Finite Group Databasebeta

← C2×#10591368 #11800708

Subgroups — C2×#10591368 #11800708

Order 1152.

2969 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D3×Dic3C211yesmaximal, characteristic
2C22×C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic
4C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic
5C22×Dic32C211yesmaximal, characteristic, complemented
6C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
7C2×#63579C211yesmaximal, characteristic, complemented
8#10591368C218yesmaximal, direct product factor
9C2×Dic3×C22⋊C4—31nomaximal
10C2×#4666—31nomaximal
11C24×C3×D3C2211yescharacteristic
12C23×C32×C4C2211yescharacteristic
13C23×C3⋊Dic3C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C22×D3×Dic3—24no—
19C22×D3×Dic3—24no—
20C22×D3×Dic3C418yescomplemented
21C22×D3×Dic3C2214yes—
22C2×C4×C3⋊Dic3—24no—
23C2×C4×C3⋊Dic3C2214yescomplemented
24C2×C3×(C2×D3)⋊C4C418yescomplemented
25C2×C3×(C2×D3)⋊C4C2214yes—
26C2×(C2×D3)⋊Dic3C418yescomplemented
27C2×(C2×D3)⋊Dic3C2214yes—
28C2×Dic32—24no—
29C2×Dic32C2214yescomplemented
30C3×C3⋊#95C2214yescomplemented
31#63579C2214yescomplemented
32C24×Dic3—31no—
33C23×C4×D3—31no—
34C22×C3×C22⋊C4—31no—
35C22×#217—31no—
36C22×(C2×D3)⋊C4—31no—
37C22×(C2×D3)⋊C4D311yescharacteristic
38C22×C4×Dic3—31no—
39C22×C4×Dic3—31no—
40C22×C4×Dic3—31no—
41C22×C4×Dic3—31no—
42C22×C4×Dic3—61no—
43C2×C3×#95—31no—
44C2×C3⋊#95—31no—
45C2×C3⋊#95—31no—
46C2×C3⋊#95D311yescharacteristic, complemented
47Dic3×C22⋊C4—38no—
48#4666—38no—
49C24×C32C2311yescharacteristic
50C23×C3×D3—22no—
51C23×C3×D3—22no—
52C23×C3×D3—22no—
53C23×C3×D3—22no—
54C23×C3×D3C2×C414yes—
55C23×C3×D3C2×C414yes—
56C23×C3×D3C2×C414yes—
57C23×C3×D3C2312yes—
58C22×C32×C4—22no—
59C22×C32×C4—22no—
60C22×C32×C4C2×C414yescomplemented
61C22×C32×C4C2312yes—
62C22×C3⋊Dic3—22no—
63C22×C3⋊Dic3—22no—
64C22×C3⋊Dic3C2×C414yes—
65C22×C3⋊Dic3C2×C414yescomplemented
66C22×C3⋊Dic3D414yes—
67C22×C3⋊Dic3D414yes—
68C22×C3⋊Dic3C2312yes—
69C22×C3⋊Dic3C2312yes—
70C22×C3×Dic3—22no—
71C22×C3×Dic3—22no—
72C22×C3×Dic3—22no—
73C22×C3×Dic3—22no—
74C22×C3×Dic3—22no—
75C22×C3×Dic3—22no—
76C22×C3×Dic3C2×C414yes—
77C22×C3×Dic3C2×C414yescomplemented
78C22×C3×Dic3C2×C414yescomplemented
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82C2×D3×Dic3—232no—
83C2×D3×Dic3—28no—
84C2×D3×Dic3—28no—
85C2×D3×Dic3C2×C4116yescomplemented
86C4×C3⋊Dic3—28no—
87C3×(C2×D3)⋊C4C2×C4116yescomplemented
88(C2×D3)⋊Dic3C2×C4116yescomplemented
89Dic32—28no—
90C2×C4×C22⋊C4—91noSylow
91C25×C3—31no—
92C24×D3C2×D311yescharacteristic
93C23×C3×C4—21no—
94C23×C3×C4—31no—
95C23×C3×C4—31no—
96C23×C3×C4—31no—
97C23×C3×C4C2×D311yescharacteristic
98C23×C3×C4C2×D311yescharacteristic
99C23×Dic3—31no—
100C23×Dic3—31no—
101C23×Dic3—31no—
102C23×Dic3—31no—
103C23×Dic3—38no—
104C23×Dic3—34no—
105C23×Dic3—61no—
