Finite Group Databasebeta

← #116331

Subgroups — #116331

Order 512.

774 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1995C211yesmaximal, characteristic
2C2×#1503C211yesmaximal, characteristic
3C2×#1503C211yesmaximal, characteristic
4#13848C211yesmaximal, characteristic
5C2×#1303C211yesmaximal, characteristic
6C2×#1303C211yesmaximal, characteristic
7C2×#1274C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#431C2211yescharacteristic
10C2×#431C2211yescharacteristic
11C2×#423C2211yescharacteristic
12C2×C4×C4⋊C4—21no—
13C2×C4×C4⋊C4C2211yescharacteristic
14C2×C4×C4⋊C4C2211yescharacteristic
15C2×#376C2211yescharacteristic
16#1995—22no—
17#1995—22no—
18C2×#339—21no—
19C2×#339—21no—
20#1503—22no—
21#1503—22no—
22#1503—22no—
23#1503C414yescomplemented
24C2×#328—22no—
25C2×#328—21no—
26C2×#328—21no—
27#1444—21no—
28#1442—21no—
29#1441—22no—
30C4×#95—21no—
31#1303—22no—
32#1303—22no—
33#1274—22no—
34C22×M16—21no—
35#533—21no—
36#533—21no—
37#533—21no—
38#533—21no—
39#533—21no—
40#533—21no—
41#533C2×C412yes—
42#533D412yes—
43C2×C4⋊Q8Q811yescharacteristic
44C2×C4⋊Q8Q811yescharacteristic
45C2×#125—21no—
46C2×C22⋊Q8—21no—
47C2×C22⋊Q8—21no—
48C2×C4×Q8—21no—
49C2×C4×Q8—21no—
50C2×#117—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—22no—
53C22×C4⋊C4—21no—
54C22×C42—21no—
55C22×C42—21no—
56C22×C42D411yescharacteristic
57C22×C42D411yescharacteristic
58C22×C42C2311yescharacteristic
59#431—21no—
60#431—21no—
61#431—21no—
62#431—21no—
63#431—21no—
64#431—21no—
65#431C2×C412yes—
66#431D412yes—
67#423—21no—
68#423—21no—
69#423—21no—
70#423D412yes—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74C2×C4⋊C8—21no—
75C2×C22⋊C8—21no—
76C2×C22⋊C8—21no—
77C2×C4×C8—21no—
78C2×C4×C8—21no—
79C4×C4⋊C4—21no—
80C4×C4⋊C4—21no—
81C4×C4⋊C4—21no—
82C4×C4⋊C4—21no—
83C4×C4⋊C4—21no—
84C4×C4⋊C4—21no—
85C4×C4⋊C4—42no—
86C4×C4⋊C4—42no—
87C4×C4⋊C4C2×C412yes—
88C4×C4⋊C4D412yes—
89#376—21no—
90#376—21no—
91#376—21no—
92#376—21no—
93C2×#95—22no—
94C2×#95—22no—
95C2×#95—22no—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95D412yes—
99C2×#95D411yescharacteristic
100C2×#95D411yescharacteristic
101#339—24no—
102#339—24no—
103#328—28no—
104#328—24no—
105#328—24no—
106C22×Q8—21no—
107C22×Q8—21no—
108C23×C4—21no—
109C23×C4—21no—
110C23×C4—22no—
111C23×C4—21no—
112C23×C4—21no—
113C23×C4C2×D411yescharacteristic
114C23×C4C2×D411yescharacteristic
115C23×C4C2×D411yescharacteristic
116C2×M16—22no—
117C2×M16—41no—
118C2×M16—41no—
119C2×M16—41no—
120C2×M16—41no—
121C2×M16—41no—
122C22×C8—41no—
123C22×C8—41no—
124C22×C8—41no—
125C4⋊Q8—21no—
126C4⋊Q8—21no—
127C4⋊Q8—21no—
128C4⋊Q8—21no—
129C4⋊Q8—21no—
130C4⋊Q8—21no—
131C4⋊Q8C4⋊C412yescomplemented
132C4⋊Q8C4⋊C412yescomplemented
133#125—22no—
134#125—22no—
135#125—41no—
136#125—41no—
137C22⋊Q8—22no—
138C22⋊Q8—22no—
139C22⋊Q8—22no—
140C22⋊Q8—22no—
141C22⋊Q8—41no—
142C22⋊Q8—41no—
143C22⋊Q8—41no—
144C22⋊Q8—41no—
145C4×Q8—22no—
146C4×Q8—22no—
147C4×Q8—22no—
148C4×Q8—22no—
149C4×Q8—41no—
150C4×Q8—41no—
151C4×Q8—41no—
152C4×Q8—41no—
153#117—22no—
154#117—22no—
155#117—41no—
156#117—41no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—44no—
164C2×C4⋊C4—44no—
165C2×C4⋊C4—44no—
166C2×C4⋊C4—44no—
167C2×C4⋊C4—44no—
168C2×C4⋊C4—41no—
169C2×C4⋊C4—41no—
170C2×C4⋊C4—41no—
171C2×C4⋊C4—41no—
172C2×C22⋊C4—41no—
173C2×C42—21no—
174C2×C42—21no—
175C2×C42—21no—
176C2×C42—21no—
177C2×C42—21no—
