Finite Group Databasebeta

← #416282

Subgroups — #416282

Order 512.

944 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1950C211yesmaximal, characteristic
2#21145C211yesmaximal, characteristic
3#20765C211yesmaximal, characteristic
4#20647C211yesmaximal, characteristic
5C2×#1805C211yesmaximal, characteristic
6C2×C4×#101C211yesmaximal, characteristic
7#11303C212yesmaximal
8#11242C212yesmaximal
9#11128C212yesmaximal
10#11062C212yesmaximal
11#10858C211yesmaximal, characteristic
12C22×C4×Q8C2211yescharacteristic
13C22×#108C2212yes—
14C2×#424C2212yes—
15C2×#423C2211yescharacteristic
16C22×C4⋊C8C2211yescharacteristic
17C2×#419C2212yes—
18C22×#103C2212yes—
19C22×#101C2211yescharacteristic
20C22×#101C2211yescharacteristic
21C2×C4×M16C2211yescharacteristic
22C2×C4×M16C2211yescharacteristic
23#2285C2211yescharacteristic
24C2×#382C2211yescharacteristic
25#1950—24no—
26#1940—22no—
27#1939—22no—
28#1836—22no—
29#1835—22no—
30#1805—22no—
31#1805—22no—
32#1805—22no—
33#1803—22no—
34C4×#101—24no—
35C2×#343C2211yescharacteristic
36C2×#343C2212yes—
37C2×#343C2211yescharacteristic
38C2×#343C2212yes—
39C2×#341C2212yes—
40#1736C2212yes—
41#1736C2212yes—
42#1736C2212yes—
43C2×#340C2212yes—
44#1729C2212yes—
45C23×Q8C2311yescharacteristic
46C22×M16C2312yes—
47C22×M16C2311yescharacteristic
48C22×M16C2311yescharacteristic
49C22×M16C2311yescharacteristic
50C22×M16C2311yescharacteristic
51C23×C8C2312yes—
52C2×C4×Q8—22no—
53C2×C4×Q8—21no—
54C2×C4×Q8—21no—
55C2×C4×Q8—21no—
56C2×C4×Q8—21no—
57C2×C4×Q8—22no—
58C2×C4×Q8—22no—
59C2×C4×Q8Q814yes—
60C2×#117C2312yes—
61C22×C4⋊C4—21no—
62C22×C4⋊C4C2312yes—
63C22×C4⋊C4C2311yescharacteristic
64C22×C42—21no—
65C22×C42C2311yescharacteristic
66C2×#108—24no—
67C2×#108—42no—
68C2×#108—42no—
69#424—24no—
70#424—42no—
71#423—22no—
72#423—22no—
73C2×C4⋊C8—22no—
74C2×C4⋊C8—22no—
75C2×C4⋊C8—24no—
76C2×C4⋊C8—21no—
77C2×C4⋊C8—21no—
78C2×C4⋊C8D412yes—
79C2×C4⋊C8D412yes—
80#419—24no—
81#419—42no—
82C2×#103—24no—
83C2×#103—24no—
84C2×#103—24no—
85C2×#103—42no—
86C2×#101—22no—
87C2×#101—22no—
88C2×#101—22no—
89C2×#101—22no—
90C2×#101—22no—
91C2×#101—22no—
92C4×M16—22no—
93C4×M16—22no—
94C4×M16—22no—
95C4×M16D414yes—
96C2×#97—21no—
97C2×#97—21no—
98C2×C4×C8—21no—
99C2×C4×C8—21no—
100#384D412yes—
101#382—21no—
102#382—21no—
103#382—21no—
104#382—21no—
105#382D412yes—
106#380—21no—
107#380—21no—
108C4×C4⋊C4—21no—
109C4×C4⋊C4—21no—
110C2×#95—21no—
111C2×#95—21no—
112#343—22no—
113#343—22no—
114#343—24no—
115#343—42no—
116#341—24no—
117#340—24no—
118#340—24no—
119#340—24no—
120#340—24no—
121#336—24no—
122C22×Q8—21no—
123C22×Q8—21no—
124C22×Q8—21no—
125C22×Q8—21no—
126C22×Q8—21no—
127C22×Q8—21no—
128C22×Q8—21no—
129C22×Q8—21no—
130C22×Q8—21no—
131C22×Q8—21no—
132C22×Q8—21no—
133C22×Q8C2×Q812yes—
134C22×Q8#4112yes—
135C22×Q8#4112yes—
136C23×C4—21no—
137C23×C4—21no—
138C23×C4—22no—
139C23×C4#4111yescharacteristic
140C23×C4#4111yescharacteristic
141C23×C4C2411yescharacteristic
142C2×M16—21no—
143C2×M16—21no—
144C2×M16—21no—
145C2×M16—21no—
146C2×M16—21no—
147C2×M16—21no—
148C2×M16—21no—
149C2×M16—21no—
150C2×M16—21no—
151C2×M16—21no—
152C2×M16—21no—
153C2×M16—21no—
154C2×M16—21no—
155C2×M16—21no—
156C2×M16—21no—
157C2×M16—21no—
158C2×M16—21no—
159C2×M16—21no—
160C2×M16—21no—
