Finite Group Databasebeta

← #15881741

Subgroups — #15881741

Order 3328.

732 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718489C212yesmaximal
2#13117313C211yesmaximal, characteristic
3#13115557C212yesmaximal
4#13115556C212yesmaximal
5#13115551C212yesmaximal
6#13114989C212yesmaximal
7#13114695C212yesmaximal
8#13114689C211yesmaximal, characteristic
9C13×#1842C211yesmaximal, characteristic
10C2×C4×Dic26C2211yescharacteristic
11C2×C13×C4⋊C8C2212yes—
12C2×C13×C4⋊C8C2212yes—
13C2×C13×C4⋊C8C2211yescharacteristic
14C2×C13×C4⋊C8C2211yescharacteristic
15C43×C13C2211yescharacteristic
16C2×#88055C2212yes—
17C2×#88054C2212yes—
18C2×#88054C2212yes—
19C2×#88054C2212yes—
20C2×#88054C2212yes—
21C2×C8×Dic13C2212yes—
22C4×C4⋊Dic13C2211yescharacteristic
23#11718594C412yes—
24#11718594C412yes—
25#11718593C2212yes—
26C4×#6101C2212yes—
27#11718590C411yescharacteristic
28#11718590C411yescharacteristic
29#11718589C411yescharacteristic
30#11718589C411yescharacteristic
31C2×C4⋊#1055C2211yescharacteristic
32C2×C4⋊#1055C2211yescharacteristic
33C2×#88043C2212yes—
34#11718489—28no—
35#11718142C2212yes—
36#11718142C2212yes—
37#11718116C2212yes—
38C22×Dic26C2×C411yescharacteristic
39C22×C8×C13C2312yes—
40C22×C8×C13C2312yes—
41C2×C42×C13C2×C411yescharacteristic
42C2×C42×C13C2×C411yescharacteristic
43C2×C42×C13C2×C411yescharacteristic
44C2×C42×C13C2×C411yescharacteristic
45C2×C42×C13C2311yescharacteristic
46C2×C42×C13C2311yescharacteristic
47C2×C42×C13C2311yescharacteristic
48C2×C4⋊Dic13C2×C411yescharacteristic
49C2×C4⋊Dic13C2×C411yescharacteristic
50C2×C4⋊Dic13C2×C411yescharacteristic
51C2×#6101C2×C412yes—
52C2×#6101C2×C412yes—
53C2×#6101C2×C412yes—
54C2×C4×Dic13C2312yes—
55C2×C4×Dic13C2312yes—
56C22×#1055C2312yes—
57C22×#1055C2312yes—
58C4×Dic26D414yes—
59C4×Dic26Q814yes—
60C13×C4⋊C8—24no—
61C13×C4⋊C8—24no—
62C13×C4⋊C8—41no—
63C13×C4⋊C8—41no—
64#88071C2×C412yes—
65#88071C2×C412yes—
66#88071C2×C412yes—
67#88071C2×C412yes—
68#88071C2×C412yes—
69#88071C2×C412yes—
70#88071C2×C412yes—
71#88055—24no—
72#88054—24no—
73#88054—24no—
74#88054—42no—
75#88054—42no—
76C8×Dic13—24no—
77C4⋊#1055—22no—
78C4⋊#1055Q814yescomplemented
79#88043—24no—
80#22723—131nomaximal, Sylow
81C22×C4×C13C22×C411yescharacteristic
82C22×C4×C13C22×C411yescharacteristic
83C22×C4×C13C22×C411yescharacteristic
84C22×C4×C13C22×C411yescharacteristic
85C22×C4×C13C22×C411yescharacteristic
86C22×C4×C13C22×C411yescharacteristic
87C22×C4×C13C2411yescharacteristic
88C22×Dic13C22×C412yes—
89C22×Dic13C22×C412yes—
90C22×Dic13C22×C412yes—
91C22×Dic13C22×C412yes—
92C2×Dic26—41no—
93C2×Dic26—41no—
94C2×Dic26C4⋊C414yes—
95C2×C8×C13—22no—
96C2×C8×C13—22no—
97C2×C8×C13—22no—
98C2×C8×C13—22no—
99C2×C8×C13—22no—
100C2×C8×C13—22no—
101C42×C13—22no—
102C42×C13—21no—
103C42×C13—21no—
104C42×C13—41no—
105C42×C13—41no—
106C42×C13—41no—
107C42×C13C2×D412yes—
108C42×C13C2×Q812yes—
109C42×C13C2×Q812yes—
110C42×C13#4112yes—
111C4⋊Dic13—41no—
112C4⋊Dic13—41no—
113C4⋊Dic13C4⋊C414yes—
114#6101—24no—
115#6101—42no—
116#6101C4⋊C418yes—
117C4×Dic13—22no—
