Finite Group Databasebeta

← #114397

Subgroups — #114397

Order 512.

920 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3229C211yesmaximal, characteristic
2#21302C211yesmaximal, characteristic
3C2×#1966C211yesmaximal, characteristic
4C2×#1550C211yesmaximal, characteristic
5C22×#332C211yesmaximal, characteristic
6C2×#1301C211yesmaximal, characteristic
7C2×#1283C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C22×C4⋊Q8C2211yescharacteristic
10#3229—22no—
11#3229—22no—
12#3229—22no—
13#3229—22no—
14C2×#498—21no—
15C2×#487—21no—
16C2×#483C414yes—
17C2×#475—22no—
18C2×#431C2211yescharacteristic
19C2×#423C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×#101—22no—
23C2×C4×M16C2211yescharacteristic
24#1985—22no—
25#1984—22no—
26#1966—22no—
27#1966—22no—
28#1729—22no—
29#1550—22no—
30#1550—22no—
31C2×#333—21no—
32C2×#332—22no—
33C2×#332—22no—
34C2×#332—22no—
35C2×#332—21no—
36#1301—22no—
37#1283—22no—
38C23×Q8—21no—
39C22×M16—21no—
40C22×M16D412yes—
41C23×C8—21no—
42C23×C8—21no—
43#533—21no—
44#533—21no—
45#533—21no—
46#533—21no—
47#533—21no—
48#533—21no—
49#533—21no—
50#533—21no—
51C2×C4⋊Q8—21no—
52C2×C4⋊Q8—21no—
53C2×C4⋊Q8—21no—
54C2×C4⋊Q8—21no—
55C2×C4⋊Q8—21no—
56C2×C4⋊Q8—21no—
57C2×C4⋊Q8—21no—
58C2×C4⋊Q8—21no—
59C2×C4⋊Q8—21no—
60C2×C4⋊Q8—21no—
61C2×C4⋊Q8D411yescharacteristic
62C2×C4⋊Q8D411yescharacteristic
63C2×C4⋊Q8D412yes—
64C2×C4⋊Q8D412yes—
65C2×#125—21no—
66C2×C22⋊Q8—21no—
67C2×C22⋊Q8C2×C412yes—
68C2×C4×Q8—21no—
69C2×C4×Q8D412yes—
70C2×#117—21no—
71C22×C4⋊C4—21no—
72C22×C4⋊C4C2×C412yes—
73C22×C42C2311yescharacteristic
74#498—24no—
75#498—24no—
76#487—24no—
77#487—24no—
78#483—28no—
79#483—28no—
80#475—28no—
81#475—28no—
82#431—21no—
83#431—21no—
84#431D412yes—
85#431D412yes—
86C2×#106—24no—
87#423—21no—
88#423—21no—
89#423—21no—
90#423D412yes—
91C2×C4⋊C8—21no—
92C2×C4⋊C8—21no—
93C2×C4⋊C8—21no—
94C2×C4⋊C8—21no—
95C2×C4⋊C8—21no—
96C2×C4⋊C8—21no—
97C2×C4⋊C8—21no—
98C2×C4⋊C8—21no—
99C2×C4⋊C8—21no—
100C2×C4⋊C8—21no—
101C2×C4⋊C8—21no—
102C2×C4⋊C8—21no—
103C2×C4⋊C8—21no—
104C2×C4⋊C8D412yes—
105C2×C4⋊C8D412yes—
106C2×#103—24no—
107C2×#101—28no—
108C2×#101—44no—
109C2×#101—44no—
110C2×C22⋊C8C2×C412yes—
111C4×M16—21no—
112C4×M16—21no—
113C4×M16—21no—
114C4×M16—21no—
115C2×#97—21no—
116C2×C4×C8—21no—
117C2×C4×C8—21no—
118#336—28no—
119#333—24no—
120#332—28no—
121#332—24no—
122C22×Q8—22no—
123C22×Q8—21no—
124C22×Q8—22no—
125C22×Q8—41no—
126C22×Q8—41no—
127C22×Q8—41no—
128C22×Q8—41no—
129C22×Q8—42no—
130C22×Q8—42no—
131C22×Q8—42no—
132C22×Q8—42no—
133C22×Q8C22⋊C412yes—
134C23×C4—22no—
135C23×C4C22×C411yescharacteristic
136C23×C4C2×D411yescharacteristic
137C23×C4#4111yescharacteristic
138C2×M16—22no—
139C2×M16—22no—
140C2×M16—22no—
141C2×M16—22no—
142C2×M16—22no—
143C2×M16—22no—
144C2×M16—41no—
145C2×M16—42no—
146C2×M16—42no—
147C2×M16SD1614yes—
148C22×C8—22no—
149C22×C8—22no—
150C22×C8—22no—
151C22×C8—22no—
152C22×C8—41no—
153C22×C8—41no—
154C22×C8—41no—
155C22×C8—41no—
156C22×C8—41no—
157C22×C8—42no—
158C22×C8—42no—
159C22×C8—82no—
160C4⋊Q8—22no—
161C4⋊Q8—22no—
162C4⋊Q8—22no—
163C4⋊Q8—22no—
164C4⋊Q8—22no—
165C4⋊Q8—21no—
