Finite Group Databasebeta

← #99592

Subgroups — #99592

Order 512.

482 conjugacy classes of subgroups.

The subgroup lattice has 437 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22295C211yesmaximal, characteristic
2C4×#483C211yesmaximal, characteristic
3#11346C211yesmaximal, characteristic
4#8706C211yesmaximal, characteristic
5#7566C211yesmaximal, characteristic
6#7029C211yesmaximal, characteristic
7#7016C211yesmaximal, characteristic
8C2×#483C411yescharacteristic
9C4×C22⋊Q8C2211yescharacteristic
10C2×C4×C4⋊C4C2211yescharacteristic
11#1985—21no—
12#1940—21no—
13#1927—21no—
14#1920—21no—
15#1917—21no—
16#1917—21no—
17#1872C411yescharacteristic
18#1853C411yescharacteristic
19#1850—21no—
20#1823C411yescharacteristic
21#1797C2211yescharacteristic
22C4×#106—21no—
23C4×#103—21no—
24#1752—21no—
25C4×C22⋊C8C2211yescharacteristic
26C4×C22⋊C8C2211yescharacteristic
27C2×#336—21no—
28C2×#336—21no—
29C2×#336C2211yescharacteristic
30C2×#336C2211yescharacteristic
31#1279—21no—
32#1279—21no—
33#1272—21no—
34#1271—21no—
35C23×C8—21no—
36C23×C8D411yescharacteristic
37C23×C8D411yescharacteristic
38C2×C22⋊Q8C2×C411yescharacteristic
39C2×C4×Q8D411yescharacteristic
40C22×C4⋊C4C2×C411yescharacteristic
41C22×C4⋊C4C2×C411yescharacteristic
42C22×C42—21no—
43C22×C42C2311yescharacteristic
44#483—22no—
45#483—22no—
46C2×#106—21no—
47C2×#106—21no—
48C2×C4⋊C8—21no—
49C2×C4⋊C8—21no—
50C2×C4⋊C8D411yescharacteristic
51C2×C4⋊C8D411yescharacteristic
52C2×#103—21no—
53C2×#103—21no—
54C2×C22⋊C8—21no—
55C2×C22⋊C8—21no—
56C2×C22⋊C8C2×C411yescharacteristic
57C2×C22⋊C8C2×C411yescharacteristic
58C2×#97—21no—
59C2×#97—21no—
60C2×C4×C8—21no—
61C2×C4×C8—21no—
62#391D411yescharacteristic
63#389D411yescharacteristic
64#387—21no—
65#385—21no—
66#380C2×C411yescharacteristic
67C4×C4⋊C4—21no—
68C4×C4⋊C4—21no—
69C4×C4⋊C4—21no—
70C4×C4⋊C4—21no—
71C4×C4⋊C4—21no—
72C4×C4⋊C4D411yescharacteristic
73C4×C22⋊C4—21no—
74C2×#95—21no—
75#340—21no—
76#340—21no—
77#340—21no—
78#340—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336—21no—
83#336—21no—
84#336—21no—
85#336—21no—
86#336—21no—
87#336—21no—
88#336—21no—
89#336—21no—
90#336—42no—
91#336—42no—
92C22×Q8C22⋊C411yescharacteristic
93C23×C4—21no—
94C23×C4—21no—
95C23×C4C22×C411yescharacteristic
96C23×C4C2×D411yescharacteristic
97C23×C4#4111yescharacteristic
98C22×C8—21no—
99C22×C8—21no—
100C22×C8—21no—
101C22×C8—22no—
102C22×C8—21no—
103C22×C8—21no—
104C22×C8—21no—
105C22×C8—21no—
106C22×C8—21no—
107C22×C8—21no—
108C22×C8—41no—
109C22×C8—41no—
110C22×C8—41no—
111C22×C8—41no—
112C22×C8—41no—
113C22×C8—41no—
114C22×C8—41no—
115C22×C8—41no—
116C22×C8—41no—
117C22×C8—41no—
118C22×C8—41no—
119C22×C8SD1612yes—
120C22⋊Q8—21no—
121C22⋊Q8—21no—
122C22⋊Q8—21no—
123C22⋊Q8—21no—
124C4×Q8—41no—
125C4×Q8—41no—
126C2×C4⋊C4—21no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—42no—
137C2×C4⋊C4C22⋊C411yescharacteristic
138C2×C4⋊C4C22⋊C411yescharacteristic
139C2×C4⋊C4C22⋊C411yescharacteristic
140C2×C4⋊C4M1612yes—
141C2×C22⋊C4—21no—
142C2×C22⋊C4—21no—
143C2×C42—21no—
144C2×C42—21no—
145C2×C42—41no—
146C2×C42—41no—
147C2×C42—41no—
148C2×C42—41no—
149C2×C42—41no—
150C2×C42—41no—
151C2×C42—41no—
152C2×C42—41no—
153C2×C42C2×D411yescharacteristic
154C2×C42C2×D411yescharacteristic
155C2×C42C2×D411yescharacteristic
156C2×C42#4111yescharacteristic
157#106—24no—
158#106—42no—
159C4⋊C8—41no—
160C4⋊C8—41no—
161C4⋊C8—81no—
162C4⋊C8—81no—
163#103—24no—
164#103—42no—
165C22⋊C8—21no—
166C22⋊C8—22no—
167C22⋊C8—21no—
168C22⋊C8—21no—
169C22⋊C8—41no—
170C22⋊C8—41no—
171C22⋊C8—41no—
172C22⋊C8M1612yes—
173#97—81no—
