Finite Group Databasebeta

← #116111

Subgroups — #116111

Order 512.

589 conjugacy classes of subgroups.

The subgroup lattice has 377 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21954C211yesmaximal, characteristic
2#21332C211yesmaximal, characteristic
3#17496C211yesmaximal, characteristic
4#17464C211yesmaximal, characteristic
5#8105C211yesmaximal, characteristic
6#8071C211yesmaximal, characteristic
7#7869C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11C2×#432C2211yescharacteristic
12C2×#431C2211yescharacteristic
13#2285C2211yescharacteristic
14C4×#117C2211yescharacteristic
15#1996—22no—
16#1996C414yes—
17#1940—22no—
18#1939—22no—
19#1798—22no—
20#1740—22no—
21#1497—22no—
22#1491—22no—
23#1485—22no—
24#1481—22no—
25#1481—22no—
26#1479—22no—
27#1305—22no—
28#1300—22no—
29#1276—22no—
30#533—21no—
31#533—21no—
32#533—21no—
33#533—21no—
34#533—21no—
35#533—21no—
36#533—21no—
37#533—21no—
38C2×C4⋊Q8Q811yescharacteristic
39C2×C4⋊Q8Q811yescharacteristic
40C2×#125—21no—
41C2×C22⋊Q8—21no—
42C2×C22⋊Q8C2×C412yes—
43C2×C4×Q8—21no—
44C2×C4×Q8D412yes—
45C2×#117—21no—
46C2×#117—21no—
47C2×#117D412yes—
48C22×C42C2311yescharacteristic
49#432—21no—
50#432—21no—
51#432—21no—
52#432—21no—
53#432—21no—
54#432—21no—
55#432—21no—
56#432—21no—
57#431—21no—
58#431—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62#431—21no—
63#431—21no—
64#431D412yes—
65#423—21no—
66#423—21no—
67C2×C4⋊C8—24no—
68C2×C4⋊C8D412yes—
69C2×C4⋊C8D412yes—
70#407—21no—
71#407—21no—
72C2×C22⋊C8—21no—
73C2×C22⋊C8—21no—
74C4×M16—21no—
75C4×M16D412yes—
76C2×#97—21no—
77C2×C4×C8—21no—
78#384—21no—
79#382—21no—
80#380C2×C412yes—
81#380D412yes—
82C4×C4⋊C4—21no—
83C4×C4⋊C4—21no—
84C4×C4⋊C4—21no—
85C4×C4⋊C4—21no—
86C4×C22⋊C4—21no—
87C4×C22⋊C4C2×C412yes—
88#376—21no—
89C43—21no—
90#342—28no—
91#336—24no—
92Q8⋊C8—28no—
93Q8⋊C8—28no—
94C22×Q8—21no—
95C22×Q8C4⋊C412yes—
96C23×C4C22×C411yescharacteristic
97C23×C4C2×D411yescharacteristic
98C23×C4C2×D411yescharacteristic
99C2×M16—22no—
100C2×M16—41no—
101C22×C8—22no—
102C22×C8—22no—
103C4⋊Q8—21no—
104C4⋊Q8—21no—
105C4⋊Q8—21no—
106C4⋊Q8—21no—
107C4⋊Q8—21no—
108C4⋊Q8—21no—
109C4⋊Q8—21no—
110C4⋊Q8—21no—
111#125—41no—
112#125—41no—
113#125—41no—
114#125—41no—
115C22⋊Q8—22no—
116C22⋊Q8—22no—
117C22⋊Q8—22no—
118C22⋊Q8—22no—
119C22⋊Q8—41no—
120C22⋊Q8—41no—
121C22⋊Q8—41no—
122C22⋊Q8—41no—
123C4×Q8—22no—
124C4×Q8—22no—
125C4×Q8—22no—
126C4×Q8—22no—
127C4×Q8—41no—
128C4×Q8—41no—
129C4×Q8—41no—
130C4×Q8—41no—
131#117—24no—
132#117—42no—
133#117—41no—
134#117—41no—
135#117—41no—
136#117—41no—
137#117—44no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—41no—
147C2×C4⋊C4C4⋊C412yes—
148C2×C22⋊C4—22no—
149C2×C22⋊C4—22no—
150C2×C22⋊C4C22⋊C414yes—
151C2×C42—22no—
152C2×C42—22no—
153C2×C42—22no—
154C2×C42—41no—
155C2×C42—41no—
156C2×C42C2×D411yescharacteristic
157C2×C42C2×D411yescharacteristic
158C2×C42C2×D411yescharacteristic
159C2×C42C2×D411yescharacteristic
160C2×C42C2×D411yescharacteristic
161C2×C42C2×Q811yescharacteristic
162C2×C42#4111yescharacteristic
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—22no—
172C4⋊C8—22no—
173C4⋊C8—41no—
174C4⋊C8—41no—
175C4⋊C8—41no—
176C4⋊C8—84no—
177C22⋊C8—22no—
178C22⋊C8—41no—
179C22⋊C8—41no—
180C22⋊C8—41no—
181C22⋊C8—41no—
182C22⋊C8—41no—
183C22⋊C8—41no—
184C22⋊C8—41no—
185#97—22no—
186#97—41no—
187#97—41no—
188#97—41no—
189C4×C8—22no—
190C4×C8—22no—
191C4×C8—41no—
192C4×C8—41no—
193#95—22no—
194#95—22no—
195#95—22no—
196#95—41no—
