Finite Group Databasebeta

← #29663948

Subgroups — #29663948

Order 15616.

638 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840165C211yesmaximal, characteristic, complemented
2#21455635C211yesmaximal, characteristic
3#21455628C211yesmaximal, characteristic
4#21454775C211yesmaximal, characteristic
5#21445222C214yesmaximal, complemented
6#21445217C214yesmaximal, complemented
7#21444577C211yesmaximal, characteristic, complemented
8#21444499C211yesmaximal, characteristic, complemented
9C61×#1548C211yesmaximal, characteristic, complemented
10C2×#14519777C2211yescharacteristic
11C4×#11758222C2211yescharacteristic
12#16840165—21no—
13#16840165—21no—
14#16840165C2214yes—
15#16840058C2212yes—
16#16840054C2212yes—
17#16840053C2212yes—
18#16840049C2212yes—
19#16840048—21no—
20#16840044—21no—
21#16840043—21no—
22#16840039—21no—
23#16839886C2212yes—
24#16839827C2212yes—
25#16839825—22no—
26#16839813—21no—
27#16839804—21no—
28#16839802—21no—
29C2×#14519710—22no—
30#16839786C2211yescharacteristic
31#16839764—21no—
32#16839761—21no—
33C2×C4×#92418C2211yescharacteristic
34C4×C8×D61—21no—
35#16839514C2214yes—
36#16839510C2214yes—
37C2×C4⋊Q8×C61C2211yescharacteristic
38C61×#431C2211yescharacteristic
39C61×#423C2211yescharacteristic
40C61×#333C2214yes—
41C2×#11758222D411yescharacteristic
42C22×Dic122—21no—
43C2×#11758194—21no—
44C22×#92418D412yes—
45C2×C8×D61—22no—
46#14519777—21no—
47#14519777—21no—
48#14519777—21no—
49#14519777C2312yes—
50C4×Dic122D411yescharacteristic
51C4×Dic122C2311yescharacteristic
52C4×D244D411yescharacteristic
53C4×D244C2311yescharacteristic
54C4×C22⋊D61—21no—
55C4×C22⋊D61—21no—
56#14519736D411yescharacteristic
57#14519734—21no—
58C2×C4⋊Dic61—21no—
59C2×C4⋊Dic61—21no—
60C42×D61—21no—
61#14519711—22no—
62#14519710—22no—
63#14519710—24no—
64#14519710—24no—
65#14519709—22no—
66#14519708—22no—
67C4⋊#92418—21no—
68C4⋊#92418C2312yes—
69#14519706—22no—
70#14519702—22no—
71#14519700—22no—
72#14519699—22no—
73#14519697—22no—
74#14519689—22no—
75C4×#92418D411yescharacteristic
76C4×#92418D411yescharacteristic
77C4×#92418C2312yes—
78C8×Dic61—22no—
79C22×Q8×C61—21no—
80C2×M16×C61—21no—
81C4⋊Q8×C61—21no—
82C4⋊Q8×C61—21no—
83C4⋊Q8×C61—21no—
84C4⋊Q8×C61C2312yes—
85C2×C4⋊C4×C61—21no—
86C2×C4⋊C4×C61—21no—
87C2×C42×C61C2311yescharacteristic
88C4⋊C8×C61—21no—
89C4⋊C8×C61C2312yes—
90C4⋊C8×C61C2312yes—
91C22⋊C8×C61—21no—
92C4×C8×C61—21no—
93C2×Q8×C61—22no—
94C2×Q8×C61—41no—
95C2×Q8×C61—82no—
96C22×C4×C61—41no—
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61#4111yescharacteristic
100C2×C22⋊D61—21no—
101C22×Dic61—41no—
102#11758222—22no—
103#11758222Q1614yes—
104C2×D244C2×D411yescharacteristic
105C2×C4×D61—21no—
106C2×C4×D61—21no—
107C2×C4×D61—21no—
108C2×Dic122—22no—
109C2×Dic122—41no—
110C2×Dic122—82no—
111C2×Dic122C2×D411yescharacteristic
112M16×C61—42no—
113C2×C8×C61—22no—
114C2×C8×C61—22no—
115C4⋊C4×C61—22no—
116C4⋊C4×C61—22no—
117C4⋊C4×C61—41no—
118C4⋊C4×C61—41no—
119C42×C61C2×D411yescharacteristic
120C42×C61C2×D411yescharacteristic
121C42×C61#4111yescharacteristic
122C42×C61C2411yescharacteristic
123C22⋊Dic61—21no—
