Finite Group Databasebeta

← #117142

Subgroups — #117142

Order 512.

656 conjugacy classes of subgroups.

The subgroup lattice has 385 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1993C211yesmaximal, characteristic
2C2×#1838C211yesmaximal, characteristic
3C2×#1549C211yesmaximal, characteristic
4C2×#1548C211yesmaximal, characteristic
5C2×#1286C211yesmaximal, characteristic
6C2×#1286C211yesmaximal, characteristic
7C2×#1281C211yesmaximal, characteristic
8C22×C4⋊Q8C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C22×#97C2211yescharacteristic
14C2×#382C2211yescharacteristic
15#1993—22no—
16#1993C414yes—
17#1838—22no—
18#1838—22no—
19C2×#341—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—
58#423—21no—
59#423—21no—
60#423—21no—
61#423—21no—
62#423—21no—
63#423—21no—
64#423D412yes—
65#423D412yes—
66C2×C4⋊C8—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—21no—
71C2×C4⋊C8—21no—
72C2×C22⋊C8—21no—
73C2×C22⋊C8—21no—
74C2×#97—21no—
75C2×#97—21no—
76C2×#97—21no—
77C2×#97—21no—
78C2×#97C2×C412yes—
79C2×#97D412yes—
80C2×C4×C8—21no—
81C2×C4×C8—21no—
82#382—21no—
83#382—21no—
84#382—21no—
85#382C2×C412yes—
86C2×#95—21no—
87C2×#95—21no—
88#341—28no—
89#340—28no—
90#333—28no—
91#332—28no—
92C22×Q8—22no—
93C22×Q8—22no—
94C22×Q8—22no—
95C22×Q8—41no—
96C22×Q8—41no—
97C22×Q8—41no—
98C22×Q8—84no—
99C23×C4—41no—
100C23×C4—41no—
101C23×C4C2×D411yescharacteristic
102C23×C4#4111yescharacteristic
103C23×C4#4111yescharacteristic
104C2×M16—22no—
105C2×M16—22no—
106C2×M16—41no—
107C2×M16—41no—
108C2×M16—42no—
109C2×M16—42no—
110C2×M16—42no—
111C2×M16—42no—
112C22×C8—22no—
113C22×C8—22no—
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—
123C4⋊Q8—22no—
124C4⋊Q8—22no—
125C4⋊Q8—22no—
126C4⋊Q8—22no—
127C4⋊Q8—22no—
128C4⋊Q8—22no—
129C4⋊Q8—22no—
130C4⋊Q8—22no—
131C4⋊Q8—22no—
132C4⋊Q8—41no—
133C4⋊Q8—41no—
134C4⋊Q8—41no—
135C4⋊Q8—41no—
136C4⋊Q8—41no—
137C4⋊Q8—41no—
138C4⋊Q8C4⋊C414yes—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—41no—
147C2×C4⋊C4—41no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—42no—
153C2×C4⋊C4—42no—
154C2×C4⋊C4—41no—
155C2×C42C22×C411yescharacteristic
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
167C4⋊C8—22no—
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—41no—
177C4⋊C8—41no—
178C4⋊C8—41no—
179C22⋊C8—22no—
180C22⋊C8—22no—
181C22⋊C8—41no—
182C22⋊C8—41no—
183#97—22no—
184#97—22no—
185#97—22no—
186#97—22no—
187C4×C8—22no—
188C4×C8—22no—
189C4×C8—41no—
190C4×C8—41no—
191#95—22no—
192#95—22no—
193#95—41no—
194#95—41no—
195C24#12411yescharacteristic
196C2×Q8—24no—
197C2×Q8—42no—
198C2×Q8—42no—
199C2×Q8—42no—
200C2×Q8—84no—
201C2×Q8—84no—
202C2×Q8—84no—
203C2×Q8—84no—
204C2×Q8—84no—
205C2×Q8—84no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—84no—
213C22×C4—82no—
214C22×C4—82no—
215C22×C4—82no—
216C22×C4C2×C22⋊C411yescharacteristic
217C22×C4C4×D411yescharacteristic
218C22×C4C4×D411yescharacteristic
219C22×C4#12011yescharacteristic
220C22×C4#12111yescharacteristic
221C22×C4#12111yescharacteristic
222C22×C4#12111yescharacteristic
223C22×C4C22⋊Q811yescharacteristic
224C22×C4C22⋊Q811yescharacteristic
