Finite Group Databasebeta

← #118404

Subgroups — #118404

Order 512.

606 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21337C211yesmaximal, characteristic
2#17814C211yesmaximal, characteristic
3#17708C211yesmaximal, characteristic
4C2×#1518C211yesmaximal, characteristic
5#10858C211yesmaximal, characteristic
6C2×#1286C211yesmaximal, characteristic
7#7918C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C2×C4×M16C2211yescharacteristic
14C2×#382C2211yescharacteristic
15#1998—22no—
16#1997—21no—
17#1997—21no—
18#1742—22no—
19C2×#343—22no—
20#1571—22no—
21#1571—22no—
22#1567—22no—
23#1550—22no—
24#1549—21no—
25#1548—21no—
26#1542—22no—
27#1518—22no—
28#1518—22no—
29C2×#328C414yes—
30#1286—22no—
31#1281—22no—
32C22×M16—21no—
33C22×M16—21no—
34C22×M16D412yes—
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⋊Q8C2×C412yes—
48C2×C4×Q8—21no—
49C2×C4×Q8Q812yes—
50C2×#117—21no—
51C22×C4⋊C4—21no—
52C22×C42C2311yescharacteristic
53#431—21no—
54#431—21no—
55#431—21no—
56#431—21no—
57#431—21no—
58#431D412yes—
59#431D412yes—
60#431D412yes—
61#423—21no—
62#423—21no—
63#423—21no—
64#423—21no—
65#423—21no—
66#423—21no—
67#423D412yes—
68#423D412yes—
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×C22⋊C8—21no—
76C2×C22⋊C8C2×C412yes—
77C4×M16—21no—
78C4×M16—21no—
79C4×M16—21no—
80C4×M16—21no—
81C2×#97—21no—
82C2×C4×C8—21no—
83C2×C4×C8—21no—
84C2×C4×C8—21no—
85#382—21no—
86#382—21no—
87#382—21no—
88#382—21no—
89C2×#95—21no—
90C2×#95C2×C412yes—
91#343—24no—
92#343—24no—
93#343—44no—
94#335—28no—
95#333—24no—
96#332—24no—
97#328—28no—
98C22×Q8—21no—
99C22×Q8C4⋊C412yes—
100C23×C4—22no—
101C23×C4C22×C411yescharacteristic
102C23×C4C2×D411yescharacteristic
103C23×C4#4111yescharacteristic
104C2×M16—22no—
105C2×M16—22no—
106C2×M16—22no—
107C2×M16—22no—
108C2×M16—22no—
109C2×M16—22no—
110C2×M16—22no—
111C2×M16—41no—
112C2×M16—41no—
113C2×M16—42no—
114C2×M16—42no—
115C2×M16—42no—
116C2×M16—42no—
117C2×M16Q1614yes—
118C22×C8—22no—
119C22×C8—22no—
120C22×C8—41no—
121C22×C8—41no—
122C22×C8—41no—
123C4⋊Q8—21no—
124C4⋊Q8—21no—
125C4⋊Q8—21no—
126C4⋊Q8—21no—
127C4⋊Q8—21no—
128C4⋊Q8—21no—
129C4⋊Q8—21no—
130C4⋊Q8—21no—
131#125—41no—
132#125—41no—
133#125—41no—
134#125—41no—
135C22⋊Q8—22no—
136C22⋊Q8—22no—
137C22⋊Q8—22no—
138C22⋊Q8—22no—
139C22⋊Q8—41no—
140C22⋊Q8—41no—
141C22⋊Q8—41no—
142C22⋊Q8—41no—
143C4×Q8—22no—
144C4×Q8—22no—
145C4×Q8—22no—
146C4×Q8—22no—
147C4×Q8—41no—
148C4×Q8—41no—
149C4×Q8—41no—
150C4×Q8—41no—
151#117—41no—
152#117—41no—
153#117—41no—
154#117—41no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—41no—
161C2×C4⋊C4—41no—
162C2×C4⋊C4—42no—
163C2×C4⋊C4—42no—
164C2×C4⋊C4C4⋊C412yes—
165C2×C22⋊C4—22no—
166C2×C42—22no—
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
177C2×C42#4111yescharacteristic
178C2×C42#4111yescharacteristic
179C4⋊C8—22no—
180C4⋊C8—22no—
181C4⋊C8—22no—
182C4⋊C8—22no—
183C4⋊C8—22no—
184C4⋊C8—22no—
185C4⋊C8—22no—
186C4⋊C8—41no—
187C4⋊C8—41no—
188C4⋊C8—41no—
189C4⋊C8—41no—
190C4⋊C8—41no—
191C22⋊C8—22no—
192C22⋊C8—22no—
193C22⋊C8—41no—
194C22⋊C8C22⋊C414yes—
195#97—41no—
196#97—41no—
197C4×C8—22no—
198C4×C8—22no—
199C4×C8—22no—
200C4×C8—41no—
201C4×C8—41no—
202C4×C8—41no—
203#95—22no—
204#95—22no—
205#95—41no—
206#95—41no—
207C24C4×D411yescharacteristic
208C2×Q8—22no—
209C2×Q8—22no—
210C2×Q8—41no—
211C2×Q8—41no—
212C2×Q8—82no—
213C2×Q8—82no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—42no—
217C22×C4—44no—
218C22×C4—81no—
219C22×C4—81no—
220C22×C4—82no—
221C22×C4—82no—
222C22×C4C2×C22⋊C411yescharacteristic
