Finite Group Databasebeta

← #117787

Subgroups — #117787

Order 512.

550 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17793C211yesmaximal, characteristic
2#17664C211yesmaximal, characteristic
3#17491C211yesmaximal, characteristic
4C2×#1493C211yesmaximal, characteristic
5#8119C211yesmaximal, characteristic
6#8078C211yesmaximal, characteristic
7#7885C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11#2920C2211yescharacteristic
12#2920C2211yescharacteristic
13C2×#423C2211yescharacteristic
14C22×C4×C8C2211yescharacteristic
15#1568—22no—
16#1567—21no—
17#1566—21no—
18#1564—22no—
19#1537—22no—
20#1534—22no—
21#1526—22no—
22#1497—22no—
23#1493—21no—
24#1493—21no—
25#1493C412yes—
26#1493C412yes—
27#1487—22no—
28#1485—22no—
29C2×Q8⋊C8—21no—
30C2×Q8⋊C8—21no—
31#1307—22no—
32#1301—22no—
33#1278—21no—
34#1278—21no—
35C22×M16—21no—
36C23×C8—21no—
37#533—21no—
38#533—21no—
39#533—21no—
40#533—21no—
41#533—21no—
42#533—21no—
43#533C2×C412yes—
44#533D412yes—
45C2×C4⋊Q8Q811yescharacteristic
46C2×C4⋊Q8Q811yescharacteristic
47C2×#125—21no—
48C2×C22⋊Q8—21no—
49C2×C22⋊Q8—21no—
50C2×C4×Q8—21no—
51C2×C4×Q8—21no—
52C2×#117—21no—
53C22×C42C2311yescharacteristic
54#432—21no—
55#432—21no—
56#432—21no—
57#432—21no—
58#432—21no—
59#432—21no—
60#432D412yes—
61#432D412yes—
62#431—21no—
63#431—21no—
64#431—21no—
65#431—21no—
66#431—21no—
67#431—21no—
68#431—21no—
69#431D412yes—
70#423—21no—
71#423—21no—
72#423—21no—
73#423—21no—
74#423—21no—
75#423—21no—
76#423C2×C412yes—
77#423D412yes—
78C2×C4⋊C8—21no—
79C2×C4⋊C8—21no—
80#407—21no—
81#407—21no—
82#407—21no—
83#407—21no—
84C4×M16—21no—
85C4×M16—21no—
86C4×M16—21no—
87C4×M16—21no—
88C2×C4×C8—21no—
89C2×C4×C8—21no—
90C2×C4×C8—21no—
91C2×C4×C8C2×C411yescharacteristic
92C2×C4×C8C2×C411yescharacteristic
93C2×C4×C8D411yescharacteristic
94C2×C4×C8D411yescharacteristic
95C2×C4×C8D411yescharacteristic
96C2×C4×C8D411yescharacteristic
97#335—24no—
98#334—24no—
99#330—28no—
100Q8⋊C8—28no—
101Q8⋊C8—22no—
102Q8⋊C8—22no—
103Q8⋊C8—22no—
104Q8⋊C8—22no—
105C22×Q8—21no—
106C22×Q8—21no—
107C23×C4#4111yescharacteristic
108C23×C4#4111yescharacteristic
109C23×C4#4111yescharacteristic
110C2×M16—22no—
111C2×M16—22no—
112C2×M16—41no—
113C2×M16—41no—
114C2×M16—41no—
115C2×M16—41no—
116C2×M16—82no—
117C22×C8—21no—
118C22×C8—21no—
119C22×C8—21no—
120C22×C8—21no—
121C22×C8—21no—
122C22×C8—21no—
123C22×C8—44no—
124C22×C8—41no—
125C4⋊Q8—21no—
126C4⋊Q8—21no—
127C4⋊Q8—21no—
128C4⋊Q8—21no—
129C4⋊Q8—21no—
130C4⋊Q8—21no—
131C4⋊Q8C4⋊C412yes—
132C4⋊Q8C4⋊C412yes—
133#125—22no—
134#125—22no—
135#125—41no—
136#125—41no—
137C22⋊Q8—22no—
138C22⋊Q8—22no—
139C22⋊Q8—22no—
140C22⋊Q8—22no—
141C22⋊Q8—41no—
142C22⋊Q8—41no—
143C22⋊Q8—41no—
144C22⋊Q8—41no—
145C4×Q8—22no—
146C4×Q8—22no—
147C4×Q8—22no—
148C4×Q8—22no—
149C4×Q8—41no—
150C4×Q8—41no—
151C4×Q8—41no—
152C4×Q8—41no—
153#117—22no—
154#117—22no—
155#117—41no—
156#117—41no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—41no—
162C2×C4⋊C4—41no—
163C2×C22⋊C4—41no—
164C2×C42—41no—
165C2×C42C22×C411yescharacteristic
166C2×C42C2×D411yescharacteristic
167C2×C42C2×D411yescharacteristic
168C2×C42C2×D411yescharacteristic
169C2×C42C2×D411yescharacteristic
170C2×C42C2×D411yescharacteristic
171C2×C42C2×D411yescharacteristic
172C2×C42C2×D411yescharacteristic
173C2×C42C2×Q811yescharacteristic
174C2×C42#4111yescharacteristic
175C2×C42#4111yescharacteristic
176C2×C42#4111yescharacteristic
177C4⋊C8—22no—
178C4⋊C8—22no—
179C4⋊C8—22no—
180C4⋊C8—22no—
181C4⋊C8—22no—
182C4⋊C8—22no—
183C4⋊C8—22no—
184C4⋊C8—41no—
185C4⋊C8—41no—
186C4⋊C8—41no—
187C4⋊C8—41no—
188C4⋊C8—41no—
189C22⋊C8—22no—
190C22⋊C8—22no—
191C22⋊C8—22no—
