Finite Group Databasebeta

← #118589

Subgroups — #118589

Order 512.

626 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21981C211yesmaximal, characteristic
2#21838C211yesmaximal, characteristic
3C2×#1992C211yesmaximal, characteristic
4C2×#1470C211yesmaximal, characteristic
5C2×#1302C211yesmaximal, characteristic
6#8040C211yesmaximal, characteristic
7#8034C211yesmaximal, characteristic
8C22×#125C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C22×#97C2211yescharacteristic
13#2285C2211yescharacteristic
14C2×#384C2211yescharacteristic
15#1992—22no—
16#1992—22no—
17#1992—21no—
18#1992—21no—
19#1989—22no—
20#1948—22no—
21#1853—22no—
22#1844—21no—
23#1834—21no—
24#1824—21no—
25#1823—21no—
26C2×#340—21no—
27C2×#340—21no—
28#1470—22no—
29#1470C414yescomplemented
30C2×#324—22no—
31#1302—22no—
32#1296—22no—
33#1295—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⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4D411yescharacteristic
54C22×C4⋊C4D411yescharacteristic
55C22×C42C2311yescharacteristic
56#432—21no—
57#432—21no—
58#432—21no—
59#432—21no—
60#432—21no—
61#432—21no—
62#432—21no—
63#432C2×C412yes—
64#431—21no—
65#431—21no—
66#431C2×C412yes—
67#431D412yes—
68C2×#106—24no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—21no—
71C2×C4⋊C8D412yes—
72C2×C22⋊C8—21no—
73C2×C22⋊C8—21no—
74C2×C22⋊C8D412yes—
75C2×#97—21no—
76C2×#97—21no—
77C2×#97—21no—
78C2×#97—21no—
79C2×#97—21no—
80C2×#97—21no—
81C2×#97—21no—
82C2×#97D412yes—
83C2×C4×C8—21no—
84#384—21no—
85#384—21no—
86#384—21no—
87#384D411yescharacteristic
88#384D411yescharacteristic
89#384D412yes—
90#382—21no—
91#380—21no—
92#380—21no—
93C4×C4⋊C4—21no—
94C4×C4⋊C4—21no—
95#340—22no—
96#340—22no—
97#340—22no—
98#340—22no—
99#340—24no—
100#340—24no—
101#340—24no—
102#324—28no—
103C23×C4—21no—
104C23×C4—21no—
105C23×C4—41no—
106C23×C4C2×D411yescharacteristic
107C23×C4C2×D411yescharacteristic
108C23×C4#4111yescharacteristic
109C22×C8—24no—
110C22×C8—22no—
111C22×C8—22no—
112C22×C8—22no—
113C22×C8—42no—
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—82no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
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⋊C4—41no—
165C2×C4⋊C4—44no—
166C2×C4⋊C4—41no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—41no—
169C2×C4⋊C4—82no—
170C2×C4⋊C4—82no—
171C2×C4⋊C4C4⋊C412yes—
172C2×C4⋊C4C4⋊C412yes—
173C2×C22⋊C4—41no—
174C2×C42—41no—
175C2×C42C22×C411yescharacteristic
176C2×C42C2×D411yescharacteristic
177C2×C42C2×D411yescharacteristic
178C2×C42C2×D411yescharacteristic
179C2×C42C2×D411yescharacteristic
180C2×C42C2×D411yescharacteristic
181C2×C42C2×Q811yescharacteristic
182C2×C42#4111yescharacteristic
183C2×C42#4111yescharacteristic
184C2×C42#4111yescharacteristic
185C2×C42#4111yescharacteristic
186C2×C42#4111yescharacteristic
187#106—84no—
188C4⋊C8—22no—
189C4⋊C8—22no—
190C4⋊C8—22no—
191C4⋊C8—22no—
192C4⋊C8—22no—
193C4⋊C8—41no—
194C22⋊C8—22no—
195C22⋊C8—22no—
196C22⋊C8—41no—
197C22⋊C8—41no—
198C22⋊C8—41no—
199C22⋊C8C22⋊C414yes—
200#97—22no—
201#97—22no—
202#97—22no—
203#97—41no—
204#97—41no—
205#97—41no—
206#97—41no—
207#97—41no—
208C4×C8—22no—
209C4×C8—22no—
210#95—41no—
211#95—41no—
212C24#12111yescharacteristic
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—41no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—42no—
230C22×C4—81no—
231C22×C4—81no—
232C22×C4—82no—
233C22×C4—82no—
234C22×C4—82no—
235C22×C4C2×C22⋊C411yescharacteristic
236C22×C4C2×C4⋊C411yescharacteristic
