Finite Group Databasebeta

← #29576387

Subgroups — #29576387

Order 15616.

512 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840049C211yesmaximal, characteristic
2#21454554C211yesmaximal, characteristic
3#21446809C211yesmaximal, characteristic, complemented
4#21444245C211yesmaximal, characteristic
5#21443693C211yesmaximal, characteristic, complemented
6#21443668C211yesmaximal, characteristic, complemented
7C61×#1549C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C2×C4×D244C2211yescharacteristic
10#16840049—21no—
11#16840049—21no—
12#16840049—21no—
13#16840049—21no—
14#16839839—21no—
15#16839832—22no—
16#16839827—21no—
17C2×#14519708C412yes—
18#16839786C2211yescharacteristic
19C2×C4⋊#92418C2211yescharacteristic
20C2×#14519697C412yes—
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×#332—22no—
31C22×D244C2×C411yescharacteristic
32C22×C4×D61—21no—
33C2×#11758194—21no—
34C2×#11758194D411yescharacteristic
35C2×#11758194D411yescharacteristic
36C2×#11758189—22no—
37M16×D61—42no—
38M16×D61—42no—
39C22×#92418C2×C412yes—
40C2×C8×D61—22no—
41C4×D244—21no—
42C4×D244—21no—
43C4×D244D411yescharacteristic
44C4×D244D411yescharacteristic
45C4×D244D411yescharacteristic
46C4×D244D411yescharacteristic
47C2×C4⋊Dic61C2×C411yescharacteristic
48C2×#11758198—21no—
49#14519708—22no—
50#14519708—22no—
51C4⋊#92418—21no—
52C4⋊#92418—21no—
53C4⋊#92418—21no—
54C4⋊#92418—21no—
55#14519697—22no—
56#14519697—22no—
57#14519689—22no—
58#14519689—22no—
59#14519688—21no—
60C4×#92418—21no—
61C22×Q8×C61—21no—
62C2×M16×C61—21no—
63C4⋊Q8×C61—21no—
64C4⋊Q8×C61—21no—
65C4⋊Q8×C61—21no—
66C4⋊Q8×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61C2×C412yes—
69C2×C42×C61C2311yescharacteristic
70C4⋊C8×C61—21no—
71C4⋊C8×C61—21no—
72C4⋊C8×C61D412yes—
73C22⋊C8×C61—21no—
74C4×C8×C61—21no—
75C23×D61—21no—
76C2×Q8×C61—41no—
77C2×Q8×C61—41no—
78C2×Q8×C61—82no—
79C22×C4×C61—22no—
80C22×C4×C61C22×C411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61#4111yescharacteristic
83C22×Dic61—21no—
84C2×D244—22no—
85C2×D244—21no—
86C2×D244—41no—
87C2×D244C22⋊C411yescharacteristic
88C2×D244C22⋊C411yescharacteristic
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61—41no—
94C2×C4×D61—41no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97M16×C61—41no—
98M16×C61—41no—
99C2×C8×C61—22no—
100C2×C8×C61—41no—
101C4⋊C4×C61—22no—
102C4⋊C4×C61—22no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C42×C61C2×D411yescharacteristic
106C42×C61C2×D411yescharacteristic
107C42×C61C2×D411yescharacteristic
108C42×C61#4111yescharacteristic
109#11758198—21no—
110#11758198—21no—
111#11758198—21no—
112#11758198—21no—
113C4⋊Dic61—21no—
114C4⋊Dic61C22⋊C411yescharacteristic
115C4⋊Dic61C22⋊C411yescharacteristic
116#11758194—21no—
117#11758194—21no—
118#11758194—21no—
119#11758194—41no—
120#11758194—41no—
121#11758194SD1612yes—
122C2×#92418—21no—
123C2×#92418—22no—
124C2×#92418—21no—
125C2×#92418—42no—
126C2×#92418—41no—
127#11758189—44no—
128C8×D61—44no—
129C23×C61C4×D411yescharacteristic
130C22×D61—21no—
131C22×D61—21no—
