Finite Group Databasebeta

← #118233

Subgroups — #118233

Order 512.

652 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21822C211yesmaximal, characteristic
2C2×#1985C211yesmaximal, characteristic
3C2×#1573C211yesmaximal, characteristic
4C2×#1461C211yesmaximal, characteristic
5C2×#1302C211yesmaximal, characteristic
6C2×#1302C211yesmaximal, characteristic
7#7879C211yesmaximal, characteristic
8C22×C4×Q8C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C2×#431C2211yescharacteristic
13C22×C4⋊C8C2211yescharacteristic
14C22×#97C2211yescharacteristic
15#1985—22no—
16#1985—21no—
17#1985—21no—
18#1985—22no—
19#1985—22no—
20#1817—22no—
21C2×#336—22no—
22#1573—22no—
23#1573—22no—
24C2×#335—21no—
25C2×#334—21no—
26#1461—22no—
27#1461—22no—
28C2×#324C414yes—
29#1302—22no—
30#1302—22no—
31#1277—22no—
32C23×Q8Q811yescharacteristic
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×Q8—21no—
45C2×C4×Q8—21no—
46C2×C4×Q8—21no—
47C22×C4⋊C4C2×C412yes—
48C22×C4⋊C4Q811yescharacteristic
49C22×C42D412yes—
50C22×C42C2311yescharacteristic
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#431—21no—
60#431—21no—
61#431—21no—
62#431—21no—
63#431—21no—
64#431—21no—
65#431D412yes—
66#431D412yes—
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⋊C8D411yescharacteristic
75C2×C4⋊C8D411yescharacteristic
76C2×C4⋊C8D412yes—
77C2×C4⋊C8D412yes—
78C2×C22⋊C8—21no—
79C2×C22⋊C8—21no—
80C2×C22⋊C8C2×C412yes—
81C2×C22⋊C8C2×C412yes—
82C2×#97—21no—
83C2×#97—21no—
84C2×#97—21no—
85C2×#97—21no—
86C2×#97—21no—
87C2×#97—21no—
88C2×#97—21no—
89C2×#97D412yes—
90C2×C4×C8—21no—
91C2×C4×C8—21no—
92#336—24no—
93#336—24no—
94#336—28no—
95#335—24no—
96#334—24no—
97#324—28no—
98C22×Q8—24no—
99C22×Q8—21no—
100C22×Q8—21no—
101C22×Q8—21no—
102C22×Q8—21no—
103C22×Q8—21no—
104C22×Q8—21no—
105C22×Q8—42no—
106C23×C4C4⋊C412yes—
107C23×C4C4⋊C412yes—
108C23×C4C22×C411yescharacteristic
109C23×C4C2×D411yescharacteristic
110C23×C4C2×Q811yescharacteristic
111C22×C8—24no—
112C22×C8—22no—
113C22×C8—22no—
114C22×C8—22no—
115C22×C8—22no—
116C22×C8—21no—
117C22×C8—21no—
118C22×C8—22no—
119C22×C8—42no—
120C22×C8—41no—
121C22×C8—41no—
122C22×C8—44no—
123C22×C8—41no—
124C22×C8—41no—
125C4×Q8—41no—
126C4×Q8—41no—
127C4×Q8—41no—
128C4×Q8—41no—
129C4×Q8—41no—
130C4×Q8—41no—
131C4×Q8—41no—
132C4×Q8—41no—
133C4×Q8—41no—
134C4×Q8—41no—
135C4×Q8—41no—
136C4×Q8—41no—
137C4×Q8—41no—
138C4×Q8—41no—
139C4×Q8—41no—
140C4×Q8—41no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C42—22no—
154C2×C42—22no—
155C2×C42—22no—
156C2×C42—22no—
157C2×C42—22no—
158C2×C42—22no—
159C2×C42C2×D411yescharacteristic
160C2×C42C2×D411yescharacteristic
161C2×C42C2×D411yescharacteristic
162C2×C42C2×D411yescharacteristic
163C2×C42C2×D411yescharacteristic
164C2×C42C2×D411yescharacteristic
165C2×C42#4111yescharacteristic
166C2×C42#4111yescharacteristic
167C2×C42#4111yescharacteristic
168C2×C42#4111yescharacteristic
169C2×C42#4111yescharacteristic
170C2×C42#4111yescharacteristic
171C4⋊C8—21no—
172C4⋊C8—22no—
173C4⋊C8—21no—
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8—21no—
177C4⋊C8—21no—
178C4⋊C8—22no—
179C4⋊C8—22no—
180C4⋊C8—22no—
181C4⋊C8—41no—
182C4⋊C8—41no—
183C4⋊C8—41no—
184C4⋊C8—41no—
185C22⋊C8—22no—
186C22⋊C8—22no—
187C22⋊C8—22no—
188C22⋊C8—41no—
189C22⋊C8—41no—
190C22⋊C8—41no—
191C22⋊C8—41no—
192C22⋊C8C22⋊C414yes—
193#97—22no—
194#97—22no—