118C4×Dic13—22no—
119C4×Dic13C2×D414yes—
120C4×Dic13C2×Q814yes—
121C2×#1055—22no—
122C2×#1055—22no—
123C2×#1055—22no—
124C2×#1055—22no—
125C2×#1055—22no—
126C2×#1055C2×Q814yes—
127C2×#446—132no—
128#2295—131no—
129#1940—132no—
130#1940—132no—
131#1939—132no—
132#1843—132no—
133#1842D1311yescharacteristic
134#1768—132no—
135#1767—131no—
136C23×C13C23×C411yescharacteristic
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13C2×C4⋊C412yes—
151C2×C4×C13C2×C4⋊C412yes—
152C2×C4×C13C4×Q812yes—
153C2×C4×C13C4×Q812yes—
154C2×C4×C13#13112yes—
155C2×C4×C13C22×D411yescharacteristic
156C2×C4×C13C22×Q811yescharacteristic
157C2×C4×C13C22×Q811yescharacteristic
158C2×C4×C13C2×#4111yescharacteristic
159C2×C4×C13H(5,𝔽2)11yescharacteristic
160C2×C4×C132−1+411yescharacteristic
161C2×Dic13—22no—
162C2×Dic13—22no—
163C2×Dic13—22no—
164C2×Dic13—22no—
165C2×Dic13—22no—
166C2×Dic13—22no—
167C2×Dic13—22no—
168C2×Dic13—22no—
169C2×Dic13—22no—
170C2×Dic13—22no—
171C2×Dic13C2×C4⋊C414yes—
172C2×Dic13C2×C4⋊C414yes—
173Dic26—44no—
174C8×C13—42no—
175C8×C13—42no—
176#1055—24no—
177#1055—42no—
178C2×C4×Q8—131no—
179#446—268no—
180C2×C4⋊C8—131no—
181C2×C4⋊C8—132no—
182C2×C4⋊C8—132no—
183C2×C4⋊C8—131no—
184C2×C4⋊C8—132no—
185C2×C4⋊C8—132no—
186C2×C4⋊C8C2×D1312yes—
187C2×C4⋊C8C2×D1312yes—
188C2×C4⋊C8C2×D1311yescharacteristic
189C2×C4⋊C8C2×D1311yescharacteristic
190C2×#97—132no—
191C2×#97—132no—
192C2×C4×C8—132no—
193#391—131no—
194#391—131no—
195#389—131no—
196#389—131no—
197#387—132no—
198#387—132no—
199C4×C4⋊C4—132no—
200C4×C4⋊C4—131no—
201#376—132no—
202C43C2×D1311yescharacteristic
203#336—132no—
204#336—132no—
205#336—132no—
206C22×C13C22×C4⋊C411yescharacteristic
207C22×C13C2×C4×Q811yescharacteristic
208C22×C13#52011yescharacteristic
209C22×C13C2×#13111yescharacteristic
210C22×C13#56811yescharacteristic
211C22×C13#56811yescharacteristic
212C22×C13#56811yescharacteristic
213C4×C13—22no—
214C4×C13—22no—
215C4×C13—22no—
216C4×C13—22no—
217C4×C13—22no—
218C4×C13—41no—
219C4×C13D4×Q811yescharacteristic
220C4×C13#55011yescharacteristic
221C4×C13#55711yescharacteristic
222C4×C13Q8211yescharacteristic
223Dic13—24no—
224Dic13—24no—
225Dic13—42no—
226Dic13—42no—
227C22×Q8—131no—
228C22×C8—132no—
229C22×C8—132no—
230C22×C8C22×D1312yes—
231C22×C8C22×D1312yes—
232C4×Q8—134no—
233C4×Q8—134no—
234C2×C4⋊C4—132no—
235C2×C4⋊C4—131no—
236C2×C4⋊C4—132no—
237C2×C4⋊C4—132no—
238C2×C4⋊C4—131no—
239C2×C4⋊C4—131no—
240C2×C42—132no—
241C2×C42—132no—
242C2×C42C4×D1311yescharacteristic
243C2×C42C4×D1311yescharacteristic
244C2×C42C4×D1311yescharacteristic
245C2×C42C4×D1311yescharacteristic
246C2×C42C22×D1311yescharacteristic
247C2×C42C22×D1311yescharacteristic
248C2×C42C22×D1311yescharacteristic
249C4⋊C8—24no—
250C4⋊C8—24no—
251C4⋊C8—41no—
252C4⋊C8—41no—
253C4⋊C8—134no—
254C4⋊C8—264no—
255C4⋊C8—264no—
256C4⋊C8—262no—
257C4⋊C8—522no—
258C4⋊C8—522no—
259#97—264no—
260#97—264no—
261C4×C8—264no—
262#95—132no—
263#95—132no—
264#95—132no—
265#95—132no—
266#95—132no—
267#95—132no—
268#95—132no—
269C2×C13Q8×C4⋊C411yescharacteristic
