Finite Group Databasebeta

← #118293

Subgroups — #118293

Order 512.

546 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17806C211yesmaximal, characteristic
2C2×#1518C211yesmaximal, characteristic
3#17479C211yesmaximal, characteristic
4#17404C211yesmaximal, characteristic
5#7959C211yesmaximal, characteristic
6#7933C211yesmaximal, characteristic
7#7914C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#432C2211yescharacteristic
12C2×#431C2211yescharacteristic
13C2×#431C2211yescharacteristic
14C2×#382C2211yescharacteristic
15#1574—22no—
16#1573—22no—
17#1564—22no—
18#1518—22no—
19#1518—22no—
20C2×#328C414yes—
21#1497—22no—
22#1493—22no—
23#1479—22no—
24#1472—22no—
25#1470—22no—
26#1467—22no—
27#1286—22no—
28#1283—22no—
29#1280—22no—
30#533—21no—
31#533—21no—
32#533—21no—
33#533—21no—
34#533—21no—
35#533—21no—
36#533—21no—
37#533—21no—
38C2×C4⋊Q8Q811yescharacteristic
39C2×C4⋊Q8Q811yescharacteristic
40C2×#125—21no—
41C2×C22⋊Q8—21no—
42C2×C22⋊Q8C2×C412yes—
43C2×C4×Q8—21no—
44C2×C4×Q8D412yes—
45C2×#117—21no—
46C22×C4⋊C4—21no—
47C22×C42C2311yescharacteristic
48#432—21no—
49#432—21no—
50#432—21no—
51#432—21no—
52#432—21no—
53#432—21no—
54#432—21no—
55#432—21no—
56#431—21no—
57#431—21no—
58#431—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62#431—21no—
63#431—21no—
64#431D412yes—
65#431D412yes—
66#431D412yes—
67#431D412yes—
68#423—21no—
69#423D412yes—
70C2×C4⋊C8—21no—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
73#407—21no—
74#407—21no—
75C2×C22⋊C8—21no—
76C2×C22⋊C8C2×C412yes—
77C2×C22⋊C8D412yes—
78C4×M16—21no—
79C4×M16—21no—
80C2×#97—21no—
81C2×C4×C8—21no—
82C2×C4×C8—21no—
83#382—21no—
84#382—21no—
85#382—21no—
86#382—21no—
87C2×#95—21no—
88C2×#95C2×C412yes—
89#335—24no—
90#334—24no—
91#328—28no—
92Q8⋊C8—28no—
93#324—28no—
94C22×Q8—21no—
95C22×Q8C4⋊C412yes—
96C23×C4—22no—
97C23×C4C22×C411yescharacteristic
98C23×C4C2×D411yescharacteristic
99C23×C4#4111yescharacteristic
100C2×M16—22no—
101C2×M16—41no—
102C22×C8—22no—
103C22×C8—22no—
104C22×C8—41no—
105C4⋊Q8—21no—
106C4⋊Q8—21no—
107C4⋊Q8—21no—
108C4⋊Q8—21no—
109C4⋊Q8—21no—
110C4⋊Q8—21no—
111C4⋊Q8—21no—
112C4⋊Q8—21no—
113#125—41no—
114#125—41no—
115#125—41no—
116#125—41no—
117C22⋊Q8—22no—
118C22⋊Q8—22no—
119C22⋊Q8—22no—
120C22⋊Q8—22no—
121C22⋊Q8—41no—
122C22⋊Q8—41no—
123C22⋊Q8—41no—
124C22⋊Q8—41no—
125C4×Q8—22no—
126C4×Q8—22no—
127C4×Q8—22no—
128C4×Q8—22no—
129C4×Q8—41no—
130C4×Q8—41no—
131C4×Q8—41no—
132C4×Q8—41no—
133#117—41no—
134#117—41no—
135#117—41no—
136#117—41no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—41no—
143C2×C4⋊C4—41no—
144C2×C4⋊C4—82no—
145C2×C4⋊C4C4⋊C412yes—
146C2×C22⋊C4—22no—
147C2×C42—22no—
148C2×C42C2×D411yescharacteristic
149C2×C42C2×D411yescharacteristic
150C2×C42C2×D411yescharacteristic
151C2×C42C2×D411yescharacteristic
152C2×C42C2×D411yescharacteristic
153C2×C42C2×D411yescharacteristic
154C2×C42C2×Q811yescharacteristic
155C2×C42#4111yescharacteristic
156C2×C42#4111yescharacteristic
157C2×C42#4111yescharacteristic
158C2×C42#4111yescharacteristic
159C2×C42#4111yescharacteristic
160C4⋊C8—22no—
161C4⋊C8—22no—
162C4⋊C8—22no—
163C4⋊C8—22no—
164C4⋊C8—22no—
165C4⋊C8—22no—
166C4⋊C8—41no—
167C4⋊C8—41no—
168C4⋊C8—41no—
169C4⋊C8—41no—
170C22⋊C8—22no—
171C22⋊C8—22no—
172C22⋊C8—22no—
173C22⋊C8—22no—
174C22⋊C8—22no—
175C22⋊C8—41no—
176C22⋊C8—41no—
177C22⋊C8—41no—
178C22⋊C8—41no—
179C22⋊C8C22⋊C414yes—
180#97—41no—
181#97—41no—
182#97—41no—
183#97—41no—
