Finite Group Databasebeta

← #99906

Subgroups — #99906

Order 512.

601 conjugacy classes of subgroups.

The subgroup lattice has 465 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22510C211yesmaximal, characteristic
2C2×#1863C211yesmaximal, characteristic
3#9879C211yesmaximal, characteristic
4#8311C211yesmaximal, characteristic
5#7576C211yesmaximal, characteristic
6#7020C211yesmaximal, characteristic
7#7016C211yesmaximal, characteristic
8C22×C4×Q8C2211yescharacteristic
9C2×#446—21no—
10C22×#107C411yescharacteristic
11C22×#103C411yescharacteristic
12C22×#103C411yescharacteristic
13C2×#389C2211yescharacteristic
14#1985—22no—
15#1984—21no—
16#1863—21no—
17#1863—21no—
18#1863—21no—
19#1863—21no—
20#1797—21no—
21#1797C2211yescharacteristic
22#1797C2211yescharacteristic
23#1749—21no—
24C4×C22⋊C8C2211yescharacteristic
25C4×C22⋊C8C2211yescharacteristic
26C2×#340C411yescharacteristic
27C2×#336C2211yescharacteristic
28C2×Q8⋊C8—21no—
29C2×Q8⋊C8—21no—
30#1280—21no—
31#1280—21no—
32#1271—22no—
33C23×Q8C2×C411yescharacteristic
34C23×C8C2×C411yescharacteristic
35C23×C8C2×C411yescharacteristic
36C2×C4×Q8—21no—
37C2×C4×Q8—21no—
38C2×C4×Q8—42no—
39C2×C4×Q8—42no—
40C2×C4×Q8D411yescharacteristic
41C2×C4×Q8D411yescharacteristic
42C2×C4×Q8D411yescharacteristic
43C2×C4×Q8D411yescharacteristic
44C22×C4⋊C4—21no—
45C22×C4⋊C4—21no—
46C22×C4⋊C4C2×C411yescharacteristic
47C22×C4⋊C4C2×C411yescharacteristic
48C22×C4⋊C4C2×C411yescharacteristic
49C22×C42—21no—
50C22×C42C2311yescharacteristic
51#446—42no—
52#446—42no—
53C2×#107—21no—
54C2×#107—21no—
55C2×#107—42no—
56C2×C4⋊C8—22no—
57C2×C4⋊C8—21no—
58C2×C4⋊C8—21no—
59C2×#103—21no—
60C2×#103—21no—
61C2×#103—22no—
62C2×#103—22no—
63C2×#103—21no—
64C2×#103—21no—
65C2×#103—42no—
66C2×C22⋊C8—21no—
67C2×C22⋊C8—21no—
68C2×C22⋊C8—21no—
69C2×C22⋊C8D411yescharacteristic
70C2×C22⋊C8D411yescharacteristic
71C2×#97—22no—
72C2×C4×C8—21no—
73C2×C4×C8—21no—
74#389—21no—
75#389—21no—
76#389—21no—
77#389—21no—
78C2×#95—21no—
79#340—21no—
80#340—21no—
81#336—22no—
82#336—22no—
83#336—21no—
84#336—21no—
85#336—21no—
86#336—21no—
87#336—21no—
88#336D412yes—
89Q8⋊C8—42no—
90Q8⋊C8—42no—
91C22×Q8—21no—
92C22×Q8—22no—
93C22×Q8—22no—
94C22×Q8—21no—
95C22×Q8—21no—
96C22×Q8—21no—
97C22×Q8—21no—
98C22×Q8—41no—
99C22×Q8—41no—
100C22×Q8C22⋊C411yescharacteristic
101C22×Q8C22⋊C411yescharacteristic
102C23×C4—21no—
103C23×C4—21no—
104C23×C4—21no—
105C23×C4—21no—
106C23×C4C22×C411yescharacteristic
107C23×C4C2×D411yescharacteristic
108C23×C4#4111yescharacteristic
109C22×C8—21no—
110C22×C8—21no—
111C22×C8—21no—
112C22×C8—21no—
113C22×C8—21no—
114C22×C8—22no—
115C22×C8—21no—
116C22×C8—21no—
117C22×C8—41no—
118C22×C8—41no—
119C22×C8—41no—
120C22×C8—41no—
121C22×C8—41no—
122C22×C8—41no—
123C22×C8M1612yes—
124C4×Q8—22no—
125C4×Q8—22no—
126C4×Q8—22no—
127C4×Q8—22no—
128C4×Q8—41no—
129C4×Q8—41no—
130C4×Q8—41no—
131C4×Q8—41no—
132C4×Q8—44no—
133C4×Q8—44no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—41no—
148C2×C4⋊C4—44no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—82no—
154C2×C4⋊C4C22⋊C411yescharacteristic
155C2×C4⋊C4C22⋊C411yescharacteristic
156C2×C4⋊C4M1612yes—
157C2×C42—21no—
158C2×C42—21no—
159C2×C42—21no—
160C2×C42—21no—
161C2×C42—41no—
162C2×C42—41no—
163C2×C42—44no—
164C2×C42C2×D411yescharacteristic
165C2×C42C2×D411yescharacteristic
166C2×C42C2×D411yescharacteristic
167C2×C42#4111yescharacteristic
168#107—42no—
169#107—42no—
170C4⋊C8—44no—
171C4⋊C8—41no—
172C4⋊C8—41no—
173C4⋊C8—41no—
174C4⋊C8—41no—
175#103—24no—
176#103—24no—
177#103—42no—
178#103—42no—
179C22⋊C8—21no—
180C22⋊C8—22no—
181C22⋊C8—21no—
182C22⋊C8—21no—
183C22⋊C8—41no—
184C22⋊C8—41no—
185C22⋊C8—41no—
186C22⋊C8—41no—
187C22⋊C8—41no—
188C22⋊C8Q1612yes—
189#97—44no—
190C4×C8—41no—
191C4×C8—41no—
192C4×C8—41no—
193C4×C8—41no—
194#95—41no—
195#95—41no—
196C24C4×D411yescharacteristic
197C2×Q8—21no—
198C2×Q8—21no—
199C2×Q8—24no—
200C2×Q8—24no—
201C2×Q8—21no—
202C2×Q8—21no—