237C22×C4#11711yescharacteristic
238C22×C4#12011yescharacteristic
239C22×C4#12011yescharacteristic
240C22×C4#12011yescharacteristic
241C22×C4#12111yescharacteristic
242C22×C4#12111yescharacteristic
243C22×C4#12111yescharacteristic
244C22×C4C22⋊Q811yescharacteristic
245C22×C4C22⋊Q811yescharacteristic
246C22×C4#12311yescharacteristic
247C22×C4#12311yescharacteristic
248C22×C4#12311yescharacteristic
249C22×C4#12411yescharacteristic
250C22×C4#12611yescharacteristic
251C22×C4#12611yescharacteristic
252C22×C4#12711yescharacteristic
253C2×C8—24no—
254C2×C8—24no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—44no—
259C2×C8—44no—
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—42no—
263C2×C8—42no—
264C2×C8—42no—
265C2×C8—81no—
266C2×C8—81no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—42no—
272C4⋊C4—44no—
273C4⋊C4—42no—
274C4⋊C4—44no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—42no—
285C4⋊C4—42no—
286C4⋊C4—42no—
287C4⋊C4—42no—
288C4⋊C4—42no—
289C4⋊C4—82no—
290C4⋊C4—81no—
291C4⋊C4—81no—
292C4⋊C4—82no—
293C4⋊C4—82no—
294C4⋊C4—82no—
295C22⋊C4—82no—
296C42—82no—
297C42C4×D411yescharacteristic
298C42C4×D411yescharacteristic
299C42C4×D411yescharacteristic
300C42C4×D411yescharacteristic
301C42#12111yescharacteristic
302C42#12111yescharacteristic
303C42#12111yescharacteristic
304C42#12111yescharacteristic
305C42C22⋊Q811yescharacteristic
306C42C22⋊Q811yescharacteristic
307C42C22⋊Q811yescharacteristic
308C42C22⋊Q811yescharacteristic
309C42#12311yescharacteristic
310C42#12311yescharacteristic
311C42#12411yescharacteristic
312C42#12411yescharacteristic
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23#38011yescharacteristic
318C23#39211yescharacteristic
319C23#39711yescharacteristic
320C23#47112yes—
321C23#47112yes—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—44no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—82no—
348C2×C4—82no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—82no—
354C2×C4—82no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—82no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—82no—
363C2×C4—164no—
364C2×C4#38511yescharacteristic
365C2×C4#38511yescharacteristic
366C2×C4#38611yescharacteristic
367C2×C4#38811yescharacteristic
368C2×C4#38811yescharacteristic
369C2×C4#39011yescharacteristic
370C2×C4#39311yescharacteristic
371C2×C4#39411yescharacteristic
372C2×C4#39411yescharacteristic
373C2×C4#39611yescharacteristic
374C2×C4#39611yescharacteristic
375C2×C4#39911yescharacteristic
376C2×C4#45412yes—
377C2×C4#45612yes—
378C8—44no—
379C8—44no—
380C8—82no—
381C8—82no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—22no—
387C22—22no—
388C22—22no—
389C22—22no—
390C22#143911yescharacteristic
391C22#181512yes—
392C22#200311yescharacteristic
393C22#200511yescharacteristic
394C22#200811yescharacteristic
395C22#200911yescharacteristic
396C22#201911yescharacteristic
397C22#201911yescharacteristic
398C22#207912yes—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—82no—
410C4—82no—
411C4—162no—
412C4—161no—
413C4—161no—
414C4#185712yes—
415C4#203812yes—
416C2—22no—
417C2—22no—
418C2#1013111yescharacteristic
419C2#1013411yescharacteristic
420C2#1013811yescharacteristic
421C2#1014311yescharacteristic
422C2#1109311yescharacteristic
423C2#1110611yescharacteristic
424C2#1113611yescharacteristic
subgroupG/H
center, socleC23#392
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
#219812
#218382
C2×#19922
C2×#14702
C2×#13022
#80402
#80342