Finite Group Databasebeta

← #115866

Subgroups — #115866

Order 512.

778 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1997C211yesmaximal, characteristic
2C2×#1981C211yesmaximal, characteristic
3#21146C211yesmaximal, characteristic
4C2×#1548C211yesmaximal, characteristic
5C2×#1292C211yesmaximal, characteristic
6C2×#1283C211yesmaximal, characteristic
7#7901C211yesmaximal, characteristic
8C22×C4⋊Q8C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#423—21no—
11C2×#423C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C22×C4⋊C8C2211yescharacteristic
14C22×#103C414yes—
15C2×C4×M16C2211yescharacteristic
16C2×C4×C4⋊C4C2211yescharacteristic
17#1997—22no—
18#1997—22no—
19#1981—22no—
20#1981—21no—
21#1981—21no—
22#1940—22no—
23#1939—22no—
24C2×#343—21no—
25C2×#343—21no—
26#1728—21no—
27#1548—22no—
28#1548—22no—
29C2×#333—22no—
30#1292—22no—
31#1283—22no—
32#1279—21no—
33#1279—21no—
34C23×Q8C2×C412yes—
35C22×M16—21no—
36C22×M16—21no—
37C22×M16D411yescharacteristic
38C22×M16D411yescharacteristic
39C23×C8C2×C412yes—
40C2×C4⋊Q8—21no—
41C2×C4⋊Q8—21no—
42C2×C4⋊Q8—21no—
43C2×C4⋊Q8—21no—
44C2×C4⋊Q8—21no—
45C2×C4⋊Q8—21no—
46C2×C4⋊Q8—21no—
47C2×C4⋊Q8—21no—
48C2×C4⋊Q8—21no—
49C2×C4⋊Q8—21no—
50C2×C4⋊Q8D412yes—
51C2×C4⋊Q8Q812yes—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4C2×C412yes—
55C22×C42—21no—
56C22×C42C2311yescharacteristic
57#431—21no—
58#431—21no—
59#431—21no—
60#431D412yes—
61#423—21no—
62#423—21no—
63#423—21no—
64#423—21no—
65#423—21no—
66#423—21no—
67#423—21no—
68#423—42no—
69#423—42no—
70#423D412yes—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74C2×C4⋊C8—24no—
75C2×C4⋊C8—21no—
76C2×C4⋊C8—21no—
77C2×C4⋊C8—21no—
78C2×C4⋊C8—21no—
79C2×C4⋊C8—21no—
80C2×C4⋊C8—21no—
81C2×C4⋊C8—21no—
82C2×C4⋊C8D412yes—
83C2×#103—24no—
84C2×#103—24no—
85C2×#103—48no—
86C2×C22⋊C8—21no—
87C4×M16—21no—
88C4×M16—21no—
89C4×M16—21no—
90C4×M16—21no—
91C2×#97—21no—
92C2×C4×C8—21no—
93C2×C4×C8—21no—
94C4×C4⋊C4—21no—
95C4×C4⋊C4—21no—
96C4×C4⋊C4D412yes—
97C4×C4⋊C4D411yescharacteristic
98C4×C4⋊C4D411yescharacteristic
99C2×#95—21no—
100#343—24no—
101#343—24no—
102#336—24no—
103#333—28no—
104C22×Q8—22no—
105C22×Q8—22no—
106C22×Q8—22no—
107C22×Q8—22no—
108C22×Q8—22no—
109C22×Q8—44no—
110C22×Q8—44no—
111C22×Q8C4⋊C414yes—
112C23×C4—22no—
113C23×C4—22no—
114C23×C4C22×C411yescharacteristic
115C23×C4C2×D411yescharacteristic
116C23×C4#4111yescharacteristic
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—21no—
126C2×M16—21no—
127C2×M16—22no—
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×M16—41no—
138C2×M16—41no—
139C2×M16SD1612yes—
140C2×M16Q1612yes—
141C22×C8—21no—
142C22×C8—21no—
143C22×C8—22no—
144C22×C8—22no—
145C22×C8—22no—
146C22×C8—22no—
147C22×C8—41no—
148C22×C8—41no—
149C22×C8—44no—
150C4⋊Q8—22no—
151C4⋊Q8—22no—
152C4⋊Q8—22no—
153C4⋊Q8—22no—
154C4⋊Q8—22no—
155C4⋊Q8—22no—
156C4⋊Q8—22no—
157C4⋊Q8—22no—
158C4⋊Q8—41no—
159C4⋊Q8—41no—
160C4⋊Q8—41no—
161C4⋊Q8—41no—
162C4⋊Q8—41no—
163C4⋊Q8—41no—
164C4⋊Q8—41no—