178C2×C42—21no—
179C2×C42—21no—
180C2×C42—21no—
181C2×C42—22no—
182C2×C42—22no—
183C2×C42—21no—
184C2×C42—21no—
185C2×C42—41no—
186C2×C42—41no—
187C2×C42—41no—
188C2×C42—41no—
189C2×C42—41no—
190C2×C42—41no—
191C2×C42—41no—
192C2×C42—41no—
193C2×C42—41no—
194C2×C42—41no—
195C2×C42—41no—
196C2×C42SD1612yes—
197C2×C42Q1612yes—
198C2×C42C22×C411yescharacteristic
199C2×C42C2×D411yescharacteristic
200C2×C42C2×D411yescharacteristic
201C2×C42C2×D411yescharacteristic
202C2×C42C2×D411yescharacteristic
203C2×C42C2×Q811yescharacteristic
204C2×C42#4111yescharacteristic
205C2×C42#4111yescharacteristic
206C2×C42#4111yescharacteristic
207C2×C42#4111yescharacteristic
208C2×C42#4111yescharacteristic
209C2×C42#4111yescharacteristic
210C4⋊C8—22no—
211C4⋊C8—22no—
212C4⋊C8—22no—
213C4⋊C8—22no—
214C4⋊C8—41no—
215C4⋊C8—41no—
216C4⋊C8—41no—
217C4⋊C8—41no—
218C22⋊C8—22no—
219C22⋊C8—22no—
220C22⋊C8—41no—
221C22⋊C8—41no—
222C4×C8—22no—
223C4×C8—22no—
224C4×C8—41no—
225C4×C8—41no—
226#95—21no—
227#95—21no—
228#95—22no—
229#95—22no—
230#95—44no—
231#95—44no—
232#95—44no—
233#95—41no—
234#95—41no—
235#95—41no—
236#95—41no—
237#95C22⋊C412yes—
238#95C22⋊C412yes—
239C24#12011yescharacteristic
240C2×Q8—22no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—82no—
245C2×Q8—82no—
246C22×C4—24no—
247C22×C4—22no—
248C22×C4—24no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—42no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—42no—
276C22×C4—41no—
277C22×C4C2×C22⋊C411yescharacteristic
278C22×C4C4×D411yescharacteristic
279C22×C4C4×D411yescharacteristic
280C22×C4#12011yescharacteristic
281C22×C4#12011yescharacteristic
282C22×C4#12111yescharacteristic
283C22×C4#12111yescharacteristic
284C22×C4#12111yescharacteristic
285C22×C4#12111yescharacteristic
286C22×C4#12111yescharacteristic
287C22×C4C22⋊Q811yescharacteristic
288C22×C4C22⋊Q811yescharacteristic
289C22×C4C22⋊Q811yescharacteristic
290C22×C4#12311yescharacteristic
291C22×C4#12411yescharacteristic
292C22×C4#12411yescharacteristic
293C22×C4#12411yescharacteristic
294C22×C4#12711yescharacteristic
295C22×C4C2×SD1611yescharacteristic
296C22×C4C2×Q1611yescharacteristic
297C22×C4#13511yescharacteristic
298C22×C4#13511yescharacteristic
299C22×C4AGL(1,ℤ/8)11yescharacteristic
300C22×C4#13711yescharacteristic
301C22×C4#13711yescharacteristic
302C22×C4#13711yescharacteristic
303M16—42no—
304M16—42no—
305M16—81no—
306M16—81no—
307C2×C8—42no—
308C2×C8—42no—
309C2×C8—42no—
310C2×C8—82no—
311C2×C8—82no—
312C2×C8—81no—
313C2×C8—81no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—44no—
319C4⋊C4—44no—
320C4⋊C4—44no—
321C4⋊C4—44no—
322C4⋊C4—416no—
323C4⋊C4—42no—
324C4⋊C4—42no—
325C4⋊C4—42no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—42no—
330C4⋊C4—41no—
331C22⋊C4—42no—
332C22⋊C4—42no—
333C42—22no—
334C42—22no—
335C42—22no—
336C42—22no—
337C42—42no—
338C42—42no—
339C42—42no—
340C42—42no—
341C42—41no—
342C42—41no—
343C42—42no—
344C42—42no—
345C42—41no—
346C42—41no—
347C42—81no—
348C42—81no—
349C42—81no—
350C42—81no—
351C42C2×C4⋊C411yescharacteristic
352C42#11711yescharacteristic
353C42C4×D411yescharacteristic
354C42C4×D411yescharacteristic
355C42#12111yescharacteristic
356C42#12111yescharacteristic
357C42#12111yescharacteristic
358C42C22⋊Q811yescharacteristic
359C42C22⋊Q811yescharacteristic
360C42C22⋊Q811yescharacteristic
361C42#12311yescharacteristic
362C42#12311yescharacteristic
