Finite Group Databasebeta

← #118477

Subgroups — #118477

Order 512.

618 conjugacy classes of subgroups.

The subgroup lattice has 427 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21838C211yesmaximal, characteristic
2C2×#1989C211yesmaximal, characteristic
3C2×#1573C211yesmaximal, characteristic
4C2×#1470C211yesmaximal, characteristic
5#8044C211yesmaximal, characteristic
6#8014C211yesmaximal, characteristic
7C2×#1285C211yesmaximal, characteristic
8C22×#125C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C22×C4⋊C8C2211yescharacteristic
13#2285C2211yescharacteristic
14C2×C4×C4⋊C4C2211yescharacteristic
15#1992—22no—
16#1989—22no—
17#1989—21no—
18#1989—21no—
19#1989—22no—
20#1824—21no—
21#1823—21no—
22C2×#340—21no—
23C2×#340—21no—
24#1573—22no—
25#1573—22no—
26C2×#335—21no—
27C2×#334—21no—
28#1470—22no—
29#1470C414yescomplemented
30C2×#324—22no—
31#1296—22no—
32#1294—22no—
33#1285—22no—
34C23×C8—21no—
35C2×#125—21no—
36C2×#125—21no—
37C2×#125—21no—
38C2×#125—21no—
39C2×#125—21no—
40C2×#125—21no—
41C2×#125—21no—
42C2×#125—21no—
43C2×#125—21no—
44C2×#125—21no—
45C2×#125C2×C412yes—
46C2×#125Q812yes—
47C2×#117—21no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4D411yescharacteristic
52C22×C4⋊C4D411yescharacteristic
53C22×C42—21no—
54C22×C42C2311yescharacteristic
55#432—21no—
56#432—21no—
57#432—21no—
58#432—21no—
59#432—21no—
60#432—21no—
61#432—21no—
62#432C2×C412yes—
63#431—21no—
64#431—21no—
65#431C2×C412yes—
66#431D412yes—
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—21no—
74C2×C4⋊C8D411yescharacteristic
75C2×C4⋊C8D411yescharacteristic
76C2×C4⋊C8D412yes—
77C2×C22⋊C8—21no—
78C2×C22⋊C8—21no—
79C2×C22⋊C8D412yes—
80C2×#97—21no—
81C2×#97—21no—
82C2×C4×C8—21no—
83#384D412yes—
84#382—21no—
85#380—21no—
86#380—21no—
87C4×C4⋊C4—21no—
88C4×C4⋊C4—21no—
89C4×C4⋊C4—21no—
90C4×C4⋊C4—21no—
91C4×C4⋊C4—21no—
92C4×C4⋊C4D412yes—
93C2×#95—21no—
94#340—22no—
95#340—22no—
96#340—22no—
97#340—22no—
98#340—24no—
99#340—24no—
100#335—24no—
101#334—24no—
102#324—28no—
103C23×C4—21no—
104C23×C4—21no—
105C23×C4—41no—
106C23×C4C2×D411yescharacteristic
107C23×C4C2×D411yescharacteristic
108C23×C4#4111yescharacteristic
109C22×C8—22no—
110C22×C8—22no—
111C22×C8—21no—
112C22×C8—21no—
113C22×C8—44no—
114C22×C8—41no—
115C22×C8—41no—
116C22×C8—41no—
117#125—22no—
118#125—22no—
119#125—22no—
120#125—22no—
121#125—22no—
122#125—22no—
123#125—22no—
124#125—22no—
125#125—41no—
126#125—41no—
127#125—41no—
128#125—41no—
129#125—41no—
130#125—41no—
131#125—41no—
132#125—41no—
133#117—81no—
134#117—81no—
135C2×C4⋊C4—24no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—42no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4—41no—
160C2×C4⋊C4—41no—
161C2×C4⋊C4—41no—
162C2×C4⋊C4—41no—
163C2×C4⋊C4—41no—
164C2×C4⋊C4C4⋊C412yes—
165C2×C4⋊C4C4⋊C412yes—
166C2×C22⋊C4—41no—
167C2×C42—22no—
168C2×C42—41no—
169C2×C42—41no—
170C2×C42—81no—
171C2×C42—81no—
172C2×C42C22×C411yescharacteristic
173C2×C42C2×D411yescharacteristic
174C2×C42C2×D411yescharacteristic
175C2×C42C2×D411yescharacteristic
176C2×C42C2×D411yescharacteristic
177C2×C42C2×D411yescharacteristic
178C2×C42C2×Q811yescharacteristic
179C2×C42#4111yescharacteristic
180C2×C42#4111yescharacteristic
181C2×C42#4111yescharacteristic
182C2×C42#4111yescharacteristic
183C2×C42#4111yescharacteristic
184C4⋊C8—22no—
185C4⋊C8—22no—
186C4⋊C8—21no—
187C4⋊C8—22no—
188C4⋊C8—21no—
189C4⋊C8—22no—
190C4⋊C8—21no—
191C4⋊C8—21no—
192C4⋊C8—22no—
193C4⋊C8—41no—
194C4⋊C8—41no—
195C4⋊C8—41no—
196C22⋊C8—22no—
197C22⋊C8—22no—
198C22⋊C8—41no—
199C22⋊C8—41no—
200C22⋊C8—41no—
201C22⋊C8C22⋊C414yes—
202#97—22no—
203#97—41no—
204#97—41no—
205#97—41no—
206C4×C8—22no—
207C4×C8—22no—
208#95—22no—
209#95—41no—
210#95—41no—
