Finite Group Databasebeta

← C2×#9092 #196085

Subgroups — C2×#9092 #196085

Order 512.

1250 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
1C2×#2983C211yesmaximal, characteristic
2C22×#441C211yesmaximal, characteristic
3C2×#1479C211yesmaximal, characteristic
4C2×#1479C211yesmaximal, characteristic
5C2×#1461C211yesmaximal, characteristic
6#9092C218yesmaximal, direct product factor
7C2×#1281C211yesmaximal, characteristic
8C2×#1275C211yesmaximal, characteristic
9C23×Q16C411yescharacteristic
10C22×C4×Q8C2211yescharacteristic
11C22×C4×Q8C2211yescharacteristic
12#2983—22no—
13#2983—22no—
14#2983—22no—
15#2983C2214yes—
16C2×#446—22no—
17C2×#446—22no—
18C2×#441—22no—
19C2×#441—22no—
20C2×#441—22no—
21C2×#441—22no—
22C2×#441C414yes—
23C2×#441C2214yes—
24C2×#432—22no—
25C2×#431C2211yescharacteristic
26C2×#431C2211yescharacteristic
27C2×#431C2211yescharacteristic
28C2×#431C2211yescharacteristic
29C22×#106C411yescharacteristic
30C22×#103C411yescharacteristic
31C22×#103C411yescharacteristic
32C22×#97C2211yescharacteristic
33#1479—22no—
34#1479—22no—
35#1479C2214yes—
36#1479C2214yes—
37C2×Q8⋊C8—22no—
38C2×Q8⋊C8—22no—
39#1461—22no—
40#1461C2214yes—
41C2×#324—22no—
42#1281C2214yes—
43#1275C2214yes—
44C23×Q8C2×C411yescharacteristic
45C23×Q8C2×C411yescharacteristic
46C22×Q16—22no—
47C22×Q16—22no—
48C22×Q16—24no—
49C22×Q16—24no—
50C22×Q16C2×C414yes—
51C23×C8C2×C411yescharacteristic
52C23×C8C2×C411yescharacteristic
53C2×C4×Q8—21no—
54C2×C4×Q8—21no—
55C2×C4×Q8—21no—
56C2×C4×Q8—21no—
57C2×C4×Q8—21no—
58C2×C4×Q8—21no—
59C2×C4×Q8—21no—
60C2×C4×Q8—21no—
61C2×C4×Q8—21no—
62C2×C4×Q8—21no—
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×Q8C2×C412yes—
70C2×C4×Q8C2×C412yes—
71C2×C4×Q8D412yes—
72C2×C4×Q8D412yes—
73C2×C4×Q8D412yes—
74C2×C4×Q8D412yes—
75C2×C4×Q8C2312yes—
76C2×C4×Q8C2312yes—
77C22×C4⋊C4—21no—
78C22×C4⋊C4—21no—
79C22×C4⋊C4C2×C411yescharacteristic
80C22×C4⋊C4C2×C411yescharacteristic
81C22×C42—21no—
82C22×C42—21no—
83C22×C42C2311yescharacteristic
84#446—28no—
85#446—28no—
86#446—28no—
87#446—28no—
88#441—28no—
89#441—28no—
90#441—28no—
91#441—28no—
92#432—28no—
93#432—28no—
94#431—21no—
95#431—21no—
96#431—21no—
97#431—21no—
98#431—21no—
99#431—21no—
100#431—21no—
101#431—21no—
102#431—21no—
103#431—21no—
104#431D412yes—
105#431D412yes—
106#431C2312yes—
107#431C2312yes—
108#431C2312yes—
109#431C2312yes—
110C2×#106—22no—
111C2×#106—22no—
112C2×#106C2×C414yes—
113C2×C4⋊C8—24no—
114C2×C4⋊C8—21no—
115C2×C4⋊C8—21no—
116C2×C4⋊C8—21no—
117C2×C4⋊C8—21no—
118C2×#103—22no—
119C2×#103—22no—
120C2×#103—22no—
121C2×#103—22no—
122C2×#103C2×C414yes—
123C2×#103C2×C414yes—
124C2×C22⋊C8—21no—
