Finite Group Databasebeta

← #115756

Subgroups — #115756

Order 512.

638 conjugacy classes of subgroups.

The subgroup lattice has 399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21954C211yesmaximal, characteristic
2#20740C211yesmaximal, characteristic
3C2×#1487C211yesmaximal, characteristic
4C2×#1467C211yesmaximal, characteristic
5C2×#1307C211yesmaximal, characteristic
6#8042C211yesmaximal, characteristic
7C2×#1287C211yesmaximal, characteristic
8C22×C4×Q8C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#432C2211yescharacteristic
12C2×#431C2211yescharacteristic
13C2×#423C2211yescharacteristic
14#2285C2211yescharacteristic
15#1940—22no—
16#1939—22no—
17#1823C412yes—
18#1803—22no—
19#1798—22no—
20#1787C412yes—
21#1763—22no—
22#1487—22no—
23#1487—22no—
24C2×Q8⋊C8—22no—
25#1467—22no—
26#1467—22no—
27C2×#324—22no—
28#1307—22no—
29#1296—22no—
30#1287—22no—
31C23×Q8C2×C411yescharacteristic
32C22×M16—21no—
33C2×C4×Q8—21no—
34C2×C4×Q8—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×Q8D412yes—
44C2×C4×Q8Q812yes—
45C2×#117—21no—
46C22×C4⋊C4—21no—
47C22×C4⋊C4C2×C411yescharacteristic
48C22×C42—21no—
49C22×C42C2311yescharacteristic
50#432—21no—
51#432—21no—
52#432—21no—
53#432—21no—
54#432—21no—
55#432—21no—
56#432—21no—
57#432—21no—
58#432—21no—
59#432—21no—
60#432—21no—
61#432D412yes—
62#431—21no—
63#431—21no—
64#431—21no—
65#431—21no—
66#423—21no—
67#423—21no—
68#423—21no—
69#423D412yes—
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⋊C8—24no—
77C2×#103—24no—
78C2×C22⋊C8—21no—
79C2×C22⋊C8—21no—
80C2×C22⋊C8C2×C412yes—
81C2×C22⋊C8D412yes—
82C2×#97—21no—
83C2×#97—21no—
84C2×#97—21no—
85C2×C4×C8D412yes—
86#384D412yes—
87#382—21no—
88#380—21no—
89#380C2×C412yes—
90C4×C4⋊C4—21no—
91C4×C4⋊C4D412yes—
92#340—24no—
93#336—24no—
94Q8⋊C8—28no—
95#324—28no—
96C22×Q8—21no—
97C22×Q8—21no—
98C22×Q8—21no—
99C22×Q8—21no—
100C22×Q8—21no—
101C22×Q8—44no—
102C22×Q8C4⋊C412yes—
103C23×C4—21no—
104C23×C4—21no—
105C23×C4C22×C411yescharacteristic
106C23×C4C2×D411yescharacteristic
107C23×C4#4111yescharacteristic
108C2×M16—22no—
109C2×M16—41no—
110C2×M16—82no—
111C22×C8—22no—
112C22×C8—22no—
113C22×C8—22no—
114C22×C8—41no—
115C22×C8—41no—
116C4×Q8—22no—
117C4×Q8—22no—
118C4×Q8—22no—
119C4×Q8—22no—
120C4×Q8—22no—
121C4×Q8—22no—
122C4×Q8—22no—
123C4×Q8—22no—
124C4×Q8—41no—
125C4×Q8—41no—
126C4×Q8—41no—
127C4×Q8—41no—
128C4×Q8—41no—
129C4×Q8—41no—
130C4×Q8—41no—
131C4×Q8—41no—
132#117—82no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—41no—
143C2×C4⋊C4—41no—
144C2×C4⋊C4—41no—
145C2×C4⋊C4—41no—
146C2×C4⋊C4C22⋊C414yes—
147C2×C4⋊C4C4⋊C412yes—
148C2×C22⋊C4—22no—
149C2×C42—22no—
150C2×C42—22no—
151C2×C42—22no—
152C2×C42—41no—
153C2×C42—41no—
154C2×C42—41no—
155C2×C42—41no—
156C2×C42C2×D411yescharacteristic
157C2×C42C2×D411yescharacteristic
158C2×C42C2×D411yescharacteristic
159C2×C42C2×D411yescharacteristic
160C2×C42C2×D411yescharacteristic
161C2×C42C2×D411yescharacteristic
162C2×C42C2×Q811yescharacteristic
163C2×C42#4111yescharacteristic
164C2×C42#4111yescharacteristic
165C2×C42#4111yescharacteristic
166C2×C42#4111yescharacteristic
167C2×C42#4111yescharacteristic
168C4⋊C8—22no—
169C4⋊C8—22no—
170C4⋊C8—22no—
171C4⋊C8—41no—
172C4⋊C8—41no—
173C4⋊C8—41no—
174C4⋊C8—41no—
175C4⋊C8—41no—
176C4⋊C8—41no—
177C4⋊C8—41no—
178C4⋊C8—41no—
179C4⋊C8—41no—
180C4⋊C8—84no—
181#103—48no—
182C22⋊C8—22no—
183C22⋊C8—22no—
184C22⋊C8—22no—
185C22⋊C8—22no—
186C22⋊C8—22no—
187C22⋊C8—41no—
188C22⋊C8—41no—
189C22⋊C8—41no—
190#97—22no—
191#97—41no—
192#97—41no—
193#97—41no—
194#97—41no—
195#97—41no—
196C4×C8—22no—
197C4×C8—22no—
198#95—22no—
199#95—22no—
200C24C4×D411yescharacteristic
