Finite Group Databasebeta

← #120079

Subgroups — #120079

Order 512.

592 conjugacy classes of subgroups.

The subgroup lattice has 403 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21944C211yesmaximal, characteristic
2#21935C211yesmaximal, characteristic
3C2×#1306C211yesmaximal, characteristic
4#8024C211yesmaximal, characteristic
5#8015C211yesmaximal, characteristic
6C2×#1293C211yesmaximal, characteristic
7#7915C211yesmaximal, characteristic
8C2×#407C2211yescharacteristic
9C2×#407C2211yescharacteristic
10C2×#407C2211yescharacteristic
11C22×C22⋊C8C2211yescharacteristic
12#2280C2211yescharacteristic
13C2×#381C2211yescharacteristic
14C2×#380C2211yescharacteristic
15#1854—22no—
16#1853C412yescomplemented
17#1852C412yescomplemented
18#1851—22no—
19#1851—22no—
20#1809—22no—
21#1798—22no—
22#1306—22no—
23#1294—22no—
24#1294—22no—
25#1293—22no—
26#1280—22no—
27C24×C4C2311yescharacteristic
28C22×M16—21no—
29C22×M16—21no—
30C22×M16—21no—
31C23×C8—21no—
32C2×#117D412yes—
33C22×C4⋊C4C2×C412yes—
34C22×C22⋊C4—21no—
35C22×C22⋊C4—21no—
36C2×#107—22no—
37C2×#106—22no—
38C2×C4⋊C8—24no—
39#407—21no—
40#407—21no—
41#407—21no—
42#407—21no—
43#407—21no—
44#407—21no—
45#407—21no—
46#407—21no—
47#407—21no—
48#407—21no—
49#407D412yes—
50#407Q812yes—
51C2×C22⋊C8—21no—
52C2×C22⋊C8—21no—
53C2×C22⋊C8—21no—
54C2×C22⋊C8—21no—
55C2×C22⋊C8—21no—
56C2×C22⋊C8—21no—
57C2×C22⋊C8—21no—
58C2×C22⋊C8—21no—
59C2×C22⋊C8C2×C412yes—
60C2×C22⋊C8D412yes—
61C2×C22⋊C8D412yes—
62C2×C22⋊C8Q812yes—
63#381—21no—
64#381—21no—
65#381—21no—
66#381—21no—
67#381Q812yes—
68#380—21no—
69#380—21no—
70#380—21no—
71#380—21no—
72#380C2×C411yescharacteristic
73#380C2×C411yescharacteristic
74#380D412yes—
75#379—21no—
76C4×C22⋊C4—21no—
77C4×C22⋊C4—21no—
78C2×#95—21no—
79C2×#95—21no—
80C2×#95—21no—
81#340—22no—
82#340—22no—
83#336—24no—
84C25#4111yescharacteristic
85C23×C4—22no—
86C23×C4—41no—
87C23×C4—82no—
88C23×C4C22×C411yescharacteristic
89C23×C4C2×D411yescharacteristic
90C23×C4C2×D411yescharacteristic
91C23×C4C2×D411yescharacteristic
92C23×C4C2×D411yescharacteristic
93C23×C4C2×D411yescharacteristic
94C23×C4C2×Q811yescharacteristic
95C23×C4C2×Q811yescharacteristic
96C23×C4C2×Q811yescharacteristic
97C23×C4#4111yescharacteristic
98C23×C4#4111yescharacteristic
99C23×C4#4111yescharacteristic
100C23×C4#4111yescharacteristic
101C23×C4#4111yescharacteristic
102C2×M16—22no—
103C2×M16—22no—
104C2×M16—41no—
105C2×M16—41no—
106C2×M16—41no—
107C2×M16—41no—
108C2×M16—82no—
109C2×M16—82no—
110C2×M16—82no—
111C22×C8—22no—
112C22×C8—22no—
113C22×C8—22no—
114C22×C8—22no—
115C22×C8—41no—
116C22×C8—41no—
117C22×C8—82no—
118#117—82no—
119C2×C4⋊C4—22no—
120C2×C4⋊C4—22no—
121C2×C4⋊C4—82no—
122C2×C4⋊C4C22⋊C412yes—
123C2×C4⋊C4C22⋊C412yes—
124C2×C22⋊C4—21no—
125C2×C22⋊C4—21no—
126C2×C22⋊C4—22no—
127C2×C22⋊C4—22no—
128C2×C22⋊C4—22no—
129C2×C22⋊C4—41no—
130C2×C22⋊C4—41no—
131C2×C22⋊C4—41no—
132C2×C22⋊C4—82no—
133C2×C22⋊C4—82no—
134C2×C42—22no—
135#107—82no—
136#106—82no—
137C4⋊C8—84no—
138C22⋊C8—22no—
139C22⋊C8—22no—
140C22⋊C8—22no—
141C22⋊C8—22no—
142C22⋊C8—22no—
143C22⋊C8—22no—
144C22⋊C8—22no—
145C22⋊C8—22no—
146C22⋊C8—22no—
147C22⋊C8—41no—
148C22⋊C8—41no—
149C22⋊C8—41no—
150C22⋊C8—41no—
151C22⋊C8—41no—
152C22⋊C8—41no—
153C22⋊C8C4⋊C414yes—
154#95—21no—
155#95—21no—
156#95—22no—
157#95—22no—
158#95—22no—
159#95—41no—
160#95—41no—
161#95—41no—
162#95—41no—
163C24—41no—
164C24—42no—
165C24—42no—
166C24—41no—
167C24C4×D411yescharacteristic
168C24#12111yescharacteristic
169C24C22⋊Q811yescharacteristic
170C24#12311yescharacteristic
171C24#12511yescharacteristic
172C24#12511yescharacteristic
173C24#12611yescharacteristic
