Finite Group Databasebeta

← #117597

Subgroups — #117597

Order 512.

990 conjugacy classes of subgroups.

The subgroup lattice has 519 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21940C211yesmaximal, characteristic
2C2×#1823C211yesmaximal, characteristic
3C2×#1823C211yesmaximal, characteristic
4#13904C211yesmaximal, characteristic
5#10854C211yesmaximal, characteristic
6#8023C211yesmaximal, characteristic
7C2×#1282C211yesmaximal, characteristic
8C23×C4⋊C4C2211yescharacteristic
9C22×C22⋊C8C2211yescharacteristic
10C22×C22⋊C8C2211yescharacteristic
11C2×#381—22no—
12C2×#380C2211yescharacteristic
13C2×#380C2211yescharacteristic
14C2×#380C2211yescharacteristic
15C2×C4×C22⋊C4C2211yescharacteristic
16#1852—22no—
17#1852—22no—
18#1823—22no—
19#1823—22no—
20#1823—22no—
21#1823C414yescomplemented
22#1808—22no—
23C2×#342—22no—
24C2×#340—22no—
25C2×#340—22no—
26#1445—22no—
27C4⋊#95—22no—
28#1294—22no—
29#1282—22no—
30C24×C4—21no—
31C24×C4C2311yescharacteristic
32C23×C8—21no—
33C23×C8D412yes—
34C22×C4⋊C4—21no—
35C22×C4⋊C4—21no—
36C22×C4⋊C4—21no—
37C22×C4⋊C4—21no—
38C22×C4⋊C4—21no—
39C22×C4⋊C4—21no—
40C22×C4⋊C4—21no—
41C22×C4⋊C4—21no—
42C22×C4⋊C4—21no—
43C22×C4⋊C4—21no—
44C22×C4⋊C4—21no—
45C22×C4⋊C4—21no—
46C22×C4⋊C4C2×C412yes—
47C22×C4⋊C4D412yes—
48C22×C4⋊C4D412yes—
49C22×C4⋊C4D412yes—
50C22×C4⋊C4Q812yes—
51C22×C22⋊C4—21no—
52C22×C22⋊C4—21no—
53C22×C22⋊C4—21no—
54C22×C22⋊C4D412yes—
55C22×C42—21no—
56C2×#107—24no—
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⋊C8C2×C412yes—
67C2×C22⋊C8D412yes—
68C2×C22⋊C8D412yes—
69#381—44no—
70#381—44no—
71#380—21no—
72#380—21no—
73#380—21no—
74#380—21no—
75#380—21no—
76#380—21no—
77#380—21no—
78#380—21no—
79#380—21no—
80#380—21no—
81#380—21no—
82#380C2×C412yes—
83C4×C22⋊C4—21no—
84C4×C22⋊C4—21no—
85C4×C22⋊C4—21no—
86C4×C22⋊C4—21no—
87C2×#95—21no—
88C2×#95—28no—
89C2×#95—21no—
90C2×#95—21no—
91C2×#95—21no—
92#342—44no—
93#340—24no—
94#340—28no—
95#340—28no—
96C25C2×D411yescharacteristic
97C23×C4—22no—
98C23×C4—22no—
99C23×C4—22no—
100C23×C4—22no—
101C23×C4—22no—
102C23×C4—22no—
103C23×C4—44no—
104C23×C4—41no—
105C23×C4—41no—
106C23×C4—41no—
107C23×C4—41no—
108C23×C4—42no—
109C23×C4—42no—
110C23×C4—42no—
111C23×C4—42no—
112C23×C4—41no—
113C23×C4C22×C411yescharacteristic
114C23×C4C2×D411yescharacteristic
115C23×C4C2×D411yescharacteristic
116C23×C4C2×D411yescharacteristic
117C23×C4C2×D411yescharacteristic
118C23×C4C2×D411yescharacteristic
119C23×C4C2×D411yescharacteristic
120C23×C4C2×Q811yescharacteristic
121C23×C4#4111yescharacteristic
122C23×C4#4111yescharacteristic
123C23×C4#4111yescharacteristic
124C23×C4#4111yescharacteristic
125C23×C4#4111yescharacteristic
126C23×C4#4111yescharacteristic
127C22×C8—22no—
128C22×C8—22no—
129C22×C8—22no—
130C22×C8—44no—
131C22×C8—44no—
132C22×C8—41no—
133C22×C8—41no—
134C22×C8C22⋊C414yes—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4—41no—
160C2×C4⋊C4—41no—
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—44no—