166C4⋊Q8—21no—
167C4⋊Q8—21no—
168C4⋊Q8—21no—
169C4⋊Q8—21no—
170C4⋊Q8—21no—
171C4⋊Q8—22no—
172C4⋊Q8—22no—
173C4⋊Q8—22no—
174C4⋊Q8—21no—
175C4⋊Q8—21no—
176C4⋊Q8—41no—
177C4⋊Q8—41no—
178C4⋊Q8—41no—
179C4⋊Q8—41no—
180C4⋊Q8—41no—
181C4⋊Q8—41no—
182C4⋊Q8—41no—
183C4⋊Q8—41no—
184#125—41no—
185#125—41no—
186#125—41no—
187#125—41no—
188C22⋊Q8—22no—
189C22⋊Q8—22no—
190C22⋊Q8—22no—
191C22⋊Q8—22no—
192C22⋊Q8—41no—
193C22⋊Q8—41no—
194C22⋊Q8—41no—
195C22⋊Q8—41no—
196C4×Q8—22no—
197C4×Q8—22no—
198C4×Q8—22no—
199C4×Q8—22no—
200C4×Q8—41no—
201C4×Q8—41no—
202C4×Q8—41no—
203C4×Q8—41no—
204#117—41no—
205#117—41no—
206#117—41no—
207#117—41no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—41no—
221C2×C4⋊C4—41no—
222C2×C4⋊C4—41no—
223C2×C4⋊C4—41no—
224C2×C4⋊C4C22⋊C414yes—
225C2×C4⋊C4C22⋊C412yes—
226C2×C22⋊C4—22no—
227C2×C42—22no—
228C2×C42C2×D411yescharacteristic
229C2×C42C2×D411yescharacteristic
230C2×C42C2×D411yescharacteristic
231C2×C42C2×D411yescharacteristic
232C2×C42C2×D411yescharacteristic
233C2×C42C2×D411yescharacteristic
234C2×C42C2×D411yescharacteristic
235C2×C42C2×D411yescharacteristic
236C2×C42C2×D411yescharacteristic
237C2×C42#4111yescharacteristic
238C2×C42#4111yescharacteristic
239C2×C42#4111yescharacteristic
240#106—216no—
241C4⋊C8—22no—
242C4⋊C8—22no—
243C4⋊C8—22no—
244C4⋊C8—22no—
245C4⋊C8—22no—
246C4⋊C8—22no—
247C4⋊C8—22no—
248C4⋊C8—22no—
249C4⋊C8—41no—
250C4⋊C8—41no—
251C4⋊C8—41no—
252C4⋊C8—41no—
253C4⋊C8—41no—
254C4⋊C8—41no—
255#103—216no—
256#101—416no—
257C22⋊C8—22no—
258C22⋊C8C22⋊C414yes—
259#97—41no—
260#97—41no—
261C4×C8—22no—
262C4×C8—22no—
263C4×C8—41no—
264C4×C8—41no—
265C24C4×D411yescharacteristic
266C2×Q8—22no—
267C2×Q8—22no—
268C2×Q8—44no—
269C2×Q8—41no—
270C2×Q8—42no—
271C2×Q8—42no—
272C2×Q8—42no—
273C2×Q8—41no—
274C2×Q8—42no—
275C2×Q8—44no—
276C2×Q8—44no—
277C2×Q8—44no—
278C2×Q8—44no—
279C2×Q8—42no—
280C2×Q8—42no—
281C2×Q8—82no—
282C2×Q8—82no—
283C2×Q8—82no—
284C2×Q8—82no—
285C2×Q8—82no—
286C2×Q8—82no—
287C2×Q8—81no—
288C2×Q8—81no—
289C2×Q8—81no—
290C2×Q8—81no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—24no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—44no—
300C22×C4—44no—
301C22×C4C2×C22⋊C411yescharacteristic
302C22×C4C2×C22⋊C411yescharacteristic
303C22×C4C2×C22⋊C411yescharacteristic
304C22×C4C4×D411yescharacteristic
305C22×C4C4×D411yescharacteristic
306C22×C4C4×D411yescharacteristic
307C22×C4#12011yescharacteristic
308C22×C4#12011yescharacteristic
309C22×C4#12111yescharacteristic
310C22×C4#12111yescharacteristic
311C22×C4#12111yescharacteristic
312C22×C4#12111yescharacteristic
313C22×C4#12111yescharacteristic
314C22×C4#12111yescharacteristic
315C22×C4#12311yescharacteristic
316C22×C4#12311yescharacteristic
317C22×C4#12411yescharacteristic
318C22×C4#12711yescharacteristic
319C22×C4C2×SD1612yes—
320C22×C4#13512yes—
321C22×C4AGL(1,ℤ/8)12yes—
322C22×C4#13712yes—
323M16—24no—
324M16—24no—
325M16—42no—
326M16—42no—
327M16—44no—
328M16—81no—
329M16—81no—
330C2×C8—24no—
331C2×C8—24no—
332C2×C8—44no—
333C2×C8—42no—
334C2×C8—42no—
335C2×C8—42no—
336C2×C8—42no—
337C2×C8—42no—
338C2×C8—44no—