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—42no—
177C22×C4—42no—
178C22×C4—42no—
179C22×C4—42no—
180C22×C4—42no—
181C22×C4—42no—
182C22×C4—42no—
183C22×C4—42no—
184C22×C4—44no—
185C22×C4—81no—
186C22×C4—81no—
187C22×C4—81no—
188C22×C4—81no—
189C22×C4—81no—
190C22×C4—81no—
191C22×C4—81no—
192C22×C4—81no—
193C22×C4—82no—
194C22×C4—82no—
195C22×C4—81no—
196C22×C4—81no—
197C22×C4—82no—
198C22×C4—82no—
199C22×C4C2×C22⋊C411yescharacteristic
200C22×C4C2×C4⋊C411yescharacteristic
201C22×C4#11711yescharacteristic
202C22×C4C4×D411yescharacteristic
203C22×C4C4×Q811yescharacteristic
204C22×C4C4×Q811yescharacteristic
205C22×C4#12011yescharacteristic
206C22×C4#12111yescharacteristic
207C22×C4#12111yescharacteristic
208C22×C4#12111yescharacteristic
209C22×C4#12111yescharacteristic
210C22×C4#12111yescharacteristic
211C22×C4C22⋊Q811yescharacteristic
212C22×C4C22⋊Q811yescharacteristic
213C22×C4C22⋊Q811yescharacteristic
214C22×C4C22⋊Q811yescharacteristic
215C22×C4C22⋊Q811yescharacteristic
216C22×C4C22⋊Q811yescharacteristic
217C22×C4C22⋊Q811yescharacteristic
218C22×C4#12311yescharacteristic
219C22×C4#12311yescharacteristic
220C22×C4#12411yescharacteristic
221C22×C4#12511yescharacteristic
222C22×C4#12511yescharacteristic
223C22×C4#12611yescharacteristic
224C22×C4C4⋊Q811yescharacteristic
225C22×C4C4⋊Q811yescharacteristic
226C22×C4C4⋊Q811yescharacteristic
227M16—82no—
228M16—82no—
229M16—82no—
230M16—82no—
231M16—82no—
232M16—82no—
233C2×C8—24no—
234C2×C8—42no—
235C2×C8—42no—
236C2×C8—44no—
237C2×C8—44no—
238C2×C8—42no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—82no—
242C2×C8—82no—
243C2×C8—82no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4—42no—
247C4⋊C4—42no—
248C4⋊C4—82no—
249C22⋊C4—82no—
250C22⋊C4—81no—
251C22⋊C4—81no—
252C22⋊C4—82no—
253C22⋊C4—82no—
254C22⋊C4—82no—
255C22⋊C4—82no—
256C22⋊C4—82no—
257C42—44no—
258C23—22no—
259C23—22no—
260C23—22no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—22no—
268C23—22no—
269C23—22no—
270C23—41no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—84no—
283C23—84no—
284C23#38611yescharacteristic
285C23#38711yescharacteristic
286C23#38911yescharacteristic
287C23#39611yescharacteristic
288C23#39811yescharacteristic
289C23#39811yescharacteristic
290C23#40011yescharacteristic
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4—162no—
332C2×C4—162no—
333C2×C4—164no—
334C2×C4#38011yescharacteristic
335C2×C4#38711yescharacteristic
336C2×C4#38911yescharacteristic
337C2×C4#39111yescharacteristic
338C2×C4#39411yescharacteristic
339C2×C4#39511yescharacteristic
340C2×C4#39611yescharacteristic
341C2×C4#39811yescharacteristic
342C8—44no—
343C8—82no—
344C8—82no—
345C8—82no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—42no—
365C22—42no—
366C22—42no—
367C22—42no—
368C22—42no—
369C22—42no—
370C22—82no—
371C22—82no—
372C22—82no—
373C22—82no—
374C22#144111yescharacteristic
375C22#188112yes—
376C22#190211yescharacteristic
377C22#190311yescharacteristic
378C22#191312yes—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—82no—
388C4—82no—
389C4—162no—
390C4—162no—
391C2—41no—
392C2—41no—
393C2—41no—
394C2—41no—
395C2—41no—
396C2—41no—
397C2#933112yes—
398C2#933212yes—
399C2#1120511yescharacteristic
400C2#1121411yescharacteristic
401C2#1121811yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC23×C4C22×C4
Frattini, cosocleC24×C4C23
prime radicalC25#41
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
16. #1853C4semidirect
17. #1852C4semidirect

Maximal subgroups

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

subgroupindex
#219442
#219352
C2×#13062
#80242
#80152
C2×#12932
#79152