195#97—41no—
196#97—41no—
197#97—41no—
198#97—41no—
199#97—41no—
200#97—41no—
201C4×C8—22no—
202C4×C8—22no—
203C4×C8—41no—
204C4×C8—41no—
205C24C2×C4⋊C411yescharacteristic
206C2×Q8—24no—
207C2×Q8—24no—
208C2×Q8—44no—
209C2×Q8—44no—
210C2×Q8—44no—
211C2×Q8—44no—
212C2×Q8—42no—
213C2×Q8—42no—
214C2×Q8—41no—
215C2×Q8—41no—
216C2×Q8—41no—
217C2×Q8—41no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
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—42no—
232C22×C4—44no—
233C22×C4#10814yes—
234C22×C4C2×C22⋊C411yescharacteristic
235C22×C4#11711yescharacteristic
236C22×C4C4×D411yescharacteristic
237C22×C4C4×D411yescharacteristic
238C22×C4C4×D411yescharacteristic
239C22×C4C4×D411yescharacteristic
240C22×C4#12011yescharacteristic
241C22×C4#12011yescharacteristic
242C22×C4#12111yescharacteristic
243C22×C4#12111yescharacteristic
244C22×C4C22⋊Q811yescharacteristic
245C22×C4C22⋊Q811yescharacteristic
246C22×C4C22⋊Q811yescharacteristic
247C22×C4C22⋊Q811yescharacteristic
248C22×C4C22⋊Q811yescharacteristic
249C22×C4C22⋊Q811yescharacteristic
250C22×C4#12311yescharacteristic
251C22×C4#12311yescharacteristic
252C2×C8—24no—
253C2×C8—24no—
254C2×C8—44no—
255C2×C8—44no—
256C2×C8—42no—
257C2×C8—44no—
258C2×C8—42no—
259C2×C8—44no—
260C2×C8—44no—
261C2×C8—42no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—42no—
265C2×C8—42no—
266C2×C8—42no—
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—42no—
270C2×C8—82no—
271C2×C8—82no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C42—42no—
281C42—42no—
282C42—42no—
283C42—42no—
284C42#12011yescharacteristic
285C42#12111yescharacteristic
286C42#12111yescharacteristic
287C42#12111yescharacteristic
288C42#12111yescharacteristic
289C42#12111yescharacteristic
290C42#12111yescharacteristic
291C42#12311yescharacteristic
292C42#12311yescharacteristic
293C42#12311yescharacteristic
294C42#12411yescharacteristic
295C42#12411yescharacteristic
296C42#12411yescharacteristic
297C42#12611yescharacteristic
298C42#12611yescharacteristic
299C42#12711yescharacteristic
300C23—22no—
301C23—22no—
302C23#38011yescharacteristic
303C23#38511yescharacteristic
304C23#38511yescharacteristic
305C23C2×#10812yes—
306C23#43012yes—
307Q8—44no—
308Q8—44no—
309Q8—44no—
310Q8—44no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—44no—
340C2×C4—44no—
341C2×C4—42no—
342C2×C4—82no—
343C2×C4#38611yescharacteristic
344C2×C4#38811yescharacteristic
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#45412yes—
356C2×C4#45612yes—
357C8—44no—
358C8—44no—
359C8—82no—
360C8—81no—
361C8—82no—
362C8—81no—
363C8—82no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—24no—
369C22—24no—
370C22#143911yescharacteristic
371C22#181011yescharacteristic
372C22#181111yescharacteristic
373C22#185512yes—
374C22#185512yes—
375C22#185712yes—
376C22#186812yes—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—44no—
388C4—82no—
389C4#200311yescharacteristic
390C4#200511yescharacteristic
391C4#203812yes—
392C2—21no—
393C2—21no—
394C2—22no—
395C2#886514yes—
396C2#1108811yescharacteristic
397C2#1109711yescharacteristic
398C2#1113611yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
socleC23#385
prime radicalC24C2×C4⋊C4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×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
#218222
C2×#19852
C2×#15732
C2×#14612
C2×#13022
#78792