Finite Group Databasebeta

← C2×#10191 #237203

Subgroups — C2×#10191 #237203

Order 512.

1274 conjugacy classes of subgroups.

The subgroup lattice has 603 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3230C211yesmaximal, characteristic
2C2×#3078C211yesmaximal, characteristic
3C22×#475C211yesmaximal, characteristic
4C2×#1548C211yesmaximal, characteristic
5C2×#1481C211yesmaximal, characteristic
6C2×#1461C211yesmaximal, characteristic
7#10191C218yesmaximal, direct product factor
8C2×#1301C211yesmaximal, characteristic
9C2×#533C2211yescharacteristic
10C22×C4⋊Q8C2211yescharacteristic
11C22×C4×Q8C2211yescharacteristic
12#3230—22no—
13#3230—22no—
14#3230—22no—
15#3230C2214yes—
16C2×#500—21no—
17C2×#487—21no—
18C2×#484—22no—
19#3078—22no—
20#3078—22no—
21#3078—22no—
22#3078C2214yes—
23C2×#479—22no—
24C2×#477—21no—
25C2×#477—22no—
26C2×#475—22no—
27C2×#475—22no—
28C2×#475—22no—
29C2×#475—22no—
30C2×#475—21no—
31C2×#475—22no—
32C2×#475C2214yes—
33C2×#431C2211yescharacteristic
34C2×#431C2211yescharacteristic
35C2×#428—21no—
36C22×#106—21no—
37C2×#423C2211yescharacteristic
38C22×C4⋊C8C2211yescharacteristic
39C2×#419—21no—
40C22×#103—21no—
41#1548—22no—
42#1548C2214yes—
43C2×#333—22no—
44#1481—22no—
45#1481C2214yes—
46C2×Q8⋊C8—22no—
47#1461—22no—
48#1461C2214yes—
49C2×#324—22no—
50#1301C2214yes—
51C23×Q8—21no—
52C23×Q8D411yescharacteristic
53C22×M16—21no—
54C23×C8—21no—
55#533—21no—
56#533—21no—
57#533—21no—
58#533—21no—
59#533—21no—
60#533—21no—
61#533D412yes—
62#533C2312yes—
63C2×C4⋊Q8—21no—
64C2×C4⋊Q8—21no—
65C2×C4⋊Q8—21no—
66C2×C4⋊Q8—21no—
67C2×C4⋊Q8—21no—
68C2×C4⋊Q8—21no—
69C2×C4⋊Q8—21no—
70C2×C4⋊Q8—21no—
71C2×C4⋊Q8—21no—
72C2×C4⋊Q8D412yes—
73C2×C4⋊Q8D411yescharacteristic
74C2×C4⋊Q8D412yes—
75C2×C4⋊Q8D411yescharacteristic
76C2×C4⋊Q8C2312yes—
77C2×#125—21no—
78C2×C22⋊Q8—21no—
79C2×C22⋊Q8—21no—
80C2×C4×Q8—21no—
81C2×C4×Q8—21no—
82C2×C4×Q8—21no—
83C2×C4×Q8—21no—
84C2×C4×Q8—21no—
85C2×C4×Q8—21no—
86C2×C4×Q8—21no—
87C2×C4×Q8—21no—
88C2×C4×Q8—21no—
89C2×C4×Q8—21no—
90C2×C4×Q8—21no—
91C2×C4×Q8—21no—
92C2×C4×Q8D412yes—
93C2×C4×Q8C2312yes—
94C2×#117—21no—
95C22×C4⋊C4—21no—
96C22×C4⋊C4—21no—
97C22×C4⋊C4—21no—
98C22×C4⋊C4D411yescharacteristic
99C22×C42—21no—
100C22×C42C2311yescharacteristic
101#500—24no—
102#500—24no—
103#487—24no—
104#487—24no—
105#484—28no—
106#484—28no—
107#479—28no—
108#479—28no—
109#477—24no—
110#477—28no—
111#477—24no—
112#477—28no—
113#475—28no—
114#475—28no—
115#475—24no—
116#475—28no—
117#475—24no—
118#475—28no—
119#431—21no—
120#431—21no—
121#431—21no—
122#431—21no—
123#431—21no—
124#431D412yes—
125#431C2312yes—
126#431C2312yes—
127#428—24no—
128#428—24no—
129C2×#107—22no—
130C2×#107—24no—
131C2×#106—24no—
132C2×#106—24no—
133C2×#106—22no—
134C2×#106—24no—
135#423—21no—
136#423—21no—
137#423D412yes—
138#423C2312yes—
139C2×C4⋊C8—21no—
