Finite Group Databasebeta

← #116586

Subgroups — #116586

Order 512.

603 conjugacy classes of subgroups.

The subgroup lattice has 409 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21306C211yesmaximal, characteristic
2#20769C211yesmaximal, characteristic
3#17708C211yesmaximal, characteristic
4C2×#1550C211yesmaximal, characteristic
5#8045C211yesmaximal, characteristic
6#7957C211yesmaximal, characteristic
7C2×#1283C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#423C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C22×C4⋊C8C2211yescharacteristic
13C2×C4×M16C2211yescharacteristic
14#2285C2211yescharacteristic
15#1986—22no—
16#1986C414yes—
17#1838—22no—
18#1837—22no—
19#1738—22no—
20#1733—22no—
21#1550—22no—
22#1550—22no—
23#1550—22no—
24#1549—21no—
25#1548—21no—
26#1542—22no—
27C2×#333—21no—
28C2×#332—21no—
29#1296—22no—
30#1286—22no—
31#1283—22no—
32C22×M16—21no—
33C22×M16—21no—
34C22×M16D412yes—
35C23×C8—21no—
36#533—21no—
37#533—21no—
38#533—21no—
39#533—21no—
40#533—21no—
41#533—21no—
42#533C2×C412yes—
43#533Q812yes—
44C2×C4⋊Q8D411yescharacteristic
45C2×C4⋊Q8D411yescharacteristic
46C2×#125—21no—
47C2×C22⋊Q8—21no—
48C2×C22⋊Q8—21no—
49C2×C4×Q8—21no—
50C2×C4×Q8—21no—
51C2×#117—21no—
52C2×#117—21no—
53C22×C42C2311yescharacteristic
54#431—21no—
55#431—21no—
56#431—21no—
57#431D412yes—
58#423—21no—
59#423—21no—
60#423—21no—
61#423—21no—
62#423—21no—
63#423—21no—
64#423D412yes—
65#423D412yes—
66C2×C4⋊C8—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—21no—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74C2×C4⋊C8—21no—
75C2×C4⋊C8—21no—
76C2×C4⋊C8D412yes—
77C2×C22⋊C8—21no—
78C4×M16—21no—
79C4×M16—21no—
80C4×M16C2×C412yes—
81C4×M16D412yes—
82C2×#97—21no—
83C2×C4×C8—21no—
84C2×C4×C8—21no—
85#384—21no—
86#382—21no—
87#380—21no—
88#380—21no—
89C4×C4⋊C4—21no—
90C4×C4⋊C4C2×C412yes—
91#341—28no—
92#339—28no—
93#333—24no—
94#333—24no—
95#332—24no—
96#332—24no—
97C22×Q8—21no—
98C22×Q8—21no—
99C23×C4C2×D411yescharacteristic
100C23×C4#4111yescharacteristic
101C23×C4#4111yescharacteristic
102C2×M16—22no—
103C2×M16—22no—
104C2×M16—22no—
105C2×M16—22no—
106C2×M16—22no—
107C2×M16—22no—
108C2×M16—22no—
109C2×M16—41no—
110C2×M16—41no—
111C2×M16—42no—
112C2×M16—42no—
113C2×M16—42no—
114C2×M16—42no—
115C2×M16C22⋊C414yes—
116C22×C8—22no—
117C22×C8—22no—
118C22×C8—41no—
119C22×C8—41no—
120C22×C8—41no—
121C22×C8—41no—
122C22×C8—41no—
123C22×C8—82no—
124C4⋊Q8—21no—
125C4⋊Q8—21no—
126C4⋊Q8—21no—
127C4⋊Q8—21no—
128C4⋊Q8—21no—
129C4⋊Q8—21no—
130C4⋊Q8C4⋊C412yes—
131C4⋊Q8C4⋊C412yes—
132#125—22no—
133#125—22no—
134#125—41no—
135#125—41no—
136C22⋊Q8—22no—
137C22⋊Q8—22no—
138C22⋊Q8—22no—
139C22⋊Q8—22no—
140C22⋊Q8—41no—
141C22⋊Q8—41no—
142C22⋊Q8—41no—
143C22⋊Q8—41no—
144C4×Q8—22no—
145C4×Q8—22no—
146C4×Q8—22no—
147C4×Q8—22no—
148C4×Q8—41no—
149C4×Q8—41no—
150C4×Q8—41no—
151C4×Q8—41no—
152#117—22no—
153#117—22no—
154#117—41no—
155#117—41no—
156#117—42no—
157#117—42no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—41no—
164C2×C4⋊C4—41no—
165C2×C4⋊C4—41no—
166C2×C4⋊C4—41no—
167C2×C22⋊C4—41no—
168C2×C22⋊C4—41no—
169C2×C42—22no—
170C2×C42—41no—
171C2×C42C22×C411yescharacteristic
172C2×C42C2×D411yescharacteristic
173C2×C42C2×D411yescharacteristic
174C2×C42C2×D411yescharacteristic
175C2×C42C2×D411yescharacteristic
176C2×C42C2×D411yescharacteristic
177C2×C42C2×D411yescharacteristic
178C2×C42C2×Q811yescharacteristic
179C2×C42#4111yescharacteristic
180C2×C42#4111yescharacteristic
181C2×C42#4111yescharacteristic
182C2×C42#4111yescharacteristic
183C4⋊C8—22no—
184C4⋊C8—22no—
185C4⋊C8—22no—
186C4⋊C8—22no—
187C4⋊C8—22no—
188C4⋊C8—22no—
189C4⋊C8—22no—
190C4⋊C8—41no—
191C4⋊C8—41no—
192C4⋊C8—41no—
193C4⋊C8—41no—
194C4⋊C8—41no—
195C4⋊C8—41no—
196C4⋊C8—41no—
197C22⋊C8—22no—
198C22⋊C8—41no—
199#97—22no—
200#97—22no—
201C4×C8—22no—
202C4×C8—22no—
203C4×C8—22no—
204C4×C8—41no—
205#95—22no—
