Finite Group Databasebeta

← C2×Dic6×#67 #11902673

Subgroups — C2×Dic6×#67 #11902673

Order 1152.

3297 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×Dic6C211yesmaximal, characteristic, complemented
2C22×D3×Dic6C211yesmaximal, characteristic, complemented
3C2×#64133C211yesmaximal, characteristic, complemented
4C2×C3×C4×#67C211yesmaximal, characteristic
5C2×Dic3×#67C212yesmaximal
6C2×#63964C212yesmaximal, complemented
7Dic6×#67C2116yesmaximal, direct product factor
8C2×#63887C212yesmaximal, complemented
9C2×#63866C211yesmaximal, characteristic, complemented
10C2×#63856C211yesmaximal, characteristic, complemented
11C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
12C2×#63839C212yesmaximal, complemented
13C2×Q8×#67—31nomaximal
14C2×D4×Dic6—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C22×#634C2211yescharacteristic
17C22×C3×#67C2211yescharacteristic
18C23×C3×Dic3C2212yes—
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×Dic6—28no—
21C22×C3×Dic6C2211yescharacteristic
22C22×C3×Dic6C2212yes—
23C22×C3×Dic6C2211yescharacteristic
24C22×C3×Dic6C2218yescomplemented
25C22×#627C2212yes—
26C22×D3×Dic3C2212yes—
27C2×D3×Dic6—28no—
28C2×D3×Dic6C2218yescomplemented
29C2×#3757C2212yes—
30C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
31#64133C2218yescomplemented
32C2×#3750C2212yes—
33C2×C3×#217C2211yescharacteristic
34C3×C4×#67C2218yes—
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38Dic3×#67C22116yes—
39C2×#3724C2212yes—
40C2×Dic3⋊Dic3C2212yes—
41C2×Dic3⋊Dic3C2212yes—
42C2×Dic3⋊Dic3C2212yes—
43#63964C22116yescomplemented
44C2×(C2×D3)⋊Dic3C2212yes—
45C2×Dic32C2212yes—
46#63887C22116yescomplemented
47#63866C2218yescomplemented
48#63856C2218yescomplemented
49Dic3×Dic6C2218yescomplemented
50#63839C22116yescomplemented
51C23×C3×Q8—31no—
52C22×D3×Q8—31no—
53C23×Dic6—31no—
54C23×Dic6D311yescharacteristic, complemented
55C2×C3×C4×D4—31no—
56Q8×#67—316no—
57C2×#946—31no—
58C2×#946—32no—
59C2×Q8×Dic3—31no—
60C2×#944—32no—
61C2×#944—31no—
62C2×D4×Dic3—32no—
63C2×C4×#67—32no—
64C2×C4×#67D311yescharacteristic
65C2×#924—31no—
66C2×#924—31no—
67C2×#924—31no—
68C2×#924—32no—
69C2×#924—61no—
70D4×Dic6—316no—
71C2×#888—32no—
72C2×#878—32no—
73C2×#878—32no—
74C2×#869—31no—
75C2×C4×Dic6—31no—
76C24×C32C2311yescharacteristic
77C23×C3×D3C2311yescharacteristic
78C22×C32×C4—24no—
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2314yes—
81C22×C32×C4C2311yescharacteristic
82C22×C3⋊Dic3C2312yes—
83C22×C3⋊Dic3C2312yes—
84C2×#634—24no—
85C2×#634C2314yes—
86C2×C3×#67Q818yescomplemented
87C2×C3×#67C2314yes—
88C22×C3×Dic3—28no—
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2311yescharacteristic
91C22×C3×Dic3C2312yes—
92C22×C3×Dic3C2318yes—
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2311yescharacteristic
