Finite Group Databasebeta

← C2×#10594626 #11900466

Subgroups — C2×#10594626 #11900466

Order 1152.

3921 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D32C211yesmaximal, characteristic, complemented
2C22×#3795C211yesmaximal, characteristic, complemented
3C2×#64106C211yesmaximal, characteristic, complemented
4C2×C3×#895C211yesmaximal, characteristic, complemented
5C2×C3×#892C211yesmaximal, characteristic, complemented
6C2×#63922C212yesmaximal, complemented
7C2×#63916C211yesmaximal, characteristic, complemented
8C2×Dic3×D12C212yesmaximal, complemented
9C2×#63891C212yesmaximal, complemented
10C2×#63880C212yesmaximal, complemented
11C2×#63857C211yesmaximal, characteristic, complemented
12#10594626C2116yesmaximal, direct product factor
13C2×#5606—31nomaximal
14C2×#5524—31nomaximal
15C23×D32C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×#634C2211yescharacteristic, complemented
18C22×C3×D12C2212yes—
19C22×C3×D12C2211yescharacteristic, complemented
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×#626C2212yes—
23C22×#625C2212yes—
24C22×#624C2211yescharacteristic
25C22×D3×Dic3C2211yescharacteristic
26C22×D3×Dic3C2211yescharacteristic
27C22×D3×Dic3C2212yescomplemented
28C2×C4×D32—28no—
29C2×C4×D32C2218yescomplemented
30C2×#3795—28no—
31C2×#3795C2218yescomplemented
32C2×C32×C4⋊C4C2211yescharacteristic, complemented
33C2×#3752C2212yes—
34C2×C4⋊(C3⋊Dic3)C2212yescomplemented
35#64106C2218yescomplemented
36C2×C3×(C2×D3)⋊C4C2212yes—
37C2×C3×(C2×D3)⋊C4C2212yescomplemented
38C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
39C2×C3×C4×Dic3C2212yescomplemented
40C3×#895C2218yescomplemented
41C3×#892C2218yescomplemented
42C2×Dic3⋊Dic3C2212yescomplemented
43C2×(C2×D3)⋊Dic3C2212yes—
44C2×(C2×D3)⋊Dic3C2212yescomplemented
45#63922C22116yescomplemented
46#63916C2218yescomplemented
47Dic3×D12C22116yescomplemented
48#63891C22116yescomplemented
49#63880C22116yescomplemented
50#63857C2218yescomplemented
51C22×#237—31no—
52C22×#235—31no—
53C23×C4×D3—31no—
54C23×C4×D3—31no—
55C2×C3×#121—31no—
56C2×C3×#117—31no—
57C2×#938—31no—
58C2×#937—32no—
59C2×D4×Dic3—32no—
60C2×#924—31no—
61#5606—316no—
62#5524—316no—
63C2×#897—31no—
64C2×#897—31no—
65C2×#897—31no—
66C2×#897—61no—
67C2×#895—31no—
68C2×#895D311yescharacteristic, complemented
69C2×#892D311yescharacteristic, complemented
70C2×#886—32no—
71C2×#883—32no—
72C2×#882—32no—
73C2×#67⋊C4—32no—
74C2×C4×D12—32no—
75C2×C4×D12—32no—
76C23×C3⋊D3C2311yescharacteristic
77C23×C3×D3C2312yes—
78C23×C3×D3C2311yescharacteristic
79C23×C3×D3C2311yescharacteristic
80C22×D32—24no—
81C22×D32—24no—
82C22×D32—24no—
83C22×D32C2314yes—
84C22×C32×C4C2312yes—
85C22×C32×C4C2311yescharacteristic
