Finite Group Databasebeta

← #116300

Subgroups — #116300

Order 512.

653 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21337C211yesmaximal, characteristic
2#21146C211yesmaximal, characteristic
3#17708C211yesmaximal, characteristic
4C2×#1503C211yesmaximal, characteristic
5C2×#1303C211yesmaximal, characteristic
6#8001C211yesmaximal, characteristic
7#7932C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#423—21no—
12C2×#423C2211yescharacteristic
13C2×#423C2211yescharacteristic
14C2×C4×M16C2211yescharacteristic
15C2×C4×C4⋊C4C2211yescharacteristic
16#1998—22no—
17#1997—21no—
18#1997—21no—
19#1940—22no—
20#1939—22no—
21#1742—21no—
22#1742—21no—
23#1728—21no—
24#1550—22no—
25#1549—21no—
26#1548—21no—
27#1542—22no—
28#1503—21no—
29#1503—21no—
30#1503—22no—
31C2×#328C414yes—
32#1303—21no—
33#1303—21no—
34#1292—22no—
35#1283—22no—
36C22×M16—21no—
37C22×M16—21no—
38C22×M16D411yescharacteristic
39C22×M16D411yescharacteristic
40#533—21no—
41#533—21no—
42#533—21no—
43#533—21no—
44#533—21no—
45#533—21no—
46#533—21no—
47#533—21no—
48C2×C4⋊Q8D411yescharacteristic
49C2×C4⋊Q8D411yescharacteristic
50C2×#125—21no—
51C2×C22⋊Q8—21no—
52C2×C22⋊Q8C2×C412yes—
53C2×C4×Q8—21no—
54C2×C4×Q8Q812yes—
55C2×#117—21no—
56C22×C4⋊C4—21no—
57C22×C42—21no—
58C22×C42C2311yescharacteristic
59#431—21no—
60#431—21no—
61#431—21no—
62#431—21no—
63#431—21no—
64#431—21no—
65#431—21no—
66#431—21no—
67#423—21no—
68#423—21no—
69#423—21no—
70#423—21no—
71#423—21no—
72#423—21no—
73#423—21no—
74#423—42no—
75#423—42no—
76#423D412yes—
77C2×C4⋊C8—21no—
78C2×C4⋊C8—21no—
79C2×C4⋊C8—24no—
80C2×C4⋊C8—21no—
81C2×C4⋊C8—21no—
82C2×C4⋊C8D412yes—
83C2×C4⋊C8D412yes—
84C2×C22⋊C8—21no—
85C2×C22⋊C8C2×C412yes—
86C4×M16—21no—
87C4×M16—21no—
88C4×M16—21no—
89C4×M16—21no—
90C2×#97—21no—
91C2×C4×C8—21no—
92C2×C4×C8—21no—
93C2×C4×C8—21no—
94C4×C4⋊C4—21no—
95C4×C4⋊C4—21no—
96C4×C4⋊C4D411yescharacteristic
97C4×C4⋊C4D411yescharacteristic
98C4×C4⋊C4D412yes—
99C2×#95C2×C412yes—
100#343—22no—
101#343—22no—
102#343—22no—
103#343—22no—
104#336—24no—
105#333—24no—
106#332—24no—
107#328—24no—
108#328—24no—
109C22×Q8—21no—
110C22×Q8C4⋊C412yes—
111C23×C4—22no—
112C23×C4C22×C411yescharacteristic
113C23×C4C2×D411yescharacteristic
114C23×C4#4111yescharacteristic
115C2×M16—21no—
116C2×M16—21no—
117C2×M16—21no—
118C2×M16—21no—
119C2×M16—21no—
120C2×M16—21no—
121C2×M16—21no—
122C2×M16—21no—
123C2×M16—21no—
124C2×M16—21no—
125C2×M16—22no—
126C2×M16—41no—
127C2×M16—41no—
128C2×M16—41no—
129C2×M16—41no—
130C2×M16—41no—
131C2×M16—41no—
132C2×M16—41no—
133C2×M16—41no—
134C2×M16—41no—
135C2×M16—41no—
136C2×M16—41no—
137C2×M16SD1612yes—
138C2×M16Q1612yes—
139C22×C8—21no—
140C22×C8—21no—
141C22×C8—22no—
142C22×C8—22no—
143C22×C8—22no—
144C22×C8—41no—
145C4⋊Q8—21no—
146C4⋊Q8—21no—
147C4⋊Q8—21no—
148C4⋊Q8—21no—
149C4⋊Q8—21no—
150C4⋊Q8—21no—
151C4⋊Q8—21no—
152C4⋊Q8—21no—
153#125—41no—
154#125—41no—
155#125—41no—
156#125—41no—
157C22⋊Q8—22no—
158C22⋊Q8—22no—
159C22⋊Q8—22no—
160C22⋊Q8—22no—
161C22⋊Q8—41no—
162C22⋊Q8—41no—
163C22⋊Q8—41no—
164C22⋊Q8—41no—
165C4×Q8—22no—
166C4×Q8—22no—
167C4×Q8—22no—
168C4×Q8—22no—
169C4×Q8—41no—
170C4×Q8—41no—
171C4×Q8—41no—
