Finite Group Databasebeta

← C2×#10595403 #11902666

Subgroups — C2×#10595403 #11902666

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
1C22×C3×D3×Q8C211yesmaximal, characteristic, complemented
2C22×#3797C211yesmaximal, characteristic, complemented
3C2×#64155C211yesmaximal, characteristic, complemented
4C2×C3×#944C211yesmaximal, characteristic, complemented
5#10595403C2116yesmaximal, direct product factor
6C2×#63904C212yesmaximal
7C2×C4×#626C211yesmaximal, characteristic
8C2×#63888C212yesmaximal, complemented
9C2×#63856C211yesmaximal, characteristic, complemented
10C2×#63851C212yesmaximal, complemented
11C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
12C2×#63839C212yesmaximal, complemented
13C2×Q8×#67—31nomaximal
14C2×#5727—31nomaximal
15C22×C32×Q8C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C2×C3×D3×Q8—28no—
18C2×C3×D3×Q8C2218yescomplemented
19C22×C3×C4×D3C2212yes—
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22C22×C3×Dic6C2212yes—
23C22×C3×Dic6C2211yescharacteristic
24C22×#627C2212yes—
25C22×#626C2211yescharacteristic
26C22×#624C2212yes—
27C2×#3797—28no—
28C2×#3797C2218yescomplemented
29#64155C2218yescomplemented
30C2×#3752C2212yes—
31C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
32C2×#3750C2212yes—
33C3×#944C2218yescomplemented
34C2×C3×Dic3⋊C4C2212yes—
35C2×C3×Dic3⋊C4C2212yes—
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×#3724C2212yes—
38C2×Dic3⋊Dic3C2212yes—
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2212yes—
43C2×Dic32C2212yes—
44#63904C22116yes—
45C4×#626C2218yes—
46#63888C22116yescomplemented
47#63856C2218yescomplemented
48#63851C22116yescomplemented
49Dic3×Dic6C2218yescomplemented
50#63839C22116yescomplemented
51C23×C3×Q8—31no—
52C22×D3×Q8—31no—
53C22×D3×Q8—31no—
54C22×D3×Q8D311yescharacteristic, complemented
55C2×C3×C4⋊Q8—31no—
56Q8×#67—316no—
57C2×#946—31no—
58C2×#946—31no—
59C2×#946—31no—
60C2×#946—32no—
61C2×#946—61no—
62C2×Q8×Dic3—31no—
63C2×#944—32no—
64C2×#944D311yescharacteristic, complemented
65C2×C4×#67—32no—
66C2×C4×#67—31no—
67C2×#924—31no—
68C2×#924—32no—
69#5727—316no—
70C2×#896—32no—
71C2×#896—32no—
72C2×#893—32no—
73C2×#888—32no—
74C2×C4×D12—31no—
75C2×C4×Dic6—31no—
76C23×C3⋊D3C2311yescharacteristic
77C23×C3×D3C2311yescharacteristic
78C2×C32×Q8—24no—
79C2×C32×Q8C2314yes—
80C22×C32×C4C2312yes—
81C22×C32×C4C2311yescharacteristic
82C22×C3⋊Dic3C2311yescharacteristic
83C22×C3⋊Dic3C2312yes—
84C2×C4×C3⋊D3—24no—
85C2×C4×C3⋊D3C2314yes—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2312yes—
90C22×C3×Dic3C2311yescharacteristic
91C3×D3×Q8—232no—
92C2×C3×C4×D3—24no—
93C2×C3×C4×D3—28no—
