Finite Group Databasebeta

← #120484

Subgroups — #120484

Order 512.

564 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21170C211yesmaximal, characteristic
2C2×#1571C211yesmaximal, characteristic
3#10850C211yesmaximal, characteristic
4#8039C211yesmaximal, characteristic
5#8026C211yesmaximal, characteristic
6C2×#1286C211yesmaximal, characteristic
7#7908C211yesmaximal, characteristic
8C2×#431C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#428—21no—
11C2×#423C2211yescharacteristic
12C22×C4⋊C8C2211yescharacteristic
13#2285C2211yescharacteristic
14C2×#382C2211yescharacteristic
15C2×C4×C4⋊C4C2211yescharacteristic
16#1949—22no—
17#1948—21no—
18#1947—21no—
19#1736—21no—
20C2×#340—21no—
21C2×#340—21no—
22#1571—22no—
23#1571C414yescomplemented
24C2×#335—22no—
25#1296—21no—
26#1296—21no—
27#1294—22no—
28#1286—22no—
29#1280—22no—
30C22×M16—21no—
31C23×C8—21no—
32C2×#117—21no—
33C22×C4⋊C4—21no—
34C22×C4⋊C4D411yescharacteristic
35C22×C4⋊C4D411yescharacteristic
36C22×C42—21no—
37C22×C42C2311yescharacteristic
38#431—21no—
39#431—21no—
40#431—21no—
41#431—21no—
42#431—21no—
43#431C2×C412yes—
44#431Q812yes—
45#431Q812yes—
46#428—42no—
47#428—42no—
48C2×#107—22no—
49C2×#106—22no—
50#423—21no—
51#423—21no—
52#423C2×C412yes—
53#423D412yes—
54C2×C4⋊C8—21no—
55C2×C4⋊C8—21no—
56C2×C4⋊C8—21no—
57C2×C4⋊C8—21no—
58C2×C4⋊C8—21no—
59C2×C4⋊C8—21no—
60C2×C4⋊C8—21no—
61C2×C4⋊C8—21no—
62C2×C4⋊C8C2×C412yes—
63C2×C4⋊C8D412yes—
64C2×C22⋊C8—21no—
65C2×C22⋊C8D412yes—
66C2×C4×C8—21no—
67C2×C4×C8—21no—
68#384D411yescharacteristic
69#384D411yescharacteristic
70#382—21no—
71#382—21no—
72#382—21no—
73#382—21no—
74#382Q812yes—
75#380—21no—
76#380—21no—
77C4×C4⋊C4—21no—
78C4×C4⋊C4—21no—
79C4×C4⋊C4—21no—
80C4×C4⋊C4—21no—
81C4×C4⋊C4—21no—
82C4×C4⋊C4—21no—
83C2×#95—21no—
84C2×#95—21no—
85C2×#95—21no—
86#340—22no—
87#340—22no—
88#340—42no—
89#340—42no—
90#335—28no—
91C23×C4—21no—
92C23×C4—21no—
93C23×C4—41no—
94C23×C4C2×D411yescharacteristic
95C23×C4C2×D411yescharacteristic
96C23×C4#4111yescharacteristic
97C2×M16—22no—
98C2×M16—22no—
99C2×M16—41no—
100C2×M16—41no—
101C2×M16—41no—
102C2×M16—41no—
103C22×C8—22no—
104C22×C8—22no—
105C22×C8—22no—
106C22×C8—41no—
107C22×C8—41no—
108C22×C8—41no—
109C22×C8—41no—
110C22×C8—41no—
111C22×C8—41no—
112C22×C8—41no—
113#117—41no—
114#117—41no—
115#117—41no—
116#117—41no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—21no—
126C2×C4⋊C4—21no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—41no—
135C2×C4⋊C4—41no—
136C2×C4⋊C4—41no—
137C2×C4⋊C4—41no—
138C2×C4⋊C4—41no—
139C2×C4⋊C4D812yes—
140C2×C4⋊C4Q1612yes—
141C2×C22⋊C4—41no—
142C2×C42—41no—
143C2×C42—41no—
144C2×C42—41no—
145C2×C42—82no—
146C2×C42C22×C411yescharacteristic
147C2×C42C2×D411yescharacteristic
148C2×C42C2×D411yescharacteristic
149C2×C42C2×D411yescharacteristic
