Finite Group Databasebeta

← #107163

Subgroups — #107163

Order 512.

738 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60250C211yesmaximal, characteristic
2#21879C211yesmaximal, characteristic
3#21337C211yesmaximal, characteristic
4#8081C211yesmaximal, characteristic
5C2×#1299C211yesmaximal, characteristic
6#8004C211yesmaximal, characteristic
7#7992C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9#2986—22no—
10#2985—22no—
11#2984—22no—
12#2983C412yes—
13#2982C412yes—
14#2962—22no—
15#2960—22no—
16#2924—22no—
17#2920C2211yescharacteristic
18#2920C2211yescharacteristic
19C2×#431C2211yescharacteristic
20C2×#423C2211yescharacteristic
21C2×#423C2211yescharacteristic
22C2×C4×M16C2211yescharacteristic
23#1998C414yes—
24#1997—21no—
25#1997—21no—
26#1997—21no—
27#1966—21no—
28#1901C414yes—
29#1801—22no—
30#1742—22no—
31#1301—22no—
32#1299—22no—
33#1292—22no—
34#1291—22no—
35C22×M16—21no—
36C22×M16—21no—
37C22×M16C2×C412yes—
38#533—21no—
39#533—21no—
40#533—21no—
41#533—21no—
42#533—21no—
43#533—21no—
44#533—21no—
45#533—21no—
46C2×C4⋊Q8D411yescharacteristic
47C2×C4⋊Q8D411yescharacteristic
48C2×#125C2×C412yes—
49C2×C22⋊Q8C2×C412yes—
50C2×C22⋊Q8Q812yes—
51C2×C4×Q8C2×C412yes—
52C2×C4×Q8D412yes—
53C2×#117D412yes—
54C22×C42C2311yescharacteristic
55#446—24no—
56#446—28no—
57#446—24no—
58#446—24no—
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#432D412yes—
68#431—24no—
69#431—21no—
70#431—21no—
71#431—21no—
72#431—21no—
73#431—21no—
74#431C2×C411yescharacteristic
75#431C2×C411yescharacteristic
76#431C2×C412yes—
77#431D412yes—
78#424—24no—
79#423—21no—
80#423—21no—
81#423—21no—
82#423—21no—
83#423—21no—
84#423—21no—
85#423—21no—
86#423—21no—
87#423C2×C412yes—
88#423D412yes—
89C2×C4⋊C8—21no—
90C2×C4⋊C8—21no—
91C2×C4⋊C8—21no—
92C2×C4⋊C8—21no—
93C2×C4⋊C8D412yes—
94C2×#101—24no—
95#407—21no—
96#407C2×C412yes—
97C2×C22⋊C8—21no—
98#405—24no—
99C4×M16—21no—
100C4×M16—21no—
101C4×M16—21no—
102C4×M16—21no—
103C4×M16—21no—
104C4×M16C2×C412yes—
105C2×#97—21no—
106C2×C4×C8—21no—
107C2×C4×C8—21no—
108#343—24no—
109#343—24no—
110#343—24no—
111C22×Q8C22⋊C412yes—
112C22×Q8C4⋊C412yes—
113C23×C4C22×C411yescharacteristic
114C23×C4C2×D411yescharacteristic
115C23×C4C2×Q811yescharacteristic
116C2×M16—22no—
117C2×M16—24no—
118C2×M16—22no—
119C2×M16—22no—
120C2×M16—22no—
121C2×M16—22no—
122C2×M16—22no—
123C2×M16—42no—
124C2×M16—41no—
125C2×M16—41no—
126C2×M16—44no—
127C2×M16—82no—
128C22×C8—22no—
129C22×C8—22no—
130C22×C8—41no—
131C22×C8—41no—
132C4⋊Q8—21no—
133C4⋊Q8—21no—
134C4⋊Q8—21no—
135C4⋊Q8—21no—
136C4⋊Q8—21no—
137C4⋊Q8—21no—
138C4⋊Q8—21no—
139C4⋊Q8—21no—
140#125—22no—
141#125—22no—
142#125—22no—
143#125—22no—
144C22⋊Q8—22no—
145C22⋊Q8—22no—
146C22⋊Q8—22no—
147C22⋊Q8—22no—
148C22⋊Q8—22no—
149C22⋊Q8—22no—
150C22⋊Q8—22no—
151C22⋊Q8—22no—
152C4×Q8—22no—
153C4×Q8—22no—
154C4×Q8—22no—
155C4×Q8—22no—
156C4×Q8—22no—
157C4×Q8—22no—
158C4×Q8—22no—
159C4×Q8—22no—
160#117—22no—
161#117—22no—
162#117—22no—
163#117—22no—
164C2×C4⋊C4C4214yes—
165C2×C4⋊C4C22⋊C412yes—
166C2×C4⋊C4C22⋊C412yes—
167C2×C4⋊C4C22⋊C412yes—
168C2×C4⋊C4C4⋊C412yes—
169C2×C4⋊C4C4⋊C414yes—
170C2×C22⋊C4C4⋊C414yes—
171C2×C42C22⋊C414yes—
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
183C2×C42#4111yescharacteristic
184C4⋊C8—28no—
185C4⋊C8—28no—
186C4⋊C8—22no—
187C4⋊C8—22no—
188C4⋊C8—22no—
189C4⋊C8—22no—
190C4⋊C8—41no—
191C4⋊C8—41no—
192C4⋊C8—41no—
193C4⋊C8—41no—
194C4⋊C8—41no—
195C4⋊C8—41no—
196C4⋊C8—41no—
197C4⋊C8—41no—
198C4⋊C8C22⋊C412yes—
199C4⋊C8C22⋊C412yes—
200C4⋊C8C22⋊C414yes—
201#101—84no—
202C22⋊C8—21no—
203C22⋊C8—21no—
204C22⋊C8—22no—
205C22⋊C8—22no—
206C22⋊C8—22no—
207C22⋊C8—22no—
208C22⋊C8—22no—
209#97—28no—
210#97—22no—
211#97—22no—
212#97—41no—
