Finite Group Databasebeta

← #99892

Subgroups — #99892

Order 512.

505 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22599C211yesmaximal, characteristic
2C2×#1918C211yesmaximal, characteristic
3#9650C211yesmaximal, characteristic
4#8706C211yesmaximal, characteristic
5#7573C211yesmaximal, characteristic
6#7020C211yesmaximal, characteristic
7#7016C211yesmaximal, characteristic
8C2×#431—21no—
9C22×#107C411yescharacteristic
10C2×#389C2211yescharacteristic
11C2×C4×C4⋊C4C2211yescharacteristic
12#1939—21no—
13#1918—21no—
14#1918—21no—
15#1918—21no—
16#1918—21no—
17#1916—22no—
18#1817—21no—
19#1797C2211yescharacteristic
20#1797C2211yescharacteristic
21C8×C4⋊C4—21no—
22C4×C22⋊C8C2211yescharacteristic
23C4×C22⋊C8C2211yescharacteristic
24C2×#340C411yescharacteristic
25C2×#340C411yescharacteristic
26C2×#340C411yescharacteristic
27C2×#336C2211yescharacteristic
28C2×#324—21no—
29C2×#324—21no—
30#1279—21no—
31#1279—21no—
32#1271—22no—
33C23×C8C2×C411yescharacteristic
34C23×C8C2×C411yescharacteristic
35C22×C4⋊C4—21no—
36C22×C4⋊C4C2×C411yescharacteristic
37C22×C4⋊C4C2×C411yescharacteristic
38C22×C4⋊C4C2×C411yescharacteristic
39C22×C4⋊C4C2×C411yescharacteristic
40C22×C42—21no—
41C22×C42C2311yescharacteristic
42#431—42no—
43#431—42no—
44C2×#107—21no—
45C2×#107—21no—
46C2×#107—22no—
47C2×#107C814yescomplemented
48C2×C4⋊C8—22no—
49C2×C4⋊C8—21no—
50C2×C4⋊C8—21no—
51C2×C22⋊C8—21no—
52C2×C22⋊C8—21no—
53C2×C22⋊C8—21no—
54C2×C22⋊C8D411yescharacteristic
55C2×C22⋊C8D411yescharacteristic
56C2×C4×C8—22no—
57C2×C4×C8—21no—
58C2×C4×C8—21no—
59#389—21no—
60#389—21no—
61#389—21no—
62#389—21no—
63C4×C4⋊C4—21no—
64C4×C4⋊C4—21no—
65C4×C4⋊C4D411yescharacteristic
66C4×C4⋊C4D411yescharacteristic
67C4×C4⋊C4D411yescharacteristic
68C4×C4⋊C4D411yescharacteristic
69C2×#95—21no—
70C2×#95—21no—
71#340—21no—
72#340—21no—
73#340—21no—
74#340—21no—
75#340—21no—
76#340—21no—
77#336—22no—
78#336—22no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336—21no—
83#336—21no—
84#336D412yes—
85#324—42no—
86#324—42no—
87C23×C4—21no—
88C23×C4—21no—
89C23×C4—21no—
90C23×C4—21no—
91C23×C4C22×C411yescharacteristic
92C23×C4C2×D411yescharacteristic
93C23×C4#4111yescharacteristic
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—21no—
97C22×C8—21no—
98C22×C8—21no—
99C22×C8—22no—
100C22×C8—21no—
101C22×C8—21no—
102C22×C8—41no—
103C22×C8—41no—
104C22×C8—41no—
105C22×C8—41no—
106C22×C8—41no—
107C22×C8—41no—
108C22×C8C2×C812yes—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4—41no—
123C2×C4⋊C4—41no—
124C2×C4⋊C4—41no—
125C2×C4⋊C4—41no—
126C2×C4⋊C4—41no—
127C2×C4⋊C4—41no—
128C2×C4⋊C4—41no—
129C2×C4⋊C4—41no—
130C2×C4⋊C4C22⋊C411yescharacteristic
131C2×C4⋊C4C22⋊C411yescharacteristic
132C2×C4⋊C4C22⋊C411yescharacteristic
133C2×C4⋊C4C22⋊C411yescharacteristic
134C2×C4⋊C4C2×C812yes—
135C2×C4⋊C4C2×C812yes—
136C2×C4⋊C4M1612yes—
137C2×C42—21no—
138C2×C42—21no—
139C2×C42—21no—
140C2×C42—21no—
141C2×C42—41no—
142C2×C42—41no—
143C2×C42—41no—
144C2×C42—41no—
145C2×C42—41no—
146C2×C42—41no—
147C2×C42C2×D411yescharacteristic
148C2×C42C2×D411yescharacteristic
149C2×C42C2×D411yescharacteristic
150C2×C42#4111yescharacteristic
151#107—24no—
152#107—24no—
153C4⋊C8—41no—
154C4⋊C8—41no—
155C4⋊C8—41no—
156C4⋊C8—41no—
157C4⋊C8—44no—
158C22⋊C8—21no—
159C22⋊C8—22no—
160C22⋊C8—21no—
161C22⋊C8—21no—
162C22⋊C8—41no—
163C22⋊C8—41no—
164C22⋊C8—41no—
165C22⋊C8—41no—
166C22⋊C8—41no—
167C22⋊C8D812yes—
168C4×C8—41no—
169C4×C8—41no—
170C4×C8—41no—
171C4×C8—41no—
172C4×C8—44no—
173#95—21no—
174#95—21no—
175#95—21no—
176#95—21no—
177#95—41no—
178#95—41no—
179C24C4×D411yescharacteristic
