Finite Group Databasebeta

← #107609

Subgroups — #107609

Order 512.

697 conjugacy classes of subgroups.

The subgroup lattice has 409 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60250C211yesmaximal, characteristic
2#17749C211yesmaximal, characteristic
3C2×#1559C211yesmaximal, characteristic
4#8079C211yesmaximal, characteristic
5#8061C211yesmaximal, characteristic
6#8058C211yesmaximal, characteristic
7#7990C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9#2986—22no—
10#2985—22no—
11#2984C414yes—
12#2983—21no—
13#2982—21no—
14#2962—22no—
15#2960—22no—
16#2924—22no—
17#2920C2211yescharacteristic
18#2920C2211yescharacteristic
19C2×#432C2211yescharacteristic
20C2×#431C2211yescharacteristic
21C2×#423C2211yescharacteristic
22C2×#423C2211yescharacteristic
23#1559—22no—
24#1559—22no—
25#1559C414yes—
26#1550C414yes—
27#1548—21no—
28#1546—21no—
29C2×#333—21no—
30C2×#332—21no—
31#1301—21no—
32#1301—21no—
33#1299—22no—
34#1298—22no—
35#1290—22no—
36C22×M16—21no—
37C22×M16—21no—
38#533—21no—
39#533—21no—
40#533—21no—
41#533—21no—
42#533C2×C412yes—
43#533C2×C412yes—
44#533D412yes—
45#533D412yes—
46C2×C4⋊Q8D411yescharacteristic
47C2×C4⋊Q8D411yescharacteristic
48C2×#125—21no—
49C2×C22⋊Q8—21no—
50C2×C22⋊Q8Q812yes—
51C2×C4×Q8—21no—
52C2×C4×Q8C2×C412yes—
53C2×#117—21no—
54C22×C42C2311yescharacteristic
55#446—24no—
56#446—24no—
57#446—24no—
58#446—28no—
59C8×Q8—24no—
60C8×Q8—24no—
61C8×Q8—24no—
62#433—28no—
63#432—24no—
64#432—21no—
65#432—21no—
66#432—21no—
67#432—21no—
68#432—21no—
69#432C2×C412yes—
70#432C2×C412yes—
71#432D412yes—
72#431—21no—
73#431—21no—
74#431—21no—
75#431—21no—
76#431—24no—
77#431—21no—
78#431—21no—
79#431C2×C412yes—
80#431D411yescharacteristic
81#431D411yescharacteristic
82#424—24no—
83#423—21no—
84#423—21no—
85#423—21no—
86#423—21no—
87#423—21no—
88#423—21no—
89#423—21no—
90#423—21no—
91#423C2×C412yes—
92#423C2×C412yes—
93C2×C4⋊C8—21no—
94C2×C4⋊C8—21no—
95C2×C4⋊C8—21no—
96C2×C4⋊C8—21no—
97C2×C4⋊C8—21no—
98C2×C4⋊C8C2×C412yes—
99#407—21no—
100#407—21no—
101C2×C22⋊C8—21no—
102C2×C22⋊C8D412yes—
103#405—24no—
104C4×M16—21no—
105C4×M16D412yes—
106C2×#97—21no—
107C2×C4×C8—21no—
108#333—24no—
109#333—24no—
110#332—24no—
111#332—24no—
112C22×Q8—21no—
113C22×Q8C4⋊C412yes—
114C23×C4C2×D411yescharacteristic
115C23×C4C2×Q811yescharacteristic
116C23×C4#4111yescharacteristic
117C2×M16—22no—
118C2×M16—22no—
119C2×M16—22no—
120C2×M16—41no—
121C2×M16—41no—
122C2×M16—41no—
123C2×M16—81no—
124C2×M16—81no—
125C2×M16—81no—
126C2×M16—81no—
127C22×C8—22no—
128C22×C8—22no—
129C22×C8—41no—
130C22×C8—41no—
131C4⋊Q8—21no—
132C4⋊Q8—21no—
133C4⋊Q8—21no—
134C4⋊Q8—21no—
135C4⋊Q8C22⋊C412yes—
136C4⋊Q8C22⋊C412yes—
137C4⋊Q8C22⋊C412yes—
138C4⋊Q8C22⋊C412yes—
139#125—22no—
140#125—22no—
141#125—22no—
142#125—22no—
143C22⋊Q8—22no—
144C22⋊Q8—22no—
145C22⋊Q8—22no—
146C22⋊Q8—22no—
147C22⋊Q8—22no—
148C22⋊Q8—22no—
149C22⋊Q8C4⋊C414yes—
150C22⋊Q8C4⋊C414yes—
151C4×Q8—22no—
152C4×Q8—22no—
153C4×Q8—22no—
154C4×Q8—22no—
155C4×Q8—22no—
156C4×Q8—22no—
157C4×Q8C4214yes—
158C4×Q8C22⋊C414yes—
159#117—22no—
160#117—22no—
161#117—22no—
162#117—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4C4⋊C412yes—
169C2×C22⋊C4—22no—
170C2×C42—22no—
171C2×C42C22×C411yescharacteristic
172C2×C42C22×C411yescharacteristic
173C2×C42C22×C411yescharacteristic
174C2×C42C2×D411yescharacteristic
175C2×C42C2×D411yescharacteristic
176C2×C42C2×D411yescharacteristic
177C2×C42C2×D411yescharacteristic
178C2×C42C2×D411yescharacteristic
179C2×C42C2×D411yescharacteristic
180C2×C42#4111yescharacteristic
181C2×C42#4111yescharacteristic
182C2×C42#4111yescharacteristic
183C4⋊C8—28no—
184C4⋊C8—28no—
185C4⋊C8—22no—
186C4⋊C8—22no—
187C4⋊C8—22no—
188C4⋊C8—22no—
189C4⋊C8—22no—
190C4⋊C8—22no—
191C4⋊C8—22no—
192C4⋊C8—22no—
193C4⋊C8—22no—
194C4⋊C8—21no—
195C4⋊C8—21no—
196C4⋊C8—22no—