124#11758198—21no—
125#11758198—21no—
126C4⋊Dic61—22no—
127C4⋊Dic61—22no—
128C4⋊Dic61—41no—
129C4⋊Dic61—41no—
130C4⋊Dic61C2×D411yescharacteristic
131C4⋊Dic61C2×D411yescharacteristic
132#11758196—21no—
133#11758196—21no—
134C4×Dic61—21no—
135C4×Dic61—21no—
136C4×Dic61—21no—
137#11758194—42no—
138C2×#92418—24no—
139C2×#92418—22no—
140C2×#92418C2×D412yes—
141C2×#92418C2×D412yes—
142C8×D61—44no—
143C23×C61#12111yescharacteristic
144C22×D61—21no—
145Q8×C61—82no—
146Q8×C61—82no—
147C2×C4×C61—22no—
148C2×C4×C61—22no—
149C2×C4×C61—42no—
150C2×C4×C61—82no—
151C2×C4×C61#12111yescharacteristic
152C2×C4×C61#12111yescharacteristic
153C2×C4×C61#12111yescharacteristic
154C2×C4×C61C2×Q1612yes—
155C2×C4×C61#13512yes—
156C2×C4×C61C22×D411yescharacteristic
157C2×C4×C61C22×D411yescharacteristic
158C2×C4×C61C2×#4111yescharacteristic
159C22⋊D61—24no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—42no—
164C2×Dic61—82no—
165D244—21no—
166D244C2×Q1612yes—
167C4×D61—24no—
168C4×D61—42no—
169C4×D61—42no—
170Dic122—21no—
171Dic122—82no—
172Dic122—82no—
173Dic122C2×Q1612yes—
174C8×C61—42no—
175C8×C61—42no—
176#92418—22no—
177#92418—42no—
178#92418#13714yes—
179#19272—611nomaximal, Sylow
180C22×C61—21no—
181C22×C61—21no—
182C22×C61#46712yes—
183C22×C61C2×#12111yescharacteristic
184C2×D61—22no—
185C2×D61—41no—
186C2×D61—41no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—82no—
190C4×C61#46712yes—
191C4×C61#47212yes—
192C4×C61C22×Q1611yescharacteristic
193C4×C61C2×#13511yescharacteristic
194C4×C61C2×#13712yes—
195Dic61—22no—
196Dic61—41no—
197Dic61—41no—
198Dic61—82no—
199C2×#500—611no—
200#3079—611no—
201#3079—611no—
202C8×#41—611no—
203#1676—614no—
204#1675—614no—
205#1567—611no—
206#1548—611no—
207#1548D6111yescharacteristic, complemented
208C2×C61—22no—
209C2×C61#303911yescharacteristic
210C2×C61C2×#46711yescharacteristic
211C2×C61C2×#47211yescharacteristic
212D61—42no—
213C2×C4⋊Q8—611no—
214C2×C4⋊Q8C2×D6111yescharacteristic
215C4×#41—611no—
216#500—614no—
217#500—1221no—
218#500—1221no—
219#477—612no—
220#477—612no—
221#476—612no—
222#476—612no—
223#475—1221no—
224#475—1221no—
225#474—1221no—
226#474—1221no—
227C8×Q8—612no—
228C8×D4—612no—
229C8×D4—1222no—
230#431—1221no—
231#431C2×D6111yescharacteristic
232#428—1221no—
233#428—1221no—
234C2×#107—1222no—
235#423—611no—
236#423C2×D6111yescharacteristic
237#417—1221no—
238#417—1221no—
239C2×C4×C8—611no—
240C2×C4×C8—1221no—
241#335—614no—
242#333—614no—
243#333C2×D6114yes—
244C61#1927211yescharacteristic, complemented, Sylow
245C2×#41—611no—
246C22×Q8—21no—
247C22×Q8—1221no—
248C2×M16—21no—
249C2×M16—1221no—
250C22×C8—612no—
251C22×C8—1222no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—612no—
256C4⋊Q8—1221no—
257C4⋊Q8—1221no—
258C4⋊Q8—1221no—
259C4⋊Q8C22×D6112yes—
260C4×Q8—611no—
261C4×Q8—611no—
262C4×D4—611no—
263C4×D4—611no—
264C4×D4—1221no—
265C4×D4—1221no—
266#117—611no—
267#117—1221no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—1221no—
271C2×C4⋊C4—1221no—
272C2×C42—1221no—
273C2×C42C22×D6111yescharacteristic
274#107—1222no—
275#107—1224no—
276#107—1224no—