94C2×C3×C4×D3C2318yes—
95C2×C3×C4×D3C2314yes—
96C2×C3×Dic6—24no—
97C2×C3×Dic6—28no—
98C2×C3×Dic6D418yescomplemented
99C2×C3×Dic6C2314yes—
100C2×C3×Dic6C2318yes—
101C2×C3×Dic6C2314yes—
102C2×#627—28no—
103C2×#627C2318yes—
104C2×#626Q818yescomplemented
105C2×#626C2314yes—
106C2×#624—28no—
107C2×#624C2318yes—
108#3797—232no—
109#3752C2318yes—
110C4⋊(C3⋊Dic3)C2314yes—
111#3750C2318yes—
112C3×Dic3⋊C4C2318yes—
113C3×Dic3⋊C4C2318yes—
114C3×C4×Dic3C2314yes—
115#3724C2318yes—
116Dic3⋊Dic3C2314yes—
117Dic3⋊Dic3C2318yes—
118#3722C2314yes—
119(C2×D3)⋊Dic3C2314yes—
120(C2×D3)⋊Dic3C2318yes—
121Dic32C2318yes—
122C2×D4×Q8—91noSylow
123C22×C3×Q8—21no—
124C22×C3×Q8—38no—
125C22×C3×Q8—31no—
126C22×C3×Q8—31no—
127C22×C3×Q8—32no—
128C22×C3×Q8—68no—
129C22×C3×Q8C2×D311yescharacteristic
130C22×C3×Q8C2×D311yescharacteristic
131C23×C3×C4—32no—
132C23×C3×C4—31no—
133C22×#67—31no—
134C2×D3×Q8—28no—
135C2×D3×Q8—38no—
136C2×D3×Q8—38no—
137C2×D3×Q8—68no—
138C2×D3×Q8—68no—
139C2×D3×Q8C2×D318yescomplemented
140C22×D12—31no—
141C22×C4×D3—31no—
142C22×C4×D3—31no—
143C22×C4×D3—32no—
144C22×C4×D3—32no—
145C22×C4×D3—61no—
146C22×C4×D3C2×D311yescharacteristic
147C22×C4×D3C2×D312yes—
148C22×Dic6—32no—
149C22×Dic6—32no—
150C22×Dic6C2×D311yescharacteristic
151C22×Dic6C2×D312yes—
152C22×Dic6C2×D311yescharacteristic
153C3×C4⋊Q8—38no—
154C2×C3×C4⋊C4—32no—
155C2×C3×C4⋊C4—32no—
156C2×C3×C42—31no—
157C2×#217—32no—
158C2×#217—31no—
159#946—38no—
160#946—38no—
161#946—38no—
162#946—316no—
163#946—68no—
164Q8×Dic3—38no—
165#944—316no—
166#944C2×D318yescomplemented
167C4×#67—316no—
168C4×#67—38no—
169C2×(C2×D3)⋊C4—31no—
170C2×(C2×D3)⋊C4—32no—
171C2×(C2×D3)⋊C4—32no—
172C2×(C2×D3)⋊C4—32no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—62no—
176C2×C4⋊Dic3—31no—
177C2×C4⋊Dic3—31no—
178C2×C4⋊Dic3—31no—
179C2×C4⋊Dic3—32no—
180C2×C4⋊Dic3—61no—
181#924—38no—
182#924—316no—
183C2×Dic3⋊C4—32no—
184C2×Dic3⋊C4—32no—
185C2×Dic3⋊C4—32no—
186C2×Dic3⋊C4—32no—
187C2×Dic3⋊C4—32no—
188C2×Dic3⋊C4—31no—
189C2×Dic3⋊C4—62no—
190C2×Dic3⋊C4C2×D312yes—
191C2×Dic3⋊C4C2×D312yes—
192C2×C4×Dic3—32no—
193C2×C4×Dic3—32no—
194C2×C4×Dic3C2×D311yescharacteristic
195#896—316no—
196#896—316no—
197#893—316no—
198#888—316no—
199C4×D12—38no—
200C4×Dic6—38no—
201C23×C32C2411yescharacteristic
202C22×C3⋊D3—22no—
203C22×C3⋊D3—22no—
204C22×C3⋊D3C2×Q814yescomplemented
205C22×C3⋊D3C2412yes—
206C22×C3×D3—22no—
207C22×C3×D3—22no—
208C22×C3×D3C2×Q814yescomplemented
209C22×C3×D3C2412yes—
210C32×Q8—28no—
211C2×C32×C4—24no—
212C2×C32×C4C2×D414yes—
213C2×C32×C4C2414yes—
214C2×C32×C4C2412yes—
215C2×C3⋊Dic3—22no—
216C2×C3⋊Dic3—24no—
217C2×C3⋊Dic3C2414yes—