150C2×C42C2×Q811yescharacteristic
151C2×C42C2×Q811yescharacteristic
152C2×C42C2×Q811yescharacteristic
153C2×C42#4111yescharacteristic
154C2×C42#4111yescharacteristic
155C2×C42#4111yescharacteristic
156C2×C42#4111yescharacteristic
157C2×C42#4111yescharacteristic
158#107—44no—
159#106—44no—
160C4⋊C8—22no—
161C4⋊C8—22no—
162C4⋊C8—22no—
163C4⋊C8—22no—
164C4⋊C8—22no—
165C4⋊C8—22no—
166C4⋊C8—22no—
167C4⋊C8—22no—
168C4⋊C8—41no—
169C4⋊C8—41no—
170C4⋊C8—41no—
171C4⋊C8C22⋊C414yes—
172C22⋊C8—22no—
173C22⋊C8—22no—
174C22⋊C8—41no—
175C22⋊C8C4⋊C414yes—
176C4×C8—22no—
177C4×C8—22no—
178C4×C8—22no—
179C4×C8—41no—
180#95—22no—
181#95—22no—
182#95—41no—
183#95—41no—
184#95—41no—
185#95—41no—
186#95—41no—
187#95—41no—
188C24#12111yescharacteristic
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—42no—
202C22×C4—81no—
203C22×C4—81no—
204C22×C4—81no—
205C22×C4—81no—
206C22×C4—81no—
207C22×C4—81no—
208C22×C4—81no—
209C22×C4—81no—
210C22×C4—81no—
211C22×C4—81no—
212C22×C4C2×C4⋊C411yescharacteristic
213C22×C4C4×D411yescharacteristic
214C22×C4C4×Q811yescharacteristic
215C22×C4#12011yescharacteristic
216C22×C4#12111yescharacteristic
217C22×C4#12111yescharacteristic
218C22×C4#12111yescharacteristic
219C22×C4#12111yescharacteristic
220C22×C4C22⋊Q811yescharacteristic
221C22×C4C22⋊Q811yescharacteristic
222C22×C4C22⋊Q811yescharacteristic
223C22×C4C22⋊Q811yescharacteristic
224C22×C4#12311yescharacteristic
225C22×C4#12311yescharacteristic
226C22×C4#12411yescharacteristic
227C22×C4#12511yescharacteristic
228C22×C4#12611yescharacteristic
229C22×C4C4⋊Q811yescharacteristic
230C22×C4C2×D811yescharacteristic
231C22×C4C2×Q1611yescharacteristic
232C22×C4#13511yescharacteristic
233C22×C4#13511yescharacteristic
234C22×C4AGL(1,ℤ/8)11yescharacteristic
235C22×C4AGL(1,ℤ/8)11yescharacteristic
236C22×C4#13711yescharacteristic
237C22×C4#13711yescharacteristic
238M16—42no—
239M16—42no—
240M16—42no—
241M16—42no—
242C2×C8—24no—
243C2×C8—24no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—81no—
253C2×C8—81no—
254C2×C8—81no—
255C2×C8—81no—
256C2×C8—81no—
257C2×C8—81no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—81no—
273C4⋊C4—81no—
274C4⋊C4—81no—
275C4⋊C4—81no—
276C4⋊C4—81no—
277C4⋊C4—81no—
278C22⋊C4—81no—
279C22⋊C4—81no—
280C42—82no—
281C42—82no—
282C42—81no—
283C42—81no—
284C42C2×C22⋊C411yescharacteristic
285C42#11711yescharacteristic
286C42C4×D411yescharacteristic
287C42C4×Q811yescharacteristic
288C42#12111yescharacteristic
289C42C22⋊Q811yescharacteristic
290C42C22⋊Q811yescharacteristic
291C42C22⋊Q811yescharacteristic
292C42C22⋊Q811yescharacteristic
293C42#12311yescharacteristic
294C42#12511yescharacteristic
295C42#12511yescharacteristic
296C42#12511yescharacteristic
297C42#12611yescharacteristic
298C42C4⋊Q811yescharacteristic
299C42C4⋊Q811yescharacteristic
