Finite Group Databasebeta

← C2×#9188 #197362

Subgroups — C2×#9188 #197362

Order 512.

1290 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2983C211yesmaximal, characteristic, complemented
2C2×#2632C211yesmaximal, characteristic
3C2×C4×#101C211yesmaximal, characteristic, complemented
4C2×#1527C212yesmaximal
5#9188C218yesmaximal, direct product factor
6C2×#1288C212yesmaximal, complemented
7C22×#124C2211yescharacteristic
8C22×C4×Q8C2211yescharacteristic
9#2983—24no—
10#2983—22no—
11#2983C2214yescomplemented
12C2×#446—24no—
13C2×#432—21no—
14C2×#432C2212yes—
15C2×#431—21no—
16C22×#101—21no—
17C2×C4×M16C2212yes—
18#2632—22no—
19#2632—22no—
20#2632C414yes—
21#2632C2214yes—
22C2×#399—21no—
23C2×#395C411yescharacteristic
24C2×#395C411yescharacteristic
25C2×#394C411yescharacteristic
26C2×#394C411yescharacteristic
27C2×#393—21no—
28C2×#388—21no—
29C2×#388—21no—
30C2×#383C2211yescharacteristic
31C4×#101—22no—
32C4×#101C2214yescomplemented
33C2×#343—21no—
34#1527—24no—
35#1527C2218yes—
36C2×#329—24no—
37#1288C2218yescomplemented
38C23×Q8C2×C411yescharacteristic
39C23×Q8D411yescharacteristic
40C23×D4C2×C411yescharacteristic
41C22×M16—22no—
42C2×#124—21no—
43C2×#124—21no—
44C2×#124—22no—
45C2×#124—22no—
46C2×#124—22no—
47C2×#124—22no—
48C2×#124C2×C412yes—
49C2×#124C2312yes—
50C2×C4×Q8—22no—
51C2×C4×Q8—22no—
52C2×C4×Q8—22no—
53C2×C4×Q8—22no—
54C2×C4×Q8C2×C412yes—
55C2×C4×Q8D412yes—
56C2×C4×Q8D412yes—
57C2×C4×Q8C2312yes—
58C22×C4⋊C4—21no—
59C22×C4⋊C4—21no—
60C22×C4⋊C4C2×C411yescharacteristic
61C22×C4⋊C4C2×C411yescharacteristic
62C22×C4⋊C4D411yescharacteristic
63C22×C22⋊C4—21no—
64C22×C22⋊C4—21no—
65C22×C22⋊C4—21no—
66C22×C22⋊C4—21no—
67C22×C22⋊C4—21no—
68C22×C22⋊C4—21no—
69C22×C42D411yescharacteristic
70C22×C42D411yescharacteristic
71C22×C42C2311yescharacteristic
72#446—216no—
73#446—216no—
74#432—24no—
75#432—24no—
76#432—22no—
77#432—22no—
78#432D414yes—
79#432C2314yes—
80#431—24no—
81#431—24no—
82C2×C4⋊C8—22no—
83C2×C4⋊C8—22no—
84C2×C4⋊C8—22no—
85C2×#101—28no—
86C2×#101—24no—
87C2×C22⋊C8—22no—
88C4×M16—22no—
89C4×M16—22no—
90C4×M16—22no—
91C4×M16C2314yes—
92C2×#97—22no—
93C2×#97—22no—
94C2×#97D414yes—
95C2×C4×C8—22no—
96C2×C4×C8—22no—
97#399—24no—
98#399—24no—
99#395—22no—
100#395—22no—
101#395C2×C414yes—
102#395C2×C414yes—
103#394—22no—
104#394—22no—
105#394C2×C414yes—
106#394C2×C414yes—
107#393—24no—
108#393—24no—
109#388—24no—
110#388—24no—
111#388—24no—
112#388—24no—
113#383—21no—
114#383—21no—
115#383C2×C412yes—
116#383C2312yes—
117C2×#95—21no—
118C2×#95—21no—
119C2×#95—21no—
120C2×#95—21no—
121C2×#95C2×C411yescharacteristic
122C2×#95C2×C411yescharacteristic
123#343—24no—
124#329—216no—
125C25—21no—
126C22×Q8—24no—
127C22×Q8—21no—
128C22×Q8—22no—
129C22×Q8—22no—
130C22×Q8—22no—
131C22×Q8—22no—
132C22×Q8—42no—
133C22×Q8—82no—
134C22×Q8C22⋊C412yes—
135C22×Q8C22×C412yes—
136C22×Q8C2×D412yes—
137C22×D4—21no—
138C22×D4—22no—
