Finite Group Databasebeta

← #119973

Subgroups — #119973

Order 512.

758 conjugacy classes of subgroups.

The subgroup lattice has 505 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20647C211yesmaximal, characteristic
2C2×#1479C211yesmaximal, characteristic
3#13942C211yesmaximal, characteristic
4C2×#1303C211yesmaximal, characteristic
5#8026C211yesmaximal, characteristic
6#8014C211yesmaximal, characteristic
7C2×#1286C211yesmaximal, characteristic
8C22×C4×Q8C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C2×#419—21no—
13C2×#391—21no—
14#2285C2211yescharacteristic
15C2×#382C2211yescharacteristic
16C2×C4×C4⋊C4C2211yescharacteristic
17#1805—22no—
18#1803C414yescomplemented
19#1736—21no—
20#1479—22no—
21#1479—22no—
22C2×Q8⋊C8—22no—
23#1441—22no—
24C4⋊#95—21no—
25#1434—22no—
26#1303—22no—
27#1294—22no—
28#1294—22no—
29#1286—22no—
30C23×Q8D411yescharacteristic
31C22×M16—21no—
32C2×C4×Q8—21no—
33C2×C4×Q8—21no—
34C2×C4×Q8—21no—
35C2×C4×Q8—21no—
36C2×C4×Q8—21no—
37C2×C4×Q8—21no—
38C2×C4×Q8—21no—
39C2×C4×Q8—21no—
40C2×C4×Q8—21no—
41C2×C4×Q8—21no—
42C2×C4×Q8C2×C412yes—
43C2×C4×Q8D412yes—
44C2×#117—21no—
45C22×C4⋊C4—21no—
46C22×C4⋊C4—21no—
47C22×C4⋊C4—21no—
48C22×C4⋊C4D411yescharacteristic
49C22×C42—21no—
50C22×C42—21no—
51C22×C42C2311yescharacteristic
52#431—21no—
53#431—21no—
54#431—21no—
55#431—21no—
56#431—21no—
57#431—21no—
58#431D412yes—
59#431D412yes—
60#423—21no—
61#423—21no—
62#423—21no—
63#423—21no—
64C2×C4⋊C8—21no—
65C2×C4⋊C8—21no—
66C2×C4⋊C8—21no—
67C2×C4⋊C8C2×C412yes—
68#419—42no—
69#419—42no—
70C2×#103—24no—
71C2×C22⋊C8—21no—
72C2×C22⋊C8—21no—
73C2×C4×C8—21no—
74C2×C4×C8—21no—
75#391—42no—
76#391—42no—
77#384C2×C412yes—
78#382—21no—
79#382—21no—
80#382—21no—
81#382—21no—
82#382—21no—
83#380—21no—
84#380—21no—
85C4×C4⋊C4—21no—
86C4×C4⋊C4—21no—
87C4×C4⋊C4—21no—
88C4×C4⋊C4—21no—
89C4×C4⋊C4—21no—
90C4×C4⋊C4—21no—
91C2×#95—24no—
92C2×#95—24no—
93C2×#95—21no—
94C2×#95D412yes—
95C2×#95D412yes—
96#340—24no—
97Q8⋊C8—28no—
98C22×Q8—21no—
99C22×Q8—21no—
100C22×Q8—21no—
101C22×Q8—21no—
102C22×Q8—21no—
103C22×Q8—21no—
104C22×Q8—21no—
105C22×Q8—21no—
106C22×Q8—21no—
107C22×Q8—21no—
108C22×Q8—21no—
109C22×Q8C22⋊C412yes—
110C22×Q8D812yes—
111C22×Q8SD1612yes—
112C23×C4—21no—
113C23×C4—21no—
114C23×C4—22no—
115C23×C4—22no—
116C23×C4C2×D411yescharacteristic
117C23×C4C2×D411yescharacteristic
118C23×C4C2×D411yescharacteristic
119C2×M16—41no—
120C2×M16—41no—
121C2×M16—41no—
122C2×M16—41no—
123C2×M16—41no—
124C2×M16—41no—
125C22×C8—22no—
126C22×C8—41no—
127C22×C8—41no—
128C4×Q8—22no—
129C4×Q8—22no—
130C4×Q8—22no—
131C4×Q8—22no—
132C4×Q8—22no—
133C4×Q8—22no—
134C4×Q8—22no—
135C4×Q8—22no—
136C4×Q8—41no—
137C4×Q8—41no—
138C4×Q8—41no—
139C4×Q8—41no—
140C4×Q8—41no—
141C4×Q8—41no—
142C4×Q8—41no—
143C4×Q8—41no—
144#117—41no—
145#117—41no—
146#117—41no—
147#117—41no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—44no—
159C2×C4⋊C4—41no—
160C2×C4⋊C4—41no—
161C2×C4⋊C4—41no—
162C2×C4⋊C4—41no—
163C2×C4⋊C4—41no—
164C2×C4⋊C4—41no—
165C2×C4⋊C4—41no—
166C2×C4⋊C4—41no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—41no—
169C2×C4⋊C4—41no—
170C2×C4⋊C4—41no—
171C2×C4⋊C4C22⋊C412yes—
172C2×C22⋊C4—41no—
173C2×C42—22no—
174C2×C42—22no—
175C2×C42—41no—
176C2×C42—41no—
177C2×C42—41no—
178C2×C42—41no—
