Finite Group Databasebeta

← #11808232

Subgroups — #11808232

Order 1152.

2333 conjugacy classes of subgroups.

The subgroup lattice has 747 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C211yesmaximal, characteristic, complemented
3C2×C4×#626C212yesmaximal, complemented
4C3×C4×#217C211yesmaximal, characteristic, complemented
5#10591724C212yesmaximal, complemented
6#10591712C212yesmaximal, complemented
7#10591395C211yesmaximal, characteristic, complemented
8#10591354C211yesmaximal, characteristic, complemented
9#10591322C211yesmaximal, characteristic, complemented
10#10591321C211yesmaximal, characteristic, complemented
11C4×#3722C212yesmaximal, complemented
12#82400—31nomaximal
13#73580—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×#638C2212yes—
16C2×#3828—24no—
17C2×#3828—28no—
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4×C3⋊D3C2212yes—
20C22×#634C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×#626C2212yes—
24C2×C3×#217C2211yescharacteristic
25C2×C3×#217C2212yes—
26C3×C4×#67—24no—
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2212yes—
31C2×Dic3⋊Dic3C2212yes—
32C2×#3722C2212yes—
33C2×#3722C2212yes—
34C2×#3722C2212yes—
35C2×(C2×D3)⋊Dic3C2212yes—
36C4×#626—28no—
37C3×C3⋊#95C2211yescharacteristic
38C3×C3⋊#95C2211yescharacteristic
39#63579C2212yes—
40#63579C2212yes—
41C22×#235—31no—
42C22×#235—31no—
43C22×#235—61no—
44C2×C3×C4×D4—31no—
45C2×C4×#67—32no—
46C2×C4×#67D311yescharacteristic, complemented
47C2×C4×D12—32no—
48C3×C4×C22⋊C4—31no—
49#5223—32no—
50C4×#217D311yescharacteristic, complemented
51#4991—31no—
52#4979—31no—
53#4961—32no—
54#4960—32no—
55#4960—31no—
56#4959—32no—
57#4947—31no—
58C4×(C2×D3)⋊C4—32no—
59C4×(C2×D3)⋊C4—32no—
60#4673—31no—
61#4672—31no—
62#4671—31no—
63#4656—31no—
64C24×C32C2311yescharacteristic
65C23×C3⋊D3C2312yes—
66C23×C3×D3C2311yescharacteristic
67C22×C32×C4—24no—
68C22×C32×C4D414yescomplemented
69C22×C32×C4C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C2×#638—24no—
72C2×#638—24no—
73C2×#638—24no—
74C22×C3⋊Dic3C2312yes—
75#3828—232no—
76C2×C4⋊(C3⋊D3)—24no—
77C2×C4⋊(C3⋊D3)—22no—
78C2×C4×C3⋊D3—24no—
79C2×C4×C3⋊D3—24no—
80C2×C4×C3⋊D3D418yescomplemented
81C2×#634—22no—
82C2×#634—24no—
83C2×C3×#67—22no—
84C2×C3×#67—22no—
85C2×C3×#67—22no—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2312yes—
91C2×C3×C4×D3—22no—
92C2×C3×C4×D3—24no—
93C2×#626—24no—
94C2×#626—24no—
95C2×#626—24no—
96C3×#217—22no—
97C3×#217—24no—
98C3×(C2×D3)⋊C4—22no—
99C3×Dic3⋊C4—22no—
100C3×C4×Dic3—22no—
101C3×C4×Dic3—24no—
102Dic3⋊Dic3—24no—
103#3722—24no—
104#3722—24no—
105#3722—24no—