218C2×C3⋊Dic3C2412yes—
219C4×C3⋊D3—28no—
220C2×C3×Dic3—24no—
221C2×C3×Dic3—22no—
222C2×C3×Dic3—22no—
223C2×C3×Dic3C2×D418yes—
224C2×C3×Dic3C2×Q814yescomplemented
225C2×C3×Dic3C2412yes—
226C2×C3×Dic3C2414yes—
227C2×C3×Dic3C2412yes—
228C2×C3×Dic3C2414yes—
229C2×C3×Dic3C2412yes—
230C3×C4×D3—28no—
231C3×C4×D3—216no—
232C3×Dic6—28no—
233C3×Dic6—216no—
234C3×Dic6C2×D4116yescomplemented
235#627—216no—
236#626C2×Q8116yescomplemented
237#624—216no—
238C23×Q8—31no—
239C23×Q8—91no—
240D4×Q8—916no—
241C2×C4⋊Q8—31no—
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—91no—
249C2×C4×D4—92no—
250C24×C3—31no—
251C23×D3—31no—
252C23×D3—31no—
253C23×D3—61no—
254C23×D3C22×D311yescharacteristic
255C2×C3×Q8—24no—
256C2×C3×Q8—24no—
257C2×C3×Q8—24no—
258C2×C3×Q8—38no—
259C2×C3×Q8—34no—
260C2×C3×Q8—38no—
261C2×C3×Q8—34no—
262C2×C3×Q8—44no—
263C2×C3×Q8—68no—
264C2×C3×Q8—632no—
265C2×C3×Q8—64no—
266C2×C3×Q8C22×D314yes—
267C2×C3×Q8C22×D314yes—
268C22×C3×C4—21no—
269C22×C3×C4—22no—
270C22×C3×C4—31no—
271C22×C3×C4—32no—
272C22×C3×C4—31no—
273C22×C3×C4—31no—
274C22×C3×C4—32no—
275C22×C3×C4—38no—
276C22×C3×C4—34no—
277C22×C3×C4—68no—
278C22×C3×C4—64no—
279C22×C3×C4C22×D312yes—
280C22×C3×C4C22×D312yes—
281C22×C3×C4C22×D311yescharacteristic
282C22×C3×C4C22×D311yescharacteristic
283C2×#67—38no—
284C2×#67—34no—
285C22×Dic3—32no—
286C22×Dic3—32no—
287C22×Dic3—31no—
288C22×Dic3—31no—
289C22×Dic3—61no—
290C22×Dic3—62no—
291C22×Dic3C22×D311yescharacteristic
292C22×Dic3C22×D311yescharacteristic
293C22×Dic3C22×D312yes—
294C22×Dic3C22×D311yescharacteristic
295C22×Dic3C22×D312yes—
296D3×Q8—232no—
297D3×Q8—632no—
298D3×Q8—632no—
299C2×D12—38no—
300C2×D12—34no—
301C2×C4×D3—24no—
302C2×C4×D3—28no—
303C2×C4×D3—34no—
304C2×C4×D3—34no—
305C2×C4×D3—38no—
306C2×C4×D3—38no—
307C2×C4×D3—64no—
308C2×C4×D3—68no—
309C2×C4×D3—64no—
310C2×C4×D3—64no—
311C2×C4×D3—68no—
312C2×C4×D3—124no—
313C2×C4×D3C22×D314yes—
314C2×C4×D3C22×D318yes—
315C2×Dic6—24no—
316C2×Dic6—28no—
317C2×Dic6—38no—
318C2×Dic6—38no—
319C2×Dic6—68no—
320C2×Dic6—68no—
321C2×Dic6#6718yescomplemented
322C2×Dic6C22×D318yes—
323C2×Dic6C22×D314yes—
324C2×Dic6C22×D314yes—
325C3×C4⋊C4—38no—
326C3×C4⋊C4—38no—
327C3×C42—34no—
328#217—38no—
329#217—34no—
330(C2×D3)⋊C4—34no—
331(C2×D3)⋊C4—38no—
332(C2×D3)⋊C4—38no—
333(C2×D3)⋊C4—38no—
334(C2×D3)⋊C4—34no—
335(C2×D3)⋊C4—34no—
336(C2×D3)⋊C4—68no—
337C4⋊Dic3—34no—
338C4⋊Dic3—34no—
339C4⋊Dic3—34no—
340C4⋊Dic3—38no—
341C4⋊Dic3—64no—
342Dic3⋊C4—38no—
343Dic3⋊C4—38no—
344Dic3⋊C4—38no—
345Dic3⋊C4—38no—
346Dic3⋊C4—34no—
347Dic3⋊C4—38no—
348Dic3⋊C4—68no—
349Dic3⋊C4C22×D318yes—
350Dic3⋊C4C22×D318yes—
351C4×Dic3—38no—