95C2×C3×C4×D3—24no—
96C2×C3×C4×D3C2314yes—
97C2×C3×Dic6—24no—
98C2×C3×Dic6—28no—
99C2×C3×Dic6—232no—
100C2×C3×Dic6D418yescomplemented
101C2×C3×Dic6C2318yes—
102C2×C3×Dic6C2314yes—
103C2×C3×Dic6C2314yes—
104C2×#627—28no—
105C2×#627C2318yes—
106C2×D3×Dic3—28no—
107C2×D3×Dic3C2318yes—
108D3×Dic6—232no—
109#3757C2318yes—
110C4⋊(C3⋊Dic3)C2314yes—
111#3750C2318yes—
112C3×#217C2314yes—
113C3×(C2×D3)⋊C4C2314yes—
114C3×Dic3⋊C4C2314yes—
115C3×C4×Dic3C2314yes—
116#3724C2318yes—
117Dic3⋊Dic3C2318yes—
118Dic3⋊Dic3C2318yes—
119Dic3⋊Dic3C2318yes—
120(C2×D3)⋊Dic3C2318yes—
121Dic32C2318yes—
122C2×D4×Q8—91noSylow
123C22×C3×Q8—31no—
124C22×C3×Q8—32no—
125C22×C3×Q8—31no—
126C22×C3×Q8—38no—
127C22×C3×Q8—68no—
128C22×C3×D4—31no—
129C23×C3×C4—21no—
130C23×C3×C4—32no—
131C23×C3×C4—31no—
132C23×C3×C4C2×D311yescharacteristic
133C23×C3×C4C2×D311yescharacteristic
134C22×#67C2×D311yescharacteristic
135C23×Dic3—32no—
136C23×Dic3C2×D312yes—
137C2×D3×Q8—38no—
138C2×D3×Q8—68no—
139C22×C4×D3—32no—
140C22×C4×D3C2×D311yescharacteristic
141C22×Dic6—28no—
142C22×Dic6—31no—
143C22×Dic6—31no—
144C22×Dic6—32no—
145C22×Dic6—32no—
146C22×Dic6—38no—
147C22×Dic6—61no—
148C22×Dic6—68no—
149C22×Dic6C2×D311yescharacteristic
150C22×Dic6C2×D312yes—
151C22×Dic6C2×D311yescharacteristic
152C22×Dic6C2×D318yescomplemented
153C3×C4×D4—38no—
154C2×C3×C4⋊C4—31no—
155C2×C3×C22⋊C4—31no—
156C2×C3×C22⋊C4—31no—
157C2×C3×C42—31no—
158C2×#217—32no—
159C2×#217—32no—
160C2×#217—32no—
161C2×#217—62no—
162C2×#217C2×D311yescharacteristic
163#946—38no—
164#946—316no—
165Q8×Dic3—38no—
166#944—316no—
167#944—38no—
168D4×Dic3—316no—
169C4×#67—316no—
170C4×#67C2×D318yes—
171C2×(C2×D3)⋊C4—32no—
172C2×(C2×D3)⋊C4C2×D311yescharacteristic
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3—31no—
175C2×C4⋊Dic3—32no—
176C2×C4⋊Dic3—32no—
177C2×C4⋊Dic3—32no—
178C2×C4⋊Dic3—61no—
179#924—38no—
180#924—38no—
181#924—38no—
182#924—316no—
183#924—68no—
184C2×Dic3⋊C4—32no—
185C2×Dic3⋊C4—32no—
186C2×Dic3⋊C4—32no—
187C2×Dic3⋊C4—32no—
188C2×Dic3⋊C4—32no—
189C2×Dic3⋊C4—32no—
190C2×Dic3⋊C4—32no—
191C2×Dic3⋊C4—62no—
192C2×Dic3⋊C4C2×D311yescharacteristic
193C2×C4×Dic3—32no—
194C2×C4×Dic3—32no—
195C2×C4×Dic3C2×D311yescharacteristic
196#888—316no—
197#878—316no—
198#878—316no—
199#869—38no—
200C4×Dic6—38no—
201C23×C32—22no—
202C23×C32—22no—
203C23×C32C2×Q814yescomplemented
204C23×C32C2412yes—
205C23×C32C2411yescharacteristic
206C22×C3×D3—22no—
207C22×C3×D3—22no—
208C22×C3×D3C2×Q814yescomplemented
209C22×C3×D3C2412yes—
210C2×C32×C4—22no—
211C2×C32×C4—28no—
212C2×C32×C4C2×D414yes—
213C2×C32×C4C2412yes—
214C2×C32×C4C2412yes—
215C2×C3⋊Dic3—24no—
216C2×C3⋊Dic3—24no—
217C2×C3⋊Dic3C2414yes—
218C2×C3⋊Dic3C2414yes—
219#634—28no—
220C3×#67C2×Q8116yescomplemented
