Finite Group Databasebeta

← #117139

Subgroups — #117139

Order 512.

700 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1993C211yesmaximal, characteristic
2C2×#1849C211yesmaximal, characteristic
3C2×#1549C211yesmaximal, characteristic
4C2×#1548C211yesmaximal, characteristic
5C2×#1286C211yesmaximal, characteristic
6C2×#1286C211yesmaximal, characteristic
7C2×#1281C211yesmaximal, characteristic
8C22×C4⋊Q8C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C22×#108—22no—
12C2×#423C2211yescharacteristic
13C2×#423C2211yescharacteristic
14C22×#97C2211yescharacteristic
15C2×#382C2211yescharacteristic
16#1993—22no—
17#1993C414yes—
18#1849—22no—
19#1849—22no—
20C2×#340—22no—
21#1549—22no—
22#1549—22no—
23#1548—22no—
24#1548—22no—
25C2×#333—22no—
26C2×#332—22no—
27#1286—22no—
28#1286—22no—
29#1281—22no—
30C23×Q8—21no—
31C22×M16—21no—
32C22×M16—21no—
33C23×C8D412yes—
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⋊Q8C2×C412yes—
44C2×C4⋊Q8D412yes—
45C2×C4⋊Q8Q812yes—
46C22×C4⋊C4—21no—
47C22×C4⋊C4—21no—
48C22×C4⋊C4—21no—
49C22×C42C2311yescharacteristic
50#431—21no—
51#431—21no—
52#431—21no—
53#431—21no—
54#431—21no—
55#431—21no—
56#431D412yes—
57#431D412yes—
58C2×#108—28no—
59C2×#108—44no—
60C2×#108—44no—
61#423—21no—
62#423—21no—
63#423—21no—
64#423—21no—
65#423—21no—
66#423—21no—
67#423D412yes—
68#423D412yes—
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×C22⋊C8—21no—
76C2×C22⋊C8—21no—
77C2×#97—21no—
78C2×#97—21no—
79C2×#97—21no—
80C2×#97—21no—
81C2×#97C2×C412yes—
82C2×#97D412yes—
83C2×C4×C8—21no—
84C2×C4×C8—21no—
85#382—21no—
86#382—21no—
87#382—21no—
88#382C2×C412yes—
89C2×#95—21no—
90C2×#95—21no—
91#340—28no—
92#333—28no—
93#332—28no—
94C22×Q8—22no—
95C22×Q8—22no—
96C22×Q8—22no—
97C22×Q8—41no—
98C22×Q8—41no—
99C22×Q8—41no—
100C22×Q8—84no—
101C23×C4—41no—
102C23×C4—41no—
103C23×C4C2×D411yescharacteristic
104C23×C4#4111yescharacteristic
105C23×C4#4111yescharacteristic
106C2×M16—22no—
107C2×M16—22no—
108C2×M16—41no—
109C2×M16—41no—
110C2×M16—42no—
111C2×M16—42no—
112C2×M16—42no—
113C2×M16—42no—
114C22×C8—22no—
115C22×C8—22no—
116C22×C8—22no—
117C22×C8—22no—
118C22×C8—41no—
119C22×C8—41no—
120C22×C8—41no—
121C22×C8—41no—
122C22×C8C22⋊C414yes—
123C22×C8SD1614yes—
124C22×C8Q1614yes—
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—22no—
134C4⋊Q8—41no—
135C4⋊Q8—41no—
136C4⋊Q8—41no—
137C4⋊Q8—41no—
138C4⋊Q8—41no—
139C4⋊Q8—41no—
140C4⋊Q8C4⋊C414yes—
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—22no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—41no—
154C2×C4⋊C4—42no—
155C2×C4⋊C4—42no—
156C2×C4⋊C4—41no—
157C2×C42C22×C411yescharacteristic
158C2×C42C2×D411yescharacteristic
159C2×C42C2×D411yescharacteristic
160C2×C42C2×D411yescharacteristic
161C2×C42C2×D411yescharacteristic
162C2×C42C2×D411yescharacteristic
163C2×C42C2×D411yescharacteristic
164C2×C42C2×Q811yescharacteristic
165C2×C42#4111yescharacteristic
166C2×C42#4111yescharacteristic
167C2×C42#4111yescharacteristic
168C2×C42#4111yescharacteristic
169#108—416no—
170C4⋊C8—22no—
171C4⋊C8—22no—
172C4⋊C8—22no—
173C4⋊C8—22no—
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8—41no—
177C4⋊C8—41no—
178C4⋊C8—41no—
179C4⋊C8—41no—
180C4⋊C8—41no—
181C4⋊C8—41no—
182C22⋊C8—22no—
183C22⋊C8—22no—
184C22⋊C8—41no—
185C22⋊C8—41no—
186#97—22no—
187#97—22no—
188#97—22no—
189#97—22no—
190C4×C8—22no—
191C4×C8—22no—
192C4×C8—41no—
193C4×C8—41no—
194#95—22no—
195#95—22no—
196#95—41no—
197#95—41no—
198C24#12411yescharacteristic
199C2×Q8—24no—