213#97—41no—
214C4×C8—28no—
215C4×C8—21no—
216C4×C8—21no—
217C4×C8—22no—
218C4×C8—22no—
219C4×C8—22no—
220C4×C8—41no—
221C4×C8—41no—
222C24C2×C4⋊C411yescharacteristic
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—22no—
226C2×Q8—22no—
227C2×Q8—44no—
228C2×Q8—42no—
229C2×Q8—42no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—42no—
235C22×C4#9514yes—
236C22×C4#9514yes—
237C22×C4C2×C4211yescharacteristic
238C22×C4C2×C22⋊C411yescharacteristic
239C22×C4C2×C22⋊C411yescharacteristic
240C22×C4C2×C22⋊C411yescharacteristic
241C22×C4C2×C4⋊C411yescharacteristic
242C22×C4C2×C4⋊C411yescharacteristic
243C22×C4C4×D411yescharacteristic
244C22×C4C4×D411yescharacteristic
245C22×C4C4×D411yescharacteristic
246C22×C4C4×D411yescharacteristic
247C22×C4#12011yescharacteristic
248C22×C4#12011yescharacteristic
249C22×C4C22⋊Q811yescharacteristic
250C22×C4C22⋊Q811yescharacteristic
251C22×C4C22⋊Q811yescharacteristic
252C22×C4C22⋊Q811yescharacteristic
253C22×C4#12311yescharacteristic
254C22×C4#12311yescharacteristic
255M16—24no—
256M16—44no—
257M16—42no—
258M16—42no—
259M16—42no—
260M16—42no—
261M16—44no—
262M16—42no—
263M16—44no—
264M16—82no—
265M16—82no—
266C2×C8—22no—
267C2×C8—24no—
268C2×C8—22no—
269C2×C8—44no—
270C2×C8—42no—
271C2×C8—42no—
272C2×C8—42no—
273C2×C8—42no—
274C2×C8—42no—
275C2×C8—42no—
276C2×C8—82no—
277C2×C8—82no—
278C4⋊C4—24no—
279C4⋊C4—24no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—24no—
283C4⋊C4—24no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—22no—
290C22⋊C4—24no—
291C22⋊C4—24no—
292C42—24no—
293C42—24no—
294C42C2×C22⋊C411yescharacteristic
295C42C2×C22⋊C411yescharacteristic
296C42#11711yescharacteristic
297C42#11711yescharacteristic
298C42C4×D411yescharacteristic
299C42C4×D411yescharacteristic
300C42C4×D411yescharacteristic
301C42C4×D411yescharacteristic
302C42#12011yescharacteristic
303C42#12011yescharacteristic
304C42#12111yescharacteristic
305C42#12111yescharacteristic
306C42#12111yescharacteristic
307C42#12111yescharacteristic
308C42#12311yescharacteristic
309C42#12311yescharacteristic
310C23—22no—
311C23—41no—
312C23—41no—
313C23C2×#9511yescharacteristic
314C23#38511yescharacteristic
315C23#38511yescharacteristic
316Q8—44no—
317Q8—44no—
318Q8—42no—
319Q8—42no—
320Q8—82no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
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—21no—
336C2×C4—21no—
337C2×C4—24no—
338C2×C4—24no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—44no—
346C2×C4—44no—
347C2×C4C4×C22⋊C411yescharacteristic
348C2×C4C4×C22⋊C411yescharacteristic
349C2×C4#37911yescharacteristic
350C2×C4#38011yescharacteristic
351C2×C4#38011yescharacteristic
352C2×C4#38111yescharacteristic
353C2×C4#38511yescharacteristic
354C2×C4#38511yescharacteristic
355C2×C4#38611yescharacteristic
356C2×C4#38611yescharacteristic
357C2×C4#38611yescharacteristic
358C2×C4#38611yescharacteristic
359C2×C4#45412yes—
360C2×C4#45612yes—
361C8—44no—
362C8—42no—
363C8—42no—
364C8—44no—
365C8—82no—
366C8—82no—
367C8—82no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—82no—
377C22C22⋊#9511yescharacteristic
378C22#185712yes—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—44no—
388C4—44no—
389C4#179312yes—
390C4#181312yes—
391C4#188611yescharacteristic
392C4#188811yescharacteristic
393C4#191411yescharacteristic
394C4#191511yescharacteristic
395C2—22no—
396C2—41no—
397C2—41no—
398C2#1075011yescharacteristic
399C2#1075511yescharacteristic
400C2#1076011yescharacteristic
subgroupG/H
center, socleC22C22⋊#95
commutatorC22×C4C2×C42
Frattini, cosocleC22×C42C23
prime radicalC24C2×C4⋊C4
LCSG ▷ C22×C4 ▷ 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
#218792
#213372
#80812
C2×#12992
#80042
#79922