352C4×Dic3—38no—
353C4×Dic3C22×D314yes—
354C22×C32C22×D412yes—
355C22×C32C22×Q812yes—
356C22×C322−1+412yes—
357C22×C32C2511yescharacteristic
358C2×C3⋊D3—28no—
359C2×C3⋊D3—22no—
360C2×C3⋊D3—22no—
361C2×C3⋊D3C22×Q814yescomplemented
362C2×C3×D3—28no—
363C2×C3×D3—22no—
364C2×C3×D3—22no—
365C2×C3×D3C22×Q814yescomplemented
366C32×C4—24no—
367C32×C4C22×D414yes—
368C3⋊Dic3—22no—
369C3⋊Dic3—24no—
370C3×Dic3—24no—
371C3×Dic3—22no—
372C3×Dic3—22no—
373C3×Dic3C22×D418yes—
374C3×Dic3C22×Q814yescomplemented
375C22×Q8—38no—
376C22×Q8—31no—
377C22×Q8—31no—
378C22×Q8—32no—
379C22×Q8—68no—
380C22×Q8—92no—
381C22×Q8—98no—
382C22×Q8—188no—
383C22×Q8D3211yescharacteristic
384C22×D4—91no—
385C23×C4—32no—
386C23×C4—31no—
387C23×C4—92no—
388C23×C4—91no—
389C4⋊Q8—38no—
390C4⋊Q8—916no—
391C22⋊Q8—916no—
392C22⋊Q8—916no—
393C22⋊Q8—98no—
394C22⋊Q8—98no—
395C4×Q8—98no—
396C4×D4—98no—
397C4×D4—916no—
398C2×C4⋊C4—32no—
399C2×C4⋊C4—32no—
400C2×C4⋊C4—91no—
401C2×C4⋊C4—92no—
402C2×C4⋊C4—92no—
403C2×C4⋊C4—91no—
404C2×C4⋊C4—92no—
405C2×C22⋊C4—91no—
406C2×C22⋊C4—91no—
407C2×C22⋊C4—92no—
408C2×C22⋊C4—92no—
409C2×C42—31no—
410C2×C42—92no—
411C23×C3—21no—
412C23×C3—34no—
413C23×C3—32no—
414C23×C3—62no—
415C23×C3—62no—
416C23×C3C23×D311yescharacteristic
417C23×C3C23×D311yescharacteristic
418C22×D3—22no—
419C22×D3—22no—
420C22×D3—34no—
421C22×D3—34no—
422C22×D3—32no—
423C22×D3—32no—
424C22×D3—64no—
425C22×D3—62no—
426C22×D3—62no—
427C22×D3—62no—
428C22×D3—62no—
429C22×D3—62no—
430C22×D3—122no—
431C22×D3—122no—
432C22×D3D3×Q814yescomplemented
433C22×D3C23×D312yes—
434C3×Q8—28no—
435C3×Q8—28no—
436C3×Q8—316no—
437C3×Q8—48no—
438C3×Q8—616no—
439C3×Q8—68no—
440C2×C3×C4—24no—
441C2×C3×C4—24no—
442C2×C3×C4—22no—
443C2×C3×C4—24no—
444C2×C3×C4—24no—
445C2×C3×C4—38no—
446C2×C3×C4—34no—
447C2×C3×C4—32no—
448C2×C3×C4—34no—
449C2×C3×C4—32no—
450C2×C3×C4—32no—
451C2×C3×C4—34no—
452C2×C3×C4—44no—
453C2×C3×C4—616no—
454C2×C3×C4—62no—
455C2×C3×C4—62no—
456C2×C3×C4—64no—
457C2×C3×C4—68no—
458C2×C3×C4D3×D414yes—
459C2×C3×C4C2×#6714yes—
460C2×C3×C4C23×D314yes—
461C2×C3×C4C23×D314yes—
462C2×C3×C4C23×D312yes—
463C2×C3×C4C23×D312yes—
464#67—316no—
465C2×Dic3—24no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—34no—
469C2×Dic3—34no—
470C2×Dic3—32no—
471C2×Dic3—32no—
472C2×Dic3—62no—
473C2×Dic3—64no—
474C2×Dic3—62no—
475C2×Dic3—64no—
476C2×Dic3—64no—
477C2×Dic3—62no—
478C2×Dic3—122no—
479C2×Dic3—124no—
480C2×Dic3D3×Q814yescomplemented
481C2×Dic3C2×#6718yes—
482C2×Dic3C23×D312yes—
483C2×Dic3C23×D312yes—
484C2×Dic3C23×D314yes—
485C2×Dic3C23×D312yes—
486C2×Dic3C23×D314yes—
487D12—316no—
488C4×D3—28no—
489C4×D3—216no—
490C4×D3—616no—
