Finite Group Databasebeta

← #116088

Subgroups — #116088

Order 512.

663 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21332C211yesmaximal, characteristic
2#20793C211yesmaximal, characteristic
3#17708C211yesmaximal, characteristic
4C2×#1542C211yesmaximal, characteristic
5#8039C211yesmaximal, characteristic
6#7957C211yesmaximal, characteristic
7#7924C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#424—22no—
12C2×#423C2211yescharacteristic
13C22×C4⋊C8C2211yescharacteristic
14#2285C2211yescharacteristic
15C4×#117C2211yescharacteristic
16#1996—22no—
17#1996C414yes—
18#1843—22no—
19#1842—22no—
20#1740—22no—
21#1550—22no—
22#1549—21no—
23#1548—21no—
24#1542—22no—
25#1542—22no—
26#1542—22no—
27C2×#333—21no—
28C2×#332—21no—
29#1296—22no—
30#1286—22no—
31#1282—22no—
32C22×M16—21no—
33C23×C8—21no—
34#533—21no—
35#533—21no—
36#533—21no—
37#533—21no—
38#533—21no—
39#533—21no—
40#533—21no—
41#533—21no—
42C2×C4⋊Q8D411yescharacteristic
43C2×C4⋊Q8D411yescharacteristic
44C2×#125—21no—
45C2×C22⋊Q8—21no—
46C2×C22⋊Q8C2×C412yes—
47C2×C4×Q8—21no—
48C2×C4×Q8Q812yes—
49C2×#117—21no—
50C2×#117—21no—
51C2×#117D412yes—
52C22×C42C2311yescharacteristic
53#431—21no—
54#431—21no—
55#431—21no—
56#431—21no—
57#431—21no—
58#431—21no—
59#431—21no—
60#431D412yes—
61#424—44no—
62#424—44no—
63#423—21no—
64#423—21no—
65#423—21no—
66#423—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—21no—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—28no—
73C2×C4⋊C8—21no—
74C2×C4⋊C8—21no—
75C2×C4⋊C8D412yes—
76C2×C4⋊C8D412yes—
77C2×C4⋊C8D412yes—
78C2×C22⋊C8—21no—
79C2×C22⋊C8—21no—
80C2×C4×C8—21no—
81C2×C4×C8—21no—
82#384—21no—
83#382—21no—
84#380—21no—
85#380C2×C412yes—
86C4×C4⋊C4—21no—
87C4×C4⋊C4—21no—
88C4×C4⋊C4—21no—
89C4×C4⋊C4—21no—
90C4×C22⋊C4C2×C412yes—
91C4×C22⋊C4D412yes—
92#376—21no—
93C43—21no—
94#342—28no—
95#333—24no—
96#333—24no—
97#332—24no—
98#332—24no—
99C22×Q8—21no—
100C22×Q8C4⋊C412yes—
101C23×C4C22×C411yescharacteristic
102C23×C4C2×D411yescharacteristic
103C23×C4C2×D411yescharacteristic
104C2×M16—41no—
105C2×M16—41no—
106C2×M16—42no—
107C2×M16—42no—
108C22×C8—22no—
109C22×C8—22no—
110C22×C8—22no—
111C22×C8—41no—
112C22×C8—41no—
113C22×C8—41no—
114C22×C8—42no—
115C22×C8—42no—
116C4⋊Q8—21no—
117C4⋊Q8—21no—
118C4⋊Q8—21no—
119C4⋊Q8—21no—
120C4⋊Q8—21no—
121C4⋊Q8—21no—
122C4⋊Q8—21no—
123C4⋊Q8—21no—
124#125—41no—
125#125—41no—
126#125—41no—
127#125—41no—
128C22⋊Q8—22no—
129C22⋊Q8—22no—
130C22⋊Q8—22no—
131C22⋊Q8—22no—
132C22⋊Q8—41no—
133C22⋊Q8—41no—
134C22⋊Q8—41no—
135C22⋊Q8—41no—
136C4×Q8—22no—
137C4×Q8—22no—
138C4×Q8—22no—
139C4×Q8—22no—
140C4×Q8—41no—
141C4×Q8—41no—
142C4×Q8—41no—
143C4×Q8—41no—
144#117—22no—
145#117—22no—
146#117—41no—
147#117—41no—
148#117—41no—
149#117—41no—
150#117—42no—
151#117—42no—
152#117SD1614yes—
153#117Q1614yes—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—41no—
162C2×C4⋊C4—41no—
163C2×C4⋊C4C4⋊C412yes—
164C2×C22⋊C4—22no—
165C2×C22⋊C4—22no—
166C2×C22⋊C4C22⋊C414yes—
167C2×C42—22no—
168C2×C42—22no—
169C2×C42—22no—
170C2×C42—22no—
171C2×C42—41no—
172C2×C42C2×D411yescharacteristic
173C2×C42C2×D411yescharacteristic
174C2×C42C2×D411yescharacteristic
175C2×C42C2×D411yescharacteristic
176C2×C42C2×D411yescharacteristic
177C2×C42C2×Q811yescharacteristic
178C2×C42#4111yescharacteristic
179C2×C42#4111yescharacteristic
180C2×C42#4111yescharacteristic
181C2×C42#4111yescharacteristic
182C2×C42#4111yescharacteristic
183C2×C42#4111yescharacteristic
184C4⋊C8—22no—
185C4⋊C8—22no—
186C4⋊C8—22no—
187C4⋊C8—22no—
188C4⋊C8—22no—
189C4⋊C8—22no—
190C4⋊C8—22no—
191C4⋊C8—416no—
192C4⋊C8—41no—
193C4⋊C8—41no—
194C4⋊C8—41no—
195C4⋊C8—41no—
196C4⋊C8—41no—
197C22⋊C8—22no—
198C22⋊C8—41no—
199C22⋊C8—41no—
200C22⋊C8—41no—
201C4×C8—22no—
202C4×C8—41no—
203C4×C8—41no—
204C4×C8—41no—
205#95—22no—
206#95—22no—
207#95—22no—
208#95—41no—
209C24C2×C22⋊C411yescharacteristic
210C2×Q8—22no—
211C2×Q8—22no—