161C2×M16—21no—
162C2×M16—22no—
163C2×M16—22no—
164C2×M16—22no—
165C2×M16—22no—
166C2×M16—22no—
167C2×M16—22no—
168C2×M16C2×D412yes—
169C2×M16C2×D412yes—
170C2×M16#4112yes—
171C2×M16#4112yes—
172C22×C8—22no—
173C22×C8—21no—
174C22×C8—21no—
175C22×C8—21no—
176C22×C8—21no—
177C22×C8—22no—
178C22×C8—22no—
179C22×C8—22no—
180C22×C8—22no—
181C22×C8—22no—
182C22×C8—22no—
183C22×C8C2×D414yes—
184C4×Q8—24no—
185C4×Q8—24no—
186C4×Q8—24no—
187C4×Q8—24no—
188C4×Q8—42no—
189C4×Q8—42no—
190C4×Q8—42no—
191C4×Q8—42no—
192#117—22no—
193#117—22no—
194#117—22no—
195#117—22no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—24no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—41no—
211C2×C4⋊C4—41no—
212C2×C4⋊C4—42no—
213C2×C4⋊C4C2×D414yes—
214C2×C4⋊C4C2×Q812yes—
215C2×C22⋊C4—22no—
216C2×C42—24no—
217C2×C42—22no—
218C2×C42—41no—
219C2×C42—41no—
220C2×C42—42no—
221C2×C42C2×D412yes—
222C2×C42C2×D411yescharacteristic
223C2×C42C2×D411yescharacteristic
224C2×C42C2×D411yescharacteristic
225C2×C42C2×D411yescharacteristic
226C2×C42C2×Q812yes—
227C2×C42#4112yes—
228C2×C42#4112yes—
229#108—48no—
230C4⋊C8—24no—
231C4⋊C8—24no—
232C4⋊C8—48no—
233C4⋊C8—42no—
234C4⋊C8—42no—
235#103—48no—
236#103—48no—
237#101—28no—
238#101—28no—
239#97—24no—
240#97—42no—
241C4×C8—24no—
242C4×C8—42no—
243#95—22no—
244#95—22no—
245#95—41no—
246#95—41no—
247#95—41no—
248#95—41no—
249C24C2×#4111yescharacteristic
250C2×Q8—22no—
251C2×Q8—22no—
252C2×Q8—22no—
253C2×Q8—22no—
254C2×Q8—22no—
255C2×Q8—22no—
256C2×Q8—22no—
257C2×Q8—22no—
258C2×Q8—22no—
259C2×Q8—22no—
260C2×Q8—22no—
261C2×Q8—22no—
262C2×Q8—22no—
263C2×Q8—22no—
264C2×Q8—22no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8#12514yes—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—24no—
282C22×C4—22no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—82no—
295C22×C4—82no—
296C22×C4—82no—
297C22×C4#12111yescharacteristic
298C22×C4#12111yescharacteristic
299C22×C4#12111yescharacteristic
300C22×C4#12111yescharacteristic
301C22×C4C22⋊Q812yes—
302C22×C4C22⋊Q812yes—
303C22×C4#12612yes—
304C22×C4#12612yes—
305C22×C4C22×D411yescharacteristic
306C22×C4C22×D411yescharacteristic
307C22×C4C22×D411yescharacteristic
308C22×C4C22×Q811yescharacteristic
309C22×C4C2×#4111yescharacteristic
310C22×C4C2×#4111yescharacteristic
311C22×C4C2×#4111yescharacteristic
312C22×C4C2×#4111yescharacteristic
313C22×C4C2×#4111yescharacteristic
314C22×C4C2×#4111yescharacteristic
315C22×C4H(5,𝔽2)11yescharacteristic
316C22×C4H(5,𝔽2)11yescharacteristic
317C22×C42−1+411yescharacteristic
318C22×C42−1+411yescharacteristic
319M16—22no—
320M16—22no—
321M16—22no—
322M16—22no—
323M16—22no—
324M16—22no—
325M16—22no—
326M16—22no—
327M16—41no—
328M16—41no—
329M16—41no—
330M16—41no—
331M16—41no—
332M16—41no—
333M16—41no—
334M16—41no—
335M16—42no—
336M16—42no—
337M16—42no—
338M16—42no—
339C2×C8—22no—
340C2×C8—22no—
341C2×C8—24no—
342C2×C8—24no—
343C2×C8—22no—
344C2×C8—24no—
345C2×C8—22no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—42no—
349C2×C8—42no—
350C2×C8—41no—
351C2×C8—41no—
352C2×C8—41no—
353C2×C8—41no—
354C2×C8—41no—
355C2×C8—41no—
356C2×C8—42no—
357C2×C8—42no—
358C2×C8—42no—
359C2×C8—42no—
360C2×C8—42no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—24no—
364C4⋊C4—24no—