125C2×C22⋊C8—21no—
126C2×C22⋊C8—21no—
127C2×C22⋊C8D412yes—
128C2×#97—24no—
129C2×#97—21no—
130C2×#97—21no—
131C2×#97—21no—
132C2×#97—21no—
133C2×#97C2×C412yes—
134C2×#97C2312yes—
135C2×C4×C8—21no—
136C2×C4×C8—21no—
137C2×C4×C8—21no—
138C2×C4×C8D412yes—
139Q8⋊C8—28no—
140Q8⋊C8—28no—
141#324—28no—
142C22×Q8—21no—
143C22×Q8—21no—
144C22×Q8—21no—
145C22×Q8—21no—
146C22×Q8—22no—
147C22×Q8—21no—
148C22×Q8—21no—
149C22×Q8—21no—
150C22×Q8—21no—
151C22×Q8—22no—
152C22×Q8—22no—
153C22×Q8—22no—
154C22×Q8—22no—
155C22×Q8—22no—
156C22×Q8—22no—
157C22×Q8C22⋊C412yes—
158C22×Q8C22⋊C412yes—
159C22×Q8M1614yes—
160C22×Q8C22×C412yes—
161C22×Q8C22×C412yes—
162C23×C4—21no—
163C23×C4—21no—
164C23×C4—21no—
165C23×C4—21no—
166C23×C4C22×C411yescharacteristic
167C23×C4C2×D411yescharacteristic
168C23×C4#4111yescharacteristic
169C2×Q16—216no—
170C2×Q16—216no—
171C2×Q16—28no—
172C2×Q16—28no—
173C2×Q16—28no—
174C22×C8—21no—
175C22×C8—21no—
176C22×C8—22no—
177C22×C8—21no—
178C22×C8—21no—
179C22×C8—22no—
180C22×C8—22no—
181C22×C8—22no—
182C22×C8—22no—
183C22×C8—41no—
184C22×C8—41no—
185C22×C8M1614yes—
186C22×C8C22×C412yes—
187C22×C8C22×C412yes—
188C4×Q8—22no—
189C4×Q8—22no—
190C4×Q8—22no—
191C4×Q8—22no—
192C4×Q8—22no—
193C4×Q8—22no—
194C4×Q8—22no—
195C4×Q8—22no—
196C4×Q8—22no—
197C4×Q8—22no—
198C4×Q8—22no—
199C4×Q8—22no—
200C4×Q8—22no—
201C4×Q8—22no—
202C4×Q8—22no—
203C4×Q8—22no—
204C4×Q8—22no—
205C4×Q8—22no—
206C4×Q8—22no—
207C4×Q8—22no—
208C4×Q8—41no—
209C4×Q8—41no—
210C4×Q8—41no—
211C4×Q8—41no—
212C4×Q8—41no—
213C4×Q8—41no—
214C4×Q8—41no—
215C4×Q8—41no—
216C4×Q8C22⋊C414yes—
217C4×Q8C22⋊C414yes—
218C4×Q8C2×D414yes—
219C4×Q8C2×D414yes—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—41no—
237C2×C4⋊C4—41no—
238C2×C4⋊C4—41no—
239C2×C4⋊C4—41no—
240C2×C4⋊C4C22⋊C412yes—
241C2×C4⋊C4C22⋊C412yes—
242C2×C4⋊C4C22×C412yes—
243C2×C4⋊C4C22×C412yes—
244C2×C42—22no—
245C2×C42—22no—
246C2×C42—22no—
247C2×C42—22no—
248C2×C42—22no—
249C2×C42—22no—
250C2×C42—22no—
251C2×C42—22no—
252C2×C42—41no—
253C2×C42—41no—
254C2×C42—41no—
255C2×C42—41no—
256C2×C42C22×C411yescharacteristic
257C2×C42C2×D411yescharacteristic
258C2×C42C2×D411yescharacteristic
259C2×C42C2×D411yescharacteristic
260C2×C42C2×D411yescharacteristic
261C2×C42C2×D411yescharacteristic
262C2×C42C2×D411yescharacteristic
263C2×C42C2×D411yescharacteristic
264C2×C42#4111yescharacteristic
265C2×C42#4111yescharacteristic
266C2×C42#4111yescharacteristic
267C2×C42C2411yescharacteristic
268#106—28no—
269C4⋊C8—216no—
270C4⋊C8—22no—
271C4⋊C8—22no—
272C4⋊C8—22no—
273C4⋊C8—22no—
274C4⋊C8—22no—
275C4⋊C8—22no—
276C4⋊C8—41no—
277C4⋊C8—41no—
278#103—28no—
279#103—28no—