221C2×C3×Dic3—22no—
222C2×C3×Dic3—24no—
223C2×C3×Dic3—22no—
224C2×C3×Dic3—216no—
225C2×C3×Dic3C2×D418yes—
226C2×C3×Dic3C2×Q814yescomplemented
227C2×C3×Dic3C2414yes—
228C2×C3×Dic3C2412yes—
229C2×C3×Dic3C2412yes—
230C2×C3×Dic3C2414yes—
231C2×C3×Dic3C2412yes—
232C3×C4×D3—28no—
233C3×Dic6—28no—
234C3×Dic6—216no—
235C3×Dic6C2×D4116yescomplemented
236#627—216no—
237D3×Dic3—216no—
238C23×Q8—31no—
239C23×Q8—91no—
240D4×Q8—916no—
241C2×C4⋊Q8—91no—
242C2×C4⋊Q8—92no—
243C2×C22⋊Q8—92no—
244C2×C22⋊Q8—92no—
245C2×C22⋊Q8—91no—
246C2×C22⋊Q8—91no—
247C2×C4×Q8—91no—
248C2×C4×D4—31no—
249C2×C4×D4—92no—
250C24×C3—21no—
251C24×C3—31no—
252C24×C3C22×D311yescharacteristic
253C24×C3C22×D311yescharacteristic
254C23×D3C22×D311yescharacteristic
255C2×C3×Q8—38no—
256C2×C3×Q8—34no—
257C2×C3×Q8—38no—
258C2×C3×Q8—34no—
259C2×C3×Q8—68no—
260C2×C3×Q8—632no—
261C2×C3×Q8—64no—
262C2×C3×D4—38no—
263C2×C3×D4—34no—
264C22×C3×C4—24no—
265C22×C3×C4—24no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—24no—
269C22×C3×C4—31no—
270C22×C3×C4—32no—
271C22×C3×C4—32no—
272C22×C3×C4—31no—
273C22×C3×C4—31no—
274C22×C3×C4—38no—
275C22×C3×C4—34no—
276C22×C3×C4—44no—
277C22×C3×C4—68no—
278C22×C3×C4—64no—
279C22×C3×C4C22×D311yescharacteristic
280C22×C3×C4C22×D311yescharacteristic
281C22×C3×C4C22×D314yes—
282C22×C3×C4C22×D314yes—
283C22×C3×C4C22×D311yescharacteristic
284C22×C3×C4C22×D311yescharacteristic
285C2×#67Dic618yesdirect product factor
286C2×#67C22×D314yes—
287C22×Dic3—28no—
288C22×Dic3—32no—
289C22×Dic3—32no—
290C22×Dic3—32no—
291C22×Dic3—32no—
292C22×Dic3—38no—
293C22×Dic3—62no—
294C22×Dic3—62no—
295C22×Dic3—68no—
296C22×Dic3C22×D318yes—
297C22×Dic3C22×D311yescharacteristic
298C22×Dic3C22×D311yescharacteristic
299C22×Dic3C22×D312yes—
300C22×Dic3C22×D311yescharacteristic
301C22×Dic3C22×D312yes—
302D3×Q8—632no—
303C2×C4×D3—24no—
304C2×C4×D3—38no—
305C2×C4×D3—68no—
306C2×C4×D3C22×D314yes—
307C2×Dic6—24no—
308C2×Dic6—28no—
309C2×Dic6—232no—
310C2×Dic6—34no—
311C2×Dic6—34no—
312C2×Dic6—38no—
313C2×Dic6—38no—
314C2×Dic6—64no—
315C2×Dic6—68no—
316C2×Dic6—64no—
317C2×Dic6—64no—
318C2×Dic6—68no—
319C2×Dic6—632no—
320C2×Dic6—124no—
321C2×Dic6#6718yesdirect product factor
322C2×Dic6C22×D314yes—
323C2×Dic6C22×D318yes—
324C2×Dic6C22×D314yes—
325C3×C4⋊C4—34no—
326C3×C22⋊C4—34no—
327C3×C22⋊C4—34no—
328C3×C42—34no—
329#217—38no—
330#217—38no—
331#217—38no—
332#217—68no—
333#217C22×D314yes—
334(C2×D3)⋊C4—38no—
335(C2×D3)⋊C4C22×D314yes—
336C4⋊Dic3—34no—
337C4⋊Dic3—34no—
338C4⋊Dic3—38no—
339C4⋊Dic3—38no—
340C4⋊Dic3—38no—
341C4⋊Dic3—64no—
342Dic3⋊C4—38no—
343Dic3⋊C4—38no—
344Dic3⋊C4—38no—
345Dic3⋊C4—38no—
346Dic3⋊C4—38no—
347Dic3⋊C4—38no—
348Dic3⋊C4—38no—
349Dic3⋊C4—68no—
350Dic3⋊C4C22×D314yes—
351C4×Dic3—38no—
352C4×Dic3—38no—
