Finite Group Databasebeta

← #117943

Subgroups — #117943

Order 512.

571 conjugacy classes of subgroups.

The subgroup lattice has 387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1567C211yesmaximal, characteristic
2#17751C211yesmaximal, characteristic
3#17749C211yesmaximal, characteristic
4C2×#1493C211yesmaximal, characteristic
5#8129C211yesmaximal, characteristic
6#8004C211yesmaximal, characteristic
7#7885C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C2×#423C2211yescharacteristic
14C22×C4×C8C2211yescharacteristic
15#1567—22no—
16#1567—22no—
17C2×#335—22no—
18#1561—22no—
19#1559—22no—
20#1552—22no—
21#1550—22no—
22#1549—21no—
23#1548—21no—
24#1546—21no—
25#1546—21no—
26#1493—21no—
27#1493—21no—
28#1493C414yes—
29C2×Q8⋊C8—22no—
30#1309—22no—
31#1292—22no—
32#1278—21no—
33#1278—21no—
34C22×M16—21no—
35C22×M16—21no—
36C22×M16—21no—
37C23×C8—21no—
38#533—21no—
39#533—21no—
40#533—21no—
41#533—21no—
42#533—21no—
43#533—21no—
44#533C2×C412yes—
45#533Q812yes—
46C2×C4⋊Q8D411yescharacteristic
47C2×C4⋊Q8D411yescharacteristic
48C2×#125—21no—
49C2×C22⋊Q8—21no—
50C2×C22⋊Q8—21no—
51C2×C4×Q8—21no—
52C2×C4×Q8—21no—
53C2×#117—21no—
54C22×C42C2311yescharacteristic
55#432—21no—
56#432—21no—
57#432—21no—
58#432—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62#431—21no—
63#423—21no—
64#423—21no—
65#423—21no—
66#423—21no—
67#423—21no—
68#423—21no—
69#423—21no—
70#423—21no—
71#423—21no—
72#423—21no—
73#423C2×C412yes—
74#423D412yes—
75#423D412yes—
76#423D412yes—
77C2×C4⋊C8—21no—
78C2×C4⋊C8—21no—
79C2×C4⋊C8—21no—
80C2×C4⋊C8—21no—
81C2×C4⋊C8—21no—
82C2×C4⋊C8D412yes—
83#407—21no—
84#407—21no—
85C4×M16—21no—
86C4×M16—21no—
87C2×C4×C8—21no—
88C2×C4×C8—21no—
89C2×C4×C8—21no—
90C2×C4×C8C2×C412yes—
91C2×C4×C8D412yes—
92C2×C4×C8D411yescharacteristic
93C2×C4×C8D411yescharacteristic
94#335—28no—
95#333—24no—
96#332—24no—
97#332—24no—
98#332—24no—
99Q8⋊C8—24no—
100Q8⋊C8—24no—
101C22×Q8—21no—
102C22×Q8—21no—
103C23×C4#4111yescharacteristic
104C23×C4#4111yescharacteristic
105C23×C4#4111yescharacteristic
106C2×M16—22no—
107C2×M16—22no—
108C2×M16—22no—
109C2×M16—22no—
110C2×M16—41no—
111C2×M16—41no—
112C2×M16—41no—
113C2×M16—41no—
114C2×M16—82no—
115C2×M16—82no—
116C2×M16—82no—
117C22×C8—21no—
118C22×C8—22no—
119C22×C8—21no—
120C22×C8—22no—
121C22×C8—22no—
122C22×C8—44no—
123C22×C8—41no—
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—22no—
185C4⋊C8—22no—
186C4⋊C8—22no—
187C4⋊C8—41no—
188C4⋊C8—41no—
189C4⋊C8—41no—
190C4⋊C8—41no—
191C4⋊C8—41no—
192C4⋊C8—41no—
193C22⋊C8—41no—
194C22⋊C8—41no—
195C22⋊C8—41no—
196C22⋊C8—41no—
197#97—41no—
198#97—41no—
199C4×C8—22no—
200C4×C8—22no—
201C4×C8—21no—
202C4×C8—21no—
203C4×C8—41no—
204C4×C8—41no—
205C4×C8C22⋊C412yes—
206C4×C8C22⋊C412yes—
207C24#12611yescharacteristic
208C2×Q8—22no—
209C2×Q8—22no—
210C2×Q8—41no—
211C2×Q8—41no—
212C2×Q8—42no—
213C2×Q8—42no—
