Finite Group Databasebeta

← #116086

Subgroups — #116086

Order 512.

926 conjugacy classes of subgroups.

The subgroup lattice has 531 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1996C211yesmaximal, characteristic
2C2×#1520C211yesmaximal, characteristic
3C22×#328C211yesmaximal, characteristic
4#13966C211yesmaximal, characteristic
5C2×#1294C211yesmaximal, characteristic
6C2×#1289C211yesmaximal, characteristic
7C2×#1282C211yesmaximal, characteristic
8C22×C22⋊Q8C2211yescharacteristic
9C22×C22⋊C8C2211yescharacteristic
10C22×C22⋊C8C2211yescharacteristic
11C2×#380C2211yescharacteristic
12C2×#380C2211yescharacteristic
13C2×C4×C22⋊C4C2211yescharacteristic
14C22×#95C2211yescharacteristic
15#1996—22no—
16#1996C414yescomplemented
17C2×#342—22no—
18#1520—22no—
19#1520—22no—
20C2×#328—22no—
21C2×#328—22no—
22C2×#328—22no—
23C2×#328—22no—
24#1442—22no—
25#1434—22no—
26C22⋊#95—22no—
27#1294—22no—
28#1289—22no—
29#1282—22no—
30C23×Q8Q811yescharacteristic
31C24×C4—21no—
32C24×C4C2311yescharacteristic
33C23×C8—21no—
34C23×C8—21no—
35C2×C22⋊Q8—21no—
36C2×C22⋊Q8—21no—
37C2×C22⋊Q8—21no—
38C2×C22⋊Q8—21no—
39C2×C22⋊Q8—21no—
40C2×C22⋊Q8—21no—
41C2×C22⋊Q8—21no—
42C2×C22⋊Q8—21no—
43C2×C22⋊Q8—21no—
44C2×C22⋊Q8—21no—
45C2×C22⋊Q8C2×C412yes—
46C2×C22⋊Q8D412yes—
47C22×C4⋊C4—21no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4Q811yescharacteristic
51C22×C22⋊C4—21no—
52C22×C22⋊C4—21no—
53C22×C22⋊C4—21no—
54C22×C22⋊C4D412yes—
55C22×C42—21no—
56C2×C22⋊C8—21no—
57C2×C22⋊C8—21no—
58C2×C22⋊C8—21no—
59C2×C22⋊C8—21no—
60C2×C22⋊C8—21no—
61C2×C22⋊C8—21no—
62C2×C22⋊C8—21no—
63C2×C22⋊C8—21no—
64C2×C22⋊C8—21no—
65C2×C22⋊C8—21no—
66C2×C22⋊C8D412yes—
67C2×C22⋊C8D412yes—
68#380—21no—
69#380—21no—
70#380—21no—
71#380—21no—
72#380—21no—
73#380—21no—
74#380—21no—
75#380C2×C412yes—
76C4×C22⋊C4—21no—
77C4×C22⋊C4—21no—
78C4×C22⋊C4C2×C412yes—
79C4×C22⋊C4D412yes—
80C2×#95—21no—
81C2×#95—21no—
82C2×#95—21no—
83C2×#95—21no—
84C2×#95—21no—
85C2×#95—21no—
86C2×#95—24no—
87C2×#95—21no—
88C2×#95—24no—
89C2×#95D412yes—
90C2×#95D412yes—
91#342—28no—
92#328—28no—
93#328—28no—
94C25C2×D411yescharacteristic
95C22×Q8—21no—
96C22×Q8—21no—
97C22×Q8—21no—
98C22×Q8—21no—
99C22×Q8—21no—
100C22×Q8—82no—
101C22×Q8C4⋊C412yes—
102C23×C4—22no—
103C23×C4—22no—
104C23×C4—21no—
105C23×C4—21no—
106C23×C4—22no—
107C23×C4—44no—
108C23×C4—41no—
109C23×C4—41no—
110C23×C4—41no—
111C23×C4—42no—
112C23×C4—42no—
113C23×C4—82no—
114C23×C4—82no—
115C23×C4C22×C411yescharacteristic
116C23×C4C2×D411yescharacteristic
117C23×C4C2×D411yescharacteristic
118C23×C4C2×D411yescharacteristic
119C23×C4C2×D411yescharacteristic
120C23×C4C2×D411yescharacteristic
121C23×C4C2×D411yescharacteristic
122C23×C4C2×Q811yescharacteristic
123C23×C4#4111yescharacteristic
124C23×C4#4111yescharacteristic
125C23×C4#4111yescharacteristic
126C23×C4#4111yescharacteristic
127C23×C4#4111yescharacteristic
128C23×C4#4111yescharacteristic
129C22×C8—22no—
130C22×C8—22no—
131C22×C8—41no—
132C22×C8—41no—
133C22×C8—41no—
134C22×C8—41no—
135C22×C8—82no—
136C22×C8—82no—
137C22⋊Q8—22no—
138C22⋊Q8—22no—
139C22⋊Q8—22no—
140C22⋊Q8—22no—
141C22⋊Q8—22no—
142C22⋊Q8—22no—
143C22⋊Q8—22no—
144C22⋊Q8—22no—
145C22⋊Q8—41no—
146C22⋊Q8—41no—
147C22⋊Q8—41no—
148C22⋊Q8—41no—
149C22⋊Q8—41no—
150C22⋊Q8—41no—