179C2×C42—41no—
180C2×C42—41no—
181C2×C42—41no—
182C2×C42—41no—
183C2×C42—41no—
184C2×C42—41no—
185C2×C42—41no—
186C2×C42C22×C411yescharacteristic
187C2×C42C2×D411yescharacteristic
188C2×C42C2×D411yescharacteristic
189C2×C42C2×D411yescharacteristic
190C2×C42#4111yescharacteristic
191C2×C42#4111yescharacteristic
192C2×C42#4111yescharacteristic
193C2×C42#4111yescharacteristic
194C2×C42#4111yescharacteristic
195C2×C42#4111yescharacteristic
196C2×C42#4111yescharacteristic
197C2×C42#4111yescharacteristic
198C4⋊C8—22no—
199C4⋊C8—22no—
200C4⋊C8—22no—
201C4⋊C8—22no—
202C4⋊C8—41no—
203C4⋊C8—41no—
204C4⋊C8—41no—
205C4⋊C8—41no—
206#103—48no—
207C22⋊C8—22no—
208C22⋊C8—22no—
209C22⋊C8—41no—
210C22⋊C8—41no—
211C4×C8—22no—
212C4×C8—22no—
213C4×C8—41no—
214C4×C8—41no—
215#95—22no—
216#95—22no—
217#95—22no—
218#95—22no—
219#95—48no—
220#95—48no—
221#95—41no—
222#95—41no—
223#95—41no—
224#95—41no—
225C24#12011yescharacteristic
226C2×Q8—22no—
227C2×Q8—22no—
228C2×Q8—22no—
229C2×Q8—22no—
230C2×Q8—22no—
231C2×Q8—22no—
232C2×Q8—22no—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8—22no—
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8—22no—
240C2×Q8—22no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×Q8#10214yes—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—24no—
258C22×C4—22no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—44no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—44no—
275C22×C4—44no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4C2×C22⋊C411yescharacteristic
281C22×C4C4×D411yescharacteristic
282C22×C4C4×D411yescharacteristic
283C22×C4#12111yescharacteristic
284C22×C4#12111yescharacteristic
285C22×C4#12111yescharacteristic
286C22×C4#12111yescharacteristic
287C22×C4#12111yescharacteristic
288C22×C4#12111yescharacteristic
289C22×C4#12111yescharacteristic
290C22×C4#12111yescharacteristic
291C22×C4#12311yescharacteristic
292C22×C4#12311yescharacteristic
293C22×C4#12311yescharacteristic
294C22×C4#12311yescharacteristic
295C22×C4#12311yescharacteristic
296C22×C4#12411yescharacteristic
297C22×C4#12411yescharacteristic
298C22×C4C2×D811yescharacteristic
299C22×C4C2×SD1611yescharacteristic
300C22×C4#13511yescharacteristic
301C22×C4#13511yescharacteristic
302C22×C4AGL(1,ℤ/8)11yescharacteristic
303C22×C4#13711yescharacteristic
304C22×C4#13711yescharacteristic
305C22×C4#13711yescharacteristic
306M16—81no—
307M16—81no—
308M16—81no—
309M16—81no—
310C2×C8—42no—
311C2×C8—42no—
312C2×C8—42no—
313C2×C8—42no—
314C2×C8—42no—
315C2×C8—82no—
316C2×C8—82no—
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—44no—
320C4⋊C4—44no—
321C4⋊C4—42no—
322C4⋊C4—42no—
323C4⋊C4—42no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—42no—
327C4⋊C4—42no—
328C4⋊C4—42no—
329C4⋊C4—82no—
330C4⋊C4—82no—
331C4⋊C4—81no—
332C4⋊C4—81no—
333C4⋊C4—81no—
334C4⋊C4—81no—
335C22⋊C4—81no—
336C22⋊C4—81no—
337C42—42no—
338C42—42no—
339C42—42no—
340C42—42no—
341C42—81no—
342C42—81no—
343C42—81no—
344C42—81no—
345C42—81no—
346C42—81no—
347C42#11711yescharacteristic
348C42#11711yescharacteristic
349C42C4×D411yescharacteristic
350C42C4×D411yescharacteristic
351C42#12011yescharacteristic
352C42#12311yescharacteristic
353C42#12311yescharacteristic
354C42#12311yescharacteristic
355C42#12311yescharacteristic
