Finite Group Databasebeta

← #29576373

Subgroups — #29576373

Order 15616.

544 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839964C211yesmaximal, characteristic
2#21454554C211yesmaximal, characteristic
3#21446809C211yesmaximal, characteristic, complemented
4#21444245C211yesmaximal, characteristic
5#21443693C211yesmaximal, characteristic, complemented
6#21443668C211yesmaximal, characteristic, complemented
7C61×#1548C211yesmaximal, characteristic, complemented
8C22×#11758201C412yes—
9C2×M16×D61—21no—
10C2×C4×D244C2211yescharacteristic
11#16839964—21no—
12#16839964—21no—
13#16839964—21no—
14#16839964—21no—
15#16839839—21no—
16#16839832—22no—
17#16839827—21no—
18#16839786C2211yescharacteristic
19C2×C4⋊#92418C2211yescharacteristic
20C2×#14519701C412yes—
21#16839725—21no—
22C4×#11758194C2211yescharacteristic
23#16839531—21no—
24#16839531—21no—
25#16839491—21no—
26#16839491—21no—
27C2×C4⋊Q8×C61C2211yescharacteristic
28C61×#431C2211yescharacteristic
29C61×#423C2211yescharacteristic
30C61×#333—22no—
31C22×D244C2×C411yescharacteristic
32C22×C4×D61—21no—
33C2×#11758201—22no—
34C2×#11758201—22no—
35C2×#11758201—44no—
36C2×#11758194—21no—
37C2×#11758194D411yescharacteristic
38C2×#11758194D411yescharacteristic
39C2×#11758189—22no—
40M16×D61—42no—
41M16×D61—42no—
42C22×#92418C2×C412yes—
43C2×C8×D61—22no—
44C4×D244—21no—
45C4×D244—21no—
46C4×D244D411yescharacteristic
47C4×D244D411yescharacteristic
48C4×D244D411yescharacteristic
49C4×D244D411yescharacteristic
50C2×C4⋊Dic61C2×C411yescharacteristic
51C2×#11758198—21no—
52C4⋊#92418—21no—
53C4⋊#92418—21no—
54C4⋊#92418—21no—
55C4⋊#92418—21no—
56#14519701—22no—
57#14519701—22no—
58#14519689—22no—
59#14519689—22no—
60#14519688—21no—
61C4×#92418—21no—
62C22×Q8×C61C2×C412yes—
63C2×M16×C61—21no—
64C4⋊Q8×C61—21no—
65C4⋊Q8×C61—21no—
66C4⋊Q8×C61—21no—
67C4⋊Q8×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C42×C61C2311yescharacteristic
71C4⋊C8×C61—21no—
72C4⋊C8×C61—21no—
73C4⋊C8×C61D412yes—
74C22⋊C8×C61—21no—
75C4×C8×C61—21no—
76C23×D61—21no—
77C2×Q8×C61—22no—
78C2×Q8×C61—22no—
79C2×Q8×C61—42no—
80C2×Q8×C61—42no—
81C22×C4×C61—22no—
82C22×C4×C61C22×C411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61#4111yescharacteristic
85C22×Dic61—21no—
86C2×D244—22no—
87C2×D244—21no—
88C2×D244—41no—
89C2×D244C22⋊C411yescharacteristic
90C2×D244C22⋊C411yescharacteristic
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61—21no—
94C2×C4×D61—21no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97C2×C4×D61—41no—
98C2×C4×D61—41no—
99M16×C61—41no—
100M16×C61—41no—
101C2×C8×C61—22no—
102C2×C8×C61—41no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—41no—
106C4⋊C4×C61—41no—
107C42×C61C2×D411yescharacteristic
108C42×C61C2×D411yescharacteristic
109C42×C61C2×D411yescharacteristic
110C42×C61#4111yescharacteristic
111#11758201—44no—
112#11758201—44no—
113#11758198—21no—
114#11758198—21no—
115#11758198—21no—
116#11758198—21no—
117C4⋊Dic61—21no—
118C4⋊Dic61C22⋊C411yescharacteristic
119C4⋊Dic61C22⋊C411yescharacteristic
120#11758194—21no—
121#11758194—21no—
122#11758194—21no—
123#11758194—41no—
124#11758194—41no—
125#11758194SD1612yescomplemented
126C2×#92418—21no—
127C2×#92418—22no—