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—42no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—81no—
214C22×C4—81no—
215C22×C4—81no—
216C22×C4C2×C22⋊C411yescharacteristic
217C22×C4C4×D411yescharacteristic
218C22×C4#12011yescharacteristic
219C22×C4#12111yescharacteristic
220C22×C4#12111yescharacteristic
221C22×C4#12311yescharacteristic
222C22×C4C22×C811yescharacteristic
223C22×C4C2×M1611yescharacteristic
224C22×C4#13111yescharacteristic
225C22×C4#13111yescharacteristic
226C22×C4C2×D811yescharacteristic
227C22×C4#13511yescharacteristic
228C22×C4AGL(1,ℤ/8)11yescharacteristic
229C22×C4AGL(1,ℤ/8)11yescharacteristic
230C2×C8—22no—
231C2×C8—22no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—42no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—42no—
238C2×C8—41no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—41no—
242C2×C8—42no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—42no—
247C2×C8—41no—
248C2×C8—81no—
249C2×C8—81no—
250C2×C8—81no—
251C2×C8—81no—
252C2×C8—81no—
253C2×C8—81no—
254C2×C8—81no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—22no—
264C4⋊C4—42no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—81no—
270C4⋊C4—81no—
271C4⋊C4—81no—
272C4⋊C4—81no—
273C4⋊C4—81no—
274C4⋊C4C22⋊C812yes—
275C4⋊C4C22⋊C812yes—
276C4⋊C4#10112yes—
277C42—21no—
278C42—21no—
279C42—21no—
280C42—21no—
281C42—41no—
282C42—41no—
283C42—41no—
284C42—41no—
285C42—41no—
286C42—41no—
287C42—41no—
288C42—41no—
289C42—41no—
290C42—41no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23#38611yescharacteristic
296C23C8×D411yescharacteristic
297C23#43511yescharacteristic
298C23C4×D811yescharacteristic
299C23#44211yescharacteristic
300C23#44311yescharacteristic
301C23#44411yescharacteristic
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—82no—
348C2×C4—82no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—161no—
357C2×C4—161no—
358C2×C4C2×C22⋊C811yescharacteristic
359C2×C4#40811yescharacteristic
360C2×C4#41011yescharacteristic
361C2×C4#41011yescharacteristic
362C2×C4C2×#10111yescharacteristic
363C2×C4#41311yescharacteristic
364C2×C4C8×D411yescharacteristic
365C2×C4#43511yescharacteristic
366C2×C4#44711yescharacteristic
367C2×C4#44911yescharacteristic
368C2×C4#45911yescharacteristic
369C2×C4#46311yescharacteristic
370C8—42no—
371C8—42no—
372C8—82no—
373C8—81no—
374C8—82no—
375C8—81no—
376C8—161no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22C8×D811yescharacteristic
390C22#158011yescharacteristic
391C22#158111yescharacteristic
392C22#158611yescharacteristic
393C22#186911yescharacteristic
394C22#187611yescharacteristic
395C22#187911yescharacteristic
396C22#189911yescharacteristic
397C22#190111yescharacteristic
398C22#190211yescharacteristic
399C22#190511yescharacteristic
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—41no—
407C4—41no—
408C4—42no—
409C4—42no—
410C4—42no—
411C4—81no—
412C4—82no—
413C4—161no—
414C4#145811yescharacteristic
415C4#146111yescharacteristic
416C4#147011yescharacteristic
417C4#147311yescharacteristic
418C2—21no—
419C2—21no—
420C2—21no—
421C2—21no—
422C2#894711yescharacteristic
423C2#908211yescharacteristic
424C2#908811yescharacteristic
425C2#924011yescharacteristic
426C2#924611yescharacteristic
427C2#925111yescharacteristic
428C2#926011yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C22×C8
Frattini, cosocleC22×C42C23
prime radicalC24C4×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
47. C2×#107C8semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#225992
C2×#19182
#96502
#87062
#75732
#70202
#70162