Finite Group Databasebeta

← #111349

Subgroups — #111349

Order 512.

934 conjugacy classes of subgroups.

The subgroup lattice has 469 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#487C211yesmaximal, characteristic
2C2×#1549C211yesmaximal, characteristic
3C2×#1548C211yesmaximal, characteristic
4C2×#1546C211yesmaximal, characteristic
5C2×#1546C211yesmaximal, characteristic
6#10844C211yesmaximal, characteristic
7#7849C211yesmaximal, characteristic
8C22×C4⋊Q8C2211yescharacteristic
9C22×C4⋊Q8C2211yescharacteristic
10C2×#487—22no—
11C2×#487—22no—
12C2×#487—22no—
13C2×#487—22no—
14C2×#487—22no—
15C2×#487C414yes—
16C2×#431C2211yescharacteristic
17C2×#431C2211yescharacteristic
18C2×#423C2211yescharacteristic
19C2×#423C2211yescharacteristic
20C22×#103—22no—
21C22×C4×C8C2211yescharacteristic
22C2×#341—22no—
23#1549—22no—
24#1549—22no—
25#1548—22no—
26#1548—22no—
27#1546—22no—
28#1546—22no—
29#1546—22no—
30#1546—22no—
31C2×#333—22no—
32C2×#332—22no—
33C2×#332—22no—
34C2×#332—22no—
35#1273—22no—
36C23×Q8—21no—
37C23×Q8—21no—
38C22×M16—21no—
39C22×M16—21no—
40C23×C8D412yes—
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⋊Q8—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⋊Q8C2×C412yes—
60C2×C4⋊Q8C2×C412yes—
61C2×C4⋊Q8D412yes—
62C2×C4⋊Q8D412yes—
63C2×C4⋊Q8D412yes—
64C2×C4⋊Q8D412yes—
65C22×C4⋊C4—21no—
66C22×C4⋊C4—21no—
67C22×C4⋊C4—21no—
68C22×C4⋊C4—21no—
69C22×C42C2311yescharacteristic
70#487—28no—
71#487—28no—
72#487—28no—
73#487—28no—
74#431—21no—
75#431—21no—
76#431—21no—
77#431—21no—
78#431—21no—
79#431—21no—
80#431—21no—
81#431—21no—
82#423—21no—
83#423—21no—
84#423—21no—
85#423—21no—
86#423—21no—
87#423—21no—
88#423D412yes—
89#423D412yes—
90C2×C4⋊C8—21no—
91C2×C4⋊C8—21no—
92C2×C4⋊C8—21no—
93C2×C4⋊C8—21no—
94C2×C4⋊C8D412yes—
95C2×C4⋊C8D412yes—
96C2×#103—28no—
97C2×#103—28no—
98C2×#103—28no—
99C2×C22⋊C8—21no—
100C2×C22⋊C8—21no—
101C2×C4×C8—21no—
102C2×C4×C8—21no—
103C2×C4×C8—21no—
104C2×C4×C8—21no—
105C2×C4×C8—21no—
106C2×C4×C8—21no—
107C2×C4×C8C2×C412yes—
108C2×C4×C8D412yes—
109#341—44no—
110#333—28no—
111#332—28no—
112#332—28no—
113#332—28no—
114C22×Q8—22no—
115C22×Q8—22no—
116C22×Q8—22no—
117C22×Q8—22no—
118C22×Q8—22no—
119C22×Q8—22no—
120C22×Q8—41no—
121C22×Q8—41no—
122C22×Q8—41no—
123C22×Q8—41no—
124C22×Q8—41no—
125C22×Q8—41no—
126C22×Q8—42no—
127C22×Q8—42no—
128C22×Q8—42no—
129C22×Q8—42no—
130C22×Q8—84no—
131C23×C4—41no—
132C23×C4—41no—
133C23×C4C2×D411yescharacteristic
134C23×C4#4111yescharacteristic
135C23×C4#4111yescharacteristic
136C2×M16—22no—
137C2×M16—22no—
138C2×M16—41no—
139C2×M16—41no—
140C2×M16—42no—
141C2×M16—42no—
142C2×M16—42no—
143C2×M16—42no—
144C22×C8—22no—
145C22×C8—22no—
146C22×C8—22no—
147C22×C8—22no—
148C22×C8—22no—
149C22×C8—22no—
150C22×C8—22no—
151C22×C8—22no—
152C22×C8—41no—
153C22×C8—41no—
154C22×C8C22⋊C414yes—
155C4⋊Q8—22no—
156C4⋊Q8—22no—
157C4⋊Q8—22no—
158C4⋊Q8—22no—
159C4⋊Q8—22no—
160C4⋊Q8—22no—
161C4⋊Q8—22no—