106C23×Dic3—61no—
107C23×Dic3—64no—
108C23×Dic3—64no—
109C23×Dic3C2×D311yescharacteristic
110C23×Dic3C2×D311yescharacteristic
111C23×Dic3C2×D311yescharacteristic
112C22×C4×D3—38no—
113C22×C4×D3—34no—
114C22×C4×D3—64no—
115C22×C4×D3—64no—
116C2×C3×C22⋊C4—38no—
117C2×C3×C22⋊C4—34no—
118C2×#217—38no—
119C2×#217—34no—
120C2×(C2×D3)⋊C4—38no—
121C2×(C2×D3)⋊C4—34no—
122C2×(C2×D3)⋊C4Dic318yescomplemented
123C2×(C2×D3)⋊C4C2×D314yes—
124C2×C4×Dic3—34no—
125C2×C4×Dic3—34no—
126C2×C4×Dic3—34no—
127C2×C4×Dic3—34no—
128C2×C4×Dic3—64no—
129C2×C4×Dic3—64no—
130C2×C4×Dic3—64no—
131C2×C4×Dic3—64no—
132C2×C4×Dic3—64no—
133C2×C4×Dic3—68no—
134C3×#95—34no—
135C3⋊#95—34no—
136C3⋊#95—34no—
137C3⋊#95C2×D314yescomplemented
138C23×C32C22×C412yes—
139C23×C32C22×C412yes—
140C23×C32C22×C412yes—
141C23×C32C2×D412yes—
142C23×C32C2×D412yes—
143C23×C32#4112yes—
144C23×C32#4112yes—
145C23×C32C2411yescharacteristic
146C22×C3×D3—28no—
147C22×C3×D3—28no—
148C22×C3×D3—28no—
149C22×C3×D3—28no—
150C22×C3×D3—28no—
151C22×C3×D3—28no—
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3—22no—
155C22×C3×D3—22no—
156C22×C3×D3C42116yescomplemented
157C22×C3×D3C22×C414yes—
158C22×C3×D3C22×C414yes—
159C22×C3×D3C22×C414yes—
160C2×C32×C4—28no—
161C2×C32×C4—22no—
162C2×C32×C4—22no—
163C2×C32×C4C22×C414yescomplemented
164C2×C3⋊Dic3—28no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3C22⋊C4116yescomplemented
168C2×C3⋊Dic3C22×C414yes—
169C2×C3⋊Dic3C22×C414yescomplemented
170C2×C3⋊Dic3C2×D414yes—
171C2×C3⋊Dic3C2×D414yes—
172C2×C3×Dic3—28no—
173C2×C3×Dic3—28no—
174C2×C3×Dic3—28no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3C22×C414yes—
182C2×C3×Dic3C22×C414yescomplemented
183C2×C3×Dic3C22×C414yescomplemented
184D3×Dic3—232no—
185C24×C4—91no—
186C22×C22⋊C4—31no—
187C22×C22⋊C4—91no—
188C22×C42—91no—
189C22×C42—91no—
190C4×C22⋊C4—98no—
191C2×#95—31no—
192C2×#95—91no—
193C24×C3—21no—
194C24×C3—34no—
195C24×C3—34no—
196C24×C3—34no—
197C24×C3—32no—
198C24×C3—62no—
199C24×C3—62no—
200C24×C3—62no—
201C24×C3—62no—
202C24×C3C22×D311yescharacteristic
203C24×C3C22×D311yescharacteristic
204C23×D3—22no—
205C23×D3—22no—
206C23×D3—22no—
207C23×D3—22no—
208C23×D3C4×D314yes—
209C23×D3C4×D314yes—
210C23×D3C2×Dic314yes—
211C23×D3C22×D312yes—
212C22×C3×C4—24no—
213C22×C3×C4—24no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—22no—
218C22×C3×C4—24no—
219C22×C3×C4—22no—
220C22×C3×C4—34no—
221C22×C3×C4—34no—
222C22×C3×C4—34no—
223C22×C3×C4—32no—
224C22×C3×C4—32no—
225C22×C3×C4—32no—
226C22×C3×C4—62no—
227C22×C3×C4—62no—
228C22×C3×C4—62no—
229C22×C3×C4—62no—
230C22×C3×C4—62no—
231C22×C3×C4—62no—
232C22×C3×C4C4×D314yescomplemented
233C22×C3×C4C2×Dic314yescomplemented
234C22×C3×C4C22×D312yes—
235C22×C3×C4C22×D312yes—
236C22×Dic3—22no—
237C22×Dic3—22no—
238C22×Dic3—22no—