139C22×D4—22no—
140C22×D4—82no—
141C22×D4C22×C412yes—
142C23×C4—21no—
143C23×C4—21no—
144C23×C4—21no—
145C23×C4C22⋊C411yescharacteristic
146C23×C4C22⋊C411yescharacteristic
147C23×C4C22⋊C411yescharacteristic
148C23×C4C22⋊C411yescharacteristic
149C23×C4C22×C411yescharacteristic
150C23×C4C2×D411yescharacteristic
151C23×C4C2×D411yescharacteristic
152C2×M16—28no—
153C2×M16—24no—
154C2×M16—44no—
155C2×M16—42no—
156C22×C8—24no—
157C22×C8—42no—
158#124—24no—
159#124—24no—
160#124—24no—
161#124—24no—
162#124—42no—
163#124—42no—
164#124—42no—
165#124—42no—
166C4×Q8—24no—
167C4×Q8—24no—
168C4×Q8—24no—
169C4×Q8—24no—
170C4×Q8—24no—
171C4×Q8—24no—
172C4×Q8—24no—
173C4×Q8—24no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—24no—
181C2×C4⋊C4—24no—
182C2×C4⋊C4—82no—
183C2×C4⋊C4—82no—
184C2×C4⋊C4C22⋊C412yes—
185C2×C4⋊C4C22⋊C412yes—
186C2×C4⋊C4C22⋊C412yes—
187C2×C4⋊C4C22×C412yes—
188C2×C4⋊C4C22×C412yes—
189C2×C4⋊C4C2×D412yes—
190C2×C22⋊C4—22no—
191C2×C22⋊C4—22no—
192C2×C22⋊C4—24no—
193C2×C22⋊C4—24no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—24no—
197C2×C22⋊C4—24no—
198C2×C22⋊C4—44no—
199C2×C22⋊C4—44no—
200C2×C22⋊C4—41no—
201C2×C22⋊C4—41no—
202C2×C22⋊C4—42no—
203C2×C22⋊C4—42no—
204C2×C22⋊C4—41no—
205C2×C22⋊C4—41no—
206C2×C22⋊C4—82no—
207C2×C22⋊C4—82no—
208C2×C42—21no—
209C2×C42—21no—
210C2×C42—21no—
211C2×C42—21no—
212C2×C42—21no—
213C2×C42—21no—
214C2×C42—21no—
215C2×C42—21no—
216C2×C42C22⋊C412yes—
217C2×C42C22⋊C412yes—
218C2×C42C22×C411yescharacteristic
219C2×C42C2×D412yes—
220C2×C42C2×D412yes—
221C2×C42C2×D412yes—
222C2×C42C2×D412yes—
223C2×C42C2×D411yescharacteristic
224C2×C42C2×D411yescharacteristic
225C2×C42#4112yes—
226C2×C42#4112yes—
227C2×C42C2411yescharacteristic
228C4⋊C8—28no—
229C4⋊C8—28no—
230C4⋊C8—24no—
231C4⋊C8—24no—
232#101—216no—
233C22⋊C8—24no—
234C22⋊C8—24no—
235#97—28no—
236#97—24no—
237#97—24no—
238#97—42no—
239#97C2×D418yes—
240C4×C8—28no—
241C4×C8—24no—
242C4×C8—42no—
243#95—22no—
244#95—22no—
245#95—24no—
246#95—24no—
247#95—21no—
248#95—21no—
249#95—22no—
250#95—22no—
251#95C22×C412yes—
252#95C22×C412yes—
253C24—22no—
254C24—42no—
255C24—42no—
256C24—42no—
257C24—42no—
258C24—41no—
259C24—41no—
260C24—42no—
261C24—42no—
262C24C2×C22⋊C411yescharacteristic
263C2×Q8—24no—
264C2×Q8—24no—
265C2×Q8—24no—
266C2×Q8—24no—
267C2×Q8—24no—
268C2×Q8—42no—
269C2×Q8—42no—
270C2×Q8—48no—
271C2×Q8—48no—
272C2×Q8—42no—
273C2×Q8—84no—
274C2×Q8—82no—
275C2×Q8—82no—
276C2×Q8—84no—
277C2×D4—24no—
278C2×D4—42no—
279C2×D4—84no—
280C2×D4—82no—
281C2×D4—84no—
282C2×D4—82no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4#10414yes—
314C22×C4C2×C22⋊C412yes—
315C22×C4C2×C22⋊C411yescharacteristic
316C22×C4C2×C22⋊C412yes—
317C22×C4C2×C22⋊C412yes—
318C22×C4C2×C22⋊C412yes—
319C22×C4C2×C22⋊C411yescharacteristic
320C22×C4C2×C22⋊C411yescharacteristic
321C22×C4C4×D412yes—
322C22×C4C4×D412yes—
323C22×C4#12011yescharacteristic
