Finite Group Databasebeta

← C2×#10594928 #11902533

Subgroups — C2×#10594928 #11902533

Order 1152.

3477 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3804C212yesmaximal, complemented
2C2×C4×#638C211yesmaximal, characteristic, complemented
3C2×C3×#930C211yesmaximal, characteristic, complemented
4C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
5C2×#63961C212yesmaximal, complemented
6C2×#63919C211yesmaximal, characteristic, complemented
7C2×#63916C211yesmaximal, characteristic, complemented
8C2×#63900C211yesmaximal, characteristic, complemented
9#10594928C2116yesmaximal, direct product factor
10C2×#63899C212yesmaximal, complemented
11C2×#63898C211yesmaximal, characteristic, complemented
12C2×#63854C212yesmaximal, complemented
13C2×#5611—31nomaximal
14C2×#5507—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C22×#638C2211yescharacteristic
17C22×C4×C3⋊D3C2211yescharacteristic
18C22×C3×#67C2212yes—
19C23×C3×Dic3C2212yes—
20C22×C3×D12C2211yescharacteristic
21C22×#627C2212yes—
22C22×#626C2212yes—
23C22×#624C2212yes—
24C2×#3804—216no—
25C2×#3804C22116yescomplemented
26C22×D3×Dic3C2212yes—
27C2×#3757C2211yescharacteristic
28C4×#638C2218yescomplemented
29C2×#3752C2211yescharacteristic
30C2×#3750C2211yescharacteristic
31C2×C4×C3⋊Dic3C2211yescharacteristic
32C3×#930C2218yescomplemented
33C2×C3×(C2×D3)⋊C4C2212yes—
34C2×C3×C4⋊Dic3C2212yes—
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C2×C3×C4⋊Dic3C2211yescharacteristic
38C2×C3×C4⋊Dic3C2218yescomplemented
39C2×#3724C2212yes—
40C2×#3724C2212yes—
41#63961C22116yescomplemented
42C2×(C2×D3)⋊Dic3C2212yes—
43C2×(C2×D3)⋊Dic3C2212yes—
44#63919C2218yescomplemented
45#63916C2218yescomplemented
46#63900C2218yescomplemented
47#63899C22116yescomplemented
48#63898C2218yescomplemented
49#63854C22116yescomplemented
50C22×#237—32no—
51C22×#235—32no—
52C2×C3×#121—31no—
53C22×C3×C4⋊C4—31no—
54C2×#938—31no—
55C2×#935—32no—
56C2×D4×Dic3—31no—
57C2×#930D311yescharacteristic, complemented
58C2×#929—32no—
59C2×C4×#67—31no—
60C2×C4×#67—31no—
61C2×C4×#67—61no—
62C22×C4⋊Dic3D311yescharacteristic, complemented
63#5611—316no—
64C2×#896—32no—
65#5507—316no—
66C2×#895—31no—
67C2×#894—32no—
68C2×#893—31no—
69C2×D3×C4⋊C4—31no—
70C2×D3×C4⋊C4—31no—
71C2×#888—31no—
72C2×#888—31no—
73C2×#883—32no—
74C2×#878—32no—
75C24×C32C2311yescharacteristic
76C23×C3⋊D3C2311yescharacteristic
77C23×C3×D3C2312yes—
78C22×C32×C4—24no—
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2314yes—
81C22×C32×C4C2311yescharacteristic
82C2×#638D418yescomplemented
83C2×#638C2314yes—
84C22×C3⋊Dic3C2311yescharacteristic
85C22×C3⋊Dic3C2311yescharacteristic
86C22×C3⋊Dic3C2311yescharacteristic
87C2×C4×C3⋊D3—24no—
88C2×C4×C3⋊D3C2314yes—
89C2×C3×#67—28no—