353C4×Dic3C22×D314yes—
354C22×C32—28no—
355C22×C32—22no—
356C22×C32—22no—
357C22×C32C22×D412yes—
358C22×C32C22×Q812yes—
359C22×C32C22×Q814yescomplemented
360C22×C322−1+412yes—
361C22×C32C2511yescharacteristic
362C2×C3×D3—28no—
363C2×C3×D3—22no—
364C2×C3×D3—22no—
365C2×C3×D3C22×Q814yescomplemented
366C32×C4—22no—
367C32×C4C22×D414yes—
368C3⋊Dic3—24no—
369C3⋊Dic3—24no—
370C3×Dic3—22no—
371C3×Dic3—24no—
372C3×Dic3—22no—
373C3×Dic3C22×D418yes—
374C3×Dic3C22×Q814yescomplemented
375C22×Q8—31no—
376C22×Q8—32no—
377C22×Q8—31no—
378C22×Q8—38no—
379C22×Q8—68no—
380C22×Q8—92no—
381C22×Q8—98no—
382C22×Q8—91no—
383C22×Q8—188no—
384C22×D4—31no—
385C23×C4—32no—
386C23×C4—31no—
387C23×C4—92no—
388C23×C4D3211yescharacteristic
389C4⋊Q8—98no—
390C4⋊Q8—916no—
391C22⋊Q8—916no—
392C22⋊Q8—916no—
393C22⋊Q8—98no—
394C22⋊Q8—98no—
395C4×Q8—98no—
396C4×D4—38no—
397C4×D4—916no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—92no—
400C2×C4⋊C4—92no—
401C2×C4⋊C4—92no—
402C2×C4⋊C4—92no—
403C2×C4⋊C4—91no—
404C2×C4⋊C4—92no—
405C2×C22⋊C4—31no—
406C2×C22⋊C4—31no—
407C2×C22⋊C4—92no—
408C2×C22⋊C4—92no—
409C2×C42—31no—
410C2×C42—92no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—22no—
416C23×C3—21no—
417C23×C3—24no—
418C23×C3—34no—
419C23×C3—32no—
420C23×C3—42no—
421C23×C3—42no—
422C23×C3—62no—
423C23×C3—62no—
424C23×C3C2×Dic614yescomplemented
425C23×C3D3×Q814yescomplemented
426C23×C3C23×D312yes—
427C23×C3C23×D312yes—
428C23×C3C23×D311yescharacteristic
429C23×C3C23×D311yescharacteristic
430C22×D3—22no—
431C22×D3—22no—
432C22×D3C2×Dic614yescomplemented
433C22×D3C23×D312yes—
434C3×Q8—316no—
435C3×Q8—616no—
436C3×Q8—68no—
437C3×D4—316no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—28no—
441C2×C3×C4—28no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—24no—
445C2×C3×C4—38no—
446C2×C3×C4—34no—
447C2×C3×C4—32no—
448C2×C3×C4—34no—
449C2×C3×C4—34no—
450C2×C3×C4—32no—
451C2×C3×C4—32no—
452C2×C3×C4—48no—
453C2×C3×C4—42no—
454C2×C3×C4—616no—
455C2×C3×C4—64no—
456C2×C3×C4—62no—
457C2×C3×C4—62no—
458C2×C3×C4—68no—
459C2×C3×C4D3×D414yes—
460C2×C3×C4C2×#6714yes—
461C2×C3×C4C23×D312yes—
462C2×C3×C4C23×D312yes—
463C2×C3×C4C23×D312yes—
464C2×C3×C4C23×D312yes—
465#67C2×Dic6116yesdirect product factor
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—24no—
469C2×Dic3—216no—
470C2×Dic3—34no—
471C2×Dic3—34no—
472C2×Dic3—34no—
473C2×Dic3—34no—
474C2×Dic3—64no—
475C2×Dic3—64no—
476C2×Dic3—64no—
477C2×Dic3—64no—
478C2×Dic3—64no—
479C2×Dic3—64no—
480C2×Dic3—616no—
481C2×Dic3—124no—
482C2×Dic3—124no—
483C2×Dic3C2×Dic614yescomplemented
484C2×Dic3C2×#6718yes—
485C2×Dic3C23×D312yes—
486C2×Dic3C23×D312yes—
487C2×Dic3C23×D314yes—
488C2×Dic3C23×D312yes—
489C2×Dic3C23×D314yes—
490C4×D3—28no—
491C4×D3—616no—
492Dic6—28no—
