Finite Group Databasebeta

← #107351

Subgroups — #107351

Order 512.

684 conjugacy classes of subgroups.

The subgroup lattice has 375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60251C211yesmaximal, characteristic
2C2×#1559C211yesmaximal, characteristic
3#17479C211yesmaximal, characteristic
4#8089C211yesmaximal, characteristic
5#8081C211yesmaximal, characteristic
6#8010C211yesmaximal, characteristic
7#7990C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9#2987C414yes—
10#2985—22no—
11#2984—22no—
12#2983—22no—
13#2962—22no—
14#2961—22no—
15#2924—22no—
16#2920C2211yescharacteristic
17#2920C2211yescharacteristic
18C2×#432C2211yescharacteristic
19C2×#432C2211yescharacteristic
20C2×#431C2211yescharacteristic
21C2×#423C2211yescharacteristic
22#1559—22no—
23#1559—22no—
24C2×#333C412yes—
25C2×#332C412yes—
26#1497C414yes—
27#1493—22no—
28#1479—22no—
29#1302—22no—
30#1301—22no—
31#1293—22no—
32#1290—22no—
33C22×M16—21no—
34#533—21no—
35#533—21no—
36#533—21no—
37#533—21no—
38#533C2×C412yes—
39#533C2×C412yes—
40#533D412yes—
41#533D412yes—
42C2×C4⋊Q8C2×C411yescharacteristic
43C2×C4⋊Q8C2×C411yescharacteristic
44C2×#125—21no—
45C2×C22⋊Q8—21no—
46C2×C22⋊Q8Q812yes—
47C2×C4×Q8—21no—
48C2×C4×Q8D412yes—
49C2×#117—21no—
50C22×C42C2311yescharacteristic
51#446—28no—
52#446—24no—
53#446—28no—
54#446—28no—
55C8×Q8—24no—
56#433—28no—
57#432—24no—
58#432—21no—
59#432—21no—
60#432—21no—
61#432—21no—
62#432—21no—
63#432—21no—
64#432—21no—
65#432—21no—
66#432C2×C412yes—
67#432C2×C412yes—
68#432C2×C412yes—
69#432D412yes—
70#431—24no—
71#431—21no—
72#431—21no—
73#431—21no—
74#431—21no—
75#431—21no—
76#431—21no—
77#431C2×C412yes—
78#431D412yes—
79#424—24no—
80#423—21no—
81#423—21no—
82#423—21no—
83#423—21no—
84#423—21no—
85#423—21no—
86C2×C4⋊C8—21no—
87C2×C4⋊C8—21no—
88C2×C4⋊C8—21no—
89C2×C4⋊C8C2×C412yes—
90C2×C4⋊C8C2×C412yes—
91#407—21no—
92#407D412yes—
93C2×C22⋊C8—21no—
94C2×C22⋊C8—21no—
95C2×C22⋊C8—21no—
96#405—24no—
97C4×M16—21no—
98C4×M16—21no—
99C2×#97—21no—
100C2×#97D412yes—
101C2×C4×C8—21no—
102#333—24no—
103#332—24no—
104Q8⋊C8—28no—
105C22×Q8—21no—
106C22×Q8C4⋊C412yes—
107C23×C4C2×D411yescharacteristic
108C23×C4C2×Q811yescharacteristic
109C23×C4#4111yescharacteristic
110C2×M16—22no—
111C2×M16—41no—
112C2×M16—41no—
113C2×M16—41no—
114C2×M16—82no—
115C22×C8—22no—
116C22×C8—22no—
117C22×C8—22no—
118C22×C8—41no—
119C4⋊Q8—21no—
120C4⋊Q8—21no—
121C4⋊Q8—21no—
122C4⋊Q8—21no—
123C4⋊Q8C4212yes—
124C4⋊Q8C4212yes—
125C4⋊Q8C22⋊C412yes—
126C4⋊Q8C22⋊C412yes—
127#125—22no—
128#125—22no—
129#125—22no—
130#125—22no—
131C22⋊Q8—22no—
132C22⋊Q8—22no—
133C22⋊Q8—22no—
134C22⋊Q8—22no—
135C22⋊Q8—22no—
136C22⋊Q8—22no—
137C22⋊Q8C4⋊C414yes—
138C22⋊Q8C4⋊C414yes—
139C4×Q8—22no—
140C4×Q8—22no—
141C4×Q8—22no—
142C4×Q8—22no—
143C4×Q8—22no—
144C4×Q8—22no—
145C4×Q8C22⋊C414yes—
146C4×Q8C22⋊C414yes—
147#117—22no—
148#117—22no—
149#117—22no—
150#117—22no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4C4⋊C412yes—
157C2×C22⋊C4—22no—
158C2×C42—22no—
159C2×C42C22×C411yescharacteristic
160C2×C42C22×C411yescharacteristic
161C2×C42C22×C411yescharacteristic
162C2×C42C2×D411yescharacteristic
163C2×C42C2×D411yescharacteristic
164C2×C42C2×D411yescharacteristic
165C2×C42C2×D411yescharacteristic
166C2×C42C2×D411yescharacteristic
167C2×C42C2×D411yescharacteristic
168C2×C42#4111yescharacteristic
169C2×C42#4111yescharacteristic
170C2×C42#4111yescharacteristic
171C4⋊C8—28no—
172C4⋊C8—28no—
173C4⋊C8—22no—
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8—22no—
177C4⋊C8—22no—
178C4⋊C8—22no—
179C4⋊C8—22no—
180C4⋊C8—22no—
181C4⋊C8—22no—
182C4⋊C8—22no—
183C4⋊C8—41no—
184C4⋊C8—41no—
185C4⋊C8—41no—
