Finite Group Databasebeta

← #481544

Subgroups — #481544

Order 512.

928 conjugacy classes of subgroups.

The subgroup lattice has 559 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34627C211yesmaximal, characteristic
2C4×#413C211yesmaximal, characteristic
3#17349C211yesmaximal, characteristic
4#11739C214yesmaximal, complemented
5#11736C214yesmaximal, complemented
6#11724C212yesmaximal, complemented
7#11700C212yesmaximal, complemented
8C2×#533C411yescharacteristic
9C2×C4×#41C2211yescharacteristic
10C2×#431—21no—
11C2×#413—21no—
12C2×C4×M16—21no—
13#2638C412yes—
14#2638C2212yes—
15#2634—21no—
16#2633—21no—
17#2628C411yescharacteristic
18#2628C2211yescharacteristic
19#2625—21no—
20#2621C411yescharacteristic
21#2621C2211yescharacteristic
22#2616—21no—
23#2399C2212yes—
24#2398C412yes—
25#2395—21no—
26#2395—21no—
27C4×C22⋊Q8—21no—
28C4×C22⋊Q8—21no—
29#2283C411yescharacteristic
30C4×#101—21no—
31C4×#101C2212yes—
32C4×#100—21no—
33C4×#100C2212yes—
34#1742C2212yes—
35#1461C2212yes—
36#1460—21no—
37#1459—21no—
38#1459C2212yes—
39#1458—21no—
40#1458C2212yes—
41#1354C2218yes—
42#1346C2218yes—
43C22×#41D411yescharacteristic
44C22×M16—22no—
45#533—41no—
46#533—41no—
47#533—41no—
48#533—41no—
49C2×C4⋊Q8C2×C411yescharacteristic
50C2×C4⋊Q8C2×C411yescharacteristic
51C2×#125—21no—
52C2×C22⋊Q8—21no—
53C2×C22⋊Q8—21no—
54C2×C22⋊Q8—21no—
55C2×C22⋊Q8C2×C412yes—
56C4×#41—41no—
57C4×#41—41no—
58C4×#41—41no—
59C4×#41—41no—
60C2×C4×Q8—21no—
61C2×C4×Q8C2×C412yes—
62C2×C4×Q8D411yescharacteristic
63C2×C4×Q8C2311yescharacteristic
64C2×C4×D4C2×C411yescharacteristic
65C2×C4×D4C2×C411yescharacteristic
66C2×C4×D4D411yescharacteristic
67C2×C4×D4D411yescharacteristic
68C2×C4×D4D411yescharacteristic
69C2×C4×D4C2311yescharacteristic
70C2×#117—21no—
71C2×#117C2×C411yescharacteristic
72C2×#117D411yescharacteristic
73C2×#117C2311yescharacteristic
74C22×C42C2×C411yescharacteristic
75C22×C42D411yescharacteristic
76C22×C42D411yescharacteristic
77#431—22no—
78#431—22no—
79#431—41no—
80#431—41no—
81C2×C4⋊C8—41no—
82#413—28no—
83C2×#101—22no—
84C2×#100—22no—
85C2×C22⋊C8—22no—
86C4×M16—22no—
87C4×M16—22no—
88C4×M16—41no—
89C4×M16—41no—
90C2×#97—41no—
91C2×C4×C8—41no—
92C2×C4×C8—41no—
93#400—22no—
94#400—21no—
95#400—21no—
96#399—21no—
97#399—21no—
98#398—21no—
99#398—21no—
100#398—22no—
101#398C2×C412yes—
102#398C2312yes—
103#397—21no—
104#397—22no—
105#397—21no—
106#397—22no—
107#397C2×C412yes—
108#397C2×C412yes—
109#395—22no—
110#395C2×C412yes—
111#395C2312yes—
112#394—22no—
113#394—22no—
114#394—22no—
115#393C2×C412yes—
116#393C2×C412yes—
117#391—21no—
118#391—21no—
119#389—21no—
120#389—21no—
121#387—22no—
122#387—22no—
123#385—22no—
124#385—22no—
125#383—21no—
126#382C2×C411yescharacteristic
127#382C2×C411yescharacteristic
128#381C2×C412yes—
129#380—21no—
130#380—21no—
131#380—21no—
132C4×C4⋊C4—21no—
133C4×C4⋊C4—22no—
134C4×C4⋊C4—22no—
135C4×C22⋊C4—21no—
136C4×C22⋊C4—22no—
137C4×C22⋊C4—22no—
138#376C2×C412yes—
139#343—22no—
140#343C2314yes—
141#324—22no—
142#324C2314yes—
143#323—22no—
144#323—22no—
145C2×#41—24no—
146C2×#41—24no—
147C2×#41—41no—
148C2×#41—41no—
149C22×Q8—21no—
150C22×Q8C22×C412yes—
151C22×Q8C2×D411yescharacteristic
152C22×D4C22⋊C411yescharacteristic
