Finite Group Databasebeta

← #16796573

Subgroups — #16796573

Order 3328.

578 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131631C212yesmaximal
2#13130483C211yesmaximal, characteristic, complemented
3#13130482C211yesmaximal, characteristic, complemented
4#13130462C212yesmaximal, complemented
5#13130459C212yesmaximal, complemented
6#13130431C211yesmaximal, characteristic, complemented
7#13130429C211yesmaximal, characteristic, complemented
8C2×#11718253C211yesmaximal, characteristic
9#13130144C212yesmaximal
10#13130045C211yesmaximal, characteristic
11#13125417C211yesmaximal, characteristic
12#11719327C2212yes—
13#11719158C2212yes—
14Q8×#1057C2212yes—
15#11719125C2211yescharacteristic
16C4×#6122C2211yescharacteristic
17C2×C4⋊#1057C2212yes—
18#11719080—22no—
19#11719080C2212yes—
20#11719078—22no—
21#11719074C2212yes—
22#11719067—22no—
23#11719062—22no—
24C13×#467C411yescharacteristic
25Q16×Dic13C2211yescharacteristic
26#11718842C411yescharacteristic
27#11718777C411yescharacteristic
28C2×C8×Dic13C2211yescharacteristic
29#11718712C412yes—
30#11718535C411yescharacteristic
31#11718534C2211yescharacteristic
32#11718453C412yes—
33#11718451C2212yes—
34Q8⋊#1057C2212yes—
35Q8⋊#1057C2212yes—
36#11718253C2211yescharacteristic
37#11718253C2212yes—
38#11718253C2211yescharacteristic
39#1057⋊C8C2211yescharacteristic
40#1057⋊C8C2211yescharacteristic
41#11718251C2211yescharacteristic
42#11718251C2211yescharacteristic
43#11718244C2212yes—
44#11718244C2212yes—
45C2×#6122D412yes—
46C22×#1057—22no—
47C2×C13×Q16C2×C411yescharacteristic
48C22×C8×C13C2×C411yescharacteristic
49C13×C22⋊Q8C2×C412yes—
50Q8×Dic13C2312yes—
51#88198C2×C412yes—
52C2×#6107C2×C412yes—
53#88178C2×C412yes—
54C2×C4×Dic13C2311yescharacteristic
55C22×#1055C2×C411yescharacteristic
56C2×Dic52C2×C411yescharacteristic
57#88143—22no—
58#88142C2×C412yes—
59#88141—22no—
60#88141C2312yes—
61#88132—22no—
62#88131—22no—
63C22⋊#1057—21no—
64#88112—22no—
65#88112—22no—
66#88112—21no—
67#88110—22no—
68#88110—22no—
69#88110D412yes—
70C4⋊#1057—22no—
71C4⋊#1057—22no—
72C4⋊#1057—22no—
73C4⋊#1057C2312yes—
74C4⋊#1057C2312yes—
75C4×#1057—22no—
76C4×#1057—22no—
77C4×#1057C2311yescharacteristic
78C4×#1057C2311yescharacteristic
79C4×#1057C2311yescharacteristic
80C4×#1057C2311yescharacteristic
81C13×#107C2×C411yescharacteristic
82C13×#103C2×C412yes—
83#88075C2×C412yes—
84#88058C2×C411yescharacteristic
85#88056C2×C412yes—
86C8×Dic13C2×C411yescharacteristic
87C8×Dic13C2×C411yescharacteristic
88C8×Dic13C2311yescharacteristic
89C8×Dic13C2311yescharacteristic
90#88050C2×C412yes—
91#88047C2×C412yes—
92#18072—131nomaximal, Sylow
93C2×Q8×C13C22×C412yes—
94C22×C4×C13C22×C411yescharacteristic
95C22×Dic13C2×D411yescharacteristic
96C22×Dic13#4111yescharacteristic
97C2×Dic26—22no—
98C2×Dic26C22×C412yes—
99#6122—24no—
