Finite Group Databasebeta

← #120087

Subgroups — #120087

Order 512.

554 conjugacy classes of subgroups.

The subgroup lattice has 471 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21953C211yesmaximal, characteristic
2C2×#1949C211yesmaximal, characteristic
3#8033C211yesmaximal, characteristic
4C2×#1290C211yesmaximal, characteristic
5C2×#1283C211yesmaximal, characteristic
6#7914C211yesmaximal, characteristic
7#7904C211yesmaximal, characteristic
8C2×#432C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C22×#107C411yescharacteristic
12C22×#106C411yescharacteristic
13C22×C4⋊C8C2211yescharacteristic
14C2×C4×M16C2211yescharacteristic
15C2×#382C2211yescharacteristic
16C2×C4×C4⋊C4C2211yescharacteristic
17#1949—21no—
18#1949—21no—
19#1949—21no—
20#1949—21no—
21#1940—22no—
22#1939—21no—
23#1939—21no—
24#1797—21no—
25#1797—21no—
26C2×#340C411yescharacteristic
27C2×#340C411yescharacteristic
28#1295—22no—
29#1290—22no—
30#1283—22no—
31#1280—21no—
32#1280—21no—
33#1279—21no—
34#1279—21no—
35C22×M16—21no—
36C23×C8C2×C411yescharacteristic
37C23×C8C2×C411yescharacteristic
38C22×C4⋊C4C2×C411yescharacteristic
39C22×C4⋊C4C2×C411yescharacteristic
40C22×C4⋊C4C2×C411yescharacteristic
41C22×C4⋊C4C2×C411yescharacteristic
42C22×C42—21no—
43C22×C42C2311yescharacteristic
44#432—21no—
45#432—21no—
46#432—21no—
47#432—21no—
48#432—21no—
49#432—21no—
50#432—21no—
51#432Q812yes—
52#431—21no—
53#431—21no—
54#431—21no—
55#431—21no—
56C2×#107—21no—
57C2×#107—21no—
58C2×#107—42no—
59C2×#106—21no—
60C2×#106—21no—
61C2×#106—42no—
62C2×C4⋊C8—21no—
63C2×C4⋊C8—21no—
64C2×C4⋊C8—21no—
65C2×C4⋊C8—21no—
66C2×C4⋊C8—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—22no—
70C2×C4⋊C8—22no—
71C2×C4⋊C8D412yes—
72C2×C4⋊C8Q812yes—
73C2×C22⋊C8—21no—
74C2×C22⋊C8—21no—
75C2×C22⋊C8D411yescharacteristic
76C2×C22⋊C8D411yescharacteristic
77C4×M16—21no—
78C4×M16—21no—
79C4×M16—21no—
80C4×M16Q812yes—
81C2×#97—21no—
82C2×#97—21no—
83C2×#97D412yes—
84C2×C4×C8—21no—
85C2×C4×C8—21no—
86#382—21no—
87#382—21no—
88#382—21no—
89#382—21no—
90C4×C4⋊C4—21no—
91C4×C4⋊C4—21no—
92C4×C4⋊C4D411yescharacteristic
93C4×C4⋊C4D411yescharacteristic
94C4×C4⋊C4D411yescharacteristic
95C4×C4⋊C4D411yescharacteristic
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—21no—
99#340—21no—
100#340—21no—
101#340—21no—
102#340—21no—
103#336—22no—
104#336—22no—
105C23×C4—21no—
106C23×C4—21no—
107C23×C4—21no—
108C23×C4—21no—
109C23×C4C22×C411yescharacteristic
110C23×C4C2×D411yescharacteristic
111C23×C4#4111yescharacteristic
112C2×M16—22no—
113C2×M16—22no—
114C2×M16—22no—
115C2×M16—41no—
116C2×M16—41no—
117C2×M16—41no—
118C22×C8—21no—
119C22×C8—21no—
120C22×C8—21no—
121C22×C8—21no—
122C22×C8—21no—
123C22×C8—21no—
124C22×C8—22no—
125C22×C8—41no—
126C22×C8—41no—
127C22×C8—41no—
128C22×C8—41no—
129C22×C8—41no—
130C22×C8—41no—
131C22×C8C4⋊C412yes—
132C22×C8C4⋊C412yes—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—41no—
142C2×C4⋊C4—41no—
143C2×C4⋊C4—41no—
144C2×C4⋊C4—41no—
145C2×C4⋊C4—41no—
146C2×C4⋊C4—41no—
147C2×C4⋊C4C22⋊C411yescharacteristic
148C2×C4⋊C4C22⋊C411yescharacteristic
149C2×C4⋊C4C22⋊C411yescharacteristic
150C2×C4⋊C4C22⋊C411yescharacteristic
151C2×C42—21no—
152C2×C42—21no—
153C2×C42—21no—
154C2×C42—21no—
155C2×C42—82no—
156C2×C42C2×D411yescharacteristic
157C2×C42C2×D411yescharacteristic
158C2×C42C2×D411yescharacteristic
159C2×C42C2×D411yescharacteristic
160C2×C42C2×Q811yescharacteristic
161C2×C42C2×Q811yescharacteristic
162C2×C42C2×Q811yescharacteristic
163C2×C42#4111yescharacteristic
164C2×C42#4111yescharacteristic
165C2×C42#4111yescharacteristic
166C2×C42#4111yescharacteristic
167C2×C42#4111yescharacteristic
168#107—42no—
169#107—42no—
170#106—42no—
171#106—42no—
172C4⋊C8—22no—
173C4⋊C8—22no—
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8—22no—
177C4⋊C8—41no—
178C4⋊C8—41no—
179C4⋊C8—41no—
180C4⋊C8—41no—
181C4⋊C8—41no—
182C4⋊C8—82no—
183C4⋊C8—82no—
184C22⋊C8—21no—
185C22⋊C8—21no—
186C22⋊C8—22no—
187C22⋊C8—21no—
188C22⋊C8—21no—
189C22⋊C8—41no—
190C22⋊C8—41no—
191C22⋊C8—41no—
192#97—22no—
193#97—22no—
194#97—22no—
195#97—22no—
196#97—41no—
197#97—41no—
198C4×C8—22no—
199C4×C8—41no—
200C4×C8—41no—
201C4×C8—41no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95—41no—
207#95—41no—
208#95—41no—
209#95—41no—
