Finite Group Databasebeta

← #115880

Subgroups — #115880

Order 512.

720 conjugacy classes of subgroups.

The subgroup lattice has 411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21259C211yesmaximal, characteristic
2#20755C211yesmaximal, characteristic
3C2×#1546C211yesmaximal, characteristic
4C22×#332C211yesmaximal, characteristic
5C2×#1301C211yesmaximal, characteristic
6C2×#1292C211yesmaximal, characteristic
7#7891C211yesmaximal, characteristic
8C22×C4⋊Q8C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#423C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C22×C4⋊C8C2211yescharacteristic
13C22×C4⋊C8C2211yescharacteristic
14C2×#419—22no—
15C4×#117C2211yescharacteristic
16#1981—22no—
17#1981C414yes—
18#1832—22no—
19#1831—22no—
20#1729—22no—
21#1546—22no—
22#1546—22no—
23C2×#332—22no—
24C2×#332—22no—
25C2×#332—22no—
26C2×#332—22no—
27#1301—22no—
28#1292—22no—
29#1279—22no—
30C23×Q8—21no—
31C22×M16—21no—
32C22×M16—21no—
33C23×C8—21no—
34C23×C8—21no—
35C2×C4⋊Q8—21no—
36C2×C4⋊Q8—21no—
37C2×C4⋊Q8—21no—
38C2×C4⋊Q8—21no—
39C2×C4⋊Q8—21no—
40C2×C4⋊Q8—21no—
41C2×C4⋊Q8—21no—
42C2×C4⋊Q8—21no—
43C2×C4⋊Q8—21no—
44C2×C4⋊Q8C2×C412yes—
45C2×C4⋊Q8D412yes—
46C2×C4⋊Q8Q812yes—
47C2×#117D412yes—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—21no—
50C22×C42C2311yescharacteristic
51#431—21no—
52#431—21no—
53#431—21no—
54#431D412yes—
55#423—21no—
56#423—21no—
57#423—21no—
58#423—21no—
59#423—21no—
60#423—21no—
61#423—21no—
62#423—21no—
63C2×C4⋊C8—21no—
64C2×C4⋊C8—21no—
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⋊C8—21no—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74C2×C4⋊C8—21no—
75C2×C4⋊C8—21no—
76C2×C4⋊C8C2×C412yes—
77C2×C4⋊C8D412yes—
78C2×C4⋊C8D412yes—
79C2×C4⋊C8D412yes—
80#419—44no—
81#419—44no—
82C2×#103—28no—
83C2×C22⋊C8—21no—
84C2×C4×C8—21no—
85C4×C4⋊C4C2×C412yes—
86C4×C4⋊C4D412yes—
87C4×C22⋊C4—21no—
88C4×C22⋊C4—21no—
89#376—21no—
90C43—21no—
91#336—28no—
92#332—28no—
93#332—28no—
94C22×Q8—22no—
95C22×Q8—22no—
96C22×Q8—22no—
97C22×Q8—41no—
98C22×Q8—41no—
99C22×Q8—41no—
100C22×Q8—42no—
101C22×Q8—42no—
102C22×Q8—42no—
103C22×Q8—42no—
104C23×C4—41no—
105C23×C4C2×D411yescharacteristic
106C23×C4#4111yescharacteristic
107C23×C4#4111yescharacteristic
108C2×M16—41no—
109C2×M16—41no—
110C2×M16—41no—
111C2×M16—41no—
112C2×M16—42no—
113C2×M16—42no—
114C2×M16—42no—
115C2×M16—42no—
116C22×C8—22no—
117C22×C8—22no—
118C22×C8—22no—
119C22×C8—22no—
120C22×C8—41no—
121C22×C8—41no—
122C22×C8—41no—
123C22×C8—41no—
124C22×C8—41no—
125C22×C8—42no—
126C22×C8—42no—
127C22×C8—82no—
128C4⋊Q8—22no—
129C4⋊Q8—22no—
130C4⋊Q8—22no—
131C4⋊Q8—22no—
132C4⋊Q8—22no—
133C4⋊Q8—22no—
134C4⋊Q8—22no—
135C4⋊Q8—22no—
136C4⋊Q8—22no—
137C4⋊Q8—41no—
138C4⋊Q8—41no—
139C4⋊Q8—41no—
140C4⋊Q8—41no—
141C4⋊Q8—41no—
142C4⋊Q8—41no—
143C4⋊Q8C4⋊C414yes—
144#117—22no—
145#117—22no—
146#117—22no—
147#117—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—41no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4—41no—
160C2×C4⋊C4C22⋊C414yes—
161C2×C22⋊C4—22no—
162C2×C42—22no—
163C2×C42—22no—
164C2×C42—22no—
165C2×C42C22×C411yescharacteristic
166C2×C42C2×D411yescharacteristic
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
177C4⋊C8—22no—
178C4⋊C8—22no—
179C4⋊C8—22no—
180C4⋊C8—22no—
181C4⋊C8—22no—
182C4⋊C8—22no—
183C4⋊C8—22no—
184C4⋊C8—22no—
185C4⋊C8—22no—
186C4⋊C8—41no—
187C4⋊C8—41no—
188C4⋊C8—41no—
189C4⋊C8—41no—
190C4⋊C8—41no—
191C4⋊C8—41no—
192C4⋊C8—41no—
193C4⋊C8—41no—
194C4⋊C8—41no—
195#103—416no—
196C22⋊C8—22no—
197C22⋊C8—41no—
198C4×C8—22no—
199C4×C8—41no—
200#95—22no—
201#95—22no—
202C24#12311yescharacteristic
203C2×Q8—24no—
204C2×Q8—42no—
205C2×Q8—42no—
206C2×Q8—42no—
207C2×Q8—44no—
208C2×Q8—44no—
209C2×Q8—44no—
210C2×Q8—44no—
211C2×Q8—44no—
212C2×Q8—44no—
213C2×Q8—82no—
214C2×Q8—82no—
215C2×Q8—82no—
216C2×Q8—82no—
217C2×Q8—81no—
218C2×Q8—81no—
219C2×Q8—81no—