203C2×Q8—21no—
204C2×Q8—21no—
205C2×Q8—21no—
206C2×Q8—21no—
207C2×Q8—21no—
208C2×Q8—21no—
209C2×Q8—42no—
210C2×Q8—42no—
211C2×Q8—42no—
212C2×Q8—42no—
213C2×Q8—42no—
214C2×Q8—42no—
215C2×Q8—42no—
216C2×Q8—42no—
217C2×Q8—41no—
218C2×Q8—41no—
219C2×Q8#9912yes—
220C2×Q8#10112yes—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—22no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—81no—
249C22×C4—81no—
250C22×C4—81no—
251C22×C4—81no—
252C22×C4—81no—
253C22×C4C2×C22⋊C411yescharacteristic
254C22×C4C4×D411yescharacteristic
255C22×C4#12011yescharacteristic
256C22×C4#12111yescharacteristic
257C22×C4#12111yescharacteristic
258C22×C4#12311yescharacteristic
259C22×C4C2×M1611yescharacteristic
260C22×C4C2×M1611yescharacteristic
261C22×C4#13111yescharacteristic
262C22×C4#13111yescharacteristic
263C22×C4C2×Q1611yescharacteristic
264C22×C4#13511yescharacteristic
265C22×C4#13711yescharacteristic
266C22×C4#13711yescharacteristic
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—42no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—42no—
275C2×C8—41no—
276C2×C8—42no—
277C2×C8—42no—
278C2×C8—41no—
279C2×C8—42no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—42no—
285C2×C8—81no—
286C2×C8—81no—
287C2×C8—81no—
288C2×C8—81no—
289C2×C8—81no—
290C2×C8—81no—
291C2×C8—81no—
292C4⋊C4—24no—
293C4⋊C4—21no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—22no—
298C4⋊C4—42no—
299C4⋊C4—42no—
300C4⋊C4—42no—
301C4⋊C4—42no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—81no—
307C4⋊C4—82no—
308C4⋊C4—82no—
309C4⋊C4#9912yes—
310C42—24no—
311C42—21no—
312C42—21no—
313C42—21no—
314C42—21no—
315C42—41no—
316C42—41no—
317C42—42no—
318C42—42no—
319C42—42no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23#38611yescharacteristic
325C23#43511yescharacteristic
326C23#43611yescharacteristic
327C23C4×Q1611yescharacteristic
328C23#44111yescharacteristic
329C23#44311yescharacteristic
330C23#44411yescharacteristic
331Q8—22no—
332Q8—22no—
333Q8—22no—
334Q8—22no—
335Q8—44no—
336Q8—44no—
337Q8—41no—
338Q8—41no—
339Q8—41no—
340Q8—41no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—21no—
361C2×C4—22no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—44no—
369C2×C4—44no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—82no—
383C2×C4—82no—
384C2×C4—82no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—82no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—161no—
392C2×C4—161no—
393C2×C4#40711yescharacteristic
394C2×C4#40811yescharacteristic
395C2×C4C2×#9911yescharacteristic
396C2×C4C2×#9911yescharacteristic
397C2×C4C2×#10111yescharacteristic
398C2×C4#41311yescharacteristic
399C2×C4#43511yescharacteristic
400C2×C4#43611yescharacteristic
401C2×C4#45111yescharacteristic
402C2×C4#45211yescharacteristic
403C2×C4#46211yescharacteristic
404C2×C4#46411yescharacteristic
405C8—42no—
406C8—42no—
407C8—81no—
408C8—82no—
409C8—82no—
410C8—81no—
411C8—161no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22#158411yescharacteristic
425C22#158711yescharacteristic
426C22#159111yescharacteristic
427C22#159311yescharacteristic
428C22#187011yescharacteristic
429C22#187611yescharacteristic
430C22#187811yescharacteristic
431C22#189811yescharacteristic
432C22#190111yescharacteristic
433C22#190311yescharacteristic
434C22#190511yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—41no—
442C4—41no—
443C4—42no—
444C4—42no—
445C4—42no—
446C4—81no—
447C4—82no—
448C4—161no—
449C4#146311yescharacteristic
450C4#146511yescharacteristic
451C4#146811yescharacteristic
452C4#147211yescharacteristic
453C2—21no—
454C2—21no—
455C2—21no—
456C2—21no—
457C2#895011yescharacteristic
458C2#908511yescharacteristic
459C2#909411yescharacteristic
460C2#924111yescharacteristic
461C2#924611yescharacteristic
462C2#925011yescharacteristic
463C2#925811yescharacteristic
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
#225102
C2×#18632
#98792
#83112
#75762
#70202
#70162