Finite Group Databasebeta

← #120064

Subgroups — #120064

Order 512.

578 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21974C211yesmaximal, characteristic
2#21171C211yesmaximal, characteristic
3#10857C211yesmaximal, characteristic
4C2×#1309C211yesmaximal, characteristic
5C2×#1299C211yesmaximal, characteristic
6#8043C211yesmaximal, characteristic
7#7903C211yesmaximal, characteristic
8C2×#431C2211yescharacteristic
9C2×#428C412yes—
10C2×#423C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C2×C4×M16C2211yescharacteristic
14C2×#384C2211yescharacteristic
15C4×#117C2211yescharacteristic
16#1948—21no—
17#1948—21no—
18#1947—21no—
19#1947—21no—
20#1939—21no—
21#1939—21no—
22#1851—22no—
23#1842—21no—
24#1831—21no—
25C2×#343—22no—
26#1736C412yes—
27#1309—22no—
28#1299—22no—
29#1296—21no—
30#1296—21no—
31#1279—21no—
32#1279—21no—
33C22×M16—21no—
34C22×M16—21no—
35C22×M16C2×C412yes—
36C22×M16D412yes—
37C2×#117C2×C411yescharacteristic
38C2×#117C2×C411yescharacteristic
39C22×C4⋊C4—21no—
40C22×C4⋊C4—21no—
41C22×C4⋊C4C2×C412yes—
42C22×C42C2311yescharacteristic
43#431—21no—
44#431—21no—
45#431—21no—
46#431—21no—
47#428—44no—
48C2×#107—22no—
49C2×#106—22no—
50#423—21no—
51#423—21no—
52#423—21no—
53#423—21no—
54#423—21no—
55#423—21no—
56#423—21no—
57#423—21no—
58#423—21no—
59#423D412yes—
60#423Q812yes—
61#423Q812yes—
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—22no—
69C2×C4⋊C8—22no—
70C2×C4⋊C8D411yescharacteristic
71C2×C4⋊C8D411yescharacteristic
72C2×C22⋊C8—21no—
73C4×M16—21no—
74C4×M16—21no—
75C4×M16—21no—
76C4×M16Q812yes—
77C2×#97—21no—
78C2×C4×C8—21no—
79C2×C4×C8—21no—
80#384—21no—
81#384—21no—
82#384—21no—
83#384—21no—
84C4×C4⋊C4D411yescharacteristic
85C4×C4⋊C4D411yescharacteristic
86C4×C4⋊C4D411yescharacteristic
87C4×C4⋊C4D411yescharacteristic
88C4×C22⋊C4—21no—
89C4×C22⋊C4—21no—
90#376—21no—
91C43—21no—
92#343—44no—
93#340—22no—
94#340—22no—
95#336—22no—
96#336—22no—
97C23×C4—22no—
98C23×C4C22×C411yescharacteristic
99C23×C4C2×D411yescharacteristic
100C23×C4#4111yescharacteristic
101C2×M16—22no—
102C2×M16—22no—
103C2×M16—22no—
104C2×M16—22no—
105C2×M16—22no—
106C2×M16—22no—
107C2×M16—22no—
108C2×M16—41no—
109C2×M16—41no—
110C2×M16—41no—
111C2×M16—41no—
112C2×M16—42no—
113C2×M16—42no—
114C2×M16—42no—
115C2×M16—42no—
116C2×M16—81no—
117C2×M16—81no—
118C2×M16C4⋊C414yes—
119C22×C8—22no—
120C22×C8—22no—
121C22×C8—21no—
122C22×C8—21no—
123C22×C8—41no—
124C22×C8—41no—
125#117—22no—
126#117—22no—
127#117—41no—
128#117—41no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—42no—
132C2×C4⋊C4—42no—
133C2×C4⋊C4—42no—
134C2×C4⋊C4—42no—
135C2×C4⋊C4—41no—
136C2×C4⋊C4—41no—
137C2×C4⋊C4—41no—
138C2×C4⋊C4—41no—
139C2×C4⋊C4—81no—
140C2×C4⋊C4—81no—
141C2×C4⋊C4C22⋊C411yescharacteristic
142C2×C4⋊C4C22⋊C411yescharacteristic
143C2×C4⋊C4C22⋊C411yescharacteristic
144C2×C4⋊C4C22⋊C411yescharacteristic
145C2×C22⋊C4—21no—
146C2×C22⋊C4—21no—
147C2×C42—21no—
148C2×C42—21no—
149C2×C42—21no—
150C2×C42—21no—
151C2×C42—21no—
152C2×C42—21no—
153C2×C42C2×D411yescharacteristic
154C2×C42C2×D411yescharacteristic
155C2×C42C2×D411yescharacteristic
156C2×C42C2×D411yescharacteristic
157C2×C42C2×Q811yescharacteristic
158C2×C42C2×Q811yescharacteristic
159C2×C42C2×Q811yescharacteristic
160C2×C42#4111yescharacteristic
161C2×C42#4111yescharacteristic
162C2×C42#4111yescharacteristic
163C2×C42#4111yescharacteristic
164C2×C42#4111yescharacteristic
165#107—44no—
166#106—44no—
167C4⋊C8—22no—
168C4⋊C8—22no—
169C4⋊C8—21no—
170C4⋊C8—21no—
171C4⋊C8—22no—
172C4⋊C8—22no—
173C4⋊C8—22no—
174C4⋊C8—22no—
175C4⋊C8—21no—
176C4⋊C8—21no—
177C4⋊C8—41no—
178C4⋊C8—41no—
179C4⋊C8—41no—
180C4⋊C8—41no—
181C4⋊C8—41no—
182C4⋊C8—41no—
183C4⋊C8—82no—
184C4⋊C8—82no—
185C22⋊C8—41no—
186C22⋊C8—41no—
187#97—22no—
188#97—41no—
189C4×C8—22no—
190C4×C8—41no—
191C4×C8—41no—
192C4×C8—41no—
193#95—21no—
194#95—21no—
195#95—21no—
196#95—21no—
197C24C4×D411yescharacteristic
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
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—42no—
215C22×C4—44no—
216C22×C4—82no—
217C22×C4—82no—
218C22×C4C2×C22⋊C411yescharacteristic
