Finite Group Databasebeta

← #99910

Subgroups — #99910

Order 512.

611 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22510C211yesmaximal, characteristic
2C2×#1865C211yesmaximal, characteristic
3#9650C211yesmaximal, characteristic
4#8311C211yesmaximal, characteristic
5#7573C211yesmaximal, characteristic
6#7020C211yesmaximal, characteristic
7#7016C211yesmaximal, characteristic
8C22×C4×Q8C2211yescharacteristic
9C2×#446—21no—
10C22×#106C411yescharacteristic
11C22×#103C411yescharacteristic
12C22×#103C411yescharacteristic
13C2×#389C2211yescharacteristic
14#1985—22no—
15#1984—21no—
16#1865—21no—
17#1865—21no—
18#1865—21no—
19#1865—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—
30C2×#324—21no—
31C2×#324—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×#106—21no—
54C2×#106—21no—
55C2×#106—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—
91#324—42no—
92#324—42no—
93C22×Q8—21no—
94C22×Q8—22no—
95C22×Q8—22no—
96C22×Q8—21no—
97C22×Q8—21no—
98C22×Q8—21no—
99C22×Q8—21no—
100C22×Q8—41no—
101C22×Q8—41no—
102C22×Q8C22⋊C411yescharacteristic
103C22×Q8C22⋊C411yescharacteristic
104C23×C4—21no—
105C23×C4—21no—
106C23×C4—21no—
107C23×C4—21no—
108C23×C4C22×C411yescharacteristic
109C23×C4C2×D411yescharacteristic
110C23×C4#4111yescharacteristic
111C22×C8—21no—
112C22×C8—21no—
113C22×C8—21no—
114C22×C8—21no—
115C22×C8—21no—
116C22×C8—22no—
117C22×C8—21no—
118C22×C8—21no—
119C22×C8—41no—
120C22×C8—41no—
121C22×C8—41no—
122C22×C8—41no—
123C22×C8—41no—
124C22×C8—41no—
125C22×C8M1612yes—
126C4×Q8—22no—
127C4×Q8—22no—
128C4×Q8—22no—
129C4×Q8—22no—
130C4×Q8—41no—
131C4×Q8—41no—
132C4×Q8—41no—
133C4×Q8—41no—
134C4×Q8—44no—
135C4×Q8—44no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4—44no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—41no—
154C2×C4⋊C4—41no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4C22⋊C411yescharacteristic
160C2×C4⋊C4C22⋊C411yescharacteristic
161C2×C4⋊C4M1612yes—
162C2×C42—21no—
163C2×C42—21no—
164C2×C42—21no—
165C2×C42—21no—
166C2×C42—41no—
167C2×C42—41no—
168C2×C42—44no—
169C2×C42C2×D411yescharacteristic
170C2×C42C2×D411yescharacteristic
171C2×C42C2×D411yescharacteristic
172C2×C42#4111yescharacteristic
173#106—42no—
174#106—42no—
175C4⋊C8—44no—
176C4⋊C8—41no—
177C4⋊C8—41no—
178C4⋊C8—41no—
179C4⋊C8—41no—
180#103—24no—
181#103—24no—
182#103—42no—
183#103—42no—
184C22⋊C8—21no—
185C22⋊C8—22no—
186C22⋊C8—21no—
187C22⋊C8—21no—
188C22⋊C8—41no—
189C22⋊C8—41no—
190C22⋊C8—41no—
191C22⋊C8—41no—
192C22⋊C8—41no—
193C22⋊C8SD1612yes—
194#97—44no—
195C4×C8—41no—
196C4×C8—41no—
197C4×C8—41no—
198C4×C8—41no—
199#95—41no—
200#95—41no—
201C24C4×D411yescharacteristic
202C2×Q8—21no—
203C2×Q8—21no—
204C2×Q8—24no—
205C2×Q8—24no—
206C2×Q8—21no—
207C2×Q8—21no—
208C2×Q8—21no—
209C2×Q8—21no—
210C2×Q8—21no—
211C2×Q8—21no—
212C2×Q8—21no—
213C2×Q8—21no—
214C2×Q8—42no—
215C2×Q8—42no—
216C2×Q8—42no—
217C2×Q8—42no—
218C2×Q8—42no—
219C2×Q8—42no—
220C2×Q8—42no—
221C2×Q8—42no—
222C2×Q8—41no—
223C2×Q8—41no—
224C2×Q8#9912yes—
225C2×Q8#10112yes—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—81no—
258C22×C4—81no—
259C22×C4—81no—
260C22×C4C2×C22⋊C411yescharacteristic
261C22×C4C4×D411yescharacteristic
262C22×C4#12011yescharacteristic
263C22×C4#12111yescharacteristic
264C22×C4#12111yescharacteristic