153C22×D4C22⋊C411yescharacteristic
154C22×D4C2×D411yescharacteristic
155C23×C4C22⋊C411yescharacteristic
156C23×C4C22⋊C411yescharacteristic
157C23×C4C22⋊C411yescharacteristic
158C23×C4C22⋊C411yescharacteristic
159C23×C4C22⋊C411yescharacteristic
160C23×C4C22⋊C411yescharacteristic
161C23×C4C22×C411yescharacteristic
162C23×C4C2×D411yescharacteristic
163C23×C4C2×D411yescharacteristic
164C2×M16—28no—
165C2×M16—24no—
166C2×M16—42no—
167C2×M16—44no—
168C22×C8—42no—
169C22×C8—42no—
170C4⋊Q8—41no—
171C4⋊Q8—41no—
172C4⋊Q8—41no—
173C4⋊Q8—41no—
174#125—42no—
175#125—42no—
176C22⋊Q8—42no—
177C22⋊Q8—42no—
178C22⋊Q8—44no—
179C22⋊Q8—44no—
180C22⋊Q8—42no—
181C22⋊Q8—42no—
182C4×Q8—41no—
183C4×Q8—41no—
184C4×Q8—41no—
185C4×Q8—41no—
186C4×Q8—42no—
187C4×Q8—42no—
188C4×Q8—41no—
189C4×Q8—41no—
190C4×Q8—41no—
191C4×Q8—41no—
192C4×D4—41no—
193C4×D4—41no—
194C4×D4—41no—
195C4×D4—41no—
196C4×D4—41no—
197C4×D4—41no—
198C4×D4—41no—
199C4×D4—41no—
200C4×D4—41no—
201C4×D4—41no—
202C4×D4—41no—
203C4×D4—41no—
204#117—41no—
205#117—41no—
206#117—41no—
207#117—41no—
208#117—41no—
209#117—41no—
210#117—42no—
211#117—42no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4C22⋊C411yescharacteristic
224C2×C4⋊C4C22⋊C411yescharacteristic
225C2×C4⋊C4C22×C412yes—
226C2×C4⋊C4C22×C411yescharacteristic
227C2×C4⋊C4C2×D411yescharacteristic
228C2×C4⋊C4C2×D411yescharacteristic
229C2×C4⋊C4C2411yescharacteristic
230C2×C22⋊C4—22no—
231C2×C22⋊C4—22no—
232C2×C22⋊C4—22no—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—22no—
235C2×C22⋊C4—22no—
236C2×C22⋊C4C22⋊C411yescharacteristic
237C2×C22⋊C4C22⋊C411yescharacteristic
238C2×C22⋊C4C22×C411yescharacteristic
239C2×C22⋊C4C22×C411yescharacteristic
240C2×C22⋊C4C2×D411yescharacteristic
241C2×C22⋊C4C2×D411yescharacteristic
242C2×C42—21no—
243C2×C42—21no—
244C2×C42—21no—
245C2×C42—21no—
246C2×C42—21no—
247C2×C42—21no—
248C2×C42—21no—
249C2×C42—21no—
250C2×C42—21no—
251C2×C42—21no—
252C2×C42—21no—
253C2×C42—21no—
254C2×C42—22no—
255C2×C42—22no—
256C2×C42C22⋊C411yescharacteristic
257C2×C42C22⋊C411yescharacteristic
258C2×C42C22⋊C411yescharacteristic
259C2×C42C22⋊C411yescharacteristic
260C2×C42C22×C411yescharacteristic
261C2×C42C22×C411yescharacteristic
262C2×C42C2×D411yescharacteristic
263C2×C42C2×D411yescharacteristic
264C2×C42C2×D411yescharacteristic
265C2×C42C2×D411yescharacteristic
266C4⋊C8—42no—
267C4⋊C8—42no—
268#101—28no—
269#100—28no—
270C22⋊C8—24no—
271C22⋊C8—42no—
272#97—42no—
273#97—42no—
274C4×C8—42no—
275C4×C8—42no—
276C4×C8—42no—
277C4×C8—42no—
278#95—22no—
279#95—21no—
280#95—21no—
281#95—22no—
282#95—22no—
283#95—22no—
284#95—22no—
285#95—22no—
286#95—22no—
287#95—22no—
288#95—22no—
289#95—22no—
290#95C22×C412yes—
291#95C22×C412yes—
292C24C2×C22⋊C411yescharacteristic
293C24C2×C22⋊C411yescharacteristic
294C24C2×C22⋊C411yescharacteristic
295#41—48no—
296#41—48no—
297C2×Q8—22no—
298C2×Q8—22no—
299C2×Q8—41no—
300C2×Q8—42no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—42no—
304C2×Q8—42no—
305C2×Q8—82no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—22no—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4—22no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—81no—
345C22×C4—81no—
346C22×C4—81no—
