Finite Group Databasebeta

← #118322

Subgroups — #118322

Order 512.

619 conjugacy classes of subgroups.

The subgroup lattice has 395 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21302C211yesmaximal, characteristic
2C2×#1571C211yesmaximal, characteristic
3#17575C211yesmaximal, characteristic
4#17486C211yesmaximal, characteristic
5#10855C211yesmaximal, characteristic
6#7932C211yesmaximal, characteristic
7#7893C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C22×C4⋊C8C2211yescharacteristic
13C2×C4×M16C2211yescharacteristic
14#2285C2211yescharacteristic
15#1985—22no—
16#1984—22no—
17C2×#344—22no—
18#1729—22no—
19#1571—22no—
20#1571—22no—
21C2×#335—22no—
22#1520C414yes—
23#1518—22no—
24#1503—22no—
25#1493—22no—
26#1487—22no—
27#1481—22no—
28#1283—22no—
29#1279—22no—
30C22×M16—21no—
31C22×M16D412yes—
32C23×C8—21no—
33#533—21no—
34#533—21no—
35#533—21no—
36#533—21no—
37#533—21no—
38#533—21no—
39#533—21no—
40#533—21no—
41C2×C4⋊Q8Q811yescharacteristic
42C2×C4⋊Q8Q811yescharacteristic
43C2×#125—21no—
44C2×C22⋊Q8—21no—
45C2×C22⋊Q8C2×C412yes—
46C2×C4×Q8—21no—
47C2×C4×Q8D412yes—
48C2×#117—21no—
49C2×#117—21no—
50C22×C42C2311yescharacteristic
51#431—21no—
52#431—21no—
53#431—21no—
54#431—21no—
55#431—21no—
56#431—21no—
57#431D412yes—
58#431D412yes—
59#423—21no—
60#423—21no—
61#423—21no—
62#423—21no—
63C2×C4⋊C8—21no—
64C2×C4⋊C8—21no—
65C2×C4⋊C8—21no—
66C2×C4⋊C8—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—21no—
71C2×C4⋊C8D412yes—
72C2×C4⋊C8D412yes—
73C2×C22⋊C8—21no—
74C2×C22⋊C8C2×C412yes—
75C4×M16—21no—
76C4×M16—21no—
77C4×M16—21no—
78C4×M16—21no—
79C2×#97—21no—
80C2×C4×C8—21no—
81C2×C4×C8—21no—
82C2×C4×C8D412yes—
83#384—21no—
84#382—21no—
85#380—21no—
86#380C2×C412yes—
87C4×C4⋊C4—21no—
88C4×C4⋊C4—21no—
89#344—44no—
90#336—28no—
91#335—28no—
92#328—28no—
93Q8⋊C8—28no—
94C22×Q8—21no—
95C22×Q8C4⋊C412yes—
96C23×C4C22×C411yescharacteristic
97C23×C4C2×D411yescharacteristic
98C23×C4#4111yescharacteristic
99C2×M16—22no—
100C2×M16—22no—
101C2×M16—22no—
102C2×M16—22no—
103C2×M16—22no—
104C2×M16—41no—
105C2×M16—41no—
106C2×M16—42no—
107C2×M16—42no—
108C2×M16Q1614yes—
109C22×C8—22no—
110C22×C8—22no—
111C22×C8—22no—
112C22×C8—22no—
113C22×C8—22no—
114C22×C8—41no—
115C22×C8—41no—
116C22×C8—42no—
117C22×C8—42no—
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—
150#117—42no—
151#117—42no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4—41no—
160C2×C4⋊C4C4⋊C412yes—
161C2×C22⋊C4—22no—
162C2×C22⋊C4—22no—
163C2×C42—22no—
164C2×C42—41no—
165C2×C42C2×D411yescharacteristic
166C2×C42C2×D411yescharacteristic
167C2×C42C2×D411yescharacteristic
168C2×C42C2×D411yescharacteristic
169C2×C42C2×D411yescharacteristic
170C2×C42C2×D411yescharacteristic
171C2×C42C2×Q811yescharacteristic
172C2×C42#4111yescharacteristic
173C2×C42#4111yescharacteristic
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—41no—
184C4⋊C8—41no—
185C4⋊C8—41no—
186C4⋊C8—41no—
187C4⋊C8—41no—
188C4⋊C8—41no—
189C22⋊C8—22no—
190C22⋊C8—41no—
191C22⋊C8—41no—
192C22⋊C8C22⋊C414yes—
193#97—41no—
194#97—41no—
195C4×C8—22no—
196C4×C8—22no—
197C4×C8—22no—
198C4×C8—22no—
199C4×C8—41no—
200C4×C8—41no—
201#95—22no—
202#95—41no—
203C24C4×D411yescharacteristic
204C2×Q8—22no—
205C2×Q8—22no—
206C2×Q8—44no—
207C2×Q8—41no—
208C2×Q8—41no—
209C2×Q8—82no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—81no—
215C22×C4C2×C22⋊C411yescharacteristic
216C22×C4C2×C4⋊C411yescharacteristic
217C22×C4#11711yescharacteristic
218C22×C4C4×D411yescharacteristic
219C22×C4C4×D411yescharacteristic
220C22×C4C4×D411yescharacteristic
221C22×C4#12011yescharacteristic
