Finite Group Databasebeta

← #118459

Subgroups — #118459

Order 512.

533 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1573C211yesmaximal, characteristic
2#17734C211yesmaximal, characteristic
3C2×#1542C211yesmaximal, characteristic
4#17385C211yesmaximal, characteristic
5#8054C211yesmaximal, characteristic
6#8002C211yesmaximal, characteristic
7#7864C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#432C2211yescharacteristic
12C2×#431C2211yescharacteristic
13C2×#431C2211yescharacteristic
14C22×C4⋊C8C2211yescharacteristic
15#1573—22no—
16#1573—22no—
17C2×#335—21no—
18C2×#334—21no—
19#1559—22no—
20#1558—21no—
21#1556—21no—
22#1542—22no—
23#1542—22no—
24#1542—21no—
25#1542—21no—
26C2×#333—21no—
27C2×#332—21no—
28#1472—22no—
29#1470—22no—
30#1461C414yes—
31#1298—22no—
32#1292—22no—
33#1275—22no—
34C23×C8—21no—
35#533—21no—
36#533—21no—
37#533—21no—
38#533—21no—
39#533—21no—
40#533—21no—
41#533—21no—
42#533—21no—
43C2×C4⋊Q8D411yescharacteristic
44C2×C4⋊Q8D411yescharacteristic
45C2×#125—21no—
46C2×C22⋊Q8—21no—
47C2×C22⋊Q8Q812yes—
48C2×C4×Q8—21no—
49C2×C4×Q8C2×C412yes—
50C2×#117—21no—
51C22×C42C2311yescharacteristic
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#431—21no—
61#431—21no—
62#431—21no—
63#431—21no—
64#431—21no—
65#431—21no—
66#431—21no—
67#431—21no—
68#431C2×C412yes—
69#431C2×C412yes—
70#431D412yes—
71#431D412yes—
72#423—21no—
73#423D412yes—
74C2×C4⋊C8—21no—
75C2×C4⋊C8—21no—
76C2×C4⋊C8—21no—
77C2×C4⋊C8—21no—
78C2×C4⋊C8—21no—
79C2×C4⋊C8—21no—
80C2×C4⋊C8—21no—
81C2×C4⋊C8D411yescharacteristic
82C2×C4⋊C8D411yescharacteristic
83C2×C4⋊C8D412yes—
84#407—21no—
85#407—21no—
86C2×C22⋊C8—21no—
87C2×C22⋊C8—21no—
88C2×C22⋊C8D412yes—
89C4×M16—21no—
90C4×M16—21no—
91C2×#97—21no—
92C2×C4×C8—21no—
93C2×C4×C8—21no—
94#335—24no—
95#334—24no—
96#333—24no—
97#333—22no—
98#333—22no—
99#332—24no—
100#332—22no—
101#332—22no—
102#324—28no—
103C22×Q8—21no—
104C22×Q8C4⋊C412yes—
105C23×C4C2×D411yescharacteristic
106C23×C4C2×Q811yescharacteristic
107C23×C4#4111yescharacteristic
108C2×M16—22no—
109C2×M16—41no—
110C22×C8—22no—
111C22×C8—21no—
112C22×C8—21no—
113C22×C8—22no—
114C22×C8—41no—
115C22×C8—41no—
116C22×C8—41no—
117C22×C8—82no—
118C4⋊Q8—21no—
119C4⋊Q8—21no—
120C4⋊Q8—21no—
121C4⋊Q8—21no—
122C4⋊Q8—21no—
123C4⋊Q8—21no—
124C4⋊Q8—21no—
125C4⋊Q8—21no—
126#125—41no—
127#125—41no—
128#125—41no—
129#125—41no—
130C22⋊Q8—22no—
131C22⋊Q8—22no—
132C22⋊Q8—22no—
133C22⋊Q8—22no—
134C22⋊Q8—41no—
135C22⋊Q8—41no—
136C22⋊Q8—41no—
137C22⋊Q8—41no—
138C4×Q8—22no—
139C4×Q8—22no—
140C4×Q8—22no—
141C4×Q8—22no—
142C4×Q8—41no—
143C4×Q8—41no—
144C4×Q8—41no—
145C4×Q8—41no—
146#117—41no—
147#117—41no—
148#117—41no—
149#117—41no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4C4⋊C412yes—
156C2×C22⋊C4—22no—
157C2×C42—22no—
158C2×C42C22×C411yescharacteristic
159C2×C42C2×D411yescharacteristic
160C2×C42C2×D411yescharacteristic
161C2×C42C2×D411yescharacteristic
162C2×C42C2×D411yescharacteristic
163C2×C42C2×D411yescharacteristic
164C2×C42C2×D411yescharacteristic
165C2×C42#4111yescharacteristic
166C2×C42#4111yescharacteristic
167C2×C42#4111yescharacteristic
168C2×C42#4111yescharacteristic
169C2×C42#4111yescharacteristic
170C4⋊C8—22no—
171C4⋊C8—22no—
172C4⋊C8—22no—
173C4⋊C8—22no—
174C4⋊C8—21no—
175C4⋊C8—21no—
176C4⋊C8—22no—
177C4⋊C8—21no—
178C4⋊C8—22no—
179C4⋊C8—21no—
180C4⋊C8—22no—
181C4⋊C8—22no—
182C4⋊C8—41no—
183C4⋊C8—41no—
184C4⋊C8—41no—
185C4⋊C8—41no—
186C22⋊C8—22no—
187C22⋊C8—22no—