168C2×C4⋊C4—44no—
169C2×C4⋊C4—44no—
170C2×C4⋊C4—41no—
171C2×C4⋊C4C4⋊C414yes—
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—42no—
179C2×C22⋊C4—42no—
180C2×C22⋊C4—41no—
181C2×C22⋊C4—41no—
182C2×C22⋊C4—41no—
183C2×C22⋊C4—41no—
184C2×C22⋊C4—41no—
185C2×C22⋊C4—42no—
186C2×C22⋊C4—42no—
187C2×C22⋊C4—42no—
188C2×C22⋊C4—42no—
189C2×C22⋊C4D814yes—
190C2×C42—44no—
191C2×C42—41no—
192C2×C42—41no—
193#107—84no—
194C22⋊C8—22no—
195C22⋊C8—22no—
196C22⋊C8—22no—
197C22⋊C8—22no—
198C22⋊C8—22no—
199C22⋊C8—22no—
200C22⋊C8—41no—
201C22⋊C8—41no—
202#95—22no—
203#95—416no—
204#95—41no—
205#95—41no—
206#95—41no—
207#95—41no—
208#95—41no—
209#95—41no—
210#95—41no—
211C24—42no—
212C24—42no—
213C24C4×D411yescharacteristic
214C24#12011yescharacteristic
215C24#12111yescharacteristic
216C24#12111yescharacteristic
217C24C22⋊Q811yescharacteristic
218C24#12311yescharacteristic
219C24#12711yescharacteristic
220C24C2×D812yes—
221C24#13512yes—
222C24AGL(1,ℤ/8)12yes—
223C24#13712yes—
224C22×C4—24no—
225C22×C4—24no—
226C22×C4—24no—
227C22×C4—24no—
228C22×C4—24no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—44no—
241C22×C4—44no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—44no—
250C22×C4—44no—
251C22×C4—44no—
252C22×C4—42no—
253C22×C4—44no—
254C22×C4—44no—
255C22×C4—44no—
256C22×C4—44no—
257C22×C4—44no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—44no—
262C22×C4—44no—
263C22×C4—82no—
264C22×C4—82no—
265C22×C4—82no—
266C22×C4—82no—
267C22×C4—82no—
268C22×C4—82no—
269C22×C4—81no—
270C22×C4—81no—
271C22×C4—81no—
272C22×C4—81no—
273C22×C4—82no—
274C22×C4—82no—
275C22×C4—81no—
276C22×C4—81no—
277C22×C4—82no—
278C22×C4—82no—
279C22×C4C2×C22⋊C411yescharacteristic
280C22×C4C2×C4⋊C411yescharacteristic
281C22×C4#11711yescharacteristic
282C22×C4C4×D411yescharacteristic
283C22×C4C4×D411yescharacteristic
284C22×C4C4×D411yescharacteristic
285C22×C4#12011yescharacteristic
286C22×C4#12011yescharacteristic
287C22×C4#12111yescharacteristic
288C22×C4#12111yescharacteristic
289C22×C4#12111yescharacteristic
290C22×C4#12111yescharacteristic
291C22×C4#12111yescharacteristic
292C22×C4#12111yescharacteristic
293C22×C4C22⋊Q811yescharacteristic
294C22×C4C22⋊Q811yescharacteristic
295C22×C4C22⋊Q811yescharacteristic
296C22×C4C22⋊Q811yescharacteristic
297C22×C4C22⋊Q811yescharacteristic
298C22×C4#12311yescharacteristic
299C22×C4#12311yescharacteristic
300C22×C4#12311yescharacteristic
301C22×C4#12311yescharacteristic
302C22×C4#12411yescharacteristic
303C22×C4#12411yescharacteristic
304C22×C4#12411yescharacteristic
305C22×C4#12611yescharacteristic
306C22×C4#12611yescharacteristic
307C2×C8—24no—
308C2×C8—44no—
309C2×C8—44no—
310C2×C8—44no—
311C2×C8—42no—
312C2×C8—82no—
313C2×C8—82no—
314C2×C8—82no—
315C4⋊C4—24no—
316C4⋊C4—24no—
317C4⋊C4—44no—
318C4⋊C4—44no—
319C4⋊C4—42no—
320C4⋊C4—42no—
321C4⋊C4—42no—
322C4⋊C4—42no—
323C4⋊C4—42no—
324C4⋊C4—42no—
325C4⋊C4—44no—
326C4⋊C4—44no—
327C4⋊C4—82no—
328C4⋊C4—82no—
329C22⋊C4—24no—
330C22⋊C4—24no—
