Finite Group Databasebeta

← #99103

Subgroups — #99103

Order 512.

988 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#380C211yesmaximal, characteristic
2#10712C211yesmaximal, characteristic
3#10712C211yesmaximal, characteristic
4#7025C212yesmaximal, complemented
5#7025C212yesmaximal, complemented
6C23×C42C2211yescharacteristic
7C22×C22⋊C8—21no—
8C22×C22⋊C8—21no—
9C2×#380C411yescharacteristic
10C2×#380C411yescharacteristic
11C2×C4×C4⋊C4C411yescharacteristic
12C2×C4×C4⋊C4C411yescharacteristic
13C2×C4×C22⋊C4—21no—
14C2×#336—21no—
15C2×#336—21no—
16C2×#336C2212yes—
17C2×#336C2212yes—
18C4⋊#95C2211yescharacteristic
19C4⋊#95C2211yescharacteristic
20#1434—21no—
21C22⋊#95—21no—
22C4×#95—21no—
23C24×C4C2×C411yescharacteristic
24C24×C4D411yescharacteristic
25C24×C4D411yescharacteristic
26C23×C8—22no—
27C23×C8—22no—
28C22×C4⋊C4C2×C411yescharacteristic
29C22×C4⋊C4C2×C411yescharacteristic
30C22×C4⋊C4C2×C411yescharacteristic
31C22×C4⋊C4C2×C411yescharacteristic
32C22×C22⋊C4—21no—
33C22×C22⋊C4—21no—
34C22×C42—22no—
35C22×C42—22no—
36C22×C42—21no—
37C22×C42—21no—
38C22×C42—42no—
39C22×C42—42no—
40C22×C42C2×C411yescharacteristic
41C22×C42D411yescharacteristic
42C22×C42D411yescharacteristic
43C22×C42C2311yescharacteristic
44C2×C22⋊C8—24no—
45C2×C22⋊C8—24no—
46C2×C22⋊C8—42no—
47C2×C22⋊C8—42no—
48C2×C22⋊C8—42no—
49C2×C22⋊C8—42no—
50#380—22no—
51#380—22no—
52#380—22no—
53#380C814yescomplemented
54C4×C4⋊C4—42no—
55C4×C4⋊C4—42no—
56C4×C22⋊C4—42no—
57C4×C22⋊C4—42no—
58C2×#95—21no—
59C2×#95—21no—
60C2×#95—21no—
61C2×#95—21no—
62C2×#95—21no—
63C2×#95—21no—
64C2×#95—21no—
65C2×#95—21no—
66#336—22no—
67#336—22no—
68#336—22no—
69#336—22no—
70#336—42no—
71#336—42no—
72C25C22⋊C411yescharacteristic
73C23×C4—22no—
74C23×C4—22no—
75C23×C4—22no—
76C23×C4—22no—
77C23×C4—21no—
78C23×C4—21no—
79C23×C4—22no—
80C23×C4—21no—
81C23×C4—21no—
82C23×C4—21no—
83C23×C4—22no—
84C23×C4—21no—
85C23×C4—21no—
86C23×C4—21no—
87C23×C4—21no—
88C23×C4—21no—
89C23×C4—22no—
90C23×C4—22no—
91C23×C4—41no—
92C23×C4—41no—
93C23×C4—41no—
94C23×C4—41no—
95C23×C4—41no—
96C23×C4—41no—
97C23×C4—41no—
98C23×C4—41no—
99C23×C4C22⋊C411yescharacteristic
100C23×C4C22⋊C411yescharacteristic
101C23×C4C22⋊C411yescharacteristic
102C23×C4C2×C812yes—
103C23×C4M1612yes—
104C23×C4D812yes—
105C23×C4SD1612yes—
106C23×C4C22×C411yescharacteristic
107C23×C4C2×D411yescharacteristic
108C23×C4C2×D411yescharacteristic
109C22×C8—24no—
110C22×C8—24no—
111C22×C8—42no—
112C22×C8—42no—
113C22×C8—42no—
114C22×C8—42no—
115C22×C8—42no—
116C22×C8—42no—
117C22×C8—42no—
118C22×C8—42no—
119C22×C8—42no—
120C22×C8—42no—
121C22×C8—42no—
122C22×C8—42no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—21no—
126C2×C4⋊C4—21no—
127C2×C4⋊C4—41no—
128C2×C4⋊C4—41no—
129C2×C4⋊C4—41no—
130C2×C4⋊C4—41no—
131C2×C4⋊C4—41no—
132C2×C4⋊C4—41no—
133C2×C4⋊C4—41no—
134C2×C4⋊C4—41no—
135C2×C4⋊C4C2×C812yes—
136C2×C4⋊C4C2×C812yes—
137C2×C4⋊C4M1612yes—
138C2×C4⋊C4M1612yes—
139C2×C22⋊C4—24no—
140C2×C22⋊C4—24no—
141C2×C22⋊C4—42no—
142C2×C22⋊C4—42no—