165C4⋊Q8—41no—
166C2×C4⋊C4—24no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—42no—
173C2×C4⋊C4—41no—
174C2×C4⋊C4—41no—
175C2×C4⋊C4—41no—
176C2×C4⋊C4—41no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4C22⋊C412yes—
182C2×C4⋊C4C22⋊C412yes—
183C2×C42—22no—
184C2×C42—21no—
185C2×C42—21no—
186C2×C42—41no—
187C2×C42—41no—
188C2×C42—41no—
189C2×C42—41no—
190C2×C42C2×D411yescharacteristic
191C2×C42C2×D411yescharacteristic
192C2×C42C2×D411yescharacteristic
193C2×C42C2×D411yescharacteristic
194C2×C42C2×D411yescharacteristic
195C2×C42C2×D411yescharacteristic
196C2×C42C2×Q811yescharacteristic
197C2×C42#4111yescharacteristic
198C2×C42#4111yescharacteristic
199C2×C42#4111yescharacteristic
200C2×C42#4111yescharacteristic
201C2×C42#4111yescharacteristic
202C4⋊C8—22no—
203C4⋊C8—22no—
204C4⋊C8—22no—
205C4⋊C8—22no—
206C4⋊C8—22no—
207C4⋊C8—48no—
208C4⋊C8—41no—
209C4⋊C8—41no—
210C4⋊C8—41no—
211C4⋊C8—41no—
212C4⋊C8—41no—
213C4⋊C8—41no—
214C4⋊C8—41no—
215C4⋊C8—41no—
216C4⋊C8—41no—
217#103—48no—
218#103—48no—
219C22⋊C8—22no—
220C22⋊C8—41no—
221#97—41no—
222#97—41no—
223C4×C8—22no—
224C4×C8—41no—
225C4×C8—41no—
226C4×C8—41no—
227#95—21no—
228#95—21no—
229#95—22no—
230C24C4×D411yescharacteristic
231C2×Q8—24no—
232C2×Q8—24no—
233C2×Q8—48no—
234C2×Q8—48no—
235C2×Q8—42no—
236C2×Q8—42no—
237C2×Q8—44no—
238C2×Q8—44no—
239C2×Q8—82no—
240C2×Q8—82no—
241C2×Q8—82no—
242C2×Q8—82no—
243C2×Q8—84no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—24no—
249C22×C4—42no—
250C22×C4—44no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—82no—
256C22×C4—84no—
257C22×C4C2×C22⋊C411yescharacteristic
258C22×C4C2×C4⋊C411yescharacteristic
259C22×C4#11711yescharacteristic
260C22×C4C4×D411yescharacteristic
261C22×C4C4×D411yescharacteristic
262C22×C4C4×D411yescharacteristic
263C22×C4#12011yescharacteristic
264C22×C4#12011yescharacteristic
265C22×C4#12111yescharacteristic
266C22×C4#12111yescharacteristic
267C22×C4#12111yescharacteristic
268C22×C4C22⋊Q811yescharacteristic
269C22×C4C22⋊Q811yescharacteristic
270C22×C4#12311yescharacteristic
271C22×C4#12311yescharacteristic
272C22×C4#12311yescharacteristic
273C22×C4#12411yescharacteristic
274C22×C4#12611yescharacteristic
275C22×C4C2×SD1611yescharacteristic
276C22×C4C2×Q1611yescharacteristic
277C22×C4#13511yescharacteristic
278C22×C4#13511yescharacteristic
279C22×C4AGL(1,ℤ/8)11yescharacteristic
280C22×C4#13711yescharacteristic
281C22×C4#13711yescharacteristic
282C22×C4#13711yescharacteristic
283M16—22no—
284M16—22no—
285M16—22no—
286M16—22no—
287M16—41no—
288M16—41no—
289M16—41no—
290M16—41no—
291M16—42no—
292M16—42no—
293M16—81no—
294M16—81no—
295M16—81no—
296M16—81no—
297M16—81no—
298M16—81no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—42no—
306C2×C8—42no—
307C2×C8—42no—
308C2×C8—42no—
309C2×C8—44no—
310C2×C8—42no—
311C2×C8—42no—
312C2×C8—82no—
313C2×C8—81no—
314C2×C8—81no—
315C2×C8—82no—
316C2×C8—82no—
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—44no—