184C4×C8—22no—
185C4×C8—22no—
186C4×C8—22no—
187C4×C8—22no—
188C4×C8—41no—
189C4×C8—41no—
190#95—22no—
191#95—22no—
192#95—41no—
193#95—41no—
194C24C4×D411yescharacteristic
195C2×Q8—22no—
196C2×Q8—22no—
197C2×Q8—44no—
198C2×Q8—41no—
199C2×Q8—41no—
200C2×Q8—82no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—44no—
208C22×C4—81no—
209C22×C4—82no—
210C22×C4—82no—
211C22×C4C2×C22⋊C411yescharacteristic
212C22×C4C2×C4⋊C411yescharacteristic
213C22×C4#11711yescharacteristic
214C22×C4C4×D411yescharacteristic
215C22×C4C4×D411yescharacteristic
216C22×C4C4×D411yescharacteristic
217C22×C4#12011yescharacteristic
218C22×C4#12111yescharacteristic
219C22×C4#12111yescharacteristic
220C22×C4#12111yescharacteristic
221C22×C4C22⋊Q811yescharacteristic
222C22×C4C22⋊Q811yescharacteristic
223C22×C4#12311yescharacteristic
224C22×C4#12311yescharacteristic
225C22×C4#12411yescharacteristic
226C22×C4#12411yescharacteristic
227C22×C4#12611yescharacteristic
228C22×C4#12711yescharacteristic
229M16—42no—
230M16—42no—
231M16—82no—
232C2×C8—24no—
233C2×C8—44no—
234C2×C8—42no—
235C2×C8—42no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—82no—
239C2×C8—82no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—42no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—82no—
253C4⋊C4—82no—
254C22⋊C4—42no—
255C22⋊C4—42no—
256C42—42no—
257C42—42no—
258C42#12011yescharacteristic
259C42#12011yescharacteristic
260C42#12111yescharacteristic
261C42#12111yescharacteristic
262C42#12111yescharacteristic
263C42#12111yescharacteristic
264C42#12111yescharacteristic
265C42C22⋊Q811yescharacteristic
266C42C22⋊Q811yescharacteristic
267C42C22⋊Q811yescharacteristic
268C42C22⋊Q811yescharacteristic
269C42#12311yescharacteristic
270C42#12311yescharacteristic
271C42#12311yescharacteristic
272C42#12411yescharacteristic
273C42#12611yescharacteristic
274C23—22no—
275C23—21no—
276C23—21no—
277C23—41no—
278C23#38511yescharacteristic
279C23#38811yescharacteristic
280C23#39011yescharacteristic
281Q8—44no—
282Q8—82no—
283Q8—82no—
284Q8—82no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—44no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—82no—
307C2×C4—82no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4—164no—
311C2×C4#38011yescharacteristic
312C2×C4#38511yescharacteristic
313C2×C4#38611yescharacteristic
314C2×C4#38811yescharacteristic
315C2×C4#39211yescharacteristic
316C2×C4#39311yescharacteristic
317C2×C4#39411yescharacteristic
318C2×C4#39411yescharacteristic
319C2×C4#39611yescharacteristic
320C2×C4#39611yescharacteristic
321C2×C4#39711yescharacteristic
322C2×C4#39911yescharacteristic
323C2×C4#47112yes—
324C2×C4#47312yes—
325C8—44no—
326C8—82no—
327C8—82no—
328C8—82no—
329C8—82no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—42no—
338C22—42no—
339C22#143911yescharacteristic
340C22#186812yes—
341C22#197711yescharacteristic
342C22#197911yescharacteristic
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—82no—
354C4—82no—
355C4—162no—
356C4#205212yes—
357C4#206412yes—
358C2—21no—
359C2—22no—
360C2—21no—
361C2—41no—
362C2#1108811yescharacteristic
363C2#1111511yescharacteristic
364C2#1112811yescharacteristic
subgroupG/H
center, socleC22#1439
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C4×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ 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
#178062
C2×#15182
#174792
#174042
#79592
#79332
#79142