214C2×Q8—82no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—42no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4#11711yescharacteristic
223C22×C4C4×D411yescharacteristic
224C22×C4C4×D411yescharacteristic
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×C4#12311yescharacteristic
234C22×C4#12311yescharacteristic
235C22×C4#12311yescharacteristic
236C22×C4#12311yescharacteristic
237C22×C4#12411yescharacteristic
238C22×C4#12411yescharacteristic
239C22×C4#12611yescharacteristic
240M16—42no—
241M16—42no—
242M16—82no—
243M16—82no—
244M16—82no—
245M16—82no—
246M16—82no—
247M16—82no—
248M16—82no—
249C2×C8—24no—
250C2×C8—22no—
251C2×C8—22no—
252C2×C8—44no—
253C2×C8—44no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—42no—
259C2×C8—42no—
260C2×C8—82no—
261C2×C8—82no—
262C2×C8—82no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C22⋊C4—42no—
276C22⋊C4—42no—
277C42—42no—
278C42—42no—
279C42C2×C22⋊C411yescharacteristic
280C42C2×C4⋊C411yescharacteristic
281C42C4×D411yescharacteristic
282C42C4×D411yescharacteristic
283C42#12011yescharacteristic
284C42#12011yescharacteristic
285C42#12011yescharacteristic
286C42#12111yescharacteristic
287C42#12111yescharacteristic
288C42#12111yescharacteristic
289C42C22⋊Q811yescharacteristic
290C42C22⋊Q811yescharacteristic
291C42C22⋊Q811yescharacteristic
292C42#12311yescharacteristic
293C42#12411yescharacteristic
294C42#12711yescharacteristic
295C23—22no—
296C23—22no—
297C23—41no—
298C23#38811yescharacteristic
299C23#39611yescharacteristic
300C23#39711yescharacteristic
301Q8—44no—
302Q8—82no—
303Q8—82no—
304Q8—81no—
305Q8—81no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4#38011yescharacteristic
331C2×C4#38511yescharacteristic
332C2×C4#38511yescharacteristic
333C2×C4#38611yescharacteristic
334C2×C4#38811yescharacteristic
335C2×C4#39011yescharacteristic
336C2×C4#39211yescharacteristic
337C2×C4#39311yescharacteristic
338C2×C4#39411yescharacteristic
339C2×C4#39411yescharacteristic
340C2×C4#39611yescharacteristic
341C2×C4#39911yescharacteristic
342C2×C4#47112yes—
343C2×C4#47212yes—
344C2×C4#47312yes—
345C2×C4#47312yes—
346C8—24no—
347C8—42no—
348C8—82no—
349C8—82no—
350C8—82no—
351C8—82no—
352C8—82no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—44no—
361C22#143911yescharacteristic
362C22#206412yes—
363C22#207812yes—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—82no—
372C4—82no—
373C4#181612yes—
374C4#197711yescharacteristic
375C4#197911yescharacteristic
376C4#201811yescharacteristic
377C4#202011yescharacteristic
378C4#205012yes—
379C4#205212yes—
380C2—22no—
381C2—22no—
382C2—41no—
383C2#1108211yescharacteristic
384C2#1110711yescharacteristic
385C2#1112811yescharacteristic
subgroupG/H
center, socleC22#1439
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#126
LCSG ▷ C2×C42 ▷ 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
C2×#15672
#177512
#177492
C2×#14932
#81292
#80042
#78852