86C22×C3⋊Dic3C2311yescharacteristic
87C22×C3⋊Dic3C2312yes—
88C2×C4×C3⋊D3—24no—
89C2×C4×C3⋊D3C2314yes—
90C2×#634—24no—
91C2×#634C2314yescomplemented
92C22×C3×Dic3C2312yes—
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C2×C3×D12—28no—
96C2×C3×D12—24no—
97C2×C3×D12C2318yes—
98C2×C3×D12C2314yescomplemented
99C2×C3×C4×D3—24no—
100C2×C3×C4×D3D418yescomplemented
101C2×C3×C4×D3C2314yes—
102C2×C3×C4×D3C2314yes—
103C2×#626—28no—
104C2×#626C2318yes—
105C2×#625—28no—
106C2×#625C2318yes—
107C2×#624—24no—
108C2×#624C2314yes—
109C2×D3×Dic3—24no—
110C2×D3×Dic3—28no—
111C2×D3×Dic3—24no—
112C2×D3×Dic3C2314yes—
113C2×D3×Dic3C2314yes—
114C2×D3×Dic3C2318yescomplemented
115C4×D32—232no—
116#3795—232no—
117C32×C4⋊C4C2314yescomplemented
118#3752C2318yes—
119C4⋊(C3⋊Dic3)C2318yescomplemented
120C3×(C2×D3)⋊C4C2318yes—
121C3×(C2×D3)⋊C4C2318yescomplemented
122C3×C4⋊Dic3C2314yescomplemented
123C3×C4×Dic3C2318yescomplemented
124Dic3⋊Dic3C2318yescomplemented
125(C2×D3)⋊Dic3C2318yes—
126(C2×D3)⋊Dic3C2318yescomplemented
127C2×#525—91noSylow
128C24×D3—31no—
129C24×D3—31no—
130C22×C3×D4—31no—
131C22×C3×D4—32no—
132C23×C3×C4—31no—
133C23×C3×C4—31no—
134C22×#67—32no—
135C22×#67—32no—
136C22×#67—32no—
137C23×Dic3—31no—
138C23×Dic3—31no—
139C23×Dic3—32no—
140C2×#237—38no—
141C2×#237—68no—
142C2×#235—38no—
143C2×#235—68no—
144C22×D12—32no—
145C22×D12C2×D312yes—
146C22×D12C2×D311yescharacteristic, complemented
147C22×C4×D3—31no—
148C22×C4×D3—31no—
149C22×C4×D3—32no—
150C22×C4×D3—31no—
151C22×C4×D3—31no—
152C22×C4×D3—31no—
153C22×C4×D3—31no—
154C22×C4×D3—38no—
155C22×C4×D3—38no—
156C22×C4×D3—61no—
157C22×C4×D3—68no—
158C22×C4×D3—68no—
159C22×C4×D3C2×D311yescharacteristic
160C22×C4×D3C2×D311yescharacteristic
161C22×Dic6—31no—
162C22×Dic6—31no—
163C22×Dic6—61no—
164C3×#121—38no—
165C3×#117—38no—
166C2×C3×C4⋊C4—21no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
169C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
170C2×C3×C22⋊C4—32no—
171C2×C3×C22⋊C4—32no—
172C2×C3×C42—32no—
173C2×#217—32no—
174C2×#217—32no—
175#938—38no—
176#937—316no—
177D4×Dic3—316no—
178C2×(C2×D3)⋊C4—32no—
179C2×(C2×D3)⋊C4—32no—
180C2×(C2×D3)⋊C4—32no—
181C2×(C2×D3)⋊C4—32no—
182C2×(C2×D3)⋊C4—62no—
183C2×(C2×D3)⋊C4C2×D312yes—
184C2×(C2×D3)⋊C4C2×D312yescomplemented
185C2×C4⋊Dic3—32no—
186C2×C4⋊Dic3—32no—
187C2×C4⋊Dic3—32no—
188C2×C4⋊Dic3—62no—
189C2×C4⋊Dic3C2×D311yescharacteristic, complemented
190#924—38no—
191C2×Dic3⋊C4—32no—
192C2×C4×Dic3C2×D312yescomplemented
193#897—38no—
194#897—38no—
195#897—38no—
196#897—68no—
197#895—38no—
198#895C2×D318yescomplemented
199#892C2×D318yescomplemented
200#886—316no—
201#883—316no—
202#882—316no—
203#67⋊C4—316no—
