Finite Group Databasebeta

← #115881

Subgroups — #115881

Order 512.

676 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21313C211yesmaximal, characteristic
2#20755C211yesmaximal, characteristic
3C2×#1548C211yesmaximal, 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
14C4×#117C2211yescharacteristic
15#1988—22no—
16#1987C414yes—
17#1832—22no—
18#1831—22no—
19#1736—22no—
20#1729—22no—
21#1548—22no—
22#1548—22no—
23C2×#333—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—
80C2×C22⋊C8—21no—
81C2×C4×C8—21no—
82C4×C4⋊C4C2×C412yes—
83C4×C4⋊C4D412yes—
84C4×C22⋊C4—21no—
85C4×C22⋊C4—21no—
86#376—21no—
87C43—21no—
88#340—28no—
89#336—28no—
90#333—28no—
91#332—28no—
92C22×Q8—22no—
93C22×Q8—22no—
94C22×Q8—22no—
95C22×Q8—41no—
96C22×Q8—41no—
97C22×Q8—41no—
98C22×Q8—82no—
99C22×Q8—82no—
100C23×C4—41no—
101C23×C4C2×D411yescharacteristic
102C23×C4#4111yescharacteristic
103C23×C4#4111yescharacteristic
104C2×M16—41no—
105C2×M16—41no—
106C2×M16—41no—
107C2×M16—41no—
108C2×M16—42no—
109C2×M16—42no—
110C2×M16—42no—
111C2×M16—42no—
112C22×C8—22no—
113C22×C8—22no—
114C22×C8—22no—
115C22×C8—22no—
116C22×C8—41no—
117C22×C8—41no—
118C22×C8—41no—
119C22×C8—41no—
120C22×C8—41no—
121C22×C8—42no—
122C22×C8—42no—
123C22×C8—82no—
124C4⋊Q8—22no—
125C4⋊Q8—22no—
126C4⋊Q8—22no—
127C4⋊Q8—22no—
128C4⋊Q8—22no—
129C4⋊Q8—22no—
130C4⋊Q8—22no—
131C4⋊Q8—22no—
132C4⋊Q8—22no—
133C4⋊Q8—41no—
134C4⋊Q8—41no—
135C4⋊Q8—41no—
136C4⋊Q8—41no—
137C4⋊Q8—41no—
138C4⋊Q8—41no—
139C4⋊Q8C4⋊C414yes—
140#117—22no—
141#117—22no—
142#117—22no—
143#117—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—41no—
154C2×C4⋊C4—41no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4C22⋊C414yes—
157C2×C22⋊C4—22no—
158C2×C42—22no—
159C2×C42—22no—
160C2×C42—22no—
161C2×C42C22×C411yescharacteristic
162C2×C42C2×D411yescharacteristic
163C2×C42C2×D411yescharacteristic
164C2×C42C2×D411yescharacteristic
165C2×C42C2×D411yescharacteristic
166C2×C42C2×D411yescharacteristic
167C2×C42C2×D411yescharacteristic
168C2×C42C2×Q811yescharacteristic
169C2×C42#4111yescharacteristic
170C2×C42#4111yescharacteristic
171C2×C42#4111yescharacteristic
172C2×C42#4111yescharacteristic
173C4⋊C8—22no—
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8—22no—
177C4⋊C8—22no—
178C4⋊C8—22no—
179C4⋊C8—22no—
180C4⋊C8—22no—
181C4⋊C8—22no—
182C4⋊C8—41no—
183C4⋊C8—41no—
184C4⋊C8—41no—
185C4⋊C8—41no—
186C4⋊C8—41no—
187C4⋊C8—41no—
188C4⋊C8—41no—
189C4⋊C8—41no—
190C4⋊C8—41no—
191C22⋊C8—22no—
192C22⋊C8—41no—
193C4×C8—22no—
194C4×C8—41no—
195#95—22no—
196#95—22no—
197C24#12311yescharacteristic
198C2×Q8—24no—
199C2×Q8—42no—
200C2×Q8—42no—
201C2×Q8—42no—
202C2×Q8—84no—
203C2×Q8—82no—
204C2×Q8—82no—
205C2×Q8—84no—
206C2×Q8—82no—
207C2×Q8—82no—
208C2×Q8—84no—
209C2×Q8—82no—
210C2×Q8—82no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—24no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—84no—
219C22×C4C2×C22⋊C411yescharacteristic
220C22×C4C4×D411yescharacteristic
221C22×C4C4×D411yescharacteristic
222C22×C4#12011yescharacteristic
223C22×C4#12111yescharacteristic
224C22×C4#12111yescharacteristic
225C22×C4#12111yescharacteristic
226C22×C4C22⋊Q811yescharacteristic
227C22×C4C22⋊Q811yescharacteristic
228C22×C4C22⋊Q811yescharacteristic
229C22×C4#12311yescharacteristic