321C4⋊C4—42no—
322C4⋊C4—42no—
323C4⋊C4—42no—
324C4⋊C4—42no—
325C4⋊C4—42no—
326C4⋊C4—42no—
327C4⋊C4—42no—
328C4⋊C4—42no—
329C4⋊C4#10014yes—
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—22no—
353C23—22no—
354C23#38511yescharacteristic
355C23#38611yescharacteristic
356C23#38811yescharacteristic
357C23C4×SD1611yescharacteristic
358C23C4×Q1611yescharacteristic
359C23#44011yescharacteristic
360C23#44111yescharacteristic
361Q8—48no—
362Q8—84no—
363Q8—84no—
364Q8—82no—
365Q8—82no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—24no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—44no—
386C2×C4—84no—
387C2×C4—84no—
388C2×C4—84no—
389C2×C4—84no—
390C2×C4—84no—
391C2×C4#38011yescharacteristic
392C2×C4#38511yescharacteristic
393C2×C4#38811yescharacteristic
394C2×C4#39011yescharacteristic
395C2×C4#39211yescharacteristic
396C2×C4#39311yescharacteristic
397C2×C4#39411yescharacteristic
398C2×C4#39411yescharacteristic
399C2×C4#39611yescharacteristic
400C2×C4#39611yescharacteristic
401C2×C4#39711yescharacteristic
402C2×C4#39911yescharacteristic
403C2×C4C2×#10012yes—
404C2×C4#41312yes—
405C2×C4#44811yescharacteristic
406C2×C4#44911yescharacteristic
407C2×C4#45011yescharacteristic
408C2×C4#45111yescharacteristic
409C2×C4#45111yescharacteristic
410C2×C4#45211yescharacteristic
411C2×C4#45211yescharacteristic
412C2×C4#45211yescharacteristic
413C2×C4#46111yescharacteristic
414C2×C4#46211yescharacteristic
415C2×C4#46311yescharacteristic
416C2×C4#46411yescharacteristic
417C2×C4#46511yescharacteristic
418C2×C4#46711yescharacteristic
419C2×C4#46811yescharacteristic
420C2×C4#47011yescharacteristic
421C2×C4#47511yescharacteristic
422C2×C4#47711yescharacteristic
423C2×C4#47911yescharacteristic
424C2×C4#47911yescharacteristic
425C2×C4#48711yescharacteristic
426C2×C4#48811yescharacteristic
427C2×C4#48911yescharacteristic
428C2×C4#49111yescharacteristic
429C8—42no—
430C8—42no—
431C8—82no—
432C8—82no—
433C8—82no—
434C8—82no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22#143911yescharacteristic
444C22#186311yescharacteristic
445C22#186511yescharacteristic
446C22#187711yescharacteristic
447C22#187811yescharacteristic
448C22#190012yes—
449C22#190212yes—
450C22#193311yescharacteristic
451C22#193511yescharacteristic
452C4—21no—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—21no—
458C4—44no—
459C4—82no—
460C4—84no—
461C4#180012yes—
462C4#196511yescharacteristic
463C4#196711yescharacteristic
464C4#200011yescharacteristic
465C4#200111yescharacteristic
466C4#202411yescharacteristic
467C4#202611yescharacteristic
468C4#204211yescharacteristic
469C4#204311yescharacteristic
470C4#206611yescharacteristic
471C4#206811yescharacteristic
472C2—21no—
473C2—21no—
474C2—21no—
475C2—21no—
476C2#924712yes—
477C2#924812yes—
478C2#1104411yescharacteristic
479C2#1105911yescharacteristic
480C2#1106711yescharacteristic
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×#19972
C2×#19812
#211462
C2×#15482
C2×#12922
C2×#12832
#79012