Finite Group Databasebeta

← #119027

Subgroups — #119027

Order 512.

626 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21312C211yesmaximal, characteristic
2C2×#1542C211yesmaximal, characteristic
3C2×#1518C211yesmaximal, characteristic
4#10850C211yesmaximal, characteristic
5C2×#1286C211yesmaximal, characteristic
6#7908C211yesmaximal, characteristic
7#7877C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C22×C4⋊C8C2211yescharacteristic
13C2×#382C2211yescharacteristic
14C2×C4×C4⋊C4C2211yescharacteristic
15#1989—22no—
16#1988—21no—
17#1987—21no—
18#1736—21no—
19#1736—21no—
20C2×#340—21no—
21C2×#340—21no—
22#1542—22no—
23#1542C414yescomplemented
24C2×#333—21no—
25C2×#332—21no—
26#1518—22no—
27#1518—22no—
28C2×#328—22no—
29#1286—22no—
30#1280—22no—
31#1277—22no—
32C22×M16—21no—
33C23×C8—21no—
34#533—21no—
35#533—21no—
36#533—21no—
37#533—21no—
38#533—21no—
39#533—21no—
40#533C2×C412yes—
41#533D412yes—
42C2×C4⋊Q8D411yescharacteristic
43C2×C4⋊Q8D411yescharacteristic
44C2×#125—21no—
45C2×C22⋊Q8—21no—
46C2×C22⋊Q8—21no—
47C2×C4×Q8—21no—
48C2×C4×Q8—21no—
49C2×#117—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4D411yescharacteristic
52C22×C4⋊C4D411yescharacteristic
53C22×C42—21no—
54C22×C42C2311yescharacteristic
55#431—21no—
56#431—21no—
57#431—21no—
58#431—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62#431C2×C412yes—
63#423—21no—
64#423—21no—
65#423—21no—
66#423—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—21no—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74C2×C4⋊C8—21no—
75C2×C4⋊C8C2×C412yes—
76C2×C4⋊C8D412yes—
77C2×C22⋊C8—21no—
78C2×C22⋊C8D412yes—
79C2×C4×C8—21no—
80C2×C4×C8—21no—
81#382—21no—
82#382—21no—
83#382—21no—
84#382D412yes—
85C4×C4⋊C4—21no—
86C4×C4⋊C4—21no—
87C4×C4⋊C4—21no—
88C4×C4⋊C4—21no—
89C2×#95—21no—
90C2×#95—21no—
91C2×#95—21no—
92#340—22no—
93#340—22no—
94#340—22no—
95#340—22no—
96#340—42no—
97#340—42no—
98#333—24no—
99#332—24no—
100#328—28no—
101C22×Q8—21no—
102C22×Q8—21no—
103C23×C4—21no—
104C23×C4—21no—
105C23×C4—41no—
106C23×C4C2×D411yescharacteristic
107C23×C4C2×D411yescharacteristic
108C23×C4#4111yescharacteristic
109C2×M16—41no—
110C2×M16—41no—
111C2×M16—41no—
112C2×M16—41no—
113C2×M16—41no—
114C2×M16—41no—
115C22×C8—22no—
116C22×C8—22no—
117C22×C8—22no—
118C22×C8—41no—
119C22×C8—41no—
120C22×C8—41no—
121C22×C8—41no—
122C22×C8—41no—
123C22×C8—41no—
124C22×C8—41no—
125C4⋊Q8—21no—
126C4⋊Q8—21no—
127C4⋊Q8—21no—
128C4⋊Q8—21no—
129C4⋊Q8—21no—
130C4⋊Q8—21no—
131C4⋊Q8C22⋊C412yes—
132C4⋊Q8C22⋊C412yes—
133#125—22no—
134#125—22no—
135#125—41no—
136#125—41no—
137C22⋊Q8—22no—
138C22⋊Q8—22no—
139C22⋊Q8—22no—
140C22⋊Q8—22no—
141C22⋊Q8—41no—
142C22⋊Q8—41no—
143C22⋊Q8—41no—
144C22⋊Q8—41no—
145C4×Q8—22no—
146C4×Q8—22no—
147C4×Q8—22no—
148C4×Q8—22no—
149C4×Q8—41no—
150C4×Q8—41no—
151C4×Q8—41no—
152C4×Q8—41no—
153#117—22no—
154#117—22no—
155#117—41no—
156#117—41no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—41no—
173C2×C4⋊C4—41no—
174C2×C4⋊C4—41no—
175C2×C4⋊C4—41no—
176C2×C4⋊C4—41no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4SD1612yes—
180C2×C4⋊C4Q1612yes—
181C2×C22⋊C4—41no—
182C2×C42—41no—
183C2×C42—41no—
184C2×C42—41no—
185C2×C42—82no—
