Finite Group Databasebeta

← C2×#10594373 #11902552

Subgroups — C2×#10594373 #11902552

Order 1152.

3473 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3796C212yesmaximal, complemented
2C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×C3×#895C211yesmaximal, characteristic, complemented
4C2×C3×#888C211yesmaximal, characteristic, complemented
5C2×#63916C211yesmaximal, characteristic, complemented
6C2×C4×#626C211yesmaximal, characteristic, complemented
7C2×Dic3×D12C211yesmaximal, characteristic, complemented
8C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
9C2×#63887C212yesmaximal, complemented
10C2×#63884C212yesmaximal, complemented
11C2×#63853C212yesmaximal, complemented
12#10594373C2116yesmaximal, direct product factor
13C2×#5726—31nomaximal
14C2×#5611—31nomaximal
15C22×C4×C3⋊D3C2212yes—
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C3×D12C2212yes—
18C22×C3×D12C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×Dic6C2212yes—
21C22×#626C2212yes—
22C22×#626C2211yescharacteristic
23C22×D3×Dic3C2212yes—
24C22×D3×Dic3C2212yes—
25C2×#3796—216no—
26C2×#3796C22116yescomplemented
27C2×C32×C4⋊C4C2211yescharacteristic
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C2×#3750C2212yes—
30C4⋊C4×C3⋊D3C2218yescomplemented
31C2×C3×(C2×D3)⋊C4C2212yes—
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×Dic3⋊C4C2212yes—
34C2×C3×C4×Dic3C2211yescharacteristic
35C3×#895C2218yescomplemented
36C3×#888C2218yescomplemented
37C2×Dic3⋊Dic3C2212yes—
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2212yes—
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2212yes—
43#63916C2218yescomplemented
44C4×#626C2218yescomplemented
45Dic3×D12C2218yescomplemented
46D3×C4⋊Dic3C2218yescomplemented
47#63887C22116yescomplemented
48#63884C22116yescomplemented
49#63853C22116yescomplemented
50C22×#239—32no—
51C22×#237—32no—
52C2×C3×C4⋊Q8—31no—
53C2×C3×#121—31no—
54C2×#946—32no—
55C2×#938—31no—
56C2×#935—32no—
57C2×D4×Dic3—31no—
58C2×C4×#67—31no—
59C22×C4⋊Dic3—31no—
60#5726—316no—
61#5611—316no—
62C2×#895—31no—
63C2×#895D311yescharacteristic, complemented
64C2×#894—32no—
65C2×#894—32no—
66C2×D3×C4⋊C4—31no—
67C2×D3×C4⋊C4—31no—
68C2×D3×C4⋊C4—31no—
69C2×D3×C4⋊C4—61no—
70C2×#888D311yescharacteristic, complemented
71C2×#883—32no—
72C2×#878—32no—
73C2×C4×D12—31no—
74C2×C4×D12—31no—
75C23×C3⋊D3C2311yescharacteristic
76C23×C3×D3C2312yes—
77C23×C3×D3C2311yescharacteristic
78C22×C32×C4C2312yes—
79C22×C32×C4C2311yescharacteristic
80C22×C3⋊Dic3C2312yes—
81C22×C3⋊Dic3C2311yescharacteristic
82C2×C4×C3⋊D3—28no—
83C2×C4×C3⋊D3—24no—
84C2×C4×C3⋊D3C2318yes—
85C2×C4×C3⋊D3C2314yes—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2311yescharacteristic