204C4×D12—316no—
205C4×D12—316no—
206C23×C32C2411yescharacteristic
207C22×C3⋊D3—22no—
208C22×C3⋊D3—22no—
209C22×C3⋊D3#4114yescomplemented
210C22×C3⋊D3C2412yes—
211C22×C3×D3—22no—
212C22×C3×D3—22no—
213C22×C3×D3—22no—
214C22×C3×D3—22no—
215C22×C3×D3—24no—
216C22×C3×D3—24no—
217C22×C3×D3—24no—
218C22×C3×D3C2×D414yes—
219C22×C3×D3#4114yescomplemented
220C22×C3×D3C2414yes—
221C22×C3×D3C2412yes—
222C22×C3×D3C2412yes—
223C2×D32—232no—
224C2×D32—28no—
225C2×D32—28no—
226C2×D32—28no—
227C2×C32×C4—24no—
228C2×C32×C4C2×D414yes—
229C2×C32×C4C2414yes—
230C2×C32×C4C2412yes—
231C2×C3⋊Dic3—22no—
232C2×C3⋊Dic3—24no—
233C2×C3⋊Dic3C2414yes—
234C2×C3⋊Dic3C2412yes—
235C4×C3⋊D3—28no—
236#634—28no—
237C2×C3×Dic3—22no—
238C2×C3×Dic3—24no—
239C2×C3×Dic3C2×D414yes—
240C2×C3×Dic3C2414yes—
241C2×C3×Dic3C2412yes—
242C2×C3×Dic3C2412yes—
243C3×D12—216no—
244C3×D12—28no—
245C3×C4×D3—28no—
246C3×C4×D3C2×D4116yescomplemented
247#626—216no—
248#625—216no—
249#624—28no—
250D3×Dic3—28no—
251D3×Dic3—216no—
252D3×Dic3—28no—
253C22×#41—91no—
254C24×C4—91no—
255#525—916no—
256C2×#123—92no—
257C2×C22⋊Q8—91no—
258C2×C22⋊Q8—91no—
259C2×#121—31no—
260C2×#121—91no—
261C2×#120—92no—
262C2×C4×D4—92no—
263C2×C4×D4—92no—
264C2×#117—31no—
265C24×C3—31no—
266C24×C3—31no—
267C24×C3—32no—
268C23×D3—31no—
269C23×D3—31no—
270C23×D3—34no—
271C23×D3—34no—
272C23×D3—61no—
273C23×D3—64no—
274C23×D3—64no—
275C23×D3—64no—
276C23×D3—64no—
277C23×D3—64no—
278C23×D3—64no—
279C23×D3C22×D312yes—
280C23×D3C22×D311yescharacteristic
281C23×D3C22×D311yescharacteristic
282C2×C3×D4—38no—
283C2×C3×D4—34no—
284C2×C3×D4—68no—
285C2×C3×D4—64no—
286C22×C3×C4—21no—
287C22×C3×C4—22no—
288C22×C3×C4—31no—
289C22×C3×C4—38no—
290C22×C3×C4—34no—
291C22×C3×C4—31no—
292C22×C3×C4—32no—
293C22×C3×C4—34no—
294C22×C3×C4—64no—
295C22×C3×C4C22×D312yes—
296C22×C3×C4C22×D312yes—
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D311yescharacteristic
299C2×#67—38no—
300C2×#67—38no—
301C2×#67—38no—
302C2×#67—68no—
303C2×#67—68no—
304C2×#67—68no—
305C22×Dic3—32no—
306C22×Dic3—32no—
307C22×Dic3—31no—
308C22×Dic3—31no—
309C22×Dic3—38no—
310C22×Dic3—34no—
311C22×Dic3—34no—
312C22×Dic3—61no—
313C22×Dic3—62no—
314C22×Dic3—64no—
315C22×Dic3—64no—
316C22×Dic3—68no—
317C22×Dic3C22×D312yes—
318C22×Dic3C22×D311yescharacteristic
319C22×Dic3C22×D311yescharacteristic
320#237—632no—
321#235—632no—
322C2×D12—28no—
323C2×D12—24no—
324C2×D12—38no—
325C2×D12—68no—
326C2×D12C22×D318yes—
327C2×D12C22×D314yescomplemented
328C2×C4×D3—24no—
329C2×C4×D3—34no—
330C2×C4×D3—38no—
331C2×C4×D3—34no—
332C2×C4×D3—34no—
333C2×C4×D3—34no—
334C2×C4×D3—34no—
335C2×C4×D3—34no—
336C2×C4×D3—64no—
337C2×C4×D3—632no—