90C2×C3×#67C2318yes—
91C22×C3×Dic3—28no—
92C22×C3×Dic3C2312yes—
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2312yes—
95C22×C3×Dic3C2318yes—
96C2×C3×D12—24no—
97C2×C3×D12C2314yes—
98C2×#627—28no—
99C2×#627C2318yes—
100C2×#626—28no—
101C2×#626C2318yes—
102C2×#624—28no—
103C2×#624C2318yes—
104#3804—264no—
105C2×D3×Dic3—28no—
106C2×D3×Dic3C2318yes—
107#3757C2314yes—
108#3752C2314yes—
109#3750C2314yes—
110C4×C3⋊Dic3C2314yes—
111C3×(C2×D3)⋊C4C2318yes—
112C3×C4⋊Dic3C2318yes—
113C3×C4⋊Dic3C2314yes—
114C3×C4⋊Dic3C2314yes—
115C3×C4⋊Dic3C2314yes—
116#3724C2318yes—
117#3724C2318yes—
118(C2×D3)⋊Dic3C2318yes—
119(C2×D3)⋊Dic3C2318yes—
120C2×#547—91noSylow
121C22×C3×D4—32no—
122C22×C3×D4—31no—
123C23×C3×C4—21no—
124C23×C3×C4—32no—
125C23×C3×C4C2×D311yescharacteristic
126C23×C3×C4C2×D311yescharacteristic
127C22×#67—31no—
128C22×#67—31no—
129C22×#67—32no—
130C22×#67—61no—
131C22×#67C2×D312yes—
132C23×Dic3—32no—
133C23×Dic3C2×D312yes—
134C2×#237—316no—
135C2×#237—616no—
136C2×#235—316no—
137C2×#235—616no—
138C22×D12—32no—
139C22×D12C2×D311yescharacteristic
140C22×C4×D3—32no—
141C22×C4×D3—31no—
142C22×C4×D3—31no—
143C22×C4×D3—32no—
144C22×C4×D3—32no—
145C22×C4×D3—61no—
146C22×Dic6—32no—
147C22×Dic6—32no—
148C3×#121—38no—
149C2×C3×C4⋊C4—31no—
150C2×C3×C4⋊C4—31no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4—32no—
153C2×C3×C4⋊C4—38no—
154C2×C3×C22⋊C4—32no—
155C2×#217—31no—
156C2×#217—31no—
157C2×#217—32no—
158C2×#217—32no—
159C2×#217—61no—
160#938—38no—
161#935—316no—
162D4×Dic3—38no—
163#930C2×D318yescomplemented
164#929—316no—
165C4×#67—38no—
166C4×#67—38no—
167C4×#67—68no—
168C2×(C2×D3)⋊C4—32no—
169C2×(C2×D3)⋊C4—32no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4—61no—
173C2×(C2×D3)⋊C4C2×D312yes—
174C2×C4⋊Dic3C2×D312yes—
175C2×C4⋊Dic3C2×D311yescharacteristic
176C2×C4⋊Dic3C2×D311yescharacteristic
177C2×C4⋊Dic3C2×D311yescharacteristic
178C2×C4⋊Dic3C2×D318yescomplemented
179C2×Dic3⋊C4—31no—
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4—32no—
182C2×Dic3⋊C4—32no—
183C2×Dic3⋊C4—32no—
184C2×Dic3⋊C4—32no—
185C2×Dic3⋊C4—61no—
186C2×C4×Dic3—31no—
187C2×C4×Dic3—31no—
188C2×C4×Dic3—61no—
189#896—316no—
190#895—38no—
191#894—316no—
192#893—38no—
193D3×C4⋊C4—38no—
194D3×C4⋊C4—38no—
195#888—38no—
196#888—38no—
197#883—316no—
198#878—316no—
199C23×C32—22no—
200C23×C32—22no—
201C23×C32C2×D414yes—
202C23×C32C2412yes—
203C23×C32C2411yescharacteristic
204C22×C3⋊D3—22no—
205C22×C3⋊D3—22no—
206C22×C3⋊D3C2×D414yes—
207C22×C3⋊D3C2412yes—
208C22×C3×D3—24no—
209C22×C3×D3—24no—
210C22×C3×D3—24no—
211C22×C3×D3C2414yes—
212C2×C32×C4—22no—
213C2×C32×C4—28no—
214C2×C32×C4#4114yescomplemented
215C2×C32×C4C2412yes—
216C2×C32×C4C2412yes—
217#638C2×D4116yescomplemented
218C2×C3⋊Dic3—22no—