90C2×C3×D12—28no—
91C2×C3×D12—24no—
92C2×C3×D12C2318yes—
93C2×C3×D12C2314yes—
94C2×C3×C4×D3—24no—
95C2×C3×C4×D3C2314yes—
96C2×C3×Dic6—28no—
97C2×C3×Dic6C2318yes—
98C2×#626—28no—
99C2×#626D418yescomplemented
100C2×#626C2318yes—
101C2×#626C2314yes—
102C2×D3×Dic3—28no—
103C2×D3×Dic3—28no—
104C2×D3×Dic3C2318yes—
105C2×D3×Dic3C2318yes—
106#3796—264no—
107C32×C4⋊C4C2314yes—
108C4⋊(C3⋊Dic3)C2314yes—
109#3750C2318yes—
110C3×(C2×D3)⋊C4C2318yes—
111C3×C4⋊Dic3C2314yes—
112C3×Dic3⋊C4C2318yes—
113C3×C4×Dic3C2314yes—
114Dic3⋊Dic3C2318yes—
115Dic3⋊Dic3C2314yes—
116#3722C2314yes—
117(C2×D3)⋊Dic3C2318yes—
118(C2×D3)⋊Dic3C2314yes—
119(C2×D3)⋊Dic3C2318yes—
120C2×#547—91noSylow
121C22×C3×Q8—32no—
122C22×C3×D4—32no—
123C22×C3×D4—31no—
124C23×C3×C4—31no—
125C22×#67—31no—
126C22×#67—32no—
127C23×Dic3—32no—
128C23×Dic3—32no—
129C2×#239—316no—
130C2×#239—616no—
131C2×#237—316no—
132C2×#237—616no—
133C22×D12—31no—
134C22×D12—32no—
135C22×D12C2×D312yes—
136C22×D12C2×D311yescharacteristic
137C22×C4×D3—32no—
138C22×C4×D3—32no—
139C22×C4×D3—32no—
140C22×C4×D3—32no—
141C22×C4×D3—31no—
142C22×C4×D3—31no—
143C22×C4×D3—61no—
144C22×C4×D3—62no—
145C22×C4×D3C2×D311yescharacteristic
146C22×Dic6C2×D312yes—
147C3×C4⋊Q8—38no—
148C3×#121—38no—
149C2×C3×C4⋊C4—21no—
150C2×C3×C4⋊C4—32no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4C2×D311yescharacteristic
153C2×C3×C4⋊C4C2×D311yescharacteristic
154C2×C3×C22⋊C4—32no—
155C2×C3×C42—31no—
156C2×#217—32no—
157C2×#217—32no—
158C2×#217—31no—
159#946—316no—
160#938—38no—
161#935—316no—
162D4×Dic3—38no—
163C4×#67—38no—
164C2×(C2×D3)⋊C4—31no—
165C2×(C2×D3)⋊C4—32no—
166C2×(C2×D3)⋊C4—32no—
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4—31no—
169C2×(C2×D3)⋊C4C2×D312yes—
170C2×C4⋊Dic3—31no—
171C2×C4⋊Dic3—31no—
172C2×C4⋊Dic3—31no—
173C2×C4⋊Dic3—32no—
174C2×C4⋊Dic3—38no—
175C2×C4⋊Dic3—61no—
176C2×C4⋊Dic3C2×D311yescharacteristic
177C2×Dic3⋊C4—32no—
178C2×Dic3⋊C4—32no—
179C2×Dic3⋊C4—31no—
180C2×Dic3⋊C4—32no—
181C2×Dic3⋊C4—62no—
182C2×Dic3⋊C4C2×D312yes—
183C2×C4×Dic3C2×D311yescharacteristic
184#895—38no—
185#895C2×D318yescomplemented
186#894—316no—
187#894—316no—
188D3×C4⋊C4—38no—
189D3×C4⋊C4—38no—
190D3×C4⋊C4—38no—
191D3×C4⋊C4—68no—
192#888C2×D318yescomplemented
193#883—316no—
194#878—316no—
195C4×D12—38no—
196C4×D12—38no—
197C23×C32C2411yescharacteristic
198C22×C3⋊D3—22no—
199C22×C3⋊D3—22no—
200C22×C3⋊D3C2×D414yes—
201C22×C3⋊D3C2412yes—
202C22×C3×D3—22no—
203C22×C3×D3—22no—
204C22×C3×D3—24no—
205C22×C3×D3—24no—
206C22×C3×D3—24no—
207C22×C3×D3C2×D414yes—
208C22×C3×D3C2414yes—
209C22×C3×D3C2412yes—
210C2×C32×C4—24no—
211C2×C32×C4#4114yescomplemented
212C2×C32×C4C2414yes—
