Finite Group Databasebeta

← #121137

Subgroups — #121137

Order 512.

661 conjugacy classes of subgroups.

The subgroup lattice has 523 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10854C211yesmaximal, characteristic
2#10854C211yesmaximal, characteristic
3#8023C211yesmaximal, characteristic
4#8023C211yesmaximal, characteristic
5C2×#1289C211yesmaximal, characteristic
6C2×#1289C211yesmaximal, characteristic
7#7907C211yesmaximal, characteristic
8C22×C22⋊C8C2211yescharacteristic
9C22×C22⋊C8C2211yescharacteristic
10C2×#380C2211yescharacteristic
11C2×#380C2211yescharacteristic
12C2×#380C2211yescharacteristic
13C2×#380C2211yescharacteristic
14C2×C4×C22⋊C4C2211yescharacteristic
15C2×#342—21no—
16C2×#342—21no—
17C2×#342—21no—
18C2×#342—21no—
19#1294—22no—
20#1294C414yescomplemented
21#1289—22no—
22#1289—22no—
23#1280—22no—
24C24×C4C2311yescharacteristic
25C23×C8—21no—
26C23×C8—21no—
27C22×C4⋊C4—21no—
28C22×C4⋊C4—21no—
29C22×C4⋊C4—21no—
30C22×C4⋊C4—21no—
31C22×C22⋊C4—21no—
32C22×C22⋊C4—21no—
33C22×C22⋊C4—21no—
34C22×C22⋊C4—21no—
35C22×C22⋊C4D411yescharacteristic
36C22×C22⋊C4D411yescharacteristic
37C22×C42—21no—
38C2×C22⋊C8—21no—
39C2×C22⋊C8—21no—
40C2×C22⋊C8—21no—
41C2×C22⋊C8—21no—
42C2×C22⋊C8—21no—
43C2×C22⋊C8—21no—
44C2×C22⋊C8—21no—
45C2×C22⋊C8—21no—
46C2×C22⋊C8—21no—
47C2×C22⋊C8—21no—
48C2×C22⋊C8C2×C412yes—
49C2×C22⋊C8D412yes—
50#380—21no—
51#380—21no—
52#380—21no—
53#380—21no—
54#380—21no—
55#380—21no—
56#380—21no—
57#380—21no—
58#380—21no—
59#380—21no—
60#380—21no—
61#380—21no—
62#380—21no—
63#380—21no—
64#380C2×C412yes—
65#380D412yes—
66C4×C22⋊C4—21no—
67C4×C22⋊C4—21no—
68C4×C22⋊C4—21no—
69C4×C22⋊C4—21no—
70C2×#95—21no—
71C2×#95—21no—
72C2×#95—21no—
73C2×#95C2×C412yes—
74C2×#95Q812yes—
75#342—42no—
76#342—42no—
77#342—42no—
78#342—42no—
79C25C2×D411yescharacteristic
80C23×C4—21no—
81C23×C4—21no—
82C23×C4—22no—
83C23×C4—22no—
84C23×C4—41no—
85C23×C4—41no—
86C23×C4—82no—
87C23×C4C22×C411yescharacteristic
88C23×C4C2×D411yescharacteristic
89C23×C4C2×D411yescharacteristic
90C23×C4C2×Q811yescharacteristic
91C23×C4#4111yescharacteristic
92C23×C4#4111yescharacteristic
93C23×C4#4111yescharacteristic
94C23×C4#4111yescharacteristic
95C23×C4#4111yescharacteristic
96C23×C4#4111yescharacteristic
97C23×C4#4111yescharacteristic
98C23×C4#4111yescharacteristic
99C23×C4#4111yescharacteristic
100C23×C4#4111yescharacteristic
101C22×C8—22no—
102C22×C8—22no—
103C22×C8—41no—
104C22×C8—41no—
105C22×C8—41no—
106C22×C8—41no—
107C22×C8—82no—
108C22×C8—82no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4—22no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—82no—
118C2×C4⋊C4—82no—
119C2×C4⋊C4—82no—
120C2×C4⋊C4—82no—
121C2×C22⋊C4—21no—
122C2×C22⋊C4—21no—
123C2×C22⋊C4—21no—
124C2×C22⋊C4—21no—
125C2×C22⋊C4—21no—
126C2×C22⋊C4—21no—
127C2×C22⋊C4—21no—
128C2×C22⋊C4—21no—
129C2×C22⋊C4—21no—
130C2×C22⋊C4—21no—
131C2×C22⋊C4—22no—
132C2×C22⋊C4—22no—
133C2×C22⋊C4—41no—
134C2×C22⋊C4—41no—
135C2×C22⋊C4—41no—
136C2×C22⋊C4—41no—
137C2×C22⋊C4—41no—
138C2×C22⋊C4—41no—
139C2×C22⋊C4—41no—
140C2×C22⋊C4—41no—
141C2×C22⋊C4—41no—
142C2×C22⋊C4—41no—
143C2×C22⋊C4—41no—
