Finite Group Databasebeta

← #189747

Subgroups — #189747

Order 512.

952 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2356C211yesmaximal, characteristic
2#21820C212yesmaximal
3#8705C212yesmaximal
4#8703C212yesmaximal
5#8701C212yesmaximal
6#8699C212yesmaximal
7#7916C212yesmaximal
8#7910C211yesmaximal, characteristic
9#7906C211yesmaximal, characteristic
10C22×C4×Q8C2211yescharacteristic
11C2×#432C2212yes—
12C2×#431C2212yes—
13#2356—22no—
14#2356—22no—
15#2356—22no—
16#2356—22no—
17C2×#391C412yes—
18C2×#387C412yes—
19C2×#387C412yes—
20C2×#383C2211yescharacteristic
21C2×#383C2211yescharacteristic
22C2×#382C2211yescharacteristic
23C2×C4×C4⋊C4C412yes—
24C2×C4×C4⋊C4C2211yescharacteristic
25C2×#376C2211yescharacteristic
26C2×#376C2211yescharacteristic
27#1985—22no—
28#1985—22no—
29#1984—22no—
30#1984—22no—
31#1817C2214yes—
32#1817C2214yes—
33#1280C2212yes—
34#1280C2212yes—
35#1280C2214yes—
36#1280C2212yes—
37#1280C2212yes—
38#1280C2214yes—
39C23×Q8C2×C411yescharacteristic
40C2×C4×Q8—22no—
41C2×C4×Q8—24no—
42C2×C4×Q8—22no—
43C2×C4×Q8D412yes—
44C2×C4×Q8D412yes—
45C2×C4×Q8D412yes—
46C2×C4×Q8D412yes—
47C22×C4⋊C4C2×C412yes—
48C22×C4⋊C4C2×C411yescharacteristic
49C22×C4⋊C4C2×C411yescharacteristic
50C22×C4⋊C4C2×C411yescharacteristic
51C22×C4⋊C4C2×C412yes—
52C22×C42C2×C412yes—
53C22×C42C2×C412yes—
54C22×C42C2×C412yes—
55C22×C42C2311yescharacteristic
56C22×C42C2311yescharacteristic
57C22×C42C2311yescharacteristic
58#432—24no—
59#432—24no—
60#431—24no—
61#431—24no—
62C2×C4⋊C8—22no—
63C2×C4⋊C8—22no—
64C2×C22⋊C8C2314yes—
65C2×C22⋊C8C2314yes—
66C2×#97—22no—
67C2×C4×C8—22no—
68#391—24no—
69#391—24no—
70#387—24no—
71#387—24no—
72#387—24no—
73#387—24no—
74#383—22no—
75#383—22no—
76#383—22no—
77#383—22no—
78#382—22no—
79#382—22no—
80C4×C4⋊C4—22no—
81C4×C4⋊C4—22no—
82C4×C4⋊C4—22no—
83C4×C4⋊C4—22no—
84C4×C4⋊C4—22no—
85C4×C4⋊C4—22no—
86#376—22no—
87#376—22no—
88#376—22no—
89#376—22no—
90C2×#95C2×C412yes—
91C2×#95C2×C412yes—
92C2×#95C2×C412yes—
93C2×#95C2×C412yes—
94C2×#95C2×C412yes—
95C2×#95C2×C412yes—
96C2×#95C2×C412yes—
97C2×#95C2311yescharacteristic
98C2×#95C2311yescharacteristic
99C2×#95C2311yescharacteristic
100C2×#95C2311yescharacteristic
101#336—24no—
102#336—24no—
103#336—24no—
104#336—24no—
105C22×Q8—22no—
106C22×Q8—22no—
107C22×Q8—42no—
108C22×Q8—42no—
109C22×Q8C22⋊C412yes—
110C22×Q8C22⋊C412yes—
111C23×C4C22×C411yescharacteristic
112C23×C4C22×C411yescharacteristic
113C23×C4C22×C411yescharacteristic
114C23×C4C22×C411yescharacteristic
115C23×C4C22×C412yes—
116C23×C4C22×C412yes—
117C23×C4C22×C412yes—
118C23×C4C22×C411yescharacteristic
119C23×C4C22×C412yes—
120C23×C4C22×C411yescharacteristic
121C23×C4C2411yescharacteristic
122C22×C8—24no—
123C22×C8—24no—
124C4×Q8—24no—
125C4×Q8—24no—
126C4×Q8—24no—
127C4×Q8—24no—
128C4×Q8—24no—
129C4×Q8—24no—
130C4×Q8—24no—
131C4×Q8—24no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—24no—
141C2×C4⋊C4—24no—
142C2×C4⋊C4—42no—
143C2×C4⋊C4—44no—
144C2×C4⋊C4C22⋊C411yescharacteristic
145C2×C4⋊C4C22⋊C411yescharacteristic
146C2×C4⋊C4C22⋊C411yescharacteristic
147C2×C4⋊C4C22⋊C411yescharacteristic
148C2×C4⋊C4C22⋊C412yes—
149C2×C4⋊C4C22⋊C412yes—
150C2×C4⋊C4C22⋊C412yes—
151C2×C4⋊C4C22⋊C412yes—
152C2×C42—22no—
153C2×C42—21no—
154C2×C42—21no—
155C2×C42—22no—
156C2×C42—21no—
157C2×C42—21no—
158C2×C42—22no—
159C2×C42—22no—
160C2×C42—22no—
161C2×C42—22no—
162C2×C42—22no—
163C2×C42—22no—