162C4⋊Q8—22no—
163C4⋊Q8—22no—
164C4⋊Q8—22no—
165C4⋊Q8—22no—
166C4⋊Q8—22no—
167C4⋊Q8—22no—
168C4⋊Q8—22no—
169C4⋊Q8—22no—
170C4⋊Q8—22no—
171C4⋊Q8—22no—
172C4⋊Q8—22no—
173C4⋊Q8—41no—
174C4⋊Q8—41no—
175C4⋊Q8—41no—
176C4⋊Q8—41no—
177C4⋊Q8—41no—
178C4⋊Q8—41no—
179C4⋊Q8—41no—
180C4⋊Q8—41no—
181C4⋊Q8—41no—
182C4⋊Q8—41no—
183C4⋊Q8—41no—
184C4⋊Q8—41no—
185C4⋊Q8C22⋊C414yes—
186C4⋊Q8C22⋊C414yes—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—41no—
200C2×C4⋊C4—41no—
201C2×C4⋊C4—41no—
202C2×C4⋊C4—41no—
203C2×C4⋊C4—41no—
204C2×C4⋊C4—41no—
205C2×C4⋊C4—41no—
206C2×C4⋊C4—41no—
207C2×C4⋊C4—41no—
208C2×C4⋊C4—41no—
209C2×C4⋊C4—41no—
210C2×C4⋊C4—41no—
211C2×C42C22×C411yescharacteristic
212C2×C42C2×D411yescharacteristic
213C2×C42C2×D411yescharacteristic
214C2×C42C2×D411yescharacteristic
215C2×C42C2×D411yescharacteristic
216C2×C42C2×D411yescharacteristic
217C2×C42C2×D411yescharacteristic
218C2×C42C2×D411yescharacteristic
219C2×C42C2×D411yescharacteristic
220C2×C42C2×D411yescharacteristic
221C2×C42#4111yescharacteristic
222C2×C42#4111yescharacteristic
223C4⋊C8—22no—
224C4⋊C8—22no—
225C4⋊C8—22no—
226C4⋊C8—22no—
227C4⋊C8—22no—
228C4⋊C8—22no—
229C4⋊C8—22no—
230C4⋊C8—22no—
231C4⋊C8—41no—
232C4⋊C8—41no—
233C4⋊C8—41no—
234C4⋊C8—41no—
235#103—232no—
236C22⋊C8—41no—
237C22⋊C8—41no—
238C22⋊C8—41no—
239C22⋊C8—41no—
240C4×C8—22no—
241C4×C8—22no—
242C4×C8—22no—
243C4×C8—22no—
244C4×C8—41no—
245C4×C8—41no—
246C4×C8—41no—
247C4×C8—41no—
248C24#12411yescharacteristic
249C2×Q8—24no—
250C2×Q8—24no—
251C2×Q8—42no—
252C2×Q8—42no—
253C2×Q8—42no—
254C2×Q8—42no—
255C2×Q8—42no—
256C2×Q8—42no—
257C2×Q8—44no—
258C2×Q8—44no—
259C2×Q8—44no—
260C2×Q8—44no—
261C2×Q8—44no—
262C2×Q8—44no—
263C2×Q8—84no—
264C2×Q8—84no—
265C2×Q8—84no—
266C2×Q8—84no—
267C2×Q8—84no—
268C2×Q8—82no—
269C2×Q8—82no—
270C2×Q8—82no—
271C2×Q8—82no—
272C2×Q8—84no—
273C2×Q8—81no—
274C2×Q8—81no—
275C2×Q8—81no—
276C2×Q8—81no—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—84no—
286C22×C4—82no—
287C22×C4—82no—
288C22×C4C2×C22⋊C411yescharacteristic
289C22×C4C4×D411yescharacteristic
290C22×C4C4×D411yescharacteristic
291C22×C4#12011yescharacteristic
292C22×C4#12011yescharacteristic
293C22×C4#12111yescharacteristic
294C22×C4#12111yescharacteristic
295C22×C4#12111yescharacteristic
296C22×C4#12111yescharacteristic
297C22×C4#12111yescharacteristic
298C22×C4#12111yescharacteristic
299C22×C4#12111yescharacteristic
300C22×C4#12111yescharacteristic
301C22×C4#12311yescharacteristic
302C22×C4#12311yescharacteristic
303C22×C4#12311yescharacteristic
304C22×C4#12311yescharacteristic
305C22×C4#12711yescharacteristic
306C22×C4#13512yes—
307C22×C4#13512yes—
308C22×C4AGL(1,ℤ/8)12yes—
309C22×C4#13712yes—
310M16—44no—
311M16—44no—
312M16—82no—
313M16—82no—
314C2×C8—24no—
315C2×C8—24no—
316C2×C8—24no—
317C2×C8—42no—
318C2×C8—42no—
319C2×C8—42no—
320C2×C8—42no—
321C2×C8—42no—
322C2×C8—42no—
323C2×C8—42no—
324C2×C8—42no—
325C2×C8—44no—
326C2×C8—44no—
