Finite Group Databasebeta

← #16784556

Subgroups — #16784556

Order 3328.

656 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130692C211yesmaximal, characteristic
2C4×C22⋊#1057C211yesmaximal, characteristic
3C2×#11718286C212yesmaximal
4C2×#11718285C212yesmaximal
5C2×#11718308C211yesmaximal, characteristic
6C22×C4⋊Dic13C2211yescharacteristic
7C22×#6101C411yescharacteristic
8C22×#6101C411yescharacteristic
9C22×#6101C2211yescharacteristic
10C22×C4×Dic13C2211yescharacteristic
11C2×C22⋊#1057C2212yes—
12C2×C22⋊#1057C2212yes—
13C2×#88112—21no—
14C2×C4×#1057—21no—
15C2×C13×#95C411yescharacteristic
16C2×#88071C411yescharacteristic
17#11718308—21no—
18#11718308—21no—
19#11718308—21no—
20#11718308—21no—
21#11718290—21no—
22#11718290—21no—
23#11718286—24no—
24#11718285—24no—
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C23×C4×C13C2×C411yescharacteristic
28C23×Dic13C2×C411yescharacteristic
29C23×Dic13C2×C411yescharacteristic
30C23×Dic13C2×C411yescharacteristic
31C23×Dic13C2311yescharacteristic
32C22×#1057—22no—
33C22×#1057—22no—
34C2×C4⋊Dic13—22no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—22no—
38C2×#6101—21no—
39C2×#6101—21no—
40C2×#6101—22no—
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6101—22no—
44C2×#6101—21no—
45C2×#6101—21no—
46C2×#6101—22no—
47C2×#6101—42no—
48C2×#6101C814yescomplemented
49C2×C4×Dic13—42no—
50C2×C4×Dic13D411yescharacteristic
51C2×C4×Dic13D411yescharacteristic
52C2×C4×Dic13D411yescharacteristic
53C2×C4×Dic13D411yescharacteristic
54C22⋊#1057—22no—
55C22⋊#1057—22no—
56C22⋊#1057—22no—
57C22⋊#1057D414yes—
58#88112—42no—
59C4×#1057—42no—
60C13×#95—21no—
61C13×#95—21no—
62#88071—21no—
63#88071—21no—
64#9650—131nomaximal, Sylow
65C24×C13C22×C411yescharacteristic
66C22×C4×C13—21no—
67C22×C4×C13—22no—
68C22×C4×C13—21no—
69C22×C4×C13—22no—
70C22×C4×C13—22no—
71C22×C4×C13—22no—
72C22×C4×C13—21no—
73C22×C4×C13—22no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13—41no—
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C2×C812yes—
80C22×Dic13—22no—
81C22×Dic13—22no—
82C22×Dic13—21no—
83C22×Dic13—22no—
84C22×Dic13—21no—
85C22×Dic13—22no—
86C22×Dic13—21no—
87C22×Dic13—22no—
88C22×Dic13—41no—
89C22×Dic13—41no—
90C22×Dic13—41no—
91C22×Dic13—41no—
92C22×Dic13C22⋊C411yescharacteristic
93C22×Dic13C22⋊C411yescharacteristic
94C22×Dic13C2×C812yes—
95C22×Dic13C2×C812yes—
96C22×Dic13M1612yes—
97C22×Dic13C2×D411yescharacteristic
98C22×Dic13C2×D411yescharacteristic
99C22×Dic13C2×D412yes—
100C22×Dic13#4112yes—
101C2×#1057—24no—
102C2×#1057—42no—
103C2×#1057—42no—
104C2×#1057—42no—
105C2×#1057—42no—
106C2×#1057—42no—
107C4⋊Dic13—42no—
108C4⋊Dic13—41no—
109C4⋊Dic13—41no—
110#6101—24no—
111#6101—24no—
112#6101—42no—
113#6101—42no—
114#6101—42no—
115#6101—41no—
116#6101—41no—
117C4×Dic13—22no—
118C4×Dic13—22no—
119C4×Dic13—41no—
120C4×Dic13—41no—
121C2×#389—131no—
122#1797—131no—
123C4×C22⋊C8—131no—
124C2×#324—132no—
125C2×#324—132no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—21no—
129C23×C13—21no—
130C23×C13C2×C22⋊C411yescharacteristic