140C2×C4⋊C8—21no—
141C2×C4⋊C8—21no—
142C2×C4⋊C8—21no—
143C2×C4⋊C8—21no—
144C2×C4⋊C8—21no—
145C2×C4⋊C8D412yes—
146C2×C4⋊C8D412yes—
147C2×C4⋊C8D412yes—
148C2×C4⋊C8C2312yes—
149#419—24no—
150#419—24no—
151C2×#103—24no—
152C2×#103—24no—
153C2×#103—22no—
154C2×#103—22no—
155C2×#103—24no—
156C2×#103—24no—
157C2×C22⋊C8—21no—
158C2×C22⋊C8D412yes—
159C2×C4×C8—21no—
160C2×C4×C8—21no—
161#333—28no—
162Q8⋊C8—28no—
163#324—28no—
164C22×Q8—21no—
165C22×Q8—22no—
166C22×Q8—21no—
167C22×Q8—21no—
168C22×Q8—21no—
169C22×Q8—21no—
170C22×Q8—21no—
171C22×Q8—21no—
172C22×Q8—22no—
173C22×Q8—22no—
174C22×Q8—22no—
175C22×Q8—22no—
176C22×Q8—22no—
177C22×Q8—41no—
178C22×Q8—41no—
179C22×Q8—41no—
180C22×Q8—84no—
181C22×Q8Q1614yes—
182C22×Q8C2×D412yes—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—41no—
186C23×C4C2×D411yescharacteristic
187C23×C4C2×D411yescharacteristic
188C23×C4#4111yescharacteristic
189C2×M16—22no—
190C2×M16—22no—
191C2×M16—42no—
192C2×M16—42no—
193C22×C8—22no—
194C22×C8—22no—
195C22×C8—22no—
196C22×C8—22no—
197C22×C8—22no—
198C22×C8—42no—
199C22×C8—42no—
200C22×C8—41no—
201C4⋊Q8—22no—
202C4⋊Q8—22no—
203C4⋊Q8—22no—
204C4⋊Q8—22no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—22no—
211C4⋊Q8—22no—
212C4⋊Q8—21no—
213C4⋊Q8—22no—
214C4⋊Q8—22no—
215C4⋊Q8—22no—
216C4⋊Q8—41no—
217C4⋊Q8—41no—
218C4⋊Q8—41no—
219C4⋊Q8—41no—
220C4⋊Q8—41no—
221C4⋊Q8—41no—
222C4⋊Q8C2×D414yes—
223C4⋊Q8C2×D412yes—
224C4⋊Q8C2×D412yes—
225#125—22no—
226#125—22no—
227#125—41no—
228#125—41no—
229C22⋊Q8—22no—
230C22⋊Q8—22no—
231C22⋊Q8—22no—
232C22⋊Q8—22no—
233C22⋊Q8—41no—
234C22⋊Q8—41no—
235C22⋊Q8—41no—
236C22⋊Q8—41no—
237C4×Q8—22no—
238C4×Q8—22no—
239C4×Q8—22no—
240C4×Q8—22no—
241C4×Q8—22no—
242C4×Q8—22no—
243C4×Q8—22no—
244C4×Q8—22no—
245C4×Q8—22no—
246C4×Q8—22no—
247C4×Q8—22no—
248C4×Q8—22no—
249C4×Q8—41no—
250C4×Q8—41no—
251C4×Q8—41no—
252C4×Q8—41no—
253C4×Q8—41no—
254C4×Q8—41no—
255C4×Q8—41no—
256C4×Q8—41no—
257C4×Q8—41no—
258C4×Q8—41no—
259C4×Q8—41no—
260C4×Q8—41no—
261#117—22no—
262#117—22no—
263#117—41no—
264#117—41no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—41no—
283C2×C4⋊C4—41no—
284C2×C4⋊C4—41no—
285C2×C4⋊C4—41no—
286C2×C4⋊C4—41no—
287C2×C4⋊C4—41no—
288C2×C4⋊C4—41no—
289C2×C4⋊C4—41no—
290C2×C4⋊C4—41no—
291C2×C4⋊C4—41no—
292C2×C4⋊C4—41no—
293C2×C4⋊C4—41no—
294C2×C4⋊C4C2×D412yes—
295C2×C22⋊C4—41no—
296C2×C42—22no—
297C2×C42—22no—
298C2×C42—41no—
299C2×C42—41no—
300C2×C42—41no—
301C2×C42—41no—
302C2×C42—41no—
303C2×C42C2×D411yescharacteristic
304C2×C42C2×D411yescharacteristic
305C2×C42C2×D411yescharacteristic
306C2×C42C2×D411yescharacteristic
307C2×C42C2×D411yescharacteristic
308C2×C42C2×D411yescharacteristic
309C2×C42C2×D411yescharacteristic
310C2×C42C2×D411yescharacteristic
311C2×C42C2×D411yescharacteristic
312C2×C42C2×D411yescharacteristic
313C2×C42#4111yescharacteristic