230C22×C4#12311yescharacteristic
231C22×C4#12311yescharacteristic
232C22×C4#12311yescharacteristic
233C22×C4#12411yescharacteristic
234C22×C4#12611yescharacteristic
235C22×C4#12611yescharacteristic
236C22×C4#12711yescharacteristic
237C22×C4#13512yes—
238C22×C4#13512yes—
239C22×C4#13712yes—
240C22×C4#13712yes—
241M16—82no—
242M16—82no—
243M16—81no—
244M16—81no—
245M16—81no—
246M16—81no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—44no—
253C2×C8—44no—
254C2×C8—44no—
255C2×C8—82no—
256C2×C8—82no—
257C2×C8—82no—
258C2×C8—82no—
259C2×C8—81no—
260C2×C8—81no—
261C2×C8—82no—
262C4⋊C4—24no—
263C4⋊C4—24no—
264C4⋊C4—24no—
265C4⋊C4—24no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—42no—
274C42—42no—
275C42—42no—
276C42—42no—
277C42—42no—
278C42—82no—
279C42C2×C4⋊C411yescharacteristic
280C42#11711yescharacteristic
281C42C4×D411yescharacteristic
282C42C4×D411yescharacteristic
283C42#12011yescharacteristic
284C42#12011yescharacteristic
285C42#12111yescharacteristic
286C42#12111yescharacteristic
287C42#12111yescharacteristic
288C42#12111yescharacteristic
289C42#12111yescharacteristic
290C42C22⋊Q811yescharacteristic
291C42C22⋊Q811yescharacteristic
292C42C22⋊Q811yescharacteristic
293C42#12411yescharacteristic
294C42#12411yescharacteristic
295C23—22no—
296C23—22no—
297C23#38611yescharacteristic
298C23#39711yescharacteristic
299C23#39911yescharacteristic
300C23#48512yes—
301C23#48512yes—
302Q8—84no—
303Q8—84no—
304Q8—84no—
305Q8—82no—
306Q8—82no—
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—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—44no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—84no—
325C2×C4—84no—
326C2×C4—84no—
327C2×C4#38011yescharacteristic
328C2×C4#38511yescharacteristic
329C2×C4#38511yescharacteristic
330C2×C4#38811yescharacteristic
331C2×C4#38811yescharacteristic
332C2×C4#39011yescharacteristic
333C2×C4#39211yescharacteristic
334C2×C4#39311yescharacteristic
335C2×C4#39411yescharacteristic
336C2×C4#39411yescharacteristic
337C2×C4#39611yescharacteristic
338C2×C4#39611yescharacteristic
339C2×C4#41612yes—
340C2×C4#41912yes—
341C2×C4#45212yes—
342C2×C4#45212yes—
343C2×C4#46412yes—
344C2×C4#46412yes—
345C2×C4#47112yes—
346C2×C4#47212yes—
347C2×C4#47912yes—
348C2×C4#47912yes—
349C2×C4#48812yes—
350C2×C4#49112yes—
351C2×C4#49511yescharacteristic
352C2×C4#49511yescharacteristic
353C2×C4#49711yescharacteristic
354C2×C4#49711yescharacteristic
355C8—82no—
356C8—82no—
357C8—82no—
358C8—82no—
359C8—82no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—24no—
365C22—24no—
366C22#143911yescharacteristic
367C22#187312yes—
368C22#190212yes—
369C22#190712yes—
370C22#207412yes—
371C22#209711yescharacteristic
372C22#209711yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—84no—
380C4—84no—
381C4#180512yes—
382C4#195811yescharacteristic
383C4#196011yescharacteristic
384C4#201511yescharacteristic
385C4#201511yescharacteristic
386C4#202612yes—
387C4#204511yescharacteristic
388C4#204611yescharacteristic
389C4#206312yes—
390C2—22no—
391C2—21no—
392C2—21no—
393C2#916814yes—
394C2#1105211yescharacteristic
395C2#1105911yescharacteristic
396C2#1106111yescharacteristic
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
#213132
#207552
C2×#15482
C22×#3322
C2×#13012
C2×#12922
#78912