339C2×C8—82no—
340C2×C8—82no—
341C2×C8—82no—
342C2×C8—82no—
343C2×C8—81no—
344C2×C8—81no—
345C2×C8—82no—
346C4⋊C4—24no—
347C4⋊C4—22no—
348C4⋊C4—24no—
349C4⋊C4—22no—
350C4⋊C4—42no—
351C4⋊C4—42no—
352C4⋊C4—42no—
353C4⋊C4—42no—
354C4⋊C4—42no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—42no—
359C4⋊C4—42no—
360C4⋊C4—42no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—42no—
364C4⋊C4—42no—
365C4⋊C4—41no—
366C22⋊C4—42no—
367C22⋊C4—42no—
368C42—42no—
369C42—42no—
370C42#12011yescharacteristic
371C42#12011yescharacteristic
372C42#12011yescharacteristic
373C42#12011yescharacteristic
374C42#12011yescharacteristic
375C42#12011yescharacteristic
376C42#12111yescharacteristic
377C42#12111yescharacteristic
378C42#12111yescharacteristic
379C42#12111yescharacteristic
380C42#12111yescharacteristic
381C42#12111yescharacteristic
382C42#12311yescharacteristic
383C42#12311yescharacteristic
384C42#12411yescharacteristic
385C42#12711yescharacteristic
386C23—22no—
387C23—22no—
388C23#38611yescharacteristic
389C23#38611yescharacteristic
390C23#39011yescharacteristic
391C23C4×SD1612yes—
392C23#44012yes—
393Q8—44no—
394Q8—82no—
395Q8—82no—
396Q8—84no—
397Q8—84no—
398Q8—82no—
399Q8—82no—
400Q8—82no—
401Q8—82no—
402Q8—81no—
403Q8—81no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—48no—
418C2×C4—44no—
419C2×C4—44no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—44no—
423C2×C4—84no—
424C2×C4—82no—
425C2×C4—82no—
426C2×C4#37911yescharacteristic
427C2×C4#38611yescharacteristic
428C2×C4#38611yescharacteristic
429C2×C4#39011yescharacteristic
430C2×C4#39211yescharacteristic
431C2×C4#39211yescharacteristic
432C2×C4#39211yescharacteristic
433C2×C4#39211yescharacteristic
434C2×C4#39411yescharacteristic
435C2×C4#39411yescharacteristic
436C2×C4#39411yescharacteristic
437C2×C4#39411yescharacteristic
438C2×C4#44812yes—
439C2×C4#44912yes—
440C2×C4#45012yes—
441C2×C4#45212yes—
442C2×C4#46012yes—
443C2×C4#46112yes—
444C2×C4#46312yes—
445C2×C4#46412yes—
446C2×C4#46512yes—
447C2×C4#46812yes—
448C2×C4#47112yes—
449C2×C4#47312yes—
450C2×C4#49211yescharacteristic
451C2×C4#49511yescharacteristic
452C2×C4#49611yescharacteristic
453C2×C4#49711yescharacteristic
454C8—44no—
455C8—44no—
456C8—82no—
457C8—82no—
458C8—82no—
459C22—21no—
460C22—21no—
461C22—24no—
462C22—24no—
463C22—21no—
464C22—21no—
465C22#143811yescharacteristic
466C22#187712yes—
467C22#188012yes—
468C22#190812yes—
469C22#191512yes—
470C22#196811yescharacteristic
471C22#197311yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—82no—
479C4—84no—
480C4—82no—
481C4#200012yes—
482C4#201211yescharacteristic
483C4#201311yescharacteristic
484C4#201411yescharacteristic
485C4#201511yescharacteristic
486C4#201911yescharacteristic
487C4#202011yescharacteristic
488C4#205212yes—
489C4#205512yes—
490C2—22no—
491C2—21no—
492C2—21no—
493C2#927214yes—
494C2#1097411yescharacteristic
495C2#1102111yescharacteristic
496C2#1102311yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C4×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#32292
#213022
C2×#19662
C2×#15502
C22×#3322
C2×#13012
C2×#12832