493Dic6—216no—
494Dic6—616no—
495Dic6—68no—
496Dic6—68no—
497Dic6—616no—
498Dic6—128no—
499Dic6C2×#67116yesdirect product factor
500C2×C32—24no—
501C2×C32D4×Q814yescomplemented
502C2×C32C23×D411yescharacteristic
503C2×C32C23×Q811yescharacteristic
504C2×C32C2×2−1+411yescharacteristic
505C3×D3—24no—
506C24—31no—
507C24C2×D3211yescharacteristic
508C2×Q8—34no—
509C2×Q8—38no—
510C2×Q8—34no—
511C2×Q8—38no—
512C2×Q8—68no—
513C2×Q8—632no—
514C2×Q8—64no—
515C2×Q8—98no—
516C2×Q8—94no—
517C2×Q8—188no—
518C2×Q8—1832no—
519C2×Q8—184no—
520C2×D4—34no—
521C2×D4—38no—
522C22×C4—24no—
523C22×C4—31no—
524C22×C4—32no—
525C22×C4—38no—
526C22×C4—31no—
527C22×C4—31no—
528C22×C4—32no—
529C22×C4—34no—
530C22×C4—68no—
531C22×C4—64no—
532C22×C4—98no—
533C22×C4—92no—
534C22×C4—92no—
535C22×C4—188no—
536C22×C4C2×D3214yes—
537C22×C4C2×D3211yescharacteristic
538C22×C4C2×D3211yescharacteristic
539C4⋊C4—34no—
540C4⋊C4—98no—
541C4⋊C4—98no—
542C4⋊C4—98no—
543C4⋊C4—98no—
544C4⋊C4—94no—
545C4⋊C4—98no—
546C22⋊C4—34no—
547C22⋊C4—34no—
548C22⋊C4—98no—
549C22⋊C4—98no—
550C42—34no—
551C42—98no—
552C22×C3—22no—
553C22×C3—22no—
554C22×C3—22no—
555C22×C3—22no—
556C22×C3—28no—
557C22×C3—28no—
558C22×C3—22no—
559C22×C3—24no—
560C22×C3—22no—
561C22×C3—22no—
562C22×C3—21no—
563C22×C3—34no—
564C22×C3—42no—
565C22×C3—42no—
566C22×C3—48no—
567C22×C3—62no—
568C22×C3—62no—
569C22×C3—68no—
570C22×C3C22×Dic612yes—
571C22×C3C22×Dic614yescomplemented
572C22×C3C2×D3×D412yes—
573C22×C3C2×D3×Q812yes—
574C22×C3C2×D3×Q814yescomplemented
575C22×C3#100712yes—
576C22×C3#101012yes—
577C22×C3C22×#6712yes—
578C22×C3C24×D311yescharacteristic
579C22×C3C24×D311yescharacteristic
580C2×D3—22no—
581C2×D3—22no—
582C2×D3—28no—
583C2×D3C22×Dic614yescomplemented
584C3×C4—22no—
585C3×C4—22no—
586C3×C4—24no—
587C3×C4—38no—
588C3×C4—34no—
589C3×C4—42no—
590C3×C4—64no—
591C3×C4—62no—
592C3×C4—62no—
593C3×C4C2×D3×D414yes—
594C3×C4C22×#6714yes—
595Dic3—22no—
596Dic3—22no—
597Dic3—24no—
598Dic3—64no—
599Dic3—64no—
600Dic3—64no—
601Dic3—64no—
602Dic3—124no—
603Dic3—124no—
604Dic3C22×Dic614yescomplemented
605Dic3C22×#6718yes—
606C32C2×D4×Q811yescharacteristic, complemented, Sylow
607C23—22no—
608C23—22no—
609C23—34no—
610C23—32no—
611C23—62no—
612C23—62no—
613C23D3×Dic614yescomplemented
614C23C22×D3212yes—
615C23C22×D3211yescharacteristic
616Q8—316no—
617Q8—616no—
618Q8—68no—
619Q8—1816no—
620Q8—188no—
621D4—316no—
622C2×C4—22no—
623C2×C4—28no—
624C2×C4—34no—
625C2×C4—38no—
626C2×C4—32no—
627C2×C4—34no—
628C2×C4—32no—
629C2×C4—32no—
630C2×C4—34no—
631C2×C4—616no—
632C2×C4—62no—
633C2×C4—64no—
634C2×C4—62no—
635C2×C4—68no—
636C2×C4—94no—
637C2×C4—94no—
638C2×C4—1816no—
639C2×C4—184no—
640C2×C4—184no—
641C2×C4D3×#6714yes—
642C2×C4C22×D3212yes—
643C2×C4C22×D3212yes—
644C2×C3—24no—