220C2×Q8—81no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—24no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—82no—
229C22×C4—82no—
230C22×C4C2×C22⋊C411yescharacteristic
231C22×C4C4×D411yescharacteristic
232C22×C4C4×D411yescharacteristic
233C22×C4#12011yescharacteristic
234C22×C4#12111yescharacteristic
235C22×C4#12111yescharacteristic
236C22×C4#12111yescharacteristic
237C22×C4C22⋊Q811yescharacteristic
238C22×C4C22⋊Q811yescharacteristic
239C22×C4C22⋊Q811yescharacteristic
240C22×C4#12311yescharacteristic
241C22×C4#12311yescharacteristic
242C22×C4#12311yescharacteristic
243C22×C4#12311yescharacteristic
244C22×C4#12411yescharacteristic
245C22×C4#12611yescharacteristic
246C22×C4#12611yescharacteristic
247C22×C4#12711yescharacteristic
248C22×C4#13512yes—
249C22×C4#13512yes—
250C22×C4AGL(1,ℤ/8)12yes—
251C22×C4AGL(1,ℤ/8)12yes—
252M16—82no—
253M16—82no—
254M16—81no—
255M16—81no—
256M16—81no—
257M16—81no—
258C2×C8—42no—
259C2×C8—42no—
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—42no—
263C2×C8—44no—
264C2×C8—44no—
265C2×C8—44no—
266C2×C8—82no—
267C2×C8—82no—
268C2×C8—82no—
269C2×C8—82no—
270C2×C8—81no—
271C2×C8—81no—
272C2×C8—82no—
273C4⋊C4—24no—
274C4⋊C4—24no—
275C4⋊C4—24no—
276C4⋊C4—24no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C42—42no—
286C42—42no—
287C42—42no—
288C42—42no—
289C42—82no—
290C42C2×C4⋊C411yescharacteristic
291C42#11711yescharacteristic
292C42C4×D411yescharacteristic
293C42C4×D411yescharacteristic
294C42#12011yescharacteristic
295C42#12011yescharacteristic
296C42#12111yescharacteristic
297C42#12111yescharacteristic
298C42#12111yescharacteristic
299C42#12111yescharacteristic
300C42#12111yescharacteristic
301C42C22⋊Q811yescharacteristic
302C42C22⋊Q811yescharacteristic
303C42C22⋊Q811yescharacteristic
304C42#12411yescharacteristic
305C42#12411yescharacteristic
306C23—22no—
307C23—22no—
308C23#38611yescharacteristic
309C23#39711yescharacteristic
310C23#39911yescharacteristic
311C23#48212yes—
312C23#48212yes—
313Q8—48no—
314Q8—82no—
315Q8—82no—
316Q8—82no—
317Q8—82no—
318Q8—84no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—44no—
333C2×C4—44no—
334C2×C4—44no—
335C2×C4—44no—
336C2×C4—84no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—84no—
340C2×C4#38011yescharacteristic
341C2×C4#38511yescharacteristic
342C2×C4#38511yescharacteristic
343C2×C4#38811yescharacteristic
344C2×C4#38811yescharacteristic
345C2×C4#39011yescharacteristic
346C2×C4#39211yescharacteristic
347C2×C4#39311yescharacteristic
348C2×C4#39411yescharacteristic
349C2×C4#39411yescharacteristic
350C2×C4#39611yescharacteristic
351C2×C4#39611yescharacteristic
352C2×C4#41612yes—
353C2×C4#41812yes—
354C2×C4#44912yes—
355C2×C4#44912yes—
356C2×C4#46312yes—
357C2×C4#46312yes—
358C2×C4#47112yes—
359C2×C4#47312yes—
360C2×C4#47812yes—
361C2×C4#47812yes—
362C2×C4#48812yes—
363C2×C4#49012yes—
364C2×C4#49511yescharacteristic
365C2×C4#49511yescharacteristic
366C2×C4#49611yescharacteristic
367C2×C4#49611yescharacteristic
368C8—82no—
369C8—82no—
370C8—82no—
371C8—82no—
372C8—82no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—24no—
378C22—24no—
379C22#143911yescharacteristic
380C22#187512yes—
381C22#190212yes—
382C22#190812yes—
383C22#207312yes—
384C22#209211yescharacteristic
385C22#209211yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—84no—
393C4—84no—
394C4#180412yes—
395C4#195811yescharacteristic
396C4#196111yescharacteristic
397C4#201211yescharacteristic
398C4#201211yescharacteristic
399C4#202512yes—
400C4#204611yescharacteristic
401C4#204711yescharacteristic
402C4#206412yes—
403C2—22no—
404C2—21no—
405C2—21no—
406C2#917214yes—
407C2#1105111yescharacteristic
408C2#1105911yescharacteristic
409C2#1106211yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#123
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#212592
#207552
C2×#15462
C22×#3322
C2×#13012
C2×#12922
#78912