106(C2×D3)⋊Dic3—24no—
107#2388—91noSylow
108C22×C3×D4—31no—
109C23×C3×C4—21no—
110C23×C3×C4—31no—
111C23×C3×C4C2×D311yescharacteristic
112C23×C3×C4C2×D311yescharacteristic
113C22×#67—32no—
114C22×#67—32no—
115C22×#67—32no—
116C22×#67—62no—
117C22×#67C2×D311yescharacteristic
118C2×#235—68no—
119C2×#235—68no—
120C2×#235—616no—
121C2×#235—68no—
122C2×#235—64no—
123C2×#235—64no—
124C22×D12—32no—
125C22×D12—31no—
126C22×D12—31no—
127C22×D12—61no—
128C22×C4×D3—32no—
129C22×C4×D3—32no—
130C22×C4×D3—62no—
131C22×C4×D3C2×D311yescharacteristic
132C22×Dic6—31no—
133C22×Dic6—31no—
134C22×Dic6—61no—
135C3×C4×D4—64no—
136C2×C3×C4⋊C4—31no—
137C2×C3×C22⋊C4—31no—
138C2×C3×C22⋊C4—32no—
139C2×C3×C22⋊C4—31no—
140C2×C3×C42—31no—
141C2×C3×C42—32no—
142C2×#217—32no—
143C2×#217C2×D312yes—
144C2×#217C2×D311yescharacteristic
145C4×#67—24no—
146C4×#67—68no—
147C2×(C2×D3)⋊C4—32no—
148C2×(C2×D3)⋊C4—32no—
149C2×(C2×D3)⋊C4—32no—
150C2×(C2×D3)⋊C4—32no—
151C2×(C2×D3)⋊C4—32no—
152C2×(C2×D3)⋊C4—32no—
153C2×(C2×D3)⋊C4—32no—
154C2×(C2×D3)⋊C4C2×D311yescharacteristic
155C2×C4⋊Dic3—32no—
156C2×Dic3⋊C4—32no—
157C2×Dic3⋊C4C2×D311yescharacteristic
158C2×C4×Dic3C2×D311yescharacteristic
159C2×C4×Dic3C2×D312yes—
160C4×D12—68no—
161C3×#95—31no—
162C3×#95—31no—
163C3⋊#95—32no—
164C3⋊#95—32no—
165C3⋊#95—32no—
166C3⋊#95—32no—
167C3⋊#95C2×D311yescharacteristic
168C3⋊#95C2×D311yescharacteristic
169C23×C32—22no—
170C23×C32—22no—
171C23×C32—21no—
172C23×C32—21no—
173C23×C32C2×D412yes—
174C23×C32C2411yescharacteristic
175C22×C3⋊D3—22no—
176C22×C3⋊D3—22no—
177C22×C3⋊D3—22no—
178C22×C3⋊D3—22no—
179C22×C3⋊D3—22no—
180C22×C3⋊D3—22no—
181C22×C3⋊D3C2×D414yes—
182C22×C3×D3—22no—
183C22×C3×D3—21no—
184C22×C3×D3—22no—
185C22×C3×D3—21no—
186C22×C3×D3#4112yescomplemented
187C2×C32×C4—22no—
188C2×C32×C4—28no—
189C2×C32×C4C2×D412yes—
190C2×C32×C4C2×D412yes—
191C2×C32×C4C2×D414yes—
192#638—216no—
193C2×C3⋊Dic3—22no—
194C2×C3⋊Dic3—22no—
195C2×C3⋊Dic3C2×D414yes—
196C4⋊(C3⋊D3)—28no—
197C4×C3⋊D3—216no—
198#634—28no—
199C3×#67—28no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—21no—
207C2×C3×Dic3—21no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3#4112yescomplemented
212C2×C3×Dic3#4114yescomplemented
213C3×C4×D3—44no—
214#626—216no—
215C22×#41—91no—
216C2×C4×D4—31no—
217C2×C4×D4—92no—
218#395—91no—
219#394—91no—
220#394—92no—
221#393—91no—
222#392—91no—
223#392—92no—
224C4×C22⋊C4—31no—
225C4×C22⋊C4—92no—
226C24×C3—21no—
227C24×C3—31no—
228C24×C3C22×D311yescharacteristic
229C24×C3C22×D311yescharacteristic
230C23×D3—32no—
231C23×D3—32no—
232C23×D3—62no—
233C23×D3C22×D311yescharacteristic
234C2×C3×D4—62no—