239C22×Dic3—22no—
240C22×Dic3—22no—
241C22×Dic3—22no—
242C22×Dic3—34no—
243C22×Dic3—34no—
244C22×Dic3—34no—
245C22×Dic3—34no—
246C22×Dic3—34no—
247C22×Dic3—34no—
248C22×Dic3—32no—
249C22×Dic3—32no—
250C22×Dic3—34no—
251C22×Dic3—34no—
252C22×Dic3—32no—
253C22×Dic3—32no—
254C22×Dic3—316no—
255C22×Dic3—64no—
256C22×Dic3—62no—
257C22×Dic3—62no—
258C22×Dic3—64no—
259C22×Dic3—64no—
260C22×Dic3—64no—
261C22×Dic3—632no—
262C22×Dic3—68no—
263C22×Dic3—68no—
264C22×Dic3—64no—
265C22×Dic3—64no—
266C22×Dic3—62no—
267C22×Dic3—62no—
268C22×Dic3—62no—
269C22×Dic3—62no—
270C22×Dic3C4×D314yes—
271C22×Dic3C4×D314yescomplemented
272C22×Dic3C2×Dic314yescomplemented
273C22×Dic3C22×D312yes—
274C22×Dic3C22×D312yes—
275C22×Dic3C22×D312yes—
276C2×C4×D3—316no—
277C2×C4×D3—632no—
278C2×C4×D3—68no—
279C2×C4×D3—68no—
280C3×C22⋊C4—316no—
281#217—316no—
282(C2×D3)⋊C4—316no—
283(C2×D3)⋊C4C2×Dic3116yescomplemented
284C4×Dic3—68no—
285C4×Dic3—68no—
286C4×Dic3—68no—
287C4×Dic3—68no—
288C4×Dic3—616no—
289C22×C32C2×C4214yes—
290C22×C32C2×C22⋊C414yes—
291C22×C32#11714yes—
292C22×C32C4×D414yes—
293C22×C32C4×D414yes—
294C22×C32C4×D414yes—
295C22×C32C4×D414yes—
296C22×C32C23×C411yescharacteristic
297C22×C32C23×C411yescharacteristic
298C22×C32C23×C411yescharacteristic
299C22×C32C22×D411yescharacteristic
300C22×C32C22×D411yescharacteristic
301C22×C32C2×#4111yescharacteristic
302C22×C32C2×#4111yescharacteristic
303C2×C3×D3—24no—
304C2×C3×D3—24no—
305C2×C3×D3—24no—
306C2×C3×D3—24no—
307C2×C3×D3—24no—
308C2×C3×D3—24no—
309C2×C3×D3—232no—
310C2×C3×D3C2×C4218yescomplemented
311C32×C4—24no—
312C3⋊Dic3—24no—
313C3⋊Dic3C2×C22⋊C418yescomplemented
314C3×Dic3—24no—
315C3×Dic3—24no—
316C3×Dic3—24no—
317C25—31no—
318C23×C4—31no—
319C23×C4—31no—
320C23×C4—31no—
321C23×C4—94no—
322C23×C4—98no—
323C23×C4—91no—
324C23×C4—91no—
325C23×C4—184no—
326C23×C4—184no—
327C23×C4D3211yescharacteristic
328C2×C22⋊C4—38no—
329C2×C22⋊C4—34no—
330C2×C22⋊C4—94no—
331C2×C22⋊C4—98no—
332C2×C42—94no—
333C2×C42—94no—
334C2×C42—184no—
335C2×C42—184no—
336#95—34no—
337#95—94no—
338C23×C3—21no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—22no—
342C23×C3—22no—
343C23×C3—22no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—316no—
347C23×C3—34no—
348C23×C3—34no—
349C23×C3—34no—
350C23×C3—68no—
351C23×C3—68no—
352C23×C3—68no—
353C23×C3—68no—
354C23×C3—68no—
355C23×C3—68no—
356C23×C3—62no—
357C23×C3—62no—
358C23×C3—62no—
359C23×C3—62no—
360C23×C3C2×C4×D312yes—
361C23×C3C2×C4×D312yes—
362C23×C3C2×C4×D312yes—
363C23×C3C2×C4×D312yes—
364C23×C3C2×C4×D312yes—
365C23×C3D3×D412yes—
366C23×C3D3×D412yes—
367C23×C3D3×D412yes—
368C23×C3D3×D412yes—
369C23×C3#23712yes—
370C23×C3#23712yes—
371C23×C3#23712yes—
372C23×C3#23912yes—
373C23×C3C22×Dic312yes—
374C23×C3C23×D311yescharacteristic
375C23×C3C23×D311yescharacteristic
