Finite Group Databasebeta

← C2×#9191 #197414

Subgroups — C2×#9191 #197414

Order 512.

1396 conjugacy classes of subgroups.

The subgroup lattice has 471 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2905C211yesmaximal, characteristic
2C2×#2628C211yesmaximal, characteristic
3C2×#1548C212yesmaximal, complemented
4C2×#1458C211yesmaximal, characteristic
5#9191C218yesmaximal, direct product factor
6C2×#1286C212yesmaximal, complemented
7C23×M16—21no—
8C22×C4⋊Q8C2211yescharacteristic
9C22×#117C2211yescharacteristic
10C2×#431C2212yes—
11#2905—24no—
12#2905—22no—
13#2905C2214yes—
14C2×#424—24no—
15C2×#423—21no—
16C2×#423C2212yes—
17#2628—22no—
18#2628—22no—
19#2628C414yes—
20#2628C2214yes—
21C2×#400—21no—
22C2×#399—21no—
23C2×#395C412yes—
24C2×#393C412yes—
25C2×#389—21no—
26C2×#382C2211yescharacteristic
27C2×#380—21no—
28#1548—24no—
29#1548C2218yescomplemented
30C2×#333—24no—
31#1458—22no—
32#1458C2214yes—
33C2×#324—21no—
34C2×#323—21no—
35#1286C2218yescomplemented
36C23×Q8C2×C412yes—
37C24×C4D411yescharacteristic
38C22×M16—22no—
39C22×M16—24no—
40C22×M16—22no—
41C22×M16—24no—
42C22×M16—44no—
43C22×M16—44no—
44C23×C8—22no—
45C2×C4⋊Q8—21no—
46C2×C4⋊Q8—21no—
47C2×C4⋊Q8—22no—
48C2×C4⋊Q8—22no—
49C2×C4⋊Q8—22no—
50C2×C4⋊Q8—22no—
51C2×C4⋊Q8C2×C412yes—
52C2×C4⋊Q8C2312yes—
53C2×#117—22no—
54C2×#117—22no—
55C2×#117—22no—
56C2×#117—22no—
57C2×#117C2×C412yes—
58C2×#117D412yes—
59C2×#117D412yes—
60C2×#117C2312yes—
61C22×C4⋊C4—21no—
62C22×C4⋊C4—21no—
63C22×C4⋊C4—21no—
64C22×C4⋊C4—22no—
65C22×C4⋊C4C2×C411yescharacteristic
66C22×C4⋊C4D411yescharacteristic
67C22×C22⋊C4—22no—
68C22×C22⋊C4C2×C411yescharacteristic
69C22×C22⋊C4D411yescharacteristic
70C22×C42D411yescharacteristic
71C22×C42C2311yescharacteristic
72#431—22no—
73#431—22no—
74#431—22no—
75#431C2314yes—
76#424—216no—
77#424—216no—
78#423—24no—
79#423—24no—
80#423—22no—
81#423—22no—
82#423D414yes—
83#423C2314yes—
84C2×C4⋊C8—24no—
85C2×C4⋊C8—22no—
86C2×C4⋊C8—22no—
87C2×C4⋊C8D414yes—
88C2×C22⋊C8—22no—
89C2×C4×C8—22no—
90#400—24no—
91#400—24no—
92#399—24no—
93#399—24no—
94#395—24no—
95#395C2×C418yes—
96#393—24no—
97#393C2×C418yes—
98#389—24no—
99#389—24no—
100#382—21no—
101#382—21no—
102#382C2×C412yes—
103#382C2312yes—
104#380—24no—
105#380—24no—
106C2×#95—22no—
107C2×#95—22no—
108C2×#95—21no—
109C2×#95C2×C412yes—
110#333—216no—
111#324—24no—
112#323—24no—
113C25C22⋊C411yescharacteristic
114C22×Q8—22no—
115C22×Q8—24no—
116C22×Q8—24no—
117C22×Q8—84no—
118C22×Q8C22×C414yes—
119C23×C4—21no—
120C23×C4—21no—
121C23×C4—21no—
122C23×C4—21no—
123C23×C4—22no—
124C23×C4—22no—
125C23×C4—22no—
126C23×C4—22no—
127C23×C4C22⋊C411yescharacteristic
128C23×C4C22⋊C412yes—
129C23×C4C22⋊C411yescharacteristic
130C23×C4C22⋊C411yescharacteristic
131C23×C4SD1614yes—
132C23×C4Q1614yes—
133C23×C4C22×C411yescharacteristic
134C23×C4C2×D412yes—
135C23×C4C2×D411yescharacteristic
136C23×C4C2×D411yescharacteristic
137C2×M16—28no—
138C2×M16—24no—
139C2×M16—24no—