223C22×C4C2×C4⋊C411yescharacteristic
224C22×C4#11711yescharacteristic
225C22×C4C4×D411yescharacteristic
226C22×C4C4×D411yescharacteristic
227C22×C4C4×D411yescharacteristic
228C22×C4#12011yescharacteristic
229C22×C4#12111yescharacteristic
230C22×C4#12111yescharacteristic
231C22×C4#12111yescharacteristic
232C22×C4C22⋊Q811yescharacteristic
233C22×C4C22⋊Q811yescharacteristic
234C22×C4#12311yescharacteristic
235C22×C4#12311yescharacteristic
236C22×C4#12411yescharacteristic
237C22×C4#12411yescharacteristic
238C22×C4#12611yescharacteristic
239C22×C4#12711yescharacteristic
240C22×C4C2×Q1612yes—
241C22×C4#13512yes—
242C22×C4AGL(1,ℤ/8)12yes—
243C22×C4#13712yes—
244M16—24no—
245M16—24no—
246M16—42no—
247M16—42no—
248M16—44no—
249M16—44no—
250M16—82no—
251M16—81no—
252M16—81no—
253C2×C8—24no—
254C2×C8—24no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—42no—
259C2×C8—42no—
260C2×C8—82no—
261C2×C8—82no—
262C2×C8—82no—
263C2×C8—81no—
264C2×C8—81no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—42no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—42no—
276C4⋊C4—41no—
277C4⋊C4—82no—
278C4⋊C4—81no—
279C4⋊C4—81no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C42—42no—
283C42—42no—
284C42#12011yescharacteristic
285C42#12011yescharacteristic
286C42#12111yescharacteristic
287C42#12111yescharacteristic
288C42#12111yescharacteristic
289C42#12111yescharacteristic
290C42#12111yescharacteristic
291C42C22⋊Q811yescharacteristic
292C42C22⋊Q811yescharacteristic
293C42C22⋊Q811yescharacteristic
294C42C22⋊Q811yescharacteristic
295C42#12311yescharacteristic
296C42#12311yescharacteristic
297C42#12311yescharacteristic
298C42#12411yescharacteristic
299C42#12611yescharacteristic
300C23—41no—
301C23—41no—
302C23#38511yescharacteristic
303C23#38811yescharacteristic
304C23#39011yescharacteristic
305C23C4×Q1612yes—
306C23#44012yes—
307Q8—82no—
308Q8—82no—
309Q8—82no—
310Q8—82no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—164no—
331C2×C4#38011yescharacteristic
332C2×C4#38511yescharacteristic
333C2×C4#38611yescharacteristic
334C2×C4#38811yescharacteristic
335C2×C4#39211yescharacteristic
336C2×C4#39311yescharacteristic
337C2×C4#39411yescharacteristic
338C2×C4#39411yescharacteristic
339C2×C4#39611yescharacteristic
340C2×C4#39611yescharacteristic
341C2×C4#39711yescharacteristic
342C2×C4#39911yescharacteristic
343C2×C4#44912yes—
344C2×C4#45112yes—
345C2×C4#46212yes—
346C2×C4#46312yes—
347C2×C4#46712yes—
348C2×C4#46812yes—
349C2×C4#47712yes—
350C2×C4#47912yes—
351C2×C4#48412yes—
352C2×C4#48512yes—
353C2×C4#49411yescharacteristic
354C2×C4#49511yescharacteristic
355C2×C4#49611yescharacteristic
356C2×C4#49711yescharacteristic
357C8—44no—
358C8—44no—
359C8—82no—
360C8—82no—
361C8—82no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—42no—
369C22—42no—
370C22#143911yescharacteristic
371C22#186312yes—
372C22#192812yes—
373C22#196911yescharacteristic
374C22#197311yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—82no—
384C4—82no—
385C4—162no—
386C4#201211yescharacteristic
387C4#201611yescharacteristic
388C4#203612yes—
389C4#206812yes—
390C4#209511yescharacteristic
391C4#209711yescharacteristic
392C2—21no—
393C2—22no—
394C2—22no—
395C2—21no—
396C2#1109011yescharacteristic
397C2#1111611yescharacteristic
398C2#1112411yescharacteristic
subgroupG/H
center, socleC22#1439
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C4×D4
LCSG ▷ C23×C4 ▷ 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
#213372
#178142
#177082
C2×#15182
#108582
C2×#12862
#79182