197C24C2×C22⋊C411yescharacteristic
198C2×Q8—22no—
199C2×Q8—22no—
200C2×Q8—44no—
201C2×Q8—41no—
202C2×Q8—41no—
203C2×Q8—82no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—24no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—81no—
212C22×C4C2×C4⋊C411yescharacteristic
213C22×C4#11711yescharacteristic
214C22×C4C4×D411yescharacteristic
215C22×C4C4×D411yescharacteristic
216C22×C4C4×D411yescharacteristic
217C22×C4C4×D411yescharacteristic
218C22×C4#12011yescharacteristic
219C22×C4#12111yescharacteristic
220C22×C4#12111yescharacteristic
221C22×C4#12111yescharacteristic
222C22×C4#12111yescharacteristic
223C22×C4#12111yescharacteristic
224C22×C4#12111yescharacteristic
225C22×C4C22⋊Q811yescharacteristic
226C22×C4C22⋊Q811yescharacteristic
227C22×C4#12311yescharacteristic
228C22×C4#12411yescharacteristic
229C22×C4#12711yescharacteristic
230M16—82no—
231M16—82no—
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—42no—
235C2×C8—42no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—42no—
239C2×C8—42no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—44no—
243C4⋊C4—44no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—42no—
249C4⋊C4—42no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—82no—
255C4⋊C4—82no—
256C22⋊C4—24no—
257C22⋊C4—42no—
258C22⋊C4—42no—
259C22⋊C4—42no—
260C22⋊C4—44no—
261C42—44no—
262C42—44no—
263C42—42no—
264C42—42no—
265C42—44no—
266C42—82no—
267C42#12011yescharacteristic
268C42#12011yescharacteristic
269C42#12111yescharacteristic
270C42#12111yescharacteristic
271C42C22⋊Q811yescharacteristic
272C42C22⋊Q811yescharacteristic
273C42C22⋊Q811yescharacteristic
274C42C22⋊Q811yescharacteristic
275C42#12311yescharacteristic
276C42#12311yescharacteristic
277C42#12311yescharacteristic
278C42#12311yescharacteristic
279C42#12411yescharacteristic
280C42#12411yescharacteristic
281C42#12611yescharacteristic
282C42#12611yescharacteristic
283C23—21no—
284C23—21no—
285C23—41no—
286C23—41no—
287C23#38011yescharacteristic
288C23#38611yescharacteristic
289C23#39011yescharacteristic
290Q8—44no—
291Q8—44no—
292Q8—82no—
293Q8—82no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
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—44no—
313C2×C4—44no—
314C2×C4—44no—
315C2×C4—44no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4—82no—
321C2×C4—82no—
322C2×C4#38511yescharacteristic
323C2×C4#38511yescharacteristic
324C2×C4#38811yescharacteristic
325C2×C4#38811yescharacteristic
326C2×C4#39211yescharacteristic
327C2×C4#39311yescharacteristic
328C2×C4#39411yescharacteristic
329C2×C4#39411yescharacteristic
330C2×C4#39611yescharacteristic
331C2×C4#39611yescharacteristic
332C2×C4#39711yescharacteristic
333C2×C4#39911yescharacteristic
334C2×C4#45512yes—
335C2×C4#45612yes—
336C8—82no—
337C8—82no—
338C8—82no—
339C8—82no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—81no—
349C22—81no—
350C22#143911yescharacteristic
351C22#188511yescharacteristic
352C22#188611yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—84no—
363C4—84no—
364C4—82no—
365C4—82no—
366C4#186812yes—
367C4#200712yes—
368C4#202812yes—
369C2—21no—
370C2—21no—
371C2—41no—
372C2—41no—
373C2#1105511yescharacteristic
374C2#1108811yescharacteristic
375C2#1109411yescharacteristic
subgroupG/H
centerC2×C4#392
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
socleC22#1439
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ 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
#213322
#174962
#174642
#81052
#80712
#78692