Finite Group Databasebeta

← #15771356

Subgroups — #15771356

Order 3328.

734 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117454C211yesmaximal, characteristic
2C2×#11718122C211yesmaximal, characteristic
3#13114555C212yesmaximal
4C2×#11718115C212yesmaximal
5C13×C4⋊#95C211yesmaximal, characteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C22×C42×C13C2211yescharacteristic
9C2×#88180C2212yes—
10C22×#6099C2212yes—
11C2×C13×#95—22no—
12#11718873—22no—
13#11718646—22no—
14#11718646—22no—
15#11718122C414yescomplemented
16#11718121—22no—
17#11718121—22no—
18#11718115—24no—
19C23×C4×C13—21no—
20C23×C4×C13—21no—
21C23×C4×C13D412yes—
22C23×C4×C13C2311yescharacteristic
23C2×C13×C4⋊C4—22no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4C2×C412yes—
29C2×C13×C4⋊C4Q812yes—
30C2×C13×C4⋊C4Q812yes—
31C2×C42×C13—22no—
32C2×C42×C13—22no—
33C2×C42×C13—21no—
34C2×C42×C13D412yes—
35C2×C22⋊Dic13—22no—
36#88180—22no—
37#88180—22no—
38#88180—22no—
39#88180—22no—
40C2×C4⋊Dic13—22no—
41C2×C4⋊Dic13—22no—
42C2×C4⋊Dic13D412yes—
43C2×C4⋊Dic13D412yes—
44C2×C4×Dic13—22no—
45C2×#6099—22no—
46C2×#6099—22no—
47C2×#6099—22no—
48C2×#6099—22no—
49C2×#6099—22no—
50C2×#6099C2×C414yes—
51C22×#1055—22no—
52C13×#95—44no—
53#88071—24no—
54#11296—131nomaximal, Sylow
55C24×C13C2×D411yescharacteristic
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—22no—
62C22×C4×C13—41no—
63C22×C4×C13—41no—
64C22×C4×C13—41no—
65C22×C4×C13—41no—
66C22×C4×C13—42no—
67C22×C4×C13—42no—
68C22×C4×C13—42no—
69C22×C4×C13—42no—
70C22×C4×C13—41no—
71C22×C4×C13—41no—
72C22×C4×C13C4⋊C414yes—
73C22×C4×C13C22×C411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D412yes—
76C22×C4×C13C2×Q811yescharacteristic
77C22×C4×C13C2×Q811yescharacteristic
78C22×C4×C13#4111yescharacteristic
79C22×C4×C13#4111yescharacteristic
80C22×C4×C13#4112yes—
81C22×C4×C13#4112yes—
82C22×C4×C13#4112yes—
83C22×Dic13—22no—
84C22×Dic13—22no—
85C13×C4⋊C4—24no—
86C13×C4⋊C4—24no—
87C13×C4⋊C4—24no—
88C13×C4⋊C4—42no—
89C42×C13—24no—
90C42×C13—42no—
91C22⋊Dic13—42no—
92C22⋊Dic13—42no—
93C4⋊Dic13—22no—
94C4⋊Dic13—22no—
95C4⋊Dic13—22no—
96C4⋊Dic13—22no—
97C4⋊Dic13—82no—
98C4⋊Dic13—82no—
99C4×Dic13—42no—
100C4×Dic13—42no—
101#6099—24no—
102#6099—24no—
103#6099—42no—
104#6099—42no—
105C2×#1055—24no—
106C2×#1055—42no—
107C2×#1055—42no—
108#2316—131no—
109C2×#343—131no—
110#1736—132no—
111C2×#339—132no—
112C4⋊#95D1311yescharacteristic
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13C2×C4⋊C411yescharacteristic
118C23×C13#12011yescharacteristic
119C23×C13#12111yescharacteristic
120C23×C13C22⋊Q811yescharacteristic
121C23×C13#12311yescharacteristic
122C23×C13#12411yescharacteristic
123C23×C13#12411yescharacteristic
124C2×C4×C13—24no—
125C2×C4×C13—24no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—42no—
134C2×C4×C13—44no—
135C2×C4×C13—44no—
136C2×C4×C13—42no—
137C2×C4×C13—82no—
138C2×C4×C13—82no—
139C2×C4×C13—81no—
140C2×C4×C13—81no—
141C2×C4×C13#11712yes—
142C2×C4×C13C4×D412yes—
143C2×C4×C13C4×D411yescharacteristic
144C2×C4×C13C4×Q811yescharacteristic
145C2×C4×C13#12112yes—
146C2×C4×C13C22⋊Q812yes—
147C2×C4×C13C22⋊Q812yes—
148C2×C4×C13#12312yes—
149C2×C4×C13#12312yes—
150C2×C4×C13#12412yes—
151C2×C4×C13#12512yes—
152C2×C4×C13#12512yes—
153C2×C4×C13#12511yescharacteristic
154C2×C4×C13#12612yes—
155C2×C4×C13#12612yes—
156C2×C4×C13C4⋊Q811yescharacteristic
157C2×Dic13—42no—
158C2×Dic13—42no—
159C2×Dic13—42no—
160C2×Dic13—42no—
161C2×Dic13—42no—
162C2×Dic13—42no—
163#1055—44no—
164C22×M16—132no—
165C2×#117—132no—
166C22×C4⋊C4C2×D1311yescharacteristic
167C22×C4⋊C4C2×D1311yescharacteristic
168C22×C42C2×D1311yescharacteristic
169#389—262no—
170#389—262no—
171#380—262no—
172C2×#95—22no—
173#343—134no—
174#340—262no—
175#340—262no—
176#339—264no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13#38211yescharacteristic
190C22×C13#38511yescharacteristic
191C22×C13#38911yescharacteristic
192C22×C13#39311yescharacteristic
193C22×C13#39411yescharacteristic
194C22×C13#39711yescharacteristic
195C22×C13#40011yescharacteristic
196C22×C13#45311yescharacteristic
197C22×C13#45411yescharacteristic
198C22×C13#45511yescharacteristic
199C22×C13#45611yescharacteristic