219C2×C3⋊Dic3—22no—
220C2×C3⋊Dic3C2×D414yes—
221C2×C3⋊Dic3C2412yes—
222C2×C3⋊Dic3C2412yes—
223C2×C3⋊Dic3C2412yes—
224C4×C3⋊D3—28no—
225C3×#67—216no—
226C2×C3×Dic3—24no—
227C2×C3×Dic3—216no—
228C2×C3×Dic3—24no—
229C2×C3×Dic3—24no—
230C2×C3×Dic3C2414yes—
231C2×C3×Dic3C2414yes—
232C2×C3×Dic3C2414yes—
233C3×D12—28no—
234#627—216no—
235#626—216no—
236#624—216no—
237D3×Dic3—216no—
238C22×#41—92no—
239#547—916no—
240C2×C4⋊Q8—91no—
241C2×#123—92no—
242C2×#123—92no—
243C2×C22⋊Q8—92no—
244C2×#121—31no—
245C2×#121—91no—
246C2×C4×D4—91no—
247C2×C4×D4—91no—
248C22×C4⋊C4—31no—
249C22×C4⋊C4—91no—
250C24×C3—21no—
251C24×C3—32no—
252C24×C3C22×D311yescharacteristic
253C24×C3C22×D311yescharacteristic
254C23×D3—31no—
255C23×D3—31no—
256C23×D3—61no—
257C23×D3C22×D312yes—
258C2×C3×D4—38no—
259C2×C3×D4—34no—
260C2×C3×D4—68no—
261C2×C3×D4—64no—
262C22×C3×C4—24no—
263C22×C3×C4—24no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—24no—
267C22×C3×C4—32no—
268C22×C3×C4—32no—
269C22×C3×C4—32no—
270C22×C3×C4—38no—
271C22×C3×C4—44no—
272C22×C3×C4—68no—
273C22×C3×C4C22×D311yescharacteristic
274C22×C3×C4C22×D311yescharacteristic
275C22×C3×C4C22×D314yes—
276C22×C3×C4C22×D314yes—
277C22×C3×C4C22×D311yescharacteristic
278C22×C3×C4C22×D311yescharacteristic
279C2×#67—28no—
280C2×#67—38no—
281C2×#67—38no—
282C2×#67—34no—
283C2×#67—34no—
284C2×#67—38no—
285C2×#67—64no—
286C2×#67—68no—
287C2×#67—68no—
288C2×#67C22×D318yes—
289C22×Dic3—28no—
290C22×Dic3—31no—
291C22×Dic3—31no—
292C22×Dic3—31no—
293C22×Dic3—31no—
294C22×Dic3—31no—
295C22×Dic3—31no—
296C22×Dic3—38no—
297C22×Dic3—61no—
298C22×Dic3—61no—
299C22×Dic3—61no—
300C22×Dic3—68no—
301C22×Dic3C22×D312yes—
302C22×Dic3C22×D312yes—
303C22×Dic3C22×D312yes—
304C22×Dic3C22×D318yes—
305#237—664no—
306#235—664no—
307C2×D12—24no—
308C2×D12—38no—
309C2×D12—68no—
310C2×D12C22×D314yes—
311C2×C4×D3—38no—
312C2×C4×D3—34no—
313C2×C4×D3—34no—
314C2×C4×D3—38no—
315C2×C4×D3—38no—
316C2×C4×D3—64no—
317C2×C4×D3—68no—
318C2×C4×D3—68no—
319C2×C4×D3—68no—
320C2×C4×D3—64no—
321C2×C4×D3—64no—
322C2×C4×D3—124no—
323C2×Dic6—38no—
324C2×Dic6—38no—
325C2×Dic6—68no—
326C2×Dic6—68no—
327C3×C4⋊C4—34no—
328C3×C4⋊C4—34no—
329C3×C4⋊C4—34no—
330C3×C4⋊C4—38no—
331C3×C22⋊C4—38no—
332#217—34no—
333#217—34no—
334#217—38no—
335#217—38no—
336#217—64no—
337(C2×D3)⋊C4—38no—
338(C2×D3)⋊C4—38no—
339(C2×D3)⋊C4—34no—
340(C2×D3)⋊C4—34no—
341(C2×D3)⋊C4—64no—
342(C2×D3)⋊C4C22×D318yes—
343C4⋊Dic3C22×D318yes—
344C4⋊Dic3C22×D314yes—
345C4⋊Dic3C22×D314yes—
346C4⋊Dic3C22×D314yes—
347Dic3⋊C4—34no—
348Dic3⋊C4—34no—
349Dic3⋊C4—38no—
350Dic3⋊C4—38no—
351Dic3⋊C4—38no—
352Dic3⋊C4—38no—
353Dic3⋊C4—64no—
354C4×Dic3—34no—
355C4×Dic3—34no—
356C4×Dic3—64no—
357C22×C32—28no—
358C22×C32—22no—
359C22×C32—22no—