186C4⋊C8—41no—
187C22⋊C8—22no—
188C22⋊C8—22no—
189C22⋊C8—22no—
190C22⋊C8—22no—
191C22⋊C8—22no—
192C22⋊C8—41no—
193C22⋊C8—41no—
194C22⋊C8—41no—
195C22⋊C8—41no—
196C22⋊C8C22⋊C414yes—
197#97—28no—
198#97—22no—
199#97—22no—
200#97—22no—
201#97—41no—
202#97—41no—
203#97C22⋊C414yes—
204C4×C8—28no—
205C4×C8—22no—
206C4×C8—22no—
207C4×C8—41no—
208C4×C8—41no—
209C24C22⋊Q811yescharacteristic
210C2×Q8—22no—
211C2×Q8—22no—
212C2×Q8—22no—
213C2×Q8—44no—
214C2×Q8—81no—
215C2×Q8—81no—
216C2×Q8#9514yes—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—41no—
220C22×C4—42no—
221C22×C4—41no—
222C22×C4—42no—
223C22×C4C2×C22⋊C411yescharacteristic
224C22×C4C2×C4⋊C411yescharacteristic
225C22×C4C2×C4⋊C411yescharacteristic
226C22×C4C2×C4⋊C411yescharacteristic
227C22×C4#11711yescharacteristic
228C22×C4C4×D411yescharacteristic
229C22×C4C4×D411yescharacteristic
230C22×C4C4×D411yescharacteristic
231C22×C4C4×D411yescharacteristic
232C22×C4#12011yescharacteristic
233C22×C4#12011yescharacteristic
234C22×C4#12111yescharacteristic
235C22×C4#12111yescharacteristic
236C22×C4C22⋊Q811yescharacteristic
237C22×C4C22⋊Q811yescharacteristic
238C22×C4C22⋊Q811yescharacteristic
239C22×C4#12311yescharacteristic
240C22×C4#12311yescharacteristic
241M16—44no—
242M16—82no—
243M16—82no—
244M16—82no—
245C2×C8—24no—
246C2×C8—24no—
247C2×C8—44no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—81no—
253C2×C8—81no—
254C2×C8—82no—
255C2×C8—82no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—24no—
260C4⋊C4—24no—
261C4⋊C4—24no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—24no—
267C4⋊C4#9514yes—
268C22⋊C4—24no—
269C22⋊C4—24no—
270C42—24no—
271C42—24no—
272C42C2×C4211yescharacteristic
273C42C2×C22⋊C411yescharacteristic
274C42C2×C22⋊C411yescharacteristic
275C42C2×C22⋊C411yescharacteristic
276C42C2×C22⋊C411yescharacteristic
277C42#11711yescharacteristic
278C42C4×D411yescharacteristic
279C42C4×D411yescharacteristic
280C42C4×D411yescharacteristic
281C42C4×D411yescharacteristic
282C42#12011yescharacteristic
283C42#12011yescharacteristic
284C42#12111yescharacteristic
285C42#12111yescharacteristic
286C42#12311yescharacteristic
287C42#12311yescharacteristic
288C23—22no—
289C23—41no—
290C23—41no—
291C23#38011yescharacteristic
292C23#38511yescharacteristic
293C23#38511yescharacteristic
294Q8—44no—
295Q8—42no—
296Q8—42no—
297Q8—82no—
298Q8—82no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—24no—
311C2×C4—24no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—44no—
323C2×C4—82no—
324C2×C4C2×#9511yescharacteristic
325C2×C4C4×C22⋊C411yescharacteristic
326C2×C4C4×C22⋊C411yescharacteristic
327C2×C4#37911yescharacteristic
328C2×C4#38011yescharacteristic
329C2×C4#38111yescharacteristic
330C2×C4#38511yescharacteristic
331C2×C4#38511yescharacteristic
332C2×C4#38611yescharacteristic
333C2×C4#38611yescharacteristic
334C2×C4#38611yescharacteristic
335C2×C4#38611yescharacteristic
336C8—44no—
337C8—44no—
338C8—82no—
339C8—82no—
340C8—82no—
341C8—82no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—82no—
351C22C22⋊#9511yescharacteristic
352C22#185812yes—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—44no—
364C4—44no—
365C4#190211yescharacteristic
366C4#190311yescharacteristic
367C4#190512yes—
368C2—22no—
369C2—41no—
370C2—41no—
371C2#1075311yescharacteristic
372C2#1078411yescharacteristic
373C2#1078611yescharacteristic
subgroupG/H
center, socleC22C22⋊#95
commutatorC42C2×C42
Frattini, cosocleC22×C42C23
prime radicalC24C22⋊Q8
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ 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
#602512
C2×#15592
#174792
#80892
#80812
#80102
#79902