Finite Group Databasebeta

← #110836

Subgroups — #110836

Order 512.

642 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1544C211yesmaximal, characteristic
2C2×#1493C211yesmaximal, characteristic
3C2×#1485C211yesmaximal, characteristic
4C2×#1450C211yesmaximal, characteristic
5C2×#1299C211yesmaximal, characteristic
6C2×#1278C211yesmaximal, characteristic
7#7880C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C2×C4×M16C2211yescharacteristic
14C22×C4×C8C2211yescharacteristic
15#1544—22no—
16#1544—22no—
17C2×#332C412yes—
18C2×#332C412yes—
19#1493—22no—
20#1493C414yes—
21#1485—22no—
22#1485C414yes—
23C2×Q8⋊C8—22no—
24C2×Q8⋊C8—21no—
25C2×Q8⋊C8—21no—
26#1450—22no—
27#1450—22no—
28C2×#322—21no—
29C2×C82—21no—
30#1299—22no—
31#1278—22no—
32#1277—22no—
33C22×M16—21no—
34C22×M16—21no—
35C23×C8—21no—
36#533—21no—
37#533—21no—
38#533—21no—
39#533—21no—
40#533—21no—
41#533—21no—
42#533C2×C412yes—
43#533C2×C412yes—
44C2×C4⋊Q8C2×C411yescharacteristic
45C2×C4⋊Q8C2×C411yescharacteristic
46C2×#125—21no—
47C2×C22⋊Q8—21no—
48C2×C22⋊Q8—21no—
49C2×C4×Q8—21no—
50C2×C4×Q8—21no—
51C2×#117—21no—
52C22×C42C2311yescharacteristic
53#431—21no—
54#431—21no—
55#431—21no—
56#431—21no—
57#431—21no—
58#431—21no—
59#431—21no—
60#431—21no—
61#431C2×C412yes—
62#431D412yes—
63#431D412yes—
64#431D412yes—
65#423—21no—
66#423—21no—
67#423—21no—
68#423C2×C412yes—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—21no—
71C2×C4⋊C8C2×C412yes—
72C2×C4⋊C8C2×C412yes—
73C2×C4⋊C8D412yes—
74C2×C22⋊C8—21no—
75C2×C22⋊C8—21no—
76C2×C22⋊C8—21no—
77C4×M16—21no—
78C4×M16—21no—
79C4×M16—21no—
80C4×M16C2×C412yes—
81C2×#97—21no—
82C2×C4×C8—21no—
83C2×C4×C8—21no—
84C2×C4×C8—21no—
85C2×C4×C8—21no—
86C2×C4×C8—21no—
87C2×C4×C8—21no—
88C2×C4×C8—21no—
89C2×C4×C8C2×C412yes—
90C2×C4×C8D411yescharacteristic
91C2×C4×C8D411yescharacteristic
92C2×C4×C8D412yes—
93#332—24no—
94#332—24no—
95Q8⋊C8—28no—
96Q8⋊C8—24no—
97Q8⋊C8—24no—
98#322—24no—
99C82—24no—
100C22×Q8—21no—
101C22×Q8—21no—
102C23×C4#4111yescharacteristic
103C23×C4#4111yescharacteristic
104C23×C4#4111yescharacteristic
105C2×M16—24no—
106C2×M16—22no—
107C2×M16—22no—
108C2×M16—42no—
109C2×M16—41no—
110C2×M16—41no—
111C2×M16—82no—
112C22×C8—28no—
113C22×C8—22no—
114C22×C8—22no—
115C22×C8—21no—
116C22×C8—21no—
117C22×C8—22no—
118C22×C8—22no—
119C22×C8—22no—
120C22×C8—41no—
121C22×C8—41no—
122C4⋊Q8—21no—
123C4⋊Q8—21no—
124C4⋊Q8—21no—
125C4⋊Q8—21no—
126C4⋊Q8—21no—
127C4⋊Q8—21no—
128C4⋊Q8C4212yes—
129C4⋊Q8C4212yes—
130#125—22no—
131#125—22no—
132#125—41no—
133#125—41no—
134C22⋊Q8—22no—
135C22⋊Q8—22no—
136C22⋊Q8—22no—
137C22⋊Q8—22no—
138C22⋊Q8—41no—
139C22⋊Q8—41no—
140C22⋊Q8—41no—
141C22⋊Q8—41no—
142C4×Q8—22no—
143C4×Q8—22no—
144C4×Q8—22no—
145C4×Q8—22no—
146C4×Q8—41no—
147C4×Q8—41no—
148C4×Q8—41no—
149C4×Q8—41no—
150#117—22no—
151#117—22no—
152#117—41no—
153#117—41no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4—41no—
160C2×C22⋊C4—41no—
161C2×C42—41no—
162C2×C42C22×C411yescharacteristic
163C2×C42C22×C411yescharacteristic
164C2×C42C22×C411yescharacteristic
165C2×C42C2×D411yescharacteristic
166C2×C42C2×D411yescharacteristic
167C2×C42C2×D411yescharacteristic
168C2×C42C2×D411yescharacteristic
169C2×C42C2×D411yescharacteristic
170C2×C42C2×D411yescharacteristic
171C2×C42#4111yescharacteristic
172C2×C42#4111yescharacteristic
173C2×C42#4111yescharacteristic
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8—22no—
177C4⋊C8—22no—
178C4⋊C8—22no—
179C4⋊C8—22no—
180C4⋊C8—41no—
181C4⋊C8—41no—
182C4⋊C8C22⋊C414yes—
183C4⋊C8C22⋊C414yes—
184C22⋊C8—22no—
185C22⋊C8—22no—
186C22⋊C8—22no—
187C22⋊C8—22no—
188C22⋊C8—41no—
189C22⋊C8—41no—
190#97—22no—
191#97—41no—
192C4×C8—22no—
193C4×C8—22no—
