Finite Group Databasebeta

← #96914

Subgroups — #96914

Order 512.

944 conjugacy classes of subgroups.

The subgroup lattice has 507 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2295C211yesmaximal, characteristic
2#10795C211yesmaximal, characteristic
3#10795C211yesmaximal, characteristic
4C2×#1272C212yesmaximal
5C2×#1271C212yesmaximal
6C22×C4×Q8C411yescharacteristic
7#2295—24no—
8#2295—24no—
9C2×#391C411yescharacteristic
10C2×#391C2211yescharacteristic
11C2×#389C411yescharacteristic
12C2×#389C2211yescharacteristic
13C2×#387—21no—
14C2×#387—21no—
15C2×C4×C4⋊C4—21no—
16C2×C4×C4⋊C4C411yescharacteristic
17C2×#376—21no—
18C2×C43C2211yescharacteristic
19C2×#336—21no—
20C2×#336—21no—
21C2×#336—21no—
22C2×#336—21no—
23C2×#336C2212yes—
24C2×#336C2212yes—
25#1272—24no—
26#1271—24no—
27C23×Q8C2×C411yescharacteristic
28C23×C8—22no—
29C23×C8—22no—
30C2×C4×Q8—22no—
31C2×C4×Q8—22no—
32C2×C4×Q8—22no—
33C2×C4×Q8—22no—
34C2×C4×Q8—22no—
35C2×C4×Q8C814yescomplemented
36C22×C4⋊C4—21no—
37C22×C4⋊C4—21no—
38C22×C4⋊C4—21no—
39C22×C4⋊C4C2×C411yescharacteristic
40C22×C4⋊C4C2×C411yescharacteristic
41C22×C4⋊C4C2×C411yescharacteristic
42C22×C42—21no—
43C22×C42—21no—
44C22×C42C2×C411yescharacteristic
45C22×C42C2×C411yescharacteristic
46C22×C42D411yescharacteristic
47C22×C42D411yescharacteristic
48C22×C42D411yescharacteristic
49C22×C42D411yescharacteristic
50C22×C42C2311yescharacteristic
51#391—22no—
52#391—22no—
53#391—22no—
54#391D414yes—
55#389—22no—
56#389—22no—
57#389—22no—
58#389D414yes—
59#387—28no—
60#387—28no—
61C4×C4⋊C4—28no—
62C4×C4⋊C4—22no—
63C4×C4⋊C4—22no—
64#376—28no—
65C2×#95—21no—
66C2×#95—21no—
67C2×#95—21no—
68C2×#95—21no—
69C2×#95—21no—
70C2×#95—21no—
71C2×#95—21no—
72C43—22no—
73C43—22no—
74#336—24no—
75#336—24no—
76#336—22no—
77#336—22no—
78#336—22no—
79#336—22no—
80#336—42no—
81#336—42no—
82C22×Q8—21no—
83C22×Q8—21no—
84C22×Q8—21no—
85C22×Q8—41no—
86C22×Q8—41no—
87C22×Q8—41no—
88C22×Q8—41no—
89C22×Q8C22⋊C412yes—
90C22×Q8C2×C812yes—
91C22×Q8M1612yes—
92C23×C4—21no—
93C23×C4—21no—
94C23×C4—21no—
95C23×C4—21no—
96C23×C4C22⋊C411yescharacteristic
97C23×C4C22⋊C411yescharacteristic
98C23×C4C22⋊C411yescharacteristic
99C23×C4C22⋊C411yescharacteristic
100C23×C4C22×C411yescharacteristic
101C23×C4C2×D411yescharacteristic
102C23×C4C2×D411yescharacteristic
103C22×C8—24no—
104C22×C8—24no—
105C22×C8—42no—
106C22×C8—42no—
107C22×C8—42no—
108C22×C8—42no—
109C22×C8—42no—
110C22×C8—42no—
111C22×C8—42no—
112C22×C8—42no—
113C22×C8—42no—
114C22×C8—42no—
115C22×C8—42no—
116C22×C8—42no—
117C4×Q8—28no—
118C4×Q8—28no—
119C4×Q8—28no—
120C4×Q8—28no—
121C2×C4⋊C4—24no—
122C2×C4⋊C4—24no—
123C2×C4⋊C4—24no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—21no—
126C2×C4⋊C4—21no—
127C2×C4⋊C4—24no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—24no—
