Finite Group Databasebeta

← #29576258

Subgroups — #29576258

Order 15616.

570 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839963C211yesmaximal, characteristic
2C2×#16839889C211yesmaximal, characteristic, complemented
3#21446624C211yesmaximal, characteristic
4#21445821C211yesmaximal, characteristic, complemented
5C2×#16839505C211yesmaximal, characteristic
6#21443653C211yesmaximal, characteristic, complemented
7C61×#1296C211yesmaximal, characteristic, complemented
8C22×#11758190—21no—
9C2×#14519774C2211yescharacteristic
10C2×C4×Dic122C2211yescharacteristic
11#16839963—22no—
12#16839963C414yescomplemented
13#16839889—22no—
14#16839889—22no—
15C2×C4⋊#92418C2211yescharacteristic
16C2×#14519706—21no—
17C2×#14519700—21no—
18C2×#14519699—21no—
19C2×#14519697—21no—
20C2×#14519697—21no—
21C2×#14519687—21no—
22C2×C4×#92418C2211yescharacteristic
23#16839524—21no—
24#16839505—22no—
25C2×C4⋊C8×C61C2211yescharacteristic
26C2×C4⋊C8×C61C2211yescharacteristic
27C61×#384C2211yescharacteristic
28C22×Dic122D411yescharacteristic
29C22×D244—21no—
30C22×D244—21no—
31C22×D244—21no—
32C2×#11758190—24no—
33C2×#11758190—42no—
34C2×#11758190—42no—
35C22×#92418—21no—
36C22×#92418D411yescharacteristic
37C22×#92418D411yescharacteristic
38#14519774—21no—
39#14519774—21no—
40#14519774—21no—
41#14519774C2×C412yes—
42C4×Dic122—21no—
43C4×Dic122—21no—
44C4×Dic122C2×C412yes—
45C4×Dic122D412yes—
46C2×C4⋊Dic61D411yescharacteristic
47C2×#11758196—21no—
48C2×C4×Dic61—21no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51#14519706—24no—
52#14519700—42no—
53#14519699—24no—
54#14519697—42no—
55#14519697—42no—
56#14519687—24no—
57C4×#92418—21no—
58C4×#92418—21no—
59C22×C8×C61—21no—
60C22×C8×C61—21no—
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C42×C61C2311yescharacteristic
65C4⋊C8×C61—21no—
66C4⋊C8×C61—21no—
67C4⋊C8×C61C2×C412yes—
68C4⋊C8×C61D412yes—
69C23×D61—41no—
70C22×C4×C61—41no—
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61#4111yescharacteristic
74C22×Dic61—21no—
75C22×Dic61—21no—
76C2×D244—22no—
77C2×D244—22no—
78C2×D244—22no—
79C2×D244—41no—
80C2×D244—41no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244—41no—
86C2×D244—41no—
87C2×D244—41no—
88C2×D244—41no—
89C2×D244—41no—
90C2×D244—81no—
91C2×D244—81no—
92C2×Dic122—21no—
93C2×Dic122—21no—
94C2×Dic122—21no—
95C2×Dic122—21no—
96C2×Dic122—21no—
97C2×Dic122C22⋊C412yes—
98C2×C8×C61—22no—
99C2×C8×C61—22no—
100C2×C8×C61—41no—
101C2×C8×C61—41no—
102C2×C8×C61—41no—
103C2×C8×C61—41no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—41no—
106C4⋊C4×C61—41no—
107C4⋊C4×C61—41no—
108C4⋊C4×C61—81no—
109C42×C61C22×C411yescharacteristic
110C42×C61C2×D411yescharacteristic
111C42×C61C2×D411yescharacteristic
112C42×C61#4111yescharacteristic
113C4⋊Dic61—21no—
114C4⋊Dic61C22⋊C412yes—
115#11758196—22no—
116#11758196—22no—
117C4×Dic61—22no—
118C4×Dic61—22no—
119C2×#92418—21no—
120C2×#92418—21no—
121C2×#92418—21no—
122C2×#92418—21no—
123C2×#92418—21no—
124C2×#92418—41no—
125C2×#92418—41no—
126C2×#92418—41no—
127C2×#92418SD1612yescomplemented
128#11758190—48no—
129C23×C61#12111yescharacteristic
130C22×D61—42no—
131C22×D61—81no—
132C22×D61—81no—
133C22×D61—81no—
134C22×D61—81no—
135C22×D61—81no—
136C22×D61—81no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—81no—
140C2×C4×C61—81no—
141C2×C4×C61—81no—
142C2×C4×C61C2×C22⋊C411yescharacteristic
143C2×C4×C61C4×D411yescharacteristic
