Finite Group Databasebeta

← #16785079

Subgroups — #16785079

Order 3328.

572 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130690C211yesmaximal, characteristic
2C4×C22⋊#1057C211yesmaximal, characteristic
3#13129674C212yesmaximal
4#13129674C212yesmaximal
5C2×#11718313C211yesmaximal, characteristic
6C22×#6101C411yescharacteristic
7C22×#6101C411yescharacteristic
8C22×C4×Dic13C2211yescharacteristic
9C2×C22⋊#1057C2212yes—
10C2×C22⋊#1057C2212yes—
11C2×C4⋊#1057—21no—
12C2×C4×#1057—21no—
13C2×C13×#95C411yescharacteristic
14C2×#88071C411yescharacteristic
15C2×#88071C2211yescharacteristic
16C2×#88071C2211yescharacteristic
17#11718313—21no—
18#11718313—21no—
19#11718313—21no—
20#11718313—21no—
21#11718290—21no—
22#11718290—21no—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×Dic13C2×C411yescharacteristic
27C23×Dic13C2×C411yescharacteristic
28C23×Dic13C2×C411yescharacteristic
29C23×Dic13C2311yescharacteristic
30C22×#1057—22no—
31C22×#1057—22no—
32C2×#6101—21no—
33C2×#6101—21no—
34C2×#6101—22no—
35C2×#6101—21no—
36C2×#6101—21no—
37C2×#6101—42no—
38C2×#6101C814yescomplemented
39C2×C4×Dic13—42no—
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C22⋊#1057—22no—
45C22⋊#1057—24no—
46C22⋊#1057Q814yes—
47C4⋊#1057—42no—
48C4×#1057—42no—
49C13×#95—21no—
50C13×#95—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#9880—131nomaximal, Sylow
58C24×C13C22×C411yescharacteristic
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—22no—
62C22×C4×C13—22no—
63C22×C4×C13—41no—
64C22×C4×C13—41no—
65C22×C4×C13—41no—
66C22×C4×C13—41no—
67C22×C4×C13—41no—
68C22×C4×C13—41no—
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C2×C812yes—
72C22×C4×C13M1612yes—
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—22no—
78C22×Dic13—22no—
79C22×Dic13—41no—
80C22×Dic13—41no—
81C22×Dic13—41no—
82C22×Dic13—41no—
83C22×Dic13—41no—
84C22×Dic13—41no—
85C22×Dic13—41no—
86C22×Dic13C22⋊C411yescharacteristic
87C22×Dic13C22⋊C411yescharacteristic
88C22×Dic13C2×C812yes—
89C22×Dic13C2×C812yes—
90C22×Dic13C2×D411yescharacteristic
91C22×Dic13C2×D411yescharacteristic
92C22×Dic13C2×Q812yes—
93C22×Dic13#4112yes—
94C2×#1057—24no—
95C2×#1057—42no—
96C2×#1057—42no—
97C2×#1057—42no—
98C2×#1057—42no—
99C2×#1057—42no—
100#6101—24no—
101#6101—24no—
102#6101—42no—
103#6101—42no—
104C4×Dic13—22no—
105C4×Dic13—22no—
106C4×Dic13—41no—
107C4×Dic13—41no—
108C2×#387—131no—
109#1797—131no—
110C4×C22⋊C8—131no—
111#1280—132no—
112#1280—132no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13C2×C22⋊C411yescharacteristic
118C23×C13C4×Q812yes—
119C23×C13C22×C811yescharacteristic
120C23×C13C2×M1611yescharacteristic
121C23×C13#13112yes—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—82no—
135C2×C4×C13—82no—
136C2×C4×C13C22⋊C812yes—
137C2×C4×C13C22⋊C812yes—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—22no—
145C2×Dic13—22no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—42no—
150C2×Dic13—42no—
151C2×Dic13—44no—
152C2×Dic13—42no—
153C2×Dic13—42no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—42no—
159C2×Dic13—42no—
160C2×Dic13#9912yes—
161C2×Dic13C22⋊Q812yes—
162C2×Dic13#12411yescharacteristic
163C2×Dic13C4⋊Q811yescharacteristic
164#1057—44no—
165#1057—82no—
166C22×C4⋊C4—131no—
167C22×C4⋊C4—131no—
168C22×C42—131no—
169C2×C4⋊C8—261no—
170C2×C22⋊C8—132no—
171C2×C22⋊C8—132no—
172C2×C4×C8—261no—
173#387—261no—
174#387—261no—
175#387—261no—
176#387—261no—
177C2×#95—131no—
178C2×#95—131no—
179C2×#95—131no—
180C2×#95#26111yescharacteristic
181#336—261no—
182#336—261no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—22no—
188C22×C13—22no—
189C22×C13—22no—
190C22×C13—22no—
191C22×C13#39111yescharacteristic
192C22×C13C2×C22⋊C811yescharacteristic
193C22×C13#40811yescharacteristic
194C22×C13C2×#9911yescharacteristic
195C22×C13#41011yescharacteristic