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23#38911yescharacteristic
305C23#39411yescharacteristic
306C23#39611yescharacteristic
307C23#46611yescharacteristic
308C23#46711yescharacteristic
309C23#46811yescharacteristic
310C23#46811yescharacteristic
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—82no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—161no—
347C2×C4—161no—
348C2×C4—161no—
349C2×C4—161no—
350C2×C4#38011yescharacteristic
351C2×C4#38611yescharacteristic
352C2×C4#38711yescharacteristic
353C2×C4#38711yescharacteristic
354C2×C4#38911yescharacteristic
355C2×C4#39111yescharacteristic
356C2×C4#39511yescharacteristic
357C2×C4#39611yescharacteristic
358C2×C4#39811yescharacteristic
359C2×C4#39811yescharacteristic
360C2×C4#39811yescharacteristic
361C2×C4#40011yescharacteristic
362C2×C4C4×D811yescharacteristic
363C2×C4C4×Q1611yescharacteristic
364C2×C4#44111yescharacteristic
365C2×C4#44211yescharacteristic
366C2×C4#44711yescharacteristic
367C2×C4#44911yescharacteristic
368C2×C4#45111yescharacteristic
369C2×C4#45211yescharacteristic
370C2×C4#45911yescharacteristic
371C2×C4#46211yescharacteristic
372C2×C4#46311yescharacteristic
373C2×C4#46411yescharacteristic
374C2×C4#47411yescharacteristic
375C2×C4#47711yescharacteristic
376C2×C4#47811yescharacteristic
377C2×C4#47911yescharacteristic
378C2×C4#48011yescharacteristic
379C2×C4#48211yescharacteristic
380C2×C4#48411yescharacteristic
381C2×C4#48511yescharacteristic
382C2×C4#49911yescharacteristic
383C2×C4#50011yescharacteristic
384C2×C4#50111yescharacteristic
385C2×C4#50111yescharacteristic
386C8—44no—
387C8—44no—
388C8—82no—
389C8—82no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22#144111yescharacteristic
403C22#194211yescharacteristic
404C22#194311yescharacteristic
405C22#203311yescharacteristic
406C22#203611yescharacteristic
407C22#204811yescharacteristic
408C22#204911yescharacteristic
409C22#205311yescharacteristic
410C22#205311yescharacteristic
411C22#206711yescharacteristic
412C22#206811yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—82no—
422C4—82no—
423C4—162no—
424C4—161no—
425C4—161no—
426C4#187811yescharacteristic
427C4#187911yescharacteristic
428C4#191811yescharacteristic
429C4#192111yescharacteristic
430C4#205711yescharacteristic
431C4#205911yescharacteristic
432C4#208311yescharacteristic
433C4#208511yescharacteristic
434C2—21no—
435C2—21no—
436C2—21no—
437C2—21no—
438C2#1046411yescharacteristic
439C2#1046611yescharacteristic
440C2#1046911yescharacteristic
441C2#1047111yescharacteristic
442C2#1121911yescharacteristic
443C2#1123611yescharacteristic
444C2#1125311yescharacteristic
subgroupG/H
center, socleC23#394
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
23. #1571C4semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#211702
C2×#15712
#108502
#80392
#80262
C2×#12862
#79082