144C2×C4×C61C4×D411yescharacteristic
145C2×C4×C61#12011yescharacteristic
146C2×C4×C61#12111yescharacteristic
147C2×C4×C61#12311yescharacteristic
148C2×C4×C61C2×SD1611yescharacteristic
149C2×C4×C61#13511yescharacteristic
150C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C61#13711yescharacteristic
155C2×C4×C61#13711yescharacteristic
156C2×Dic61—22no—
157C2×Dic61—22no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162D244—42no—
163D244—42no—
164D244—42no—
165D244—42no—
166D244—82no—
167D244—82no—
168D244—81no—
169D244—81no—
170D244—81no—
171D244—81no—
172Dic122—22no—
173Dic122—22no—
174Dic122—41no—
175Dic122—41no—
176C8×C61—42no—
177C8×C61—42no—
178#92418—22no—
179#92418—41no—
180#92418—81no—
181#9230—611nomaximal, Sylow
182C22×C61#38611yescharacteristic
183C22×C61#46011yescharacteristic
184C22×C61#46411yescharacteristic
185C22×C61#46811yescharacteristic
186C22×C61#46911yescharacteristic
187C22×C61#47111yescharacteristic
188C22×C61#47211yescharacteristic
189C2×D61—82no—
190C2×D61—82no—
191C2×D61—82no—
192C2×D61—161no—
193C2×D61—161no—
194C2×D61—161no—
195C2×D61—161no—
196C4×C61—21no—
197C4×C61—21no—
198C4×C61—161no—
199C4×C61#41711yescharacteristic
200C4×C61#41811yescharacteristic
201C4×C61C4×SD1611yescharacteristic
202C4×C61#44011yescharacteristic
203C4×C61#44811yescharacteristic
204C4×C61#44911yescharacteristic
205C4×C61#46811yescharacteristic
206C4×C61#46911yescharacteristic
207Dic61—42no—
208Dic61—42no—
209C2×#460—611no—
210C2×#446—611no—
211#1957—611no—
212#1803—611no—
213C2×#331—611no—
214#1296D6111yescharacteristic, complemented
215#1277—611no—
216C2×C61#168611yescharacteristic
217C2×C61#168811yescharacteristic
218C2×C61#169811yescharacteristic
219C2×C61#170211yescharacteristic
220C2×C61#188011yescharacteristic
221C2×C61#189511yescharacteristic
222C2×C61#190711yescharacteristic
223D61—162no—
224C22×SD16—1221no—
225C2×#127—611no—
226C2×C4×Q8—611no—
227#460—614no—
228#460—1222no—
229#446—1222no—
230#446—1222no—
231C2×C4⋊C8—611no—
232C2×C4⋊C8—1221no—
233C2×C4⋊C8C2×D6111yescharacteristic
234C2×C4⋊C8C2×D6111yescharacteristic
235C2×#103—1221no—
236C2×#102—1221no—
237C2×#102—1221no—
238C2×#102—1221no—
239C2×#97—1221no—
240C2×C4×C8—611no—
241#384C2×D6111yescharacteristic
242#340—1221no—
243#331—1222no—
244C61#923011yescharacteristic, complemented, Sylow
245C22×Q8—611no—
246C22×D4—1221no—
247C22×D4—1221no—
248C22×D4—1221no—
249C2×SD16—1224no—
250C2×SD16—2442no—
251C2×SD16—2442no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—611no—
255C22×C8—611no—
256C22×C8—1221no—
257#127—612no—
258#127—1221no—
259#127—1221no—
260#127—1221no—
261C4×Q8—612no—
262C4×Q8—612no—
263C4×Q8—1221no—
264C4×Q8—1221no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—611no—
269C2×C4⋊C4—1221no—
270C2×C42—1221no—
271C2×C42C22×D6111yescharacteristic
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—1224no—
275C4⋊C8—1221no—
276C4⋊C8—1221no—
277C4⋊C8C4×D6112yes—
278C4⋊C8D24412yes—
279#103—2442no—
280#102—1224no—
281#102—2442no—
282#102—2442no—
283#97—1224no—
284C4×C8—1221no—
285C4×C8—1221no—
286C24—2441no—
287C2×Q8—612no—
288C2×Q8—1221no—
289C2×Q8—1221no—
290C2×Q8—1221no—
291C2×Q8—1221no—
292C2×Q8—1221no—
293C2×D4—1222no—
294C2×D4—1222no—
295C2×D4—1222no—
296C2×D4—4881no—
297C2×D4—4881no—
298C2×D4—2441no—
299C2×D4—2441no—
300C2×D4—2441no—
301C2×D4—2441no—
302C2×D4—2441no—
303C2×D4—2441no—