131C2×C4⋊C4—41no—
132C2×C4⋊C4—41no—
133C2×C4⋊C4—41no—
134C2×C4⋊C4—41no—
135C2×C4⋊C4—42no—
136C2×C4⋊C4—42no—
137C2×C4⋊C4—42no—
138C2×C4⋊C4—41no—
139C2×C4⋊C4—41no—
140C2×C4⋊C4C22⋊C412yes—
141C2×C4⋊C4C22⋊C412yes—
142C2×C4⋊C4C22⋊C412yes—
143C2×C4⋊C4C2×C812yes—
144C2×C4⋊C4M1612yes—
145C2×C42—24no—
146C2×C42—24no—
147C2×C42—24no—
148C2×C42—21no—
149C2×C42—21no—
150C2×C42—22no—
151C2×C42—21no—
152C2×C42—21no—
153C2×C42—22no—
154C2×C42—24no—
155C2×C42—22no—
156C2×C42—22no—
157C2×C42—21no—
158C2×C42—21no—
159C2×C42—22no—
160C2×C42—22no—
161C2×C42—22no—
162C2×C42—22no—
163C2×C42—21no—
164C2×C42—21no—
165C2×C42—41no—
166C2×C42—41no—
167C2×C42—41no—
168C2×C42—41no—
169C2×C42—41no—
170C2×C42—41no—
171C2×C42—42no—
172C2×C42—42no—
173C2×C42C2×C812yes—
174C2×C42M1612yes—
175C2×C42SD1612yes—
176C2×C42Q1612yes—
177C2×C42C2×D412yes—
178C2×C42C2×D412yes—
179#95—24no—
180#95—24no—
181#95—24no—
182#95—24no—
183#95—24no—
184#95—24no—
185#95—24no—
186C24C2×C22⋊C411yescharacteristic
187C2×Q8—22no—
188C2×Q8—22no—
189C2×Q8—22no—
190C2×Q8—42no—
191C2×Q8—42no—
192C2×Q8—42no—
193C2×Q8—42no—
194C2×Q8—42no—
195C2×Q8—42no—
196C2×Q8—42no—
197C2×Q8—42no—
198C2×Q8—42no—
199C2×Q8—42no—
200C2×Q8—42no—
201C2×Q8—42no—
202C2×Q8C22⋊C814yes—
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—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—21no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4C22⋊C812yes—
266C22×C4C22⋊C812yes—
267C22×C4#10312yes—
268C22×C4#10312yes—
269C22×C4#10412yes—
270C22×C4#10412yes—
271C22×C4C2×C22⋊C411yescharacteristic
272C22×C4C2×C22⋊C411yescharacteristic
273C22×C4#12012yes—
274C22×C4#12012yes—
275C22×C4C22×C811yescharacteristic
276C22×C4C2×M1611yescharacteristic
277C22×C4C2×M1611yescharacteristic
278C22×C4C2×M1611yescharacteristic
279C22×C4C2×SD1611yescharacteristic
280C22×C4C2×Q1611yescharacteristic
281C22×C4#13512yes—
282C22×C4AGL(1,ℤ/8)11yescharacteristic
283C22×C4#13712yes—
284C22×C4#13711yescharacteristic
285C2×C8—44no—
286C2×C8—44no—
287C2×C8—44no—
288C2×C8—44no—
289C2×C8—44no—
290C2×C8—44no—
291C2×C8—82no—
292C2×C8—82no—
293C2×C8—82no—
294C2×C8—82no—
295C2×C8—82no—
296C2×C8—82no—
297C2×C8—82no—
298C2×C8—82no—
299C4⋊C4—216no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—48no—
308C4⋊C4—44no—
309C4⋊C4—44no—
310C4⋊C4C22⋊C814yes—
311C42—216no—
312C42—22no—
313C42—22no—
314C42—22no—
315C42—22no—
316C42—24no—
317C42—24no—
318C42—42no—
319C42—42no—
320C42—44no—
321C42—44no—
322C42—42no—
323C42—42no—
324C42—48no—
325C42—42no—
326C42—42no—
327C23#37911yescharacteristic
328C23C2×C22⋊C811yescharacteristic
329C23#40711yescharacteristic
330C23#41011yescharacteristic
331C23#41011yescharacteristic
332C23#41311yescharacteristic
333C23#41311yescharacteristic
334C23C2×#10311yescharacteristic
335C23#41611yescharacteristic