213C2×C32×C4C2412yes—
214C2×C3⋊Dic3—22no—
215C2×C3⋊Dic3—24no—
216C2×C3⋊Dic3C2412yes—
217C2×C3⋊Dic3C2414yes—
218C4×C3⋊D3—28no—
219C4×C3⋊D3—216no—
220C2×C3×Dic3—24no—
221C2×C3×Dic3—22no—
222C2×C3×Dic3—22no—
223C2×C3×Dic3C2×D414yes—
224C2×C3×Dic3C2412yes—
225C2×C3×Dic3C2414yes—
226C2×C3×Dic3C2412yes—
227C2×C3×Dic3C2412yes—
228C3×D12—216no—
229C3×D12—28no—
230C3×C4×D3—28no—
231C3×Dic6—216no—
232#626—216no—
233#626C2×D4116yescomplemented
234D3×Dic3—216no—
235D3×Dic3—216no—
236C22×#41—92no—
237#547—916no—
238C2×C4⋊Q8—31no—
239C2×#123—92no—
240C2×#123—92no—
241C2×C22⋊Q8—92no—
242C2×#121—31no—
243C2×#121—91no—
244C2×C4×D4—91no—
245C2×C4×D4—91no—
246C22×C4⋊C4—91no—
247C22×C4⋊C4—91no—
248C24×C3—31no—
249C24×C3—32no—
250C23×D3—31no—
251C23×D3—31no—
252C23×D3—61no—
253C23×D3C22×D312yes—
254C23×D3C22×D311yescharacteristic
255C2×C3×Q8—38no—
256C2×C3×Q8—68no—
257C2×C3×D4—34no—
258C2×C3×D4—38no—
259C2×C3×D4—68no—
260C2×C3×D4—64no—
261C22×C3×C4—21no—
262C22×C3×C4—22no—
263C22×C3×C4—31no—
264C22×C3×C4—31no—
265C22×C3×C4—32no—
266C22×C3×C4—31no—
267C22×C3×C4—34no—
268C22×C3×C4—64no—
269C22×C3×C4C22×D312yes—
270C22×C3×C4C22×D312yes—
271C22×C3×C4C22×D311yescharacteristic
272C22×C3×C4C22×D311yescharacteristic
273C2×#67—38no—
274C2×#67—34no—
275C2×#67—38no—
276C2×#67—68no—
277C22×Dic3—31no—
278C22×Dic3—31no—
279C22×Dic3—32no—
280C22×Dic3—32no—
281C22×Dic3—38no—
282C22×Dic3—38no—
283C22×Dic3—61no—
284C22×Dic3—62no—
285C22×Dic3—68no—
286C22×Dic3—68no—
287C22×Dic3C22×D311yescharacteristic
288C22×Dic3C22×D311yescharacteristic
289C22×Dic3C22×D312yes—
290C22×Dic3C22×D311yescharacteristic
291#239—664no—
292#237—664no—
293C2×D12—28no—
294C2×D12—24no—
295C2×D12—38no—
296C2×D12—34no—
297C2×D12—38no—
298C2×D12—68no—
299C2×D12C22×D314yes—
300C2×D12C22×D318yes—
301C2×C4×D3—24no—
302C2×C4×D3—38no—
303C2×C4×D3—38no—
304C2×C4×D3—34no—
305C2×C4×D3—38no—
306C2×C4×D3—38no—
307C2×C4×D3—34no—
308C2×C4×D3—64no—
309C2×C4×D3—68no—
310C2×C4×D3—68no—
311C2×C4×D3—68no—
312C2×C4×D3—68no—
313C2×C4×D3—68no—
314C2×C4×D3—68no—
315C2×C4×D3—64no—
316C2×C4×D3—64no—
317C2×C4×D3—128no—
318C2×C4×D3C22×D314yes—
319C2×Dic6—28no—
320C2×Dic6C22×D318yes—
321C3×C4⋊C4—24no—
322C3×C4⋊C4—34no—
323C3×C4⋊C4—38no—
324C3×C4⋊C4C22×D314yes—
325C3×C4⋊C4C22×D314yes—
326C3×C22⋊C4—38no—
327C3×C42—34no—
328#217—38no—
329#217—38no—
330#217—34no—
331(C2×D3)⋊C4—34no—
332(C2×D3)⋊C4—38no—
333(C2×D3)⋊C4—38no—
334(C2×D3)⋊C4—34no—
335(C2×D3)⋊C4—34no—
336(C2×D3)⋊C4C22×D318yes—
337C4⋊Dic3—34no—
338C4⋊Dic3—34no—
339C4⋊Dic3—34no—
340C4⋊Dic3—38no—
341C4⋊Dic3—64no—
342C4⋊Dic3C22×D314yes—
343Dic3⋊C4—38no—
344Dic3⋊C4—38no—
345Dic3⋊C4—34no—
346Dic3⋊C4—38no—
347Dic3⋊C4—68no—
348Dic3⋊C4C22×D318yes—
349C4×Dic3C22×D314yes—