172C4×Q8—41no—
173#117—41no—
174#117—41no—
175#117—41no—
176#117—41no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—44no—
186C2×C4⋊C4C4⋊C412yes—
187C2×C22⋊C4—22no—
188C2×C42—22no—
189C2×C42—21no—
190C2×C42—21no—
191C2×C42—22no—
192C2×C42—41no—
193C2×C42—41no—
194C2×C42—41no—
195C2×C42—41no—
196C2×C42C2×D411yescharacteristic
197C2×C42C2×D411yescharacteristic
198C2×C42C2×D411yescharacteristic
199C2×C42C2×D411yescharacteristic
200C2×C42C2×D411yescharacteristic
201C2×C42C2×D411yescharacteristic
202C2×C42C2×Q811yescharacteristic
203C2×C42#4111yescharacteristic
204C2×C42#4111yescharacteristic
205C2×C42#4111yescharacteristic
206C2×C42#4111yescharacteristic
207C2×C42#4111yescharacteristic
208C4⋊C8—22no—
209C4⋊C8—22no—
210C4⋊C8—22no—
211C4⋊C8—22no—
212C4⋊C8—22no—
213C4⋊C8—22no—
214C4⋊C8—48no—
215C4⋊C8—41no—
216C4⋊C8—41no—
217C4⋊C8—41no—
218C4⋊C8—41no—
219C4⋊C8—41no—
220C4⋊C8—41no—
221C22⋊C8—22no—
222C22⋊C8—22no—
223C22⋊C8—41no—
224C22⋊C8—41no—
225#97—41no—
226#97—41no—
227C4×C8—41no—
228C4×C8—41no—
229C4×C8—41no—
230C4×C8—41no—
231C4×C8—41no—
232C4×C8—41no—
233#95—22no—
234#95C22⋊C412yes—
235#95C22⋊C412yes—
236C24C4×D411yescharacteristic
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—82no—
242C2×Q8—82no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—42no—
248C22×C4—44no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—81no—
252C22×C4—82no—
253C22×C4C2×C22⋊C411yescharacteristic
254C22×C4C2×C4⋊C411yescharacteristic
255C22×C4#11711yescharacteristic
256C22×C4C4×D411yescharacteristic
257C22×C4C4×D411yescharacteristic
258C22×C4C4×D411yescharacteristic
259C22×C4#12011yescharacteristic
260C22×C4#12011yescharacteristic
261C22×C4#12111yescharacteristic
262C22×C4#12111yescharacteristic
263C22×C4#12111yescharacteristic
264C22×C4C22⋊Q811yescharacteristic
265C22×C4C22⋊Q811yescharacteristic
266C22×C4#12311yescharacteristic
267C22×C4#12311yescharacteristic
268C22×C4#12311yescharacteristic
269C22×C4#12411yescharacteristic
270C22×C4#12611yescharacteristic
271C22×C4C2×SD1611yescharacteristic
272C22×C4C2×Q1611yescharacteristic
273C22×C4#13511yescharacteristic
274C22×C4#13511yescharacteristic
275C22×C4AGL(1,ℤ/8)11yescharacteristic
276C22×C4#13711yescharacteristic
277C22×C4#13711yescharacteristic
278C22×C4#13711yescharacteristic
279M16—22no—
280M16—22no—
281M16—22no—
282M16—22no—
283M16—41no—
284M16—41no—
285M16—41no—
286M16—41no—
287M16—42no—
288M16—42no—
289M16—81no—
290M16—81no—
291M16—81no—
292M16—81no—
293M16—81no—
294M16—81no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—42no—
302C2×C8—42no—
303C2×C8—42no—
304C2×C8—42no—
305C2×C8—42no—
306C2×C8—42no—
307C2×C8—81no—
308C2×C8—81no—
309C2×C8—82no—
310C2×C8—82no—
311C4⋊C4—24no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—42no—
315C4⋊C4—44no—
316C4⋊C4—42no—
317C4⋊C4—42no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—42no—
324C4⋊C4—41no—
325C4⋊C4—42no—
326C22⋊C4—42no—
327C22⋊C4—42no—
328C42—42no—
329C42—42no—
330C42—42no—
331C42—42no—
332C42—41no—
333C42—41no—
334C42—41no—
335C42—41no—
336C42#12011yescharacteristic
337C42#12111yescharacteristic
338C42#12111yescharacteristic