225C22×C4C22⋊Q811yescharacteristic
226C22×C4#12311yescharacteristic
227C22×C4#12311yescharacteristic
228C22×C4#12311yescharacteristic
229C22×C4#12411yescharacteristic
230C22×C4#12411yescharacteristic
231C22×C4#12611yescharacteristic
232C22×C4#12611yescharacteristic
233C22×C4#12711yescharacteristic
234C22×C4#13512yes—
235C22×C4#13512yes—
236C22×C4#13712yes—
237C22×C4#13712yes—
238M16—44no—
239M16—44no—
240M16—81no—
241M16—81no—
242M16—81no—
243M16—81no—
244C2×C8—24no—
245C2×C8—24no—
246C2×C8—24no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—42no—
253C2×C8—42no—
254C2×C8—42no—
255C2×C8—82no—
256C2×C8—82no—
257C2×C8—82no—
258C2×C8—82no—
259C4⋊C4—24no—
260C4⋊C4—24no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—44no—
268C4⋊C4—81no—
269C4⋊C4—81no—
270C42C2×C4⋊C411yescharacteristic
271C42#11711yescharacteristic
272C42C4×D411yescharacteristic
273C42C4×D411yescharacteristic
274C42#12011yescharacteristic
275C42#12011yescharacteristic
276C42#12111yescharacteristic
277C42#12111yescharacteristic
278C42#12111yescharacteristic
279C42#12111yescharacteristic
280C42#12111yescharacteristic
281C42C22⋊Q811yescharacteristic
282C42C22⋊Q811yescharacteristic
283C42C22⋊Q811yescharacteristic
284C42#12311yescharacteristic
285C42#12311yescharacteristic
286C23—22no—
287C23—22no—
288C23#39011yescharacteristic
289C23#39311yescharacteristic
290C23#39711yescharacteristic
291C23#48812yes—
292C23#49112yes—
293Q8—84no—
294Q8—84no—
295Q8—84no—
296Q8—84no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—44no—
310C2×C4—84no—
311C2×C4—84no—
312C2×C4—84no—
313C2×C4—82no—
314C2×C4—82no—
315C2×C4—82no—
316C2×C4—164no—
317C2×C4#38011yescharacteristic
318C2×C4#38511yescharacteristic
319C2×C4#38511yescharacteristic
320C2×C4#38611yescharacteristic
321C2×C4#38811yescharacteristic
322C2×C4#38811yescharacteristic
323C2×C4#39211yescharacteristic
324C2×C4#39411yescharacteristic
325C2×C4#39411yescharacteristic
326C2×C4#39611yescharacteristic
327C2×C4#39611yescharacteristic
328C2×C4#39911yescharacteristic
329C2×C4#41612yes—
330C2×C4#41912yes—
331C2×C4#45212yes—
332C2×C4#45212yes—
333C2×C4#46412yes—
334C2×C4#46412yes—
335C2×C4#47912yes—
336C2×C4#47912yes—
337C2×C4#48512yes—
338C2×C4#48512yes—
339C2×C4#49511yescharacteristic
340C2×C4#49511yescharacteristic
341C2×C4#49711yescharacteristic
342C2×C4#49711yescharacteristic
343C8—44no—
344C8—82no—
345C8—82no—
346C8—82no—
347C8—82no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—24no—
353C22—24no—
354C22#143911yescharacteristic
355C22#195811yescharacteristic
356C22#196011yescharacteristic
357C22#202612yes—
358C22#207412yes—
359C22#208112yes—
360C22#208212yes—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—84no—
370C4—162no—
371C4#180512yes—
372C4#187312yes—
373C4#201511yescharacteristic
374C4#201511yescharacteristic
375C4#209711yescharacteristic
376C4#209711yescharacteristic
377C2—21no—
378C2—21no—
379C2—22no—
380C2#1063614yes—
381C2#1105211yescharacteristic
382C2#1113311yescharacteristic
383C2#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×#18382
C2×#15492
C2×#15482
C2×#12862
C2×#12812