Finite Group Databasebeta

← #120133

Subgroups — #120133

Order 512.

588 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21362C211yesmaximal, characteristic
2C4×#424C211yesmaximal, characteristic
3C2×#1299C211yesmaximal, characteristic
4#8028C211yesmaximal, characteristic
5#7903C211yesmaximal, characteristic
6#7897C211yesmaximal, characteristic
7C2×#1278C211yesmaximal, characteristic
8C2×#431C2211yescharacteristic
9C2×#424—21no—
10C2×#423C2211yescharacteristic
11C2×C4×M16C2211yescharacteristic
12C2×C4×M16C2211yescharacteristic
13C22×C4×C8C2211yescharacteristic
14#2285C2211yescharacteristic
15C4×#117C2211yescharacteristic
16#1948C411yescharacteristic
17#1948C411yescharacteristic
18#1947C411yescharacteristic
19#1947C411yescharacteristic
20#1854—21no—
21#1854—21no—
22C4×#107—21no—
23C4×#106—21no—
24#1768—22no—
25C4×C4⋊C8—22no—
26#1729—21no—
27#1299—22no—
28#1295—22no—
29#1279—22no—
30#1279—21no—
31#1279—21no—
32#1278—22no—
33C22×M16—21no—
34C22×M16—21no—
35C22×M16—21no—
36C23×C8—21no—
37C2×#117—21no—
38C2×#117D411yescharacteristic
39C2×#117D411yescharacteristic
40C22×C42C2311yescharacteristic
41#431—21no—
42#431—21no—
43#431D412yes—
44#431Q812yes—
45C2×#107—21no—
46C2×#107—21no—
47C2×#106—21no—
48C2×#106—21no—
49#424—24no—
50#424—24no—
51#423—21no—
52#423—21no—
53#423—21no—
54#423Q812yes—
55C2×C4⋊C8—24no—
56C2×C4⋊C8—21no—
57C2×C4⋊C8—21no—
58C2×C4⋊C8C2×C411yescharacteristic
59C2×C4⋊C8C2×C411yescharacteristic
60C2×C22⋊C8—21no—
61C4×M16—21no—
62C4×M16—21no—
63C4×M16—21no—
64C4×M16—21no—
65C4×M16—21no—
66C4×M16—21no—
67C4×M16—21no—
68C4×M16Q812yes—
69C2×#97—21no—
70C2×#97D412yes—
71C2×C4×C8—21no—
72C2×C4×C8—21no—
73C2×C4×C8—21no—
74C2×C4×C8—21no—
75C2×C4×C8—21no—
76C2×C4×C8—21no—
77C2×C4×C8—21no—
78C2×C4×C8—21no—
79C2×C4×C8D412yes—
80#384C2×C411yescharacteristic
81#384C2×C411yescharacteristic
82#382—21no—
83#380—21no—
84#380—21no—
85C4×C4⋊C4—21no—
86C4×C4⋊C4—21no—
87C4×C4⋊C4C2×C411yescharacteristic
88C4×C4⋊C4C2×C411yescharacteristic
89C4×C4⋊C4D411yescharacteristic
90C4×C4⋊C4D411yescharacteristic
91C4×C22⋊C4—21no—
92C4×C22⋊C4—21no—
93#376—21no—
94C43—21no—
95#340—21no—
96#340—21no—
97#340—21no—
98#340—21no—
99#336—24no—
100C23×C4C2×D411yescharacteristic
101C23×C4#4111yescharacteristic
102C23×C4#4111yescharacteristic
103C2×M16—22no—
104C2×M16—22no—
105C2×M16—22no—
106C2×M16—22no—
107C2×M16—22no—
108C2×M16—22no—
109C2×M16—41no—
110C2×M16—41no—
111C2×M16—41no—
112C2×M16—41no—
113C2×M16—41no—
114C2×M16—41no—
115C2×M16—41no—
116C2×M16—41no—
117C2×M16—81no—
118C2×M16—81no—
119C22×C8—22no—
120C22×C8—22no—
121C22×C8—21no—
122C22×C8—21no—
123C22×C8—22no—
124C22×C8—22no—
125C22×C8—41no—
126C22×C8—41no—
127C22×C8—41no—
128C22×C8—41no—
129C22×C8—41no—
130C22×C8—41no—
131#117—22no—
132#117—22no—
133#117—41no—
134#117—41no—
135#117—81no—
136#117—81no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4C22⋊C411yescharacteristic
144C2×C4⋊C4C22⋊C411yescharacteristic
145C2×C4⋊C4C22⋊C411yescharacteristic
146C2×C4⋊C4C22⋊C411yescharacteristic
147C2×C22⋊C4—21no—
148C2×C22⋊C4—21no—
149C2×C22⋊C4—41no—
150C2×C42—21no—
151C2×C42—21no—
152C2×C42—21no—
153C2×C42—21no—
154C2×C42—21no—
155C2×C42—21no—
156C2×C42—41no—
157C2×C42C22×C411yescharacteristic
158C2×C42C2×D411yescharacteristic
159C2×C42C2×D411yescharacteristic
160C2×C42C2×D411yescharacteristic
161C2×C42C2×D411yescharacteristic
162C2×C42C2×Q811yescharacteristic
163C2×C42C2×Q811yescharacteristic
164C2×C42C2×Q811yescharacteristic
165C2×C42#4111yescharacteristic
166C2×C42#4111yescharacteristic
167C2×C42#4111yescharacteristic
168C2×C42#4111yescharacteristic
169#107—42no—
170#107—42no—
171#106—42no—
172#106—42no—
173C4⋊C8—216no—
174C4⋊C8—21no—
175C4⋊C8—21no—
176C4⋊C8—22no—
177C4⋊C8—22no—
178C4⋊C8—41no—
179C4⋊C8—41no—
180C4⋊C8C4⋊C412yes—
181C4⋊C8C4⋊C412yes—
182C22⋊C8—22no—
183C22⋊C8—22no—
184#97—22no—
185#97—22no—
186#97—22no—
187#97—41no—
188C4×C8—22no—
189C4×C8—22no—
190C4×C8—22no—
191C4×C8—22no—
192C4×C8—22no—
193C4×C8—41no—
194C4×C8—41no—
195C4×C8—41no—
196C4×C8—41no—
197C4×C8—41no—
198#95—21no—
199#95—21no—
200#95—21no—
201#95—21no—
202#95—41no—
203#95—41no—
204C24#12311yescharacteristic
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—21no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4C2×C22⋊C411yescharacteristic
