Finite Group Databasebeta

← #116576

Subgroups — #116576

Order 512.

629 conjugacy classes of subgroups.

The subgroup lattice has 399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1986C211yesmaximal, characteristic
2#20769C211yesmaximal, characteristic
3#17486C211yesmaximal, characteristic
4#17486C211yesmaximal, characteristic
5C2×#1303C211yesmaximal, characteristic
6#7932C211yesmaximal, characteristic
7#7901C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C2×C4×M16C2211yescharacteristic
14C2×C4×C4⋊C4C2211yescharacteristic
15#1986—22no—
16#1986C414yes—
17#1838—22no—
18#1837—22no—
19#1738—22no—
20C2×#339—22no—
21#1493—22no—
22#1493—22no—
23#1487—22no—
24#1487—22no—
25#1481—22no—
26#1481—22no—
27#1303—22no—
28#1283—22no—
29#1279—22no—
30C22×M16—21no—
31C22×M16—21no—
32C22×M16D412yes—
33#533—21no—
34#533—21no—
35#533—21no—
36#533—21no—
37#533—21no—
38#533—21no—
39#533C2×C412yes—
40#533D412yes—
41C2×C4⋊Q8Q811yescharacteristic
42C2×C4⋊Q8Q811yescharacteristic
43C2×#125—21no—
44C2×C22⋊Q8—21no—
45C2×C22⋊Q8—21no—
46C2×C4×Q8—21no—
47C2×C4×Q8—21no—
48C2×#117—21no—
49C22×C4⋊C4—21no—
50C22×C42—21no—
51C22×C42C2311yescharacteristic
52#431—21no—
53#431—21no—
54#431—21no—
55#431—21no—
56#431—21no—
57#431—21no—
58#431—21no—
59#431D412yes—
60#423—21no—
61#423—21no—
62#423—21no—
63#423—21no—
64#423—21no—
65#423—21no—
66#423D412yes—
67#423D412yes—
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×C22⋊C8—21no—
75C2×C22⋊C8—21no—
76C4×M16—21no—
77C4×M16—21no—
78C4×M16C2×C412yes—
79C4×M16D412yes—
80C2×#97—21no—
81C2×C4×C8—21no—
82C2×C4×C8—21no—
83C2×C4×C8D412yes—
84C4×C4⋊C4—21no—
85C4×C4⋊C4—21no—
86C4×C4⋊C4—21no—
87C4×C4⋊C4C2×C412yes—
88C2×#95—21no—
89#341—28no—
90#339—28no—
91Q8⋊C8—28no—
92Q8⋊C8—28no—
93C22×Q8—21no—
94C22×Q8—21no—
95C23×C4—41no—
96C23×C4C2×D411yescharacteristic
97C23×C4#4111yescharacteristic
98C23×C4#4111yescharacteristic
99C2×M16—22no—
100C2×M16—22no—
101C2×M16—22no—
102C2×M16—22no—
103C2×M16—22no—
104C2×M16—22no—
105C2×M16—22no—
106C2×M16—41no—
107C2×M16—41no—
108C2×M16—42no—
109C2×M16—42no—
110C2×M16—42no—
111C2×M16—42no—
112C2×M16C22⋊C414yes—
113C22×C8—22no—
114C22×C8—22no—
115C22×C8—41no—
116C22×C8—41no—
117C22×C8—41no—
118C4⋊Q8—21no—
119C4⋊Q8—21no—
120C4⋊Q8—21no—
121C4⋊Q8—21no—
122C4⋊Q8—21no—
123C4⋊Q8—21no—
124C4⋊Q8C4⋊C412yes—
125C4⋊Q8C4⋊C412yes—
126#125—22no—
127#125—22no—
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—22no—
147#117—22no—
148#117—41no—
149#117—41no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—44no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C22⋊C4—41no—
160C2×C42—22no—
161C2×C42—41no—
162C2×C42—42no—
163C2×C42—42no—
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×Q811yescharacteristic
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—41no—
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⋊C8—41no—
193#97—22no—
194#97—22no—
195C4×C8—22no—
196C4×C8—22no—
197C4×C8—22no—
198C4×C8—22no—
199C4×C8—22no—
200C4×C8—41no—
201#95—22no—
202#95—41no—
203C24#12411yescharacteristic
204C2×Q8—22no—
205C2×Q8—22no—
206C2×Q8—41no—
207C2×Q8—41no—
208C2×Q8—82no—
209C2×Q8—82no—
210C22×C4—42no—
211C22×C4—44no—
212C22×C4—42no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—81no—
216C22×C4—82no—
217C22×C4—82no—
218C22×C4C2×C22⋊C411yescharacteristic
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×C4C22⋊Q811yescharacteristic