197C4⋊C8—41no—
198C4⋊C8—41no—
199C4⋊C8—41no—
200C4⋊C8—41no—
201C4⋊C8—41no—
202C22⋊C8—22no—
203C22⋊C8—22no—
204C22⋊C8—22no—
205C22⋊C8—22no—
206C22⋊C8—41no—
207C22⋊C8—41no—
208C22⋊C8—41no—
209C22⋊C8C22⋊C412yes—
210C22⋊C8C22⋊C412yes—
211#97—28no—
212#97—22no—
213#97—41no—
214#97—41no—
215#97C22⋊C414yes—
216C4×C8—28no—
217C4×C8—22no—
218C4×C8—21no—
219C4×C8—21no—
220C4×C8—22no—
221C4×C8—41no—
222C24C22⋊Q811yescharacteristic
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—22no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—82no—
231C2×Q8#9514yes—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—42no—
239C22×C4—81no—
240C22×C4C2×C22⋊C411yescharacteristic
241C22×C4C2×C4⋊C411yescharacteristic
242C22×C4C2×C4⋊C411yescharacteristic
243C22×C4C2×C4⋊C411yescharacteristic
244C22×C4#11711yescharacteristic
245C22×C4C4×D411yescharacteristic
246C22×C4C4×D411yescharacteristic
247C22×C4C4×D411yescharacteristic
248C22×C4C4×D411yescharacteristic
249C22×C4#12011yescharacteristic
250C22×C4#12011yescharacteristic
251C22×C4#12111yescharacteristic
252C22×C4#12111yescharacteristic
253C22×C4C22⋊Q811yescharacteristic
254C22×C4C22⋊Q811yescharacteristic
255C22×C4C22⋊Q811yescharacteristic
256C22×C4#12311yescharacteristic
257C22×C4#12311yescharacteristic
258M16—44no—
259M16—82no—
260M16—82no—
261M16—81no—
262M16—81no—
263M16—82no—
264M16—82no—
265C2×C8—22no—
266C2×C8—24no—
267C2×C8—22no—
268C2×C8—44no—
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—42no—
272C2×C8—42no—
273C2×C8—82no—
274C2×C8—81no—
275C2×C8—81no—
276C2×C8—82no—
277C4⋊C4—24no—
278C4⋊C4—22no—
279C4⋊C4—24no—
280C4⋊C4—24no—
281C4⋊C4—24no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4#9514yes—
289C22⋊C4—24no—
290C22⋊C4—24no—
291C42—24no—
292C42—24no—
293C42C2×C4211yescharacteristic
294C42C2×C22⋊C411yescharacteristic
295C42C2×C22⋊C411yescharacteristic
296C42C2×C22⋊C411yescharacteristic
297C42C2×C22⋊C411yescharacteristic
298C42#11711yescharacteristic
299C42C4×D411yescharacteristic
300C42C4×D411yescharacteristic
301C42C4×D411yescharacteristic
302C42C4×D411yescharacteristic
303C42#12011yescharacteristic
304C42#12011yescharacteristic
305C42#12111yescharacteristic
306C42#12111yescharacteristic
307C42#12311yescharacteristic
308C42#12311yescharacteristic
309C23—21no—
310C23—21no—
311C23—41no—
312C23—41no—
313C23#38011yescharacteristic
314C23#38511yescharacteristic
315C23#38511yescharacteristic
316Q8—44no—
317Q8—42no—
318Q8—42no—
319Q8—42no—
320Q8—42no—
321Q8—82no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—24no—
336C2×C4—24no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—82no—
349C2×C4C2×#9511yescharacteristic
350C2×C4C4×C22⋊C411yescharacteristic
351C2×C4C4×C22⋊C411yescharacteristic
352C2×C4#37911yescharacteristic
353C2×C4#38011yescharacteristic
354C2×C4#38111yescharacteristic
355C2×C4#38511yescharacteristic
356C2×C4#38511yescharacteristic
357C2×C4#38611yescharacteristic
358C2×C4#38611yescharacteristic
359C2×C4#38611yescharacteristic
360C2×C4#38611yescharacteristic
361C2×C4#47111yescharacteristic
362C2×C4#47111yescharacteristic
363C2×C4#47211yescharacteristic
364C2×C4#47311yescharacteristic
365C8—42no—
366C8—42no—
367C8—44no—
368C8—82no—
369C8—82no—
370C8—82no—
371C8—82no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—81no—
381C22—81no—
382C22C22⋊#9511yescharacteristic
383C22#181511yescharacteristic
384C22#181611yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—44no—
395C4—44no—
396C4#190512yes—
397C4#190711yescharacteristic
398C4#190711yescharacteristic
399C4#190811yescharacteristic
400C4#190811yescharacteristic
401C2—21no—
402C2—21no—
403C2—41no—
404C2—41no—
405C2#1076711yescharacteristic
406C2#1077411yescharacteristic
407C2#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
#602502
#177492
C2×#15592
#80792
#80612
#80582
#79902