128C2×#92418—21no—
129C2×#92418—42no—
130C2×#92418—41no—
131#11758189—44no—
132C8×D61—44no—
133C23×C61C4×D411yescharacteristic
134C22×D61—21no—
135C22×D61—21no—
136C22×D61—42no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—81no—
140Q8×C61—42no—
141Q8×C61—42no—
142Q8×C61—82no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—41no—
146C2×C4×C61—42no—
147C2×C4×C61—82no—
148C2×C4×C61C2×C22⋊C411yescharacteristic
149C2×C4×C61C4×D411yescharacteristic
150C2×C4×C61#12011yescharacteristic
151C2×C4×C61#12111yescharacteristic
152C2×C4×C61#12111yescharacteristic
153C2×C4×C61#12311yescharacteristic
154C2×C4×C61C2×SD1611yescharacteristic
155C2×C4×C61#13511yescharacteristic
156C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C61#13711yescharacteristic
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162D244—21no—
163D244—21no—
164D244—21no—
165D244—42no—
166D244#10012yes—
167C4×D61—41no—
168C4×D61—41no—
169C4×D61—41no—
170C4×D61—41no—
171C4×D61—41no—
172C4×D61—41no—
173C4×D61—41no—
174C4×D61—41no—
175C8×C61—42no—
176C8×C61—81no—
177#92418—22no—
178#92418—42no—
179#92418—41no—
180#92418—81no—
181#9247—611nomaximal, Sylow
182C22×C61—21no—
183C22×C61—21no—
184C22×C61#38611yescharacteristic
185C22×C61C4×SD1611yescharacteristic
186C22×C61#44011yescharacteristic
187C2×D61—22no—
188C2×D61—41no—
189C2×D61—41no—
190C2×D61—41no—
191C2×D61—41no—
192C2×D61—41no—
193C2×D61—82no—
194C2×D61—82no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61—21no—
198C4×C61—82no—
199C4×C61C2×#10011yescharacteristic
200C4×C61#41311yescharacteristic
201C4×C61#45011yescharacteristic
202C4×C61#45211yescharacteristic
203C4×C61#46111yescharacteristic
204C4×C61#46311yescharacteristic
205Dic61—41no—
206Dic61—41no—
207C2×#461—611no—
208D4×M16—611no—
209#1997—611no—
210#1548D6111yescharacteristic, complemented
211#1486—611no—
212#1292—611no—
213#1283—611no—
214C2×C61—21no—
215C2×C61—21no—
216C2×C61#187711yescharacteristic
217C2×C61#190011yescharacteristic
218C2×C61#190211yescharacteristic
219D61—42no—
220D61—81no—
221C22×SD16—612no—
222C22×M16—1221no—
223C2×C4⋊Q8C2×D6111yescharacteristic
224C2×C4×D4—611no—
225#461—1221no—
226#461—1221no—
227#461—1221no—
228#461—1221no—
229#436—1221no—
230#435—1222no—
231C8×D4—1221no—
232#431C2×D6111yescharacteristic
233#423—611no—
234#423C2×D6111yescharacteristic
235C2×C4⋊C8—611no—
236C2×#103—612no—
237#407—1221no—
238C4×M16—611no—
239#343—1221no—
240#343—1221no—
241#333—22no—
242D4⋊C8—1221no—
243D4⋊C8—1221no—
244C61#924711yescharacteristic, complemented, Sylow
245C22×Q8C4×D6112yes—
246C22×D4—611no—
247C23×C4—1221no—
248C2×SD16—1222no—
249C2×SD16—1222no—
250C2×SD16—2444no—
251C2×M16—21no—
252C2×M16—611no—
253C2×M16—611no—
254C2×M16—1222no—
255C2×M16—1221no—
256C2×M16—2442no—
257C2×M16—2442no—
258C22×C8—612no—
259C22×C8—1222no—
260C4⋊Q8—21no—
261C4⋊Q8—21no—
262C4⋊Q8—21no—
263C4⋊Q8—21no—
264C4×D4—611no—
265C4×D4—611no—
266C4×D4—611no—
267C4×D4—611no—
268C4×D4—1221no—
269C4×D4—1221no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—611no—
273C2×C22⋊C4—1221no—
274C2×C42C22×D6111yescharacteristic
275C4⋊C8—21no—
276C4⋊C8—21no—
277C4⋊C8—1221no—
278C4⋊C8—1221no—
279C4⋊C8—1221no—
280C4⋊C8—1221no—
281C4⋊C8C22⋊D6112yes—