324C22×C4#12011yescharacteristic
325C22×C4#12112yes—
326C22×C4#12112yes—
327C22×C4#12311yescharacteristic
328C22×C4#12311yescharacteristic
329C22×C4C23×C411yescharacteristic
330C22×C4C22×D411yescharacteristic
331C22×C4C22×D411yescharacteristic
332M16—28no—
333M16—48no—
334M16—44no—
335C2×C8—28no—
336C2×C8—48no—
337C2×C8—48no—
338C2×C8—44no—
339C4⋊C4—24no—
340C4⋊C4—24no—
341C4⋊C4—24no—
342C4⋊C4—24no—
343C4⋊C4—24no—
344C4⋊C4—24no—
345C4⋊C4—84no—
346C4⋊C4—84no—
347C22⋊C4—48no—
348C22⋊C4—42no—
349C22⋊C4—44no—
350C22⋊C4—42no—
351C22⋊C4—42no—
352C22⋊C4—42no—
353C22⋊C4—44no—
354C22⋊C4—48no—
355C22⋊C4—84no—
356C22⋊C4—84no—
357C42—22no—
358C42—22no—
359C42—22no—
360C42—22no—
361C42—22no—
362C42—22no—
363C42—22no—
364C42—22no—
365C42C4×D412yes—
366C42C4×D412yes—
367C42#12012yes—
368C42#12112yes—
369C42#12112yes—
370C42#12312yes—
371C42C22×D412yes—
372C42C2×#4112yes—
373C23—22no—
374C23—22no—
375C23—42no—
376C23—42no—
377C23—42no—
378C23—42no—
379C23—42no—
380C23—42no—
381C23—42no—
382C23—82no—
383C23—82no—
384C23—84no—
385C23—84no—
386C23—84no—
387C23—84no—
388C23—82no—
389C23—82no—
390C23—82no—
391C23—82no—
392C23#38611yescharacteristic
393C23#38611yescharacteristic
394C23C2×#10412yes—
395C23#42112yes—
396C23C22×C22⋊C411yescharacteristic
397Q8—48no—
398Q8—48no—
399Q8—84no—
400Q8—84no—
401D4—84no—
402D4—84no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—81no—
444C2×C4—81no—
445C2×C4—84no—
446C2×C4—84no—
447C2×C4—82no—
448C2×C4—82no—
449C2×C4#38611yescharacteristic
450C2×C4#38611yescharacteristic
451C2×C4#38612yes—
452C2×C4#38612yes—
453C2×C4C2×#10414yes—
454C2×C4C2×C4×D412yes—
455C2×C4C2×#12011yescharacteristic
456C2×C4C2×#12112yes—
457C2×C4C2×#12311yescharacteristic
458C8—48no—
459C8—48no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—24no—
465C22—24no—
466C22—82no—
467C22—82no—
468C22—82no—
469C22—82no—
470C22—82no—
471C22—82no—
472C22—82no—
473C22—164no—
474C22—164no—
475C22#187112yes—
476C22#187112yes—
477C22#191212yes—
478C22#191412yes—
479C22C2×#38611yescharacteristic
480C22C22×#10411yescharacteristic
481C22C2×#42111yescharacteristic
482C4—21no—
483C4—21no—
484C4—21no—
485C4—21no—
486C4—22no—
487C4—22no—
488C4—22no—
489C4—22no—
490C4—24no—
491C4—42no—
492C4—42no—
493C4—42no—
494C4—82no—
495C4—82no—
496C4—82no—
497C2—21no—
498C2—21no—
499C2—22no—
500C2—162no—
501C2#918814yesdirect product factor
502C2C2×#187111yescharacteristic
503C2C2×#191211yescharacteristic
504C2C2×#191411yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radicalC23×D4C2×C4
LCSG ▷ C22×C4 ▷ 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
1. C2×#2983C2semidirect
3. C2×C4×#101C2semidirect
5. #9188C2direct (N × H)
6. C2×#1288C2semidirect
11. #2983C22semidirect
32. C4×#101C22semidirect
37. #1288C22semidirect
501. C2#9188direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#29832
C2×#26322
C2×C4×#1012
C2×#15272
#91882
C2×#12882