331C22⋊C4—42no—
332C22⋊C4—42no—
333C22⋊C4—44no—
334C22⋊C4—82no—
335C22⋊C4—82no—
336C22⋊C4—82no—
337C22⋊C4—81no—
338C22⋊C4—81no—
339C22⋊C4—81no—
340C22⋊C4—81no—
341C42—82no—
342C42—82no—
343C23—22no—
344C23—22no—
345C23—22no—
346C23—22no—
347C23—22no—
348C23—22no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—44no—
358C23—44no—
359C23—44no—
360C23—44no—
361C23#38511yescharacteristic
362C23#38811yescharacteristic
363C23#39011yescharacteristic
364C23#39211yescharacteristic
365C23#39411yescharacteristic
366C23#39611yescharacteristic
367C23#39911yescharacteristic
368C23C4×D812yes—
369C23#44012yes—
370C23#44712yes—
371C23#45212yes—
372C23#45912yes—
373C23#46412yes—
374C23#46612yes—
375C23#46812yes—
376C23#47412yes—
377C23#47812yes—
378C23#48012yes—
379C23#48212yes—
380C23#49311yescharacteristic
381C23#49511yescharacteristic
382C23#49611yescharacteristic
383C23#49711yescharacteristic
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
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—48no—
412C2×C4—48no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—82no—
416C2×C4—82no—
417C2×C4—84no—
418C2×C4—84no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4—84no—
422C2×C4—82no—
423C2×C4—82no—
424C2×C4—82no—
425C2×C4—82no—
426C2×C4—84no—
427C2×C4—82no—
428C2×C4—88no—
429C2×C4—82no—
430C2×C4—82no—
431C2×C4—82no—
432C2×C4—82no—
433C2×C4—82no—
434C2×C4—82no—
435C2×C4—82no—
436C2×C4—82no—
437C2×C4—162no—
438C2×C4—162no—
439C2×C4—164no—
440C2×C4#38011yescharacteristic
441C2×C4#38511yescharacteristic
442C2×C4#38611yescharacteristic
443C2×C4#38811yescharacteristic
444C2×C4#39311yescharacteristic
445C2×C4#39411yescharacteristic
446C2×C4#39611yescharacteristic
447C2×C4#39711yescharacteristic
448C2×C4#45814yes—
449C8—44no—
450C8—82no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—24no—
464C22—24no—
465C22—22no—
466C22—22no—
467C22—24no—
468C22—22no—
469C22—24no—
470C22—22no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—42no—
475C22—42no—
476C22—42no—
477C22—42no—
478C22—42no—
479C22#143911yescharacteristic
480C22#186212yes—
481C22#192512yes—
482C22#197011yescharacteristic
483C22#197311yescharacteristic
484C22#200912yes—
485C22#201111yescharacteristic
486C22#201511yescharacteristic
487C22#202212yes—
488C22#203312yes—
489C22#206712yes—
490C22#209211yescharacteristic
491C22#209311yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—84no—
499C4—84no—
500C4—162no—
501C4—162no—
502C4—162no—
503C4#189012yes—
504C4#203012yes—
505C2—22no—
506C2—21no—
507C2—22no—
508C2—21no—
509C2—21no—
510C2—22no—
511C2—22no—
512C2—21no—
513C2#995212yes—
514C2#996112yes—
515C2#1107011yescharacteristic
516C2#1112311yescharacteristic
517C2#1113011yescharacteristic
subgroupG/H
center, socleC23#392
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
21. #1823C4semidirect

Maximal subgroups

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

subgroupindex
#219402
C2×#18232
#139042
#108542
#80232
C2×#12822