200C2×Q8—42no—
201C2×Q8—42no—
202C2×Q8—42no—
203C2×Q8—84no—
204C2×Q8—84no—
205C2×Q8—84no—
206C2×Q8—84no—
207C2×Q8—84no—
208C2×Q8—84no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—84no—
216C22×C4—82no—
217C22×C4—82no—
218C22×C4—82no—
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#12411yescharacteristic
233C22×C4#12411yescharacteristic
234C22×C4#12611yescharacteristic
235C22×C4#12611yescharacteristic
236C22×C4#12711yescharacteristic
237C22×C4C2×SD1612yes—
238C22×C4C2×Q1612yes—
239C22×C4AGL(1,ℤ/8)12yes—
240C22×C4#13712yes—
241M16—44no—
242M16—44no—
243M16—81no—
244M16—81no—
245M16—81no—
246M16—81no—
247C2×C8—24no—
248C2×C8—24no—
249C2×C8—24no—
250C2×C8—24no—
251C2×C8—24no—
252C2×C8—24no—
253C2×C8—42no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—82no—
258C2×C8—82no—
259C2×C8—82no—
260C2×C8—82no—
261C2×C8#10318yes—
262C4⋊C4—24no—
263C4⋊C4—24no—
264C4⋊C4—42no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—44no—
271C4⋊C4—81no—
272C4⋊C4—81no—
273C42C2×C4⋊C411yescharacteristic
274C42#11711yescharacteristic
275C42C4×D411yescharacteristic
276C42C4×D411yescharacteristic
277C42#12011yescharacteristic
278C42#12011yescharacteristic
279C42#12111yescharacteristic
280C42#12111yescharacteristic
281C42#12111yescharacteristic
282C42#12111yescharacteristic
283C42#12111yescharacteristic
284C42C22⋊Q811yescharacteristic
285C42C22⋊Q811yescharacteristic
286C42C22⋊Q811yescharacteristic
287C42#12311yescharacteristic
288C42#12311yescharacteristic
289C23—22no—
290C23—22no—
291C23#39011yescharacteristic
292C23#39311yescharacteristic
293C23#39711yescharacteristic
294C23#48712yes—
295C23#48912yes—
296Q8—84no—
297Q8—84no—
298Q8—84no—
299Q8—84no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
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—84no—
314C2×C4—84no—
315C2×C4—84no—
316C2×C4—82no—
317C2×C4—82no—
318C2×C4—82no—
319C2×C4—164no—
320C2×C4#38011yescharacteristic
321C2×C4#38511yescharacteristic
322C2×C4#38511yescharacteristic
323C2×C4#38611yescharacteristic
324C2×C4#38811yescharacteristic
325C2×C4#38811yescharacteristic
326C2×C4#39211yescharacteristic
327C2×C4#39411yescharacteristic
328C2×C4#39411yescharacteristic
329C2×C4#39611yescharacteristic
330C2×C4#39611yescharacteristic
331C2×C4#39911yescharacteristic
332C2×C4C2×#10312yes—
333C2×C4#41712yes—
334C2×C4#45012yes—
335C2×C4#45112yes—
336C2×C4#46012yes—
337C2×C4#46212yes—
338C2×C4#47512yes—
339C2×C4#47712yes—
340C2×C4#48312yes—
341C2×C4#48412yes—
342C2×C4#49211yescharacteristic
343C2×C4#49411yescharacteristic
344C2×C4#49611yescharacteristic
345C2×C4#49711yescharacteristic
346C8—28no—
347C8—82no—
348C8—82no—
349C8—82no—
350C8—82no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—24no—
356C22—24no—
357C22#143911yescharacteristic
358C22#195611yescharacteristic
359C22#195911yescharacteristic
360C22#202412yes—
361C22#207212yes—
362C22#208112yes—
363C22#208212yes—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—84no—
373C4—162no—
374C4#180312yes—
375C4#187212yes—
376C4#201411yescharacteristic
377C4#201611yescharacteristic
378C4#209511yescharacteristic
379C4#209611yescharacteristic
380C2—21no—
381C2—21no—
382C2—22no—
383C2#1063314yes—
384C2#1105011yescharacteristic
385C2#1113311yescharacteristic
386C2#1113411yescharacteristic
subgroupG/H
center, socleC23#397
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#124
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
C2×#19932
C2×#18492
C2×#15492
C2×#15482
C2×#12862
C2×#12812