143C2×C22⋊C4—42no—
144C2×C22⋊C4—42no—
145C2×C42—22no—
146C2×C42—22no—
147C2×C42—21no—
148C2×C42—21no—
149C2×C42—22no—
150C2×C42—22no—
151C2×C42—22no—
152C2×C42—22no—
153C2×C42—48no—
154C2×C42—48no—
155C2×C42—41no—
156C2×C42—41no—
157C2×C42—41no—
158C2×C42—41no—
159C2×C42—42no—
160C2×C42—42no—
161C2×C42—42no—
162C2×C42—42no—
163C2×C42—42no—
164C2×C42—42no—
165C2×C42#4112yes—
166C2×C42#4112yes—
167C22⋊C8—48no—
168C22⋊C8—48no—
169#95—24no—
170#95—24no—
171#95—42no—
172#95—42no—
173#95—41no—
174#95—41no—
175#95—41no—
176#95—41no—
177#95—42no—
178#95—41no—
179#95—41no—
180C24—21no—
181C24—21no—
182C24—21no—
183C24—21no—
184C24—21no—
185C24—21no—
186C24—21no—
187C24—21no—
188C24—21no—
189C24—21no—
190C24—21no—
191C24—21no—
192C24C22⋊C812yes—
193C24#10212yes—
194C24#10412yes—
195C24C2×C22⋊C411yescharacteristic
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—24no—
213C22×C4—24no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—24no—
227C22×C4—24no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—24no—
233C22×C4—24no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—44no—
245C22×C4—44no—
246C22×C4—44no—
247C22×C4—44no—
248C22×C4—44no—
249C22×C4—44no—
250C22×C4—44no—
251C22×C4—44no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4C22⋊C812yes—
289C22×C4#9912yes—
290C22×C4#9912yes—
291C22×C4#10212yes—
292C22×C4#10412yes—
293C22×C4#11711yescharacteristic
294C22×C4#11711yescharacteristic
295C22×C4#12312yes—
296C22×C4#12312yes—
297C22×C4C22×C811yescharacteristic
298C22×C4C2×M1611yescharacteristic
299C22×C4C2×M1611yescharacteristic
300C22×C4C2×M1611yescharacteristic
301C22×C4C2×D811yescharacteristic
302C22×C4C2×SD1611yescharacteristic
303C22×C4#13512yes—
304C22×C4AGL(1,ℤ/8)11yescharacteristic
305C22×C4#13712yes—
306C22×C4#13711yescharacteristic
307C2×C8—44no—
308C2×C8—44no—
309C2×C8—44no—
310C2×C8—44no—
311C2×C8—44no—
312C2×C8—44no—
313C2×C8—82no—
314C2×C8—82no—
315C2×C8—82no—
316C2×C8—82no—
317C2×C8—82no—
318C2×C8—82no—
319C2×C8—82no—
320C2×C8—82no—
321C4⋊C4—42no—
322C4⋊C4—42no—
323C4⋊C4—42no—
324C4⋊C4—42no—
325C4⋊C4—42no—
326C4⋊C4—42no—
327C4⋊C4—42no—
328C4⋊C4—42no—
329C22⋊C4—48no—
330C22⋊C4—48no—
331C42—24no—
332C42—24no—
333C42—42no—
334C42—42no—
335C42—44no—
336C42—44no—
337C42—84no—
338C42—84no—
339C23—22no—
340C23—22no—
341C23—22no—
342C23—22no—
343C23—22no—
344C23—22no—
345C23—22no—
346C23—22no—
347C23—22no—
348C23—22no—
349C23—22no—
350C23—22no—
351C23—22no—
352C23—22no—
353C23—22no—
354C23—22no—
355C23—22no—
356C23—22no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23D4⋊C814yes—
374C23#38111yescharacteristic
375C23C2×C22⋊C811yescharacteristic
376C23#40711yescharacteristic
377C23C2×#9911yescharacteristic
378C23C2×#9911yescharacteristic
379C23#41311yescharacteristic
380C23#41311yescharacteristic
381C23C2×#10211yescharacteristic
382C23#41611yescharacteristic
383C23#41711yescharacteristic
384C23#41911yescharacteristic
385C23C2×#10411yescharacteristic
386C23C2×#10411yescharacteristic
387C23#42111yescharacteristic