224C22×C4C4×D411yescharacteristic
225C22×C4C4×D411yescharacteristic
226C22×C4#12011yescharacteristic
227C22×C4#12111yescharacteristic
228C22×C4#12111yescharacteristic
229C22×C4#12111yescharacteristic
230C22×C4C22⋊Q811yescharacteristic
231C22×C4C22⋊Q811yescharacteristic
232C22×C4C22⋊Q811yescharacteristic
233C22×C4#12411yescharacteristic
234C22×C4#12511yescharacteristic
235C22×C4#12511yescharacteristic
236C22×C4#12511yescharacteristic
237C22×C4#12511yescharacteristic
238C22×C4#12611yescharacteristic
239C22×C4#12611yescharacteristic
240C22×C4C4⋊Q811yescharacteristic
241M16—24no—
242M16—42no—
243M16—42no—
244M16—42no—
245M16—42no—
246M16—42no—
247M16—42no—
248M16—42no—
249M16—82no—
250M16—82no—
251C2×C8—24no—
252C2×C8—24no—
253C2×C8—22no—
254C2×C8—22no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—42no—
259C2×C8—42no—
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—42no—
263C2×C8—42no—
264C2×C8—42no—
265C2×C8—42no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—42no—
271C2×C8—81no—
272C2×C8—81no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—81no—
288C4⋊C4—81no—
289C4⋊C4#10412yes—
290C4⋊C4#10412yes—
291C22⋊C4—24no—
292C22⋊C4—42no—
293C22⋊C4—82no—
294C42—24no—
295C42—42no—
296C42—41no—
297C42—41no—
298C42—41no—
299C42—41no—
300C42—41no—
301C42—41no—
302C42—41no—
303C42—41no—
304C42—81no—
305C42—81no—
306C42C2×C4⋊C411yescharacteristic
307C42#11711yescharacteristic
308C42C4×Q811yescharacteristic
309C42C4×Q811yescharacteristic
310C42#12111yescharacteristic
311C42#12111yescharacteristic
312C42#12111yescharacteristic
313C42C22⋊Q811yescharacteristic
314C42C22⋊Q811yescharacteristic
315C42C22⋊Q811yescharacteristic
316C42C22⋊Q811yescharacteristic
317C42C22⋊Q811yescharacteristic
318C42#12311yescharacteristic
319C42#12311yescharacteristic
320C42C4⋊Q811yescharacteristic
321C42C4⋊Q811yescharacteristic
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23#38611yescharacteristic
329C23#39811yescharacteristic
330C23#40011yescharacteristic
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
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—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4#38011yescharacteristic
380C2×C4#38711yescharacteristic
381C2×C4#38711yescharacteristic
382C2×C4#38911yescharacteristic
383C2×C4#38911yescharacteristic
384C2×C4#39111yescharacteristic
385C2×C4#39411yescharacteristic
386C2×C4#39511yescharacteristic
387C2×C4#39611yescharacteristic
388C2×C4#39611yescharacteristic
389C2×C4#39811yescharacteristic
390C2×C4#39811yescharacteristic
391C2×C4C2×#10411yescharacteristic
392C2×C4C2×#10411yescharacteristic
393C2×C4#42111yescharacteristic
394C2×C4#42111yescharacteristic
395C2×C4#44311yescharacteristic
396C2×C4#44311yescharacteristic
397C2×C4#44411yescharacteristic
398C2×C4#44411yescharacteristic
399C2×C4#47111yescharacteristic
400C2×C4#47111yescharacteristic
401C2×C4#47211yescharacteristic
402C2×C4#47311yescharacteristic
403C8—44no—
404C8—44no—
405C8—44no—
406C8—42no—
407C8—42no—
408C8—82no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22#144111yescharacteristic
420C22#187611yescharacteristic
421C22#187611yescharacteristic
422C22#189611yescharacteristic
423C22#189711yescharacteristic
424C22#190711yescharacteristic
425C22#190811yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—21no—
430C4—21no—
431C4—21no—
432C4—42no—
433C4—42no—
434C4—81no—
435C4—81no—
436C4—161no—
437C4—161no—
438C4#180611yescharacteristic
439C4#180611yescharacteristic
440C4#192211yescharacteristic
441C4#192211yescharacteristic
442C4#194511yescharacteristic
443C4#194611yescharacteristic
444C4#198611yescharacteristic
445C4#198611yescharacteristic
446C4#206311yescharacteristic
447C4#206411yescharacteristic
448C4#208911yescharacteristic
449C4#209011yescharacteristic
450C2—41no—
451C2—41no—
452C2#921111yescharacteristic
453C2#921211yescharacteristic
454C2#921311yescharacteristic
455C2#921411yescharacteristic
456C2#1121611yescharacteristic
457C2#1122111yescharacteristic
458C2#1122611yescharacteristic
subgroupG/H
centerC22×C4#121
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
socleC23#386
prime radicalC24#123
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×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
#213622
C4×#4242
C2×#12992
#80282
#79032
#78972
C2×#12782