Finite Group Databasebeta

← #99909

Subgroups — #99909

Order 512.

473 conjugacy classes of subgroups.

The subgroup lattice has 417 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22629C211yesmaximal, characteristic
2C2×#1919C211yesmaximal, characteristic
3#9650C211yesmaximal, characteristic
4#8707C211yesmaximal, characteristic
5#7573C211yesmaximal, characteristic
6#7020C211yesmaximal, characteristic
7#7016C211yesmaximal, characteristic
8C22×#106C411yescharacteristic
9C2×#389C2211yescharacteristic
10C2×C4×C4⋊C4C2211yescharacteristic
11#1939—21no—
12#1919—21no—
13#1919—21no—
14#1919—21no—
15#1919—21no—
16#1917—22no—
17#1797—21no—
18#1797C2211yescharacteristic
19#1797C2211yescharacteristic
20#1770—21no—
21#1749—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
42C2×#106—22no—
43C2×#106—21no—
44C2×#106—21no—
45C2×#106—22no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8—22no—
49C2×C22⋊C8—21no—
50C2×C22⋊C8—21no—
51C2×C22⋊C8—21no—
52C2×C22⋊C8D411yescharacteristic
53C2×C22⋊C8D411yescharacteristic
54C2×#97—22no—
55C2×C4×C8—21no—
56C2×C4×C8—21no—
57#389—21no—
58#389—21no—
59#389—21no—
60#389—21no—
61C4×C4⋊C4—21no—
62C4×C4⋊C4—21no—
63C4×C4⋊C4D411yescharacteristic
64C4×C4⋊C4D411yescharacteristic
65C4×C4⋊C4D411yescharacteristic
66C4×C4⋊C4D411yescharacteristic
67C2×#95—21no—
68C2×#95—21no—
69#340—21no—
70#340—21no—
71#340—21no—
72#340—21no—
73#340—21no—
74#340—21no—
75#336—22no—
76#336—22no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336D412yes—
83#324—42no—
84#324—42no—
85C23×C4—21no—
86C23×C4—21no—
87C23×C4—21no—
88C23×C4—21no—
89C23×C4C22×C411yescharacteristic
90C23×C4C2×D411yescharacteristic
91C23×C4#4111yescharacteristic
92C22×C8—21no—
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—21no—
97C22×C8—22no—
98C22×C8—21no—
99C22×C8—21no—
100C22×C8—41no—
101C22×C8—41no—
102C22×C8—41no—
103C22×C8—41no—
104C22×C8—41no—
105C22×C8—41no—
106C22×C8M1612yes—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
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—22no—
116C2×C4⋊C4—21no—
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⋊C4M1612yes—
135C2×C42—21no—
136C2×C42—21no—
137C2×C42—21no—
138C2×C42—21no—
139C2×C42—41no—
140C2×C42—41no—
141C2×C42—82no—
142C2×C42C2×D411yescharacteristic
143C2×C42C2×D411yescharacteristic
144C2×C42C2×D411yescharacteristic
145C2×C42#4111yescharacteristic
146#106—24no—
147#106—24no—
148C4⋊C8—41no—
149C4⋊C8—41no—
150C4⋊C8—41no—
151C4⋊C8—41no—
152C4⋊C8—82no—
153C22⋊C8—21no—
154C22⋊C8—22no—
155C22⋊C8—21no—
156C22⋊C8—21no—
157C22⋊C8—41no—
158C22⋊C8—41no—
159C22⋊C8—41no—
160C22⋊C8—41no—
161C22⋊C8—41no—
162C22⋊C8SD1612yes—
163#97—82no—
164C4×C8—41no—
165C4×C8—41no—
166C4×C8—41no—
167C4×C8—41no—
168#95—21no—
169#95—21no—
170#95—21no—
171#95—21no—
172#95—41no—
173#95—41no—
174C24C4×D411yescharacteristic
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—22no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—41no—
189C22×C4—41no—
190C22×C4—42no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—81no—
205C22×C4—81no—
206C22×C4—81no—
207C22×C4—81no—
208C22×C4—81no—
209C22×C4C2×C22⋊C411yescharacteristic
210C22×C4C4×D411yescharacteristic
211C22×C4#12011yescharacteristic
212C22×C4#12111yescharacteristic
213C22×C4#12111yescharacteristic
214C22×C4#12311yescharacteristic
215C22×C4C2×M1611yescharacteristic
216C22×C4C2×M1611yescharacteristic
217C22×C4#13111yescharacteristic
218C22×C4#13111yescharacteristic
219C22×C4C2×SD1611yescharacteristic
220C22×C4#13511yescharacteristic
221C22×C4AGL(1,ℤ/8)11yescharacteristic
222C22×C4#13711yescharacteristic
223C2×C8—22no—
224C2×C8—22no—
225C2×C8—41no—
226C2×C8—41no—
227C2×C8—42no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—42no—
231C2×C8—41no—
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—42no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—42no—
241C2×C8—81no—
242C2×C8—81no—
243C2×C8—81no—
244C2×C8—81no—
245C2×C8—81no—
246C2×C8—81no—
247C2×C8—81no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—22no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—22no—
257C4⋊C4—42no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—81no—
265C4⋊C4—81no—
266C4⋊C4—81no—
267C4⋊C4—81no—
268C4⋊C4—81no—
269C4⋊C4#10112yes—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—41no—
275C42—41no—
276C42—42no—
277C42—42no—
278C42—81no—
279C42—81no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23#38611yescharacteristic
285C23#43511yescharacteristic
286C23#43611yescharacteristic
287C23C4×SD1611yescharacteristic
288C23#44011yescharacteristic
289C23#44311yescharacteristic
290C23#44411yescharacteristic
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—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—161no—
344C2×C4—161no—
345C2×C4#40711yescharacteristic
346C2×C4#40811yescharacteristic
347C2×C4#41011yescharacteristic
348C2×C4#41011yescharacteristic
349C2×C4C2×#10111yescharacteristic
350C2×C4#41311yescharacteristic
351C2×C4#43511yescharacteristic
352C2×C4#43611yescharacteristic
353C2×C4#44811yescharacteristic
354C2×C4#44911yescharacteristic
355C2×C4#46011yescharacteristic
356C2×C4#46411yescharacteristic
357C8—42no—
358C8—42no—
359C8—81no—
360C8—82no—
361C8—82no—
362C8—81no—
363C8—161no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22#158211yescharacteristic
377C22#158511yescharacteristic
378C22#159011yescharacteristic
379C22#159211yescharacteristic
380C22#187011yescharacteristic
381C22#187611yescharacteristic
382C22#188011yescharacteristic
383C22#189911yescharacteristic
384C22#190111yescharacteristic
385C22#190211yescharacteristic
386C22#190411yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—41no—
394C4—41no—
395C4—42no—
396C4—81no—
397C4—81no—
398C4—81no—
399C4—82no—
400C4—161no—
401C4#146411yescharacteristic
402C4#146711yescharacteristic
403C4#147011yescharacteristic
404C4#147311yescharacteristic
405C2—21no—
406C2—21no—
407C2—21no—
408C2—21no—
409C2#895211yescharacteristic
410C2#908611yescharacteristic
411C2#909111yescharacteristic
412C2#924011yescharacteristic
413C2#924511yescharacteristic
414C2#925211yescharacteristic
415C2#926111yescharacteristic
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 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#226292
C2×#19192
#96502
#87072
#75732
#70202
#70162