144C2×C22⋊C4—41no—
145C2×C22⋊C4—41no—
146C2×C22⋊C4—41no—
147C2×C22⋊C4—41no—
148C2×C22⋊C4—41no—
149C2×C22⋊C4—41no—
150C2×C22⋊C4—41no—
151C2×C22⋊C4—41no—
152C2×C22⋊C4—41no—
153C2×C22⋊C4—41no—
154C2×C22⋊C4—41no—
155C2×C22⋊C4D812yes—
156C2×C22⋊C4SD1612yes—
157C2×C42—41no—
158C2×C42—41no—
159C2×C42—82no—
160C22⋊C8—22no—
161C22⋊C8—22no—
162C22⋊C8—22no—
163C22⋊C8—22no—
164C22⋊C8—41no—
165C22⋊C8—41no—
166C22⋊C8—41no—
167C22⋊C8—41no—
168#95—22no—
169#95—22no—
170#95—22no—
171#95—22no—
172#95—22no—
173#95—22no—
174#95—41no—
175#95—41no—
176#95—41no—
177#95—41no—
178C24—81no—
179C24—81no—
180C24C4×D411yescharacteristic
181C24#12111yescharacteristic
182C24#12111yescharacteristic
183C24C22⋊Q811yescharacteristic
184C24#12311yescharacteristic
185C24#12311yescharacteristic
186C24#12411yescharacteristic
187C24C2×D811yescharacteristic
188C24C2×SD1611yescharacteristic
189C24#13511yescharacteristic
190C24#13511yescharacteristic
191C24AGL(1,ℤ/8)11yescharacteristic
192C24#13711yescharacteristic
193C24#13711yescharacteristic
194C24#13711yescharacteristic
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—42no—
198C22×C4—42no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—81no—
217C22×C4—81no—
218C22×C4—81no—
219C22×C4—81no—
220C22×C4—81no—
221C22×C4—81no—
222C22×C4—81no—
223C22×C4—81no—
224C22×C4—81no—
225C22×C4—81no—
226C22×C4—81no—
227C22×C4—82no—
228C22×C4—82no—
229C22×C4—82no—
230C22×C4—82no—
231C22×C4—81no—
232C22×C4—81no—
233C22×C4—81no—
234C22×C4—81no—
235C22×C4—82no—
236C22×C4—82no—
237C22×C4—82no—
238C22×C4—82no—
239C22×C4#11711yescharacteristic
240C22×C4#11711yescharacteristic
241C22×C4#11711yescharacteristic
242C22×C4C4×D411yescharacteristic
243C22×C4C4×D411yescharacteristic
244C22×C4C4×Q811yescharacteristic
245C22×C4#12111yescharacteristic
246C22×C4C22⋊Q811yescharacteristic
247C22×C4C22⋊Q811yescharacteristic
248C22×C4#12311yescharacteristic
249C22×C4#12311yescharacteristic
250C22×C4#12311yescharacteristic
251C22×C4#12311yescharacteristic
252C22×C4#12411yescharacteristic
253C22×C4#12411yescharacteristic
254C22×C4#12511yescharacteristic
255C22×C4#12511yescharacteristic
256C22×C4#12511yescharacteristic
257C22×C4#12611yescharacteristic
258C22×C4#12611yescharacteristic
259C22×C4#12611yescharacteristic
260C22×C4#12611yescharacteristic
261C22×C4#12611yescharacteristic
262C22×C4#12611yescharacteristic
263C22×C4#12611yescharacteristic
264C22×C4#12611yescharacteristic
265C22×C4#12611yescharacteristic
266C22×C4#12611yescharacteristic
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—82no—
270C2×C8—82no—
271C2×C8—82no—
272C2×C8—82no—
273C2×C8—82no—
274C2×C8—82no—
275C4⋊C4—82no—
276C4⋊C4—82no—
277C4⋊C4—82no—
278C4⋊C4—82no—
279C4⋊C4—82no—
280C4⋊C4—82no—
281C4⋊C4—82no—
282C4⋊C4—82no—
283C22⋊C4—22no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—42no—
292C22⋊C4—42no—
293C22⋊C4—42no—
294C22⋊C4—42no—
295C22⋊C4—81no—
296C22⋊C4—81no—
297C22⋊C4—81no—
298C22⋊C4—81no—
299C22⋊C4—81no—
300C22⋊C4—81no—
301C22⋊C4—81no—
302C22⋊C4—81no—
303C22⋊C4—81no—
304C22⋊C4—81no—
305C22⋊C4—81no—
306C22⋊C4—81no—
307C42—82no—
308C42—82no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—81no—
