Finite Group Databasebeta

← C2×#68951 #10792617

Subgroups — C2×#68951 #10792617

Order 768.

2350 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#877C211yesmaximal, characteristic
2C22×#877C212yesmaximal
3C2×C3×#342C211yesmaximal, characteristic
4C2×#4527C212yesmaximal
5C2×#4526C211yesmaximal, characteristic
6#68951C218yesmaximal, direct product factor
7C2×#1740—31nomaximal, Sylow
8C24×Dic3C2211yescharacteristic
9C22×C3×C22⋊C4C2211yescharacteristic
10C22×C3×C22⋊C4C2212yes—
11C22×#217C2211yescharacteristic
12C22×#217C2212yes—
13C22×Dic3⋊C4—22no—
14C22×Dic3⋊C4C412yescomplemented
15C22×C4×Dic3—22no—
16C22×C4×Dic3C412yescomplemented
17C2×#877—24no—
18C2×#877—24no—
19C2×#877—22no—
20C2×#877—22no—
21C2×#877—28no—
22C2×#877C414yescomplemented
23C2×#877C4116yescomplemented
24C2×#877C2214yes—
25C2×#877C2218yes—
26C3×#342C2214yes—
27#4527C2218yes—
28#4526C2214yes—
29C22×#117—31no—
30C22×#117—32no—
31#1740—38no—
32C2×#342—31no—
33C2×#342—32no—
34C2×#342D311yescharacteristic
35C25×C3C2311yescharacteristic
36C23×C3×C4—22no—
37C23×C3×C4C2×C412yes—
38C23×Dic3—22no—
39C23×Dic3C2×C412yes—
40C23×Dic3C2×C412yes—
41C23×Dic3C2×C418yes—
42C23×Dic3C2×C411yescharacteristic
43C23×Dic3C2×C411yescharacteristic
44C23×Dic3D414yes—
45C23×Dic3D414yes—
46C23×Dic3D412yes—
47C23×Dic3D412yes—
48C23×Dic3Q814yes—
49C23×Dic3C2312yes—
50C2×C3×C22⋊C4—22no—
51C2×C3×C22⋊C4—22no—
52C2×C3×C22⋊C4—22no—
53C2×C3×C22⋊C4—24no—
54C2×C3×C22⋊C4C2×C412yes—
55C2×C3×C22⋊C4C2×C418yes—
56C2×C3×C22⋊C4C2312yes—
57C2×C3×C22⋊C4C2314yes—
58C2×#217—22no—
59C2×#217—22no—
60C2×#217—22no—
61C2×#217—24no—
62C2×#217C2×C412yes—
63C2×#217C2×C418yes—
64C2×#217C2312yes—
65C2×#217C2314yes—
66C2×Dic3⋊C4—24no—
67C2×Dic3⋊C4—24no—
68C2×Dic3⋊C4—216no—
69C2×Dic3⋊C4—28no—
70C2×Dic3⋊C4C2×C418yescomplemented
71C2×C4×Dic3—24no—
72C2×C4×Dic3—22no—
73C2×C4×Dic3—22no—
74C2×C4×Dic3—216no—
75C2×C4×Dic3—28no—
76C2×C4×Dic3C2×C418yescomplemented
77#877—28no—
78#877—28no—
79#877—232no—
80#877—28no—
81#877—28no—
82#877—216no—
83#877C2×C4132yescomplemented
84C24×C4—31no—
85C2×#117—34no—
86C2×#117—34no—
87C2×#117—316no—
88C2×#117—38no—
89C2×#117—68no—
90C2×#117—64no—
91C2×#117—62no—
92C2×#117—64no—
93C2×#117—62no—
94C22×C4⋊C4—32no—
95C22×C4⋊C4—62no—
96C22×C22⋊C4—32no—
97C22×C22⋊C4—31no—
98C22×C22⋊C4C2×D311yescharacteristic
99C22×C22⋊C4C2×D312yes—
100C22×C42—32no—
101C22×C42—62no—
102#342—34no—
103#342—38no—
104#342C2×D314yes—
105C24×C3—44no—
106C24×C3C22×C411yescharacteristic
107C24×C3C22×C414yes—
108C24×C3C22×C411yescharacteristic
109C24×C3C2×D412yes—
110C24×C3C2×D412yes—
111C24×C3C2×D412yes—