350C22×C32C22×D412yes—
351C22×C32C2×#4112yes—
352C22×C322−1+412yes—
353C22×C32C2511yescharacteristic
354C2×C3⋊D3—28no—
355C2×C3⋊D3—22no—
356C2×C3⋊D3—22no—
357C2×C3⋊D3C22×D414yes—
358C2×C3×D3—28no—
359C2×C3×D3—22no—
360C2×C3×D3—22no—
361C2×C3×D3—24no—
362C2×C3×D3—24no—
363C2×C3×D3—24no—
364C2×C3×D3—48no—
365C2×C3×D3C22×D414yes—
366C32×C4—24no—
367C32×C4C2×#4114yescomplemented
368C3⋊Dic3—22no—
369C3⋊Dic3—24no—
370C3×Dic3—24no—
371C3×Dic3—22no—
372C3×Dic3—22no—
373C3×Dic3C22×D414yes—
374C2×#41—916no—
375C2×#41—1816no—
376C22×Q8—32no—
377C22×D4—31no—
378C22×D4—32no—
379C22×D4—91no—
380C22×D4—92no—
381C23×C4—31no—
382C23×C4—92no—
383C23×C4—92no—
384C23×C4—91no—
385C23×C4—92no—
386C4⋊Q8—38no—
387#123—916no—
388#123—916no—
389C22⋊Q8—916no—
390#121—38no—
391#121—98no—
392C4×D4—98no—
393C4×D4—98no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—32no—
396C2×C4⋊C4—98no—
397C2×C4⋊C4—92no—
398C2×C4⋊C4—91no—
399C2×C4⋊C4—91no—
400C2×C4⋊C4—92no—
401C2×C4⋊C4—98no—
402C2×C4⋊C4D3211yescharacteristic
403C2×C22⋊C4—32no—
404C2×C22⋊C4—91no—
405C2×C22⋊C4—91no—
406C2×C22⋊C4—92no—
407C2×C22⋊C4—92no—
408C2×C42—31no—
409C23×C3—21no—
410C23×C3—34no—
411C23×C3—32no—
412C23×C3—34no—
413C23×C3—62no—
414C23×C3—62no—
415C23×C3—64no—
416C23×C3—64no—
417C23×C3—64no—
418C23×C3C23×D311yescharacteristic
419C23×C3C23×D311yescharacteristic
420C22×D3—22no—
421C22×D3—22no—
422C22×D3—24no—
423C22×D3—24no—
424C22×D3—24no—
425C22×D3—34no—
426C22×D3—34no—
427C22×D3—32no—
428C22×D3—32no—
429C22×D3—64no—
430C22×D3—62no—
431C22×D3—64no—
432C22×D3—64no—
433C22×D3—62no—
434C22×D3—62no—
435C22×D3—62no—
436C22×D3—62no—
437C22×D3D3×D414yes—
438C22×D3C23×D314yes—
439C22×D3C23×D312yes—
440C3×Q8—616no—
441C3×D4—616no—
442C3×D4—68no—
443C2×C3×C4—24no—
444C2×C3×C4—24no—
445C2×C3×C4—22no—
446C2×C3×C4—24no—
447C2×C3×C4—24no—
448C2×C3×C4—34no—
449C2×C3×C4—32no—
450C2×C3×C4—32no—
451C2×C3×C4—34no—
452C2×C3×C4—32no—
453C2×C3×C4—44no—
454C2×C3×C4—64no—
455C2×C3×C4—62no—
456C2×C3×C4—62no—
457C2×C3×C4—68no—
458C2×C3×C4#23714yescomplemented
459C2×C3×C4#23914yescomplemented
460C2×C3×C4C23×D314yes—
461C2×C3×C4C23×D314yes—
462C2×C3×C4C23×D312yes—
463C2×C3×C4C23×D312yes—
464#67—316no—
465#67—616no—
466C2×Dic3—24no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—32no—
470C2×Dic3—32no—
471C2×Dic3—34no—
472C2×Dic3—34no—
473C2×Dic3—62no—
474C2×Dic3—64no—
475C2×Dic3—616no—
476C2×Dic3—64no—
477C2×Dic3—64no—
478C2×Dic3—64no—
479C2×Dic3—62no—
480C2×Dic3—62no—
481C2×Dic3—616no—
482C2×Dic3—124no—
483C2×Dic3D3×D414yes—
484C2×Dic3C23×D312yes—
485C2×Dic3C23×D312yes—
486C2×Dic3C23×D314yes—
487C2×Dic3C23×D312yes—
488D12—216no—
489D12—28no—
490D12—316no—
491D12—616no—
492C4×D3—28no—