327C2×C8—81no—
328C2×C8—81no—
329C2×C8—81no—
330C2×C8—81no—
331C4⋊C4—24no—
332C4⋊C4—24no—
333C4⋊C4—24no—
334C4⋊C4—24no—
335C4⋊C4—42no—
336C4⋊C4—42no—
337C4⋊C4—42no—
338C4⋊C4—42no—
339C4⋊C4—42no—
340C4⋊C4—42no—
341C4⋊C4—42no—
342C4⋊C4—42no—
343C4⋊C4—42no—
344C4⋊C4—42no—
345C4⋊C4—42no—
346C4⋊C4—42no—
347C42C2×C22⋊C411yescharacteristic
348C42C2×C22⋊C411yescharacteristic
349C42C4×D411yescharacteristic
350C42C4×D411yescharacteristic
351C42#12011yescharacteristic
352C42#12011yescharacteristic
353C42#12011yescharacteristic
354C42#12011yescharacteristic
355C42#12011yescharacteristic
356C42#12011yescharacteristic
357C42#12111yescharacteristic
358C42#12111yescharacteristic
359C42#12111yescharacteristic
360C42#12111yescharacteristic
361C42#12411yescharacteristic
362C42#12711yescharacteristic
363C23—22no—
364C23—22no—
365C23#39011yescharacteristic
366C23#39411yescharacteristic
367C23#39411yescharacteristic
368C23#48812yes—
369C23#48912yes—
370Q8—48no—
371Q8—84no—
372Q8—84no—
373Q8—84no—
374Q8—82no—
375Q8—82no—
376Q8—82no—
377Q8—82no—
378Q8—84no—
379Q8—84no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—84no—
393C2×C4—84no—
394C2×C4—82no—
395C2×C4—82no—
396C2×C4—84no—
397C2×C4—84no—
398C2×C4—84no—
399C2×C4#37911yescharacteristic
400C2×C4#38611yescharacteristic
401C2×C4#38611yescharacteristic
402C2×C4#38611yescharacteristic
403C2×C4#38611yescharacteristic
404C2×C4#39011yescharacteristic
405C2×C4#39211yescharacteristic
406C2×C4#39211yescharacteristic
407C2×C4#39211yescharacteristic
408C2×C4#39211yescharacteristic
409C2×C4#39411yescharacteristic
410C2×C4#39411yescharacteristic
411C2×C4#41612yes—
412C2×C4#41712yes—
413C2×C4#44912yes—
414C2×C4#44912yes—
415C2×C4#45212yes—
416C2×C4#45212yes—
417C2×C4#46312yes—
418C2×C4#46312yes—
419C2×C4#46412yes—
420C2×C4#46412yes—
421C2×C4#47114yes—
422C2×C4#47314yes—
423C2×C4#49511yescharacteristic
424C2×C4#49511yescharacteristic
425C2×C4#49611yescharacteristic
426C2×C4#49711yescharacteristic
427C8—44no—
428C8—82no—
429C8—82no—
430C8—82no—
431C8—82no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—24no—
437C22—24no—
438C22#143811yescharacteristic
439C22#195811yescharacteristic
440C22#195911yescharacteristic
441C22#197712yes—
442C22#197912yes—
443C22#204212yes—
444C22#204212yes—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—84no—
450C4—84no—
451C4#178812yes—
452C4#198312yes—
453C4#201211yescharacteristic
454C4#201211yescharacteristic
455C4#201511yescharacteristic
456C4#201511yescharacteristic
457C4#201912yes—
458C4#202012yes—
459C4#204612yes—
460C4#204712yes—
461C2—22no—
462C2—22no—
463C2#977012yes—
464C2#977512yes—
465C2#1100911yescharacteristic
466C2#1102811yescharacteristic
467C2#1102911yescharacteristic
subgroupG/H
center, socleC23#390
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#124
LCSG ▷ C2×C42 ▷ 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
C22×#4872
C2×#15492
C2×#15482
C2×#15462
#108442
#78492