112C24×C3C2×Q812yes—
113C24×C3C2411yescharacteristic
114C22×C3×C4—22no—
115C22×C3×C4—22no—
116C22×C3×C4—28no—
117C22×C3×C4—24no—
118C22×C3×C4—48no—
119C22×C3×C4—44no—
120C22×C3×C4C22×C414yes—
121C22×Dic3—22no—
122C22×Dic3—22no—
123C22×Dic3—28no—
124C22×Dic3—24no—
125C22×Dic3—48no—
126C22×Dic3—44no—
127C22×Dic3C4214yes—
128C22×Dic3C4214yes—
129C22×Dic3C4218yes—
130C22×Dic3C22⋊C414yes—
131C22×Dic3C22⋊C414yes—
132C22×Dic3C22⋊C4116yes—
133C22×Dic3C22⋊C412yes—
134C22×Dic3C22⋊C418yes—
135C22×Dic3C22⋊C411yescharacteristic
136C22×Dic3C22⋊C411yescharacteristic
137C22×Dic3C22⋊C412yes—
138C22×Dic3C22⋊C418yes—
139C22×Dic3C22⋊C412yes—
140C22×Dic3C4⋊C418yes—
141C22×Dic3C4⋊C418yes—
142C22×Dic3C4⋊C414yes—
143C22×Dic3C4⋊C414yes—
144C22×Dic3C4⋊C4116yes—
145C22×Dic3C4⋊C418yes—
146C22×Dic3C22×C414yes—
147C22×Dic3C22×C418yes—
148C22×Dic3C22×C412yes—
149C22×Dic3C22×C412yes—
150C22×Dic3C2×D414yes—
151C22×Dic3C2×D414yes—
152C22×Dic3C2×D414yes—
153C22×Dic3C2×Q814yes—
154C3×C22⋊C4—24no—
155C3×C22⋊C4—28no—
156C3×C22⋊C4—24no—
157C3×C22⋊C4—24no—
158C3×C22⋊C4C22×C418yes—
159#217—24no—
160#217—28no—
161#217—24no—
162#217—24no—
163#217C22×C418yes—
164Dic3⋊C4—216no—
165Dic3⋊C4—232no—
166C4×Dic3—28no—
167C4×Dic3—28no—
168C4×Dic3—232no—
169C25C22×D311yescharacteristic
170C23×C4—22no—
171C23×C4—31no—
172C23×C4—38no—
173C23×C4—32no—
174C23×C4—31no—
175C23×C4—32no—
176C23×C4—34no—
177C23×C4—34no—
178C23×C4—32no—
179C23×C4—34no—
180C23×C4—32no—
181C23×C4—32no—
182C23×C4—62no—
183C23×C4C4×D312yes—
184#117—332no—
185#117—68no—
186#117—68no—
187#117—68no—
188#117—68no—
189#117—632no—
190#117—616no—
191C2×C4⋊C4—38no—
192C2×C4⋊C4—64no—
193C2×C4⋊C4—64no—
194C2×C4⋊C4—616no—
195C2×C4⋊C4—68no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4—24no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—38no—
201C2×C22⋊C4—34no—
202C2×C22⋊C4—32no—
203C2×C22⋊C4—32no—
204C2×C22⋊C4—62no—
205C2×C22⋊C4—64no—
206C2×C22⋊C4—62no—
207C2×C22⋊C4—62no—
208C2×C22⋊C4C4×D312yes—
209C2×C22⋊C4C4×D318yes—
210C2×C22⋊C4C22×D312yes—
211C2×C22⋊C4C22×D314yes—
212C2×C42—38no—
213C2×C42—616no—
214C2×C42—68no—
215C2×C42—64no—
216C2×C42—62no—
217C2×C42—62no—
218C23×C3—24no—
219C23×C3—28no—
220C23×C3—42no—
221C23×C3—48no—
222C23×C3—44no—
223C23×C3—44no—
224C23×C3—44no—
225C23×C3—42no—
226C23×C3C2×C4212yes—
227C23×C3C2×C4212yes—
228C23×C3C2×C22⋊C412yes—
229C23×C3C2×C22⋊C411yescharacteristic
230C23×C3C2×C22⋊C414yes—
231C23×C3C2×C22⋊C414yes—
232C23×C3C2×C22⋊C411yescharacteristic
233C23×C3C2×C4⋊C412yes—
234C23×C3C2×C4⋊C414yes—
235C23×C3C2×C4⋊C412yes—
236C23×C3C2×C4⋊C414yes—