491C4×D3—68no—
492C4×D3—68no—
493C4×D3—616no—
494C4×D3—128no—
495Dic6—28no—
496Dic6—216no—
497Dic6—616no—
498Dic6—616no—
499Dic6C2×#67116yescomplemented
500C2×C32D4×Q814yescomplemented
501C2×C32C23×D411yescharacteristic
502C2×C32C23×Q811yescharacteristic
503C2×C32C2×2−1+411yescharacteristic
504C3⋊D3—24no—
505C3×D3—24no—
506C24—31no—
507C24—91no—
508C2×Q8—24no—
509C2×Q8—34no—
510C2×Q8—34no—
511C2×Q8—38no—
512C2×Q8—38no—
513C2×Q8—68no—
514C2×Q8—632no—
515C2×Q8—64no—
516C2×Q8—98no—
517C2×Q8—188no—
518C2×Q8—1832no—
519C2×Q8C2×D3214yes—
520C2×D4—94no—
521C2×D4—98no—
522C22×C4—31no—
523C22×C4—32no—
524C22×C4—31no—
525C22×C4—32no—
526C22×C4—31no—
527C22×C4—38no—
528C22×C4—34no—
529C22×C4—68no—
530C22×C4—64no—
531C22×C4—98no—
532C22×C4—92no—
533C22×C4—91no—
534C22×C4—94no—
535C22×C4—188no—
536C22×C4—184no—
537C22×C4C2×D3212yes—
538C22×C4C2×D3211yescharacteristic
539C4⋊C4—38no—
540C4⋊C4—38no—
541C4⋊C4—94no—
542C4⋊C4—98no—
543C4⋊C4—98no—
544C4⋊C4—94no—
545C4⋊C4—98no—
546C22⋊C4—94no—
547C22⋊C4—94no—
548C22⋊C4—98no—
549C22⋊C4—98no—
550C42—34no—
551C42—98no—
552C22×C3—22no—
553C22×C3—22no—
554C22×C3—22no—
555C22×C3—21no—
556C22×C3—34no—
557C22×C3—62no—
558C22×C3—62no—
559C22×C3—68no—
560C22×C3C2×D3×D412yes—
561C22×C3C2×D3×Q812yes—
562C22×C3C2×D3×Q812yes—
563C22×C3#100712yes—
564C22×C3#100712yes—
565C22×C3C22×#6712yes—
566C22×C3C24×D311yescharacteristic
567C22×C3C24×D311yescharacteristic
568C2×D3—22no—
569C2×D3—22no—
570C2×D3—28no—
571C2×D3—34no—
572C2×D3—34no—
573C2×D3—64no—
574C2×D3—62no—
575C2×D3—62no—
576C2×D3—62no—
577C2×D3—62no—
578C2×D3—68no—
579C2×D3—68no—
580C2×D3—122no—
581C2×D3—122no—
582C2×D3—128no—
583C2×D3C2×D3×Q814yescomplemented
584C3×C4—24no—
585C3×C4—24no—
586C3×C4—24no—
587C3×C4—38no—
588C3×C4—34no—
589C3×C4—44no—
590C3×C4—62no—
591C3×C4—62no—
592C3×C4—64no—
593C3×C4C2×D3×D414yes—
594C3×C4C22×#6714yes—
595Dic3—24no—
596Dic3—22no—
597Dic3—22no—
598Dic3—62no—
599Dic3—64no—
600Dic3—64no—
601Dic3—62no—
602Dic3—122no—
603Dic3—124no—
604Dic3C2×D3×Q814yescomplemented
605Dic3C22×#6718yes—
606C32C2×D4×Q811yescharacteristic, complemented, Sylow
607C23—34no—
608C23—32no—
609C23—62no—
610C23—62no—
611C23—94no—
612C23—92no—
613C23—182no—
614C23—182no—
615C23C22×D3211yescharacteristic
616Q8—28no—
617Q8—316no—
618Q8—616no—
619Q8—68no—
620Q8—1816no—
621D4—916no—
622C2×C4—24no—
623C2×C4—34no—
624C2×C4—38no—
625C2×C4—32no—
626C2×C4—34no—
627C2×C4—32no—
628C2×C4—34no—
629C2×C4—32no—
630C2×C4—616no—
631C2×C4—62no—
632C2×C4—62no—
633C2×C4—64no—
634C2×C4—68no—
635C2×C4—94no—
636C2×C4—92no—
637C2×C4—1816no—
638C2×C4—184no—
639C2×C4—182no—
640C2×C4—188no—
641C2×C4D3×#6714yes—