206#95—41no—
207C24#12411yescharacteristic
208C2×Q8—22no—
209C2×Q8—22no—
210C2×Q8—41no—
211C2×Q8—41no—
212C2×Q8—81no—
213C2×Q8—81no—
214C2×Q8—82no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4—42no—
220C22×C4—81no—
221C22×C4C2×C22⋊C411yescharacteristic
222C22×C4C4×D411yescharacteristic
223C22×C4C4×D411yescharacteristic
224C22×C4#12011yescharacteristic
225C22×C4#12111yescharacteristic
226C22×C4#12111yescharacteristic
227C22×C4#12111yescharacteristic
228C22×C4C22⋊Q811yescharacteristic
229C22×C4C22⋊Q811yescharacteristic
230C22×C4C22⋊Q811yescharacteristic
231C22×C4#12311yescharacteristic
232C22×C4#12311yescharacteristic
233C22×C4#12311yescharacteristic
234C22×C4#12411yescharacteristic
235C22×C4#12411yescharacteristic
236C22×C4#12611yescharacteristic
237C22×C4#12611yescharacteristic
238C22×C4#12711yescharacteristic
239C22×C4#13512yes—
240C22×C4#13512yes—
241C22×C4#13712yes—
242C22×C4#13712yes—
243M16—24no—
244M16—24no—
245M16—42no—
246M16—42no—
247M16—44no—
248M16—44no—
249M16—82no—
250M16—81no—
251M16—81no—
252C2×C8—24no—
253C2×C8—42no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—42no—
259C2×C8—82no—
260C2×C8—82no—
261C2×C8—82no—
262C2×C8—82no—
263C2×C8—81no—
264C2×C8—81no—
265C2×C8—82no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—81no—
279C4⋊C4—81no—
280C4⋊C4—82no—
281C4⋊C4—81no—
282C4⋊C4—81no—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C22⋊C4—82no—
286C42—42no—
287C42—42no—
288C42—44no—
289C42C2×C4⋊C411yescharacteristic
290C42#11711yescharacteristic
291C42C4×D411yescharacteristic
292C42C4×D411yescharacteristic
293C42#12011yescharacteristic
294C42#12011yescharacteristic
295C42#12111yescharacteristic
296C42#12111yescharacteristic
297C42#12111yescharacteristic
298C42#12111yescharacteristic
299C42#12111yescharacteristic
300C42C22⋊Q811yescharacteristic
301C42C22⋊Q811yescharacteristic
302C42C22⋊Q811yescharacteristic
303C42#12311yescharacteristic
304C42#12311yescharacteristic
305C23—41no—
306C23—41no—
307C23#39011yescharacteristic
308C23#39311yescharacteristic
309C23#39711yescharacteristic
310C23#48812yes—
311C23#49112yes—
312Q8—82no—
313Q8—82no—
314Q8—82no—
315Q8—81no—
316Q8—81no—
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—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4#38011yescharacteristic
340C2×C4#38511yescharacteristic
341C2×C4#38511yescharacteristic
342C2×C4#38611yescharacteristic
343C2×C4#38811yescharacteristic
344C2×C4#38811yescharacteristic
345C2×C4#39211yescharacteristic
346C2×C4#39411yescharacteristic
347C2×C4#39411yescharacteristic
348C2×C4#39611yescharacteristic
349C2×C4#39611yescharacteristic
350C2×C4#39911yescharacteristic
351C2×C4#41612yes—
352C2×C4#41912yes—
353C2×C4#45212yes—
354C2×C4#45212yes—
355C2×C4#46412yes—
356C2×C4#46412yes—
357C2×C4#47912yes—
358C2×C4#47912yes—
359C2×C4#48512yes—
360C2×C4#48512yes—
361C2×C4#49511yescharacteristic
362C2×C4#49511yescharacteristic
363C2×C4#49711yescharacteristic
364C2×C4#49711yescharacteristic
365C8—44no—
366C8—82no—
367C8—82no—
368C8—82no—
369C8—82no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—42no—
377C22—42no—
378C22#143911yescharacteristic
379C22#195811yescharacteristic
380C22#196011yescharacteristic
381C22#202612yes—
382C22#207412yes—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—82no—
391C4—82no—
392C4—162no—
393C4#180512yes—
394C4#187312yes—
395C4#201511yescharacteristic
396C4#201511yescharacteristic
397C4#204811yescharacteristic
398C4#204911yescharacteristic
399C4#209711yescharacteristic
400C4#209711yescharacteristic
401C2—21no—
402C2—22no—
403C2—21no—
404C2—22no—
405C2#1105211yescharacteristic
406C2#1111611yescharacteristic
407C2#1112011yescharacteristic
subgroupG/H
center, socleC22#1439
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#124
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
#213062
#207692
#177082
C2×#15502
#80452
#79572
C2×#12832