388C23#42111yescharacteristic
389C2×C4—22no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—22no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—48no—
430C2×C4—48no—
431C2×C4—48no—
432C2×C4—48no—
433C2×C4—44no—
434C2×C4—44no—
435C2×C4—44no—
436C2×C4—44no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—81no—
461C2×C4—81no—
462C2×C4—81no—
463C2×C4—81no—
464C2×C4—81no—
465C2×C4—81no—
466C2×C4—81no—
467C2×C4—81no—
468C2×C4—81no—
469C2×C4—81no—
470C2×C4—81no—
471C2×C4—81no—
472C2×C4—81no—
473C2×C4#32714yes—
474C2×C4#43111yescharacteristic
475C2×C4#43111yescharacteristic
476C2×C4#43211yescharacteristic
477C2×C4#43211yescharacteristic
478C2×C4#48012yes—
479C2×C4#48212yes—
480C2×C4#48312yes—
481C2×C4#48512yes—
482C8—84no—
483C8—84no—
484C22—24no—
485C22—24no—
486C22—24no—
487C22—42no—
488C22—42no—
489C22—42no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22#145911yescharacteristic
500C22#145911yescharacteristic
501C22#146511yescharacteristic
502C22#146511yescharacteristic
503C22C2×D4⋊C811yescharacteristic
504C22#147611yescharacteristic
505C22#147711yescharacteristic
506C22#147911yescharacteristic
507C22#148611yescharacteristic
508C22#148811yescharacteristic
509C22#148911yescharacteristic
510C22#149111yescharacteristic
511C22C2×#32711yescharacteristic
512C22#150111yescharacteristic
513C22#150411yescharacteristic
514C22#150811yescharacteristic
515C22#151111yescharacteristic
516C22#151311yescharacteristic
517C22#151611yescharacteristic
518C22#151911yescharacteristic
519C22#152411yescharacteristic
520C22#152911yescharacteristic
521C22#153211yescharacteristic
522C22#153511yescharacteristic
523C22#154011yescharacteristic
524C22#154711yescharacteristic
525C22#155411yescharacteristic
526C22#155911yescharacteristic
527C22#181711yescharacteristic
528C22#181911yescharacteristic
529C22#182211yescharacteristic
530C22#182311yescharacteristic
531C22#182511yescharacteristic
532C22#182611yescharacteristic
533C22#182611yescharacteristic
534C4—22no—
535C4—24no—
536C4—22no—
537C4—22no—
538C4—22no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—42no—
544C4—42no—
545C4—82no—
546C4—82no—
547C4—82no—
548C4—82no—
549C2—44no—
550C2#756511yescharacteristic
551C2#758311yescharacteristic
552C2#758611yescharacteristic
553C2#760011yescharacteristic
554C2#761611yescharacteristic
555C2#762311yescharacteristic
556C2#763411yescharacteristic
557C2#764711yescharacteristic
558C2#870011yescharacteristic
559C2#870611yescharacteristic
560C2#870811yescharacteristic
561C2#871211yescharacteristic
562C2#871511yescharacteristic
563C2#872011yescharacteristic
564C2#872611yescharacteristic
subgroupG/H
center, socleC24C2×C22⋊C4
commutatorC22×C4C22×C8
Frattini, cosocleC22×C42C23
prime radicalC25C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C24 ◁ C23×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #7025C2semidirect
5. #7025C2semidirect
53. #380C8semidirect

Maximal subgroups

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

subgroupindex
C4×#3802
#107122
#70252