192C22⋊C8—41no—
193C22⋊C8—41no—
194C22⋊C8—41no—
195C22⋊C8—41no—
196C22⋊C8—41no—
197#97—22no—
198#97—22no—
199#97—41no—
200#97—41no—
201C4×C8—21no—
202C4×C8—21no—
203C4×C8—21no—
204C4×C8—21no—
205C4×C8—22no—
206C4×C8—21no—
207C4×C8—21no—
208C4×C8—41no—
209C4×C8—41no—
210C4×C8—41no—
211C4×C8C22⋊C411yescharacteristic
212C4×C8C22⋊C411yescharacteristic
213C4×C8C22⋊C411yescharacteristic
214C4×C8C22⋊C411yescharacteristic
215C24#12611yescharacteristic
216C2×Q8—22no—
217C2×Q8—22no—
218C2×Q8—44no—
219C2×Q8—41no—
220C2×Q8—41no—
221C2×Q8—82no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4#11711yescharacteristic
229C22×C4C4×D411yescharacteristic
230C22×C4C4×D411yescharacteristic
231C22×C4#12111yescharacteristic
232C22×C4#12111yescharacteristic
233C22×C4#12111yescharacteristic
234C22×C4#12111yescharacteristic
235C22×C4#12111yescharacteristic
236C22×C4C22⋊Q811yescharacteristic
237C22×C4C22⋊Q811yescharacteristic
238C22×C4C22⋊Q811yescharacteristic
239C22×C4#12311yescharacteristic
240C22×C4#12311yescharacteristic
241C22×C4#12311yescharacteristic
242C22×C4#12311yescharacteristic
243C22×C4#12411yescharacteristic
244C22×C4#12411yescharacteristic
245C22×C4#12611yescharacteristic
246M16—42no—
247M16—42no—
248M16—82no—
249M16—82no—
250M16—82no—
251M16—82no—
252M16—82no—
253C2×C8—24no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—42no—
259C2×C8—42no—
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—42no—
263C2×C8—42no—
264C2×C8—42no—
265C2×C8—42no—
266C2×C8—42no—
267C2×C8—42no—
268C2×C8—82no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—42no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C42—42no—
284C42—42no—
285C42C2×C22⋊C411yescharacteristic
286C42C2×C4⋊C411yescharacteristic
287C42C4×D411yescharacteristic
288C42C4×D411yescharacteristic
289C42#12011yescharacteristic
290C42#12011yescharacteristic
291C42#12011yescharacteristic
292C42#12111yescharacteristic
293C42#12111yescharacteristic
294C42#12111yescharacteristic
295C42C22⋊Q811yescharacteristic
296C42C22⋊Q811yescharacteristic
297C42C22⋊Q811yescharacteristic
298C42#12311yescharacteristic
299C42#12411yescharacteristic
300C42#12711yescharacteristic
301C23—22no—
302C23—41no—
303C23—41no—
304C23#38811yescharacteristic
305C23#39611yescharacteristic
306C23#39711yescharacteristic
307Q8—44no—
308Q8—44no—
309Q8—82no—
310Q8—82no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4#38011yescharacteristic
335C2×C4#38511yescharacteristic
336C2×C4#38511yescharacteristic
337C2×C4#38611yescharacteristic
338C2×C4#38811yescharacteristic
339C2×C4#39011yescharacteristic
340C2×C4#39211yescharacteristic
341C2×C4#39311yescharacteristic
342C2×C4#39411yescharacteristic
343C2×C4#39411yescharacteristic
344C2×C4#39611yescharacteristic
345C2×C4#39911yescharacteristic
346C2×C4#47112yes—
347C2×C4#47312yes—
348C8—22no—
349C8—22no—
350C8—41no—
351C8—41no—
352C8—82no—
353C8—82no—
354C8—82no—
355C8—82no—
356C8—82no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—44no—
366C22#143911yescharacteristic
367C22#206412yes—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—82no—
377C4—82no—
378C4#181412yes—
379C4#186112yes—
380C4#197711yescharacteristic
381C4#197911yescharacteristic
382C4#205212yes—
383C2—22no—
384C2—41no—
385C2—41no—
386C2#1108011yescharacteristic
387C2#1110411yescharacteristic
388C2#1112811yescharacteristic
subgroupG/H
centerC2×C4#394
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
socleC22#1439
prime radicalC24#126
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ 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
#177932
#176642
#174912
C2×#14932
#81192
#80782
#78852