Finite Group Databasebeta

← #118541

Subgroups — #118541

Order 512.

568 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21889C211yesmaximal, characteristic
2C2×#1573C211yesmaximal, characteristic
3#17755C211yesmaximal, characteristic
4#17575C211yesmaximal, characteristic
5#8044C211yesmaximal, characteristic
6#7984C211yesmaximal, characteristic
7#7926C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C22×C4⋊C8C2211yescharacteristic
13#2285C2211yescharacteristic
14#2283C2211yescharacteristic
15#1988—21no—
16#1981—21no—
17#1892—22no—
18#1805—22no—
19#1573—22no—
20#1573—22no—
21C2×#335—21no—
22C2×#334—21no—
23#1556—21no—
24#1556—21no—
25#1552—22no—
26#1552—21no—
27#1552—21no—
28#1520—22no—
29#1518C414yescomplemented
30#1503—22no—
31#1296—22no—
32#1289—22no—
33#1282—22no—
34C23×C8—21no—
35#533—21no—
36#533—21no—
37#533—21no—
38#533—21no—
39#533—21no—
40#533—21no—
41#533C2×C412yes—
42#533Q812yes—
43C2×C4⋊Q8D411yescharacteristic
44C2×C4⋊Q8D411yescharacteristic
45C2×#125—21no—
46C2×C22⋊Q8—21no—
47C2×C22⋊Q8—21no—
48C2×C4×Q8—21no—
49C2×C4×Q8—21no—
50C2×#117—21no—
51C2×#117—21no—
52C22×C42C2311yescharacteristic
53#432—21no—
54#432—21no—
55#432—21no—
56#432—21no—
57#432—21no—
58#432—21no—
59#432—21no—
60#432—21no—
61#431—21no—
62#431—21no—
63#431C2×C412yes—
64#431D412yes—
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×C4⋊C8D411yescharacteristic
74C2×C4⋊C8D411yescharacteristic
75C2×#103—24no—
76C2×C22⋊C8—21no—
77C2×C22⋊C8—21no—
78C2×C22⋊C8D412yes—
79C2×#97—21no—
80C2×#97—21no—
81C2×C4×C8—21no—
82#384—21no—
83#383—21no—
84#382—21no—
85#382C2×C412yes—
86#381—21no—
87#380—21no—
88#380—21no—
89#380D412yes—
90C4×C4⋊C4—21no—
91C4×C4⋊C4—21no—
92C4×C4⋊C4—21no—
93C4×C22⋊C4—21no—
94#376—21no—
95#340—24no—
96#335—24no—
97#334—24no—
98#332—22no—
99#332—22no—
100#332—22no—
101#332—22no—
102#328—28no—
103C22×Q8—21no—
104C22×Q8—21no—
105C23×C4C2×D411yescharacteristic
106C23×C4C2×D411yescharacteristic
107C23×C4#4111yescharacteristic
108C22×C8—22no—
109C22×C8—22no—
110C22×C8—21no—
111C22×C8—21no—
112C22×C8—22no—
113C22×C8—41no—
114C22×C8—41no—
115C22×C8—82no—
116C4⋊Q8—21no—
117C4⋊Q8—21no—
118C4⋊Q8—21no—
119C4⋊Q8—21no—
120C4⋊Q8—21no—
121C4⋊Q8—21no—
122C4⋊Q8C4⋊C412yes—
123C4⋊Q8C4⋊C412yes—
124#125—22no—
125#125—22no—
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—82no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C22⋊C4—22no—
160C2×C22⋊C4—41no—
161C2×C22⋊C4—41no—
162C2×C42—41no—
163C2×C42—41no—
164C2×C42—41no—
165C2×C42C22×C411yescharacteristic
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—21no—
179C4⋊C8—21no—
180C4⋊C8—22no—
181C4⋊C8—21no—
182C4⋊C8—22no—
183C4⋊C8—21no—
184C4⋊C8—22no—
185C4⋊C8—22no—
186C4⋊C8—22no—
187C4⋊C8—41no—
188C4⋊C8—41no—
189#103—84no—
190C22⋊C8—22no—
191C22⋊C8—41no—
192C22⋊C8—41no—
193C22⋊C8—41no—
194C22⋊C8—41no—
195C22⋊C8C22⋊C414yes—
196#97—41no—
197#97—41no—
198#97—41no—
199#97—41no—
200C4×C8—22no—
201C4×C8—22no—
202#95—22no—
203#95—22no—
204#95—22no—
205#95—41no—
206#95—41no—
207#95—41no—
208C24#12111yescharacteristic
209C2×Q8—22no—
210C2×Q8—22no—
