Finite Group Databasebeta

← #16795246

Subgroups — #16795246

Order 3328.

678 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131731C211yesmaximal, characteristic
2#13131729C211yesmaximal, characteristic
3#13130430C214yesmaximal, complemented
4#13130423C214yesmaximal, complemented
5#13130385C211yesmaximal, characteristic
6#13130140C211yesmaximal, characteristic
7#13130138C211yesmaximal, characteristic
8#13130039C211yesmaximal, characteristic
9C2×#11718451C211yesmaximal, characteristic
10C2×Q8×Dic13C2211yescharacteristic
11C22×#6107C411yescharacteristic
12C2×#88141C2211yescharacteristic
13Q8×#1057—22no—
14Q8×#1057C2214yes—
15#11719125—22no—
16#11719119—22no—
17#11719119C2211yescharacteristic
18#11719119C2211yescharacteristic
19#11719119C2211yescharacteristic
20#11719119C2211yescharacteristic
21#11719074—22no—
22#11719074C2214yes—
23C2×C13×#103C411yescharacteristic
24C2×#88056C411yescharacteristic
25C2×C8×Dic13C2211yescharacteristic
26C2×#88047C411yescharacteristic
27#11718451C412yes—
28#11718451C412yes—
29#11718451C2212yes—
30#11718451C2212yes—
31Q8⋊#1057C2214yes—
32#11718256C2212yes—
33#11718255C2212yes—
34#11718251C2212yes—
35C8×#1057C2212yes—
36#11718244C2214yes—
37C22×Q8×C13C2×C411yescharacteristic
38C22×Dic26C2×C411yescharacteristic
39C22×C8×C13C2×C411yescharacteristic
40C2×C13×C4⋊C4C2×C411yescharacteristic
41Q8×Dic13—21no—
42Q8×Dic13—21no—
43Q8×Dic13C2×C412yes—
44Q8×Dic13C2312yes—
45C2×#6107C818yescomplemented
46C2×#6107C2×C412yes—
47C2×#6107C2×C412yes—
48C2×C4⋊Dic13—21no—
49C2×C4⋊Dic13C2×C411yescharacteristic
50C2×#6101—21no—
51C2×C4×Dic13—21no—
52C2×C4×Dic13—21no—
53C2×C4×Dic13C2311yescharacteristic
54C22×#1055C2×C411yescharacteristic
55#88141—21no—
56#88141—21no—
57#88141C2×C412yes—
58#88141C2312yes—
59C22⋊#1057—21no—
60C22⋊#1057—21no—
61C22⋊#1057—21no—
62C22⋊#1057D412yes—
63#88112—24no—
64C4⋊#1057—24no—
65C4⋊#1057—21no—
66C4⋊#1057D412yes—
67C4⋊#1057C2312yes—
68C4⋊#1057C2312yes—
69C4×#1057—24no—
70C4×#1057—24no—
71C4×#1057—21no—
72C4×#1057—21no—
73C4×#1057C2312yes—
74C4×#1057C2312yes—
75C13×#103C2×C412yes—
76C13×#103C2×C412yes—
77#88056C2×C412yes—
78#88056C2×C412yes—
79C8×Dic13C2×C411yescharacteristic
80C8×Dic13C2×C411yescharacteristic
81C8×Dic13C2311yescharacteristic
82C8×Dic13C2311yescharacteristic
83#88047C2×C412yes—
84#88047C2×C412yes—
85#17856—131nomaximal, Sylow
86C2×Q8×C13—21no—
87C2×Q8×C13—22no—
88C2×Q8×C13C2×C814yes—
89C2×Q8×C13C22×C412yes—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13C22×C411yescharacteristic
93C22×Dic13—21no—
94C22×Dic13—21no—
95C22×Dic13C2×D411yescharacteristic
96C22×Dic13#4111yescharacteristic
97C2×Dic26—21no—
98C2×Dic26—22no—
99C2×Dic26C2×C814yes—
100C2×Dic26C22×C412yes—
101C2×#1057—22no—
102C2×#1057—22no—
103C2×#1057—22no—
104C2×#1057C2×D414yes—
105C2×C8×C13—22no—
