Finite Group Databasebeta

← #115940

Subgroups — #115940

Order 512.

602 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21836C211yesmaximal, characteristic
2#21353C211yesmaximal, characteristic
3C22×#330C211yesmaximal, characteristic
4C2×#1470C211yesmaximal, characteristic
5C2×#1302C211yesmaximal, characteristic
6#8036C211yesmaximal, characteristic
7C2×#1281C211yesmaximal, characteristic
8C22×#125C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C22×#97C2211yescharacteristic
13C22×#97C2211yescharacteristic
14#2283C2211yescharacteristic
15#1991—22no—
16#1989—22no—
17#1940—22no—
18#1850—22no—
19#1824C412yes—
20#1823C412yes—
21#1768—22no—
22C2×#330—22no—
23C2×#330—22no—
24C2×#330—22no—
25#1470—22no—
26#1470—22no—
27C2×#324—22no—
28#1302—22no—
29#1295—22no—
30#1281—22no—
31C23×C8—21no—
32C23×C8—21no—
33C2×#125—21no—
34C2×#125—21no—
35C2×#125—21no—
36C2×#125—21no—
37C2×#125—21no—
38C2×#125—21no—
39C2×#125—21no—
40C2×#125—21no—
41C2×#125—21no—
42C2×#125—21no—
43C2×#125D412yes—
44C2×#125Q812yes—
45C22×C4⋊C4—21no—
46C22×C4⋊C4—21no—
47C22×C4⋊C4C2×C411yescharacteristic
48C22×C4⋊C4C2×C411yescharacteristic
49C22×C42C2311yescharacteristic
50#432—21no—
51#432—21no—
52#432—21no—
53#432D412yes—
54#431—21no—
55#431—21no—
56#431—21no—
57#431—21no—
58#431—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62C2×C4⋊C8—21no—
63C2×C4⋊C8—24no—
64C2×C4⋊C8—21no—
65C2×C4⋊C8—21no—
66C2×C22⋊C8—21no—
67C2×C22⋊C8C2×C412yes—
68C2×C22⋊C8D412yes—
69C2×#97—21no—
70C2×#97—21no—
71C2×#97—21no—
72C2×#97—21no—
73C2×#97—21no—
74C2×#97—21no—
75C2×#97—21no—
76C2×#97—21no—
77C2×#97—21no—
78C2×#97—21no—
79C2×#97—21no—
80C2×#97D412yes—
81C2×#97D412yes—
82C2×C4×C8—21no—
83C2×C4×C8—21no—
84#383—21no—
85#382D412yes—
86#381—21no—
87#380C2×C412yes—
88C4×C4⋊C4D412yes—
89C4×C22⋊C4—21no—
90#376—21no—
91#340—24no—
92#340—24no—
93#336—24no—
94#330—28no—
95#324—28no—
96C23×C4—21no—
97C23×C4—21no—
98C23×C4C22×C411yescharacteristic
99C23×C4C2×D411yescharacteristic
100C23×C4#4111yescharacteristic
101C22×C8—24no—
102C22×C8—22no—
103C22×C8—22no—
104C22×C8—22no—
105C22×C8—22no—
106C22×C8—44no—
107C22×C8—42no—
108C22×C8—41no—
109C22×C8—41no—
110C22×C8—41no—
111C22×C8—41no—
112C22×C8—41no—
113#125—22no—
114#125—22no—
115#125—22no—
116#125—22no—
117#125—22no—
118#125—22no—
119#125—22no—
120#125—22no—
121#125—41no—
122#125—41no—
123#125—41no—
124#125—41no—
125#125—41no—
126#125—41no—
127#125—41no—
128#125—41no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—41no—
144C2×C4⋊C4—41no—
145C2×C4⋊C4—41no—
146C2×C4⋊C4—41no—
147C2×C4⋊C4—41no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4C22⋊C414yes—
152C2×C4⋊C4C4⋊C412yes—
153C2×C4⋊C4C4⋊C412yes—
154C2×C22⋊C4—22no—
155C2×C42—22no—
156C2×C42C2×D411yescharacteristic
157C2×C42C2×D411yescharacteristic
158C2×C42C2×D411yescharacteristic
159C2×C42C2×D411yescharacteristic
160C2×C42C2×D411yescharacteristic
161C2×C42C2×D411yescharacteristic
162C2×C42C2×Q811yescharacteristic
163C2×C42#4111yescharacteristic
164C2×C42#4111yescharacteristic
165C2×C42#4111yescharacteristic
166C2×C42#4111yescharacteristic
167C2×C42#4111yescharacteristic
168C4⋊C8—22no—
169C4⋊C8—48no—
170C4⋊C8—41no—
171C4⋊C8—41no—
172C4⋊C8—41no—
173C4⋊C8—41no—
174C4⋊C8—41no—
175C22⋊C8—22no—
176C22⋊C8—22no—
177C22⋊C8—22no—
178C22⋊C8—22no—
179C22⋊C8—22no—
180C22⋊C8—41no—
181#97—22no—
182#97—22no—
183#97—22no—
