Finite Group Databasebeta

← #401153

Subgroups — #401153

Order 512.

1180 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1981C211yesmaximal, characteristic
2C2×#1927C212yesmaximal
3C2×#1919C211yesmaximal, characteristic
4#15188C211yesmaximal, characteristic
5#13818C211yesmaximal, characteristic
6#11255C211yesmaximal, characteristic
7#11227C211yesmaximal, characteristic
8#11067C212yesmaximal
9#11067C212yesmaximal
10#11010C211yesmaximal, characteristic
11#10932C212yesmaximal
12C22×C4⋊Q8C2211yescharacteristic
13C22×#106C2211yescharacteristic
14C22×C4⋊C8C2211yescharacteristic
15C22×#103C2212yes—
16C22×#103C2212yes—
17C22×#103C2212yes—
18C22×#103C2212yes—
19C2×#391C2212yes—
20C2×#391C2212yes—
21C2×#389C2211yescharacteristic
22C2×#389C2212yes—
23C2×C4×C4⋊C4C2212yes—
24C2×C4×C4⋊C4C2211yescharacteristic
25#1981—24no—
26#1927—28no—
27#1919—24no—
28C2×#340C2211yescharacteristic
29C2×#340C2211yescharacteristic
30C2×#340C2211yescharacteristic
31C2×#340C2212yes—
32C2×#340C2212yes—
33C2×#336C2211yescharacteristic
34C2×#336C2212yes—
35C2×#336C2212yes—
36#1442—22no—
37#1441—21no—
38#1441—21no—
39#1436—22no—
40C4⋊#95—21no—
41C4⋊#95C2211yescharacteristic
42C4×#95—21no—
43C4×#95C2211yescharacteristic
44C23×Q8C2312yes—
45C23×C8C2312yes—
46C23×C8C2311yescharacteristic
47C23×C8C2311yescharacteristic
48C2×C4⋊Q8—24no—
49C2×C4⋊Q8—22no—
50C2×C4⋊Q8—22no—
51C2×C4⋊Q8—42no—
52C22×C4⋊C4—22no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4C2311yescharacteristic
57C22×C4⋊C4C2311yescharacteristic
58C22×C4⋊C4C2312yes—
59C22×C4⋊C4C2311yescharacteristic
60C22×C4⋊C4C2311yescharacteristic
61C22×C42—21no—
62C22×C42—22no—
63C22×C42C2312yes—
64C22×C42C2311yescharacteristic
65C2×#106—22no—
66C2×#106—22no—
67C2×#106D414yes—
68C2×C4⋊C8—22no—
69C2×C4⋊C8—42no—
70C2×#103—24no—
71C2×#103—24no—
72C2×#103—24no—
73C2×#103—24no—
74C2×#103—24no—
75C2×#103—24no—
76C2×#103—24no—
77C2×#103—24no—
78C2×#103—24no—
79C2×#103—24no—
80C2×#103—42no—
81C2×#103—42no—
82#391—24no—
83#391—24no—
84#391—42no—
85#391—42no—
86#389—24no—
87#389—24no—
88#389—22no—
89#389—22no—
90C4×C4⋊C4—22no—
91C4×C4⋊C4—24no—
92C4×C4⋊C4—42no—
93C4×C4⋊C4D414yes—
94C2×#95—22no—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95—22no—
98C2×#95—22no—
99C2×#95—22no—
100C2×#95—22no—
101C2×#95—22no—
102C2×#95—21no—
103C2×#95—21no—
104C2×#95D411yescharacteristic
105C2×#95D411yescharacteristic
106C2×#95D412yes—
107#340—22no—
108#340—22no—
109#340—22no—
110#340—24no—
111#340—42no—
112#336—24no—
113#336—22no—
114#336—42no—
115C22×Q8—22no—
116C22×Q8—22no—
117C22×Q8—22no—
118C22×Q8—22no—
119C22×Q8—22no—
120C22×Q8—22no—
121C22×Q8—22no—
122C22×Q8—22no—
123C22×Q8—22no—
124C22×Q8—22no—
125C22×Q8—22no—
126C22×Q8—22no—
127C22×Q8—22no—
128C22×Q8#4114yes—
129C23×C4—21no—
130C23×C4—21no—
131C23×C4—22no—
132C23×C4—21no—
133C23×C4—22no—
134C23×C4—21no—
135C23×C4C2×D412yes—
136C23×C4C2×D411yescharacteristic
137C23×C4C2×D412yes—
138C23×C4C2×D411yescharacteristic
139C23×C4C2411yescharacteristic
140C22×C8—21no—
141C22×C8—22no—
142C22×C8—22no—
143C22×C8—21no—
144C22×C8—21no—