493C4×D3—616no—
494C4×D3—616no—
495C4×D3—616no—
496C4×D3—616no—
497C4×D3—616no—
498C4×D3—68no—
499C4×D3—68no—
500C4×D3—1216no—
501Dic6—216no—
502C2×C32#54714yescomplemented
503C2×C32C23×D411yescharacteristic
504C2×C32C22×#4111yescharacteristic
505C2×C32C2×2−1+411yescharacteristic
506C3⋊D3—24no—
507C3×D3—24no—
508C3×D3—44no—
509C24—31no—
510C24—32no—
511C24—91no—
512#41—1864no—
513C2×Q8—38no—
514C2×Q8—68no—
515C2×D4—34no—
516C2×D4—38no—
517C2×D4—68no—
518C2×D4—64no—
519C2×D4—94no—
520C2×D4—98no—
521C2×D4—98no—
522C2×D4—188no—
523C22×C4—31no—
524C22×C4—31no—
525C22×C4—31no—
526C22×C4—32no—
527C22×C4—34no—
528C22×C4—64no—
529C22×C4—98no—
530C22×C4—98no—
531C22×C4—91no—
532C22×C4—92no—
533C22×C4—94no—
534C22×C4—98no—
535C22×C4—188no—
536C22×C4—188no—
537C22×C4—188no—
538C22×C4—184no—
539C22×C4C2×D3212yes—
540C22×C4C2×D3211yescharacteristic
541C4⋊C4—34no—
542C4⋊C4—38no—
543C4⋊C4—98no—
544C4⋊C4—94no—
545C4⋊C4—94no—
546C4⋊C4—98no—
547C4⋊C4C2×D3214yes—
548C22⋊C4—38no—
549C22⋊C4—94no—
550C22⋊C4—94no—
551C22⋊C4—98no—
552C22⋊C4—98no—
553C42—34no—
554C22×C3—22no—
555C22×C3—22no—
556C22×C3—22no—
557C22×C3—21no—
558C22×C3—34no—
559C22×C3—62no—
560C22×C3—62no—
561C22×C3—68no—
562C22×C3—64no—
563C22×C3—64no—
564C22×C3—64no—
565C22×C3—128no—
566C22×C3C2×D3×D412yes—
567C22×C3C2×D3×D412yes—
568C22×C3C2×#23712yes—
569C22×C3C2×#23912yes—
570C22×C3#100712yes—
571C22×C3#101012yes—
572C22×C3C24×D311yescharacteristic
573C22×C3C24×D311yescharacteristic
574C2×D3—22no—
575C2×D3—22no—
576C2×D3—28no—
577C2×D3—24no—
578C2×D3—24no—
579C2×D3—24no—
580C2×D3—34no—
581C2×D3—34no—
582C2×D3—48no—
583C2×D3—64no—
584C2×D3—64no—
585C2×D3—616no—
586C2×D3—64no—
587C2×D3—62no—
588C2×D3—62no—
589C2×D3—62no—
590C2×D3—62no—
591C2×D3—68no—
592C2×D3—68no—
593C2×D3C2×D3×D414yes—
594C3×C4—24no—
595C3×C4—24no—
596C3×C4—24no—
597C3×C4—34no—
598C3×C4—44no—
599C3×C4—64no—
600C3×C4—62no—
601C3×C4—62no—
602C3×C4C2×#23714yescomplemented
603C3×C4C2×#23914yescomplemented
604Dic3—24no—
605Dic3—22no—
606Dic3—22no—
607Dic3—64no—
608Dic3—64no—
609Dic3—64no—
610Dic3—62no—
611Dic3—62no—
612Dic3—124no—
613Dic3C2×D3×D414yes—
614C32C2×#54711yescharacteristic, complemented, Sylow
615C23—34no—
616C23—32no—
617C23—34no—
618C23—62no—
619C23—62no—
620C23—64no—
621C23—64no—
622C23—64no—
623C23—94no—
624C23—92no—
625C23—182no—
626C23—182no—
627C23C22×D3211yescharacteristic
628Q8—616no—
629D4—616no—
630D4—68no—
631D4—916no—
632D4—1816no—
633C2×C4—24no—
634C2×C4—34no—
635C2×C4—32no—
636C2×C4—32no—
637C2×C4—32no—
638C2×C4—34no—
639C2×C4—62no—
640C2×C4—64no—
641C2×C4—62no—
642C2×C4—68no—
643C2×C4—92no—
644C2×C4—94no—
645C2×C4—1816no—
646C2×C4—1816no—
647C2×C4—1816no—
648C2×C4—182no—