212C2×Q8—41no—
213C2×Q8—41no—
214C2×Q8—82no—
215C2×Q8—82no—
216C22×C4—24no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—81no—
222C22×C4C2×C4⋊C411yescharacteristic
223C22×C4#11711yescharacteristic
224C22×C4C4×D411yescharacteristic
225C22×C4C4×D411yescharacteristic
226C22×C4C4×D411yescharacteristic
227C22×C4C4×D411yescharacteristic
228C22×C4#12011yescharacteristic
229C22×C4#12111yescharacteristic
230C22×C4#12111yescharacteristic
231C22×C4#12111yescharacteristic
232C22×C4#12111yescharacteristic
233C22×C4#12111yescharacteristic
234C22×C4#12111yescharacteristic
235C22×C4C22⋊Q811yescharacteristic
236C22×C4C22⋊Q811yescharacteristic
237C22×C4#12311yescharacteristic
238C22×C4#12411yescharacteristic
239C22×C4#12711yescharacteristic
240C22×C4C2×SD1612yes—
241C22×C4C2×Q1612yes—
242C22×C4AGL(1,ℤ/8)12yes—
243C22×C4#13712yes—
244M16—82no—
245M16—81no—
246M16—81no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—44no—
252C2×C8—44no—
253C2×C8—82no—
254C2×C8—82no—
255C2×C8—81no—
256C2×C8—81no—
257C2×C8—82no—
258C4⋊C4—24no—
259C4⋊C4—24no—
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—42no—
263C4⋊C4—42no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—82no—
273C4⋊C4—82no—
274C4⋊C4—81no—
275C4⋊C4—81no—
276C22⋊C4—24no—
277C22⋊C4—42no—
278C22⋊C4—42no—
279C22⋊C4—44no—
280C22⋊C4#10318yes—
281C42—24no—
282C42—24no—
283C42—44no—
284C42—42no—
285C42—42no—
286C42—82no—
287C42—82no—
288C42#12011yescharacteristic
289C42#12011yescharacteristic
290C42#12111yescharacteristic
291C42#12111yescharacteristic
292C42C22⋊Q811yescharacteristic
293C42C22⋊Q811yescharacteristic
294C42C22⋊Q811yescharacteristic
295C42C22⋊Q811yescharacteristic
296C42#12311yescharacteristic
297C42#12311yescharacteristic
298C42#12311yescharacteristic
299C42#12311yescharacteristic
300C42#12411yescharacteristic
301C42#12411yescharacteristic
302C42#12611yescharacteristic
303C42#12611yescharacteristic
304C23—41no—
305C23—41no—
306C23#38011yescharacteristic
307C23#38611yescharacteristic
308C23#39011yescharacteristic
309C23C2×#10312yes—
310C23#41712yes—
311Q8—82no—
312Q8—82no—
313Q8—82no—
314Q8—82no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—28no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—44no—
329C2×C4—44no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4#38511yescharacteristic
338C2×C4#38511yescharacteristic
339C2×C4#38811yescharacteristic
340C2×C4#38811yescharacteristic
341C2×C4#39211yescharacteristic
342C2×C4#39311yescharacteristic
343C2×C4#39411yescharacteristic
344C2×C4#39411yescharacteristic
345C2×C4#39611yescharacteristic
346C2×C4#39611yescharacteristic
347C2×C4#39711yescharacteristic
348C2×C4#39911yescharacteristic
349C2×C4#45012yes—
350C2×C4#45112yes—
351C2×C4#46012yes—
352C2×C4#46212yes—
353C2×C4#47512yes—
354C2×C4#47712yes—
355C2×C4#48312yes—
356C2×C4#48412yes—
357C2×C4#48712yes—
358C2×C4#48912yes—
359C2×C4#49211yescharacteristic
360C2×C4#49411yescharacteristic
361C2×C4#49611yescharacteristic
362C2×C4#49711yescharacteristic
363C8—82no—
364C8—82no—
365C8—82no—
366C8—82no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—42no—
374C22—42no—
375C22#143911yescharacteristic
376C22#180312yes—
377C22#187212yes—
378C22#195611yescharacteristic
379C22#195911yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—48no—
388C4—82no—
389C4—82no—
390C4—162no—
391C4#201411yescharacteristic
392C4#201611yescharacteristic
393C4#202412yes—
394C4#205312yes—
395C4#207212yes—
396C4#209511yescharacteristic
397C4#209611yescharacteristic
398C2—22no—
399C2—21no—
400C2—22no—
401C2—21no—
402C2#1105011yescharacteristic
403C2#1109011yescharacteristic
404C2#1109211yescharacteristic
subgroupG/H
centerC2×C4#393
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
socleC22#1439
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ 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
#213322
#207932
#177082
C2×#15422
#80392
#79572
#79242