145C22×C8—22no—
146C22×C8—22no—
147C22×C8—22no—
148C22×C8—22no—
149C22×C8—22no—
150C22×C8—22no—
151C22×C8—22no—
152C22×C8—22no—
153C22×C8—22no—
154C22×C8—21no—
155C22×C8—21no—
156C22×C8C2×D412yes—
157C4⋊Q8—28no—
158C4⋊Q8—48no—
159C4⋊Q8—44no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—28no—
180C2×C4⋊C4—44no—
181C2×C4⋊C4—44no—
182C2×C4⋊C4—42no—
183C2×C4⋊C4—42no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—42no—
186C2×C4⋊C4—42no—
187C2×C4⋊C4—82no—
188C2×C4⋊C4—82no—
189C2×C4⋊C4C2×D412yes—
190C2×C4⋊C4C2×D412yes—
191C2×C4⋊C4C2×D412yes—
192C2×C4⋊C4C2×D412yes—
193C2×C4⋊C4#4114yes—
194C2×C4⋊C4#4112yes—
195C2×C4⋊C4#4114yes—
196C2×C42—22no—
197C2×C42—22no—
198C2×C42—22no—
199C2×C42—22no—
200C2×C42—22no—
201C2×C42—22no—
202C2×C42—22no—
203C2×C42—22no—
204C2×C42—24no—
205C2×C42—44no—
206C2×C42—44no—
207C2×C42—82no—
208C2×C42—82no—
209C2×C42C2×D412yes—
210C2×C42#4112yes—
211#106—28no—
212C4⋊C8—44no—
213#103—216no—
214#103—48no—
215#103—48no—
216#103—48no—
217#95—28no—
218#95—24no—
219#95—22no—
220#95—22no—
221#95—24no—
222#95—44no—
223#95—44no—
224#95—44no—
225#95—44no—
226#95—44no—
227#95—42no—
228#95—42no—
229#95—81no—
230C24C22×D411yescharacteristic
231C2×Q8—24no—
232C2×Q8—24no—
233C2×Q8—24no—
234C2×Q8—24no—
235C2×Q8—24no—
236C2×Q8—24no—
237C2×Q8—42no—
238C2×Q8—42no—
239C2×Q8—42no—
240C2×Q8—42no—
241C2×Q8—42no—
242C2×Q8—42no—
243C2×Q8—42no—
244C2×Q8—42no—
245C2×Q8—42no—
246C2×Q8—42no—
247C2×Q8—42no—
248C2×Q8—42no—
249C2×Q8—42no—
250C2×Q8—42no—
251C2×Q8—42no—
252C2×Q8—42no—
253C2×Q8—42no—
254C2×Q8—42no—
255C2×Q8—42no—
256C2×Q8—42no—
257C2×Q8—42no—
258C2×Q8—42no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—24no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—24no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—24no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—41no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—41no—
303C22×C4—42no—
304C22×C4—41no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—42no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—42no—
314C22×C4#12112yes—
315C22×C4#12112yes—
316C22×C4#13512yes—
317C22×C4#13714yes—
318C22×C4#13712yes—
319C22×C4C22×D411yescharacteristic
320C22×C4C22×D411yescharacteristic
321C22×C4C2×#4111yescharacteristic
322C22×C4C2×#4112yes—
323C22×C4C2×#4112yes—
324C22×C4C2×#4112yes—
325C22×C4C2×#4111yescharacteristic
326C22×C4H(5,𝔽2)12yes—
327C22×C4H(5,𝔽2)11yescharacteristic
328C22×C42−1+411yescharacteristic
329C2×C8—22no—
330C2×C8—24no—
331C2×C8—41no—
332C2×C8—42no—
333C2×C8—41no—
334C2×C8—42no—
335C2×C8—42no—
336C2×C8—41no—
337C2×C8—42no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—42no—
341C2×C8—42no—
342C2×C8—42no—
343C2×C8—42no—
344C2×C8—42no—
345C2×C8—42no—
346C4⋊C4—24no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—24no—
353C4⋊C4—24no—
354C4⋊C4—22no—
355C4⋊C4—48no—
356C4⋊C4—48no—
357C4⋊C4—41no—
358C4⋊C4—42no—
359C4⋊C4—41no—
360C4⋊C4—42no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—42no—
364C4⋊C4—88no—
365C4⋊C4—84no—
366C4⋊C4#12114yes—
367C4⋊C4#12414yes—