314C2×C42C2411yescharacteristic
315#107—28no—
316#107—216no—
317#106—216no—
318#106—28no—
319C4⋊C8—22no—
320C4⋊C8—22no—
321C4⋊C8—22no—
322C4⋊C8—22no—
323C4⋊C8—22no—
324C4⋊C8—22no—
325C4⋊C8—22no—
326C4⋊C8—22no—
327C4⋊C8—22no—
328C4⋊C8—41no—
329C4⋊C8C2×D414yes—
330C4⋊C8C2×D414yes—
331#103—216no—
332#103—28no—
333#103—28no—
334#103—216no—
335C22⋊C8—22no—
336C22⋊C8—22no—
337C22⋊C8—41no—
338C22⋊C8C2×D414yes—
339C4×C8—22no—
340C4×C8—22no—
341C4×C8—22no—
342C4×C8—41no—
343C24#12111yescharacteristic
344C2×Q8—22no—
345C2×Q8—24no—
346C2×Q8—22no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8—24no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—24no—
354C2×Q8—24no—
355C2×Q8—24no—
356C2×Q8—24no—
357C2×Q8—44no—
358C2×Q8—42no—
359C2×Q8—41no—
360C2×Q8—41no—
361C2×Q8—41no—
362C2×Q8—41no—
363C2×Q8—42no—
364C2×Q8—42no—
365C2×Q8—42no—
366C2×Q8—42no—
367C2×Q8—42no—
368C2×Q8—42no—
369C2×Q8—42no—
370C2×Q8—44no—
371C2×Q8—84no—
372C2×Q8—84no—
373C2×Q8—84no—
374C2×Q8—84no—
375C2×Q8—84no—
376C2×Q8—84no—
377C2×Q8C2×Q1614yes—
378C22×C4—24no—
379C22×C4—22no—
380C22×C4—24no—
381C22×C4—22no—
382C22×C4—42no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—41no—
388C22×C4—42no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—42no—
393C22×C4—84no—
394C22×C4—82no—
395C22×C4#12011yescharacteristic
396C22×C4#12011yescharacteristic
397C22×C4#12011yescharacteristic
398C22×C4#12011yescharacteristic
399C22×C4#12011yescharacteristic
400C22×C4#12011yescharacteristic
401C22×C4#12111yescharacteristic
402C22×C4#12111yescharacteristic
403C22×C4#12111yescharacteristic
404C22×C4#12111yescharacteristic
405C22×C4#12111yescharacteristic
406C22×C4#12111yescharacteristic
407C22×C4#12111yescharacteristic
408C22×C4#12711yescharacteristic
409C22×C4#12711yescharacteristic
410C22×C4C2×Q1612yes—
411C22×C4#13512yes—
412C22×C4#13712yes—
413C22×C4#13712yes—
414C22×C4C22×D411yescharacteristic
415C22×C4C22×D411yescharacteristic
416C22×C4C2×#4111yescharacteristic
417M16—42no—
418M16—42no—
419M16—44no—
420C2×C8—24no—
421C2×C8—24no—
422C2×C8—24no—
423C2×C8—44no—
424C2×C8—42no—
425C2×C8—42no—
426C2×C8—44no—
427C2×C8—44no—
428C2×C8—44no—
429C2×C8—42no—
430C2×C8—82no—
431C4⋊C4—24no—
432C4⋊C4—22no—
433C4⋊C4—24no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—42no—
440C4⋊C4—42no—
441C4⋊C4—42no—
442C4⋊C4—42no—
443C4⋊C4—42no—
444C4⋊C4—42no—
445C4⋊C4—41no—
446C4⋊C4—41no—
447C4⋊C4—42no—
448C4⋊C4—42no—
449C4⋊C4—42no—
450C4⋊C4—42no—
451C4⋊C4—42no—
452C4⋊C4—42no—
453C4⋊C4—41no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—42no—
458C4⋊C4—42no—
459C22⋊C4—42no—
460C22⋊C4—42no—
461C42—42no—
462C42—42no—
463C42—42no—
464C42—42no—
465C42—42no—
466C42—42no—
467C42#12011yescharacteristic
468C42#12011yescharacteristic
469C42#12011yescharacteristic
470C42#12011yescharacteristic