228C22×C4#12311yescharacteristic
229C22×C4#12311yescharacteristic
230C22×C4#12311yescharacteristic
231C22×C4#12411yescharacteristic
232C22×C4#12411yescharacteristic
233C22×C4#12611yescharacteristic
234C22×C4#12611yescharacteristic
235C22×C4#12711yescharacteristic
236C22×C4#13512yes—
237C22×C4#13512yes—
238C22×C4#13712yes—
239C22×C4#13712yes—
240M16—24no—
241M16—24no—
242M16—42no—
243M16—42no—
244M16—44no—
245M16—44no—
246M16—82no—
247M16—81no—
248M16—81no—
249C2×C8—24no—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—42no—
253C2×C8—42no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—82no—
257C2×C8—82no—
258C2×C8—81no—
259C2×C8—81no—
260C2×C8—82no—
261C4⋊C4—24no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—42no—
267C4⋊C4—44no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C22⋊C4—42no—
277C22⋊C4—42no—
278C42—42no—
279C42—42no—
280C42—44no—
281C42—81no—
282C42—81no—
283C42C2×C4⋊C411yescharacteristic
284C42#11711yescharacteristic
285C42C4×D411yescharacteristic
286C42C4×D411yescharacteristic
287C42#12011yescharacteristic
288C42#12011yescharacteristic
289C42#12111yescharacteristic
290C42#12111yescharacteristic
291C42#12111yescharacteristic
292C42#12111yescharacteristic
293C42#12111yescharacteristic
294C42C22⋊Q811yescharacteristic
295C42C22⋊Q811yescharacteristic
296C42C22⋊Q811yescharacteristic
297C42#12311yescharacteristic
298C42#12311yescharacteristic
299C23—41no—
300C23—41no—
301C23#39011yescharacteristic
302C23#39311yescharacteristic
303C23#39711yescharacteristic
304C23#48812yes—
305C23#49112yes—
306Q8—44no—
307Q8—44no—
308Q8—82no—
309Q8—82no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
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—44no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—88no—
329C2×C4—82no—
330C2×C4#38011yescharacteristic
331C2×C4#38511yescharacteristic
332C2×C4#38511yescharacteristic
333C2×C4#38611yescharacteristic
334C2×C4#38811yescharacteristic
335C2×C4#38811yescharacteristic
336C2×C4#39211yescharacteristic
337C2×C4#39411yescharacteristic
338C2×C4#39411yescharacteristic
339C2×C4#39611yescharacteristic
340C2×C4#39611yescharacteristic
341C2×C4#39911yescharacteristic
342C2×C4#41612yes—
343C2×C4#41912yes—
344C2×C4#45212yes—
345C2×C4#45212yes—
346C2×C4#46412yes—
347C2×C4#46412yes—
348C2×C4#47912yes—
349C2×C4#47912yes—
350C2×C4#48512yes—
351C2×C4#48512yes—
352C2×C4#49511yescharacteristic
353C2×C4#49511yescharacteristic
354C2×C4#49711yescharacteristic
355C2×C4#49711yescharacteristic
356C8—44no—
357C8—82no—
358C8—82no—
359C8—82no—
360C8—82no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—42no—
368C22—42no—
369C22#143911yescharacteristic
370C22#195811yescharacteristic
371C22#196011yescharacteristic
372C22#202612yes—
373C22#207412yes—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—84no—
382C4—82no—
383C4—82no—
384C4#180512yes—
385C4#186112yes—
386C4#187312yes—
387C4#201511yescharacteristic
388C4#201511yescharacteristic
389C4#209711yescharacteristic
390C4#209711yescharacteristic
391C2—21no—
392C2—22no—
393C2—21no—
394C2—22no—
395C2#1105211yescharacteristic
396C2#1111411yescharacteristic
397C2#1111811yescharacteristic
subgroupG/H
centerC2×C4#392
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
socleC22#1439
prime radicalC24#124
LCSG ▷ C2×C42 ▷ 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
C2×#19862
#207692
#174862
C2×#13032
#79322
#79012