Finite Group Databasebeta

← #116279

Subgroups — #116279

Order 512.

591 conjugacy classes of subgroups.

The subgroup lattice has 389 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21973C211yesmaximal, characteristic
2#21311C211yesmaximal, characteristic
3#17718C211yesmaximal, characteristic
4#17562C211yesmaximal, characteristic
5#8092C211yesmaximal, characteristic
6#7988C211yesmaximal, characteristic
7#7941C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C22×C4⋊C8C2211yescharacteristic
13#2283C2211yescharacteristic
14C4×#117C2211yescharacteristic
15#1989—22no—
16#1988—21no—
17#1987—21no—
18#1939—22no—
19#1850—22no—
20#1843—21no—
21#1832—21no—
22#1735—22no—
23#1554—22no—
24#1548—21no—
25#1546—21no—
26#1542—21no—
27#1542—21no—
28#1515C414yescomplemented
29#1511—22no—
30#1503—22no—
31#1303—22no—
32#1290—22no—
33#1284—22no—
34C23×C8D412yes—
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#432C2×C412yes—
56#432D412yes—
57#431—21no—
58#431—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62#431—21no—
63#431—21no—
64#431—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—21no—
73C2×C4⋊C8—24no—
74C2×C4⋊C8D411yescharacteristic
75C2×C4⋊C8D411yescharacteristic
76#407—21no—
77#407—21no—
78C2×C22⋊C8—21no—
79C4×M16—21no—
80C4×M16—21no—
81C2×C4×C8—21no—
82#383C2×C412yes—
83#382—21no—
84#381D412yes—
85#380—21no—
86C4×C4⋊C4—21no—
87C4×C4⋊C4D412yes—
88C4×C4⋊C4D412yes—
89C4×C22⋊C4—21no—
90C4×C22⋊C4—21no—
91C4×C22⋊C4—21no—
92#376—21no—
93#376—21no—
94C43—21no—
95#340—24no—
96#340—24no—
97#336—24no—
98#333—22no—
99#333—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
108C2×M16—41no—
109C2×M16—41no—
110C22×C8—22no—
111C22×C8—22no—
112C22×C8—21no—
113C22×C8—21no—
114C22×C8—22no—
115C22×C8—44no—
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—24no—
145#117—22no—
146#117—22no—
147#117—42no—
148#117—41no—
149#117—41no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—41no—
158C2×C22⋊C4—22no—
159C2×C22⋊C4—41no—
160C2×C22⋊C4—41no—
161C2×C42—22no—
162C2×C42—22no—
163C2×C42—41no—
164C2×C42—41no—
165C2×C42—41no—
166C2×C42C22×C411yescharacteristic
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
177C2×C42#4111yescharacteristic
178C4⋊C8—22no—
179C4⋊C8—21no—
180C4⋊C8—21no—
181C4⋊C8—22no—
182C4⋊C8—21no—
183C4⋊C8—21no—
184C4⋊C8—41no—
185C4⋊C8—41no—
186C4⋊C8—41no—
187C4⋊C8—41no—
188C4⋊C8—41no—
189C4⋊C8—41no—
190C4⋊C8—84no—
191C22⋊C8—22no—
192C22⋊C8—22no—
193C22⋊C8—41no—
194C22⋊C8—41no—
195C22⋊C8—41no—
196C22⋊C8—41no—
197#97—22no—
198#97—22no—
199C4×C8—41no—
200C4×C8—41no—
201C4×C8—41no—
202C4×C8—41no—
203#95—22no—
204#95—22no—
205#95—22no—
206#95—22no—
207#95—41no—
208#95C22⋊C414yes—
209C24#12111yescharacteristic
210C2×Q8—22no—
211C2×Q8—22no—
212C2×Q8—41no—
213C2×Q8—41no—
214C2×Q8—82no—
215C2×Q8—82no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—24no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4C2×C22⋊C411yescharacteristic
225C22×C4C4×D411yescharacteristic
226C22×C4C4×D411yescharacteristic
227C22×C4#12011yescharacteristic
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#12311yescharacteristic
240C22×C4#12411yescharacteristic
241C22×C4#12611yescharacteristic
242M16—82no—
243M16—82no—
244C2×C8—44no—
245C2×C8—42no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—44no—
252C2×C8—42no—
253C2×C8—82no—
254C4⋊C4—24no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—44no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—42no—
267C4⋊C4—41no—
268C4⋊C4—42no—
269C22⋊C4—44no—
270C22⋊C4—44no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C42—44no—
274C42—42no—
275C42—42no—
276C42—42no—
277C42—42no—
278C42—82no—
279C42—82no—
280C42C2×C4⋊C411yescharacteristic
281C42#11711yescharacteristic
282C42C4×D411yescharacteristic
283C42C4×D411yescharacteristic
284C42#12011yescharacteristic
285C42#12111yescharacteristic
286C42#12111yescharacteristic
287C42C22⋊Q811yescharacteristic
288C42C22⋊Q811yescharacteristic
289C42C22⋊Q811yescharacteristic
290C42#12311yescharacteristic
291C42#12311yescharacteristic
292C42#12411yescharacteristic
293C42#12411yescharacteristic
294C42#12611yescharacteristic
295C42#12711yescharacteristic
296C23—22no—
297C23—22no—
298C23—41no—
299C23#38611yescharacteristic
300C23#39411yescharacteristic
301C23#39611yescharacteristic
302Q8—82no—
303Q8—82no—
304Q8—82no—
305Q8—82no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—44no—
326C2×C4—44no—
327C2×C4—44no—
328C2×C4—44no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4#38011yescharacteristic
336C2×C4#38511yescharacteristic
337C2×C4#38511yescharacteristic
338C2×C4#38811yescharacteristic
339C2×C4#38811yescharacteristic
340C2×C4#39011yescharacteristic
341C2×C4#39211yescharacteristic
342C2×C4#39311yescharacteristic
343C2×C4#39411yescharacteristic
344C2×C4#39611yescharacteristic
345C2×C4#39711yescharacteristic
346C2×C4#39911yescharacteristic
347C2×C4#45512yes—
348C2×C4#45612yes—
349C8—82no—
350C8—82no—
351C8—81no—
352C8—82no—
353C8—81no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—44no—
362C22#143911yescharacteristic
363C22#188212yes—
364C22#205312yes—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—84no—
375C4—84no—
376C4—82no—
377C4—82no—
378C4#200411yescharacteristic
379C4#200511yescharacteristic
380C4#202812yes—
381C4#208012yes—
382C2—22no—
383C2—22no—
384C2—41no—
385C2#1106411yescharacteristic
386C2#1108611yescharacteristic
387C2#1109211yescharacteristic
subgroupG/H
centerC2×C4#393
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
socleC22#1439
prime radicalC24#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
28. #1515C4semidirect

Maximal subgroups

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

subgroupindex
#219732
#213112
#177182
#175622
#80922
#79882
#79412