360C22×C32C22×D414yes—
361C22×C32C22×D412yes—
362C22×C32C2×#4112yes—
363C22×C322−1+412yes—
364C22×C32C2511yescharacteristic
365C2×C3⋊D3—28no—
366C2×C3⋊D3—22no—
367C2×C3⋊D3—22no—
368C2×C3⋊D3C22×D414yes—
369C2×C3×D3—24no—
370C2×C3×D3—24no—
371C2×C3×D3—24no—
372C2×C3×D3—48no—
373C32×C4—22no—
374C32×C4C2×#4114yescomplemented
375C3⋊Dic3—22no—
376C3⋊Dic3—22no—
377C3⋊Dic3C22×D414yes—
378C3×Dic3—24no—
379C3×Dic3—24no—
380C3×Dic3—24no—
381C2×#41—916no—
382C2×#41—1816no—
383C22×Q8—92no—
384C22×D4—32no—
385C22×D4—31no—
386C22×D4—92no—
387C22×D4—91no—
388C23×C4—32no—
389C23×C4—92no—
390C23×C4—92no—
391C23×C4—91no—
392C23×C4D3211yescharacteristic
393C4⋊Q8—98no—
394#123—916no—
395#123—916no—
396C22⋊Q8—916no—
397#121—38no—
398#121—98no—
399C4×D4—98no—
400C4×D4—98no—
401C2×C4⋊C4—31no—
402C2×C4⋊C4—31no—
403C2×C4⋊C4—32no—
404C2×C4⋊C4—38no—
405C2×C4⋊C4—31no—
406C2×C4⋊C4—98no—
407C2×C4⋊C4—92no—
408C2×C4⋊C4—92no—
409C2×C4⋊C4—91no—
410C2×C22⋊C4—32no—
411C2×C22⋊C4—92no—
412C2×C22⋊C4—92no—
413C2×C22⋊C4—91no—
414C2×C22⋊C4—91no—
415C2×C42—91no—
416C23×C3—22no—
417C23×C3—22no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—21no—
422C23×C3—24no—
423C23×C3—34no—
424C23×C3—42no—
425C23×C3—42no—
426C23×C3—64no—
427C23×C3—64no—
428C23×C3—64no—
429C23×C3D3×D414yes—
430C23×C3D3×D414yes—
431C23×C3C23×D312yes—
432C23×C3C23×D312yes—
433C23×C3C23×D311yescharacteristic
434C23×C3C23×D311yescharacteristic
435C22×D3—24no—
436C22×D3—24no—
437C22×D3—24no—
438C22×D3—34no—
439C22×D3—34no—
440C22×D3—32no—
441C22×D3—32no—
442C22×D3—64no—
443C22×D3—62no—
444C22×D3—62no—
445C22×D3—62no—
446C22×D3—62no—
447C22×D3—62no—
448C22×D3—122no—
449C22×D3—122no—
450C22×D3C23×D314yes—
451C3×D4—616no—
452C3×D4—68no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—28no—
456C2×C3×C4—28no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—24no—
460C2×C3×C4—34no—
461C2×C3×C4—34no—
462C2×C3×C4—34no—
463C2×C3×C4—48no—
464C2×C3×C4—42no—
465C2×C3×C4—64no—
466C2×C3×C4—64no—
467C2×C3×C4—64no—
468C2×C3×C4—616no—
469C2×C3×C4#23514yescomplemented
470C2×C3×C4#23714yescomplemented
471C2×C3×C4C23×D312yes—
472C2×C3×C4C23×D312yes—
473C2×C3×C4C23×D312yes—
474C2×C3×C4C23×D312yes—
475#67—216no—
476#67—316no—
477#67—316no—
478#67—616no—
479#67—616no—
480C2×Dic3—24no—
481C2×Dic3—24no—
482C2×Dic3—24no—
483C2×Dic3—216no—
484C2×Dic3—34no—
485C2×Dic3—34no—
486C2×Dic3—32no—
487C2×Dic3—32no—
488C2×Dic3—32no—
489C2×Dic3—32no—
490C2×Dic3—32no—
491C2×Dic3—32no—
492C2×Dic3—64no—
493C2×Dic3—62no—
494C2×Dic3—62no—
495C2×Dic3—62no—
496C2×Dic3—616no—
497C2×Dic3—62no—
498C2×Dic3—62no—
499C2×Dic3—62no—
500C2×Dic3—62no—
501C2×Dic3—122no—
502C2×Dic3—122no—
503C2×Dic3C23×D314yes—
504C2×Dic3C23×D314yes—
505C2×Dic3C23×D314yes—
506D12—28no—
507D12—616no—
508C4×D3—616no—