194C4×C8—22no—
195C4×C8—21no—
196C4×C8—22no—
197C4×C8—22no—
198C4×C8—21no—
199C4×C8—22no—
200C4×C8—22no—
201C4×C8—41no—
202C4×C8—41no—
203C4×C8—41no—
204C4×C8C22⋊C412yes—
205C4×C8C22⋊C412yes—
206C24#12611yescharacteristic
207C2×Q8—22no—
208C2×Q8—22no—
209C2×Q8—41no—
210C2×Q8—41no—
211C2×Q8—42no—
212C2×Q8—44no—
213C2×Q8—42no—
214C22×C4—24no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—41no—
220C22×C4—41no—
221C22×C4#11711yescharacteristic
222C22×C4#11711yescharacteristic
223C22×C4#11711yescharacteristic
224C22×C4C4×D411yescharacteristic
225C22×C4C4×D411yescharacteristic
226C22×C4C4×D411yescharacteristic
227C22×C4C4×D411yescharacteristic
228C22×C4C4×D411yescharacteristic
229C22×C4C4×D411yescharacteristic
230C22×C4#12111yescharacteristic
231C22×C4#12111yescharacteristic
232C22×C4#12111yescharacteristic
233C22×C4#12311yescharacteristic
234C22×C4#12311yescharacteristic
235C22×C4#12311yescharacteristic
236C22×C4#12411yescharacteristic
237C22×C4#12411yescharacteristic
238C22×C4#12411yescharacteristic
239M16—24no—
240M16—44no—
241M16—42no—
242M16—82no—
243M16—82no—
244C2×C8—24no—
245C2×C8—24no—
246C2×C8—28no—
247C2×C8—28no—
248C2×C8—22no—
249C2×C8—22no—
250C2×C8—24no—
251C2×C8—24no—
252C2×C8—44no—
253C2×C8—42no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—42no—
259C2×C8—42no—
260C2×C8—44no—
261C2×C8—82no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—41no—
267C4⋊C4—42no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—41no—
273C4⋊C4—42no—
274C22⋊C4—42no—
275C22⋊C4—42no—
276C42—42no—
277C42—42no—
278C42C2×C4211yescharacteristic
279C42C2×C22⋊C411yescharacteristic
280C42C2×C22⋊C411yescharacteristic
281C42C2×C22⋊C411yescharacteristic
282C42C4×D411yescharacteristic
283C42C4×D411yescharacteristic
284C42C4×D411yescharacteristic
285C42C4×D411yescharacteristic
286C42C4×D411yescharacteristic
287C42C4×D411yescharacteristic
288C42#12011yescharacteristic
289C42#12111yescharacteristic
290C42#12111yescharacteristic
291C42#12111yescharacteristic
292C42#12611yescharacteristic
293C42#12711yescharacteristic
294C23—22no—
295C23—22no—
296C23—22no—
297C23#38811yescharacteristic
298C23#38811yescharacteristic
299C23#38811yescharacteristic
300Q8—44no—
301Q8—42no—
302Q8—42no—
303Q8—82no—
304Q8—82no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4C4×C22⋊C411yescharacteristic
329C2×C4C4×C22⋊C411yescharacteristic
330C2×C4C4×C22⋊C411yescharacteristic
331C2×C4#38611yescharacteristic
332C2×C4#38611yescharacteristic
333C2×C4#38611yescharacteristic
334C2×C4#38811yescharacteristic
335C2×C4#38811yescharacteristic
336C2×C4#38811yescharacteristic
337C2×C4#39011yescharacteristic
338C2×C4#39011yescharacteristic
339C2×C4#39011yescharacteristic
340C2×C4#44312yes—
341C2×C4#44314yes—
342C2×C4#44412yes—
343C2×C4#47112yes—
344C2×C4#47312yes—
345C8—24no—
346C8—24no—
347C8—44no—
348C8—44no—
349C8—44no—
350C8—82no—
351C8—82no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—44no—
359C22#143711yescharacteristic
360C22#192912yes—
361C22#193012yes—
362C22#193712yes—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—82no—
370C4—82no—
371C4#176412yes—
372C4#176411yescharacteristic
373C4#176511yescharacteristic
374C4#187612yes—
375C4#190812yes—
376C4#197412yes—
377C4#197711yescharacteristic
378C4#197911yescharacteristic
379C2—41no—
380C2—41no—
381C2#958514yes—
382C2#1092911yescharacteristic
383C2#1093411yescharacteristic
384C2#1094211yescharacteristic
subgroupG/H
centerC22×C4#121
commutatorC42C2×C42
Frattini, cosocleC22×C42C23
socleC23#388
prime radicalC24#126
LCSG ▷ C42 ▷ 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
C2×#15442
C2×#14932
C2×#14852
C2×#14502
C2×#12992
C2×#12782
#78802