338C2×C4×D3—64no—
339C2×C4×D3—64no—
340C2×C4×D3—68no—
341C2×C4×D3—64no—
342C2×C4×D3—64no—
343C2×C4×D3—64no—
344C2×C4×D3—64no—
345C2×C4×D3—632no—
346C2×C4×D3—124no—
347C2×C4×D3D1218yescomplemented
348C2×C4×D3C22×D314yes—
349C2×C4×D3C22×D314yes—
350C2×Dic6—34no—
351C2×Dic6—34no—
352C2×Dic6—64no—
353C2×Dic6—64no—
354C2×Dic6—64no—
355C2×Dic6—124no—
356C3×C4⋊C4—24no—
357C3×C4⋊C4—34no—
358C3×C4⋊C4C22×D314yescomplemented
359C3×C4⋊C4C22×D314yescomplemented
360C3×C22⋊C4—38no—
361C3×C22⋊C4—38no—
362C3×C42—38no—
363#217—38no—
364#217—38no—
365(C2×D3)⋊C4—38no—
366(C2×D3)⋊C4—38no—
367(C2×D3)⋊C4—38no—
368(C2×D3)⋊C4—38no—
369(C2×D3)⋊C4—68no—
370(C2×D3)⋊C4C22×D318yes—
371(C2×D3)⋊C4C22×D318yescomplemented
372C4⋊Dic3—38no—
373C4⋊Dic3—38no—
374C4⋊Dic3—38no—
375C4⋊Dic3—68no—
376C4⋊Dic3C22×D314yescomplemented
377Dic3⋊C4—38no—
378C4×Dic3C22×D318yescomplemented
379C22×C32C22×D412yes—
380C22×C32C2×#4112yes—
381C22×C32C2×#4112yes—
382C22×C32C2511yescharacteristic
383C2×C3⋊D3—28no—
384C2×C3⋊D3—22no—
385C2×C3⋊D3—22no—
386C2×C3⋊D3C2×#4114yescomplemented
387C2×C3×D3—28no—
388C2×C3×D3—28no—
389C2×C3×D3—22no—
390C2×C3×D3—22no—
391C2×C3×D3—22no—
392C2×C3×D3—22no—
393C2×C3×D3—24no—
394C2×C3×D3—24no—
395C2×C3×D3—24no—
396C2×C3×D3—48no—
397C2×C3×D3C22×D414yes—
398C2×C3×D3C2×#4114yescomplemented
399D32—232no—
400C32×C4—24no—
401C32×C4C22×D414yes—
402C3⋊Dic3—22no—
403C3⋊Dic3—24no—
404C3×Dic3—22no—
405C3×Dic3—24no—
406C3×Dic3C22×D414yes—
407C25—91no—
408C2×#41—98no—
409C2×#41—188no—
410C22×Q8—91no—
411C22×D4—32no—
412C22×D4—31no—
413C22×D4—92no—
414C22×D4—92no—
415C23×C4—31no—
416C23×C4—31no—
417C23×C4—91no—
418C23×C4—98no—
419C23×C4—91no—
420C23×C4—92no—
421C23×C4—91no—
422C23×C4—91no—
423C23×C4—188no—
424#123—916no—
425C22⋊Q8—98no—
426C22⋊Q8—98no—
427#121—38no—
428#121—98no—
429#120—916no—
430C4×D4—916no—
431C4×D4—916no—
432#117—38no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—92no—
435C2×C4⋊C4—92no—
436C2×C4⋊C4D3211yescharacteristic, complemented
437C2×C22⋊C4—32no—
438C2×C22⋊C4—32no—
439C2×C22⋊C4—92no—
440C2×C22⋊C4—92no—
441C2×C22⋊C4—92no—
442C2×C42—32no—
443C23×C3—21no—
444C23×C3—34no—
445C23×C3—34no—
446C23×C3—32no—
447C23×C3—32no—
448C23×C3—34no—
449C23×C3—62no—
450C23×C3—62no—
451C23×C3—62no—
452C23×C3—62no—
453C23×C3—64no—
454C23×C3—64no—
455C23×C3—64no—
456C23×C3C23×D311yescharacteristic
457C23×C3C23×D311yescharacteristic
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—24no—
463C22×D3—24no—
464C22×D3—24no—
465C22×D3—34no—
466C22×D3—34no—
467C22×D3—32no—
468C22×D3—32no—
469C22×D3—64no—
470C22×D3—62no—
471C22×D3—68no—
472C22×D3—68no—
473C22×D3—68no—
474C22×D3—68no—
475C22×D3—632no—
476C22×D3—632no—
477C22×D3—62no—
