Finite Group Databasebeta

← #108359

Subgroups — #108359

Order 512.

820 conjugacy classes of subgroups.

The subgroup lattice has 495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34215C211yesmaximal, characteristic
2#17708C211yesmaximal, characteristic
3#17486C211yesmaximal, characteristic
4#10856C211yesmaximal, characteristic
5C2×#1286C211yesmaximal, characteristic
6C2×#1286C211yesmaximal, characteristic
7#7924C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C2×#423C2211yescharacteristic
13#2368—22no—
14#2368C414yes—
15#2355—22no—
16#2355—22no—
17#2331—21no—
18#2331—21no—
19#2317—21no—
20C4×#125—22no—
21C2×#382C2211yescharacteristic
22#2274—21no—
23C4×#117C2211yescharacteristic
24C2×#344—21no—
25C2×#344—21no—
26#1550—22no—
27#1549—21no—
28#1548—21no—
29#1542C414yescomplemented
30#1493C414yescomplemented
31#1487—22no—
32#1481—22no—
33#1286—22no—
34#1286—22no—
35#1282—22no—
36C22×M16—21no—
37C22×M16—21no—
38#533—21no—
39#533—21no—
40#533—21no—
41#533—21no—
42#533C2×C412yes—
43#533C2×C412yes—
44#533D412yes—
45#533Q812yes—
46C2×C4⋊Q8D411yescharacteristic
47C2×C4⋊Q8D411yescharacteristic
48C2×#125—21no—
49C2×C22⋊Q8—21no—
50C2×C22⋊Q8C2×C412yes—
51C2×C4×Q8—21no—
52C2×C4×Q8D412yes—
53C2×#117—21no—
54C2×#117D411yescharacteristic
55C2×#117D411yescharacteristic
56C22×C4⋊C4—21no—
57C22×C42C2311yescharacteristic
58#431—21no—
59#431—21no—
60#431—21no—
61#431—21no—
62#431—21no—
63#431—21no—
64#431—21no—
65#431C2×C412yes—
66#423—21no—
67#423—21no—
68#423—21no—
69#423—21no—
70#423—21no—
71#423—21no—
72#423—21no—
73#423C2×C412yes—
74C2×C4⋊C8—21no—
75C2×C4⋊C8—21no—
76C2×C4⋊C8—21no—
77C2×C4⋊C8—21no—
78C2×C4⋊C8—21no—
79C2×C4⋊C8C2×C412yes—
80C2×C22⋊C8—21no—
81C2×C22⋊C8—21no—
82C2×C4×C8—21no—
83C2×C4×C8C2×C412yes—
84#391—24no—
85#391—24no—
86#389—22no—
87#389—22no—
88#387—24no—
89#387—24no—
90#387—24no—
91#387—24no—
92#385—24no—
93#384—22no—
94#382—22no—
95#382—21no—
96#382—21no—
97#382D412yes—
98#382D412yes—
99C4×C4⋊C4—22no—
100C4×C4⋊C4—22no—
101C4×C4⋊C4—24no—
102C4×C4⋊C4—22no—
103C4×C4⋊C4—22no—
104C4×C4⋊C4—21no—
105C4×C4⋊C4—21no—
106C4×C4⋊C4—24no—
107C4×C22⋊C4—24no—
108C4×C22⋊C4C2×C412yes—
109C4×C22⋊C4D412yes—
110#376—21no—
111C2×#95—21no—
112C2×#95C2×C412yes—
113C43—21no—
114#344—42no—
115#344—42no—
116#333—24no—
117#332—24no—
118Q8⋊C8—28no—
119C22×Q8—21no—
120C22×Q8C22⋊C412yes—
121C23×C4—22no—
122C23×C4C22×C411yescharacteristic
123C23×C4C2×D411yescharacteristic
124C23×C4C2×D411yescharacteristic
125C2×M16—22no—
126C2×M16—41no—
127C2×M16—41no—
128C2×M16—41no—
129C2×M16—41no—
130C2×M16—41no—
131C2×M16—41no—
132C2×M16—41no—
133C2×M16—41no—
134C2×M16—41no—
135C2×M16—41no—
136C2×M16—41no—
137C22×C8—22no—
138C22×C8—22no—
139C22×C8—41no—
140C22×C8—41no—
141C4⋊Q8—21no—
142C4⋊Q8—21no—
143C4⋊Q8—21no—
144C4⋊Q8—21no—
145C4⋊Q8C22⋊C412yes—
146C4⋊Q8C22⋊C412yes—
147C4⋊Q8C4⋊C412yes—
148C4⋊Q8C4⋊C412yes—
149#125—22no—
150#125—22no—
151#125—22no—
152#125—22no—
153C22⋊Q8—22no—
154C22⋊Q8—22no—
155C22⋊Q8—22no—
156C22⋊Q8—22no—
157C22⋊Q8—22no—
158C22⋊Q8—22no—
159C22⋊Q8C4214yes—
160C22⋊Q8C4⋊C414yes—
161C4×Q8—22no—
162C4×Q8—22no—
163C4×Q8—22no—
164C4×Q8—22no—
165C4×Q8—22no—
166C4×Q8—22no—
167C4×Q8C22⋊C414yes—
168C4×Q8C4⋊C414yes—
169#117—22no—
170#117—22no—
171#117—22no—
172#117—22no—
173#117—21no—
174#117—21no—
175#117—21no—
176#117—21no—
177#117—21no—
178#117—21no—