376C22×D3—28no—
377C22×D3—28no—
378C22×D3—28no—
379C22×D3—28no—
380C22×D3—28no—
381C22×D3—28no—
382C22×D3—22no—
383C22×D3—22no—
384C22×D3—22no—
385C22×D3—22no—
386C22×D3C4×Dic3116yescomplemented
387C22×D3C2×C4×D314yes—
388C22×D3C2×C4×D314yes—
389C22×D3C22×Dic314yes—
390C2×C3×C4—24no—
391C2×C3×C4—24no—
392C2×C3×C4—216no—
393C2×C3×C4—28no—
394C2×C3×C4—28no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—24no—
400C2×C3×C4—34no—
401C2×C3×C4—34no—
402C2×C3×C4—34no—
403C2×C3×C4—68no—
404C2×C3×C4—68no—
405C2×C3×C4—68no—
406C2×C3×C4—62no—
407C2×C3×C4—62no—
408C2×C3×C4—62no—
409C2×C3×C4—62no—
410C2×C3×C4—62no—
411C2×C3×C4—62no—
412C2×C3×C4C2×C4×D314yescomplemented
413C2×C3×C4C22×Dic314yescomplemented
414C2×Dic3—28no—
415C2×Dic3—28no—
416C2×Dic3—28no—
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—22no—
423C2×Dic3—316no—
424C2×Dic3—316no—
425C2×Dic3—34no—
426C2×Dic3—34no—
427C2×Dic3—34no—
428C2×Dic3—34no—
429C2×Dic3—34no—
430C2×Dic3—34no—
431C2×Dic3—34no—
432C2×Dic3—34no—
433C2×Dic3—616no—
434C2×Dic3—64no—
435C2×Dic3—64no—
436C2×Dic3—64no—
437C2×Dic3—64no—
438C2×Dic3—632no—
439C2×Dic3—64no—
440C2×Dic3—64no—
441C2×Dic3—616no—
442C2×Dic3—68no—
443C2×Dic3—68no—
444C2×Dic3—62no—
445C2×Dic3—62no—
446C2×Dic3—62no—
447C2×Dic3—62no—
448C2×Dic3C2×C4×D314yes—
449C2×Dic3C2×C4×D314yescomplemented
450C2×Dic3C22×Dic314yescomplemented
451C4×D3—632no—
452C2×C32C4×C22⋊C418yescomplemented
453C2×C32C22×C4211yescharacteristic
454C2×C32C22×C22⋊C411yescharacteristic
455C2×C32C2×#11711yescharacteristic
456C2×C32C2×C4×D411yescharacteristic
457C2×C32C2×C4×D411yescharacteristic
458C2×C32C2×C4×D411yescharacteristic
459C2×C32C2×C4×D411yescharacteristic
460C3×D3—28no—
461C24—32no—
462C24—34no—
463C24—34no—
464C24—34no—
465C24—62no—
466C24—62no—
467C24—62no—
468C24—62no—
469C24C2×D3211yescharacteristic
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—32no—
473C22×C4—32no—
474C22×C4—32no—
475C22×C4—34no—
476C22×C4—34no—
477C22×C4—34no—
478C22×C4—62no—
479C22×C4—62no—
480C22×C4—62no—
481C22×C4—62no—
482C22×C4—62no—
483C22×C4—62no—
484C22×C4—916no—
485C22×C4—92no—
486C22×C4—94no—
487C22×C4—94no—
488C22×C4—94no—
489C22×C4—92no—
490C22×C4—94no—
491C22×C4—188no—
492C22×C4—188no—
493C22×C4—1832no—
494C22×C4—182no—
495C22×C4—182no—
496C22×C4D3×Dic314yescomplemented
497C22×C4C2×D3212yes—
498C22⋊C4—316no—
499C22⋊C4—916no—
500C42—188no—
501C42—188no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—24no—
510C22×C3—24no—
511C22×C3—24no—
512C22×C3—24no—
513C22×C3—24no—
514C22×C3—24no—
515C22×C3—24no—
516C22×C3—38no—
517C22×C3—632no—
518C22×C3—64no—
519C22×C3—64no—
520C22×C3—64no—
521C22×C3—64no—
522C22×C3—64no—
523C22×C3—64no—
524C22×C3C42×D314yes—
525C22×C3#87714yes—
526C22×C3D3×C22⋊C414yes—
527C22×C3D3×C22⋊C414yes—
528C22×C3#67⋊C414yes—