196C22×C13#41311yescharacteristic
197C22×C13#41311yescharacteristic
198C22×C13C8×Q812yes—
199C22×C13#44612yes—
200C4×C13—22no—
201C4×C13—22no—
202C4×C13—81no—
203C4×C13—81no—
204Dic13—22no—
205Dic13—22no—
206Dic13—21no—
207Dic13—21no—
208Dic13—42no—
209Dic13—42no—
210Dic13—41no—
211C23×C4—131no—
212C23×C4—131no—
213C23×C4—131no—
214C23×C4—131no—
215C23×C4C2×#26111yescharacteristic
216C23×C4C2×#26111yescharacteristic
217C23×C4C2×#26111yescharacteristic
218C22×C8—262no—
219C22×C8—262no—
220C2×C4⋊C4—134no—
221C2×C4⋊C4—262no—
222C2×C4⋊C4—261no—
223C2×C4⋊C4—261no—
224C2×C4⋊C4—261no—
225C2×C4⋊C4—261no—
226C2×C4⋊C4—522no—
227C2×C42—131no—
228C2×C42—131no—
229C2×C42—131no—
230C2×C42—131no—
231C2×C42—522no—
232C4⋊C8—522no—
233C22⋊C8—134no—
234C22⋊C8—262no—
235C22⋊C8—264no—
236C4×C8—522no—
237#95—21no—
238#95—21no—
239#95—261no—
240#95—261no—
241#95—261no—
242#95—261no—
243#95—261no—
244#95—261no—
245C2×C13—22no—
246C2×C13—22no—
247C2×C13#145811yescharacteristic
248C2×C13#145911yescharacteristic
249C2×C13#146811yescharacteristic
250C2×C13#147311yescharacteristic
251C2×C13#198411yescharacteristic
252C2×C13#199611yescharacteristic
253C2×C13#199811yescharacteristic
254C24C22×#26111yescharacteristic
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—131no—
266C22×C4—131no—
267C22×C4—131no—
268C22×C4—132no—
269C22×C4—132no—
270C22×C4—131no—
271C22×C4—132no—
272C22×C4—132no—
273C22×C4—262no—
274C22×C4—261no—
275C22×C4—261no—
276C22×C4—262no—
277C22×C4—261no—
278C22×C4—261no—
279C22×C4—521no—
280C22×C4—521no—
281C22×C4—521no—
282C22×C4—521no—
283C22×C4—521no—
284C22×C4—521no—
285C22×C4—521no—
286C22×C4D13⋊C812yes—
287C22×C4#611812yes—
288C22×C4C22⋊#26111yescharacteristic
289C22×C4C22⋊#26111yescharacteristic
290C2×C8—264no—
291C2×C8—522no—
292C2×C8—522no—
293C2×C8—522no—
294C2×C8—522no—
295C2×C8—522no—
296C4⋊C4—264no—
297C4⋊C4—264no—
298C4⋊C4—522no—
299C4⋊C4—522no—
300C42—262no—
301C42—262no—
302C42—521no—
303C42—521no—
304C13#988011yescharacteristic, complemented, Sylow
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23C2×D13⋊C811yescharacteristic
310C23C2×#611811yescharacteristic
311C23#8823812yes—
312C23Q8×#26112yes—
313C23C2×C22⋊#26111yescharacteristic
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—132no—
329C2×C4—132no—
330C2×C4—131no—
331C2×C4—131no—
332C2×C4—261no—
333C2×C4—261no—
334C2×C4—261no—
335C2×C4—261no—
336C2×C4—261no—
337C2×C4—261no—
338C2×C4—262no—
339C2×C4—262no—
340C2×C4—261no—
341C2×C4—261no—
342C2×C4—261no—
343C2×C4—522no—
344C2×C4—522no—
345C2×C4—524no—
346C2×C4—522no—
347C2×C4—522no—
348C2×C4—521no—
349C2×C4—521no—
350C2×C4—521no—
351C2×C4—521no—
352C2×C4—522no—
353C2×C4—522no—
354C2×C4#8811112yes—
355C2×C4#8811112yes—
356C8—524no—
357C8—1042no—
358C22—22no—
359C22—22no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—22no—
365C22—22no—
366C22#1171907412yes—
367C22#1171908012yes—
368C22#1171911611yescharacteristic
369C22C2×#8811111yescharacteristic
370C22#1171913211yescharacteristic
371C22D13⋊#9911yescharacteristic
372C22#1171914711yescharacteristic
373C22#1171914811yescharacteristic
374C22(C2×#261)⋊Q811yescharacteristic
375C4—22no—
376C4—22no—
377C4—81no—
378C4—81no—
379C4—262no—
380C4—261no—
381C4—261no—
382C4—262no—
383C4—522no—
384C4—522no—
385C4—521no—
386C2—22no—
387C2—22no—
388C2#1313006911yescharacteristic
389C2#1313007411yescharacteristic
390C2#1313010211yescharacteristic
391C2#1313011711yescharacteristic
392C2#1313100611yescharacteristic
393C2#1313102711yescharacteristic
394C2#1313103011yescharacteristic
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#9880
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
38. C2×#6101C8semidirect
304. C13#9880semidirect

Maximal subgroups

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

subgroupindex
#131306902
C4×C22⋊#10572
#131296742
C2×#117183132
#988013