179#117SD1612yes—
180#117Q1612yes—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—24no—
191C2×C4⋊C4—24no—
192C2×C4⋊C4—41no—
193C2×C4⋊C4—41no—
194C2×C4⋊C4—41no—
195C2×C4⋊C4—41no—
196C2×C4⋊C4C22⋊C412yes—
197C2×C22⋊C4—22no—
198C2×C22⋊C4C22⋊C412yes—
199C2×C22⋊C4C22⋊C412yes—
200C2×C42—22no—
201C2×C42—21no—
202C2×C42—21no—
203C2×C42—24no—
204C2×C42—24no—
205C2×C42—22no—
206C2×C42—22no—
207C2×C42C22×C411yescharacteristic
208C2×C42C22×C411yescharacteristic
209C2×C42C2×D411yescharacteristic
210C2×C42C2×D411yescharacteristic
211C2×C42C2×D411yescharacteristic
212C2×C42C2×D411yescharacteristic
213C2×C42C2×D411yescharacteristic
214C2×C42C2×Q811yescharacteristic
215C2×C42#4111yescharacteristic
216C2×C42#4111yescharacteristic
217C2×C42#4111yescharacteristic
218C2×C42#4111yescharacteristic
219C4⋊C8—22no—
220C4⋊C8—22no—
221C4⋊C8—22no—
222C4⋊C8—22no—
223C4⋊C8—22no—
224C4⋊C8—41no—
225C4⋊C8—41no—
226C4⋊C8—41no—
227C4⋊C8—41no—
228C4⋊C8—41no—
229C4⋊C8—41no—
230C4⋊C8—41no—
231C22⋊C8—22no—
232C22⋊C8—41no—
233C22⋊C8—41no—
234C22⋊C8—41no—
235C4×C8—22no—
236C4×C8—22no—
237C4×C8—22no—
238C4×C8—41no—
239#95—24no—
240#95—24no—
241#95—24no—
242#95—24no—
243#95—22no—
244#95—22no—
245#95—22no—
246#95—22no—
247#95—22no—
248#95C22⋊C414yes—
249C24C2×C22⋊C411yescharacteristic
250C2×Q8—22no—
251C2×Q8—22no—
252C2×Q8—22no—
253C2×Q8—82no—
254C2×Q8—82no—
255C2×Q8#9514yes—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—24no—
260C22×C4—22no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—81no—
264C22×C4—81no—
265C22×C4—82no—
266C22×C4—82no—
267C22×C4C2×C4211yescharacteristic
268C22×C4C2×C22⋊C411yescharacteristic
269C22×C4C2×C22⋊C411yescharacteristic
270C22×C4C2×C4⋊C411yescharacteristic
271C22×C4#11711yescharacteristic
272C22×C4#11711yescharacteristic
273C22×C4C4×D411yescharacteristic
274C22×C4C4×D411yescharacteristic
275C22×C4C4×D411yescharacteristic
276C22×C4C4×D411yescharacteristic
277C22×C4#12011yescharacteristic
278C22×C4#12011yescharacteristic
279C22×C4#12011yescharacteristic
280C22×C4#12011yescharacteristic
281C22×C4#12111yescharacteristic
282C22×C4#12111yescharacteristic
283C22×C4C22⋊Q811yescharacteristic
284C22×C4C22⋊Q811yescharacteristic
285C22×C4C2×SD1611yescharacteristic
286C22×C4C2×Q1611yescharacteristic
287C22×C4#13511yescharacteristic
288C22×C4#13511yescharacteristic
289C22×C4AGL(1,ℤ/8)11yescharacteristic
290C22×C4#13711yescharacteristic
291C22×C4#13711yescharacteristic
292C22×C4#13711yescharacteristic
293M16—42no—
294M16—42no—
295M16—81no—
296M16—81no—
297M16—81no—
298M16—81no—
299M16—81no—
300M16—81no—
301C2×C8—42no—
302C2×C8—42no—
303C2×C8—42no—
304C2×C8—42no—
305C2×C8—42no—
306C2×C8—42no—
307C2×C8—82no—
308C2×C8—81no—
309C2×C8—81no—
310C2×C8—82no—
311C4⋊C4—24no—
312C4⋊C4—24no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—24no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—24no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—42no—
325C4⋊C4—42no—
326C4⋊C4—41no—
327C4⋊C4—42no—
328C4⋊C4—42no—
329C4⋊C4—41no—
330C4⋊C4—84no—
331C4⋊C4—84no—
332C4⋊C4#9514yes—
333C22⋊C4—24no—
334C22⋊C4—24no—
335C22⋊C4—22no—
336C22⋊C4—22no—
337C22⋊C4—22no—
338C22⋊C4#10314yes—
339C42—24no—
340C42—24no—
341C42—22no—
342C42—22no—
343C42—41no—
344C42—41no—
345C42—82no—
346C42—82no—
347C42—84no—
348C42—84no—
349C42C2×C22⋊C411yescharacteristic