211C2×Q8—42no—
212C2×Q8—42no—
213C2×Q8—41no—
214C2×Q8—41no—
215C2×Q8—82no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—41no—
219C22×C4—42no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4C2×C22⋊C411yescharacteristic
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×C4C22⋊Q811yescharacteristic
235C22×C4C22⋊Q811yescharacteristic
236C22×C4C22⋊Q811yescharacteristic
237C22×C4#12311yescharacteristic
238C22×C4#12311yescharacteristic
239C22×C4#12411yescharacteristic
240C22×C4#12411yescharacteristic
241C22×C4#12611yescharacteristic
242C22×C4#12711yescharacteristic
243C2×C8—24no—
244C2×C8—44no—
245C2×C8—44no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—82no—
251C2×C8—82no—
252C2×C8—82no—
253C2×C8—81no—
254C2×C8—81no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—42no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—42no—
269C4⋊C4—82no—
270C4⋊C4—82no—
271C4⋊C4—81no—
272C4⋊C4—81no—
273C22⋊C4—42no—
274C22⋊C4—42no—
275C22⋊C4—42no—
276C22⋊C4—42no—
277C22⋊C4—82no—
278C42—42no—
279C42—42no—
280C42—82no—
281C42—82no—
282C42C2×C4⋊C411yescharacteristic
283C42#11711yescharacteristic
284C42C4×D411yescharacteristic
285C42C4×D411yescharacteristic
286C42#12011yescharacteristic
287C42#12011yescharacteristic
288C42#12111yescharacteristic
289C42#12111yescharacteristic
290C42C22⋊Q811yescharacteristic
291C42C22⋊Q811yescharacteristic
292C42C22⋊Q811yescharacteristic
293C42#12311yescharacteristic
294C42#12311yescharacteristic
295C42#12311yescharacteristic
296C42#12411yescharacteristic
297C42#12611yescharacteristic
298C23—41no—
299C23—41no—
300C23#39011yescharacteristic
301C23#39411yescharacteristic
302C23#39611yescharacteristic
303C23#47112yes—
304C23#47312yes—
305Q8—44no—
306Q8—82no—
307Q8—82no—
308Q8—81no—
309Q8—81no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—82no—
340C2×C4—82no—
341C2×C4—82no—
342C2×C4—82no—
343C2×C4#38011yescharacteristic
344C2×C4#38511yescharacteristic
345C2×C4#38511yescharacteristic
346C2×C4#38611yescharacteristic
347C2×C4#38811yescharacteristic
348C2×C4#38811yescharacteristic
349C2×C4#39211yescharacteristic
350C2×C4#39311yescharacteristic
351C2×C4#39411yescharacteristic
352C2×C4#39611yescharacteristic
353C2×C4#39711yescharacteristic
354C2×C4#39911yescharacteristic
355C8—44no—
356C8—82no—
357C8—82no—
358C8—81no—
359C8—81no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—42no—
367C22—42no—
368C22#143911yescharacteristic
369C22#197711yescharacteristic
370C22#197911yescharacteristic
371C22#205212yes—
372C22#206412yes—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—82no—
384C4—82no—
385C4—162no—
386C4—162no—
387C4#200811yescharacteristic
388C4#200911yescharacteristic
389C4#205312yes—
390C2—21no—
391C2—22no—
392C2—22no—
393C2—21no—
394C2#1109211yescharacteristic
395C2#1111711yescharacteristic
396C2#1112811yescharacteristic
subgroupG/H
center, socleC22#1439
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
29. #1518C4semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#218892
C2×#15732
#177552
#175752
#80442
#79842
#79262