Finite Group Databasebeta

← C2×#11798 #481813

Subgroups — C2×#11798 #481813

Order 512.

1352 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2392C211yesmaximal, characteristic
2C2×#1820C211yesmaximal, characteristic, complemented
3C2×#1464C211yesmaximal, characteristic, complemented
4#11798C218yesmaximal, direct product factor
5C2×#1344C212yesmaximal, complemented
6C2×#1343C212yesmaximal
7C22×C4×D4—21no—
8C22×C4×D4C411yescharacteristic, complemented
9C22×#117C2211yescharacteristic
10C2×#432—21no—
11#2392—22no—
12#2392—22no—
13#2392C414yescomplemented
14#2392C2214yes—
15C2×#398C411yescharacteristic, complemented
16C2×#397C2211yescharacteristic
17C2×#396—21no—
18C2×#394—21no—
19C2×#394C411yescharacteristic, complemented
20C2×#392C2211yescharacteristic
21C2×#381—21no—
22C2×C4×C4⋊C4C411yescharacteristic, complemented
23C2×C4×C22⋊C4—21no—
24#1820—22no—
25#1820C2214yescomplemented
26C2×#342—21no—
27C2×#342C2212yes—
28#1464—22no—
29#1464C2214yescomplemented
30C2×#324—21no—
31C2×#323C2212yes—
32#1344C2218yescomplemented
33#1343C2218yes—
34C23×D4—21no—
35C23×D4C2×C411yescharacteristic
36C24×C4—21no—
37C24×C4D411yescharacteristic
38C2×C4×D4—24no—
39C2×C4×D4—24no—
40C2×C4×D4—22no—
41C2×C4×D4—42no—
42C2×C4×D4—41no—
43C2×C4×D4—41no—
44C2×C4×D4—48no—
45C2×C4×D4C2×C414yescomplemented
46C2×#117—41no—
47C2×#117—41no—
48C2×#117—42no—
49C2×#117C2×C412yes—
50C2×#117D412yes—
51C2×#117D412yes—
52C2×#117C2312yes—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4C2×C411yescharacteristic
56C22×C4⋊C4C2×C411yescharacteristic
57C22×C4⋊C4D411yescharacteristic
58C22×C22⋊C4—21no—
59C22×C22⋊C4—21no—
60C22×C22⋊C4—21no—
61C22×C22⋊C4—21no—
62C22×C22⋊C4—21no—
63C22×C22⋊C4—22no—
64C22×C22⋊C4D411yescharacteristic
65C22×C22⋊C4C2311yescharacteristic
66C22×C42—21no—
67C22×C42C2×C411yescharacteristic
68C22×C42D411yescharacteristic
69#432—24no—
70#432—42no—
71C2×C4⋊C8—41no—
72C2×C22⋊C8—22no—
73C2×#97—41no—
74#398—22no—
75#398C2×C414yescomplemented
76#397—21no—
77#397—21no—
78#397C2×C412yes—
79#397C2312yes—
80#396—24no—
81#396—24no—
82#394—22no—
83#394—24no—
84#394—24no—
85#394C2×C414yescomplemented
86#392—21no—
87#392—21no—
88#392C2×C412yes—
89#392C2312yes—
90#381—24no—
91#381—42no—
92C4×C4⋊C4—22no—
93C4×C4⋊C4C2×C414yescomplemented
94C4×C22⋊C4—24no—
95C4×C22⋊C4—24no—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—41no—
99C2×#95—41no—
100C2×#95C2×C411yescharacteristic
101C2×#95C2×C411yescharacteristic
102#342—22no—
103#342—24no—
104#342C2314yes—
105#324—24no—
106#323—22no—
107#323C2314yes—
108C25—21no—
109C25C2×D411yescharacteristic
110C22×D4—22no—
111C22×D4—22no—
112C22×D4—21no—
113C22×D4—41no—
114C22×D4—41no—
115C22×D4—44no—
116C22×D4—44no—
117C22×D4—44no—
118C22×D4—44no—
119C22×D4C22×C412yes—
120C23×C4—21no—
121C23×C4—24no—
122C23×C4—21no—
123C23×C4—21no—
124C23×C4—22no—
125C23×C4—21no—
126C23×C4—21no—
127C23×C4—24no—
128C23×C4—42no—
129C23×C4—44no—
130C23×C4—44no—
131C23×C4—42no—
132C23×C4—41no—
133C23×C4—41no—
134C23×C4—42no—
135C23×C4C22⋊C411yescharacteristic
136C23×C4C22⋊C412yes—
137C23×C4C22⋊C411yescharacteristic
138C23×C4C22⋊C411yescharacteristic
139C23×C4C22⋊C411yescharacteristic
