Finite Group Databasebeta

← C2×#9034 #195016

Subgroups — C2×#9034 #195016

Order 512.

1302 conjugacy classes of subgroups.

The subgroup lattice has 495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2921C211yesmaximal, characteristic
2C2×#2396C211yesmaximal, characteristic
3C2×#1487C212yesmaximal, complemented
4C2×#1458C211yesmaximal, characteristic
5#9034C218yesmaximal, direct product factor
6C2×#1303C212yesmaximal, complemented
7C22×C4×Q8C2211yescharacteristic
8C22×#117C2211yescharacteristic
9#2921—24no—
10#2921—22no—
11#2921C2214yes—
12C2×#433—24no—
13C2×#431C2212yes—
14C2×#423C2212yes—
15C2×#407—21no—
16C2×C4×M16—21no—
17#2396—22no—
18#2396—22no—
19#2396C414yes—
20#2396C2214yes—
21C2×#400C411yescharacteristic
22C2×#399C411yescharacteristic
23C2×#398—21no—
24C2×#396—21no—
25C2×#395C411yescharacteristic
26C2×#393C411yescharacteristic
27C2×C4×C4⋊C4—21no—
28C2×C4×C4⋊C4C2211yescharacteristic
29C2×C4×C22⋊C4—21no—
30#1487—24no—
31#1487C2218yescomplemented
32C2×Q8⋊C8—24no—
33#1458—22no—
34#1458C2214yes—
35C2×#324—21no—
36C2×#323—21no—
37#1303C2218yescomplemented
38C23×Q8C2×C411yescharacteristic
39C24×C4D411yescharacteristic
40C22×M16—22no—
41C2×C4×Q8—21no—
42C2×C4×Q8—21no—
43C2×C4×Q8—22no—
44C2×C4×Q8—22no—
45C2×C4×Q8—22no—
46C2×C4×Q8—22no—
47C2×C4×Q8C2×C412yes—
48C2×C4×Q8C2312yes—
49C2×#117—22no—
50C2×#117—22no—
51C2×#117—22no—
52C2×#117—22no—
53C2×#117C2×C412yes—
54C2×#117D412yes—
55C2×#117D412yes—
56C2×#117C2312yes—
57C22×C4⋊C4—21no—
58C22×C4⋊C4—21no—
59C22×C4⋊C4—21no—
60C22×C4⋊C4—21no—
61C22×C4⋊C4C2×C411yescharacteristic
62C22×C4⋊C4C2×C411yescharacteristic
63C22×C4⋊C4D411yescharacteristic
64C22×C22⋊C4—21no—
65C22×C22⋊C4—21no—
66C22×C22⋊C4C2×C411yescharacteristic
67C22×C22⋊C4D411yescharacteristic
68C22×C42—21no—
69C22×C42—21no—
70C22×C42D411yescharacteristic
71C22×C42C2311yescharacteristic
72#433—216no—
73#433—216no—
74#431—22no—
75#431—22no—
76#431—22no—
77#431C2314yes—
78#423—22no—
79#423—22no—
80#423D414yes—
81#423C2314yes—
82C2×C4⋊C8—22no—
83C2×C4⋊C8—22no—
84C2×C4⋊C8D414yes—
85#407—24no—
86#407—24no—
87C2×C22⋊C8—24no—
88C2×C22⋊C8—22no—
89C4×M16—24no—
90C4×M16—24no—
91C2×#97—22no—
92C2×C4×C8—22no—
93C2×C4×C8—22no—
94#400—22no—
95#400C2×C414yes—
96#399—22no—
97#399C2×C414yes—
98#398—24no—
99#398—24no—
100#396—24no—
101#396—24no—
102#395—22no—
103#395C2×C414yes—
104#393—22no—
105#393C2×C414yes—
106C4×C4⋊C4—24no—
107C4×C4⋊C4—21no—
108C4×C4⋊C4—21no—
109C4×C4⋊C4—24no—
110C4×C4⋊C4C2×C412yes—
111C4×C4⋊C4C2312yes—
112C4×C22⋊C4—24no—
113C4×C22⋊C4—24no—
114C2×#95—21no—
115C2×#95—21no—
116C2×#95—21no—
117C2×#95—21no—
118C2×#95C2×C411yescharacteristic
119C2×#95C2×C411yescharacteristic
120Q8⋊C8—216no—
121#324—24no—
122#323—24no—
123C25C22⋊C411yescharacteristic
124C22×Q8—21no—
125C22×Q8—22no—
126C22×Q8—22no—
127C22×Q8—44no—
128C22×Q8C22×C412yes—
129C23×C4—21no—
130C23×C4—21no—
131C23×C4—21no—
132C23×C4—21no—
133C23×C4—21no—