235C2×C3×D4—62no—
236C2×C3×D4—62no—
237C22×C3×C4—28no—
238C22×C3×C4—24no—
239C22×C3×C4—24no—
240C22×C3×C4—24no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—31no—
244C22×C3×C4—32no—
245C22×C3×C4—31no—
246C22×C3×C4—32no—
247C22×C3×C4—31no—
248C22×C3×C4—62no—
249C22×C3×C4—64no—
250C22×C3×C4D1214yescomplemented
251C22×C3×C4#6714yescomplemented
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D311yescharacteristic
254C22×C3×C4C22×D311yescharacteristic
255C22×C3×C4C22×D311yescharacteristic
256C2×#67—22no—
257C2×#67—22no—
258C2×#67—22no—
259C2×#67—64no—
260C2×#67—64no—
261C2×#67—64no—
262C2×#67—64no—
263C2×#67—64no—
264C2×#67—64no—
265C2×#67—68no—
266C2×#67—68no—
267C2×#67—68no—
268C2×#67—64no—
269C2×#67—64no—
270C2×#67—64no—
271C22×Dic3—32no—
272C22×Dic3—32no—
273C22×Dic3—62no—
274C22×Dic3C22×D311yescharacteristic
275C22×Dic3C22×D312yes—
276C22×Dic3C22×D311yescharacteristic
277C22×Dic3C22×D311yescharacteristic
278C22×Dic3C22×D312yes—
279#235—664no—
280#235—632no—
281#235—632no—
282C2×D12—64no—
283C2×D12—64no—
284C2×D12—68no—
285C2×D12—64no—
286C2×D12—64no—
287C2×D12—64no—
288C2×D12—64no—
289C2×D12—62no—
290C2×D12—62no—
291C2×C4×D3—24no—
292C2×C4×D3—22no—
293C2×C4×D3—38no—
294C2×C4×D3—38no—
295C2×C4×D3—68no—
296C2×C4×D3—68no—
297C2×C4×D3—68no—
298C2×C4×D3—64no—
299C2×C4×D3—64no—
300C2×C4×D3—64no—
301C2×C4×D3—64no—
302C2×Dic6—64no—
303C2×Dic6—64no—
304C2×Dic6—68no—
305C2×Dic6—64no—
306C2×Dic6—62no—
307C2×Dic6—62no—
308C3×C4⋊C4—62no—
309C3×C22⋊C4—64no—
310C3×C22⋊C4—62no—
311C3×C22⋊C4—62no—
312C3×C42—62no—
313C3×C42—64no—
314#217—22no—
315#217—24no—
316#217—64no—
317(C2×D3)⋊C4—22no—
318(C2×D3)⋊C4—64no—
319(C2×D3)⋊C4—64no—
320(C2×D3)⋊C4—64no—
321(C2×D3)⋊C4—64no—
322(C2×D3)⋊C4—64no—
323(C2×D3)⋊C4—64no—
324(C2×D3)⋊C4—64no—
325C4⋊Dic3—64no—
326Dic3⋊C4—22no—
327Dic3⋊C4—64no—
328C4×Dic3—24no—
329C4×Dic3—22no—
330C22×C32—22no—
331C22×C32—22no—
332C22×C32—22no—
333C22×C32—42no—
334C22×C32—42no—
335C22×C32C22×D411yescharacteristic
336C22×C32C22×D412yes—
337C22×C32C2×#4111yescharacteristic
338C22×C32C2×#4112yes—
339C22×C32C2×#4111yescharacteristic
340C2×C3⋊D3—24no—
341C2×C3⋊D3—24no—
342C2×C3⋊D3—24no—
343C2×C3⋊D3—42no—
344C2×C3⋊D3—42no—
345C2×C3⋊D3—42no—
346C2×C3⋊D3—42no—
347C2×C3×D3—24no—
348C2×C3×D3—22no—
349C2×C3×D3—41no—
350C2×C3×D3—42no—
351C2×C3×D3—41no—
352C32×C4—22no—
353C32×C4#12014yes—
354C3⋊Dic3—24no—
355C3×Dic3—24no—
356C3×Dic3—22no—
357C3×Dic3—41no—
358C3×Dic3—42no—
359C3×Dic3—41no—
360C2×#41—188no—
361C2×#41—184no—
362C22×Q8—91no—
363C22×D4—31no—
364C22×D4—92no—
365C22×D4—92no—
366C22×D4—91no—
367C23×C4—31no—
368C23×C4—92no—