642C2×C4C22×D3214yes—
643C2×C4C22×D3212yes—
644C2×C3—21no—
645C2×C3—21no—
646C2×C3—24no—
647C2×C3—21no—
648C2×C3—64no—
649C2×C3#572714yescomplemented
650C2×C3Q8×#6714yescomplemented
651C2×C3C22×D3×D411yescharacteristic
652C2×C3C22×D3×Q811yescharacteristic
653C2×C3C22×D3×Q811yescharacteristic
654C2×C3C2×#100711yescharacteristic
655C2×C3C2×#100711yescharacteristic
656C2×C3C23×#6711yescharacteristic
657D3—24no—
658D3—64no—
659D3—64no—
660D3—124no—
661C22—34no—
662C22—62no—
663C22—68no—
664C22—62no—
665C22—94no—
666C22—182no—
667C22—188no—
668C22—182no—
669C22#6431612yes—
670C22D32×Q812yes—
671C22C2×D3×#6712yes—
672C22C23×D3211yescharacteristic
673C4—24no—
674C4—34no—
675C4—38no—
676C4—62no—
677C4—62no—
678C4—64no—
679C4—184no—
680C4—182no—
681C4C2×D3×#6714yes—
682C3—21no—
683C3C2×#572711yescharacteristic, complemented
684C3C2×Q8×#6711yescharacteristic, complemented
685C2—64no—
686C2—184no—
687C2#1059540314yesdirect product factor
688C2C2×#6431611yescharacteristic
689C2C2×D32×Q811yescharacteristic
690C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
prime radicalC22×#626C22
hypercenterC22×Q8D32
hypocenterC32C2×D4×Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×Q8C2semidirect
2. C22×#3797C2semidirect
3. C2×#64155C2semidirect
4. C2×C3×#944C2semidirect
5. #10595403C2direct (N × H)
8. C2×#63888C2semidirect
9. C2×#63856C2semidirect
10. C2×#63851C2semidirect
11. C2×Dic3×Dic6C2semidirect
12. C2×#63839C2semidirect
18. C2×C3×D3×Q8C22semidirect
28. C2×#3797C22semidirect
29. #64155C22semidirect
33. C3×#944C22semidirect
46. #63888C22semidirect
47. #63856C22semidirect
48. #63851C22semidirect
49. Dic3×Dic6C22semidirect
50. #63839C22semidirect
54. C22×D3×Q8D3semidirect
64. C2×#944D3semidirect
98. C2×C3×Dic6D4semidirect
104. C2×#626Q8semidirect
139. C2×D3×Q8C2×D3semidirect
166. #944C2×D3semidirect
204. C22×C3⋊D3C2×Q8semidirect
208. C22×C3×D3C2×Q8semidirect
224. C2×C3×Dic3C2×Q8semidirect
234. C3×Dic6C2×D4semidirect
236. #626C2×Q8semidirect
321. C2×Dic6#67semidirect
361. C2×C3⋊D3C22×Q8semidirect
365. C2×C3×D3C22×Q8semidirect
374. C3×Dic3C22×Q8semidirect
432. C22×D3D3×Q8semidirect
480. C2×Dic3D3×Q8semidirect
499. Dic6C2×#67semidirect
500. C2×C32D4×Q8semidirect
583. C2×D3C2×D3×Q8semidirect
604. Dic3C2×D3×Q8semidirect
606. C32C2×D4×Q8semidirect
649. C2×C3#5727semidirect
650. C2×C3Q8×#67semidirect
683. C3C2×#5727semidirect
684. C3C2×Q8×#67semidirect
687. C2#10595403direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×Q82
C22×#37972
C2×#641552
C2×C3×#9442
#105954032
C2×#639042
C2×C4×#6262
C2×#638882
C2×#638562
C2×#638512
C2×Dic3×Dic62
C2×#638392
C2×Q8×#673
C2×#57273