237C23×C3C23×C411yescharacteristic
238C23×C3C23×C412yes—
239C23×C3C22×D412yes—
240C23×C3C22×D411yescharacteristic
241C23×C3C22×Q811yescharacteristic
242C2×C3×C4—24no—
243C2×C3×C4—28no—
244C2×C3×C4—48no—
245C2×C3×C4—416no—
246C2×C3×C4—44no—
247C2×C3×C4—44no—
248C2×C3×C4—44no—
249C2×Dic3—24no—
250C2×Dic3—28no—
251C2×Dic3—48no—
252C2×Dic3—416no—
253C2×Dic3—44no—
254C2×Dic3—44no—
255C2×Dic3—44no—
256C2×Dic3#9518yes—
257C2×Dic3#95116yes—
258C2×Dic3#9518yes—
259C2×Dic3#95116yes—
260C2×Dic3#9514yes—
261C2×Dic3#9518yes—
262C2×Dic3#9514yes—
263C2×Dic3C2×C4214yes—
264C2×Dic3C2×C4214yes—
265C2×Dic3C2×C22⋊C418yes—
266C2×Dic3C2×C22⋊C412yes—
267C2×Dic3C2×C22⋊C412yes—
268C2×Dic3C2×C22⋊C418yes—
269C2×Dic3C2×C22⋊C414yes—
270C2×Dic3C2×C4⋊C418yes—
271C2×Dic3C2×C4⋊C418yes—
272C2×Dic3C2×C4⋊C414yes—
273C2×Dic3C2×C4⋊C414yes—
274C24—44no—
275C24C2×C4×D311yescharacteristic
276C24C2×C4×D314yes—
277C24C2×C4×D311yescharacteristic
278C24D3×D412yes—
279C24D3×D412yes—
280C24D3×D412yes—
281C24D3×Q812yes—
282C24C23×D311yescharacteristic
283C22×C4—22no—
284C22×C4—28no—
285C22×C4—22no—
286C22×C4—24no—
287C22×C4—34no—
288C22×C4—34no—
289C22×C4—38no—
290C22×C4—38no—
291C22×C4—32no—
292C22×C4—32no—
293C22×C4—38no—
294C22×C4—34no—
295C22×C4—34no—
296C22×C4—316no—
297C22×C4—31no—
298C22×C4—31no—
299C22×C4—32no—
300C22×C4—34no—
301C22×C4—38no—
302C22×C4—38no—
303C22×C4—34no—
304C22×C4—38no—
305C22×C4—316no—
306C22×C4—32no—
307C22×C4—32no—
308C22×C4—38no—
309C22×C4—34no—
310C22×C4—34no—
311C22×C4—34no—
312C22×C4—34no—
313C22×C4—34no—
314C22×C4—48no—
315C22×C4—44no—
316C22×C4—68no—
317C22×C4—62no—
318C22×C4—62no—
319C22×C4—64no—
320C22×C4—128no—
321C22×C4—124no—
322C22×C4C2×C4×D314yes—
323C4⋊C4—616no—
324C4⋊C4—632no—
325C22⋊C4—24no—
326C22⋊C4—28no—
327C22⋊C4—24no—
328C22⋊C4—24no—
329C22⋊C4—38no—
330C22⋊C4—68no—
331C22⋊C4—64no—
332C22⋊C4—64no—
333C22⋊C4—64no—
334C22⋊C4C2×C4×D318yes—
335C42—68no—
336C42—68no—
337C42—632no—
338C22×C3—22no—
339C22×C3—22no—
340C22×C3—24no—
341C22×C3—24no—
342C22×C3—28no—
343C22×C3—24no—
344C22×C3—24no—
345C22×C3—28no—
346C22×C3—42no—
347C22×C3—44no—
348C22×C3—42no—
349C22×C3—44no—
350C22×C3—42no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3C2×#9512yes—
354C22×C3C2×#9514yes—
355C22×C3C2×#9512yes—
356C22×C3#41014yes—
357C22×C3C22×C4211yescharacteristic
358C22×C3C22×C22⋊C412yes—
359C22×C3C22×C22⋊C411yescharacteristic
360C22×C3C22×C4⋊C411yescharacteristic
361C22×C3C22×C4⋊C412yes—
362C3×C4—48no—
363C3×C4—44no—
364Dic3—48no—
365Dic3—44no—
366Dic3C2×#9514yes—
367Dic3C2×#9514yes—
368Dic3C2×#9518yes—
369C23—24no—