478C22×D3—62no—
479C22×D3—62no—
480C22×D3—62no—
481C22×D3—68no—
482C22×D3—68no—
483C22×D3—122no—
484C22×D3—122no—
485C22×D3C2×D1214yes—
486C22×D3#23714yescomplemented
487C22×D3C23×D314yes—
488C22×D3C23×D312yes—
489C22×D3C23×D312yes—
490C3×D4—616no—
491C3×D4—68no—
492C2×C3×C4—24no—
493C2×C3×C4—24no—
494C2×C3×C4—22no—
495C2×C3×C4—24no—
496C2×C3×C4—24no—
497C2×C3×C4—34no—
498C2×C3×C4—32no—
499C2×C3×C4—316no—
500C2×C3×C4—32no—
501C2×C3×C4—34no—
502C2×C3×C4—44no—
503C2×C3×C4—62no—
504C2×C3×C4—64no—
505C2×C3×C4—68no—
506C2×C3×C4C2×D1214yes—
507C2×C3×C4D3×D414yes—
508C2×C3×C4C23×D314yes—
509C2×C3×C4C23×D314yes—
510C2×C3×C4C23×D312yes—
511C2×C3×C4C23×D312yes—
512#67—616no—
513#67—616no—
514#67—616no—
515C2×Dic3—22no—
516C2×Dic3—24no—
517C2×Dic3—34no—
518C2×Dic3—34no—
519C2×Dic3—32no—
520C2×Dic3—32no—
521C2×Dic3—62no—
522C2×Dic3—64no—
523C2×Dic3—68no—
524C2×Dic3—64no—
525C2×Dic3—62no—
526C2×Dic3—64no—
527C2×Dic3—62no—
528C2×Dic3—68no—
529C2×Dic3—616no—
530C2×Dic3—124no—
531C2×Dic3—122no—
532C2×Dic3C2×D1214yes—
533C2×Dic3C23×D314yes—
534C2×Dic3C23×D312yes—
535C2×Dic3C23×D312yes—
536D12—216no—
537D12—28no—
538D12—616no—
539C4×D3—28no—
540C4×D3—68no—
541C4×D3—68no—
542C4×D3—616no—
543C4×D3—68no—
544C4×D3—68no—
545C4×D3—68no—
546C4×D3—68no—
547C4×D3—128no—
548C4×D3C2×D12116yescomplemented
549Dic6—68no—
550Dic6—68no—
551Dic6—128no—
552C2×C32#52514yescomplemented
553C2×C32C23×D411yescharacteristic
554C2×C32C22×#4111yescharacteristic
555C2×C32C22×#4111yescharacteristic
556C3⋊D3—24no—
557C3×D3—24no—
558C3×D3—24no—
559C3×D3—44no—
560C24—31no—
561C24—31no—
562C24—32no—
563C24—94no—
564C24—91no—
565C24—184no—
566C24—184no—
567C24—184no—
568#41—1832no—
569C2×Q8—94no—
570C2×Q8—184no—
571C2×D4—38no—
572C2×D4—34no—
573C2×D4—68no—
574C2×D4—64no—
575C2×D4—98no—
576C2×D4—98no—
577C2×D4—188no—
578C2×D4—188no—
579C22×C4—31no—
580C22×C4—34no—
581C22×C4—38no—
582C22×C4—32no—
583C22×C4—31no—
584C22×C4—34no—
585C22×C4—64no—
586C22×C4—94no—
587C22×C4—94no—
588C22×C4—98no—
589C22×C4—94no—
590C22×C4—91no—
591C22×C4—92no—
592C22×C4—94no—
593C22×C4—184no—
594C22×C4—1832no—
595C22×C4—184no—
596C22×C4—188no—
597C22×C4—184no—
598C22×C4—184no—
599C22×C4C2×D3212yes—
600C22×C4C2×D3211yescharacteristic
601C4⋊C4—34no—
602C4⋊C4—98no—
603C4⋊C4—98no—
604C4⋊C4C2×D3214yescomplemented
605C22⋊C4—38no—
606C22⋊C4—38no—
607C22⋊C4—98no—
608C22⋊C4—98no—
609C22⋊C4—98no—
610C42—38no—
611C22×C3—22no—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—21no—
615C22×C3—34no—
616C22×C3—34no—
617C22×C3—62no—
618C22×C3—62no—
619C22×C3—62no—
620C22×C3—62no—
621C22×C3—68no—
622C22×C3—68no—
623C22×C3—64no—
624C22×C3—64no—
625C22×C3—64no—
626C22×C3—128no—
627C22×C3C22×D1212yes—