368C42—22no—
369C42—22no—
370C42—24no—
371C42—42no—
372C42—42no—
373C42—42no—
374C42—42no—
375C42—84no—
376C42—88no—
377C23C2×#12111yescharacteristic
378C23#52512yes—
379C23D4211yescharacteristic
380C23#54612yes—
381C23#54811yescharacteristic
382C23C2×#13511yescharacteristic
383C23C2×#13712yes—
384C23C2×#13711yescharacteristic
385C23#57711yescharacteristic
386C23#57712yes—
387C23#57811yescharacteristic
388Q8—44no—
389Q8—44no—
390Q8—44no—
391Q8—44no—
392Q8—82no—
393Q8—82no—
394Q8—82no—
395Q8—82no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—22no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—24no—
408C2×C4—42no—
409C2×C4—44no—
410C2×C4—42no—
411C2×C4—44no—
412C2×C4—44no—
413C2×C4—42no—
414C2×C4—44no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—44no—
425C2×C4—42no—
426C2×C4—44no—
427C2×C4—44no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—44no—
431C2×C4—44no—
432C2×C4—44no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—82no—
439C2×C4—82no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—82no—
443C2×C4—82no—
444C2×C4—82no—
445C2×C4—82no—
446C2×C4—82no—
447C2×C4—81no—
448C2×C4—82no—
449C2×C4—81no—
450C2×C4—81no—
451C2×C4—81no—
452C2×C4—81no—
453C2×C4—82no—
454C2×C4—82no—
455C2×C4#46414yes—
456C2×C4C2×#12111yescharacteristic
457C2×C4#52511yescharacteristic
458C2×C4#52512yes—
459C2×C4C2×#12411yescharacteristic
460C2×C4#52912yes—
461C2×C4#52912yes—
462C2×C4#53211yescharacteristic
463C2×C4#53511yescharacteristic
464C2×C4#53711yescharacteristic
465C2×C4#53812yes—
466C2×C4#54212yes—
467C2×C4#54711yescharacteristic
468C2×C4#55012yes—
469C2×C4#55112yes—
470C2×C4#55212yes—
471C2×C4#55312yes—
472C2×C4#55311yescharacteristic
473C2×C4#55912yes—
474C8—42no—
475C8—81no—
476C8—82no—
477C22#241111yescharacteristic
478C22#241611yescharacteristic
479C22#245612yes—
480C22#245812yes—
481C22#285011yescharacteristic
482C22C2×#46411yescharacteristic
483C22#303911yescharacteristic
484C22#304211yescharacteristic
485C22#304611yescharacteristic
486C22#310712yes—
487C22#311312yes—
488C22#312012yes—
489C22#312312yes—
490C22#326612yes—
491C22#327611yescharacteristic
492C22#328411yescharacteristic
493C22#330112yes—
494C22#331212yes—
495C22#331612yes—
496C22#332912yes—
497C22#336411yescharacteristic
498C22#336911yescharacteristic
499C22#337212yes—
500C4—24no—
501C4—44no—
502C4—44no—
503C4—44no—
504C4—42no—
505C4—82no—
506C4—84no—
507C4—82no—
508C4—84no—
509C4—161no—
510C4#239211yescharacteristic
511C4#247912yes—
512C4#254811yescharacteristic
513C4#256211yescharacteristic
514C4#259712yes—
515C4#266211yescharacteristic
516C2#1481311yescharacteristic
517C2#2448311yescharacteristic
518C2#2449811yescharacteristic
519C2#2472911yescharacteristic
520C2#2474811yescharacteristic
521C2#2662712yes—
522C2#2663612yes—
523C2#2669912yes—
524C2#2671112yes—
525C2#3303311yescharacteristic
526C2#3304011yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C4×#95 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#19812
C2×#19272
C2×#19192
#151882
#138182
#112552
#112272
#110672
#110102
#109322