369C23×C4D3211yescharacteristic
370C4×D4—64no—
371C4×D4—188no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—92no—
374C2×C22⋊C4—31no—
375C2×C22⋊C4—32no—
376C2×C22⋊C4—31no—
377C2×C22⋊C4—92no—
378C2×C22⋊C4—92no—
379C2×C22⋊C4—92no—
380C2×C22⋊C4—92no—
381C2×C42—31no—
382C2×C42—32no—
383#95—31no—
384#95—31no—
385#95—92no—
386#95—92no—
387C23×C3—24no—
388C23×C3—22no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—22no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—22no—
398C23×C3—32no—
399C23×C3—42no—
400C23×C3—41no—
401C23×C3—41no—
402C23×C3—61no—
403C23×C3—62no—
404C23×C3—62no—
405C23×C3—61no—
406C23×C3C2×D1212yes—
407C23×C3C2×#6712yes—
408C23×C3C23×D311yescharacteristic
409C23×C3C23×D311yescharacteristic
410C22×D3—21no—
411C22×D3—22no—
412C22×D3—22no—
413C22×D3—21no—
414C22×D3—34no—
415C22×D3—34no—
416C22×D3—64no—
417C22×D3—64no—
418C22×D3—64no—
419C22×D3—62no—
420C22×D3—62no—
421C22×D3—62no—
422C22×D3—62no—
423C22×D3—62no—
424C22×D3—62no—
425C22×D3—62no—
426C22×D3—62no—
427C22×D3—62no—
428C22×D3—62no—
429C22×D3—62no—
430C22×D3—62no—
431C22×D3—122no—
432C22×D3—122no—
433C22×D3—122no—
434C22×D3—122no—
435C22×D3#23512yescomplemented
436C3×D4—68no—
437C2×C3×C4—24no—
438C2×C3×C4—216no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—28no—
442C2×C3×C4—28no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—24no—
446C2×C3×C4—32no—
447C2×C3×C4—34no—
448C2×C3×C4—61no—
449C2×C3×C4—62no—
450C2×C3×C4—62no—
451C2×C3×C4—61no—
452C2×C3×C4—61no—
453C2×C3×C4—61no—
454C2×C3×C4—62no—
455C2×C3×C4—62no—
456C2×C3×C4—62no—
457C2×C3×C4—62no—
458C2×C3×C4—62no—
459C2×C3×C4—124no—
460C2×C3×C4C2×D1212yes—
461C2×C3×C4C2×D1212yes—
462C2×C3×C4D3×D414yes—
463C2×C3×C4D3×D414yes—
464C2×C3×C4C2×#6712yes—
465C2×C3×C4C2×#6712yes—
466#67—28no—
467#67—616no—
468#67—632no—
469#67—616no—
470#67—616no—
471C2×Dic3—21no—
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—21no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—34no—
483C2×Dic3—34no—
484C2×Dic3—64no—
485C2×Dic3—64no—
486C2×Dic3—64no—
487C2×Dic3—62no—
488C2×Dic3—62no—
489C2×Dic3—62no—
490C2×Dic3—62no—
491C2×Dic3#23512yescomplemented
492C2×Dic3#23514yescomplemented
493D12—616no—
494D12—68no—
495D12—68no—
496D12—616no—
497C4×D3—44no—
498C4×D3—632no—
499C4×D3—616no—
500C4×D3—616no—
501Dic6—616no—
502Dic6—68no—
503Dic6—68no—
504C2×C32—42no—
505C2×C32C2×#12011yescharacteristic
506C2×C32#52511yescharacteristic
507C2×C32#52512yes—
508C2×C32#53211yescharacteristic
509C2×C32#53212yes—
510C3⋊D3—44no—
511C3×D3—42no—
512C24—31no—
513C24—92no—
514C24C2×D3211yescharacteristic
515#41—1832no—
516C2×Q8—184no—