106C2×C8×C13C22×C411yescharacteristic
107C2×C8×C13C22×C411yescharacteristic
108C13×C4⋊C4—21no—
109C13×C4⋊C4C22×C412yes—
110#6107C2×C818yes—
111#6107C2×C818yes—
112C4⋊Dic13—21no—
113C4⋊Dic13—22no—
114C4⋊Dic13—22no—
115C4⋊Dic13C22×C412yes—
116#6101—22no—
117#6101—22no—
118C4×Dic13—22no—
119C4×Dic13—22no—
120C4×Dic13—22no—
121C4×Dic13—22no—
122C4×Dic13C22×C411yescharacteristic
123C4×Dic13C2×D411yescharacteristic
124C4×Dic13#4111yescharacteristic
125C4×Dic13C2411yescharacteristic
126C2×#1055C2×C814yes—
127C2×#1055C22×C411yescharacteristic
128C2×#1055C22×C411yescharacteristic
129#2982—131no—
130#2982—131no—
131C2×C4×Q16—131no—
132#1579—134no—
133C8×Q16—134no—
134#1564—131no—
135#1479—131no—
136#1479—131no—
137#1450—131no—
138C23×C13C4×D411yescharacteristic
139Q8×C13—22no—
140Q8×C13—24no—
141Q8×C13C22×C814yes—
142C2×C4×C13—22no—
143C2×C4×C13—24no—
144C2×C4×C13—22no—
145C2×C4×C13—81no—
146C2×C4×C13C4×D411yescharacteristic
147C2×C4×C13C22×C812yes—
148C2×C4×C13#13112yes—
149C2×C4×C13C23×C411yescharacteristic
150C2×Dic13—22no—
151C2×Dic13—24no—
152C2×Dic13—22no—
153C2×Dic13—22no—
154C2×Dic13—41no—
155C2×Dic13—81no—
156C2×Dic13C4×D411yescharacteristic
157C2×Dic13C4×D411yescharacteristic
158C2×Dic13C22×D411yescharacteristic
159C2×Dic13C2×#4111yescharacteristic
160Dic26—22no—
161Dic26—24no—
162Dic26C22×C814yes—
163#1057—24no—
164#1057—42no—
165#1057—42no—
166#1057—42no—
167C8×C13—21no—
168C8×C13—21no—
169#1055C22×C812yes—
170#1055C22×C812yes—
171C22×Q16—131no—
172C2×C4×Q8—131no—
173C2×C4×Q8—131no—
174C8×Q8—134no—
175C8×Q8—134no—
176C8×Q8—262no—
177C8×Q8—262no—
178C4×Q16—132no—
179C4×Q16—132no—
180C4×Q16—132no—
181C4×Q16—132no—
182#431—131no—
183#431—131no—
184#431—131no—
185#431—131no—
186#431—262no—
187#431—262no—
188C2×#107—131no—
189C2×#103—131no—
190C2×#103#26111yescharacteristic
191C2×C4×C8—131no—
192#335—132no—
193#334—132no—
194Q8⋊C8—134no—
195Q8⋊C8—134no—
196#322—132no—
197C82—132no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13C8×D412yes—
201C22×C13C2×C4×D411yescharacteristic
202C4×C13—24no—
203C4×C13—42no—
204C4×C13C8×D412yes—
205C4×C13C23×C811yescharacteristic
206C4×C13C2×#13111yescharacteristic
207Dic13—24no—
208Dic13—21no—
209Dic13—21no—
210Dic13—21no—
211Dic13—42no—
212Dic13#57812yes—
213C22×Q8—131no—
214C22×Q8C2×#26111yescharacteristic
215C2×Q16—138no—
216C2×Q16—132no—
217C2×Q16—132no—
218C22×C8—131no—
219C22×C8C2×#26111yescharacteristic
220C4×Q8—132no—
221C4×Q8—132no—
222C4×Q8—132no—
223C4×Q8—132no—
224C4×Q8—261no—
225C4×Q8—261no—
226C4×Q8—261no—
227C4×Q8—261no—
228C2×C4⋊C4—131no—
229C2×C4⋊C4—261no—
230C2×C4⋊C4—261no—
231C2×C4⋊C4C2×#26111yescharacteristic
232C2×C42—131no—
233C2×C42—261no—
234C2×C42—261no—
235#107—132no—
236#107—132no—
237C4⋊C8—132no—
238C4⋊C8—132no—
239C4⋊C8—132no—
240C4⋊C8—261no—
241C4⋊C8—264no—