370C23—28no—
371C23—48no—
372C23—42no—
373C23—44no—
374C23—44no—
375C23—44no—
376C23—42no—
377C23C42×D312yes—
378C23C42×D312yes—
379C23D3×C22⋊C412yes—
380C23D3×C22⋊C414yes—
381C23D3×C22⋊C411yescharacteristic
382C23D3×C22⋊C414yes—
383C23D3×C22⋊C411yescharacteristic
384C23D3×C4⋊C412yes—
385C23D3×C4⋊C414yes—
386C23D3×C4⋊C414yes—
387C23D3×C4⋊C412yes—
388C23C22×C4×D311yescharacteristic
389C23C22×C4×D312yes—
390C23C2×D3×D412yes—
391C23C2×D3×D411yescharacteristic
392C23C2×D3×Q811yescharacteristic
393C2×C4—24no—
394C2×C4—28no—
395C2×C4—38no—
396C2×C4—316no—
397C2×C4—38no—
398C2×C4—316no—
399C2×C4—34no—
400C2×C4—38no—
401C2×C4—34no—
402C2×C4—34no—
403C2×C4—34no—
404C2×C4—38no—
405C2×C4—32no—
406C2×C4—32no—
407C2×C4—38no—
408C2×C4—34no—
409C2×C4—34no—
410C2×C4—34no—
411C2×C4—38no—
412C2×C4—38no—
413C2×C4—416no—
414C2×C4—48no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4—44no—
418C2×C4—68no—
419C2×C4—64no—
420C2×C4—1216no—
421C2×C4—128no—
422C2×C4—124no—
423C2×C4—124no—
424C2×C4—124no—
425C2×C3—22no—
426C2×C3—21no—
427C2×C3—22no—
428C2×C3—22no—
429C2×C3—24no—
430C2×C3—21no—
431C2×C3#174014yescomplemented
432C2×C3C22×#9511yescharacteristic
433C2×C3C2×#41012yes—
434C22—28no—
435C22—24no—
436C22—24no—
437C22—28no—
438C22—22no—
439C22—22no—
440C22—24no—
441C22—24no—
442C22—42no—
443C22—44no—
444C22—42no—
445C22—44no—
446C22—42no—
447C22—41no—
448C22—41no—
449C22D3×#9512yes—
450C22D3×#9514yes—
451C22D3×#9512yes—
452C22#474014yes—
453C22C2×C42×D311yescharacteristic
454C22C2×D3×C22⋊C412yes—
455C22C2×D3×C22⋊C411yescharacteristic
456C22C2×D3×C4⋊C411yescharacteristic
457C22C2×D3×C4⋊C412yes—
458C4—34no—
459C4—38no—
460C4—34no—
461C4—48no—
462C4—44no—
463C4—128no—
464C4—124no—
465C3C2×#174011yescharacteristic, complemented, Sylow
466C2—22no—
467C2—24no—
468C2—22no—
469C2—21no—
470C2—21no—
471C2—22no—
472C2#6895114yesdirect product factor
473C2C2×D3×#9511yescharacteristic
474C2C2×#474012yes—
subgroupG/H
centerC23D3×C22⋊C4
commutatorC22×C3C22×C42
FrattiniC24C23×D3
FittingC2×C3×#342C2
socleC23×C3C2×C22⋊C4
prime radicalC25×C3C23
cosocleC24×C3C24
hypercenterC2×#342D3
hypocenterC3C2×#1740
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
6. #68951C2direct (N × H)
14. C22×Dic3⋊C4C4semidirect
16. C22×C4×Dic3C4semidirect
22. C2×#877C4semidirect
23. C2×#877C4semidirect
70. C2×Dic3⋊C4C2×C4semidirect
76. C2×C4×Dic3C2×C4semidirect
83. #877C2×C4semidirect
431. C2×C3#1740semidirect
465. C3C2×#1740semidirect
472. C2#68951direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#8772
C2×C3×#3422
C2×#45272
C2×#45262
#689512
C2×#17403