509C4×D3—616no—
510C4×D3—616no—
511C4×D3—68no—
512C4×D3—68no—
513C4×D3—128no—
514Dic6—616no—
515Dic6—616no—
516C2×C32—24no—
517C2×C32#54714yescomplemented
518C2×C32C23×D411yescharacteristic
519C2×C32C22×#4111yescharacteristic
520C2×C32C2×2−1+411yescharacteristic
521C3⋊D3—24no—
522C3×D3—44no—
523C24—32no—
524C24—91no—
525C24C2×D3211yescharacteristic
526#41—1864no—
527C2×Q8—98no—
528C2×Q8—188no—
529C2×D4—38no—
530C2×D4—34no—
531C2×D4—68no—
532C2×D4—64no—
533C2×D4—98no—
534C2×D4—94no—
535C2×D4—98no—
536C2×D4—188no—
537C22×C4—24no—
538C22×C4—38no—
539C22×C4—32no—
540C22×C4—32no—
541C22×C4—32no—
542C22×C4—68no—
543C22×C4—98no—
544C22×C4—98no—
545C22×C4—91no—
546C22×C4—91no—
547C22×C4—91no—
548C22×C4—94no—
549C22×C4—188no—
550C22×C4—188no—
551C22×C4—184no—
552C22×C4C2×D3214yes—
553C22×C4C2×D3211yescharacteristic
554C22×C4C2×D3211yescharacteristic
555C4⋊C4—34no—
556C4⋊C4—34no—
557C4⋊C4—38no—
558C4⋊C4—34no—
559C4⋊C4—98no—
560C4⋊C4—98no—
561C4⋊C4—94no—
562C22⋊C4—38no—
563C22⋊C4—98no—
564C22⋊C4—98no—
565C22⋊C4—94no—
566C22⋊C4—94no—
567C42—94no—
568C22×C3—22no—
569C22×C3—22no—
570C22×C3—22no—
571C22×C3—22no—
572C22×C3—28no—
573C22×C3—28no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—24no—
577C22×C3—22no—
578C22×C3—21no—
579C22×C3—42no—
580C22×C3—42no—
581C22×C3—48no—
582C22×C3—64no—
583C22×C3—64no—
584C22×C3—64no—
585C22×C3—128no—
586C22×C3C2×#23512yes—
587C22×C3C2×D3×D414yes—
588C22×C3C2×D3×D414yes—
589C22×C3C2×D3×D412yes—
590C22×C3C2×D3×D412yes—
591C22×C3C2×#23712yes—
592C22×C3#100712yes—
593C22×C3#101012yes—
594C22×C3C24×D311yescharacteristic
595C22×C3C24×D311yescharacteristic
596C2×D3—24no—
597C2×D3—24no—
598C2×D3—24no—
599C2×D3—34no—
600C2×D3—34no—
601C2×D3—48no—
602C2×D3—64no—
603C2×D3—62no—
604C2×D3—62no—
605C2×D3—62no—
606C2×D3—62no—
607C2×D3—68no—
608C2×D3—68no—
609C2×D3—122no—
610C2×D3—122no—
611C2×D3—128no—
612C3×C4—22no—
613C3×C4—22no—
614C3×C4—24no—
615C3×C4—42no—
616C3×C4—64no—
617C3×C4—64no—
618C3×C4—64no—
619C3×C4C2×#23514yescomplemented
620C3×C4C2×#23714yescomplemented
621Dic3—24no—
622Dic3—24no—
623Dic3—24no—
624Dic3—34no—
625Dic3—34no—
626Dic3—64no—
627Dic3—62no—
628Dic3—62no—
629Dic3—62no—
630Dic3—62no—
631Dic3—122no—
632Dic3—122no—
633C32C2×#54711yescharacteristic, complemented, Sylow
634C23—22no—
635C23—22no—
636C23—34no—
637C23—64no—
638C23—64no—
639C23—64no—
640C23—94no—
641C23—92no—
642C23—182no—
643C23—182no—
644C23#380214yes—
645C23C22×D3212yes—
646C23C22×D3211yescharacteristic
647Q8—1816no—
648D4—616no—
649D4—68no—
650D4—916no—
651D4—1816no—
652C2×C4—22no—
653C2×C4—28no—
654C2×C4—34no—
655C2×C4—34no—
656C2×C4—34no—
657C2×C4—64no—
658C2×C4—64no—
659C2×C4—616no—
660C2×C4—64no—
661C2×C4—94no—
662C2×C4—92no—
663C2×C4—92no—
664C2×C4—92no—