347C22×C4#10414yes—
348C22×C4C2×C22⋊C411yescharacteristic
349C22×C4C2×C22⋊C411yescharacteristic
350C22×C4C2×C22⋊C411yescharacteristic
351C22×C4C2×C22⋊C411yescharacteristic
352C22×C4C2×C22⋊C411yescharacteristic
353C22×C4C2×C22⋊C411yescharacteristic
354C22×C4C2×C22⋊C411yescharacteristic
355C22×C4C2×C22⋊C411yescharacteristic
356C22×C4C2×C22⋊C411yescharacteristic
357C22×C4#13514yes—
358C22×C4C23×C411yescharacteristic
359C22×C4C22×D411yescharacteristic
360C22×C4C22×D411yescharacteristic
361M16—28no—
362M16—48no—
363M16—44no—
364C2×C8—44no—
365C2×C8—48no—
366C2×C8—44no—
367C2×C8—84no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—42no—
375C4⋊C4—42no—
376C4⋊C4—42no—
377C4⋊C4—44no—
378C4⋊C4—44no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—42no—
382C4⋊C4—42no—
383C4⋊C4—42no—
384C4⋊C4—42no—
385C4⋊C4—44no—
386C4⋊C4—82no—
387C4⋊C4—82no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—44no—
395C22⋊C4—44no—
396C22⋊C4—44no—
397C22⋊C4—82no—
398C22⋊C4—82no—
399C22⋊C4—82no—
400C42—21no—
401C42—21no—
402C42—21no—
403C42—21no—
404C42—21no—
405C42—21no—
406C42—21no—
407C42—21no—
408C42—21no—
409C42—21no—
410C42—21no—
411C42—21no—
412C42—21no—
413C42—21no—
414C42—21no—
415C42—21no—
416C42—21no—
417C42—21no—
418C42—44no—
419C42—42no—
420C42—42no—
421C42#9911yescharacteristic
422C42#9911yescharacteristic
423C42#9911yescharacteristic
424C42#9911yescharacteristic
425C23—21no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23#41612yes—
439C23C2×#10412yes—
440C23C22×C22⋊C411yescharacteristic
441Q8—44no—
442Q8—84no—
443Q8—82no—
444Q8—82no—
445D4—44no—
446D4—44no—
447D4—44no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—81no—
494C2×C4—81no—
495C2×C4—81no—
496C2×C4—81no—
497C2×C4—81no—
498C2×C4—81no—
499C2×C4C2×#9911yescharacteristic
500C2×C4C2×#9911yescharacteristic
501C2×C4C2×#9911yescharacteristic
502C2×C4C2×#9911yescharacteristic
503C2×C4C2×#9911yescharacteristic
504C2×C4C2×#9911yescharacteristic
505C2×C4#41612yes—
506C2×C4C2×#10412yes—
507C2×C4C2×#10412yes—
508C2×C4C2×#13512yes—
509C8—48no—
510C8—84no—
511C22—21no—
512C22—21no—
513C22—22no—
514C22—22no—
515C22—42no—
516C22—42no—
517C22—41no—
518C22—41no—
519C22—41no—
520C22—41no—
521C22—41no—
522C22—41no—
523C22—41no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22—81no—
528C22C22×#9911yescharacteristic
529C22C2×#41611yescharacteristic
530C22C22×#10411yescharacteristic
531C4—21no—
532C4—21no—
533C4—21no—
534C4—22no—
535C4—22no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—82no—
544C4—82no—
545C4—82no—
546C4—82no—
547C4#150112yes—
548C4#150112yes—
549C4#213512yes—
550C2—21no—
551C2—21no—
552C2—42no—
553C2—42no—
554C2—81no—
555C2C2×#150111yescharacteristic
556C2#3334711yescharacteristic
557C2C2×#213511yescharacteristic
subgroupG/H
centerC2×C4C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
socleC22C22×#99
prime radicalC22×#41D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×#41 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #11739C2semidirect
5. #11736C2semidirect
6. #11724C2semidirect
7. #11700C2semidirect

Maximal subgroups

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

subgroupindex
#346272
C4×#4132
#173492
#117392
#117362
#117242
#117002