Finite Group Databasebeta

← #115845

Subgroups — #115845

Order 512.

624 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21979C211yesmaximal, characteristic
2#21840C211yesmaximal, characteristic
3C2×#1997C211yesmaximal, characteristic
4C2×#1556C211yesmaximal, characteristic
5C2×#1307C211yesmaximal, characteristic
6#8035C211yesmaximal, characteristic
7C2×#1291C211yesmaximal, characteristic
8C22×C4⋊Q8C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#432C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C2×C4×M16C2211yescharacteristic
14#2283C2211yescharacteristic
15#1997—22no—
16#1997—22no—
17#1993—22no—
18#1987—22no—
19#1940—22no—
20#1851—22no—
21#1843—21no—
22#1832—21no—
23#1823C414yes—
24C2×#343—22no—
25#1556—22no—
26#1556—22no—
27C2×#332—21no—
28C2×#332—21no—
29#1307—22no—
30#1295—22no—
31#1291—22no—
32C23×Q8—21no—
33C22×M16—21no—
34C22×M16D412yes—
35C2×C4⋊Q8—21no—
36C2×C4⋊Q8—21no—
37C2×C4⋊Q8—21no—
38C2×C4⋊Q8—21no—
39C2×C4⋊Q8—21no—
40C2×C4⋊Q8—21no—
41C2×C4⋊Q8—21no—
42C2×C4⋊Q8—21no—
43C2×C4⋊Q8—21no—
44C2×C4⋊Q8—21no—
45C2×C4⋊Q8D412yes—
46C2×C4⋊Q8Q812yes—
47C22×C4⋊C4—21no—
48C22×C4⋊C4C2×C412yes—
49C22×C42C2311yescharacteristic
50#432—21no—
51#432—21no—
52#432—21no—
53#432—21no—
54#432—21no—
55#432—21no—
56#432—21no—
57#432—21no—
58#432—21no—
59#432—21no—
60#432—21no—
61#432D412yes—
62#423—21no—
63#423—21no—
64#423—21no—
65#423—21no—
66C2×C4⋊C8—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—24no—
71C2×C4⋊C8D411yescharacteristic
72C2×C4⋊C8D411yescharacteristic
73C2×C22⋊C8—21no—
74C2×C22⋊C8—21no—
75C2×C22⋊C8C2×C412yes—
76C4×M16—21no—
77C4×M16—21no—
78C4×M16—21no—
79C4×M16D412yes—
80C2×#97—21no—
81C2×#97—21no—
82C2×#97—21no—
83C2×#97—21no—
84C2×C4×C8—21no—
85#383—21no—
86#382D412yes—
87#381—21no—
88#380C2×C412yes—
89C4×C4⋊C4D412yes—
90C4×C22⋊C4—21no—
91#376—21no—
92#343—28no—
93#340—28no—
94#336—24no—
95#332—24no—
96#332—24no—
97C22×Q8—22no—
98C22×Q8—22no—
99C22×Q8—41no—
100C22×Q8—41no—
101C22×Q8—41no—
102C22×Q8—41no—
103C22×Q8—84no—
104C23×C4—22no—
105C23×C4C22×C411yescharacteristic
106C23×C4C2×D411yescharacteristic
107C23×C4#4111yescharacteristic
108C2×M16—24no—
109C2×M16—22no—
110C2×M16—22no—
111C2×M16—22no—
112C2×M16—42no—
113C2×M16—41no—
114C2×M16—44no—
115C22×C8—22no—
116C22×C8—22no—
117C22×C8—21no—
118C22×C8—21no—
119C22×C8—41no—
120C22×C8—41no—
121C4⋊Q8—22no—
122C4⋊Q8—22no—
123C4⋊Q8—22no—
124C4⋊Q8—22no—
125C4⋊Q8—22no—
126C4⋊Q8—22no—
127C4⋊Q8—22no—
128C4⋊Q8—22no—
129C4⋊Q8—41no—
130C4⋊Q8—41no—
131C4⋊Q8—41no—
132C4⋊Q8—41no—
133C4⋊Q8—41no—
134C4⋊Q8—41no—
135C4⋊Q8—41no—
136C4⋊Q8—41no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—41no—
145C2×C4⋊C4—41no—
146C2×C4⋊C4—41no—
147C2×C4⋊C4—41no—
148C2×C4⋊C4C22⋊C414yes—
149C2×C4⋊C4C4⋊C414yes—
150C2×C22⋊C4—22no—
151C2×C42—22no—
152C2×C42C2×D411yescharacteristic
153C2×C42C2×D411yescharacteristic
154C2×C42C2×D411yescharacteristic
155C2×C42C2×D411yescharacteristic
156C2×C42C2×D411yescharacteristic
157C2×C42C2×D411yescharacteristic
158C2×C42C2×Q811yescharacteristic
159C2×C42#4111yescharacteristic
160C2×C42#4111yescharacteristic
161C2×C42#4111yescharacteristic
162C2×C42#4111yescharacteristic
163C2×C42#4111yescharacteristic
164C4⋊C8—22no—
165C4⋊C8—21no—
166C4⋊C8—21no—
167C4⋊C8—21no—
168C4⋊C8—21no—
169C4⋊C8—41no—
170C4⋊C8—41no—
171C4⋊C8—41no—
172C4⋊C8—41no—
173C4⋊C8—41no—
174C4⋊C8—41no—
175C4⋊C8—41no—
176C4⋊C8—84no—
177C22⋊C8—22no—
178C22⋊C8—22no—