339C42#12111yescharacteristic
340C42#12111yescharacteristic
341C42#12111yescharacteristic
342C42C22⋊Q811yescharacteristic
343C42C22⋊Q811yescharacteristic
344C42C22⋊Q811yescharacteristic
345C42C22⋊Q811yescharacteristic
346C42#12311yescharacteristic
347C42#12311yescharacteristic
348C42#12411yescharacteristic
349C42#12411yescharacteristic
350C42#12611yescharacteristic
351C42#12711yescharacteristic
352C23—41no—
353C23—41no—
354C23#38511yescharacteristic
355C23#38611yescharacteristic
356C23#38811yescharacteristic
357C23C4×SD1611yescharacteristic
358C23C4×Q1611yescharacteristic
359C23#44011yescharacteristic
360C23#44111yescharacteristic
361Q8—82no—
362Q8—82no—
363Q8—82no—
364Q8—82no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—24no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—84no—
386C2×C4—84no—
387C2×C4—82no—
388C2×C4—82no—
389C2×C4#38011yescharacteristic
390C2×C4#38511yescharacteristic
391C2×C4#38811yescharacteristic
392C2×C4#39011yescharacteristic
393C2×C4#39211yescharacteristic
394C2×C4#39311yescharacteristic
395C2×C4#39411yescharacteristic
396C2×C4#39411yescharacteristic
397C2×C4#39611yescharacteristic
398C2×C4#39611yescharacteristic
399C2×C4#39711yescharacteristic
400C2×C4#39911yescharacteristic
401C2×C4#44811yescharacteristic
402C2×C4#44911yescharacteristic
403C2×C4#45011yescharacteristic
404C2×C4#45111yescharacteristic
405C2×C4#45111yescharacteristic
406C2×C4#45211yescharacteristic
407C2×C4#45211yescharacteristic
408C2×C4#45211yescharacteristic
409C2×C4#46111yescharacteristic
410C2×C4#46211yescharacteristic
411C2×C4#46311yescharacteristic
412C2×C4#46411yescharacteristic
413C2×C4#46511yescharacteristic
414C2×C4#46711yescharacteristic
415C2×C4#46811yescharacteristic
416C2×C4#47011yescharacteristic
417C2×C4#47511yescharacteristic
418C2×C4#47711yescharacteristic
419C2×C4#47911yescharacteristic
420C2×C4#47911yescharacteristic
421C2×C4#48711yescharacteristic
422C2×C4#48811yescharacteristic
423C2×C4#48911yescharacteristic
424C2×C4#49111yescharacteristic
425C8—42no—
426C8—42no—
427C8—82no—
428C8—82no—
429C8—82no—
430C8—82no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22#143911yescharacteristic
442C22#186311yescharacteristic
443C22#186511yescharacteristic
444C22#187711yescharacteristic
445C22#187811yescharacteristic
446C22#193311yescharacteristic
447C22#193511yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—21no—
455C4—44no—
456C4—82no—
457C4—82no—
458C4—82no—
459C4#200011yescharacteristic
460C4#200111yescharacteristic
461C4#202411yescharacteristic
462C4#202611yescharacteristic
463C4#204211yescharacteristic
464C4#204311yescharacteristic
465C4#205012yes—
466C4#206611yescharacteristic
467C4#206811yescharacteristic
468C2—21no—
469C2—21no—
470C2—21no—
471C2—21no—
472C2—21no—
473C2—21no—
474C2#1106711yescharacteristic
475C2#1108211yescharacteristic
476C2#1109011yescharacteristic
subgroupG/H
centerC2×C4#393
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
socleC22#1439
prime radicalC24C4×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ 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
#213372
#211462
#177082
C2×#15032
C2×#13032
#80012
#79322