280C22⋊C8—22no—
281C22⋊C8—22no—
282C22⋊C8—22no—
283C22⋊C8—22no—
284C22⋊C8—22no—
285C22⋊C8—41no—
286C22⋊C8—41no—
287C22⋊C8C2×D414yes—
288#97—216no—
289#97—22no—
290#97—22no—
291#97—22no—
292#97—22no—
293C4×C8—22no—
294C4×C8—22no—
295C4×C8—22no—
296C4×C8—22no—
297C4×C8—22no—
298C4×C8—41no—
299C4×C8—41no—
300C4×C8C2×D414yes—
301C24C4×D411yescharacteristic
302C2×Q8—22no—
303C2×Q8—22no—
304C2×Q8—22no—
305C2×Q8—22no—
306C2×Q8—24no—
307C2×Q8—22no—
308C2×Q8—22no—
309C2×Q8—22no—
310C2×Q8—22no—
311C2×Q8—22no—
312C2×Q8—22no—
313C2×Q8—22no—
314C2×Q8—22no—
315C2×Q8—24no—
316C2×Q8—24no—
317C2×Q8—24no—
318C2×Q8—24no—
319C2×Q8—24no—
320C2×Q8—24no—
321C2×Q8—24no—
322C2×Q8—24no—
323C2×Q8—41no—
324C2×Q8—41no—
325C2×Q8—42no—
326C2×Q8—42no—
327C2×Q8—42no—
328C2×Q8—42no—
329C2×Q8—42no—
330C2×Q8—42no—
331C2×Q8—42no—
332C2×Q8—42no—
333C2×Q8—42no—
334C2×Q8—42no—
335C2×Q8—42no—
336C2×Q8C2×C22⋊C414yes—
337C2×Q8C2×M1614yes—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—24no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—82no—
357C22×C4—82no—
358C22×C4C2×C22⋊C411yescharacteristic
359C22×C4C2×C22⋊C411yescharacteristic
360C22×C4C4×D411yescharacteristic
361C22×C4C4×D411yescharacteristic
362C22×C4C4×D411yescharacteristic
363C22×C4C4×D411yescharacteristic
364C22×C4C4×D411yescharacteristic
365C22×C4#12011yescharacteristic
366C22×C4#12011yescharacteristic
367C22×C4#12111yescharacteristic
368C22×C4#12111yescharacteristic
369C22×C4#12111yescharacteristic
370C22×C4#12111yescharacteristic
371C22×C4#12311yescharacteristic
372C22×C4#12311yescharacteristic
373C22×C4C2×M1612yes—
374C22×C4C2×M1612yes—
375C22×C4#13112yes—
376C22×C4#13112yes—
377C22×C4C23×C411yescharacteristic
378C22×C4C22×D411yescharacteristic
379C22×C4C2×#4111yescharacteristic
380Q16—232no—
381C2×C8—22no—
382C2×C8—22no—
383C2×C8—24no—
384C2×C8—24no—
385C2×C8—22no—
386C2×C8—24no—
387C2×C8—24no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—44no—
391C2×C8—44no—
392C2×C8—42no—
393C2×C8—42no—
394C2×C8—42no—
395C2×C8—42no—
396C2×C8—82no—
397C2×C8—82no—
398C2×C8C2×M1614yes—
399C4⋊C4—22no—
400C4⋊C4—24no—
401C4⋊C4—24no—
402C4⋊C4—24no—
403C4⋊C4—24no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—42no—
409C4⋊C4—42no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4—42no—
413C4⋊C4—42no—
414C4⋊C4C2×C22⋊C414yes—
415C42—24no—
416C42—24no—
417C42—24no—
418C42—24no—
419C42—42no—
420C42—42no—
421C42—42no—
422C42—42no—
423C42C2×C22⋊C411yescharacteristic
424C42C2×C22⋊C411yescharacteristic
425C42C4×D411yescharacteristic
426C42C4×D411yescharacteristic
427C42#12011yescharacteristic
428C42#12011yescharacteristic
429C42#12111yescharacteristic