151C22⋊Q8—41no—
152C22⋊Q8—41no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—41no—
162C2×C4⋊C4—41no—
163C2×C4⋊C4—41no—
164C2×C4⋊C4—41no—
165C2×C4⋊C4—41no—
166C2×C4⋊C4—41no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—82no—
169C2×C4⋊C4—82no—
170C2×C4⋊C4C4⋊C412yes—
171C2×C22⋊C4—22no—
172C2×C22⋊C4—22no—
173C2×C22⋊C4—22no—
174C2×C22⋊C4—22no—
175C2×C22⋊C4—22no—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4—41no—
180C2×C22⋊C4—41no—
181C2×C22⋊C4—41no—
182C2×C22⋊C4—41no—
183C2×C22⋊C4—42no—
184C2×C22⋊C4—42no—
185C2×C22⋊C4—41no—
186C2×C22⋊C4—41no—
187C2×C22⋊C4—41no—
188C2×C22⋊C4—42no—
189C2×C22⋊C4—42no—
190C2×C22⋊C4C22⋊C414yes—
191C2×C42—22no—
192C2×C42—22no—
193C2×C42—82no—
194C22⋊C8—22no—
195C22⋊C8—22no—
196C22⋊C8—22no—
197C22⋊C8—22no—
198C22⋊C8—41no—
199C22⋊C8—41no—
200C22⋊C8—41no—
201C22⋊C8—41no—
202#95—22no—
203#95—22no—
204#95—22no—
205#95—22no—
206#95—22no—
207#95—22no—
208#95—22no—
209#95—48no—
210#95—41no—
211#95—41no—
212#95—41no—
213#95—84no—
214C24—42no—
215C24—42no—
216C24C2×C22⋊C411yescharacteristic
217C24#12011yescharacteristic
218C24#12111yescharacteristic
219C24C22⋊Q811yescharacteristic
220C24#12311yescharacteristic
221C24#12411yescharacteristic
222C24#12711yescharacteristic
223C24#13512yes—
224C24#13512yes—
225C24#13712yes—
226C24#13712yes—
227C2×Q8—22no—
228C2×Q8—22no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—82no—
232C2×Q8—82no—
233C2×Q8—82no—
234C2×Q8—82no—
235C2×Q8—82no—
236C2×Q8—82no—
237C22×C4—24no—
238C22×C4—24no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—44no—
248C22×C4—44no—
249C22×C4—44no—
250C22×C4—42no—
251C22×C4—44no—
252C22×C4—44no—
253C22×C4—42no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—44no—
261C22×C4—44no—
262C22×C4—44no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4—44no—
266C22×C4—81no—
267C22×C4—81no—
268C22×C4—81no—
269C22×C4—81no—
270C22×C4—81no—
271C22×C4—81no—
272C22×C4—81no—
273C22×C4—81no—
274C22×C4—88no—
275C22×C4—88no—
276C22×C4—82no—
277C22×C4—82no—
278C22×C4—82no—
279C22×C4—81no—
280C22×C4—81no—
281C22×C4—82no—
282C22×C4—82no—
283C22×C4—82no—
284C22×C4—82no—
285C22×C4—82no—
286C22×C4C2×C4⋊C411yescharacteristic
287C22×C4#11711yescharacteristic
288C22×C4C4×D411yescharacteristic
289C22×C4C4×D411yescharacteristic
290C22×C4C4×D411yescharacteristic
291C22×C4C4×D411yescharacteristic
292C22×C4#12011yescharacteristic
293C22×C4#12011yescharacteristic
294C22×C4#12111yescharacteristic
295C22×C4#12111yescharacteristic
296C22×C4#12111yescharacteristic
297C22×C4#12111yescharacteristic
298C22×C4#12111yescharacteristic
299C22×C4#12111yescharacteristic
300C22×C4#12111yescharacteristic
301C22×C4C22⋊Q811yescharacteristic
302C22×C4C22⋊Q811yescharacteristic
303C22×C4C22⋊Q811yescharacteristic
304C22×C4C22⋊Q811yescharacteristic
305C22×C4C22⋊Q811yescharacteristic
306C22×C4#12311yescharacteristic
307C22×C4#12311yescharacteristic
308C22×C4#12311yescharacteristic
309C22×C4#12311yescharacteristic
310C22×C4#12411yescharacteristic
311C22×C4#12411yescharacteristic
312C22×C4#12611yescharacteristic
313C22×C4#12611yescharacteristic
314C2×C8—42no—
315C2×C8—42no—
316C2×C8—82no—
317C2×C8—82no—
318C2×C8—82no—
319C2×C8—82no—
320C2×C8—82no—
321C2×C8—82no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—42no—
325C4⋊C4—42no—