665C2×C4—1816no—
666C2×C4—1816no—
667C2×C4—182no—
668C2×C4—182no—
669C2×C4—188no—
670C2×C4#380414yescomplemented
671C2×C4C22×D3212yes—
672C2×C4C22×D3212yes—
673C2×C3—24no—
674C2×C3—24no—
675C2×C3—21no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—24no—
679C2×C3—44no—
680C2×C3—124no—
681C2×C3#550714yescomplemented
682C2×C3#561114yescomplemented
683C2×C3C22×#23511yescharacteristic
684C2×C3C22×D3×D411yescharacteristic
685C2×C3C22×D3×D411yescharacteristic
686C2×C3C22×#23711yescharacteristic
687C2×C3C2×#100711yescharacteristic
688C2×C3C2×#101011yescharacteristic
689D3—44no—
690D3—64no—
691D3—64no—
692D3—124no—
693C22—22no—
694C22—22no—
695C22—28no—
696C22—64no—
697C22—64no—
698C22—64no—
699C22—94no—
700C22—128no—
701C22—182no—
702C22—182no—
703C22—188no—
704C22#6429712yes—
705C22C2×#380214yes—
706C22C2×#380212yes—
707C22C2×#380412yes—
708C22C23×D3211yescharacteristic
709C4—22no—
710C4—64no—
711C4—64no—
712C4—64no—
713C4—94no—
714C4—182no—
715C4—182no—
716C4C2×#380414yescomplemented
717C3—21no—
718C3C2×#550711yescharacteristic, complemented
719C3C2×#561111yescharacteristic, complemented
720C2—24no—
721C2—124no—
722C2—184no—
723C2#1059492814yesdirect product factor
724C2C2×#6429711yescharacteristic
725C2C22×#380211yescharacteristic
726C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#547
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3804C2semidirect
2. C2×C4×#638C2semidirect
3. C2×C3×#930C2semidirect
4. C22×C3×C4⋊Dic3C2semidirect
5. C2×#63961C2semidirect
6. C2×#63919C2semidirect
7. C2×#63916C2semidirect
8. C2×#63900C2semidirect
9. #10594928C2direct (N × H)
10. C2×#63899C2semidirect
11. C2×#63898C2semidirect
12. C2×#63854C2semidirect
25. C2×#3804C22semidirect
28. C4×#638C22semidirect
32. C3×#930C22semidirect
38. C2×C3×C4⋊Dic3C22semidirect
41. #63961C22semidirect
44. #63919C22semidirect
45. #63916C22semidirect
46. #63900C22semidirect
47. #63899C22semidirect
48. #63898C22semidirect
49. #63854C22semidirect
57. C2×#930D3semidirect
62. C22×C4⋊Dic3D3semidirect
82. C2×#638D4semidirect
163. #930C2×D3semidirect
178. C2×C4⋊Dic3C2×D3semidirect
214. C2×C32×C4#41semidirect
217. #638C2×D4semidirect
374. C32×C4C2×#41semidirect
469. C2×C3×C4#235semidirect
470. C2×C3×C4#237semidirect
517. C2×C32#547semidirect
619. C3×C4C2×#235semidirect
620. C3×C4C2×#237semidirect
633. C32C2×#547semidirect
670. C2×C4#3804semidirect
681. C2×C3#5507semidirect
682. C2×C3#5611semidirect
716. C4C2×#3804semidirect
718. C3C2×#5507semidirect
719. C3C2×#5611semidirect
723. C2#10594928direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38042
C2×C4×#6382
C2×C3×#9302
C22×C3×C4⋊Dic32
C2×#639612
C2×#639192
C2×#639162
C2×#639002
#105949282
C2×#638992
C2×#638982
C2×#638542
C2×#56113
C2×#55073