265C22×C4#12311yescharacteristic
266C22×C4C2×M1611yescharacteristic
267C22×C4C2×M1611yescharacteristic
268C22×C4#13111yescharacteristic
269C22×C4#13111yescharacteristic
270C22×C4C2×SD1611yescharacteristic
271C22×C4#13511yescharacteristic
272C22×C4AGL(1,ℤ/8)11yescharacteristic
273C22×C4#13711yescharacteristic
274C2×C8—22no—
275C2×C8—22no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—42no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—42no—
282C2×C8—41no—
283C2×C8—42no—
284C2×C8—42no—
285C2×C8—41no—
286C2×C8—42no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—42no—
292C2×C8—81no—
293C2×C8—81no—
294C2×C8—81no—
295C2×C8—81no—
296C2×C8—81no—
297C2×C8—81no—
298C2×C8—81no—
299C4⋊C4—24no—
300C4⋊C4—21no—
301C4⋊C4—22no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—22no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—42no—
308C4⋊C4—42no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—81no—
314C4⋊C4—81no—
315C4⋊C4—81no—
316C4⋊C4—81no—
317C4⋊C4—81no—
318C4⋊C4#9912yes—
319C42—24no—
320C42—21no—
321C42—21no—
322C42—21no—
323C42—21no—
324C42—41no—
325C42—41no—
326C42—42no—
327C42—42no—
328C42—42no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23#38611yescharacteristic
334C23#43511yescharacteristic
335C23#43611yescharacteristic
336C23C4×SD1611yescharacteristic
337C23#44011yescharacteristic
338C23#44311yescharacteristic
339C23#44411yescharacteristic
340Q8—22no—
341Q8—22no—
342Q8—22no—
343Q8—22no—
344Q8—44no—
345Q8—44no—
346Q8—41no—
347Q8—41no—
348Q8—41no—
349Q8—41no—
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—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—44no—
378C2×C4—44no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—82no—
394C2×C4—82no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—161no—
403C2×C4—161no—
404C2×C4#40711yescharacteristic
405C2×C4#40811yescharacteristic
406C2×C4C2×#9911yescharacteristic
407C2×C4C2×#9911yescharacteristic
408C2×C4C2×#10111yescharacteristic
409C2×C4#41311yescharacteristic
410C2×C4#43511yescharacteristic
411C2×C4#43611yescharacteristic
412C2×C4#44811yescharacteristic
413C2×C4#44911yescharacteristic
414C2×C4#46011yescharacteristic
415C2×C4#46411yescharacteristic
416C8—42no—
417C8—42no—
418C8—81no—
419C8—82no—
420C8—82no—
421C8—81no—
422C8—161no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22#158211yescharacteristic
436C22#158511yescharacteristic
437C22#159011yescharacteristic
438C22#159211yescharacteristic
439C22#187011yescharacteristic
440C22#187611yescharacteristic
441C22#188011yescharacteristic
442C22#189811yescharacteristic
443C22#190111yescharacteristic
444C22#190211yescharacteristic
445C22#190511yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—41no—
453C4—41no—
454C4—42no—
455C4—42no—
456C4—42no—
457C4—81no—
458C4—82no—
459C4—161no—
460C4#146311yescharacteristic
461C4#146511yescharacteristic
462C4#146811yescharacteristic
463C4#147211yescharacteristic
464C2—21no—
465C2—21no—
466C2—21no—
467C2—21no—
468C2#895211yescharacteristic
469C2#908511yescharacteristic
470C2#909211yescharacteristic
471C2#923911yescharacteristic
472C2#924611yescharacteristic
473C2#925211yescharacteristic
474C2#926211yescharacteristic
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×#18652
#96502
#83112
#75732
#70202
#70162