649C2×C4—184no—
650C2×C4—188no—
651C2×C4#379614yescomplemented
652C2×C4C22×D3214yes—
653C2×C4C22×D3212yes—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—24no—
657C2×C3—21no—
658C2×C3—64no—
659C2×C3—124no—
660C2×C3#561114yescomplemented
661C2×C3#572614yescomplemented
662C2×C3C22×D3×D411yescharacteristic
663C2×C3C22×D3×D411yescharacteristic
664C2×C3C22×#23711yescharacteristic
665C2×C3C22×#23911yescharacteristic
666C2×C3C2×#100711yescharacteristic
667C2×C3C2×#101011yescharacteristic
668D3—24no—
669D3—44no—
670D3—68no—
671D3—64no—
672D3—64no—
673C22—34no—
674C22—62no—
675C22—68no—
676C22—62no—
677C22—64no—
678C22—64no—
679C22—64no—
680C22—94no—
681C22—128no—
682C22—182no—
683C22—188no—
684C22—182no—
685C22C2×#379612yes—
686C22D32×D412yes—
687C22#6431512yes—
688C22C23×D3211yescharacteristic
689C4—24no—
690C4—34no—
691C4—62no—
692C4—64no—
693C4—62no—
694C4—182no—
695C4—184no—
696C4C2×#379614yescomplemented
697C3—21no—
698C3C2×#561111yescharacteristic, complemented
699C3C2×#572611yescharacteristic, complemented
700C2—64no—
701C2—124no—
702C2—184no—
703C2#1059437314yesdirect product factor
704C2C22×#379611yescharacteristic
705C2C2×D32×D411yescharacteristic
706C2C2×#6431511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#547
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#3796C2semidirect
2. C2×C4⋊C4×C3⋊D3C2semidirect
3. C2×C3×#895C2semidirect
4. C2×C3×#888C2semidirect
5. C2×#63916C2semidirect
6. C2×C4×#626C2semidirect
7. C2×Dic3×D12C2semidirect
8. C2×D3×C4⋊Dic3C2semidirect
9. C2×#63887C2semidirect
10. C2×#63884C2semidirect
11. C2×#63853C2semidirect
12. #10594373C2direct (N × H)
26. C2×#3796C22semidirect
30. C4⋊C4×C3⋊D3C22semidirect
35. C3×#895C22semidirect
36. C3×#888C22semidirect
43. #63916C22semidirect
44. C4×#626C22semidirect
45. Dic3×D12C22semidirect
46. D3×C4⋊Dic3C22semidirect
47. #63887C22semidirect
48. #63884C22semidirect
49. #63853C22semidirect
63. C2×#895D3semidirect
70. C2×#888D3semidirect
99. C2×#626D4semidirect
185. #895C2×D3semidirect
192. #888C2×D3semidirect
211. C2×C32×C4#41semidirect
233. #626C2×D4semidirect
367. C32×C4C2×#41semidirect
458. C2×C3×C4#237semidirect
459. C2×C3×C4#239semidirect
502. C2×C32#547semidirect
602. C3×C4C2×#237semidirect
603. C3×C4C2×#239semidirect
614. C32C2×#547semidirect
651. C2×C4#3796semidirect
660. C2×C3#5611semidirect
661. C2×C3#5726semidirect
696. C4C2×#3796semidirect
698. C3C2×#5611semidirect
699. C3C2×#5726semidirect
703. C2#10594373direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37962
C2×C4⋊C4×C3⋊D32
C2×C3×#8952
C2×C3×#8882
C2×#639162
C2×C4×#6262
C2×Dic3×D122
C2×D3×C4⋊Dic32
C2×#638872
C2×#638842
C2×#638532
#105943732
C2×#57263
C2×#56113