134C23×C4—21no—
135C23×C4—24no—
136C23×C4—24no—
137C23×C4—21no—
138C23×C4—21no—
139C23×C4C22⋊C411yescharacteristic
140C23×C4C22⋊C412yes—
141C23×C4C22⋊C411yescharacteristic
142C23×C4C22⋊C411yescharacteristic
143C23×C4C22×C411yescharacteristic
144C23×C4C2×D412yes—
145C23×C4C2×D411yescharacteristic
146C23×C4C2×D411yescharacteristic
147C2×M16—24no—
148C2×M16—24no—
149C2×M16—44no—
150C2×M16—44no—
151C22×C8—24no—
152C22×C8—42no—
153C4×Q8—24no—
154C4×Q8—24no—
155C4×Q8—24no—
156C4×Q8—24no—
157C4×Q8—42no—
158C4×Q8—42no—
159C4×Q8—42no—
160C4×Q8—42no—
161#117—24no—
162#117—24no—
163#117—24no—
164#117—24no—
165#117—24no—
166#117—24no—
167#117—24no—
168#117—24no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—24no—
177C2×C4⋊C4—24no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—44no—
183C2×C4⋊C4—44no—
184C2×C4⋊C4—44no—
185C2×C4⋊C4—42no—
186C2×C4⋊C4—42no—
187C2×C4⋊C4C22⋊C412yes—
188C2×C4⋊C4C22⋊C412yes—
189C2×C4⋊C4C22×C412yes—
190C2×C4⋊C4C22×C412yes—
191C2×C4⋊C4C2×D412yes—
192C2×C22⋊C4—22no—
193C2×C22⋊C4—22no—
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⋊C4C22⋊C412yes—
201C2×C22⋊C4C22⋊C412yes—
202C2×C22⋊C4C22×C412yes—
203C2×C22⋊C4C2×D412yes—
204C2×C42—21no—
205C2×C42—21no—
206C2×C42—21no—
207C2×C42—21no—
208C2×C42—22no—
209C2×C42—22no—
210C2×C42—22no—
211C2×C42—22no—
212C2×C42—41no—
213C2×C42—41no—
214C2×C42—41no—
215C2×C42—41no—
216C2×C42—44no—
217C2×C42C22⋊C412yes—
218C2×C42C22×C411yescharacteristic
219C2×C42C2×D412yes—
220C2×C42C2×D412yes—
221C2×C42C2×D412yes—
222C2×C42C2×D411yescharacteristic
223C2×C42C2×D411yescharacteristic
224C2×C42#4112yes—
225C2×C42#4112yes—
226C2×C42C2411yescharacteristic
227C4⋊C8—24no—
228C4⋊C8—24no—
229C4⋊C8—24no—
230C4⋊C8—24no—
231C4⋊C8—42no—
232C4⋊C8C2×D418yes—
233C22⋊C8—216no—
234C22⋊C8—24no—
235C22⋊C8—42no—
236#97—28no—
237C4×C8—28no—
238C4×C8—24no—
239C4×C8—42no—
240#95—24no—
241#95—24no—
242#95—24no—
243#95—24no—
244#95—21no—
245#95—21no—
246#95C22×C412yes—
247#95C22×C412yes—
248C24—21no—
249C24—22no—
250C24—21no—
251C24—22no—
252C24—42no—
253C24—42no—
254C24C2×C22⋊C411yescharacteristic
255C24C2×C22⋊C412yes—
256C2×Q8—28no—
257C2×Q8—24no—
258C2×Q8—44no—
259C2×Q8—44no—
260C2×Q8—44no—
261C2×Q8—48no—
262C2×Q8—42no—
263C22×C4—24no—
264C22×C4—24no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—42no—
292C22×C4—44no—
293C22×C4—44no—
294C22×C4—44no—
295C22×C4—44no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—42no—
305C22×C4C2×C22⋊C412yes—
306C22×C4C2×C22⋊C412yes—
307C22×C4C2×C22⋊C412yes—
308C22×C4C2×C22⋊C411yescharacteristic
309C22×C4C2×C22⋊C411yescharacteristic
310C22×C4C2×C22⋊C411yescharacteristic
311C22×C4C4×D412yes—
312C22×C4C4×D412yes—
313C22×C4#12011yescharacteristic
314C22×C4#12011yescharacteristic
315C22×C4#12112yes—
316C22×C4#12112yes—
317C22×C4#12311yescharacteristic
318C22×C4#12311yescharacteristic
319C22×C4#13514yes—
320C22×C4#13714yes—
321C22×C4C23×C411yescharacteristic