140C2×M16—48no—
141C2×M16—416no—
142C2×M16—48no—
143C2×M16—48no—
144C2×M16—44no—
145C2×M16—44no—
146C22×C8—28no—
147C22×C8—24no—
148C22×C8—48no—
149C22×C8—42no—
150C4⋊Q8—24no—
151C4⋊Q8—24no—
152C4⋊Q8—24no—
153C4⋊Q8—24no—
154C4⋊Q8—42no—
155C4⋊Q8—42no—
156C4⋊Q8—42no—
157C4⋊Q8—42no—
158#117—24no—
159#117—24no—
160#117—24no—
161#117—24no—
162#117—24no—
163#117—24no—
164#117—24no—
165#117—24no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
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—28no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4—42no—
180C2×C4⋊C4—42no—
181C2×C4⋊C4—41no—
182C2×C4⋊C4—41no—
183C2×C4⋊C4—42no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—84no—
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—22no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—28no—
195C2×C22⋊C4—84no—
196C2×C22⋊C4C22⋊C412yes—
197C2×C22⋊C4C22⋊C412yes—
198C2×C22⋊C4C22×C412yes—
199C2×C22⋊C4C2×D412yes—
200C2×C42—21no—
201C2×C42—21no—
202C2×C42—21no—
203C2×C42—21no—
204C2×C42C22⋊C412yes—
205C2×C42C22×C411yescharacteristic
206C2×C42C2×D412yes—
207C2×C42C2×D412yes—
208C2×C42C2×D412yes—
209C2×C42C2×D411yescharacteristic
210C2×C42C2×D411yescharacteristic
211C2×C42#4112yes—
212C2×C42#4112yes—
213C2×C42C2411yescharacteristic
214C4⋊C8—216no—
215C4⋊C8—24no—
216C4⋊C8—24no—
217C4⋊C8—24no—
218C4⋊C8—24no—
219C4⋊C8—42no—
220C4⋊C8C2×D418yes—
221C22⋊C8—24no—
222C22⋊C8—42no—
223C4×C8—24no—
224C4×C8—42no—
225#95—28no—
226#95—22no—
227#95—28no—
228#95—22no—
229#95—22no—
230#95C22×C414yes—
231C24—21no—
232C24—21no—
233C24—22no—
234C24—42no—
235C24—42no—
236C24#10314yes—
237C24C2×C22⋊C411yescharacteristic
238C24C2×C22⋊C412yes—
239C2×Q8—28no—
240C2×Q8—44no—
241C2×Q8—88no—
242C2×Q8—84no—
243C2×Q8—84no—
244C2×Q8—88no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—24no—
259C22×C4—24no—
260C22×C4—24no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—24no—
268C22×C4—24no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—44no—
274C22×C4—44no—
275C22×C4—44no—
276C22×C4—44no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—44no—
280C22×C4#10314yes—
281C22×C4#10318yes—
282C22×C4C2×C22⋊C412yes—
283C22×C4C2×C22⋊C412yes—
284C22×C4C2×C22⋊C412yes—
285C22×C4C2×C22⋊C411yescharacteristic
286C22×C4C2×C22⋊C411yescharacteristic
287C22×C4C2×C22⋊C411yescharacteristic
288C22×C4C4×D412yes—
289C22×C4C4×D412yes—
290C22×C4#12011yescharacteristic
291C22×C4#12011yescharacteristic
292C22×C4#12112yes—
293C22×C4#12112yes—
294C22×C4#12311yescharacteristic
295C22×C4#12311yescharacteristic
296C22×C4C2×SD1614yes—
297C22×C4C2×SD1612yes—
298C22×C4C2×Q1614yes—
299C22×C4C2×Q1612yes—
300C22×C4AGL(1,ℤ/8)12yes—
301C22×C4#13712yes—
302C22×C4C23×C411yescharacteristic
303C22×C4C22×D411yescharacteristic
304C22×C4C22×D411yescharacteristic
305M16—416no—
306M16—44no—
307M16—44no—
308M16—48no—
309C2×C8—28no—
310C2×C8—416no—
311C2×C8—48no—
312C2×C8—44no—
313C2×C8—84no—
314C4⋊C4—24no—
315C4⋊C4—24no—