164C2×C42—24no—
165C2×C42—24no—
166C2×C42—42no—
167C2×C42—42no—
168C2×C42—44no—
169C2×C42C2×D412yes—
170C2×C42C2×D412yes—
171C2×C42C2×D412yes—
172C2×C42C2×D412yes—
173C2×C42C2×D412yes—
174C2×C42C2×D412yes—
175C2×C42#4112yes—
176C2×C42#4114yes—
177C2×C42#4112yes—
178C4⋊C8—44no—
179C4⋊C8—44no—
180C22⋊C8—24no—
181C22⋊C8—24no—
182C22⋊C8—24no—
183C22⋊C8—24no—
184#97—44no—
185C4×C8—44no—
186#95—24no—
187#95—24no—
188#95—22no—
189#95—22no—
190#95—22no—
191#95—22no—
192#95—24no—
193#95—24no—
194#95—24no—
195#95—22no—
196#95—22no—
197#95—22no—
198#95—22no—
199C24C23×C411yescharacteristic
200C2×Q8—24no—
201C2×Q8—24no—
202C2×Q8—24no—
203C2×Q8—24no—
204C2×Q8—42no—
205C2×Q8—42no—
206C2×Q8—48no—
207C2×Q8—48no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4C2×C22⋊C412yes—
249C22×C4C2×C22⋊C411yescharacteristic
250C22×C4C2×C22⋊C411yescharacteristic
251C22×C4C2×C22⋊C412yes—
252C22×C4C2×C22⋊C412yes—
253C22×C4C2×C22⋊C411yescharacteristic
254C22×C4C2×C22⋊C411yescharacteristic
255C22×C4C2×C22⋊C411yescharacteristic
256C22×C4C2×C22⋊C411yescharacteristic
257C22×C4#11712yes—
258C22×C4#11712yes—
259C22×C4#11712yes—
260C22×C4#11712yes—
261C22×C4#13114yes—
262C22×C4C22×D412yes—
263C22×C4C2×#4112yes—
264C22×C4C2×#4111yescharacteristic
265C22×C4C2×#4111yescharacteristic
266C2×C8—48no—
267C2×C8—48no—
268C2×C8—44no—
269C2×C8—44no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—24no—
275C4⋊C4—24no—
276C4⋊C4—24no—
277C4⋊C4—24no—
278C4⋊C4—48no—
279C4⋊C4—44no—
280C4⋊C4—44no—
281C42—22no—
282C42—22no—
283C42—22no—
284C42—22no—
285C42—22no—
286C42—22no—
287C42—22no—
288C42—22no—
289C42—44no—
290C42—44no—
291C42—44no—
292C42—44no—
293C42—44no—
294C42—44no—
295C42#12314yes—
296C42#12314yes—
297C42#12314yes—
298C42#12314yes—
299C23—22no—
300C23—21no—
301C23—21no—
302C23C22×C22⋊C411yescharacteristic
303C23C2×#11711yescharacteristic
304C23C2×#11711yescharacteristic
305C23C2×#13112yes—
306C23#56812yes—
307Q8—48no—
308Q8—48no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—24no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—24no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—24no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—24no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—44no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—44no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—82no—
360C2×C4—82no—
361C2×C4—82no—
362C2×C4—82no—
363C2×C4—82no—
364C2×C4—82no—
365C2×C4#38112yes—
366C2×C4#38112yes—
367C2×C4#38114yes—
368C2×C4#41312yes—
369C2×C4#41312yes—
370C2×C4C2×#12312yes—
371C2×C4C2×#12312yes—
372C8—84no—
373C8—84no—
374C22—22no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22C2×#38111yescharacteristic
383C22#288012yes—
384C22#288412yes—
385C22C2×#41311yescharacteristic
386C22C2×#41311yescharacteristic
387C22#292211yescharacteristic
388C22#292311yescharacteristic
389C22#292512yes—
390C4—22no—
391C4—22no—
392C4—22no—
393C4—22no—
394C4—22no—
395C4—22no—
396C4—24no—
397C4—44no—
398C4—41no—
399C4—41no—
400C4—42no—
401C4—42no—
402C4—82no—
403C4—82no—
404C4—82no—
405C2—21no—
406C2—21no—
407C2—22no—
408C2#1742312yes—
409C2#1742812yes—
410C2#2068411yescharacteristic
411C2#2069111yescharacteristic
412C2#2069411yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutator, prime radicalC24C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#23562
#218202
#87052
#87032
#87012
#86992
#79162
#79102
#79062