131C23×C13C4×D412yes—
132C23×C13C22×C811yescharacteristic
133C23×C13C2×M1611yescharacteristic
134C23×C13#13112yes—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—22no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—24no—
142C2×C4×C13—44no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—42no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—82no—
150C2×C4×C13#10112yes—
151C2×Dic13—21no—
152C2×Dic13—21no—
153C2×Dic13—21no—
154C2×Dic13—21no—
155C2×Dic13—21no—
156C2×Dic13—21no—
157C2×Dic13—24no—
158C2×Dic13—24no—
159C2×Dic13—22no—
160C2×Dic13—24no—
161C2×Dic13—42no—
162C2×Dic13—42no—
163C2×Dic13—41no—
164C2×Dic13—41no—
165C2×Dic13—42no—
166C2×Dic13—41no—
167C2×Dic13—41no—
168C2×Dic13—41no—
169C2×Dic13—82no—
170C2×Dic13C22⋊C812yes—
171C2×Dic13C22⋊C812yes—
172C2×Dic13#9912yes—
173C2×Dic13#10112yes—
174C2×Dic13#12112yes—
175C2×Dic13#12411yescharacteristic
176C2×Dic13#12711yescharacteristic
177#1057—44no—
178#1057—82no—
179C22×C4⋊C4—131no—
180C22×C4⋊C4—131no—
181C22×C4⋊C4—131no—
182C22×C4⋊C4—131no—
183C22×C42—131no—
184C2×C4⋊C8—261no—
185C2×C22⋊C8—132no—
186C2×C22⋊C8—132no—
187C2×C4×C8—261no—
188#389—261no—
189#389—261no—
190#389—261no—
191#389—261no—
192C2×#95—131no—
193C2×#95#26111yescharacteristic
194#336—261no—
195#336—261no—
196#324—264no—
197#324—264no—
198C22×C13—22no—
199C22×C13—22no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—22no—
205C22×C13—22no—
206C22×C13#39011yescharacteristic
207C22×C13C2×C22⋊C811yescharacteristic
208C22×C13#40811yescharacteristic
209C22×C13C2×#9911yescharacteristic
210C22×C13#41011yescharacteristic
211C22×C13C2×#10111yescharacteristic
212C22×C13C2×#10111yescharacteristic
213C22×C13C8×D412yes—
214C22×C13#43612yes—
215C4×C13—22no—
216C4×C13—42no—
217C4×C13—41no—
218C4×C13—81no—
219Dic13—22no—
220Dic13—21no—
221Dic13—21no—
222Dic13—22no—
223Dic13—42no—
224Dic13—81no—
225Dic13#32414yescomplemented
226C23×C4—131no—
227C23×C4—131no—
228C23×C4—131no—
229C23×C4—131no—
230C23×C4C2×#26111yescharacteristic
231C23×C4C2×#26111yescharacteristic
232C23×C4C2×#26111yescharacteristic
233C22×C8—262no—
234C22×C8—262no—
235C2×C4⋊C4—134no—
236C2×C4⋊C4—262no—
237C2×C4⋊C4—261no—
238C2×C4⋊C4—261no—
239C2×C4⋊C4—262no—
240C2×C4⋊C4—262no—
241C2×C4⋊C4—262no—
242C2×C4⋊C4—261no—
243C2×C4⋊C4—261no—
244C2×C4⋊C4—261no—
245C2×C4⋊C4—261no—
246C2×C4⋊C4—262no—
247C2×C4⋊C4—261no—
248C2×C4⋊C4—261no—
249C2×C4⋊C4—522no—
250C2×C42—131no—
251C2×C42—131no—
252C2×C42—131no—
253C2×C42—131no—
254C2×C42—522no—
255C4⋊C8—522no—
256C22⋊C8—134no—
257C22⋊C8—262no—
258C22⋊C8—262no—
259C22⋊C8—262no—
260C4×C8—522no—
261#95—21no—
262#95—21no—
263#95—261no—
264#95—261no—
265C2×C13—22no—
266C2×C13—22no—
267C2×C13C2×#32411yescharacteristic
268C2×C13#146111yescharacteristic
269C2×C13#147011yescharacteristic
270C2×C13#147211yescharacteristic
271C2×C13#195411yescharacteristic
272C2×C13#196411yescharacteristic
273C2×C13#196611yescharacteristic
274C24C22×#26111yescharacteristic
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—21no—