132C22×D61—42no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—81no—
136Q8×C61—82no—
137Q8×C61—82no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—41no—
141C2×C4×C61—42no—
142C2×C4×C61—82no—
143C2×C4×C61C2×C22⋊C411yescharacteristic
144C2×C4×C61C4×D411yescharacteristic
145C2×C4×C61#12011yescharacteristic
146C2×C4×C61#12111yescharacteristic
147C2×C4×C61#12111yescharacteristic
148C2×C4×C61#12311yescharacteristic
149C2×C4×C61C2×SD1611yescharacteristic
150C2×C4×C61#13511yescharacteristic
151C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C61#13711yescharacteristic
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157D244—21no—
158D244—21no—
159D244—21no—
160D244—42no—
161D244#10112yes—
162C4×D61—41no—
163C4×D61—41no—
164C4×D61—41no—
165C4×D61—41no—
166C4×D61—41no—
167C4×D61—41no—
168C4×D61—41no—
169C4×D61—41no—
170C8×C61—42no—
171C8×C61—81no—
172#92418—22no—
173#92418—42no—
174#92418—41no—
175#92418—81no—
176#9249—611nomaximal, Sylow
177C22×C61—21no—
178C22×C61—21no—
179C22×C61#38611yescharacteristic
180C22×C61C4×SD1611yescharacteristic
181C22×C61#44011yescharacteristic
182C2×D61—22no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—41no—
186C2×D61—41no—
187C2×D61—41no—
188C2×D61—82no—
189C2×D61—82no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—82no—
194C4×C61C2×#10111yescharacteristic
195C4×C61#41311yescharacteristic
196C4×C61#45011yescharacteristic
197C4×C61#45211yescharacteristic
198C4×C61#46111yescharacteristic
199C4×C61#46311yescharacteristic
200Dic61—41no—
201Dic61—41no—
202C2×#476—611no—
203D4×M16—611no—
204#1997—611no—
205#1549D6111yescharacteristic, complemented
206#1486—611no—
207#1292—611no—
208#1283—611no—
209C2×C61—21no—
210C2×C61—21no—
211C2×C61#187711yescharacteristic
212C2×C61#190111yescharacteristic
213C2×C61#190311yescharacteristic
214D61—42no—
215D61—81no—
216C22×M16—1221no—
217C2×C4⋊Q8C2×D6111yescharacteristic
218C2×C4×D4—611no—
219#476—1221no—
220#476—1221no—
221#476—1221no—
222#476—1221no—
223#436—1221no—
224#435—1222no—
225C8×D4—1221no—
226#431C2×D6111yescharacteristic
227C2×#106—612no—
228#423—611no—
229#423C2×D6111yescharacteristic
230C2×C4⋊C8—611no—
231C2×#102—612no—
232#407—1221no—
233C4×M16—611no—
234#343—1221no—
235#343—1221no—
236#332—22no—
237D4⋊C8—1221no—
238D4⋊C8—1221no—
239C61#924911yescharacteristic, complemented, Sylow
240C22×Q8—21no—
241C22×D4—611no—
242C23×C4—1221no—
243C2×M16—21no—
244C2×M16—611no—
245C2×M16—611no—
246C2×M16—1222no—
247C2×M16—1221no—
248C2×M16—2442no—
249C2×M16—2442no—
250C22×C8—612no—
251C22×C8—1222no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4×D4—611no—
257C4×D4—611no—
258C4×D4—611no—
259C4×D4—611no—
260C4×D4—1221no—
261C4×D4—1221no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—611no—
264C2×C4⋊C4C4×D6112yes—
265C2×C22⋊C4—1221no—
266C2×C42C22×D6111yescharacteristic
267#106—1222no—
268#106—1222no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—1221no—
272C4⋊C8—1221no—
273C4⋊C8—1221no—
274C4⋊C8—1221no—
275C4⋊C8C22⋊D6112yes—
276#102—1222no—
277#102—1222no—
