Finite Group Databasebeta

← #29582608

Subgroups — #29582608

Order 15616.

626 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840141C211yesmaximal, characteristic, complemented
2C2×#16840043C211yesmaximal, characteristic
3C2×#16840039C211yesmaximal, characteristic
4#21446612C211yesmaximal, characteristic
5C2×#16839509C211yesmaximal, characteristic, complemented
6#21443653C211yesmaximal, characteristic, complemented
7C2×C61×#332C211yesmaximal, characteristic, complemented
8C22×#11758202—22no—
9C2×#14519777C2211yescharacteristic
10C2×C4×D244C2211yescharacteristic
11#16840141—22no—
12#16840141—22no—
13#16840043—22no—
14#16840043—22no—
15#16840039—22no—
16#16840039—22no—
17C2×#14519711—21no—
18C2×#14519710—21no—
19C2×C4⋊#92418C2211yescharacteristic
20C2×#14519699—21no—
21C2×#14519697—21no—
22C2×#14519689—22no—
23C2×C4×#92418C2211yescharacteristic
24#16839509—22no—
25C2×C4⋊Q8×C61C2211yescharacteristic
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×C4⋊C8×C61C2211yescharacteristic
28C61×#332—22no—
29C22×Dic122—21no—
30C22×D244D411yescharacteristic
31C22×C4×D61—21no—
32C2×#11758202—28no—
33C2×#11758202—44no—
34C2×#11758202—44no—
35C22×#92418—21no—
36C22×#92418D412yes—
37#14519777—21no—
38#14519777—21no—
39#14519777—21no—
40#14519777D412yes—
41C4×D244—21no—
42C4×D244—21no—
43C4×D244—21no—
44C4×D244—21no—
45C2×C4⋊Dic61—21no—
46C2×C4⋊Dic61—21no—
47C2×C4⋊Dic61D411yescharacteristic
48C2×#11758198—21no—
49#14519711—24no—
50#14519710—24no—
51C4⋊#92418—21no—
52C4⋊#92418D412yes—
53#14519699—24no—
54#14519697—24no—
55#14519689—44no—
56C4×#92418—21no—
57C4×#92418—21no—
58C22×Q8×C61—21no—
59C22×C8×C61—21no—
60C22×C8×C61—21no—
61C4⋊Q8×C61—21no—
62C4⋊Q8×C61—21no—
63C4⋊Q8×C61—21no—
64C4⋊Q8×C61D412yes—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C42×C61C2311yescharacteristic
68C4⋊C8×C61—21no—
69C4⋊C8×C61—21no—
70C4⋊C8×C61—21no—
71C4⋊C8×C61D412yes—
72C23×D61—21no—
73C2×Q8×C61—22no—
74C2×Q8×C61—41no—
75C2×Q8×C61—42no—
76C2×Q8×C61—42no—
77C22×C4×C61—41no—
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61#4111yescharacteristic
81C22×Dic61—21no—
82C22×Dic61—41no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244—21no—
87C2×D244—21no—
88C2×D244Q1612yescomplemented
89C2×C4×D61—41no—
90C2×C4×D61—41no—
91C2×C4×D61—42no—
92C2×C4×D61—42no—
93C2×Dic122—22no—
94C2×Dic122—42no—
95C2×Dic122—42no—
96C2×Dic122—41no—
97C2×C8×C61—22no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C2×C8×C61—41no—
101C2×C8×C61—42no—
102C4⋊C4×C61—22no—
103C4⋊C4×C61—22no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—41no—
106C42×C61C2×D411yescharacteristic
107C42×C61C2×D411yescharacteristic
108C42×C61C2×D411yescharacteristic
109C42×C61C2×D411yescharacteristic
110#11758202—416no—
111#11758198—41no—
112#11758198—41no—
113C4⋊Dic61—22no—
114C4⋊Dic61—21no—
115C4⋊Dic61—21no—
116C4⋊Dic61—22no—
117C4⋊Dic61—41no—
118C4⋊Dic61—41no—
119C2×#92418—22no—
120C2×#92418—22no—
121C2×#92418—22no—
122C2×#92418—41no—
123C2×#92418—41no—
124C2×#92418D814yes—
125C23×C61#12111yescharacteristic
126C22×D61—22no—
127C22×D61—41no—
128C22×D61—42no—