219C22×C4C2×C4⋊C411yescharacteristic
220C22×C4#11711yescharacteristic
221C22×C4C4×D411yescharacteristic
222C22×C4C4×Q811yescharacteristic
223C22×C4C4×Q811yescharacteristic
224C22×C4#12011yescharacteristic
225C22×C4#12111yescharacteristic
226C22×C4#12111yescharacteristic
227C22×C4#12111yescharacteristic
228C22×C4C22⋊Q811yescharacteristic
229C22×C4C22⋊Q811yescharacteristic
230C22×C4#12311yescharacteristic
231C22×C4#12311yescharacteristic
232C22×C4#12511yescharacteristic
233C22×C4#12511yescharacteristic
234C22×C4#12611yescharacteristic
235C22×C4C4⋊Q811yescharacteristic
236M16—24no—
237M16—42no—
238M16—42no—
239M16—42no—
240M16—44no—
241M16—44no—
242M16—44no—
243M16—82no—
244M16—82no—
245M16—82no—
246C2×C8—24no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—41no—
257C2×C8—42no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—42no—
261C2×C8—41no—
262C2×C8—81no—
263C2×C8—81no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—82no—
273C4⋊C4—82no—
274C4⋊C4—82no—
275C4⋊C4—81no—
276C4⋊C4—81no—
277C4⋊C4—81no—
278C4⋊C4—81no—
279C4⋊C4#10012yes—
280C4⋊C4#10112yes—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C42—42no—
284C42—42no—
285C42—41no—
286C42—41no—
287C42—41no—
288C42—41no—
289C42—41no—
290C42—41no—
291C42—41no—
292C42—41no—
293C42#12111yescharacteristic
294C42#12111yescharacteristic
295C42#12111yescharacteristic
296C42C22⋊Q811yescharacteristic
297C42C22⋊Q811yescharacteristic
298C42C22⋊Q811yescharacteristic
299C42C22⋊Q811yescharacteristic
300C42C22⋊Q811yescharacteristic
301C42C22⋊Q811yescharacteristic
302C42#12311yescharacteristic
303C42#12411yescharacteristic
304C42#12511yescharacteristic
305C42#12511yescharacteristic
306C42#12611yescharacteristic
307C42C4⋊Q811yescharacteristic
308C42C4⋊Q811yescharacteristic
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23#38611yescharacteristic
316C23#38711yescharacteristic
317C23#38911yescharacteristic
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
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—22no—
349C2×C4—22no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—82no—
361C2×C4—82no—
362C2×C4—82no—
363C2×C4—164no—
364C2×C4#38011yescharacteristic
365C2×C4#38711yescharacteristic
366C2×C4#38911yescharacteristic
367C2×C4#39111yescharacteristic
368C2×C4#39411yescharacteristic
369C2×C4#39511yescharacteristic
370C2×C4#39611yescharacteristic
371C2×C4#39611yescharacteristic
372C2×C4#39811yescharacteristic
373C2×C4#39811yescharacteristic
374C2×C4#39811yescharacteristic
375C2×C4#40011yescharacteristic
376C2×C4C2×#10011yescharacteristic
377C2×C4C2×#10111yescharacteristic
378C2×C4#41311yescharacteristic
379C2×C4#41311yescharacteristic
380C2×C4#45311yescharacteristic
381C2×C4#45411yescharacteristic
382C2×C4#45511yescharacteristic
383C2×C4#45611yescharacteristic
384C2×C4#47111yescharacteristic
385C2×C4#47111yescharacteristic
386C2×C4#47211yescharacteristic
387C2×C4#47311yescharacteristic
388C8—44no—
389C8—44no—
390C8—82no—
391C8—81no—
392C8—82no—
393C8—81no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22#144111yescharacteristic
405C22#188211yescharacteristic
406C22#188311yescharacteristic
407C22#190011yescharacteristic
408C22#190111yescharacteristic
409C22#190711yescharacteristic
410C22#190811yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—42no—
418C4—42no—
419C4—81no—
420C4—81no—
421C4—162no—
422C4#180011yescharacteristic
423C4#180111yescharacteristic
424C4#199711yescharacteristic
425C4#199811yescharacteristic
426C4#203711yescharacteristic
427C4#203811yescharacteristic
428C4#206011yescharacteristic
429C4#206111yescharacteristic
430C4#206311yescharacteristic
431C4#206411yescharacteristic
432C4#208911yescharacteristic
433C4#209011yescharacteristic
434C2—41no—
435C2—41no—
436C2#935311yescharacteristic
437C2#935611yescharacteristic
438C2#935711yescharacteristic
439C2#936011yescharacteristic
440C2#1120411yescharacteristic
441C2#1121611yescharacteristic
442C2#1121711yescharacteristic
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
#219742
#211712
#108572
C2×#13092
C2×#12992
#80432
#79032