210C24C4×D411yescharacteristic
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—21no—
222C22×C4—21no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—81no—
238C22×C4—81no—
239C22×C4—81no—
240C22×C4—81no—
241C22×C4—81no—
242C22×C4—81no—
243C22×C4C2×C22⋊C411yescharacteristic
244C22×C4C2×C4⋊C411yescharacteristic
245C22×C4#11711yescharacteristic
246C22×C4C4×D411yescharacteristic
247C22×C4C4×Q811yescharacteristic
248C22×C4C4×Q811yescharacteristic
249C22×C4#12011yescharacteristic
250C22×C4#12111yescharacteristic
251C22×C4#12111yescharacteristic
252C22×C4#12111yescharacteristic
253C22×C4C22⋊Q811yescharacteristic
254C22×C4C22⋊Q811yescharacteristic
255C22×C4#12311yescharacteristic
256C22×C4#12311yescharacteristic
257C22×C4#12511yescharacteristic
258C22×C4#12511yescharacteristic
259C22×C4#12611yescharacteristic
260C22×C4C4⋊Q811yescharacteristic
261M16—24no—
262M16—42no—
263M16—42no—
264M16—42no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—42no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—42no—
277C2×C8—42no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—42no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—42no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—42no—
287C2×C8—42no—
288C2×C8—81no—
289C2×C8—81no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—42no—
297C4⋊C4—42no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—81no—
303C4⋊C4—81no—
304C4⋊C4#10012yes—
305C4⋊C4#10112yes—
306C42—42no—
307C42—42no—
308C42—81no—
309C42—81no—
310C42#12111yescharacteristic
311C42#12111yescharacteristic
312C42#12111yescharacteristic
313C42C22⋊Q811yescharacteristic
314C42C22⋊Q811yescharacteristic
315C42C22⋊Q811yescharacteristic
316C42C22⋊Q811yescharacteristic
317C42C22⋊Q811yescharacteristic
318C42C22⋊Q811yescharacteristic
319C42#12311yescharacteristic
320C42#12411yescharacteristic
321C42#12511yescharacteristic
322C42#12511yescharacteristic
323C42#12611yescharacteristic
324C42C4⋊Q811yescharacteristic
325C42C4⋊Q811yescharacteristic
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23#38611yescharacteristic
331C23#38711yescharacteristic
332C23#38911yescharacteristic
333C23#44311yescharacteristic
334C23#44311yescharacteristic
335C23#44411yescharacteristic
336C23#44411yescharacteristic
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—21no—
362C2×C4—21no—
363C2×C4—22no—
364C2×C4—22no—
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—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—82no—
380C2×C4—82no—
381C2×C4—82no—
382C2×C4—82no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—161no—
390C2×C4—161no—
391C2×C4—161no—
392C2×C4—161no—
393C2×C4#38011yescharacteristic
394C2×C4#38711yescharacteristic
395C2×C4#38911yescharacteristic
396C2×C4#39111yescharacteristic
397C2×C4#39411yescharacteristic
398C2×C4#39511yescharacteristic
399C2×C4#39611yescharacteristic
400C2×C4#39611yescharacteristic
401C2×C4#39811yescharacteristic
402C2×C4#39811yescharacteristic
403C2×C4#39811yescharacteristic
404C2×C4#40011yescharacteristic
405C2×C4C2×#10011yescharacteristic
406C2×C4C2×#10111yescharacteristic
407C2×C4#41311yescharacteristic
408C2×C4#41311yescharacteristic
409C8—44no—
410C8—42no—
411C8—42no—
412C8—81no—
413C8—81no—
414C8—82no—
415C8—82no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22#144111yescharacteristic
429C22#187611yescharacteristic
430C22#187611yescharacteristic
431C22#190011yescharacteristic
432C22#190111yescharacteristic
433C22#190411yescharacteristic
434C22#190511yescharacteristic
435C22#192211yescharacteristic
436C22#192211yescharacteristic
437C22#194511yescharacteristic
438C22#194611yescharacteristic
439C4—21no—
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—42no—
450C4—42no—
451C4—81no—
452C4—81no—
453C4—161no—
454C4—161no—
455C4#180011yescharacteristic
456C4#180111yescharacteristic
457C4#199711yescharacteristic
458C4#199811yescharacteristic
459C2—21no—
460C2—21no—
461C2—21no—
462C2—21no—
463C2#924311yescharacteristic
464C2#924411yescharacteristic
465C2#924511yescharacteristic
466C2#924611yescharacteristic
467C2#1120411yescharacteristic
468C2#1121311yescharacteristic
469C2#1122111yescharacteristic
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
#219532
C2×#19492
#80332
C2×#12902
C2×#12832
#79142
#79042