129C22×D61—41no—
130C22×D61—42no—
131Q8×C61—44no—
132Q8×C61—81no—
133Q8×C61—81no—
134C2×C4×C61—22no—
135C2×C4×C61—42no—
136C2×C4×C61—82no—
137C2×C4×C61#12011yescharacteristic
138C2×C4×C61#12011yescharacteristic
139C2×C4×C61#12011yescharacteristic
140C2×C4×C61#12111yescharacteristic
141C2×C4×C61#12111yescharacteristic
142C2×C4×C61#12711yescharacteristic
143C2×C4×C61C2×D812yes—
144C2×C4×C61C2×Q1611yescharacteristic
145C2×C4×C61#13511yescharacteristic
146C2×C4×C61AGL(1,ℤ/8)12yes—
147C2×C4×C61#13711yescharacteristic
148C2×C4×C61#13711yescharacteristic
149C2×Dic61—42no—
150C2×Dic61—41no—
151C2×Dic61—42no—
152C2×Dic61—82no—
153D244—22no—
154D244—22no—
155D244—41no—
156D244—41no—
157C4×D61—82no—
158C4×D61—81no—
159C4×D61—81no—
160Dic122—44no—
161Dic122—81no—
162Dic122—81no—
163C8×C61—42no—
164C8×C61—81no—
165#92418—24no—
166#92418—42no—
167#10274—611nomaximal, Sylow
168C22×C61#39211yescharacteristic
169C22×C61#45912yes—
170C22×C61#46711yescharacteristic
171C22×C61#47011yescharacteristic
172C22×C61#47312yes—
173C2×D61—44no—
174C2×D61—42no—
175C2×D61—82no—
176C2×D61—81no—
177C2×D61—81no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—82no—
181C4×C61#44712yes—
182C4×C61#45111yescharacteristic
183C4×C61#45111yescharacteristic
184C4×C61#45211yescharacteristic
185C4×C61#45211yescharacteristic
186C4×C61#49311yescharacteristic
187C4×C61#49611yescharacteristic
188Dic61—82no—
189Dic61—81no—
190C2×#494—611no—
191C2×#474—611no—
192C2×#474—611no—
193#1954—611no—
194C2×#332—611no—
195C2×#332D6111yescharacteristic, complemented
196#1277—611no—
197C2×C61#166912yes—
198C2×C61#168912yes—
199C2×C61#200111yescharacteristic
200C2×C61#201111yescharacteristic
201C2×C61#202011yescharacteristic
202D61—82no—
203C22×Q16—1222no—
204C2×C4⋊Q8—611no—
205C2×C4⋊Q8C2×D6111yescharacteristic
206C2×C4×D4—611no—
207#494—1222no—
208#494—1222no—
209#474—1222no—
210#474—1222no—
211#474—1222no—
212#474—1222no—
213C2×#107—1221no—
214C2×#107—1221no—
215C2×C4⋊C8—611no—
216C2×C4⋊C8C2×D6111yescharacteristic
217C2×C4⋊C8C2×D6111yescharacteristic
218C2×#102—1221no—
219C2×#102—1221no—
220C2×C22⋊C8—1222no—
221C2×C4×C8—611no—
222#332—22no—
223#332—1222no—
224C61#1027411yescharacteristic, complemented, Sylow
225C22×Q8—21no—
226C22×Q8—1221no—
227C22×D4—611no—
228C23×C4—1221no—
229C2×Q16—1228no—
230C2×Q16—2444no—
231C2×Q16—2444no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—612no—
235C22×C8—1221no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—612no—
240C4⋊Q8—1221no—
241C4⋊Q8—1221no—
242C4⋊Q8—1221no—
243C4⋊Q8D24412yes—
244C4×D4—1221no—
245C4×D4—1221no—
246C4×D4—1221no—
247C4×D4—1221no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—611no—
251C2×C4⋊C4—1221no—
252C2×C4⋊C4—1221no—
253C2×C22⋊C4—1221no—
254C2×C42C22×D6111yescharacteristic
255#107—1224no—
256#107—1224no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8—612no—
261C4⋊C8—1221no—
262C4⋊C8C22⋊D6112yes—
263#102—1224no—
264#102—1224no—
265C22⋊C8—2444no—
266C4×C8—1221no—
267C4×C8—1221no—
268C24—1221no—
269C2×Q8—22no—
270C2×Q8—41no—
271C2×Q8—42no—
272C2×Q8—42no—
273C2×Q8—1222no—
