Finite Group Databasebeta

← #107446

Subgroups — #107446

Order 512.

716 conjugacy classes of subgroups.

The subgroup lattice has 387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60250C211yesmaximal, characteristic
2#17718C211yesmaximal, characteristic
3C2×#1485C211yesmaximal, characteristic
4#8064C211yesmaximal, characteristic
5#8054C211yesmaximal, characteristic
6#7884C211yesmaximal, characteristic
7#7882C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9#2986—22no—
10#2985—22no—
11#2984—22no—
12#2983—21no—
13#2982—21no—
14#2962C414yes—
15#2960—22no—
16#2924—22no—
17#2920C2211yescharacteristic
18#2920C2211yescharacteristic
19C2×#431C2211yescharacteristic
20C2×#431C2211yescharacteristic
21C2×#431C2211yescharacteristic
22C2×C4×M16C2211yescharacteristic
23#1554—22no—
24#1548C412yes—
25#1546C412yes—
26#1542—22no—
27#1485—22no—
28#1485C414yes—
29C2×Q8⋊C8—22no—
30#1299—22no—
31#1298—22no—
32#1278—22no—
33#1278—21no—
34#1278—21no—
35C22×M16—21no—
36#533—21no—
37#533—21no—
38#533—21no—
39#533—21no—
40#533C2×C412yes—
41#533C2×C412yes—
42#533D412yes—
43#533D412yes—
44C2×C4⋊Q8C2×C411yescharacteristic
45C2×C4⋊Q8C2×C411yescharacteristic
46C2×#125—21no—
47C2×C22⋊Q8—21no—
48C2×C22⋊Q8Q812yes—
49C2×C4×Q8—21no—
50C2×C4×Q8D412yes—
51C2×#117—21no—
52C22×C42C2311yescharacteristic
53#446—24no—
54#446—24no—
55#446—28no—
56#446—24no—
57C8×Q8—24no—
58C8×Q8—24no—
59C8×Q8—24no—
60#433—28no—
61#432—24no—
62#432—21no—
63#432—21no—
64#432—21no—
65#432—21no—
66#431—24no—
67#431—21no—
68#431—21no—
69#431—21no—
70#431—21no—
71#431—21no—
72#431—21no—
73#431—21no—
74#431—21no—
75#431—21no—
76#431—21no—
77#431—21no—
78#431—21no—
79#431C2×C412yes—
80#431C2×C412yes—
81#431D411yescharacteristic
82#431D411yescharacteristic
83#431D412yes—
84#424—24no—
85#423C2×C412yes—
86#423D412yes—
87C2×C4⋊C8—21no—
88C2×C4⋊C8—21no—
89C2×C4⋊C8C2×C412yes—
90#407—21no—
91#407D412yes—
92C2×C22⋊C8—21no—
93C2×C22⋊C8—21no—
94C2×C22⋊C8—21no—
95#405—24no—
96C4×M16—21no—
97C4×M16—21no—
98C4×M16—21no—
99C4×M16—21no—
100C4×M16C2×C412yes—
101C4×M16C2×C412yes—
102C2×#97—21no—
103C2×C4×C8—21no—
104C2×C4×C8—21no—
105C2×C4×C8—21no—
106C2×C4×C8—21no—
107#333—24no—
108#332—24no—
109Q8⋊C8—28no—
110C22×Q8—21no—
111C22×Q8C4⋊C412yes—
112C23×C4C2×D411yescharacteristic
113C23×C4C2×Q811yescharacteristic
114C23×C4#4111yescharacteristic
115C2×M16—24no—
116C2×M16—22no—
117C2×M16—22no—
118C2×M16—42no—
119C2×M16—41no—
120C2×M16C22⋊C414yes—
121C22×C8—22no—
122C22×C8—41no—
123C22×C8—41no—
124C22×C8—41no—
125C4⋊Q8—21no—
126C4⋊Q8—21no—
127C4⋊Q8—21no—
128C4⋊Q8—21no—
129C4⋊Q8C4212yes—
130C4⋊Q8C4212yes—
131C4⋊Q8C22⋊C412yes—
132C4⋊Q8C22⋊C412yes—
133#125—22no—
134#125—22no—
135#125—22no—
136#125—22no—
137C22⋊Q8—22no—
138C22⋊Q8—22no—
139C22⋊Q8—22no—
140C22⋊Q8—22no—
141C22⋊Q8—22no—
142C22⋊Q8—22no—
143C22⋊Q8C4⋊C414yes—
144C22⋊Q8C4⋊C414yes—
145C4×Q8—22no—
146C4×Q8—22no—
147C4×Q8—22no—
148C4×Q8—22no—
149C4×Q8—22no—
150C4×Q8—22no—
151C4×Q8C22⋊C414yes—
152C4×Q8C22⋊C414yes—
153#117—22no—
154#117—22no—
155#117—22no—
156#117—22no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4C4⋊C412yes—
163C2×C22⋊C4—22no—
164C2×C42—22no—
165C2×C42C22×C411yescharacteristic
166C2×C42C22×C411yescharacteristic
167C2×C42C22×C411yescharacteristic
168C2×C42C2×D411yescharacteristic
169C2×C42C2×D411yescharacteristic
170C2×C42C2×D411yescharacteristic
171C2×C42C2×D411yescharacteristic
172C2×C42C2×D411yescharacteristic
173C2×C42C2×D411yescharacteristic
174C2×C42#4111yescharacteristic
175C2×C42#4111yescharacteristic
176C2×C42#4111yescharacteristic
177C4⋊C8—28no—
178C4⋊C8—28no—
179C4⋊C8—22no—
180C4⋊C8—22no—
181C4⋊C8—22no—
182C4⋊C8—22no—
183C4⋊C8—22no—
184C4⋊C8—22no—
185C4⋊C8—22no—
186C4⋊C8—41no—
187C4⋊C8—41no—