270C2×C13#290511yescharacteristic
271C2×C13#290611yescharacteristic
272C2×C13#296111yescharacteristic
273C2×C13#296211yescharacteristic
274C2×C13#299211yescharacteristic
275C2×C13#299511yescharacteristic
276C2×Q8—134no—
277C2×Q8—521no—
278C2×Q8—521no—
279C22×C4—132no—
280C22×C4—132no—
281C22×C4—132no—
282C22×C4—132no—
283C22×C4C2×C4×D1311yescharacteristic
284C22×C4C2×C4×D1311yescharacteristic
285C22×C4C2×C4×D1311yescharacteristic
286C22×C4C2×C4×D1311yescharacteristic
287C22×C4C2×C4×D1311yescharacteristic
288C22×C4C2×C4×D1311yescharacteristic
289C22×C4C23×D1311yescharacteristic
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—134no—
297C2×C8—262no—
298C2×C8—262no—
299C2×C8—262no—
300C2×C8—262no—
301C2×C8—262no—
302C4⋊C4—138no—
303C4⋊C4—134no—
304C4⋊C4—264no—
305C4⋊C4—522no—
306C4⋊C4—521no—
307C4⋊C4—521no—
308C42—22no—
309C42—21no—
310C42—21no—
311C42—41no—
312C42—41no—
313C42—41no—
314C42—134no—
315C42—134no—
316C42—262no—
317C42—262no—
318C42D4×D1312yes—
319C42#612912yes—
320C42Q8×D1312yes—
321C42Q8×D1312yes—
322C13#2272311yescharacteristic, complemented, Sylow
323C23C22×C4×D1311yescharacteristic
324Q8—524no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—134no—
339C2×C4—134no—
340C2×C4—262no—
341C2×C4—262no—
342C2×C4—262no—
343C2×C4—262no—
344C2×C4—262no—
345C2×C4—262no—
346C2×C4—262no—
347C2×C4—262no—
348C2×C4—262no—
349C2×C4—262no—
350C2×C4#8814112yes—
351C2×C4#8814112yes—
352C2×C4C4⋊C4×D1312yes—
353C2×C4C4⋊C4×D1312yes—
354C2×C4#8815512yes—
355C2×C4C2×D4×D1311yescharacteristic
356C2×C4C2×#612911yescharacteristic
357C2×C4#8825111yescharacteristic
358C2×C4C2×Q8×D1311yescharacteristic
359C2×C4C2×Q8×D1311yescharacteristic
360C2×C4#8825411yescharacteristic
361C8—42no—
362C8—42no—
363C8—264no—
364C8—522no—
365C22C2×#8814111yescharacteristic
366C22C2×C4⋊C4×D1311yescharacteristic
367C22#1171920911yescharacteristic
368C22C2×#8815511yescharacteristic
369C22#1171945011yescharacteristic
370C22#1171945011yescharacteristic
371C22#1171945011yescharacteristic
372C4—22no—
373C4—22no—
374C4—22no—
375C4—22no—
376C4—22no—
377C4—41no—
378C4—264no—
379C4—264no—
380C4—522no—
381C4—522no—
382C4#1171942311yescharacteristic
383C4#1171942611yescharacteristic
384C4#1171942711yescharacteristic
385C4#1171943211yescharacteristic
386C2#1311774811yescharacteristic
387C2#1312339811yescharacteristic
388C2#1312340111yescharacteristic
389C2#1312377311yescharacteristic
390C2#1312377911yescharacteristic
391C2#1312397211yescharacteristic
392C2#1312400311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socle, prime radicalC23×C13C23×C4
FittingC13×#1842C2
cosocleC22×C4×C13C24
hypercenter#1842D13
hypocenterC13#22723
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1842

Complements

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

NH ≅ G/Ntype
78. C4⋊#1055Q8semidirect
322. C13#22723semidirect

Maximal subgroups

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

subgroupindex
C2×#117184892
#131173132
#131155572
#131155562
#131155512
#131149892
#131146952
#131146892
C13×#18422
#2272313