Finite Group Databasebeta

← #117422

Subgroups — #117422

Order 512.

567 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17817C211yesmaximal, characteristic
2#17715C211yesmaximal, characteristic
3#17479C211yesmaximal, characteristic
4C2×#1493C211yesmaximal, characteristic
5#7934C211yesmaximal, characteristic
6#7885C211yesmaximal, characteristic
7#7872C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C2×#431C2211yescharacteristic
13C2×#423C2211yescharacteristic
14C22×C4×C8C2211yescharacteristic
15#1574—22no—
16#1573—22no—
17#1567—21no—
18#1566—21no—
19#1552—22no—
20#1549C411yescharacteristic
21#1549C411yescharacteristic
22#1546C411yescharacteristic
23#1546C411yescharacteristic
24#1544—22no—
25#1497—22no—
26#1493—21no—
27#1493—21no—
28#1493—22no—
29#1493—22no—
30#1479—22no—
31C2×Q8⋊C8—22no—
32#1283—22no—
33#1278—22no—
34#1277—22no—
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#533D412yes—
44#533Q812yes—
45C2×C4⋊Q8C2×C411yescharacteristic
46C2×C4⋊Q8C2×C411yescharacteristic
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#431—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62#431—21no—
63#431—21no—
64#431—21no—
65#431—21no—
66#431—21no—
67#431C2×C411yescharacteristic
68#431C2×C411yescharacteristic
69#431D412yes—
70#431D412yes—
71#423—21no—
72#423—21no—
73#423—21no—
74#423—21no—
75#423C2×C411yescharacteristic
76#423C2×C411yescharacteristic
77#423D411yescharacteristic
78#423D411yescharacteristic
79C2×C4⋊C8—21no—
80C2×C4⋊C8—21no—
81C2×C4⋊C8D412yes—
82C2×C4⋊C8D412yes—
83#407—21no—
84#407—21no—
85C2×C22⋊C8—21no—
86C2×C22⋊C8—21no—
87C4×M16—21no—
88C4×M16—21no—
89C2×C4×C8—21no—
90C2×C4×C8—21no—
91C2×C4×C8—21no—
92C2×C4×C8—21no—
93C2×C4×C8—21no—
94C2×C4×C8—21no—
95C2×C4×C8—21no—
96C2×C4×C8D412yes—
97#335—24no—
98#334—24no—
99#332—22no—
100#332—22no—
101#332—22no—
102#332—22no—
103Q8⋊C8—28no—
104Q8⋊C8—24no—
105Q8⋊C8—24no—
106C22×Q8—21no—
107C22×Q8—21no—
108C23×C4#4111yescharacteristic
109C23×C4#4111yescharacteristic
110C23×C4#4111yescharacteristic
111C2×M16—21no—
112C2×M16—21no—
113C2×M16—21no—
114C2×M16—21no—
115C2×M16—41no—
116C2×M16—41no—
117C2×M16—82no—
118C22×C8—24no—
119C22×C8—22no—
120C22×C8—22no—
121C22×C8—22no—
122C22×C8—42no—
123C22×C8—41no—
124C22×C8—41no—
125C22×C8—41no—
126C4⋊Q8—21no—
127C4⋊Q8—21no—
128C4⋊Q8—21no—
129C4⋊Q8—21no—
130C4⋊Q8—21no—
131C4⋊Q8—21no—
132C4⋊Q8C4⋊C412yes—
133C4⋊Q8C4⋊C412yes—
134#125—22no—
135#125—22no—
136#125—41no—
137#125—41no—
138C22⋊Q8—22no—
139C22⋊Q8—22no—
140C22⋊Q8—22no—
141C22⋊Q8—22no—
142C22⋊Q8—41no—
143C22⋊Q8—41no—
144C22⋊Q8—41no—
145C22⋊Q8—41no—
146C4×Q8—22no—
147C4×Q8—22no—
148C4×Q8—22no—
149C4×Q8—22no—
150C4×Q8—41no—
151C4×Q8—41no—
152C4×Q8—41no—
153C4×Q8—41no—
154#117—22no—
155#117—22no—
156#117—41no—
157#117—41no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—41no—
163C2×C4⋊C4—41no—
164C2×C22⋊C4—41no—
165C2×C42—41no—
166C2×C42C22×C411yescharacteristic
167C2×C42C2×D411yescharacteristic
168C2×C42C2×D411yescharacteristic
169C2×C42C2×D411yescharacteristic
170C2×C42C2×D411yescharacteristic
171C2×C42C2×D411yescharacteristic
172C2×C42C2×D411yescharacteristic
173C2×C42C2×D411yescharacteristic
174C2×C42C2×Q811yescharacteristic
175C2×C42#4111yescharacteristic
176C2×C42#4111yescharacteristic
177C2×C42#4111yescharacteristic
178C4⋊C8—21no—
179C4⋊C8—21no—
180C4⋊C8—21no—
181C4⋊C8—21no—
182C4⋊C8—22no—
183C4⋊C8—21no—
184C4⋊C8—21no—
185C4⋊C8—21no—
186C4⋊C8—22no—
187C4⋊C8—21no—
188C4⋊C8—22no—
189C4⋊C8—22no—
190C4⋊C8—41no—
191C4⋊C8—41no—
192C4⋊C8—41no—
193C4⋊C8C22⋊C412yes—
194C4⋊C8C22⋊C412yes—