365C4⋊C4—44no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—44no—
369C4⋊C4—44no—
370C4⋊C4—42no—
371C4⋊C4—42no—
372C4⋊C4—42no—
373C4⋊C4—42no—
374C4⋊C4—82no—
375C22⋊C4—42no—
376C22⋊C4—42no—
377C42—42no—
378C42—42no—
379C42—44no—
380C42—44no—
381C42#12112yes—
382C42#12112yes—
383C42#12112yes—
384C42#12112yes—
385C42C22⋊Q812yes—
386C42C22⋊Q812yes—
387C42C22⋊Q812yes—
388C42C22⋊Q812yes—
389C23—22no—
390C23—22no—
391C23C2×#12111yescharacteristic
392C23C2×C22⋊Q811yescharacteristic
393C23C2×#12611yescharacteristic
394C23#52911yescharacteristic
395C23#52911yescharacteristic
396C23#54211yescharacteristic
397C23#54211yescharacteristic
398Q8—24no—
399Q8—24no—
400Q8—42no—
401Q8—42no—
402Q8—42no—
403Q8—42no—
404Q8—42no—
405Q8—42no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—24no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—44no—
423C2×C4—44no—
424C2×C4—44no—
425C2×C4—82no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4—82no—
429C2×C4—82no—
430C2×C4—82no—
431C2×C4—162no—
432C2×C4—162no—
433C2×C4#39612yes—
434C2×C4#39612yes—
435C2×C4#39612yes—
436C2×C4#39612yes—
437C2×C4C2×#12111yescharacteristic
438C2×C4C2×#12111yescharacteristic
439C2×C4C2×C22⋊Q811yescharacteristic
440C2×C4C2×C22⋊Q811yescharacteristic
441C2×C4#52511yescharacteristic
442C2×C4#52511yescharacteristic
443C2×C4C2×#12511yescharacteristic
444C2×C4#53311yescharacteristic
445C2×C4#53511yescharacteristic
446C2×C4#53611yescharacteristic
447C2×C4#54411yescharacteristic
448C2×C4#54411yescharacteristic
449C2×C4#54611yescharacteristic
450C2×C4#54611yescharacteristic
451C2×C4#54611yescharacteristic
452C2×C4#54711yescharacteristic
453C2×C4#54811yescharacteristic
454C2×C4#54811yescharacteristic
455C2×C4#54811yescharacteristic
456C2×C4#55011yescharacteristic
457C2×C4#55211yescharacteristic
458C2×C4#55211yescharacteristic
459C2×C4#55211yescharacteristic
460C2×C4#55311yescharacteristic
461C2×C4#55311yescharacteristic
462C2×C4#55311yescharacteristic
463C2×C4#55511yescharacteristic
464C2×C4#55611yescharacteristic
465C8—42no—
466C8—42no—
467C8—44no—
468C8—42no—
469C8—42no—
470C8—82no—
471C22—22no—
472C22—22no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—22no—
478C22—22no—
479C22C2×#39611yescharacteristic
480C22#242611yescharacteristic
481C22#242711yescharacteristic
482C22#249411yescharacteristic
483C22#249511yescharacteristic
484C22#262811yescharacteristic
485C22#285111yescharacteristic
486C22#306712yes—
487C22#306912yes—
488C4—22no—
489C4—22no—
490C4—22no—
491C4—22no—
492C4—44no—
493C4—84no—
494C4—82no—
495C4—162no—
496C4#241411yescharacteristic
497C4#241511yescharacteristic
498C4#243911yescharacteristic
499C4#244111yescharacteristic
500C4#244211yescharacteristic
501C4#244211yescharacteristic
502C4#253511yescharacteristic
503C4#253611yescharacteristic
504C2—21no—
505C2—21no—
506C2—21no—
507C2—21no—
508C2#1522011yescharacteristic
509C2#2360111yescharacteristic
510C2#2360311yescharacteristic
511C2#2531712yes—
512C2#2536312yes—
subgroupG/H
center, socleC23C2×#121
commutator, Frattini, cosocleC23×C4C24
prime radicalC24C2×#41
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ 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×#19502
#211452
#207652
#206472
C2×#18052
C2×C4×#1012
#113032
#112422
#111282
#110622
#108582