174#97—81no—
175C4×C8—41no—
176C4×C8—41no—
177C4×C8—41no—
178C4×C8—41no—
179#95—21no—
180#95—21no—
181#95—21no—
182#95—21no—
183#95—21no—
184#95—41no—
185#95—41no—
186C24C4×D411yescharacteristic
187C2×Q8—21no—
188C2×Q8—21no—
189C2×Q8—41no—
190C2×Q8—41no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—22no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—22no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4C2×C22⋊C411yescharacteristic
220C22×C4C4×D411yescharacteristic
221C22×C4#12011yescharacteristic
222C22×C4#12111yescharacteristic
223C22×C4#12111yescharacteristic
224C22×C4#12311yescharacteristic
225C22×C4C2×M1611yescharacteristic
226C22×C4C2×M1611yescharacteristic
227C22×C4#13111yescharacteristic
228C22×C4#13111yescharacteristic
229C22×C4C2×SD1611yescharacteristic
230C22×C4#13511yescharacteristic
231C22×C4AGL(1,ℤ/8)11yescharacteristic
232C22×C4#13711yescharacteristic
233C2×C8—22no—
234C2×C8—22no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—42no—
240C2×C8—41no—
241C2×C8—42no—
242C2×C8—41no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—81no—
258C2×C8—81no—
259C2×C8—81no—
260C2×C8—81no—
261C2×C8—81no—
262C2×C8—81no—
263C2×C8—81no—
264C2×C8—81no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—22no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—81no—
280C4⋊C4—81no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C42—21no—
286C42—21no—
287C42—21no—
288C42—21no—
289C42—41no—
290C42—41no—
291C42—41no—
292C42—41no—
293C42—41no—
294C42—41no—
295C42—81no—
296C42—81no—
297C42—81no—
298C42—81no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23#38611yescharacteristic
304C23#43511yescharacteristic
305C23#43611yescharacteristic
306C23C4×SD1611yescharacteristic
307C23#44011yescharacteristic
308C23#44311yescharacteristic
309C23#44411yescharacteristic
310Q8—42no—
311Q8—81no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
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—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4#40711yescharacteristic
365C2×C4#40811yescharacteristic
366C2×C4#43511yescharacteristic
367C2×C4#43611yescharacteristic
368C2×C4#44811yescharacteristic
369C2×C4#44911yescharacteristic
370C2×C4#45511yescharacteristic
371C2×C4#45611yescharacteristic
372C2×C4#45811yescharacteristic
373C2×C4#45811yescharacteristic
374C2×C4#46011yescharacteristic
375C2×C4#46411yescharacteristic
376C8—42no—
377C8—42no—
378C8—81no—
379C8—82no—
380C8—82no—
381C8—81no—
382C8—81no—
383C8—81no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22#158211yescharacteristic
397C22#158511yescharacteristic
398C22#159011yescharacteristic
399C22#159211yescharacteristic
400C22#187011yescharacteristic
401C22#187611yescharacteristic
402C22#188011yescharacteristic
403C22#188111yescharacteristic
404C22#188211yescharacteristic
405C22#189011yescharacteristic
406C22#189111yescharacteristic
407C4—21no—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—41no—
414C4—41no—
415C4—81no—
416C4—81no—
417C4—82no—
418C4—81no—
419C4—82no—
420C4—81no—
421C4#160811yescharacteristic
422C4#160911yescharacteristic
423C4#161111yescharacteristic
424C4#161211yescharacteristic
425C2—21no—
426C2—21no—
427C2—21no—
428C2—21no—
429C2#895211yescharacteristic
430C2#895511yescharacteristic
431C2#896811yescharacteristic
432C2#903811yescharacteristic
433C2#904411yescharacteristic
434C2#905011yescharacteristic
435C2#905111yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
socleC23#386
prime radicalC24C4×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#222952
C4×#4832
#113462
#87062
#75662
#70292
#70162