316C4⋊C4—24no—
317C4⋊C4—24no—
318C4⋊C4—42no—
319C4⋊C4—44no—
320C4⋊C4—42no—
321C4⋊C4—42no—
322C4⋊C4—42no—
323C4⋊C4—44no—
324C4⋊C4—42no—
325C4⋊C4—42no—
326C4⋊C4—44no—
327C4⋊C4—88no—
328C22⋊C4—24no—
329C22⋊C4—24no—
330C22⋊C4—24no—
331C22⋊C4—24no—
332C22⋊C4—88no—
333C42—22no—
334C42—22no—
335C42—22no—
336C42—22no—
337C42C4×D412yes—
338C42C4×D412yes—
339C42#12012yes—
340C42#12112yes—
341C42#12112yes—
342C42#12312yes—
343C42C22×D412yes—
344C42C2×#4112yes—
345C23—22no—
346C23—22no—
347C23—24no—
348C23—22no—
349C23—22no—
350C23—24no—
351C23—42no—
352C23—48no—
353C23—42no—
354C23—42no—
355C23—42no—
356C23—81no—
357C23—81no—
358C23—84no—
359C23#38611yescharacteristic
360C23#38611yescharacteristic
361C23C2×#10312yes—
362C23C2×#10314yes—
363C23#41712yes—
364C23C22×C22⋊C411yescharacteristic
365Q8—88no—
366Q8—88no—
367C2×C4—22no—
368C2×C4—24no—
369C2×C4—24no—
370C2×C4—24no—
371C2×C4—24no—
372C2×C4—22no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—28no—
376C2×C4—28no—
377C2×C4—24no—
378C2×C4—24no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—44no—
396C2×C4—44no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—88no—
400C2×C4—84no—
401C2×C4—84no—
402C2×C4#38612yes—
403C2×C4#38612yes—
404C2×C4#38611yescharacteristic
405C2×C4#38611yescharacteristic
406C2×C4C2×#10314yes—
407C2×C4C2×#10312yes—
408C2×C4#41712yes—
409C2×C4#45012yes—
410C2×C4#45012yes—
411C2×C4#45112yes—
412C2×C4#45112yes—
413C2×C4#48312yes—
414C2×C4#48312yes—
415C2×C4#48412yes—
416C2×C4#48412yes—
417C2×C4C2×C4×D412yes—
418C2×C4C2×#12011yescharacteristic
419C2×C4C2×#12112yes—
420C2×C4C2×#12311yescharacteristic
421C2×C4C22×SD1611yescharacteristic
422C2×C4C22×Q1611yescharacteristic
423C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
424C2×C4C2×#13711yescharacteristic
425C8—48no—
426C8—84no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—24no—
432C22—24no—
433C22—24no—
434C22—44no—
435C22—42no—
436C22—42no—
437C22—48no—
438C22—82no—
439C22—84no—
440C22#187212yes—
441C22#187212yes—
442C22#190912yes—
443C22#191412yes—
444C22C2×#38611yescharacteristic
445C22C22×#10311yescharacteristic
446C22C2×#41711yescharacteristic
447C4—22no—
448C4—22no—
449C4—22no—
450C4—22no—
451C4—24no—
452C4—42no—
453C4—42no—
454C4—84no—
455C4—84no—
456C4#187212yes—
457C4#187212yes—
458C4C2×#45011yescharacteristic
459C4C2×#45111yescharacteristic
460C4C2×#48311yescharacteristic
461C4C2×#48411yescharacteristic
462C2—21no—
463C2—21no—
464C2—22no—
465C2—44no—
466C2#919114yesdirect product factor
467C2C2×#187211yescharacteristic
468C2C2×#190911yescharacteristic
469C2C2×#191411yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radicalC25C22⋊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
3. C2×#1548C2semidirect
5. #9191C2direct (N × H)
6. C2×#1286C2semidirect
29. #1548C22semidirect
35. #1286C22semidirect
466. C2#9191direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#29052
C2×#26282
C2×#15482
C2×#14582
#91912
C2×#12862