242C4⋊C8—264no—
243#103—132no—
244#103—132no—
245#103C2×#26112yes—
246#103C2×#26112yes—
247C22⋊C8—132no—
248C22⋊C8—261no—
249C22⋊C8—261no—
250C22⋊C8—261no—
251C4×C8—132no—
252C4×C8—131no—
253C4×C8—131no—
254C4×C8—131no—
255C4×C8—131no—
256C4×C8—132no—
257C4×C8—261no—
258C4×C8—261no—
259C4×C8—264no—
260C4×C8—264no—
261C2×C13—22no—
262C2×C13C2×C8×D411yescharacteristic
263C2×C13#295011yescharacteristic
264C2×C13#295711yescharacteristic
265C2×Q8—22no—
266C2×Q8—21no—
267C2×Q8—134no—
268C2×Q8—132no—
269C2×Q8—262no—
270C2×Q8—261no—
271C2×Q8D13⋊C814yes—
272C2×Q8C22×#26112yes—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—131no—
276C22×C4—131no—
277C22×C4—261no—
278C22×C4—261no—
279C22×C4C22×#26111yescharacteristic
280Q16—138no—
281Q16—138no—
282C2×C8—22no—
283C2×C8—134no—
284C2×C8—131no—
285C2×C8—131no—
286C2×C8—134no—
287C2×C8—262no—
288C2×C8—262no—
289C2×C8—262no—
290C2×C8C22×#26111yescharacteristic
291C2×C8C22×#26111yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—132no—
294C4⋊C4—262no—
295C4⋊C4—262no—
296C4⋊C4—262no—
297C4⋊C4—262no—
298C4⋊C4—261no—
299C4⋊C4C22×#26112yes—
300C42—131no—
301C42—131no—
302C42—131no—
303C42—131no—
304C42—262no—
305C42—262no—
306C42—262no—
307C42—262no—
308C13#1785611yescharacteristic, complemented, Sylow
309C23D4×#26111yescharacteristic
310Q8—24no—
311Q8—22no—
312Q8—134no—
313Q8—264no—
314Q8—262no—
315Q8C2×D13⋊C814yes—
316C2×C4—24no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—81no—
320C2×C4—131no—
321C2×C4—131no—
322C2×C4—131no—
323C2×C4—131no—
324C2×C4—262no—
325C2×C4—264no—
326C2×C4—262no—
327C2×C4—262no—
328C2×C4—521no—
329C2×C4—1041no—
330C2×C4C2×D13⋊C812yes—
331C2×C4#8823812yes—
332C2×C4D4×#26111yescharacteristic
333C2×C4C23×#26111yescharacteristic
334C8—21no—
335C8—21no—
336C8—132no—
337C8—132no—
338C8—264no—
339C8—522no—
340C8—522no—
341C8—522no—
342C22—21no—
343C22—21no—
344C22#1171906312yes—
345C22C2×D4×#26111yescharacteristic
346C4—24no—
347C4—42no—
348C4—132no—
349C4—264no—
350C4—261no—
351C4—261no—
352C4—261no—
353C4—522no—
354C4#1171906312yes—
355C4C22×D13⋊C811yescharacteristic
356C4C2×#8823811yescharacteristic
357C2—22no—
358C2C2×#1171906311yescharacteristic
359C2#1313159711yescharacteristic
360C2#1313161411yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC4×C13C23×C8
FrattiniC2×C4C23×#261
FittingC2×C13×#103C4
socleC22×C13C2×C4×D4
prime radicalC23×C13C4×D4
cosocleC4×Dic13C24
hypercenterC2×#103#261
hypocenterC13#17856
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. #13130430C2semidirect
4. #13130423C2semidirect
45. C2×#6107C8semidirect
308. C13#17856semidirect

Maximal subgroups

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

subgroupindex
#131317312
#131317292
#131304302
#131304232
#131303852
#131301402
#131301382
#131300392
C2×#117184512
#1785613