186C2×C42C22×C411yescharacteristic
187C2×C42C2×D411yescharacteristic
188C2×C42C2×D411yescharacteristic
189C2×C42C2×D411yescharacteristic
190C2×C42C2×D411yescharacteristic
191C2×C42#4111yescharacteristic
192C2×C42#4111yescharacteristic
193C2×C42#4111yescharacteristic
194C2×C42#4111yescharacteristic
195C2×C42#4111yescharacteristic
196C2×C42#4111yescharacteristic
197C2×C42#4111yescharacteristic
198C4⋊C8—22no—
199C4⋊C8—22no—
200C4⋊C8—22no—
201C4⋊C8—22no—
202C4⋊C8—22no—
203C4⋊C8—41no—
204C4⋊C8—41no—
205C4⋊C8—41no—
206C4⋊C8—41no—
207C4⋊C8—41no—
208C4⋊C8—41no—
209C4⋊C8—41no—
210C22⋊C8—22no—
211C22⋊C8—22no—
212C22⋊C8—22no—
213C22⋊C8—41no—
214C4×C8—22no—
215C4×C8—41no—
216C4×C8—41no—
217C4×C8—41no—
218#95—22no—
219#95—22no—
220#95—41no—
221#95—41no—
222#95—41no—
223#95—41no—
224C24#12111yescharacteristic
225C2×Q8—22no—
226C2×Q8—22no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—81no—
230C2×Q8—81no—
231C2×Q8—81no—
232C2×Q8—81no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—42no—
246C22×C4—81no—
247C22×C4—81no—
248C22×C4—81no—
249C22×C4—81no—
250C22×C4—81no—
251C22×C4—81no—
252C22×C4—81no—
253C22×C4—81no—
254C22×C4—81no—
255C22×C4—81no—
256C22×C4#11711yescharacteristic
257C22×C4C4×D411yescharacteristic
258C22×C4C4×D411yescharacteristic
259C22×C4#12011yescharacteristic
260C22×C4#12011yescharacteristic
261C22×C4#12111yescharacteristic
262C22×C4#12111yescharacteristic
263C22×C4#12111yescharacteristic
264C22×C4#12111yescharacteristic
265C22×C4#12311yescharacteristic
266C22×C4#12311yescharacteristic
267C22×C4#12311yescharacteristic
268C22×C4#12311yescharacteristic
269C22×C4#12311yescharacteristic
270C22×C4#12411yescharacteristic
271C22×C4#12411yescharacteristic
272C22×C4#12411yescharacteristic
273C22×C4#12611yescharacteristic
274C22×C4C2×SD1611yescharacteristic
275C22×C4C2×Q1611yescharacteristic
276C22×C4#13511yescharacteristic
277C22×C4#13511yescharacteristic
278C22×C4AGL(1,ℤ/8)11yescharacteristic
279C22×C4#13711yescharacteristic
280C22×C4#13711yescharacteristic
281C22×C4#13711yescharacteristic
282M16—81no—
283M16—81no—
284M16—81no—
285M16—81no—
286C2×C8—42no—
287C2×C8—42no—
288C2×C8—42no—
289C2×C8—42no—
290C2×C8—42no—
291C2×C8—42no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8—42no—
295C2×C8—42no—
296C2×C8—81no—
297C2×C8—81no—
298C2×C8—81no—
299C2×C8—81no—
300C2×C8—81no—
301C2×C8—81no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—22no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—42no—
311C4⋊C4—42no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—42no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—42no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—42no—
323C4⋊C4—42no—
324C4⋊C4—81no—
325C4⋊C4—81no—
326C22⋊C4—42no—
327C22⋊C4—42no—
328C42—42no—
329C42—42no—
330C42—82no—
331C42—82no—
332C42C2×C22⋊C411yescharacteristic
333C42#11711yescharacteristic
334C42C4×D411yescharacteristic
335C42C4×D411yescharacteristic
336C42#12111yescharacteristic
337C42#12111yescharacteristic
338C42#12111yescharacteristic
339C42#12311yescharacteristic
340C42#12311yescharacteristic
341C42#12311yescharacteristic
342C42#12311yescharacteristic
343C42#12311yescharacteristic
344C42#12411yescharacteristic
