C8×D61—21no—
64C2×C8×D61D412yes—
65C2×C8×D61D412yes—
66C22⋊#92418—22no—
67#14519689—22no—
68#14519689—22no—
69C2×#41×C61C2×C411yescharacteristic
70C2×M16×C61C2×C411yescharacteristic
71C22×C8×C61C2×C411yescharacteristic
72C22⋊C8×C61—22no—
73C23×D61—21no—
74C23×D61#4111yescharacteristic
75C22×#6923—42no—
76#41×C61—22no—
77#41×C61—22no—
78C2×Q8×C61C4⋊C411yescharacteristic
79C2×D4×C61—21no—
80C2×D4×C61C4⋊C411yescharacteristic
81C22×C4×C61—21no—
82C22×C4×C61C22×C411yescharacteristic
83C2×C22⋊D61—21no—
84C2×C22⋊D61—21no—
85C2×C22⋊D61—21no—
86C22×Dic61—21no—
87C22×Dic61#4111yescharacteristic
88#11758226—22no—
89#11758226—22no—
90Q8×D61—22no—
91Q8×D61—22no—
92#11758224—22no—
93#11758224—22no—
94#11758224—42no—
95#11758224—42no—
96D4×D61—22no—
97D4×D61—22no—
98D4×D61—42no—
99D4×D61—42no—
100#11758222—22no—
101#11758222—22no—
102#11758222—42no—
103#11758222—42no—
104C2×D244—21no—
105C2×D244C4⋊C411yescharacteristic
106C2×C4×D61—21no—
107C2×C4×D61—21no—
108C2×C4×D61—21no—
109C2×C4×D61—41no—
110C2×C4×D61—41no—
111C2×C4×D61—41no—
112C2×C4×D61—41no—
113C2×C4×D61C2×D412yes—
114C2×C4×D61C2×D411yescharacteristic
115C2×C4×D61C2×D412yes—
116C2×C4×D61C2×D411yescharacteristic
117C2×C4×D61C2×D411yescharacteristic
118C2×C4×D61C2×Q811yescharacteristic
119C2×C4×D61#4112yes—
120C2×C4×D61#4112yes—
121C2×Dic122—21no—
122C2×Dic122C4⋊C411yescharacteristic
123C22⋊#6923—24no—
124C22⋊#6923—42no—
125C2×#92420—24no—
126C2×#92420—42no—
127C2×#92420—42no—
128C4⋊#6923—24no—
129C4⋊#6923—42no—
130C4×#6923—24no—
131C4×#6923—42no—
132#11758213—24no—
133#11758213—24no—
134#11758213—42no—
135#11758213—42no—
136M16×C61—22no—
137C2×C8×C61—22no—
138C2×C8×C61—21no—
139C2×C8×C61C22⋊C412yes—
140#11758194—22no—
141C2×#92418—22no—
142C2×#92418—21no—
143C2×#92418C22⋊C412yes—
144#11758189—42no—
145C8×D61—22no—
146C8×D61—24no—
147C8×D61—22no—
148C8×D61—41no—
149C8×D61—41no—
150C23×C61—21no—
151C23×C61#11711yescharacteristic
152C22×D61—21no—
153C22×D61—42no—
154C22×D61—44no—
155C22×D61—41no—
156C22×D61—41no—
157C22×D61#12111yescharacteristic
158C22×D61C22⋊Q811yescharacteristic
159C22×D61#12312yes—
160C22×D61#12412yes—
161C2×#6923—44no—
162C2×#6923—84no—
163Q8×C61—22no—
164D4×C61—22no—
165D4×C61—42no—
166C2×C4×C61—21no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61C2×C22⋊C411yescharacteristic
170C2×C4×C61C2×C4⋊C411yescharacteristic
171C2×C4×C61C4×D412yes—
172C2×C4×C61C4×D412yes—
173C22⋊D61—42no—
174C22⋊D61—42no—
175C22⋊D61—42no—
176C2×Dic61—21no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61#12112yes—
180C2×Dic61#12111yescharacteristic
181C2×Dic61C22⋊Q811yescharacteristic
182C2×Dic61#12612yes—
183D244—22no—
184D244—42no—
185C4×D61—41no—
186C4×D61—41no—
187C4×D61—41no—
188C4×D61—41no—
189C4×D61—41no—
190C4×D61—41no—
191C4×D61#12012yes—
192C4×D61#12011yescharacteristic
193C4×D61#12112yes—
194C4×D61#12112yes—
195C4×D61C22⋊Q812yes—
196C4×D61C22⋊Q812yes—
197C4×D61#12312yes—
198C4×D61#12311yescharacteristic