336C23#41711yescharacteristic
337C23#41911yescharacteristic
338C23C2×#10411yescharacteristic
339C23C2×#10411yescharacteristic
340C23#42111yescharacteristic
341C23#42111yescharacteristic
342Q8—44no—
343Q8—44no—
344Q8—44no—
345Q8—44no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—22no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—22no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—24no—
386C2×C4—24no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4Q8⋊C814yes—
430C2×C4C2×C22⋊C811yescharacteristic
431C2×C4C2×C22⋊C811yescharacteristic
432C2×C4#40711yescharacteristic
433C2×C4#40711yescharacteristic
434C2×C4#44812yes—
435C2×C4#44912yes—
436C2×C4#45112yes—
437C2×C4#45212yes—
438C8—84no—
439C8—84no—
440C22#145811yescharacteristic
441C22#145811yescharacteristic
442C22#146411yescharacteristic
443C22#146411yescharacteristic
444C22C2×Q8⋊C811yescharacteristic
445C22#147611yescharacteristic
446C22#147711yescharacteristic
447C22#147911yescharacteristic
448C22#148711yescharacteristic
449C22#148811yescharacteristic
450C22#148911yescharacteristic
451C22#149111yescharacteristic
452C22#150011yescharacteristic
453C22#150311yescharacteristic
454C22#150611yescharacteristic
455C22#150911yescharacteristic
456C22#151211yescharacteristic
457C22#151511yescharacteristic
458C22#151811yescharacteristic
459C22#152111yescharacteristic
460C22#152411yescharacteristic
461C22#152911yescharacteristic
462C22#153211yescharacteristic
463C22#153511yescharacteristic
464C22#154211yescharacteristic
465C22#155011yescharacteristic
466C22#155411yescharacteristic
467C22#155911yescharacteristic
468C22#177911yescharacteristic
469C22#178211yescharacteristic
470C22#178511yescharacteristic
471C22#178711yescharacteristic
472C22#178811yescharacteristic
473C22#178911yescharacteristic
474C22#178911yescharacteristic
475C4—21no—
476C4—21no—
477C4—21no—
478C4—21no—
479C4—24no—
480C4—22no—
481C4—22no—
482C4—22no—
483C4—22no—
484C4—44no—
485C4—42no—
486C4—44no—
487C4—42no—
488C4—42no—
489C4—82no—
490C4—82no—
491C2#756211yescharacteristic
492C2#757711yescharacteristic
493C2#758111yescharacteristic
494C2#759611yescharacteristic
495C2#761111yescharacteristic
496C2#761511yescharacteristic
497C2#763011yescharacteristic
498C2#764411yescharacteristic
499C2#830011yescharacteristic
500C2#831111yescharacteristic
501C2#831211yescharacteristic
502C2#833011yescharacteristic
503C2#833311yescharacteristic
504C2#833611yescharacteristic
505C2#834311yescharacteristic
subgroupG/H
center, socle, prime radicalC24C2×C22⋊C4
commutatorC22×C4C22×C8
Frattini, cosocleC22×C42C23
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
35. C2×C4×Q8C8semidirect

Maximal subgroups

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

subgroupindex
C2×#22952
#107952
C2×#12722
C2×#12712