Finite Group Databasebeta

← #120077

Subgroups — #120077

Order 512.

504 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21987C211yesmaximal, characteristic
2#21979C211yesmaximal, characteristic
3#10857C211yesmaximal, characteristic
4C2×#1307C211yesmaximal, characteristic
5#8040C211yesmaximal, characteristic
6#8035C211yesmaximal, characteristic
7C2×#1291C211yesmaximal, characteristic
8C2×#432C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C2×C4×M16C2211yescharacteristic
13C2×#384C2211yescharacteristic
14#2283C2211yescharacteristic
15#1948—21no—
16#1947—21no—
17#1940—21no—
18#1940—21no—
19#1853C412yes—
20#1852C412yes—
21#1851—22no—
22#1847—21no—
23#1843—21no—
24#1836—21no—
25#1832—21no—
26C2×#343—22no—
27#1307—22no—
28#1296—21no—
29#1296—21no—
30#1295—21no—
31#1295—21no—
32#1291—22no—
33C22×M16—21no—
34C22×M16D412yes—
35C22×C4⋊C4—21no—
36C22×C4⋊C4—21no—
37C22×C4⋊C4C2×C412yes—
38C22×C42C2311yescharacteristic
39#432—21no—
40#432—21no—
41#432—21no—
42#432—21no—
43#432—21no—
44#432—21no—
45#432—21no—
46#432—21no—
47#432—21no—
48#432D412yes—
49#432Q812yes—
50#432Q812yes—
51C2×#107—22no—
52C2×#106—22no—
53#423—21no—
54#423—21no—
55#423—21no—
56#423—21no—
57C2×C4⋊C8—21no—
58C2×C4⋊C8—21no—
59C2×C4⋊C8—21no—
60C2×C4⋊C8—21no—
61C2×C4⋊C8—22no—
62C2×C4⋊C8—22no—
63C2×C4⋊C8D411yescharacteristic
64C2×C4⋊C8D411yescharacteristic
65C2×C22⋊C8—21no—
66C2×C22⋊C8—21no—
67C2×C22⋊C8C2×C412yes—
68C4×M16—21no—
69C4×M16—21no—
70C4×M16—21no—
71C4×M16Q812yes—
72C2×#97—21no—
73C2×#97—21no—
74C2×#97—21no—
75C2×#97—21no—
76C2×C4×C8—21no—
77#384—21no—
78#384—21no—
79#384—21no—
80#384—21no—
81#383—21no—
82#382D411yescharacteristic
83#382D411yescharacteristic
84#381—21no—
85#380C2×C411yescharacteristic
86#380C2×C411yescharacteristic
87C4×C4⋊C4D411yescharacteristic
88C4×C4⋊C4D411yescharacteristic
89C4×C22⋊C4—21no—
90#376—21no—
91#343—44no—
92#340—22no—
93#340—22no—
94#336—22no—
95#336—22no—
96C23×C4—22no—
97C23×C4C22×C411yescharacteristic
98C23×C4C2×D411yescharacteristic
99C23×C4#4111yescharacteristic
100C2×M16—22no—
101C2×M16—22no—
102C2×M16—22no—
103C2×M16—22no—
104C2×M16—22no—
105C2×M16—41no—
106C2×M16—41no—
107C2×M16—41no—
108C2×M16—42no—
109C2×M16—42no—
110C22×C8—22no—
111C22×C8—22no—
112C22×C8—21no—
113C22×C8—21no—
114C22×C8—41no—
115C22×C8—41no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—22no—
118C2×C4⋊C4—42no—
119C2×C4⋊C4—42no—
120C2×C4⋊C4—41no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4—41no—
123C2×C4⋊C4—41no—
124C2×C4⋊C4—82no—
125C2×C4⋊C4—82no—
126C2×C4⋊C4C22⋊C411yescharacteristic
127C2×C4⋊C4C22⋊C411yescharacteristic
128C2×C4⋊C4C22⋊C411yescharacteristic
129C2×C4⋊C4C22⋊C411yescharacteristic
130C2×C22⋊C4—21no—
131C2×C22⋊C4—21no—
132C2×C42—21no—
133C2×C42—21no—
134C2×C42C2×D411yescharacteristic
135C2×C42C2×D411yescharacteristic
136C2×C42C2×D411yescharacteristic
137C2×C42C2×D411yescharacteristic
138C2×C42C2×Q811yescharacteristic
139C2×C42C2×Q811yescharacteristic
140C2×C42C2×Q811yescharacteristic
141C2×C42#4111yescharacteristic
142C2×C42#4111yescharacteristic
143C2×C42#4111yescharacteristic
144C2×C42#4111yescharacteristic
145C2×C42#4111yescharacteristic
146#107—82no—
147#106—82no—
148C4⋊C8—22no—
149C4⋊C8—21no—
150C4⋊C8—21no—
151C4⋊C8—22no—
152C4⋊C8—22no—
153C4⋊C8—21no—
154C4⋊C8—21no—
155C4⋊C8—41no—
156C4⋊C8—41no—
157C4⋊C8—41no—
158C4⋊C8—41no—
159C4⋊C8—41no—
160C4⋊C8—82no—
161C4⋊C8—82no—
162C22⋊C8—22no—
163C22⋊C8—22no—
164C22⋊C8—41no—
165C22⋊C8—41no—
166C22⋊C8—41no—
167C22⋊C8C4⋊C414yes—
168#97—22no—
169#97—22no—
170#97—22no—
171#97—22no—
172#97—41no—
173#97—41no—
174#97—41no—
175#97—41no—
176C4×C8—22no—
177C4×C8—41no—
178#95—21no—
179#95—21no—
180#95—21no—
181#95—21no—
182#95—21no—
183#95—21no—
184#95—21no—