201C2×Q8—24no—
202C2×Q8—24no—
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8—44no—
206C2×Q8—42no—
207C2×Q8—42no—
208C2×Q8—44no—
209C2×Q8—44no—
210C2×Q8—44no—
211C2×Q8—41no—
212C2×Q8—41no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—24no—
216C22×C4—22no—
217C22×C4—24no—
218C22×C4—22no—
219C22×C4—41no—
220C22×C4—42no—
221C22×C4—41no—
222C22×C4—42no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4—81no—
228C22×C4—81no—
229C22×C4C2×C22⋊C411yescharacteristic
230C22×C4C2×C4⋊C411yescharacteristic
231C22×C4#11711yescharacteristic
232C22×C4C4×D411yescharacteristic
233C22×C4C4×D411yescharacteristic
234C22×C4C4×D411yescharacteristic
235C22×C4#12011yescharacteristic
236C22×C4#12011yescharacteristic
237C22×C4#12111yescharacteristic
238C22×C4#12111yescharacteristic
239C22×C4#12111yescharacteristic
240C22×C4C22⋊Q811yescharacteristic
241C22×C4C22⋊Q811yescharacteristic
242C22×C4#12311yescharacteristic
243C22×C4#12311yescharacteristic
244C22×C4#12311yescharacteristic
245C22×C4#12411yescharacteristic
246C22×C4#12611yescharacteristic
247M16—82no—
248M16—82no—
249C2×C8—44no—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—42no—
253C2×C8—42no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—42no—
259C2×C8—81no—
260C2×C8—81no—
261C2×C8—82no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—44no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—82no—
274C22⋊C4—82no—
275C42—44no—
276C42—42no—
277C42—42no—
278C42—42no—
279C42—42no—
280C42#12011yescharacteristic
281C42#12111yescharacteristic
282C42#12111yescharacteristic
283C42#12111yescharacteristic
284C42#12111yescharacteristic
285C42#12111yescharacteristic
286C42C22⋊Q811yescharacteristic
287C42C22⋊Q811yescharacteristic
288C42C22⋊Q811yescharacteristic
289C42C22⋊Q811yescharacteristic
290C42#12311yescharacteristic
291C42#12311yescharacteristic
292C42#12411yescharacteristic
293C42#12411yescharacteristic
294C42#12611yescharacteristic
295C42#12711yescharacteristic
296C23—22no—
297C23—21no—
298C23—21no—
299C23—22no—
300C23#38511yescharacteristic
301C23#38611yescharacteristic
302C23#38811yescharacteristic
303Q8—24no—
304Q8—24no—
305Q8—44no—
306Q8—42no—
307Q8—42no—
308Q8—44no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—24no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—44no—
333C2×C4—44no—
334C2×C4—42no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—82no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—82no—
343C2×C4#38011yescharacteristic
344C2×C4#38511yescharacteristic
345C2×C4#38811yescharacteristic
346C2×C4#39011yescharacteristic
347C2×C4#39211yescharacteristic
348C2×C4#39311yescharacteristic
349C2×C4#39411yescharacteristic
350C2×C4#39411yescharacteristic
351C2×C4#39611yescharacteristic
352C2×C4#39611yescharacteristic
353C2×C4#39711yescharacteristic
354C2×C4#39911yescharacteristic
355C2×C4#47112yes—
356C2×C4#47312yes—
357C8—82no—
358C8—82no—
359C8—82no—
360C8—82no—
361C8—82no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—42no—
369C22—42no—
370C22#143911yescharacteristic
371C22#189112yes—
372C22#190411yescharacteristic
373C22#190511yescharacteristic
374C22#190812yes—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—44no—
386C4—82no—
387C4—84no—
388C4#204611yescharacteristic
389C4#204711yescharacteristic
390C4#206412yes—
391C2—41no—
392C2—41no—
393C2#952712yes—
394C2#952812yes—
395C2#1105711yescharacteristic
396C2#1106211yescharacteristic
397C2#1107111yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C4×D4
LCSG ▷ C23×C4 ▷ 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
#219542
#207402
C2×#14872
C2×#14672
C2×#13072
#80422
C2×#12872