199C4×D61#12411yescharacteristic
200C4×D61#12711yescharacteristic
201Dic122—22no—
202Dic122—42no—
203#92420—44no—
204C8×C61—22no—
205C8×C61—41no—
206#92418—22no—
207#92418—41no—
208#11108—611nomaximal, Sylow
209C22×C61—22no—
210C22×C61—42no—
211C22×C61—41no—
212C22×C61#38011yescharacteristic
213C22×C61#38812yes—
214C2×D61—22no—
215C2×D61—22no—
216C2×D61—42no—
217C2×D61—42no—
218C2×D61—42no—
219C2×D61—41no—
220C2×D61—82no—
221C2×D61—82no—
222C2×D61#39311yescharacteristic
223C2×D61#39412yes—
224C2×D61#39911yescharacteristic
225#6923—84no—
226C4×C61—41no—
227C4×C61#38512yes—
228C4×C61#38611yescharacteristic
229C4×C61#39011yescharacteristic
230Dic61—41no—
231Dic61#39211yescharacteristic
232Dic61#39612yes—
233Dic61#39711yescharacteristic
234C22×#108—611no—
235C2×#421—612no—
236C2×#408—611no—
237C2×#344—612no—
238#1735—611no—
239C2×C61—22no—
240C2×C61—81no—
241C2×C61#143911yescharacteristic
242C2×C61#181412yes—
243D61—22no—
244D61—21no—
245D61—21no—
246D61—81no—
247C22×#41—611no—
248C22×M16—612no—
249C22×M16—611no—
250C23×C8—611no—
251C2×#117—612no—
252C2×#108—1222no—
253C2×#108—1224no—
254#421—1224no—
255#421—1224no—
256C2×#104—1222no—
257C2×#104—1222no—
258#408—611no—
259#408—611no—
260#408—611no—
261#408—1222no—
262#408#692311yescharacteristic, complemented
263C2×C22⋊C8—1222no—
264#344—1224no—
265#340—1222no—
266C61#1110811yescharacteristic, complemented, Sylow
267C2×#41—611no—
268C2×#41—611no—
269C2×#41—611no—
270C2×#41—1221no—
271C2×#41—1221no—
272C2×#41—1222no—
273C2×#41—1222no—
274C2×#41—1222no—
275C2×#41—1222no—
276C2×#41C2×#692311yescharacteristic
277C22×Q8—611no—
278C22×D4—611no—
279C22×D4—1221no—
280C23×C4—611no—
281C23×C4—1221no—
282C2×M16—614no—
283C2×M16—611no—
284C2×M16—1221no—
285C2×M16—1222no—
286C2×M16—1222no—
287C2×M16—1222no—
288C2×M16—1222no—
289C2×M16—1222no—
290C2×M16—1222no—
291C2×M16—1222no—
292C2×M16C2×#692311yescharacteristic
293C22×C8—611no—
294C22×C8—612no—
295C22×C8—612no—
296C22×C8—1222no—
297C22×C8—1222no—
298C22×C8—1221no—
299C22×C8—1222no—
300C22×C8C2×#692311yescharacteristic
301#117—614no—
302#117—1222no—
303#117—1222no—
304#117—1222no—
305C2×C4⋊C4—1222no—
306C2×C22⋊C4—1222no—
307C2×C42—1222no—
308#108—1228no—
309#104—1228no—
310#104—1228no—
311C22⋊C8—22no—
312C22⋊C8—1222no—
313C22⋊C8—1222no—
314C22⋊C8—1222no—
315C24—611no—
316C24—1221no—
317#41—22no—
318#41—22no—
319#41—1222no—
320#41—1222no—
321#41—1222no—
322#41—1222no—
323#41—1222no—
324#41—1222no—
325#41—2442no—
326#41—2442no—
327#41—2442no—
328#41—2442no—
329C2×Q8—611no—
330C2×Q8—1221no—
331C2×Q8—1222no—
332C2×Q8—1222no—
333C2×Q8C4⋊#692311yescharacteristic
334C2×D4—21no—
335C2×D4—611no—
336C2×D4—1221no—
337C2×D4—1222no—
338C2×D4—1222no—
339C2×D4—1221no—
340C2×D4—1221no—
341C2×D4—1221no—
342C2×D4—2442no—
343C2×D4—2442no—
344C2×D4C4⋊#692311yescharacteristic
345C22×C4—21no—
346C22×C4—611no—
347C22×C4—611no—
348C22×C4—611no—
349C22×C4—611no—
350C22×C4—611no—