185#95—21no—
186C24C4×D411yescharacteristic
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—42no—
200C22×C4—44no—
201C22×C4—82no—
202C22×C4—82no—
203C22×C4C2×C22⋊C411yescharacteristic
204C22×C4C2×C4⋊C411yescharacteristic
205C22×C4#11711yescharacteristic
206C22×C4C4×D411yescharacteristic
207C22×C4C4×Q811yescharacteristic
208C22×C4C4×Q811yescharacteristic
209C22×C4#12011yescharacteristic
210C22×C4#12111yescharacteristic
211C22×C4#12111yescharacteristic
212C22×C4#12111yescharacteristic
213C22×C4C22⋊Q811yescharacteristic
214C22×C4C22⋊Q811yescharacteristic
215C22×C4#12311yescharacteristic
216C22×C4#12311yescharacteristic
217C22×C4#12511yescharacteristic
218C22×C4#12511yescharacteristic
219C22×C4#12611yescharacteristic
220C22×C4C4⋊Q811yescharacteristic
221M16—24no—
222M16—42no—
223M16—42no—
224M16—42no—
225M16—44no—
226M16—82no—
227C2×C8—24no—
228C2×C8—42no—
229C2×C8—42no—
230C2×C8—42no—
231C2×C8—42no—
232C2×C8—42no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—42no—
236C2×C8—42no—
237C2×C8—41no—
238C2×C8—42no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—42no—
242C2×C8—41no—
243C2×C8—81no—
244C2×C8—81no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—82no—
252C4⋊C4—82no—
253C4⋊C4—82no—
254C4⋊C4—82no—
255C4⋊C4—81no—
256C4⋊C4—81no—
257C22⋊C4—81no—
258C22⋊C4—81no—
259C42—41no—
260C42—41no—
261C42—41no—
262C42—41no—
263C42#12111yescharacteristic
264C42#12111yescharacteristic
265C42#12111yescharacteristic
266C42C22⋊Q811yescharacteristic
267C42C22⋊Q811yescharacteristic
268C42C22⋊Q811yescharacteristic
269C42C22⋊Q811yescharacteristic
270C42C22⋊Q811yescharacteristic
271C42C22⋊Q811yescharacteristic
272C42#12311yescharacteristic
273C42#12411yescharacteristic
274C42#12511yescharacteristic
275C42#12511yescharacteristic
276C42#12611yescharacteristic
277C42C4⋊Q811yescharacteristic
278C42C4⋊Q811yescharacteristic
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23#38611yescharacteristic
286C23#38711yescharacteristic
287C23#38911yescharacteristic
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
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—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—164no—
330C2×C4#38011yescharacteristic
331C2×C4#38711yescharacteristic
332C2×C4#38911yescharacteristic
333C2×C4#39111yescharacteristic
334C2×C4#39411yescharacteristic
335C2×C4#39511yescharacteristic
336C2×C4#39611yescharacteristic
337C2×C4#39611yescharacteristic
338C2×C4#39811yescharacteristic
339C2×C4#39811yescharacteristic
340C2×C4#39811yescharacteristic
341C2×C4#40011yescharacteristic
342C2×C4#45311yescharacteristic
343C2×C4#45411yescharacteristic
344C2×C4#45511yescharacteristic
345C2×C4#45611yescharacteristic
346C8—44no—
347C8—44no—
348C8—82no—
349C8—81no—
350C8—82no—
351C8—81no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22#144111yescharacteristic
363C22#188211yescharacteristic
364C22#188311yescharacteristic
365C22#190211yescharacteristic
366C22#190311yescharacteristic
367C22#191411yescharacteristic
368C22#191511yescharacteristic
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—81no—
380C4—81no—
381C4—81no—
382C4—81no—
383C4—162no—
384C4#203711yescharacteristic
385C4#203811yescharacteristic
386C4#206011yescharacteristic
387C4#206111yescharacteristic
388C2—41no—
389C2—41no—
390C2#933711yescharacteristic
391C2#933811yescharacteristic
392C2#933911yescharacteristic
393C2#934011yescharacteristic
394C2#1120611yescharacteristic
395C2#1121411yescharacteristic
396C2#1121711yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C4×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ 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
#219872
#219792
#108572
C2×#13072
#80402
#80352
C2×#12912