188C22⋊C8—22no—
189C22⋊C8—41no—
190C22⋊C8—41no—
191C22⋊C8—41no—
192C22⋊C8—41no—
193C22⋊C8—41no—
194C22⋊C8—41no—
195C22⋊C8C22⋊C414yes—
196#97—41no—
197#97—41no—
198#97—41no—
199#97—41no—
200C4×C8—22no—
201C4×C8—22no—
202C4×C8—22no—
203C4×C8—22no—
204C4×C8—41no—
205C4×C8—41no—
206C24C22⋊Q811yescharacteristic
207C2×Q8—22no—
208C2×Q8—22no—
209C2×Q8—44no—
210C2×Q8—41no—
211C2×Q8—41no—
212C2×Q8—82no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4C2×C22⋊C411yescharacteristic
220C22×C4C2×C4⋊C411yescharacteristic
221C22×C4#11711yescharacteristic
222C22×C4#12111yescharacteristic
223C22×C4#12111yescharacteristic
224C22×C4#12111yescharacteristic
225C22×C4#12111yescharacteristic
226C22×C4#12111yescharacteristic
227C22×C4#12111yescharacteristic
228C22×C4#12111yescharacteristic
229C22×C4#12111yescharacteristic
230C22×C4C22⋊Q811yescharacteristic
231C22×C4C22⋊Q811yescharacteristic
232C22×C4C22⋊Q811yescharacteristic
233C22×C4C22⋊Q811yescharacteristic
234C22×C4C22⋊Q811yescharacteristic
235C22×C4#12611yescharacteristic
236C22×C4#12611yescharacteristic
237M16—82no—
238M16—82no—
239C2×C8—24no—
240C2×C8—44no—
241C2×C8—42no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—82no—
250C2×C8—82no—
251C2×C8—82no—
252C2×C8—82no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—42no—
256C4⋊C4—42no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—42no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—42no—
265C22⋊C4—42no—
266C22⋊C4—42no—
267C42—42no—
268C42—42no—
269C42C4×D411yescharacteristic
270C42C4×D411yescharacteristic
271C42C4×D411yescharacteristic
272C42C4×D411yescharacteristic
273C42#12011yescharacteristic
274C42#12011yescharacteristic
275C42#12011yescharacteristic
276C42#12311yescharacteristic
277C42#12311yescharacteristic
278C42#12311yescharacteristic
279C42#12311yescharacteristic
280C42#12311yescharacteristic
281C42#12411yescharacteristic
282C42#12411yescharacteristic
283C42#12411yescharacteristic
284C42#12711yescharacteristic
285C23—22no—
286C23—22no—
287C23—41no—
288C23#38011yescharacteristic
289C23#39611yescharacteristic
290C23#39611yescharacteristic
291Q8—82no—
292Q8—82no—
293Q8—82no—
294Q8—82no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—44no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—82no—
318C2×C4#38511yescharacteristic
319C2×C4#38511yescharacteristic
320C2×C4#38611yescharacteristic
321C2×C4#38811yescharacteristic
322C2×C4#38811yescharacteristic
323C2×C4#39011yescharacteristic
324C2×C4#39211yescharacteristic
325C2×C4#39311yescharacteristic
326C2×C4#39411yescharacteristic
327C2×C4#39411yescharacteristic
328C2×C4#39711yescharacteristic
329C2×C4#39911yescharacteristic
330C2×C4#47112yes—
331C2×C4#47312yes—
332C8—44no—
333C8—82no—
334C8—82no—
335C8—82no—
336C8—81no—
337C8—82no—
338C8—81no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—44no—
347C22#143911yescharacteristic
348C22#181312yes—
349C22#206412yes—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—82no—
360C4—82no—
361C4#193012yes—
362C4#201911yescharacteristic
363C4#202011yescharacteristic
364C4#205312yes—
365C2—22no—
366C2—22no—
367C2—41no—
368C2#1109211yescharacteristic
369C2#1109911yescharacteristic
370C2#1114511yescharacteristic
subgroupG/H
centerC2×C4#388
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
socleC22#1439
prime radicalC24C22⋊Q8
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
C2×#15732
#177342
C2×#15422
#173852
#80542
#80022
#78642