430C42#12111yescharacteristic
431C42#12111yescharacteristic
432C42#12111yescharacteristic
433C42#12311yescharacteristic
434C42#12311yescharacteristic
435C42C22×D411yescharacteristic
436C42C22×D411yescharacteristic
437C42C22×D411yescharacteristic
438C42C2×#4111yescharacteristic
439C23—22no—
440C23—22no—
441C23#38611yescharacteristic
442C23#38611yescharacteristic
443C23#43512yes—
444C23#43612yes—
445C23C2×C4×D411yescharacteristic
446Q8—24no—
447Q8—24no—
448Q8—24no—
449Q8—24no—
450Q8—42no—
451Q8—44no—
452Q8—44no—
453Q8—44no—
454Q8—44no—
455Q8—42no—
456Q8—42no—
457Q8—42no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—44no—
474C2×C4—44no—
475C2×C4—44no—
476C2×C4—44no—
477C2×C4—44no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—82no—
484C2×C4—82no—
485C2×C4—82no—
486C2×C4—82no—
487C2×C4—82no—
488C2×C4#38611yescharacteristic
489C2×C4#38611yescharacteristic
490C2×C4#38611yescharacteristic
491C2×C4#38611yescharacteristic
492C2×C4#38611yescharacteristic
493C2×C4#38611yescharacteristic
494C2×C4#40712yes—
495C2×C4#40712yes—
496C2×C4#40812yes—
497C2×C4#40812yes—
498C2×C4#43512yes—
499C2×C4#43512yes—
500C2×C4#43512yes—
501C2×C4#43612yes—
502C2×C4#43612yes—
503C2×C4#43612yes—
504C2×C4C22×C22⋊C411yescharacteristic
505C2×C4C2×C4×D411yescharacteristic
506C2×C4C2×#12011yescharacteristic
507C2×C4C2×#12111yescharacteristic
508C2×C4C2×#12111yescharacteristic
509C2×C4C2×#12311yescharacteristic
510C2×C4C22×M1611yescharacteristic
511C2×C4C22×M1611yescharacteristic
512C2×C4C2×#13111yescharacteristic
513C2×C4C2×#13111yescharacteristic
514C8—24no—
515C8—44no—
516C8—44no—
517C8—42no—
518C8—82no—
519C8—82no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—24no—
525C22—24no—
526C22#187012yes—
527C22#187012yes—
528C22#190212yes—
529C22#190512yes—
530C22C2×#38611yescharacteristic
531C22C2×#43511yescharacteristic
532C22C2×#43611yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—21no—
537C4—21no—
538C4—21no—
539C4—21no—
540C4—21no—
541C4—44no—
542C4—44no—
543C4—44no—
544C4—82no—
545C4#187012yes—
546C4#187012yes—
547C4C2×#40711yescharacteristic
548C4C2×#40811yescharacteristic
549C4C2×#43511yescharacteristic
550C4C2×#43611yescharacteristic
551C2—22no—
552C2—21no—
553C2—21no—
554C2#909214yesdirect product factor
555C2C2×#187011yescharacteristic
556C2C2×#190211yescharacteristic
557C2C2×#190511yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radicalC24C4×D4
LCSG ▷ C22×C4 ▷ C2 ▷ 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
6. #9092C2direct (N × H)
554. C2#9092direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#29832
C22×#4412
C2×#14792
C2×#14612
#90922
C2×#12812
C2×#12752