282#103—1222no—
283#103—1222no—
284C22⋊C8—21no—
285C22⋊C8—1222no—
286C22⋊C8—1222no—
287#97—1221no—
288C4×C8—21no—
289C4×C8—1221no—
290C24—1221no—
291C2×Q8—22no—
292C2×Q8—22no—
293C2×Q8—42no—
294C2×Q8—42no—
295C2×D4—611no—
296C2×D4—611no—
297C2×D4—1222no—
298C2×D4—1221no—
299C2×D4—2441no—
300C22×C4—22no—
301C22×C4—1221no—
302C22×C4—1221no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4—2441no—
307C22×C4—2441no—
308C22×C4—2441no—
309C22×C4—2441no—
310C22×C4C2×C4×D6111yescharacteristic
311C22×C4D4×D6111yescharacteristic
312C22×C4#1175822411yescharacteristic
313SD16—2444no—
314SD16—2444no—
315M16—41no—
316M16—41no—
317M16—612no—
318M16—1221no—
319M16—1221no—
320M16—1221no—
321M16—2444no—
322M16—2441no—
323M16—2441no—
324C2×C8—22no—
325C2×C8—41no—
326C2×C8—1221no—
327C2×C8—1222no—
328C2×C8—1221no—
329C2×C8—2444no—
330C2×C8—2441no—
331C2×C8—2442no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—611no—
337C4⋊C4—611no—
338C4⋊C4—1221no—
339C22⋊C4—1221no—
340C22⋊C4—1221no—
341C22⋊C4—1221no—
342C22⋊C4—1221no—
343C42#1175822211yescharacteristic
344C42D4×D6111yescharacteristic
345C42D4×D6111yescharacteristic
346C42C2×C22⋊D6111yescharacteristic
347C23—1221no—
348C23—1221no—
349C23—4881no—
350C23—2442no—
351C23—2441no—
352C23—2441no—
353C23#1451973711yescharacteristic
354Q8—42no—
355Q8—42no—
356Q8—82no—
357D4—612no—
358D4—1221no—
359D4—1221no—
360D4—1221no—
361D4—2442no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—82no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4C22⋊C4×D6111yescharacteristic
380C2×C4C4×C22⋊D6111yescharacteristic
381C2×C4#1451974511yescharacteristic
382C2×C4#1451974811yescharacteristic
383C2×C4#1451975011yescharacteristic
384C2×C4#1451975911yescharacteristic
385C2×C4SD16×D6111yescharacteristic
386C2×C4#1451980011yescharacteristic
387C2×C4#1451980411yescharacteristic
388C2×C4#1451980911yescharacteristic
389C8—42no—
390C8—81no—
391C8—1222no—
392C8—4881no—
393C8—2442no—
394C8—2441no—
395C22—21no—
396C22—21no—
397C22—1222no—
398C22—4882no—
399C22—4882no—
400C22—2441no—
401C22—2441no—
402C22—2441no—
403C22—2441no—
404C22—2441no—
405C22#1683963811yescharacteristic
406C22#1683984711yescharacteristic
407C22#1683986511yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—82no—
412C4—2441no—
413C4—2441no—
414C4#100×D6111yescharacteristic
415C4#1683974311yescharacteristic
416C4#1683991111yescharacteristic
417C4#1683992311yescharacteristic
418C4#1683996611yescharacteristic
419C4#1683998011yescharacteristic
420C2—21no—
421C2—21no—
422C2—4881no—
423C2—2442no—
424C2#2144615011yescharacteristic
425C2#2144627911yescharacteristic
426C2#2144628911yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1548C2
socleC22×C61#386
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1548D61
hypocenterC61#9247
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
3. #21446809C2semidirect
5. #21443693C2semidirect
6. #21443668C2semidirect
7. C61×#1548C2semidirect
125. #11758194SD16semidirect
210. #1548D61semidirect
244. C61#9247semidirect

Maximal subgroups

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

subgroupindex
C2×#168399642
#214545542
#214468092
#214442452
#214436932
#214436682
C61×#15482
#924761