184#97—22no—
185#97—22no—
186#97—41no—
187#97—41no—
188#97—41no—
189#97—41no—
190#97—41no—
191C4×C8—41no—
192C4×C8—41no—
193C4×C8—41no—
194C4×C8—41no—
195#95—22no—
196#95—22no—
197#95—22no—
198#95—22no—
199C24C4×D411yescharacteristic
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—24no—
204C22×C4—22no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—82no—
214C22×C4C2×C22⋊C411yescharacteristic
215C22×C4C2×C4⋊C411yescharacteristic
216C22×C4#11711yescharacteristic
217C22×C4C4×D411yescharacteristic
218C22×C4C4×D411yescharacteristic
219C22×C4C4×D411yescharacteristic
220C22×C4#12011yescharacteristic
221C22×C4#12011yescharacteristic
222C22×C4#12111yescharacteristic
223C22×C4#12111yescharacteristic
224C22×C4#12111yescharacteristic
225C22×C4C22⋊Q811yescharacteristic
226C22×C4C22⋊Q811yescharacteristic
227C22×C4#12311yescharacteristic
228C22×C4#12311yescharacteristic
229C22×C4#12311yescharacteristic
230C22×C4#12411yescharacteristic
231C22×C4#12611yescharacteristic
232C2×C8—24no—
233C2×C8—24no—
234C2×C8—44no—
235C2×C8—44no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—44no—
239C2×C8—44no—
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—44no—
243C2×C8—44no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—82no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—44no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C22⋊C4—42no—
266C22⋊C4—42no—
267C42—44no—
268C42#12011yescharacteristic
269C42#12111yescharacteristic
270C42#12111yescharacteristic
271C42#12111yescharacteristic
272C42#12111yescharacteristic
273C42#12111yescharacteristic
274C42C22⋊Q811yescharacteristic
275C42C22⋊Q811yescharacteristic
276C42C22⋊Q811yescharacteristic
277C42C22⋊Q811yescharacteristic
278C42#12311yescharacteristic
279C42#12311yescharacteristic
280C42#12411yescharacteristic
281C42#12411yescharacteristic
282C42#12611yescharacteristic
283C42#12711yescharacteristic
284C23—22no—
285C23—22no—
286C23#38511yescharacteristic
287C23#38611yescharacteristic
288C23#38811yescharacteristic
289C23#44312yes—
290C23#44412yes—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—44no—
312C2×C4—44no—
313C2×C4—44no—
314C2×C4—44no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—82no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—82no—
323C2×C4#38011yescharacteristic
324C2×C4#38511yescharacteristic
325C2×C4#38811yescharacteristic
326C2×C4#39011yescharacteristic
327C2×C4#39211yescharacteristic
328C2×C4#39311yescharacteristic
329C2×C4#39411yescharacteristic
330C2×C4#39411yescharacteristic
331C2×C4#39611yescharacteristic
332C2×C4#39611yescharacteristic
333C2×C4#39711yescharacteristic
334C2×C4#39911yescharacteristic
335C8—44no—
336C8—44no—
337C8—82no—
338C8—82no—
339C8—82no—
340C22—21no—
341C22—21no—
342C22—24no—
343C22—24no—
344C22—21no—
345C22—21no—
346C22#143911yescharacteristic
347C22#186612yes—
348C22#187612yes—
349C22#190612yes—
350C22#191512yes—
351C22#193711yescharacteristic
352C22#193811yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—84no—
366C4—82no—
367C4—82no—
368C2—22no—
369C2—21no—
370C2—21no—
371C2#926614yes—
372C2#1104811yescharacteristic
373C2#1106011yescharacteristic
374C2#1106811yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C4×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#218362
#213532
C22×#3302
C2×#14702
C2×#13022
#80362
C2×#12812