517C2×Q8—182no—
518C2×D4—62no—
519C2×D4—62no—
520C2×D4—62no—
521C2×D4—184no—
522C2×D4—184no—
523C2×D4—184no—
524C2×D4—184no—
525C2×D4—184no—
526C2×D4—184no—
527C2×D4—184no—
528C2×D4—182no—
529C22×C4—24no—
530C22×C4—32no—
531C22×C4—31no—
532C22×C4—32no—
533C22×C4—31no—
534C22×C4—31no—
535C22×C4—62no—
536C22×C4—64no—
537C22×C4—92no—
538C22×C4—98no—
539C22×C4—184no—
540C22×C4—184no—
541C22×C4#62614yescomplemented
542C22×C4C2×D3211yescharacteristic
543C22×C4C2×D3211yescharacteristic
544C4⋊C4—62no—
545C4⋊C4—184no—
546C22⋊C4—64no—
547C22⋊C4—62no—
548C22⋊C4—62no—
549C22⋊C4—184no—
550C22⋊C4—184no—
551C22⋊C4—184no—
552C22⋊C4—184no—
553C42—62no—
554C42—64no—
555C22×C3—24no—
556C22×C3—22no—
557C22×C3—22no—
558C22×C3—22no—
559C22×C3—22no—
560C22×C3—22no—
561C22×C3—22no—
562C22×C3—21no—
563C22×C3—22no—
564C22×C3—21no—
565C22×C3—21no—
566C22×C3—22no—
567C22×C3—42no—
568C22×C3—42no—
569C22×C3—44no—
570C22×C3—44no—
571C22×C3—42no—
572C22×C3—42no—
573C22×C3—42no—
574C22×C3—42no—
575C22×C3—62no—
576C22×C3—64no—
577C22×C3—121no—
578C22×C3—121no—
579C22×C3—122no—
580C22×C3C22×D1211yescharacteristic
581C22×C3C2×#23512yes—
582C22×C3C2×#23511yescharacteristic
583C22×C3C2×#23511yescharacteristic
584C22×C3C2×D3×D412yes—
585C22×C3C2×D3×D412yes—
586C22×C3D3×#4111yescharacteristic
587C22×C3D3×#4111yescharacteristic
588C22×C3D3×#4112yes—
589C22×C3C22×#6711yescharacteristic
590C2×D3—22no—
591C2×D3—24no—
592C2×D3—41no—
593C2×D3—42no—
594C2×D3—41no—
595C2×D3—68no—
596C2×D3—64no—
597C2×D3—64no—
598C2×D3—64no—
599C2×D3—64no—
600C2×D3—64no—
601C2×D3—64no—
602C2×D3—124no—
603C2×D3—124no—
604C2×D3—124no—
605C2×D3—124no—
606C2×D3—124no—
607C2×D3—124no—
608C2×D3—122no—
609C2×D3—122no—
610C2×D3—122no—
611C2×D3—122no—
612C2×D3—122no—
613C2×D3—122no—
614C2×D3—122no—
615C2×D3—122no—
616C3×C4—24no—
617C3×C4—22no—
618C3×C4—22no—
619C3×C4—24no—
620C3×C4—62no—
621C3×C4—64no—
622C3×C4—121no—
623C3×C4—121no—
624C3×C4—122no—
625C3×C4#88214yes—
626C3×C4#93714yes—
627Dic3—22no—
628Dic3—24no—
629Dic3—41no—
630Dic3—42no—
631Dic3—41no—
632Dic3—68no—
633Dic3—64no—
634Dic3—64no—
635C32#238811yescharacteristic, complemented, Sylow
636C23—22no—
637C23—21no—
638C23—21no—
639C23—22no—
640C23—32no—
641C23—61no—
642C23—62no—
643C23—61no—
644C23—62no—
645C23—94no—
646C23—182no—
647C23—182no—
648C23—182no—
649C23—182no—
650C23—182no—
651C23—182no—
652C23C2×#62612yes—
653C23C22×D3211yescharacteristic
654Q8—188no—
655D4—68no—
656D4—188no—
657D4—1816no—
658D4—1816no—
659C2×C4—22no—
660C2×C4—28no—
661C2×C4—34no—
662C2×C4—32no—
663C2×C4—61no—
664C2×C4—62no—
665C2×C4—61no—
666C2×C4—62no—
667C2×C4—62no—