140C23×C4C22×C411yescharacteristic
141C23×C4C2×D412yes—
142C23×C4C2×D411yescharacteristic
143C22×C8—42no—
144C4×D4—44no—
145C4×D4—44no—
146C4×D4—44no—
147C4×D4—44no—
148C4×D4—416no—
149C4×D4—416no—
150#117—42no—
151#117—42no—
152#117—42no—
153#117—42no—
154#117—42no—
155#117—42no—
156#117—42no—
157#117—42no—
158C2×C4⋊C4—24no—
159C2×C4⋊C4—24no—
160C2×C4⋊C4—21no—
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—44no—
168C2×C4⋊C4—44no—
169C2×C4⋊C4C22⋊C412yes—
170C2×C4⋊C4C22⋊C412yes—
171C2×C4⋊C4C22×C412yes—
172C2×C4⋊C4C22×C412yes—
173C2×C4⋊C4C2×D412yes—
174C2×C22⋊C4—22no—
175C2×C22⋊C4—22no—
176C2×C22⋊C4—24no—
177C2×C22⋊C4—24no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4—24no—
180C2×C22⋊C4—22no—
181C2×C22⋊C4—24no—
182C2×C22⋊C4—41no—
183C2×C22⋊C4—41no—
184C2×C22⋊C4—41no—
185C2×C22⋊C4—41no—
186C2×C22⋊C4—44no—
187C2×C22⋊C4—42no—
188C2×C22⋊C4—42no—
189C2×C22⋊C4—44no—
190C2×C22⋊C4—44no—
191C2×C22⋊C4—44no—
192C2×C22⋊C4—44no—
193C2×C22⋊C4—44no—
194C2×C22⋊C4—42no—
195C2×C22⋊C4C22⋊C412yes—
196C2×C22⋊C4C22×C411yescharacteristic
197C2×C22⋊C4C2×D412yes—
198C2×C22⋊C4C2×D411yescharacteristic
199C2×C22⋊C4C2×D411yescharacteristic
200C2×C22⋊C4C2411yescharacteristic
201C2×C42—22no—
202C2×C42—21no—
203C2×C42—21no—
204C2×C42—21no—
205C2×C42—21no—
206C2×C42—22no—
207C2×C42—24no—
208C2×C42—44no—
209C2×C42C22⋊C412yes—
210C2×C42C22⋊C412yes—
211C2×C42C22×C412yes—
212C2×C42C2×D412yes—
213C4⋊C8—44no—
214C22⋊C8—24no—
215C22⋊C8—42no—
216#97—44no—
217#95—24no—
218#95—22no—
219#95—21no—
220#95—21no—
221#95—22no—
222#95—44no—
223#95—44no—
224#95C22×C412yes—
225#95C22×C412yes—
226C24—21no—
227C24—21no—
228C24—22no—
229C24—24no—
230C24—22no—
231C24—42no—
232C24—42no—
233C24—42no—
234C24—42no—
235C24—42no—
236C24—41no—
237C24—41no—
238C24—42no—
239C24—42no—
240C24C2×C22⋊C411yescharacteristic
241C24C2×C22⋊C411yescharacteristic
242C24AGL(1,ℤ/8)14yes—
243C24C22×D411yescharacteristic
244C2×D4—42no—
245C2×D4—42no—
246C2×D4—44no—
247C2×D4—44no—
248C2×D4—44no—
249C2×D4—44no—
250C2×D4—44no—
251C2×D4—44no—
252C2×D4—48no—
253C2×D4—432no—
254C2×D4—44no—
255C2×D4—44no—
256C2×D4—44no—
257C2×D4—44no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—24no—
261C22×C4—22no—
262C22×C4—24no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—24no—
273C22×C4—22no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—44no—
285C22×C4—44no—
286C22×C4—48no—
287C22×C4—48no—
288C22×C4—48no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—44no—
303C22×C4—44no—
304C22×C4—44no—
305C22×C4—88no—
306C22×C4—84no—
307C22×C4—84no—
308C22×C4—84no—
309C22×C4—84no—
310C22×C4—84no—
311C22×C4#9912yes—
312C22×C4#9911yescharacteristic
313C22×C4#9911yescharacteristic
314C22×C4C2×C22⋊C412yes—
315C22×C4C2×C22⋊C412yes—
316C22×C4C2×C22⋊C411yescharacteristic
317C22×C4C2×C22⋊C411yescharacteristic
318C22×C4C2×C22⋊C412yes—
319C22×C4C2×C22⋊C412yes—
320C22×C4C23×C411yescharacteristic
321C22×C4C22×D411yescharacteristic
322C2×C8—44no—
323C2×C8—84no—
324C4⋊C4—42no—
325C4⋊C4—42no—
326C4⋊C4—42no—
327C4⋊C4—42no—
328C4⋊C4—42no—
329C4⋊C4—48no—
330C4⋊C4—42no—
331C4⋊C4—48no—
332C22⋊C4—42no—
333C22⋊C4—41no—
334C22⋊C4—42no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—44no—