471C42#12011yescharacteristic
472C42#12011yescharacteristic
473C42#12111yescharacteristic
474C42#12111yescharacteristic
475C42#12111yescharacteristic
476C42#12111yescharacteristic
477C42#12711yescharacteristic
478C42#12711yescharacteristic
479C42C22×D411yescharacteristic
480C42C22×D411yescharacteristic
481C42C22×D411yescharacteristic
482C42C22×D411yescharacteristic
483C23—22no—
484C23—22no—
485C23#39211yescharacteristic
486C23#39211yescharacteristic
487C23#46712yes—
488C23#47012yes—
489C23C2×#12111yescharacteristic
490Q8—24no—
491Q8—24no—
492Q8—44no—
493Q8—42no—
494Q8—42no—
495Q8—44no—
496Q8—44no—
497Q8—44no—
498Q8—84no—
499Q8—82no—
500Q8—84no—
501Q8—82no—
502Q8—84no—
503Q8—84no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—44no—
518C2×C4—44no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—44no—
524C2×C4—82no—
525C2×C4—84no—
526C2×C4—84no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4—84no—
530C2×C4—82no—
531C2×C4—82no—
532C2×C4#39211yescharacteristic
533C2×C4#39211yescharacteristic
534C2×C4#39211yescharacteristic
535C2×C4#39211yescharacteristic
536C2×C4#39211yescharacteristic
537C2×C4#39211yescharacteristic
538C2×C4#45112yes—
539C2×C4#45112yes—
540C2×C4#45112yes—
541C2×C4#45112yes—
542C2×C4#45212yes—
543C2×C4#45212yes—
544C2×C4#45212yes—
545C2×C4#45212yes—
546C2×C4#46712yes—
547C2×C4#47012yes—
548C2×C4#47114yes—
549C2×C4C2×#12011yescharacteristic
550C2×C4C2×#12011yescharacteristic
551C2×C4C2×#12011yescharacteristic
552C2×C4C2×#12111yescharacteristic
553C2×C4C2×#12111yescharacteristic
554C2×C4C2×#12711yescharacteristic
555C2×C4C22×Q1611yescharacteristic
556C2×C4C2×#13511yescharacteristic
557C2×C4C2×#13711yescharacteristic
558C2×C4C2×#13711yescharacteristic
559C8—44no—
560C8—44no—
561C8—44no—
562C8—82no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—24no—
568C22—24no—
569C22#200112yes—
570C22#200112yes—
571C22#200912yes—
572C22#201912yes—
573C22C2×#39211yescharacteristic
574C22C2×#46711yescharacteristic
575C22C2×#47011yescharacteristic
576C4—21no—
577C4—21no—
578C4—21no—
579C4—21no—
580C4—21no—
581C4—21no—
582C4—44no—
583C4—82no—
584C4—82no—
585C4—84no—
586C4—82no—
587C4#200112yes—
588C4#200112yes—
589C4#201912yes—
590C4C2×#45111yescharacteristic
591C4C2×#45111yescharacteristic
592C4C2×#45211yescharacteristic
593C4C2×#45211yescharacteristic
594C4C2×#47112yes—
595C2—22no—
596C2—21no—
597C2—21no—
598C2#1019114yesdirect product factor
599C2C2×#200111yescharacteristic
600C2C2×#200911yescharacteristic
601C2C2×#201911yescharacteristic
subgroupG/H
center, socleC23#392
commutator, Frattini, cosocleC2×C42C24
prime radicalC24#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
7. #10191C2direct (N × H)
598. C2#10191direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#32302
C2×#30782
C22×#4752
C2×#15482
C2×#14812
C2×#14612
#101912
C2×#13012