277#107—1222no—
278#106—1222no—
279#106—1222no—
280C4⋊C8—21no—
281C4⋊C8—612no—
282C4⋊C8—1222no—
283C4⋊C8—1221no—
284C4⋊C8C22×D6112yes—
285C4⋊C8C22×D6112yes—
286#103—1222no—
287#103—1222no—
288#102—1222no—
289#102—1222no—
290C22⋊C8—21no—
291C22⋊C8—1222no—
292C4×C8—21no—
293C4×C8—611no—
294C4×C8—611no—
295C4×C8—612no—
296C4×C8—1222no—
297#41—614no—
298#41—1222no—
299C2×Q8—22no—
300C2×Q8—41no—
301C2×Q8—82no—
302C2×Q8—611no—
303C2×Q8—1222no—
304C2×Q8—4882no—
305C2×Q8—2441no—
306C2×D4—611no—
307C2×D4—1221no—
308C22×C4—41no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4—1221no—
312C22×C4—2441no—
313C22×C4#1175822211yescharacteristic
314C22×C4D4×D6111yescharacteristic
315C22×C4D4×D6111yescharacteristic
316M16—42no—
317M16—2442no—
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—612no—
321C2×C8—612no—
322C2×C8—1224no—
323C2×C8—1222no—
324C2×C8—2444no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—611no—
330C4⋊C4—611no—
331C4⋊C4—1221no—
332C4⋊C4—1221no—
333C4⋊C4—1222no—
334C4⋊C4—1222no—
335C4⋊C4—2441no—
336C4⋊C4—2441no—
337C22⋊C4—1221no—
338C22⋊C4—1221no—
339C22⋊C4—1221no—
340C42—1221no—
341C42—1221no—
342C42—1221no—
343C42#1175822211yescharacteristic
344C42D4×D6111yescharacteristic
345C42D4×D6111yescharacteristic
346C42C23×D6111yescharacteristic
347C23—1221no—
348C23#1451975011yescharacteristic
349Q8—82no—
350Q8—82no—
351Q8—612no—
352Q8—1221no—
353Q8—4882no—
354Q8—4882no—
355D4—612no—
356D4—1224no—
357D4—1221no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—42no—
361C2×C4—82no—
362C2×C4—1221no—
363C2×C4—1224no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—4882no—
367C2×C4—2442no—
368C2×C4—2442no—
369C2×C4—2442no—
370C2×C4#1451975011yescharacteristic
371C2×C4#1451975011yescharacteristic
372C2×C4#1451975011yescharacteristic
373C2×C4Q16×D6112yes—
374C2×C4#1451979812yes—
375C2×C4C2×D4×D6111yescharacteristic
376C2×C4C2×D4×D6111yescharacteristic
377C2×C4C2×#1175822211yescharacteristic
378C8—42no—
379C8—42no—
380C8—614no—
381C8—1222no—
382C8—2442no—
383C22—21no—
384C22—21no—
385C22—1222no—
386C22—2441no—
387C22—2441no—
388C22#1684000212yes—
389C22C2×#1451975011yescharacteristic
390C4—21no—
391C4—21no—
392C4—82no—
393C4—1222no—
394C4—4882no—
395C4—2441no—
396C4—2441no—
397C4#1684000212yes—
398C4#1684003112yes—
399C4C2×Q16×D6111yescharacteristic
400C4C2×#1451979811yescharacteristic
401C4#137×D6112yes—
402C2—22no—
403C2—2442no—
404C2#2145530511yescharacteristic
405C2C2×#1684000211yescharacteristic
406C2C2×#1684003111yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1548C2
socleC22×C61C2×#121
prime radicalC2×#11758222D4
hypercenter#1548D61
hypocenterC61#19272
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
1. C2×#16840165C2semidirect
5. #21445222C2semidirect
6. #21445217C2semidirect
7. #21444577C2semidirect
8. #21444499C2semidirect
9. C61×#1548C2semidirect
207. #1548D61semidirect
244. C61#19272semidirect

Maximal subgroups

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

subgroupindex
C2×#168401652
#214556352
#214556282
#214547752
#214452222
#214452172
#214445772
#214444992
C61×#15482
#1927261