356C42#12311yescharacteristic
357C42#12411yescharacteristic
358C42#12411yescharacteristic
359C42#12611yescharacteristic
360C42#12611yescharacteristic
361C42#12611yescharacteristic
362C42#12611yescharacteristic
363C23—22no—
364C23—22no—
365C23#38611yescharacteristic
366C23#39411yescharacteristic
367C23#39411yescharacteristic
368C23#44711yescharacteristic
369C23#44811yescharacteristic
370C23#45211yescharacteristic
371C23#45211yescharacteristic
372Q8—24no—
373Q8—24no—
374Q8—42no—
375Q8—42no—
376Q8—42no—
377Q8—42no—
378Q8—42no—
379Q8—42no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—24no—
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—44no—
400C2×C4—44no—
401C2×C4—44no—
402C2×C4—44no—
403C2×C4—42no—
404C2×C4—82no—
405C2×C4—82no—
406C2×C4—82no—
407C2×C4—82no—
408C2×C4—82no—
409C2×C4—82no—
410C2×C4—82no—
411C2×C4—82no—
412C2×C4—84no—
413C2×C4—84no—
414C2×C4—82no—
415C2×C4—82no—
416C2×C4—82no—
417C2×C4—82no—
418C2×C4#38111yescharacteristic
419C2×C4#38611yescharacteristic
420C2×C4#38811yescharacteristic
421C2×C4#38811yescharacteristic
422C2×C4#38811yescharacteristic
423C2×C4#38811yescharacteristic
424C2×C4#39411yescharacteristic
425C2×C4#39411yescharacteristic
426C2×C4#39711yescharacteristic
427C2×C4#39711yescharacteristic
428C2×C4#39711yescharacteristic
429C2×C4#39711yescharacteristic
430C2×C4C2×#10211yescharacteristic
431C2×C4#41611yescharacteristic
432C2×C4#41711yescharacteristic
433C2×C4#41911yescharacteristic
434C2×C4#46511yescharacteristic
435C2×C4#46511yescharacteristic
436C2×C4#46611yescharacteristic
437C2×C4#46611yescharacteristic
438C2×C4#46811yescharacteristic
439C2×C4#46811yescharacteristic
440C2×C4#47011yescharacteristic
441C2×C4#47011yescharacteristic
442C2×C4#48011yescharacteristic
443C2×C4#48011yescharacteristic
444C2×C4#48011yescharacteristic
445C2×C4#48111yescharacteristic
446C2×C4#48211yescharacteristic
447C2×C4#48211yescharacteristic
448C2×C4#48311yescharacteristic
449C2×C4#48311yescharacteristic
450C2×C4#48511yescharacteristic
451C2×C4#48511yescharacteristic
452C2×C4#48511yescharacteristic
453C2×C4#48511yescharacteristic
454C8—82no—
455C8—82no—
456C8—82no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22#144011yescharacteristic
466C22#187311yescharacteristic
467C22#187411yescharacteristic
468C22#190512yes—
469C22#190612yes—
470C22#203311yescharacteristic
471C22#203311yescharacteristic
472C22#203511yescharacteristic
473C22#203511yescharacteristic
474C4—21no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—44no—
483C4—84no—
484C4—82no—
485C4—162no—
486C4—162no—
487C4#182311yescharacteristic
488C4#182511yescharacteristic
489C4#189311yescharacteristic
490C4#189411yescharacteristic
491C4#207511yescharacteristic
492C4#207511yescharacteristic
493C4#207711yescharacteristic
494C4#207711yescharacteristic
495C2—21no—
496C2—21no—
497C2—21no—
498C2—21no—
499C2#917812yes—
500C2#918012yes—
501C2#1118411yescharacteristic
502C2#1119311yescharacteristic
503C2#1119911yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#120
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
18. #1803C4semidirect

Maximal subgroups

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

subgroupindex
#206472
C2×#14792
#139422
C2×#13032
#80262
#80142
C2×#12862