322C22×C4C22×D411yescharacteristic
323C22×C4C22×D411yescharacteristic
324M16—44no—
325M16—44no—
326M16—48no—
327C2×C8—28no—
328C2×C8—48no—
329C2×C8—44no—
330C2×C8—84no—
331C4⋊C4—24no—
332C4⋊C4—24no—
333C4⋊C4—24no—
334C4⋊C4—24no—
335C4⋊C4—24no—
336C4⋊C4—44no—
337C4⋊C4—44no—
338C4⋊C4—48no—
339C4⋊C4—48no—
340C4⋊C4—44no—
341C4⋊C4—42no—
342C4⋊C4—44no—
343C22⋊C4—24no—
344C22⋊C4—24no—
345C22⋊C4—24no—
346C22⋊C4—24no—
347C22⋊C4—48no—
348C22⋊C4—48no—
349C42—22no—
350C42—22no—
351C42—22no—
352C42—22no—
353C42—42no—
354C42—42no—
355C42—44no—
356C42—42no—
357C42—42no—
358C42—44no—
359C42C4×D412yes—
360C42C4×D412yes—
361C42#12012yes—
362C42#12112yes—
363C42#12112yes—
364C42#12312yes—
365C42C22×D412yes—
366C42C2×#4112yes—
367C23—22no—
368C23—22no—
369C23—22no—
370C23—22no—
371C23—22no—
372C23—42no—
373C23—42no—
374C23—48no—
375C23—42no—
376C23—42no—
377C23—42no—
378C23—42no—
379C23—81no—
380C23—81no—
381C23—84no—
382C23#38611yescharacteristic
383C23#38611yescharacteristic
384C23#41612yes—
385C23#41912yes—
386C23C22×C22⋊C411yescharacteristic
387Q8—28no—
388Q8—44no—
389Q8—48no—
390C2×C4—24no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—48no—
407C2×C4—42no—
408C2×C4—44no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—44no—
415C2×C4—42no—
416C2×C4—44no—
417C2×C4—44no—
418C2×C4—44no—
419C2×C4—44no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—84no—
431C2×C4—82no—
432C2×C4—82no—
433C2×C4#38612yes—
434C2×C4#38612yes—
435C2×C4#38611yescharacteristic
436C2×C4#38611yescharacteristic
437C2×C4#41612yes—
438C2×C4#41912yes—
439C2×C4#45214yes—
440C2×C4#45214yes—
441C2×C4#48514yes—
442C2×C4#48514yes—
443C2×C4C2×C4×D412yes—
444C2×C4C2×#12011yescharacteristic
445C2×C4C2×#12112yes—
446C2×C4C2×#12311yescharacteristic
447C2×C4C2×#13512yes—
448C2×C4C2×#13712yes—
449C8—48no—
450C8—84no—
451C22—24no—
452C22—24no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—44no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22—82no—
462C22—84no—
463C22—84no—
464C22#187312yes—
465C22#187312yes—
466C22#188412yes—
467C22#189112yes—
468C22C2×#38611yescharacteristic
469C22C2×#41611yescharacteristic
470C22C2×#41911yescharacteristic
471C4—22no—
472C4—22no—
473C4—22no—
474C4—22no—
475C4—44no—
476C4—42no—
477C4—42no—
478C4—44no—
479C4—42no—
480C4—82no—
481C4—82no—
482C4#187312yes—
483C4#187312yes—
484C4C2×#45212yes—
485C4C2×#48512yes—
486C2—21no—
487C2—21no—
488C2—22no—
489C2—82no—
490C2#903414yesdirect product factor
491C2C2×#187311yescharacteristic
492C2C2×#188411yescharacteristic
493C2C2×#189111yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socleC23#386
prime radicalC25C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#1487C2semidirect
5. #9034C2direct (N × H)
6. C2×#1303C2semidirect
31. #1487C22semidirect
37. #1303C22semidirect
490. C2#9034direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#29212
C2×#23962
C2×#14872
C2×#14582
#90342
C2×#13032