339C22⋊C4—44no—
340C22⋊C4—48no—
341C22⋊C4—48no—
342C22⋊C4—48no—
343C22⋊C4—44no—
344C22⋊C4—44no—
345C22⋊C4—44no—
346C22⋊C4—44no—
347C22⋊C4—84no—
348C42—22no—
349C42—22no—
350C42—22no—
351C42—22no—
352C42—22no—
353C42—22no—
354C42—22no—
355C42—22no—
356C42—48no—
357C23—22no—
358C23—22no—
359C23—21no—
360C23—21no—
361C23—24no—
362C23—21no—
363C23—21no—
364C23—24no—
365C23—24no—
366C23—41no—
367C23—41no—
368C23—48no—
369C23—41no—
370C23—41no—
371C23—42no—
372C23—48no—
373C23—42no—
374C23—44no—
375C23—42no—
376C23—48no—
377C23—42no—
378C23—42no—
379C23—42no—
380C23—44no—
381C23—42no—
382C23—42no—
383C23—84no—
384C23—81no—
385C23—81no—
386C23—84no—
387C23—84no—
388C23—82no—
389C23—82no—
390C23—82no—
391C23—82no—
392C23C2×#9911yescharacteristic
393C23C2×#9911yescharacteristic
394C23#41812yes—
395C23#41812yes—
396C23#42112yes—
397C23C22×C22⋊C411yescharacteristic
398C23C2×AGL(1,ℤ/8)12yes—
399D4—44no—
400D4—416no—
401D4—416no—
402D4—44no—
403D4—48no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—24no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—24no—
410C2×C4—22no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—22no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—44no—
420C2×C4—44no—
421C2×C4—44no—
422C2×C4—44no—
423C2×C4—42no—
424C2×C4—48no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—88no—
447C2×C4—88no—
448C2×C4—81no—
449C2×C4—81no—
450C2×C4—84no—
451C2×C4—82no—
452C2×C4—82no—
453C2×C4—84no—
454C2×C4—84no—
455C2×C4—84no—
456C2×C4—168no—
457C2×C4C2×#9912yes—
458C2×C4C2×#9912yes—
459C8—84no—
460C22—24no—
461C22—24no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—22no—
467C22—22no—
468C22—42no—
469C22—42no—
470C22—44no—
471C22—44no—
472C22—48no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—44no—
478C22—81no—
479C22—81no—
480C22—84no—
481C22—82no—
482C22—82no—
483C22—88no—
484C22—88no—
485C22—82no—
486C22—82no—
487C22#151012yes—
488C22#151012yes—
489C22#212012yes—
490C22#212612yes—
491C22C22×#9911yescharacteristic
492C22C2×#41811yescharacteristic
493C22C2×#42111yescharacteristic
494C4—22no—
495C4—22no—
496C4—44no—
497C4—41no—
498C4—41no—
499C4—42no—
500C4—41no—
501C4—42no—
502C4—41no—
503C4—42no—
504C4—82no—
505C4—82no—
506C4—164no—
507C2—21no—
508C2—21no—
509C2—22no—
510C2—42no—
511C2—42no—
512C2—84no—
513C2#1179814yesdirect product factor
514C2C2×#151011yescharacteristic
515C2C2×#212011yescharacteristic
516C2C2×#212611yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C22⋊C4C24
prime radicalC2×#392C22
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#117 ◁ G
LECSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1820C2semidirect
3. C2×#1464C2semidirect
4. #11798C2direct (N × H)
5. C2×#1344C2semidirect
8. C22×C4×D4C4semidirect
13. #2392C4semidirect
15. C2×#398C4semidirect
19. C2×#394C4semidirect
22. C2×C4×C4⋊C4C4semidirect
25. #1820C22semidirect
29. #1464C22semidirect
32. #1344C22semidirect
45. C2×C4×D4C2×C4semidirect
75. #398C2×C4semidirect
85. #394C2×C4semidirect
93. C4×C4⋊C4C2×C4semidirect
513. C2#11798direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#23922
C2×#18202
C2×#14642
#117982
C2×#13442
C2×#13432