179C22⋊C8—22no—
180C22⋊C8—41no—
181C22⋊C8—41no—
182C22⋊C8—41no—
183#97—22no—
184#97—22no—
185#97—41no—
186#97—41no—
187#97—41no—
188#97—41no—
189#97—41no—
190#97—41no—
191C4×C8—22no—
192C4×C8—41no—
193#95—22no—
194#95—22no—
195#95—22no—
196#95—22no—
197C24C4×D411yescharacteristic
198C2×Q8—42no—
199C2×Q8—42no—
200C2×Q8—42no—
201C2×Q8—42no—
202C2×Q8—84no—
203C2×Q8—84no—
204C2×Q8—84no—
205C2×Q8—84no—
206C2×Q8—84no—
207C2×Q8—84no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—24no—
211C22×C4—24no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—84no—
217C22×C4C2×C22⋊C411yescharacteristic
218C22×C4C2×C4⋊C411yescharacteristic
219C22×C4#11711yescharacteristic
220C22×C4C4×D411yescharacteristic
221C22×C4C4×D411yescharacteristic
222C22×C4C4×D411yescharacteristic
223C22×C4#12011yescharacteristic
224C22×C4#12011yescharacteristic
225C22×C4#12111yescharacteristic
226C22×C4#12111yescharacteristic
227C22×C4#12111yescharacteristic
228C22×C4C22⋊Q811yescharacteristic
229C22×C4C22⋊Q811yescharacteristic
230C22×C4#12311yescharacteristic
231C22×C4#12311yescharacteristic
232C22×C4#12311yescharacteristic
233C22×C4#12411yescharacteristic
234C22×C4#12611yescharacteristic
235M16—24no—
236M16—42no—
237M16—44no—
238M16—44no—
239M16—82no—
240C2×C8—44no—
241C2×C8—42no—
242C2×C8—44no—
243C2×C8—42no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—44no—
250C2×C8—42no—
251C2×C8—82no—
252C4⋊C4—24no—
253C4⋊C4—24no—
254C4⋊C4—44no—
255C4⋊C4—42no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C22⋊C4—82no—
262C42—42no—
263C42—42no—
264C42#12011yescharacteristic
265C42#12111yescharacteristic
266C42#12111yescharacteristic
267C42#12111yescharacteristic
268C42#12111yescharacteristic
269C42#12111yescharacteristic
270C42C22⋊Q811yescharacteristic
271C42C22⋊Q811yescharacteristic
272C42C22⋊Q811yescharacteristic
273C42C22⋊Q811yescharacteristic
274C42#12311yescharacteristic
275C42#12311yescharacteristic
276C42#12411yescharacteristic
277C42#12411yescharacteristic
278C42#12611yescharacteristic
279C42#12711yescharacteristic
280C23—22no—
281C23—22no—
282C23—22no—
283C23#38511yescharacteristic
284C23#38611yescharacteristic
285C23#38811yescharacteristic
286Q8—84no—
287Q8—84no—
288Q8—84no—
289Q8—84no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—44no—
310C2×C4—44no—
311C2×C4—44no—
312C2×C4—44no—
313C2×C4—84no—
314C2×C4—84no—
315C2×C4—84no—
316C2×C4#38011yescharacteristic
317C2×C4#38511yescharacteristic
318C2×C4#38811yescharacteristic
319C2×C4#39011yescharacteristic
320C2×C4#39211yescharacteristic
321C2×C4#39311yescharacteristic
322C2×C4#39411yescharacteristic
323C2×C4#39411yescharacteristic
324C2×C4#39611yescharacteristic
325C2×C4#39611yescharacteristic
326C2×C4#39711yescharacteristic
327C2×C4#39911yescharacteristic
328C2×C4#45512yes—
329C2×C4#45612yes—
330C8—44no—
331C8—82no—
332C8—82no—
333C8—81no—
334C8—82no—
335C8—81no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—44no—
343C22#143911yescharacteristic
344C22#188212yes—
345C22#190312yes—
346C22#191512yes—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—84no—
358C4—84no—
359C4#200411yescharacteristic
360C4#200511yescharacteristic
361C4#202812yes—
362C2—41no—
363C2—41no—
364C2#933814yes—
365C2#1104811yescharacteristic
366C2#1105811yescharacteristic
367C2#1106411yescharacteristic
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
#219792
#218402
C2×#19972
C2×#15562
C2×#13072
#80352
C2×#12912