529C22×C3#67⋊C414yes—
530C22×C3#67⋊C414yes—
531C22×C3#67⋊C414yes—
532C22×C3#89214yes—
533C22×C3#89314yes—
534C22×C3#89314yes—
535C22×C3C2×C4×Dic314yes—
536C22×C3D4×Dic314yes—
537C22×C3D4×Dic314yes—
538C22×C3C22×C4×D311yescharacteristic
539C22×C3C22×C4×D311yescharacteristic
540C22×C3C22×C4×D311yescharacteristic
541C22×C3C22×C4×D311yescharacteristic
542C22×C3C22×C4×D311yescharacteristic
543C22×C3C2×D3×D411yescharacteristic
544C22×C3C2×D3×D411yescharacteristic
545C22×C3C2×D3×D411yescharacteristic
546C22×C3C2×D3×D411yescharacteristic
547C22×C3C2×#23711yescharacteristic
548C22×C3C2×#23711yescharacteristic
549C22×C3C2×#23711yescharacteristic
550C22×C3C2×#23911yescharacteristic
551C22×C3C23×Dic311yescharacteristic
552C2×D3—232no—
553C2×D3—24no—
554C2×D3—24no—
555C2×D3—24no—
556C2×D3—24no—
557C2×D3—24no—
558C2×D3—24no—
559C2×D3C2×C4×Dic318yescomplemented
560C3×C4—28no—
561C3×C4—24no—
562C3×C4—24no—
563C3×C4—64no—
564C3×C4—64no—
565C3×C4—64no—
566Dic3—24no—
567Dic3—24no—
568Dic3—24no—
569Dic3—38no—
570Dic3—38no—
571Dic3—68no—
572Dic3—68no—
573Dic3—64no—
574Dic3—64no—
575C32C2×C4×C22⋊C411yescharacteristic, complemented, Sylow
576C23—34no—
577C23—34no—
578C23—34no—
579C23—316no—
580C23—62no—
581C23—62no—
582C23—62no—
583C23—62no—
584C23—68no—
585C23—68no—
586C23—68no—
587C23—68no—
588C23—68no—
589C23—68no—
590C23#379612yes—
591C23C4×D3212yes—
592C23C4×D3212yes—
593C23#380212yes—
594C23C2×D3×Dic312yes—
595C23#380512yes—
596C23#381112yes—
597C23C22×D3211yescharacteristic
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—28no—
601C2×C4—34no—
602C2×C4—34no—
603C2×C4—34no—
604C2×C4—62no—
605C2×C4—62no—
606C2×C4—62no—
607C2×C4—62no—
608C2×C4—62no—
609C2×C4—62no—
610C2×C4—68no—
611C2×C4—68no—
612C2×C4—68no—
613C2×C4—94no—
614C2×C4—94no—
615C2×C4—94no—
616C2×C4—916no—
617C2×C4—94no—
618C2×C4—1832no—
619C2×C4—182no—
620C2×C4—182no—
621C2×C4—188no—
622C2×C4C2×D3×Dic314yescomplemented
623C2×C3—21no—
624C2×C3—21no—
625C2×C3—21no—
626C2×C3—21no—
627C2×C3—28no—
628C2×C3—21no—
629C2×C3—21no—
630C2×C3—21no—
631C2×C3—68no—
632C2×C3#466618yescomplemented
633C2×C3Dic3×C22⋊C418yescomplemented
634C2×C3C2×C42×D311yescharacteristic
635C2×C3C2×#87711yescharacteristic
636C2×C3C2×D3×C22⋊C411yescharacteristic
637C2×C3C2×D3×C22⋊C411yescharacteristic
638C2×C3C2×#67⋊C411yescharacteristic
639C2×C3C2×#67⋊C411yescharacteristic
640C2×C3C2×#67⋊C411yescharacteristic
641C2×C3C2×#67⋊C411yescharacteristic
642C2×C3C2×#89211yescharacteristic
643C2×C3C2×#89311yescharacteristic
644C2×C3C2×#89311yescharacteristic
645C2×C3C22×C4×Dic311yescharacteristic
646C2×C3C2×D4×Dic311yescharacteristic
647C2×C3C2×D4×Dic311yescharacteristic
648D3—28no—
649C22—38no—
650C22—64no—
651C22—64no—
652C22—64no—
653C22—632no—
654C22—64no—
655C22—64no—
656C22—64no—
657C22C4×D3×Dic314yes—