645C2×C3—24no—
646C2×C3—21no—
647C2×C3—21no—
648C2×C3—24no—
649C2×C3—21no—
650C2×C3—44no—
651C2×C3—64no—
652C2×C3D4×Dic614yescomplemented
653C2×C3Q8×#6714yescomplemented
654C2×C3C23×Dic611yescharacteristic
655C2×C3C22×D3×D411yescharacteristic
656C2×C3C22×D3×Q811yescharacteristic
657C2×C3C2×#100711yescharacteristic
658C2×C3C2×#101011yescharacteristic
659C2×C3C23×#6711yescharacteristic
660D3—24no—
661C22—22no—
662C22—28no—
663C22—22no—
664C22—34no—
665C22—62no—
666C22—68no—
667C22—62no—
668C22C2×D3×Dic612yes—
669C22C2×D3×Dic614yescomplemented
670C22#6429712yes—
671C22C2×D3×#6712yes—
672C22C23×D3211yescharacteristic
673C4—22no—
674C4—34no—
675C4—38no—
676C4—62no—
677C4—64no—
678C4—62no—
679C4—184no—
680C4—184no—
681C4C2×D3×#6714yes—
682C3—21no—
683C3C2×D4×Dic611yescharacteristic, complemented
684C3C2×Q8×#6711yescharacteristic, complemented
685C2—24no—
686C2—64no—
687C2Dic6×#6714yesdirect product factor
688C2C22×D3×Dic611yescharacteristic
689C2C2×#6429711yescharacteristic
690C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32C2×D4×Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×C3×Dic6C2semidirect
2. C22×D3×Dic6C2semidirect
3. C2×#64133C2semidirect
6. C2×#63964C2semidirect
7. Dic6×#67C2direct (N × H)
8. C2×#63887C2semidirect
9. C2×#63866C2semidirect
10. C2×#63856C2semidirect
11. C2×Dic3×Dic6C2semidirect
12. C2×#63839C2semidirect
24. C22×C3×Dic6C22semidirect
28. C2×D3×Dic6C22semidirect
31. #64133C22semidirect
43. #63964C22semidirect
46. #63887C22semidirect
47. #63866C22semidirect
48. #63856C22semidirect
49. Dic3×Dic6C22semidirect
50. #63839C22semidirect
54. C23×Dic6D3semidirect
86. C2×C3×#67Q8semidirect
100. C2×C3×Dic6D4semidirect
152. C22×Dic6C2×D3semidirect
203. C23×C32C2×Q8semidirect
208. C22×C3×D3C2×Q8semidirect
220. C3×#67C2×Q8semidirect
226. C2×C3×Dic3C2×Q8semidirect
235. C3×Dic6C2×D4semidirect
285. C2×#67Dic6direct (N × H)
321. C2×Dic6#67direct (N × H)
359. C22×C32C22×Q8semidirect
365. C2×C3×D3C22×Q8semidirect
374. C3×Dic3C22×Q8semidirect
424. C23×C3C2×Dic6semidirect
425. C23×C3D3×Q8semidirect
432. C22×D3C2×Dic6semidirect
465. #67C2×Dic6direct (N × H)
483. C2×Dic3C2×Dic6semidirect
499. Dic6C2×#67direct (N × H)
501. C2×C32D4×Q8semidirect
571. C22×C3C22×Dic6semidirect
574. C22×C3C2×D3×Q8semidirect
583. C2×D3C22×Dic6semidirect
604. Dic3C22×Dic6semidirect
606. C32C2×D4×Q8semidirect
613. C23D3×Dic6semidirect
652. C2×C3D4×Dic6semidirect
653. C2×C3Q8×#67semidirect
669. C22C2×D3×Dic6semidirect
683. C3C2×D4×Dic6semidirect
684. C3C2×Q8×#67semidirect
687. C2Dic6×#67direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×Dic62
C22×D3×Dic62
C2×#641332
C2×C3×C4×#672
C2×Dic3×#672
C2×#639642
Dic6×#672
C2×#638872
C2×#638662
C2×#638562
C2×Dic3×Dic62
C2×#638392
C2×Q8×#673
C2×D4×Dic63