326C4⋊C4—42no—
327C4⋊C4—42no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—82no—
331C4⋊C4—82no—
332C4⋊C4—82no—
333C4⋊C4—82no—
334C22⋊C4—24no—
335C22⋊C4—24no—
336C22⋊C4—42no—
337C22⋊C4—42no—
338C22⋊C4—42no—
339C22⋊C4—42no—
340C22⋊C4—42no—
341C22⋊C4—42no—
342C22⋊C4—44no—
343C22⋊C4—82no—
344C22⋊C4—81no—
345C22⋊C4—81no—
346C22⋊C4—81no—
347C22⋊C4—81no—
348C42—82no—
349C42—82no—
350C23—22no—
351C23—22no—
352C23—22no—
353C23—22no—
354C23—22no—
355C23—22no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—44no—
363C23—44no—
364C23—41no—
365C23—41no—
366C23—44no—
367C23—44no—
368C23#38011yescharacteristic
369C23#38611yescharacteristic
370C23#39011yescharacteristic
371C23#39211yescharacteristic
372C23#39311yescharacteristic
373C23#39711yescharacteristic
374C23#39911yescharacteristic
375C23#41612yes—
376C23#41912yes—
377C23#45212yes—
378C23#45212yes—
379C23#46412yes—
380C23#46412yes—
381C23#47912yes—
382C23#47912yes—
383C23#48512yes—
384C23#48512yes—
385C23#48812yes—
386C23#49112yes—
387C23#49511yescharacteristic
388C23#49511yescharacteristic
389C23#49711yescharacteristic
390C23#49711yescharacteristic
391Q8—82no—
392Q8—82no—
393Q8—82no—
394Q8—82no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—44no—
424C2×C4—44no—
425C2×C4—44no—
426C2×C4—48no—
427C2×C4—44no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—84no—
431C2×C4—84no—
432C2×C4—82no—
433C2×C4—84no—
434C2×C4—82no—
435C2×C4—82no—
436C2×C4—88no—
437C2×C4—84no—
438C2×C4—84no—
439C2×C4—82no—
440C2×C4—82no—
441C2×C4—82no—
442C2×C4—82no—
443C2×C4—82no—
444C2×C4—82no—
445C2×C4—82no—
446C2×C4—82no—
447C2×C4—88no—
448C2×C4—82no—
449C2×C4—82no—
450C2×C4—82no—
451C2×C4—164no—
452C2×C4#38511yescharacteristic
453C2×C4#38511yescharacteristic
454C2×C4#38811yescharacteristic
455C2×C4#38811yescharacteristic
456C2×C4#39411yescharacteristic
457C2×C4#39411yescharacteristic
458C2×C4#39611yescharacteristic
459C2×C4#39611yescharacteristic
460C8—82no—
461C8—82no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—24no—
475C22—24no—
476C22—24no—
477C22—24no—
478C22—24no—
479C22—24no—
480C22—42no—
481C22—41no—
482C22—41no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—42no—
488C22—41no—
489C22—41no—
490C22#143911yescharacteristic
491C22#180512yes—
492C22#187312yes—
493C22#195811yescharacteristic
494C22#196011yescharacteristic
495C22#201511yescharacteristic
496C22#201511yescharacteristic
497C22#202612yes—
498C22#203112yes—
499C22#203212yes—
500C22#207412yes—
501C22#209711yescharacteristic
502C22#209711yescharacteristic
503C4—21no—
504C4—21no—
505C4—21no—
506C4—21no—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—21no—
511C4—84no—
512C4—84no—
513C4—82no—
514C4—82no—
515C4—162no—
516C4—162no—
517C2—21no—
518C2—22no—
519C2—21no—
520C2—21no—
521C2—22no—
522C2—22no—
523C2—21no—
524C2—21no—
525C2—21no—
526C2#1037714yes—
527C2#1105211yescharacteristic
528C2#1108911yescharacteristic
529C2#1109111yescharacteristic
subgroupG/H
center, socleC23#393
commutatorC23×C4C22×C4
Frattini, cosocleC24×C4C23
prime radicalC25C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
16. #1996C4semidirect

Maximal subgroups

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

subgroupindex
C2×#19962
C2×#15202
C22×#3282
#139662
C2×#12942
C2×#12892
C2×#12822