188C4⋊C8C22⋊C412yes—
189C4⋊C8C22⋊C412yes—
190C22⋊C8—21no—
191C22⋊C8—21no—
192C22⋊C8—22no—
193C22⋊C8—22no—
194C22⋊C8—22no—
195C22⋊C8—22no—
196C22⋊C8—22no—
197C22⋊C8—41no—
198C22⋊C8—41no—
199C22⋊C8—41no—
200C22⋊C8—41no—
201#97—28no—
202#97—22no—
203#97—22no—
204#97—41no—
205#97—41no—
206C4×C8—28no—
207C4×C8—22no—
208C4×C8—22no—
209C4×C8—22no—
210C4×C8—22no—
211C4×C8—21no—
212C4×C8—22no—
213C4×C8—21no—
214C4×C8—41no—
215C4×C8—41no—
216C4×C8—41no—
217C4×C8—41no—
218C24C22⋊Q811yescharacteristic
219C2×Q8—22no—
220C2×Q8—22no—
221C2×Q8—22no—
222C2×Q8—44no—
223C2×Q8—42no—
224C2×Q8—42no—
225C2×Q8#9514yes—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4C2×C22⋊C411yescharacteristic
233C22×C4C2×C4⋊C411yescharacteristic
234C22×C4C2×C4⋊C411yescharacteristic
235C22×C4C2×C4⋊C411yescharacteristic
236C22×C4#11711yescharacteristic
237C22×C4C4×D411yescharacteristic
238C22×C4C4×D411yescharacteristic
239C22×C4C4×D411yescharacteristic
240C22×C4C4×D411yescharacteristic
241C22×C4#12011yescharacteristic
242C22×C4#12011yescharacteristic
243C22×C4#12111yescharacteristic
244C22×C4#12111yescharacteristic
245C22×C4C22⋊Q811yescharacteristic
246C22×C4C22⋊Q811yescharacteristic
247C22×C4C22⋊Q811yescharacteristic
248C22×C4#12311yescharacteristic
249C22×C4#12311yescharacteristic
250M16—24no—
251M16—44no—
252M16—42no—
253M16—44no—
254M16—42no—
255M16—42no—
256C2×C8—22no—
257C2×C8—24no—
258C2×C8—22no—
259C2×C8—44no—
260C2×C8—44no—
261C2×C8—42no—
262C2×C8—42no—
263C2×C8—42no—
264C2×C8—42no—
265C2×C8—82no—
266C2×C8—82no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—24no—
271C4⋊C4—24no—
272C4⋊C4—24no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—24no—
278C4⋊C4#9514yes—
279C22⋊C4—24no—
280C22⋊C4—24no—
281C42—24no—
282C42—24no—
283C42C2×C4211yescharacteristic
284C42C2×C22⋊C411yescharacteristic
285C42C2×C22⋊C411yescharacteristic
286C42C2×C22⋊C411yescharacteristic
287C42C2×C22⋊C411yescharacteristic
288C42#11711yescharacteristic
289C42C4×D411yescharacteristic
290C42C4×D411yescharacteristic
291C42C4×D411yescharacteristic
292C42C4×D411yescharacteristic
293C42#12011yescharacteristic
294C42#12011yescharacteristic
295C42#12111yescharacteristic
296C42#12111yescharacteristic
297C42#12311yescharacteristic
298C42#12311yescharacteristic
299C23—22no—
300C23—41no—
301C23—41no—
302C23#38011yescharacteristic
303C23#38511yescharacteristic
304C23#38511yescharacteristic
305Q8—44no—
306Q8—44no—
307Q8—44no—
308Q8—42no—
309Q8—42no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—44no—
332C2×C4—82no—
333C2×C4C2×#9511yescharacteristic
334C2×C4C4×C22⋊C411yescharacteristic
335C2×C4C4×C22⋊C411yescharacteristic
336C2×C4#37911yescharacteristic
337C2×C4#38011yescharacteristic
338C2×C4#38111yescharacteristic
339C2×C4#38511yescharacteristic
340C2×C4#38511yescharacteristic
341C2×C4#38611yescharacteristic
342C2×C4#38611yescharacteristic
343C2×C4#38611yescharacteristic
344C2×C4#38611yescharacteristic
345C2×C4#44312yes—
346C2×C4#44412yes—
347C8—44no—
348C8—42no—
349C8—42no—
350C8—44no—
351C8—82no—
352C8—82no—
353C8—82no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—82no—
363C22C22⋊#9511yescharacteristic
364C22#186612yes—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—44no—
374C4—44no—
375C4#176411yescharacteristic
376C4#176511yescharacteristic
377C4#179612yes—
378C4#185812yes—
379C4#187612yes—
380C2—22no—
381C2—41no—
382C2—41no—
383C2#1075311yescharacteristic
384C2#1077711yescharacteristic
385C2#1079111yescharacteristic
subgroupG/H
centerC2×C4#379
commutatorC42C2×C42
Frattini, cosocleC22×C42C23
socleC22C22⋊#95
prime radicalC24C22⋊Q8
LCSG ▷ C42 ▷ 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
#602502
#177182
C2×#14852
#80642
#80542
#78842
#78822