628C22×C3C2×D3×D412yes—
629C22×C3C2×#23712yes—
630C22×C3D3×#4112yes—
631C22×C3D3×#4112yes—
632C22×C3D3×#4112yes—
633C22×C3C24×D311yescharacteristic
634C22×C3C24×D311yescharacteristic
635C2×D3—22no—
636C2×D3—22no—
637C2×D3—22no—
638C2×D3—22no—
639C2×D3—28no—
640C2×D3—28no—
641C2×D3—24no—
642C2×D3—24no—
643C2×D3—24no—
644C2×D3—34no—
645C2×D3—34no—
646C2×D3—48no—
647C2×D3—64no—
648C2×D3—632no—
649C2×D3—632no—
650C2×D3—62no—
651C2×D3—62no—
652C2×D3—62no—
653C2×D3—62no—
654C2×D3—68no—
655C2×D3—68no—
656C2×D3—122no—
657C2×D3—122no—
658C2×D3—128no—
659C2×D3C22×D1214yes—
660C2×D3C2×#23714yescomplemented
661C3×C4—24no—
662C3×C4—24no—
663C3×C4—24no—
664C3×C4—34no—
665C3×C4—44no—
666C3×C4—62no—
667C3×C4—64no—
668C3×C4C22×D1214yes—
669C3×C4C2×D3×D414yes—
670Dic3—22no—
671Dic3—24no—
672Dic3—64no—
673Dic3—62no—
674Dic3—64no—
675Dic3—62no—
676Dic3—124no—
677Dic3—122no—
678Dic3C22×D1214yes—
679C32C2×#52511yescharacteristic, complemented, Sylow
680C23—34no—
681C23—34no—
682C23—32no—
683C23—32no—
684C23—34no—
685C23—62no—
686C23—62no—
687C23—62no—
688C23—62no—
689C23—64no—
690C23—64no—
691C23—64no—
692C23—94no—
693C23—92no—
694C23—188no—
695C23—188no—
696C23—188no—
697C23—1832no—
698C23—182no—
699C23—182no—
700C23C22×D3211yescharacteristic
701Q8—188no—
702D4—616no—
703D4—68no—
704D4—1816no—
705D4—1816no—
706C2×C4—24no—
707C2×C4—34no—
708C2×C4—32no—
709C2×C4—316no—
710C2×C4—34no—
711C2×C4—32no—
712C2×C4—62no—
713C2×C4—64no—
714C2×C4—68no—
715C2×C4—92no—
716C2×C4—94no—
717C2×C4—188no—
718C2×C4—188no—
719C2×C4—1816no—
720C2×C4—188no—
721C2×C4—182no—
722C2×C4—184no—
723C2×C4—188no—
724C2×C4D3×D1214yes—
725C2×C4C22×D3214yes—
726C2×C4C22×D3212yes—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—24no—
730C2×C3—21no—
731C2×C3—64no—
732C2×C3—64no—
733C2×C3—124no—
734C2×C3#552414yescomplemented
735C2×C3#560614yescomplemented
736C2×C3C23×D1211yescharacteristic
737C2×C3C22×D3×D411yescharacteristic
738C2×C3C22×#23711yescharacteristic
739C2×C3C2×D3×#4111yescharacteristic
740C2×C3C2×D3×#4111yescharacteristic
741C2×C3C2×D3×#4111yescharacteristic
742D3—24no—
743D3—24no—
744D3—44no—
745D3—64no—
746D3—64no—
747D3—124no—
748C22—34no—
749C22—34no—
750C22—62no—
751C22—62no—
752C22—68no—
753C22—68no—
754C22—62no—
755C22—62no—
756C22—64no—
757C22—64no—
758C22—64no—
759C22—94no—
760C22—128no—
761C22—1832no—
762C22—182no—
763C22—182no—
764C22—188no—
765C22C2×D3×D1212yes—
766C22D3×#23712yes—
767C22#6431912yes—
768C22C23×D3211yescharacteristic
769C4—24no—
770C4—34no—
771C4—62no—
772C4—64no—
773C4—182no—
774C4—184no—
775C4C2×D3×D1214yes—
776C3—21no—
777C3C2×#552411yescharacteristic, complemented
778C3C2×#560611yescharacteristic, complemented