363C42#12311yescharacteristic
364C42#12311yescharacteristic
365C42#12611yescharacteristic
366C42#12611yescharacteristic
367C23—22no—
368C23—22no—
369C23#38611yescharacteristic
370C23#39211yescharacteristic
371C23#39311yescharacteristic
372C23#45011yescharacteristic
373C23#45111yescharacteristic
374C23#45211yescharacteristic
375C23#45211yescharacteristic
376Q8—82no—
377Q8—82no—
378Q8—82no—
379Q8—82no—
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—44no—
394C2×C4—42no—
395C2×C4—44no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—44no—
399C2×C4—44no—
400C2×C4—44no—
401C2×C4—42no—
402C2×C4—44no—
403C2×C4—44no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—81no—
410C2×C4—82no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4—81no—
414C2×C4—82no—
415C2×C4—82no—
416C2×C4—82no—
417C2×C4—82no—
418C2×C4—82no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4—82no—
423C2×C4#38011yescharacteristic
424C2×C4#38511yescharacteristic
425C2×C4#38511yescharacteristic
426C2×C4#38811yescharacteristic
427C2×C4#38811yescharacteristic
428C2×C4#39011yescharacteristic
429C2×C4#39411yescharacteristic
430C2×C4#39411yescharacteristic
431C2×C4#39611yescharacteristic
432C2×C4#39611yescharacteristic
433C2×C4#39711yescharacteristic
434C2×C4#39911yescharacteristic
435C2×C4C4×SD1611yescharacteristic
436C2×C4C4×Q1611yescharacteristic
437C2×C4#44011yescharacteristic
438C2×C4#44111yescharacteristic
439C2×C4#44811yescharacteristic
440C2×C4#44911yescharacteristic
441C2×C4#45111yescharacteristic
442C2×C4#45211yescharacteristic
443C2×C4#46111yescharacteristic
444C2×C4#46211yescharacteristic
445C2×C4#46311yescharacteristic
446C2×C4#46411yescharacteristic
447C2×C4#46511yescharacteristic
448C2×C4#46711yescharacteristic
449C2×C4#46811yescharacteristic
450C2×C4#47011yescharacteristic
451C2×C4#47511yescharacteristic
452C2×C4#47711yescharacteristic
453C2×C4#47911yescharacteristic
454C2×C4#47911yescharacteristic
455C2×C4#48711yescharacteristic
456C2×C4#48811yescharacteristic
457C2×C4#48911yescharacteristic
458C2×C4#49111yescharacteristic
459C8—82no—
460C8—82no—
461C8—82no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—22no—
467C22—22no—
468C22—22no—
469C22—22no—
470C22#143911yescharacteristic
471C22#187711yescharacteristic
472C22#187811yescharacteristic
473C22#200011yescharacteristic
474C22#200111yescharacteristic
475C22#202411yescharacteristic
476C22#202611yescharacteristic
477C22#203112yes—
478C22#203112yes—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—21no—
485C4—21no—
486C4—21no—
487C4—44no—
488C4—82no—
489C4—84no—
490C4—82no—
491C4—82no—
492C4—82no—
493C4—82no—
494C4#186311yescharacteristic
495C4#186511yescharacteristic
496C4#193311yescharacteristic
497C4#193511yescharacteristic
498C4#204211yescharacteristic
499C4#204311yescharacteristic
500C4#206611yescharacteristic
501C4#206811yescharacteristic
502C2—21no—
503C2—21no—
504C2—21no—
505C2—21no—
506C2#1037112yes—
507C2#1037312yes—
508C2#1106711yescharacteristic
509C2#1108111yescharacteristic
510C2#1109111yescharacteristic
subgroupG/H
centerC22×C4#124
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
socleC23#393
prime radicalC24#120
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
23. #1503C4semidirect
131. C4⋊Q8C4⋊C4semidirect
132. C4⋊Q8C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#19952
C2×#15032
#138482
C2×#13032
C2×#12742