195C22⋊C8—21no—
196C22⋊C8—21no—
197C22⋊C8—22no—
198C22⋊C8—22no—
199C22⋊C8—41no—
200C22⋊C8—41no—
201C22⋊C8—41no—
202C22⋊C8—41no—
203C22⋊C8—41no—
204#97—41no—
205#97—41no—
206C4×C8—21no—
207C4×C8—21no—
208C4×C8—22no—
209C4×C8—22no—
210C4×C8—22no—
211C4×C8—22no—
212C4×C8—41no—
213C4×C8—41no—
214C4×C8—41no—
215C4×C8—41no—
216C4×C8—41no—
217C24#12611yescharacteristic
218C2×Q8—22no—
219C2×Q8—22no—
220C2×Q8—44no—
221C2×Q8—41no—
222C2×Q8—41no—
223C2×Q8—42no—
224C2×Q8—42no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—42no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4#11711yescharacteristic
233C22×C4C4×D411yescharacteristic
234C22×C4C4×D411yescharacteristic
235C22×C4#12111yescharacteristic
236C22×C4#12111yescharacteristic
237C22×C4#12111yescharacteristic
238C22×C4#12111yescharacteristic
239C22×C4#12111yescharacteristic
240C22×C4C22⋊Q811yescharacteristic
241C22×C4C22⋊Q811yescharacteristic
242C22×C4C22⋊Q811yescharacteristic
243C22×C4#12311yescharacteristic
244C22×C4#12311yescharacteristic
245C22×C4#12311yescharacteristic
246C22×C4#12311yescharacteristic
247C22×C4#12411yescharacteristic
248C22×C4#12411yescharacteristic
249C22×C4#12611yescharacteristic
250M16—42no—
251M16—42no—
252M16—42no—
253M16—42no—
254M16—82no—
255M16—82no—
256C2×C8—24no—
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—44no—
260C2×C8—44no—
261C2×C8—42no—
262C2×C8—42no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—82no—
270C2×C8—82no—
271C2×C8—82no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—42no—
284C22⋊C4—42no—
285C22⋊C4—42no—
286C42—42no—
287C42—42no—
288C42C2×C22⋊C411yescharacteristic
289C42C2×C4⋊C411yescharacteristic
290C42C4×D411yescharacteristic
291C42C4×D411yescharacteristic
292C42#12011yescharacteristic
293C42#12011yescharacteristic
294C42#12011yescharacteristic
295C42#12111yescharacteristic
296C42#12111yescharacteristic
297C42#12111yescharacteristic
298C42C22⋊Q811yescharacteristic
299C42C22⋊Q811yescharacteristic
300C42C22⋊Q811yescharacteristic
301C42#12311yescharacteristic
302C42#12411yescharacteristic
303C42#12711yescharacteristic
304C23—22no—
305C23—22no—
306C23—41no—
307C23#38811yescharacteristic
308C23#39611yescharacteristic
309C23#39711yescharacteristic
310Q8—44no—
311Q8—44no—
312Q8—82no—
313Q8—81no—
314Q8—81no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4#38011yescharacteristic
340C2×C4#38511yescharacteristic
341C2×C4#38511yescharacteristic
342C2×C4#38611yescharacteristic
343C2×C4#38811yescharacteristic
344C2×C4#39011yescharacteristic
345C2×C4#39211yescharacteristic
346C2×C4#39311yescharacteristic
347C2×C4#39411yescharacteristic
348C2×C4#39411yescharacteristic
349C2×C4#39611yescharacteristic
350C2×C4#39911yescharacteristic
351C2×C4#44312yes—
352C2×C4#44412yes—
353C2×C4#47112yes—
354C2×C4#47312yes—
355C8—44no—
356C8—42no—
357C8—42no—
358C8—82no—
359C8—81no—
360C8—81no—
361C8—82no—
362C8—81no—
363C8—81no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—44no—
372C22#143911yescharacteristic
373C22#192912yes—
374C22#206412yes—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—82no—
383C4—82no—
384C4#186612yes—
385C4#188112yes—
386C4#193012yes—
387C4#197411yescharacteristic
388C4#197511yescharacteristic
389C4#201911yescharacteristic
390C4#202011yescharacteristic
391C2—22no—
392C2—22no—
393C2—41no—
394C2#1106511yescharacteristic
395C2#1112511yescharacteristic
396C2#1114511yescharacteristic
subgroupG/H
centerC2×C4#392
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
#178172
#177152
#174792
C2×#14932
#79342
#78852
#78722