779C2—64no—
780C2—64no—
781C2—124no—
782C2—184no—
783C2#1059462614yesdirect product factor
784C2C22×D3×D1211yescharacteristic
785C2C2×D3×#23711yescharacteristic
786C2C2×#6431911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#525
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×C4×D32C2semidirect
2. C22×#3795C2semidirect
3. C2×#64106C2semidirect
4. C2×C3×#895C2semidirect
5. C2×C3×#892C2semidirect
6. C2×#63922C2semidirect
7. C2×#63916C2semidirect
8. C2×Dic3×D12C2semidirect
9. C2×#63891C2semidirect
10. C2×#63880C2semidirect
11. C2×#63857C2semidirect
12. #10594626C2direct (N × H)
17. C22×#634C22semidirect
19. C22×C3×D12C22semidirect
27. C22×D3×Dic3C22semidirect
29. C2×C4×D32C22semidirect
31. C2×#3795C22semidirect
32. C2×C32×C4⋊C4C22semidirect
34. C2×C4⋊(C3⋊Dic3)C22semidirect
35. #64106C22semidirect
37. C2×C3×(C2×D3)⋊C4C22semidirect
38. C2×C3×C4⋊Dic3C22semidirect
39. C2×C3×C4×Dic3C22semidirect
40. C3×#895C22semidirect
41. C3×#892C22semidirect
42. C2×Dic3⋊Dic3C22semidirect
44. C2×(C2×D3)⋊Dic3C22semidirect
45. #63922C22semidirect
46. #63916C22semidirect
47. Dic3×D12C22semidirect
48. #63891C22semidirect
49. #63880C22semidirect
50. #63857C22semidirect
68. C2×#895D3semidirect
69. C2×#892D3semidirect
91. C2×#634C23semidirect
98. C2×C3×D12C23semidirect
100. C2×C3×C4×D3D4semidirect
114. C2×D3×Dic3C23semidirect
117. C32×C4⋊C4C23semidirect
119. C4⋊(C3⋊Dic3)C23semidirect
121. C3×(C2×D3)⋊C4C23semidirect
122. C3×C4⋊Dic3C23semidirect
123. C3×C4×Dic3C23semidirect
124. Dic3⋊Dic3C23semidirect
126. (C2×D3)⋊Dic3C23semidirect
146. C22×D12C2×D3semidirect
168. C2×C3×C4⋊C4C2×D3semidirect
169. C2×C3×C4⋊C4C2×D3semidirect
184. C2×(C2×D3)⋊C4C2×D3semidirect
189. C2×C4⋊Dic3C2×D3semidirect
192. C2×C4×Dic3C2×D3semidirect
198. #895C2×D3semidirect
199. #892C2×D3semidirect
209. C22×C3⋊D3#41semidirect
219. C22×C3×D3#41semidirect
246. C3×C4×D3C2×D4semidirect
327. C2×D12C22×D3semidirect
347. C2×C4×D3D12semidirect
358. C3×C4⋊C4C22×D3semidirect
359. C3×C4⋊C4C22×D3semidirect
371. (C2×D3)⋊C4C22×D3semidirect
376. C4⋊Dic3C22×D3semidirect
378. C4×Dic3C22×D3semidirect
386. C2×C3⋊D3C2×#41semidirect
398. C2×C3×D3C2×#41semidirect
436. C2×C4⋊C4D32semidirect
486. C22×D3#237semidirect
548. C4×D3C2×D12semidirect
552. C2×C32#525semidirect
604. C4⋊C4C2×D32semidirect
660. C2×D3C2×#237semidirect
679. C32C2×#525semidirect
734. C2×C3#5524semidirect
735. C2×C3#5606semidirect
777. C3C2×#5524semidirect
778. C3C2×#5606semidirect
783. C2#10594626direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D322
C22×#37952
C2×#641062
C2×C3×#8952
C2×C3×#8922
C2×#639222
C2×#639162
C2×Dic3×D122
C2×#638912
C2×#638802
C2×#638572
#105946262
C2×#56063
C2×#55243