668C2×C4—62no—
669C2×C4—62no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—94no—
675C2×C4—124no—
676C2×C4—182no—
677C2×C4—182no—
678C2×C4—1816no—
679C2×C4C2×#62612yes—
680C2×C4C2×#62612yes—
681C2×C4#381114yes—
682C2×C3—22no—
683C2×C3—21no—
684C2×C3—22no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—44no—
688C2×C3—42no—
689C2×C3—42no—
690C2×C3—122no—
691C2×C3#547711yescharacteristic
692C2×C3C2×#88211yescharacteristic
693C2×C3#552411yescharacteristic
694C2×C3#554712yes—
695C2×C3#554712yes—
696C2×C3#554812yes—
697C2×C3#554812yes—
698C2×C3#579111yescharacteristic
699C2×C3C2×#93711yescharacteristic
700C2×C3#583211yescharacteristic
701D3—42no—
702D3—128no—
703D3—124no—
704D3—124no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—42no—
709C22—42no—
710C22—64no—
711C22—62no—
712C22—121no—
713C22—122no—
714C22—121no—
715C22—184no—
716C22—184no—
717C22—184no—
718C22—362no—
719C22—362no—
720C22—362no—
721C22—362no—
722C22D3×#23511yescharacteristic
723C22D3×#23512yes—
724C22D3×#23511yescharacteristic
725C22C22×#62611yescharacteristic
726C22C2×#381112yes—
727C4—22no—
728C4—64no—
729C4—62no—
730C4—121no—
731C4—122no—
732C4—121no—
733C4—184no—
734C4#6398114yes—
735C3—21no—
736C3#7358011yescharacteristic, complemented
737C3#8240011yescharacteristic, complemented
738C2—42no—
739C2—122no—
740C2—364no—
741C2#1059501712yes—
742C2#1059502311yescharacteristic
743C2#1059502911yescharacteristic
744C2#1059507612yes—
745C2C2×#6398111yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, socle, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
hypercenterC23×C4D32
hypocenterC32#2388
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3828C2semidirect
2. C2×C3×C4×#67C2semidirect
3. C2×C4×#626C2semidirect
4. C3×C4×#217C2semidirect
5. #10591724C2semidirect
6. #10591712C2semidirect
7. #10591395C2semidirect
8. #10591354C2semidirect
9. #10591322C2semidirect
10. #10591321C2semidirect
11. C4×#3722C2semidirect
46. C2×C4×#67D3semidirect
50. C4×#217D3semidirect
68. C22×C32×C4D4semidirect
80. C2×C4×C3⋊D3D4semidirect
186. C22×C3×D3#41semidirect
211. C2×C3×Dic3#41semidirect
212. C2×C3×Dic3#41semidirect
250. C22×C3×C4D12semidirect
251. C22×C3×C4#67semidirect
435. C22×D3#235semidirect
491. C2×Dic3#235semidirect
492. C2×Dic3#235semidirect
541. C22×C4#626semidirect
635. C32#2388semidirect
736. C3#73580semidirect
737. C3#82400semidirect

Maximal subgroups

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

subgroupindex
C22×#38282
C2×C3×C4×#672
C2×C4×#6262
C3×C4×#2172
#105917242
#105917122
#105913952
#105913542
#105913222
#105913212
C4×#37222
#824003
#735803