658C22#6387814yes—
659C22#6388114yes—
660C22#6389814yes—
661C22#6390214yes—
662C22#6392114yes—
663C22#67⋊Dic314yes—
664C22C2×#379611yescharacteristic
665C22C2×C4×D3211yescharacteristic
666C22C2×C4×D3211yescharacteristic
667C22C2×#380211yescharacteristic
668C22C22×D3×Dic311yescharacteristic
669C22C2×#380511yescharacteristic
670C22C2×#381111yescharacteristic
671C4—24no—
672C4—64no—
673C4—64no—
674C4—64no—
675C4—98no—
676C4—184no—
677C3—21no—
678C3C2×#466611yescharacteristic, complemented
679C3C2×Dic3×C22⋊C411yescharacteristic, complemented
680C2—68no—
681C2#1059136818yesdirect product factor
682C2C2×C4×D3×Dic311yescharacteristic
683C2C2×#6387811yescharacteristic
684C2C2×#6388111yescharacteristic
685C2C2×#6389811yescharacteristic
686C2C2×#6390211yescharacteristic
687C2C2×#6392111yescharacteristic
688C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
centerC24C2×D32
commutatorC2×C32C22×C42
FrattiniC23C22×D32
FittingC23×C32×C4C22
socleC24×C32C23
prime radicalC24×C3×D3C22
cosocleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×C4×C22⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×C3⋊Dic3C2semidirect
5. C22×Dic32C2semidirect
6. C2×C3×C3⋊#95C2semidirect
7. C2×#63579C2semidirect
8. #10591368C2direct (N × H)
20. C22×D3×Dic3C4semidirect
23. C2×C4×C3⋊Dic3C22semidirect
24. C2×C3×(C2×D3)⋊C4C4semidirect
26. C2×(C2×D3)⋊Dic3C4semidirect
29. C2×Dic32C22semidirect
30. C3×C3⋊#95C22semidirect
31. #63579C22semidirect
46. C2×C3⋊#95D3semidirect
60. C22×C32×C4C2×C4semidirect
65. C22×C3⋊Dic3C2×C4semidirect
77. C22×C3×Dic3C2×C4semidirect
78. C22×C3×Dic3C2×C4semidirect
85. C2×D3×Dic3C2×C4semidirect
87. C3×(C2×D3)⋊C4C2×C4semidirect
88. (C2×D3)⋊Dic3C2×C4semidirect
122. C2×(C2×D3)⋊C4Dic3semidirect
137. C3⋊#95C2×D3semidirect
156. C22×C3×D3C42semidirect
163. C2×C32×C4C22×C4semidirect
167. C2×C3⋊Dic3C22⋊C4semidirect
169. C2×C3⋊Dic3C22×C4semidirect
182. C2×C3×Dic3C22×C4semidirect
183. C2×C3×Dic3C22×C4semidirect
232. C22×C3×C4C4×D3semidirect
233. C22×C3×C4C2×Dic3semidirect
271. C22×Dic3C4×D3semidirect
272. C22×Dic3C2×Dic3semidirect
283. (C2×D3)⋊C4C2×Dic3semidirect
310. C2×C3×D3C2×C42semidirect
313. C3⋊Dic3C2×C22⋊C4semidirect
386. C22×D3C4×Dic3semidirect
412. C2×C3×C4C2×C4×D3semidirect
413. C2×C3×C4C22×Dic3semidirect
449. C2×Dic3C2×C4×D3semidirect
450. C2×Dic3C22×Dic3semidirect
452. C2×C32C4×C22⋊C4semidirect
496. C22×C4D3×Dic3semidirect
559. C2×D3C2×C4×Dic3semidirect
575. C32C2×C4×C22⋊C4semidirect
622. C2×C4C2×D3×Dic3semidirect
632. C2×C3#4666semidirect
633. C2×C3Dic3×C22⋊C4semidirect
678. C3C2×#4666semidirect
679. C3C2×Dic3×C22⋊C4semidirect
681. C2#10591368direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D3×Dic32
C22×C4×C3⋊Dic32
C22×C3×(C2×D3)⋊C42
C22×(C2×D3)⋊Dic32
C22×Dic322
C2×C3×C3⋊#952
C2×#635792
#105913682
C2×Dic3×C22⋊C43
C2×#46663