100C2×#1057—22no—
101C2×#1057—22no—
102C2×#1057—21no—
103C2×#1057—21no—
104C2×#1057—44no—
105C2×#1057C2×D412yes—
106C2×#1057C2×D412yes—
107C13×Q16—22no—
108C2×C8×C13—22no—
109C2×C8×C13C22×C411yescharacteristic
110C2×C8×C13C22×C411yescharacteristic
111C13×C4⋊C4—22no—
112C13×C4⋊C4C22×C412yes—
113C13×C22⋊C4—22no—
114C22⋊Dic13—22no—
115#6107—42no—
116C4⋊Dic13—22no—
117C4⋊Dic13C22×C412yes—
118#6101—22no—
119#6101—22no—
120#6101—22no—
121#6101—22no—
122#6101—22no—
123C4×Dic13—22no—
124C4×Dic13—22no—
125C4×Dic13C22×C411yescharacteristic
126C4×Dic13C2×D411yescharacteristic
127C4×Dic13#4111yescharacteristic
128C4×Dic13C2411yescharacteristic
129C2×#1055—41no—
130C2×#1055C22×C411yescharacteristic
131C2×#1055C22×C411yescharacteristic
132Dic52—22no—
133#3170—131no—
134#2962—132no—
135#1593—131no—
136#1593—131no—
137#1587—132no—
138#1587—132no—
139#1579—131no—
140#1579—131no—
141C2×#334—131no—
142#1481—132no—
143#1451—131no—
144C23×C13C4×D411yescharacteristic
145Q8×C13—22no—
146Q8×C13—22no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—22no—
150C2×C4×C13—22no—
151C2×C4×C13C4×D411yescharacteristic
152C2×C4×C13C23×C411yescharacteristic
153C2×Dic13—22no—
154C2×Dic13—22no—
155C2×Dic13—41no—
156C2×Dic13C4×D411yescharacteristic
157C2×Dic13C4×D411yescharacteristic
158C2×Dic13#13714yes—
159C2×Dic13C22×D411yescharacteristic
160C2×Dic13C2×#4111yescharacteristic
161Dic26—22no—
162Dic26—22no—
163Dic26—82no—
164#1057—22no—
165#1057—22no—
166#1057—41no—
167#1057—41no—
168#1057—42no—
169#1057—42no—
170C8×C13—21no—
171C8×C13#13112yes—
172#1055—21no—
173#1055—21no—
174#533—132no—
175#500—131no—
176#494—131no—
177#487—132no—
178#467—131no—
179#467—132no—
180#467#26111yescharacteristic
181#446—132no—
182#446—132no—
183#446—262no—
184#446—262no—
185C8×Q8—132no—
186C8×Q8—132no—
187C4×Q16—131no—
188C4×Q16—131no—
189C4×Q16—132no—
190#431—131no—
191#424—262no—
192C2×C4⋊C8—132no—
193#405—262no—
194C4×M16—131no—
195C2×C4×C8—131no—
196#334—131no—
197#334—132no—
198#334—131no—
199Q8⋊C8—132no—
200Q8⋊C8—132no—
201Q8⋊C8—132no—
202Q8⋊C8—132no—
203#322—131no—
204#322—131no—
205#322—131no—
206#322—131no—
207C22×C13—21no—
208C22×C13—21no—
209C22×C13#44112yes—
210C22×C13C2×C4×D411yescharacteristic
211C4×C13—21no—
212C4×C13—42no—
213C4×C13—42no—
214C4×C13C2×#13111yescharacteristic
215C4×C13#56811yescharacteristic
216Dic13—21no—
217Dic13—21no—
218Dic13—42no—
219Dic13—42no—
220Dic13#44112yes—
221Dic13C2×#13712yes—
222C2×Q16—132no—
223C2×Q16—131no—
224C2×Q16C2×#26111yescharacteristic
225C2×M16—132no—
226C22×C8—131no—
227C22×C8—262no—
228C22×C8C2×#26111yescharacteristic
229C4⋊Q8—132no—
230C4⋊Q8—132no—
231#125—262no—
232C22⋊Q8—132no—
233C22⋊Q8—262no—
234C22⋊Q8C2×#26112yes—
235C4×Q8—132no—
236C4×Q8—132no—
237C4×Q8—262no—
238#117—262no—
239C2×C42—131no—
240#107—131no—