351C22×C4—612no—
352C22×C4—612no—
353C22×C4—612no—
354C22×C4—612no—
355C22×C4—1221no—
356C22×C4—1221no—
357C22×C4—1221no—
358C22×C4—1221no—
359C22×C4—2441no—
360C22×C4—2441no—
361C22×C4—2441no—
362C22×C4—2441no—
363C22×C4—2442no—
364C22×C4C22×#692311yescharacteristic
365M16—22no—
366M16—1224no—
367M16—1224no—
368M16—1222no—
369M16—2442no—
370M16—2442no—
371M16—2442no—
372C2×C8—22no—
373C2×C8—21no—
374C2×C8—612no—
375C2×C8—1222no—
376C2×C8—1224no—
377C2×C8—1222no—
378C2×C8—1222no—
379C2×C8—1224no—
380C2×C8—1221no—
381C2×C8—2441no—
382C2×C8—2441no—
383C2×C8—2442no—
384C2×C8—2442no—
385C2×C8C22⋊#692312yes—
386C4⋊C4—1224no—
387C4⋊C4—2442no—
388C22⋊C4—1224no—
389C22⋊C4—2442no—
390C42—1224no—
391C42—2442no—
392C23—21no—
393C23—611no—
394C23—611no—
395C23—612no—
396C23—612no—
397C23—1221no—
398C23—2442no—
399C23—2441no—
400C23—2441no—
401C23—2444no—
402C23#1451985611yescharacteristic
403Q8—22no—
404Q8—1222no—
405Q8—2442no—
406D4—22no—
407D4—42no—
408D4—1222no—
409D4—2442no—
410D4—2442no—
411D4—2442no—
412D4—2442no—
413C2×C4—21no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—611no—
417C2×C4—611no—
418C2×C4—612no—
419C2×C4—612no—
420C2×C4—612no—
421C2×C4—612no—
422C2×C4—612no—
423C2×C4—612no—
424C2×C4—611no—
425C2×C4—612no—
426C2×C4—611no—
427C2×C4—612no—
428C2×C4—611no—
429C2×C4—611no—
430C2×C4—1221no—
431C2×C4—4884no—
432C2×C4—2441no—
433C2×C4—2441no—
434C2×C4—2441no—
435C2×C4—2441no—
436C2×C4—2441no—
437C2×C4—2441no—
438C2×C4—2444no—
439C2×C4—2441no—
440C2×C4—2441no—
441C2×C4C2×C22⋊#692311yescharacteristic
442C2×C4C2×C4⋊#692311yescharacteristic
443C2×C4D4×#692312yes—
444C2×C4D4×#692312yes—
445C8—22no—
446C8—41no—
447C8—1222no—
448C8—2444no—
449C8—2441no—
450C22—22no—
451C22—41no—
452C22—42no—
453C22—612no—
454C22—611no—
455C22—611no—
456C22—1222no—
457C22—1222no—
458C22—4882no—
459C22—4882no—
460C22—2442no—
461C22—2442no—
462C22—2441no—
463C22—2442no—
464C22#1684070411yescharacteristic
465C22#1684071212yes—
466C4—41no—
467C4—611no—
468C4—612no—
469C4—611no—
470C4—4884no—
471C4—2441no—
472C4#1684070912yes—
473C4#1684071011yescharacteristic
474C4#1684071411yescharacteristic
475C2—22no—
476C2—81no—
477C2—1222no—
478C2—1221no—
479C2—1221no—
480C2—4881no—
481C2#2146100211yescharacteristic
482C2#2146170512yes—
subgroupG/H
centerC22#16840704
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#408C4
socleC22×C61#380
prime radicalC2×#41×D61C22
cosocleC22×C4×D61C23
hypercenter#408#6923
hypocenterC61#11108
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
1. C22×#14519847C2semidirect
3. C2×#16840645C2semidirect
4. #21461505C2semidirect
19. #16839730C4semidirect
20. #16839729C4semidirect
21. #16839728C4semidirect
24. C61×#408C4semidirect
262. #408#6923semidirect
266. C61#11108semidirect

Maximal subgroups

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

subgroupindex
C22×#145198472
C2×#168407592
C2×#168406452
#214615052
#408×D612
#1110861