200C4×C13—44no—
201C4×C13—44no—
202C4×C13—82no—
203C4×C13#38712yes—
204C4×C13#38812yes—
205C4×C13#39812yes—
206C4×C13#40012yes—
207Dic13—82no—
208Dic13—82no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4C22⋊D1312yes—
212C23×C4C22×D1311yescharacteristic
213C2×M16—134no—
214C2×M16—262no—
215C2×M16—262no—
216C2×M16—262no—
217C2×M16—262no—
218C2×M16—262no—
219C22×C8—262no—
220#117—262no—
221#117—262no—
222#117—262no—
223#117—262no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—132no—
230C2×C4⋊C4—132no—
231C2×C4⋊C4—262no—
232C2×C4⋊C4—262no—
233C2×C4⋊C4Dic2612yes—
234C2×C4⋊C4Dic2612yes—
235C2×C4⋊C4C4×D1312yes—
236C2×C22⋊C4—262no—
237C2×C42—22no—
238C2×C42—22no—
239C2×C42—21no—
240C2×C42—262no—
241C2×C42D5212yes—
242#95—44no—
243#95—264no—
244C2×C13—21no—
245C2×C13—21no—
246C2×C13—21no—
247C2×C13—21no—
248C2×C13#144211yescharacteristic
249C2×C13#185611yescharacteristic
250C2×C13#185711yescharacteristic
251C2×C13#202711yescharacteristic
252C2×C13#202811yescharacteristic
253C2×C13#203911yescharacteristic
254C2×C13#204011yescharacteristic
255C24C2×C22⋊D1311yescharacteristic
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—262no—
273C22×C4—262no—
274C22×C4#610114yes—
275C22×C4C2×Dic2611yescharacteristic
276C22×C4C2×Dic2611yescharacteristic
277C22×C4C2×C4×D1311yescharacteristic
278C22×C4C2×D5211yescharacteristic
279C22×C4#612711yescharacteristic
280C22×C4#612711yescharacteristic
281C22×C4D4×D1312yes—
282C22×C4#612912yes—
283C22×C4#612912yes—
284C22×C4#613112yes—
285M16—264no—
286M16—264no—
287M16—522no—
288M16—522no—
289C2×C8—264no—
290C2×C8—522no—
291C2×C8—522no—
292C4⋊C4—24no—
293C4⋊C4—24no—
294C4⋊C4—24no—
295C4⋊C4—42no—
296C4⋊C4—262no—
297C4⋊C4—262no—
298C4⋊C4—262no—
299C4⋊C4—262no—
300C4⋊C4—1042no—
301C4⋊C4—1042no—
302C22⋊C4—522no—
303C22⋊C4—522no—
304C42—24no—
305C42—42no—
306C42—522no—
307C42—522no—
308C13#1129611yescharacteristic, complemented, Sylow
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23C2×#610111yescharacteristic
314C23#8817811yescharacteristic
315C23#8818411yescharacteristic
316C23#8818911yescharacteristic
317C23#8819011yescharacteristic
318C23#8819111yescharacteristic
319C23#8820111yescharacteristic
320C2×C4—24no—
321C2×C4—24no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—44no—
331C2×C4—44no—
332C2×C4—42no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—522no—
338C2×C4—522no—
339C2×C4—522no—
340C2×C4—522no—
341C2×C4—522no—
342C2×C4—522no—
343C2×C4C4×Dic2611yescharacteristic
344C2×C4#8812311yescharacteristic
345C2×C4#8812411yescharacteristic
346C2×C4C4×D5211yescharacteristic
347C2×C4#8813212yes—
348C2×C4#8813212yes—
349C2×C4#8813312yes—
350C2×C4#8813512yes—
351C2×C4#8813912yes—
352C2×C4#8814012yes—
353C2×C4#8814412yes—
354C2×C4#8814412yes—
355C2×C4#8814612yes—
356C2×C4#8814812yes—
357C2×C4#8814912yes—
358C2×C4#8815212yes—
359C8—524no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22#1171858911yescharacteristic
373C22#1171860711yescharacteristic
374C22#1171860811yescharacteristic
375C22#1171861411yescharacteristic
376C22#1171863811yescharacteristic
377C22#1171864711yescharacteristic
378C22#1171865211yescharacteristic
379C22#1171872211yescharacteristic
380C22#1171872311yescharacteristic
381C22#1171873811yescharacteristic
382C22#1171875611yescharacteristic
383C4—44no—
384C4—44no—
385C4—82no—
386C4—1042no—
387C4—1042no—
388C4#1171831612yes—
389C4#1171832112yes—
390C4#1171832212yes—
391C4#1171833112yes—
392C2—21no—
393C2—21no—
394C2—21no—
395C2—21no—
396C2#1311309211yescharacteristic
397C2#1311504511yescharacteristic
398C2#1311505011yescharacteristic
399C2#1311599211yescharacteristic
400C2#1311599711yescharacteristic
401C2#1311606011yescharacteristic
402C2#1311606511yescharacteristic
subgroupG/H
centerC23#88191
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×C4⋊#95C2
socleC23×C13#120
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenterC4⋊#95D13
hypocenterC13#11296
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
15. #11718122C4semidirect
308. C13#11296semidirect

Maximal subgroups

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

subgroupindex
#131174542
C2×#117181222
#131145552
C2×#117181152
C13×C4⋊#952
#1129613