280C22×C4—22no—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—131no—
287C22×C4—132no—
288C22×C4—132no—
289C22×C4—131no—
290C22×C4—131no—
291C22×C4—131no—
292C22×C4—132no—
293C22×C4—132no—
294C22×C4—132no—
295C22×C4—262no—
296C22×C4—262no—
297C22×C4—261no—
298C22×C4—262no—
299C22×C4—262no—
300C22×C4—261no—
301C22×C4—261no—
302C22×C4—262no—
303C22×C4—521no—
304C22×C4—521no—
305C22×C4—521no—
306C22×C4—521no—
307C22×C4D13⋊C812yes—
308C22×C4C22⋊#26111yescharacteristic
309C22×C4C22⋊#26111yescharacteristic
310C2×C8—264no—
311C2×C8—522no—
312C2×C8—522no—
313C2×C8—522no—
314C2×C8—522no—
315C2×C8—522no—
316C4⋊C4—264no—
317C4⋊C4—264no—
318C4⋊C4—522no—
319C4⋊C4—521no—
320C4⋊C4—521no—
321C4⋊C4—522no—
322C4⋊C4—521no—
323C4⋊C4—521no—
324C4⋊C4—522no—
325C4⋊C4—522no—
326C42—262no—
327C42—262no—
328C42—521no—
329C42—521no—
330C13#965011yescharacteristic, complemented, Sylow
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23C2×D13⋊C811yescharacteristic
336C23D13⋊M1611yescharacteristic
337C23#8823812yes—
338C23D4×#26112yes—
339C23C2×C22⋊#26111yescharacteristic
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—24no—
343C2×C4—22no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—44no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—82no—
355C2×C4—132no—
356C2×C4—132no—
357C2×C4—132no—
358C2×C4—132no—
359C2×C4—132no—
360C2×C4—131no—
361C2×C4—131no—
362C2×C4—264no—
363C2×C4—264no—
364C2×C4—261no—
365C2×C4—261no—
366C2×C4—261no—
367C2×C4—261no—
368C2×C4—261no—
369C2×C4—261no—
370C2×C4—264no—
371C2×C4—262no—
372C2×C4—522no—
373C2×C4—522no—
374C2×C4—522no—
375C2×C4—521no—
376C2×C4—521no—
377C2×C4—521no—
378C2×C4—521no—
379C2×C4—521no—
380C2×C4—1042no—
381C2×C4#8811312yes—
382C8—524no—
383C8—1042no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—22no—
389C22—22no—
390C22—22no—
391C22—22no—
392C22#1171906312yes—
393C22#1171906612yes—
394C22#1171911611yescharacteristic
395C22D13⋊(C22⋊C8)11yescharacteristic
396C22C2×#8811311yescharacteristic
397C22D13⋊#9911yescharacteristic
398C22#1171914611yescharacteristic
399C22#1171915111yescharacteristic
400C22D13⋊#10111yescharacteristic
401C4—22no—
402C4—41no—
403C4—42no—
404C4—81no—
405C4—134no—
406C4—262no—
407C4—262no—
408C4—261no—
409C4—261no—
410C4—522no—
411C4—1041no—
412C2—22no—
413C2—22no—
414C2D13⋊#32411yescharacteristic
415C2#1313007811yescharacteristic
416C2#1313010811yescharacteristic
417C2#1313011511yescharacteristic
418C2#1313095911yescharacteristic
419C2#1313097711yescharacteristic
420C2#1313097911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC23×C13C22×C8
FrattiniC24C22×#261
FittingC2×C13×#95C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22×C4
cosocleC23×Dic13C23
hypercenterC2×#95#261
hypocenterC13#9650
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
48. C2×#6101C8semidirect
225. Dic13#324semidirect
330. C13#9650semidirect

Maximal subgroups

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

subgroupindex
#131306922
C4×C22⋊#10572
C2×#117182862
C2×#117182852
C2×#117183082
#965013