274C2×Q8—2442no—
275C2×Q8—2442no—
276C2×Q8—2441no—
277C2×D4—612no—
278C2×D4—1221no—
279C2×D4—1221no—
280C2×D4—1221no—
281C2×D4—1221no—
282C2×D4—1221no—
283C22×C4—41no—
284C22×C4—1221no—
285C22×C4—2441no—
286C22×C4—2441no—
287C22×C4—2441no—
288C22×C4—2442no—
289C22×C4—2442no—
290C22×C4#1175822211yescharacteristic
291C22×C4D4×D6111yescharacteristic
292C22×C4D4×D6111yescharacteristic
293Q16—24416no—
294C2×C8—22no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—42no—
299C2×C8—614no—
300C2×C8—1222no—
301C2×C8—1222no—
302C2×C8—1222no—
303C2×C8—2441no—
304C2×C8—2441no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—1222no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4—1222no—
313C4⋊C4—2441no—
314C4⋊C4—2441no—
315C22⋊C4—2441no—
316C22⋊C4—2441no—
317C42C2×D24411yescharacteristic
318C42D4×D6111yescharacteristic
319C42D4×D6111yescharacteristic
320C42C2×C22⋊D6111yescharacteristic
321C23—1222no—
322C23—2442no—
323C23—2441no—
324C23—2442no—
325C23—2441no—
326C23#1451975011yescharacteristic
327Q8—44no—
328Q8—81no—
329Q8—81no—
330Q8—4881no—
331Q8—4881no—
332Q8—2444no—
333D4—1222no—
334D4—1222no—
335D4—2441no—
336D4—2441no—
337C2×C4—22no—
338C2×C4—42no—
339C2×C4—82no—
340C2×C4—4882no—
341C2×C4—4881no—
342C2×C4—4881no—
343C2×C4—4882no—
344C2×C4—2442no—
345C2×C4—2441no—
346C2×C4—2442no—
347C2×C4#1451974511yescharacteristic
348C2×C4#1451974711yescharacteristic
349C2×C4#1451974711yescharacteristic
350C2×C4#1451975011yescharacteristic
351C2×C4#1451975111yescharacteristic
352C2×C4#1451977311yescharacteristic
353C2×C4D8×D6112yes—
354C2×C4Q16×D6111yescharacteristic
355C2×C4#1451979811yescharacteristic
356C2×C4#1451980412yes—
357C2×C4#1451980611yescharacteristic
358C2×C4#1451980911yescharacteristic
359C8—42no—
360C8—81no—
361C8—1224no—
362C8—2442no—
363C22—4881no—
364C22—4882no—
365C22—4881no—
366C22—2444no—
367C22—2442no—
368C22#1683967111yescharacteristic
369C22#1683995612yes—
370C22#1684000211yescharacteristic
371C22#1684001911yescharacteristic
372C22#1684003612yes—
373C4—21no—
374C4—21no—
375C4—82no—
376C4—4881no—
377C4—4882no—
378C4#1683989712yes—
379C4#1683991611yescharacteristic
380C4#1683991911yescharacteristic
381C4#1683992111yescharacteristic
382C4#1683992711yescharacteristic
383C4#1684013711yescharacteristic
384C4#1684014811yescharacteristic
385C2—4882no—
386C2#2144518312yes—
387C2#2144530712yes—
388C2#2144682811yescharacteristic
389C2#2144689111yescharacteristic
390C2#2144693911yescharacteristic
subgroupG/H
centerC23#14519750
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC2×C61×#332C2
socleC23×C61#121
prime radicalC22×D244D4
hypercenterC2×#332D61
hypocenterC61#10274
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
1. C2×#16840141C2semidirect
5. C2×#16839509C2semidirect
6. #21443653C2semidirect
7. C2×C61×#332C2semidirect
88. C2×D244Q16semidirect
195. C2×#332D61semidirect
224. C61#10274semidirect

Maximal subgroups

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

subgroupindex
C2×#168401412
C2×#168400432
C2×#168400392
#214466122
C2×#168395092
#214436532
C2×C61×#3322
#1027461