304C2×D4—2441no—
305C2×D4—2441no—
306C2×D4—2441no—
307C2×D4—2441no—
308C2×D4—2441no—
309C22×C4—41no—
310C22×C4—1221no—
311C22×C4—1221no—
312C22×C4#1175822211yescharacteristic
313C22×C4D4×D6111yescharacteristic
314C22×C4D4×D6111yescharacteristic
315SD16—2448no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—612no—
323C2×C8—1221no—
324C2×C8—1221no—
325C2×C8—1221no—
326C2×C8—1221no—
327C2×C8—1221no—
328C2×C8—2441no—
329C2×C8—2441no—
330C2×C8—2441no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—81no—
336C4⋊C4—612no—
337C4⋊C4—1222no—
338C4⋊C4—1221no—
339C4⋊C4—1222no—
340C42—1222no—
341C42—1222no—
342C42C2×C4×D6111yescharacteristic
343C42C2×D24411yescharacteristic
344C42D4×D6111yescharacteristic
345C42#1175822611yescharacteristic
346C23—4881no—
347C23—4881no—
348C23—4881no—
349C23—4881no—
350C23—4881no—
351C23—4881no—
352C23—2442no—
353C23#1451975011yescharacteristic
354Q8—1222no—
355Q8—1222no—
356Q8—2441no—
357Q8—2441no—
358D4—4882no—
359D4—4882no—
360D4—4881no—
361D4—4881no—
362D4—4881no—
363D4—4881no—
364D4—2442no—
365D4—2442no—
366D4—2442no—
367D4—2442no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—1222no—
374C2×C4—1222no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4C22⋊C4×D6111yescharacteristic
380C2×C4#1451973911yescharacteristic
381C2×C4C4×D24411yescharacteristic
382C2×C4#1451974711yescharacteristic
383C2×C4#1451975211yescharacteristic
384C2×C4#1451976211yescharacteristic
385C2×C4SD16×D6111yescharacteristic
386C2×C4#1451979811yescharacteristic
387C2×C4#1451980111yescharacteristic
388C2×C4#1451980111yescharacteristic
389C2×C4#1451980411yescharacteristic
390C2×C4#1451980411yescharacteristic
391C2×C4#1451980911yescharacteristic
392C2×C4#1451980911yescharacteristic
393C8—42no—
394C8—42no—
395C8—1222no—
396C8—4881no—
397C8—2441no—
398C22—9761no—
399C22—9761no—
400C22—9761no—
401C22—9761no—
402C22—4882no—
403C22—4882no—
404C22—4882no—
405C22#1683964011yescharacteristic
406C22#1683996111yescharacteristic
407C22#1683998711yescharacteristic
408C22#1684001111yescharacteristic
409C22#1684001411yescharacteristic
410C22#1684002811yescharacteristic
411C22#1684003111yescharacteristic
412C4—21no—
413C4—21no—
414C4—161no—
415C4—2442no—
416C4—2442no—
417C4#1683976211yescharacteristic
418C4#1683976511yescharacteristic
419C4#1683984911yescharacteristic
420C4#1683986111yescharacteristic
421C4#1683990211yescharacteristic
422C4#1683990811yescharacteristic
423C4#1684000911yescharacteristic
424C4#1684001611yescharacteristic
425C2—9762no—
426C2#2144529411yescharacteristic
427C2#2144530211yescharacteristic
428C2#2144536211yescharacteristic
429C2#2144539011yescharacteristic
430C2#2144617511yescharacteristic
431C2#2144625611yescharacteristic
432C2#2144632811yescharacteristic
subgroupG/H
centerC23#14519750
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1296C2
socleC23×C61#121
prime radicalC2×#14519774C22
cosocleC2×C42×C61C23
hypercenter#1296D61
hypocenterC61#9230
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. C2×#16839889C2semidirect
4. #21445821C2semidirect
6. #21443653C2semidirect
7. C61×#1296C2semidirect
12. #16839963C4semidirect
127. C2×#92418SD16semidirect
214. #1296D61semidirect
244. C61#9230semidirect

Maximal subgroups

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

subgroupindex
C2×#168399632
C2×#168398892
#214466242
#214458212
C2×#168395052
#214436532
C61×#12962
#923061