241#107—132no—
242#107C2×#26111yescharacteristic
243C4⋊C8—132no—
244C4⋊C8—132no—
245C4⋊C8—262no—
246C4⋊C8—261no—
247C4⋊C8—262no—
248C4⋊C8—262no—
249C4⋊C8—262no—
250C4⋊C8—262no—
251#103—132no—
252#103—132no—
253#103—132no—
254#103C2×#26112yes—
255C22⋊C8—261no—
256#97—132no—
257#97—262no—
258#97—262no—
259C4×C8—131no—
260C4×C8—131no—
261C4×C8—131no—
262C4×C8—131no—
263C4×C8—131no—
264C4×C8—131no—
265C4×C8—131no—
266C4×C8—131no—
267C4×C8—262no—
268C4×C8—262no—
269C2×C13—22no—
270C2×C13#293511yescharacteristic
271C2×C13C2×#44111yescharacteristic
272C2×C13#295711yescharacteristic
273C2×Q8—132no—
274C2×Q8—262no—
275C2×Q8C22×#26112yes—
276C22×C4—131no—
277C22×C4—131no—
278C22×C4C22×#26111yescharacteristic
279Q16—22no—
280Q16—262no—
281Q16—522no—
282M16—264no—
283C2×C8—22no—
284C2×C8—132no—
285C2×C8—132no—
286C2×C8—131no—
287C2×C8—131no—
288C2×C8—261no—
289C2×C8—261no—
290C2×C8—262no—
291C2×C8—262no—
292C2×C8—521no—
293C2×C8—524no—
294C2×C8C22×#26111yescharacteristic
295C2×C8C22×#26111yescharacteristic
296C4⋊C4—22no—
297C4⋊C4—132no—
298C4⋊C4—262no—
299C4⋊C4—262no—
300C4⋊C4—262no—
301C4⋊C4—262no—
302C4⋊C4—262no—
303C4⋊C4—262no—
304C4⋊C4C22×#26112yes—
305C22⋊C4—22no—
306C22⋊C4—262no—
307C42—131no—
308C42—131no—
309C42—131no—
310C42—131no—
311C42—262no—
312C42—262no—
313C13#1807211yescharacteristic, complemented, Sylow
314C23D4×#26111yescharacteristic
315Q8—22no—
316Q8—22no—
317Q8—262no—
318Q8—262no—
319Q8—1042no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—134no—
325C2×C4—131no—
326C2×C4—131no—
327C2×C4—131no—
328C2×C4—131no—
329C2×C4—262no—
330C2×C4—262no—
331C2×C4—521no—
332C2×C4D4×#26111yescharacteristic
333C2×C4C23×#26111yescharacteristic
334C8—21no—
335C8—262no—
336C8—262no—
337C8—261no—
338C8—261no—
339C8—522no—
340C8—522no—
341C8—521no—
342C8—521no—
343C8#8823812yes—
344C22—21no—
345C22—21no—
346C22#1171911012yes—
347C22C2×D4×#26111yescharacteristic
348C4—21no—
349C4—42no—
350C4—42no—
351C4—132no—
352C4—132no—
353C4—261no—
354C4—261no—
355C4—522no—
356C4—522no—
357C4C2×#8823811yescharacteristic
358C4#1171962911yescharacteristic
359C2—22no—
360C2#1313157811yescharacteristic
361C2C2×#1171911011yescharacteristic
362C2#1313161511yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#467C4
socleC22×C13C2×C4×D4
prime radicalC23×C13C4×D4
cosocleC4×Dic13C24
hypercenter#467#261
hypocenterC13#18072
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
2. #13130483C2semidirect
3. #13130482C2semidirect
4. #13130462C2semidirect
5. #13130459C2semidirect
6. #13130431C2semidirect
7. #13130429C2semidirect
313. C13#18072semidirect

Maximal subgroups

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

subgroupindex
#131316312
#131304832
#131304822
#131304622
#131304592
#131304312
#131304292
C2×#117182532
#131301442
#131300452
#131254172
#1807213