350C42C2×C22⋊C411yescharacteristic
351C42C2×C4⋊C411yescharacteristic
352C42C2×C4⋊C411yescharacteristic
353C42C4×D411yescharacteristic
354C42C4×D411yescharacteristic
355C42C4×D411yescharacteristic
356C42C4×D411yescharacteristic
357C42#12111yescharacteristic
358C42#12111yescharacteristic
359C42C22⋊Q811yescharacteristic
360C42C22⋊Q811yescharacteristic
361C42#12311yescharacteristic
362C42#12311yescharacteristic
363C42#12311yescharacteristic
364C42#12311yescharacteristic
365C23—41no—
366C23—41no—
367C23C4×C22⋊C411yescharacteristic
368C23#37911yescharacteristic
369C23#38011yescharacteristic
370C23C2×#10311yescharacteristic
371C23#41611yescharacteristic
372C23#41711yescharacteristic
373C23#41911yescharacteristic
374Q8—44no—
375Q8—82no—
376Q8—82no—
377Q8—82no—
378C2×C4—24no—
379C2×C4—24no—
380C2×C4—24no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—44no—
402C2×C4—44no—
403C2×C4—42no—
404C2×C4—44no—
405C2×C4—162no—
406C2×C4—162no—
407C2×C4C2×#9511yescharacteristic
408C2×C4C4×C22⋊C411yescharacteristic
409C2×C4#38011yescharacteristic
410C2×C4#38111yescharacteristic
411C2×C4#38511yescharacteristic
412C2×C4#38511yescharacteristic
413C2×C4#38511yescharacteristic
414C2×C4#38511yescharacteristic
415C2×C4#38611yescharacteristic
416C2×C4#38611yescharacteristic
417C2×C4#38611yescharacteristic
418C2×C4#38611yescharacteristic
419C2×C4C4×SD1611yescharacteristic
420C2×C4C4×SD1611yescharacteristic
421C2×C4C4×Q1611yescharacteristic
422C2×C4C4×Q1611yescharacteristic
423C2×C4#44011yescharacteristic
424C2×C4#44011yescharacteristic
425C2×C4#44111yescharacteristic
426C2×C4#44111yescharacteristic
427C2×C4#44811yescharacteristic
428C2×C4#44811yescharacteristic
429C2×C4#44911yescharacteristic
430C2×C4#44911yescharacteristic
431C2×C4#45111yescharacteristic
432C2×C4#45111yescharacteristic
433C2×C4#45211yescharacteristic
434C2×C4#45211yescharacteristic
435C2×C4#46011yescharacteristic
436C2×C4#46211yescharacteristic
437C2×C4#46411yescharacteristic
438C2×C4#46411yescharacteristic
439C2×C4#47511yescharacteristic
440C2×C4#47711yescharacteristic
441C2×C4#47911yescharacteristic
442C2×C4#47911yescharacteristic
443C8—82no—
444C8—82no—
445C8—82no—
446C8—82no—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22C22⋊#9511yescharacteristic
458C22C4×#10311yescharacteristic
459C22#176311yescharacteristic
460C22#178711yescharacteristic
461C22#178811yescharacteristic
462C22#180311yescharacteristic
463C22#180511yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—21no—
469C4—21no—
470C4—21no—
471C4—21no—
472C4—44no—
473C4—44no—
474C4—44no—
475C4—82no—
476C4—84no—
477C4#186311yescharacteristic
478C4#186311yescharacteristic
479C4#186511yescharacteristic
480C4#186511yescharacteristic
481C4#187811yescharacteristic
482C4#187811yescharacteristic
483C4#188011yescharacteristic
484C4#188011yescharacteristic
485C2—21no—
486C2—21no—
487C2—21no—
488C2—21no—
489C2—21no—
490C2—21no—
491C2#1075611yescharacteristic
492C2#1078911yescharacteristic
493C2#1079211yescharacteristic
subgroupG/H
center, socleC22C22⋊#95
commutatorC22×C4C2×C42
Frattini, cosocleC22×C42C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
29. #1542C4semidirect
30. #1493C4semidirect

Maximal subgroups

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

subgroupindex
#342152
#177082
#174862
#108562
C2×#12862
#79242