211#95—41no—
212C24#12111yescharacteristic
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—42no—
222C22×C4—44no—
223C22×C4—42no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—42no—
233C22×C4—82no—
234C22×C4—81no—
235C22×C4—81no—
236C22×C4—82no—
237C22×C4C2×C22⋊C411yescharacteristic
238C22×C4C2×C4⋊C411yescharacteristic
239C22×C4#11711yescharacteristic
240C22×C4#12011yescharacteristic
241C22×C4#12011yescharacteristic
242C22×C4#12111yescharacteristic
243C22×C4#12111yescharacteristic
244C22×C4#12111yescharacteristic
245C22×C4#12111yescharacteristic
246C22×C4#12111yescharacteristic
247C22×C4C22⋊Q811yescharacteristic
248C22×C4C22⋊Q811yescharacteristic
249C22×C4#12311yescharacteristic
250C22×C4#12311yescharacteristic
251C22×C4#12311yescharacteristic
252C22×C4#12311yescharacteristic
253C22×C4#12411yescharacteristic
254C22×C4#12411yescharacteristic
255C2×C8—24no—
256C2×C8—44no—
257C2×C8—44no—
258C2×C8—42no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—42no—
262C2×C8—42no—
263C2×C8—42no—
264C2×C8—82no—
265C2×C8—82no—
266C2×C8—82no—
267C4⋊C4—24no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—44no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—42no—
286C4⋊C4—42no—
287C4⋊C4—42no—
288C4⋊C4—82no—
289C4⋊C4—82no—
290C22⋊C4—81no—
291C22⋊C4—81no—
292C42—82no—
293C42—82no—
294C42—82no—
295C42C4×D411yescharacteristic
296C42C4×D411yescharacteristic
297C42C4×D411yescharacteristic
298C42C4×D411yescharacteristic
299C42#12011yescharacteristic
300C42#12111yescharacteristic
301C42#12111yescharacteristic
302C42C22⋊Q811yescharacteristic
303C42C22⋊Q811yescharacteristic
304C42C22⋊Q811yescharacteristic
305C42C22⋊Q811yescharacteristic
306C42#12311yescharacteristic
307C42#12411yescharacteristic
308C42#12611yescharacteristic
309C42#12611yescharacteristic
310C42#12711yescharacteristic
311C23—22no—
312C23—22no—
313C23#38011yescharacteristic
314C23#39411yescharacteristic
315C23#39411yescharacteristic
316C23#47111yescharacteristic
317C23#47111yescharacteristic
318C23#47211yescharacteristic
319C23#47311yescharacteristic
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—84no—
351C2×C4—84no—
352C2×C4—82no—
353C2×C4—82no—
354C2×C4—82no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—82no—
360C2×C4—82no—
361C2×C4—82no—
362C2×C4—82no—
363C2×C4—82no—
364C2×C4#38511yescharacteristic
365C2×C4#38511yescharacteristic
366C2×C4#38611yescharacteristic
367C2×C4#38811yescharacteristic
368C2×C4#38811yescharacteristic
369C2×C4#39011yescharacteristic
370C2×C4#39211yescharacteristic
371C2×C4#39311yescharacteristic
372C2×C4#39611yescharacteristic
373C2×C4#39611yescharacteristic
374C2×C4#39711yescharacteristic
375C2×C4#39911yescharacteristic
376C2×C4#45412yes—
377C2×C4#45612yes—
378C8—44no—
379C8—82no—
380C8—81no—
381C8—82no—
382C8—81no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22#143911yescharacteristic
392C22#181511yescharacteristic
393C22#181611yescharacteristic
394C22#203812yes—
395C22#205111yescharacteristic
396C22#205111yescharacteristic
397C22#205211yescharacteristic
398C22#205211yescharacteristic
399C22#205312yes—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—21no—
410C4—84no—
411C4—82no—
412C4—82no—
413C4—162no—
414C4#185712yes—
415C4#200311yescharacteristic
416C4#200511yescharacteristic
417C2—21no—
418C2—21no—
419C2—21no—
420C2—21no—
421C2#1050912yes—
422C2#1051112yes—
423C2#1109211yescharacteristic
424C2#1110511yescharacteristic
425C2#1113611yescharacteristic
subgroupG/H
center, socleC23#394
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
29. #1470C4semidirect

Maximal subgroups

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

subgroupindex
#218382
C2×#19892
C2×#15732
C2×#14702
#80442
#80142
C2×#12852