345C42#12611yescharacteristic
346C42#12611yescharacteristic
347C42#12611yescharacteristic
348C23—21no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23#38811yescharacteristic
353C23#39411yescharacteristic
354C23#39411yescharacteristic
355C23#46511yescharacteristic
356C23#46711yescharacteristic
357C23#46811yescharacteristic
358C23#47011yescharacteristic
359Q8—82no—
360Q8—82no—
361Q8—82no—
362Q8—82no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—82no—
384C2×C4—82no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—82no—
394C2×C4—82no—
395C2×C4—82no—
396C2×C4—82no—
397C2×C4—82no—
398C2×C4—161no—
399C2×C4—161no—
400C2×C4—161no—
401C2×C4—161no—
402C2×C4#38111yescharacteristic
403C2×C4#38611yescharacteristic
404C2×C4#38611yescharacteristic
405C2×C4#38811yescharacteristic
406C2×C4#38811yescharacteristic
407C2×C4#38811yescharacteristic
408C2×C4#39411yescharacteristic
409C2×C4#39411yescharacteristic
410C2×C4#39711yescharacteristic
411C2×C4#39711yescharacteristic
412C2×C4#39711yescharacteristic
413C2×C4#39711yescharacteristic
414C2×C4C4×SD1611yescharacteristic
415C2×C4C4×Q1611yescharacteristic
416C2×C4#44011yescharacteristic
417C2×C4#44111yescharacteristic
418C2×C4#44811yescharacteristic
419C2×C4#44911yescharacteristic
420C2×C4#45111yescharacteristic
421C2×C4#45211yescharacteristic
422C2×C4#46011yescharacteristic
423C2×C4#46111yescharacteristic
424C2×C4#46211yescharacteristic
425C2×C4#46211yescharacteristic
426C2×C4#46311yescharacteristic
427C2×C4#46411yescharacteristic
428C2×C4#46411yescharacteristic
429C2×C4#46411yescharacteristic
430C2×C4#48311yescharacteristic
431C2×C4#48411yescharacteristic
432C2×C4#48511yescharacteristic
433C2×C4#48511yescharacteristic
434C2×C4#48711yescharacteristic
435C2×C4#48811yescharacteristic
436C2×C4#48911yescharacteristic
437C2×C4#49111yescharacteristic
438C8—82no—
439C8—82no—
440C8—82no—
441C8—82no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22#144011yescharacteristic
455C22#193311yescharacteristic
456C22#193511yescharacteristic
457C22#203511yescharacteristic
458C22#203611yescharacteristic
459C22#204811yescharacteristic
460C22#204911yescharacteristic
461C22#205311yescharacteristic
462C22#205311yescharacteristic
463C22#205511yescharacteristic
464C22#205611yescharacteristic
465C4—21no—
466C4—21no—
467C4—21no—
468C4—21no—
469C4—21no—
470C4—21no—
471C4—21no—
472C4—21no—
473C4—82no—
474C4—82no—
475C4—82no—
476C4—82no—
477C4—162no—
478C4#187811yescharacteristic
479C4#188011yescharacteristic
480C4#192711yescharacteristic
481C4#192811yescharacteristic
482C4#204211yescharacteristic
483C4#204311yescharacteristic
484C4#207211yescharacteristic
485C4#207411yescharacteristic
486C2—21no—
487C2—21no—
488C2—21no—
489C2—21no—
490C2#1046811yescharacteristic
491C2#1046911yescharacteristic
492C2#1047011yescharacteristic
493C2#1047111yescharacteristic
494C2#1115211yescharacteristic
495C2#1117611yescharacteristic
496C2#1119011yescharacteristic
subgroupG/H
center, socleC23#394
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
23. #1542C4semidirect

Maximal subgroups

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

subgroupindex
#213122
C2×#15422
C2×#15182
#108502
C2×#12862
#79082
#78772