222C22×C4#12111yescharacteristic
223C22×C4#12111yescharacteristic
224C22×C4#12111yescharacteristic
225C22×C4C22⋊Q811yescharacteristic
226C22×C4C22⋊Q811yescharacteristic
227C22×C4#12311yescharacteristic
228C22×C4#12311yescharacteristic
229C22×C4#12411yescharacteristic
230C22×C4#12411yescharacteristic
231C22×C4#12611yescharacteristic
232C22×C4#12711yescharacteristic
233C22×C4C2×Q1612yes—
234C22×C4#13512yes—
235C22×C4AGL(1,ℤ/8)12yes—
236C22×C4#13712yes—
237M16—24no—
238M16—24no—
239M16—42no—
240M16—42no—
241M16—82no—
242M16—81no—
243M16—81no—
244C2×C8—24no—
245C2×C8—24no—
246C2×C8—44no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—44no—
253C2×C8—44no—
254C2×C8—82no—
255C2×C8—81no—
256C2×C8—81no—
257C2×C8—82no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—44no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—41no—
264C4⋊C4—42no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—42no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—82no—
272C4⋊C4—82no—
273C22⋊C4—42no—
274C22⋊C4—42no—
275C22⋊C4—44no—
276C42—42no—
277C42—42no—
278C42—81no—
279C42—81no—
280C42#12011yescharacteristic
281C42#12011yescharacteristic
282C42#12111yescharacteristic
283C42#12111yescharacteristic
284C42#12111yescharacteristic
285C42#12111yescharacteristic
286C42#12111yescharacteristic
287C42C22⋊Q811yescharacteristic
288C42C22⋊Q811yescharacteristic
289C42C22⋊Q811yescharacteristic
290C42C22⋊Q811yescharacteristic
291C42#12311yescharacteristic
292C42#12311yescharacteristic
293C42#12311yescharacteristic
294C42#12411yescharacteristic
295C42#12611yescharacteristic
296C23—41no—
297C23—41no—
298C23#38511yescharacteristic
299C23#38811yescharacteristic
300C23#39011yescharacteristic
301C23C4×Q1612yes—
302C23#44012yes—
303Q8—44no—
304Q8—82no—
305Q8—82no—
306Q8—82no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—41no—
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—44no—
320C2×C4—44no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—82no—
324C2×C4—82no—
325C2×C4—82no—
326C2×C4#38011yescharacteristic
327C2×C4#38511yescharacteristic
328C2×C4#38611yescharacteristic
329C2×C4#38811yescharacteristic
330C2×C4#39211yescharacteristic
331C2×C4#39311yescharacteristic
332C2×C4#39411yescharacteristic
333C2×C4#39411yescharacteristic
334C2×C4#39611yescharacteristic
335C2×C4#39611yescharacteristic
336C2×C4#39711yescharacteristic
337C2×C4#39911yescharacteristic
338C2×C4#44912yes—
339C2×C4#45112yes—
340C2×C4#46212yes—
341C2×C4#46312yes—
342C2×C4#46712yes—
343C2×C4#46812yes—
344C2×C4#47712yes—
345C2×C4#47912yes—
346C2×C4#48412yes—
347C2×C4#48512yes—
348C2×C4#49411yescharacteristic
349C2×C4#49511yescharacteristic
350C2×C4#49611yescharacteristic
351C2×C4#49711yescharacteristic
352C8—44no—
353C8—44no—
354C8—82no—
355C8—82no—
356C8—82no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—42no—
364C22—42no—
365C22#143911yescharacteristic
366C22#186312yes—
367C22#192812yes—
368C22#196911yescharacteristic
369C22#197311yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—82no—
378C4—82no—
379C4—162no—
380C4#186812yes—
381C4#201211yescharacteristic
382C4#201611yescharacteristic
383C4#203612yes—
384C4#206812yes—
385C4#209511yescharacteristic
386C4#209711yescharacteristic
387C2—21no—
388C2—22no—
389C2—22no—
390C2—21no—
391C2#1108811yescharacteristic
392C2#1111811yescharacteristic
393C2#1112411yescharacteristic
subgroupG/H
centerC2×C4#392
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
socleC22#1439
prime radicalC24C4×D4
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
#213022
C2×#15712
#175752
#174862
#108552
#79322
#78932