324C23—81no—
325C23—81no—
326C23—81no—
327C23—81no—
328C23—81no—
329C23—81no—
330C23—81no—
331C23#38711yescharacteristic
332C23#38811yescharacteristic
333C23#38811yescharacteristic
334C23#39611yescharacteristic
335C23#39711yescharacteristic
336C23#39711yescharacteristic
337C23#40011yescharacteristic
338C23C4×D811yescharacteristic
339C23C4×SD1611yescharacteristic
340C23#44011yescharacteristic
341C23#44111yescharacteristic
342C23#45911yescharacteristic
343C23#46111yescharacteristic
344C23#46411yescharacteristic
345C23#46411yescharacteristic
346C23#46511yescharacteristic
347C23#46611yescharacteristic
348C23#46811yescharacteristic
349C23#47011yescharacteristic
350C23#47411yescharacteristic
351C23#47511yescharacteristic
352C23#47811yescharacteristic
353C23#47911yescharacteristic
354C23#48011yescharacteristic
355C23#48011yescharacteristic
356C23#48111yescharacteristic
357C23#48211yescharacteristic
358C23#48311yescharacteristic
359C23#48511yescharacteristic
360C23#48511yescharacteristic
361C23#48511yescharacteristic
362C23#48611yescharacteristic
363C23#48811yescharacteristic
364C23#48911yescharacteristic
365C23#49111yescharacteristic
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—82no—
401C2×C4—82no—
402C2×C4—82no—
403C2×C4—82no—
404C2×C4—82no—
405C2×C4—82no—
406C2×C4—82no—
407C2×C4—82no—
408C2×C4—82no—
409C2×C4—82no—
410C2×C4—82no—
411C2×C4—82no—
412C2×C4—82no—
413C2×C4—82no—
414C2×C4—82no—
415C2×C4—82no—
416C2×C4—162no—
417C2×C4—162no—
418C2×C4—162no—
419C2×C4—162no—
420C2×C4—162no—
421C2×C4—162no—
422C2×C4—162no—
423C2×C4—162no—
424C2×C4#38311yescharacteristic
425C2×C4#38711yescharacteristic
426C2×C4#38711yescharacteristic
427C2×C4#38811yescharacteristic
428C2×C4#39711yescharacteristic
429C2×C4#40011yescharacteristic
430C2×C4#40011yescharacteristic
431C2×C4#40111yescharacteristic
432C8—82no—
433C8—82no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22#144311yescharacteristic
477C22#191811yescharacteristic
478C22#191911yescharacteristic
479C22#192511yescharacteristic
480C22#192711yescharacteristic
481C22#193411yescharacteristic
482C22#193511yescharacteristic
483C22#206611yescharacteristic
484C22#206711yescharacteristic
485C22#207111yescharacteristic
486C22#207411yescharacteristic
487C22#207511yescharacteristic
488C22#207711yescharacteristic
489C22#209911yescharacteristic
490C22#210111yescharacteristic
491C4—21no—
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—82no—
499C4—82no—
500C4—162no—
501C4—162no—
502C4—162no—
503C4—162no—
504C4#210412yes—
505C2—21no—
506C2—21no—
507C2—21no—
508C2—21no—
509C2—21no—
510C2—21no—
511C2—21no—
512C2—21no—
513C2—21no—
514C2—21no—
515C2—21no—
516C2—21no—
517C2—21no—
518C2—21no—
519C2#1130911yescharacteristic
520C2#1131511yescharacteristic
521C2#1131811yescharacteristic
subgroupG/H
center, socleC22#1443
commutatorC23×C4C22×C4
Frattini, cosocleC24×C4C23
prime radicalC25C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
20. #1294C4semidirect

Maximal subgroups

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

subgroupindex
#108542
#80232
C2×#12892
#79072