278C22⋊C8—21no—
279C22⋊C8—1222no—
280C22⋊C8—1222no—
281#97—1221no—
282C4×C8—21no—
283C4×C8—1221no—
284C24—1221no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—82no—
288C2×D4—611no—
289C2×D4—611no—
290C2×D4—1222no—
291C2×D4—1221no—
292C2×D4—2441no—
293C22×C4—22no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—2441no—
300C22×C4—2441no—
301C22×C4—2441no—
302C22×C4—2441no—
303C22×C4C2×C4×D6111yescharacteristic
304C22×C4D4×D6111yescharacteristic
305C22×C4#1175822411yescharacteristic
306M16—41no—
307M16—41no—
308M16—612no—
309M16—1221no—
310M16—1221no—
311M16—1221no—
312M16—2444no—
313M16—2441no—
314M16—2441no—
315C2×C8—22no—
316C2×C8—41no—
317C2×C8—1221no—
318C2×C8—1222no—
319C2×C8—1221no—
320C2×C8—2444no—
321C2×C8—2441no—
322C2×C8—2442no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—611no—
328C4⋊C4—611no—
329C4⋊C4—1221no—
330C22⋊C4—1221no—
331C22⋊C4—1221no—
332C22⋊C4—1221no—
333C22⋊C4—1221no—
334C42#1175822211yescharacteristic
335C42D4×D6111yescharacteristic
336C42D4×D6111yescharacteristic
337C42C2×C22⋊D6111yescharacteristic
338C23—1221no—
339C23—1221no—
340C23—4881no—
341C23—2442no—
342C23—2441no—
343C23—2441no—
344C23#1451973711yescharacteristic
345Q8—82no—
346Q8—82no—
347D4—612no—
348D4—1221no—
349D4—1221no—
350D4—1221no—
351D4—2442no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—82no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4C22⋊C4×D6111yescharacteristic
370C2×C4C4×C22⋊D6111yescharacteristic
371C2×C4#1451974511yescharacteristic
372C2×C4#1451974811yescharacteristic
373C2×C4#1451975011yescharacteristic
374C2×C4#1451975911yescharacteristic
375C2×C4SD16×D6111yescharacteristic
376C2×C4#1451980011yescharacteristic
377C2×C4#1451980411yescharacteristic
378C2×C4#1451980911yescharacteristic
379C8—42no—
380C8—81no—
381C8—1222no—
382C8—4881no—
383C8—2442no—
384C8—2441no—
385C22—21no—
386C22—21no—
387C22—1222no—
388C22—4882no—
389C22—4882no—
390C22—2441no—
391C22—2441no—
392C22—2441no—
393C22—2441no—
394C22—2441no—
395C22#1683963811yescharacteristic
396C22#1683984711yescharacteristic
397C22#1683986511yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—82no—
402C4—2441no—
403C4—2441no—
404C4#101×D6111yescharacteristic
405C4#1683974511yescharacteristic
406C4#1683991111yescharacteristic
407C4#1683992311yescharacteristic
408C4#1683996611yescharacteristic
409C4#1683998011yescharacteristic
410C2—21no—
411C2—21no—
412C2—4881no—
413C2—2442no—
414C2#2144615011yescharacteristic
415C2#2144628411yescharacteristic
416C2#2144629611yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1549C2
socleC22×C61#386
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1549D61
hypocenterC61#9249
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
3. #21446809C2semidirect
5. #21443693C2semidirect
6. #21443668C2semidirect
7. C61×#1549C2semidirect
205. #1549D61semidirect
239. C61#9249semidirect

Maximal subgroups

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

subgroupindex
C2×#168400492
#214545542
#214468092
#214442452
#214436932
#214436682
C61×#15492
#924961