Finite Group Databasebeta

← C2×#10594632 #11900465

Subgroups — C2×#10594632 #11900465

Order 1152.

3925 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D32C211yesmaximal, characteristic, complemented
2C22×#3796C211yesmaximal, characteristic, complemented
3C2×#64101C211yesmaximal, characteristic, complemented
4C2×C3×#897C211yesmaximal, characteristic, complemented
5C2×C3×#895C211yesmaximal, characteristic, complemented
6C2×#63922C212yesmaximal, complemented
7C2×#63908C211yesmaximal, characteristic, complemented
8C2×#63902C212yesmaximal, complemented
9C2×#63898C212yesmaximal, complemented
10C2×#63856C211yesmaximal, characteristic, complemented
11C2×#63854C212yesmaximal, complemented
12#10594632C2116yesmaximal, direct product factor
13C2×#5627—31nomaximal
14C2×#5606—31nomaximal
15C23×D32C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C3×D12C2212yes—
18C22×C3×D12C2211yescharacteristic, complemented
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic, complemented
22C22×#626C2212yes—
23C22×#625C2212yes—
24C22×#624C2211yescharacteristic
25C22×D3×Dic3C2211yescharacteristic
26C22×D3×Dic3C2211yescharacteristic
27C22×D3×Dic3C2212yescomplemented
28C2×C4×D32—28no—
29C2×C4×D32C2218yescomplemented
30C2×#3796—28no—
31C2×#3796C2218yescomplemented
32C2×C32×C4⋊C4C2211yescharacteristic, complemented
33C2×#3752C2212yes—
34C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
35C2×C4×C3⋊Dic3C2212yescomplemented
36#64101C2218yescomplemented
37C2×C3×(C2×D3)⋊C4C2212yes—
38C2×C3×(C2×D3)⋊C4C2212yescomplemented
39C2×C3×C4⋊Dic3C2212yescomplemented
40C3×#897C2218yescomplemented
41C3×#895C2218yescomplemented
42C2×#3724C2212yescomplemented
43C2×(C2×D3)⋊Dic3C2212yes—
44C2×(C2×D3)⋊Dic3C2212yescomplemented
45#63922C22116yescomplemented
46#63908C2218yescomplemented
47#63902C22116yescomplemented
48#63898C22116yescomplemented
49#63856C2218yescomplemented
50#63854C22116yescomplemented
51C22×#239—31no—
52C22×#237—31no—
53C23×C4×D3—31no—
54C23×C4×D3—31no—
55C2×C3×C22⋊Q8—31no—
56C2×C3×#121—31no—
57C2×#946—31no—
58C2×#938—31no—
59C2×#937—32no—
60C2×D4×Dic3—32no—
61C2×#930—31no—
62C2×#924—31no—
63#5627—316no—
64#5606—316no—
65C2×#897D311yescharacteristic, complemented
66C2×#895D311yescharacteristic, complemented
67C2×#894—32no—
68C2×#893—32no—
69C2×#892—31no—
70C2×#892—31no—
71C2×#892—61no—
72C2×#883—32no—
73C2×#882—32no—
74C2×#67⋊C4—32no—
75C2×#67⋊C4—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⋊Dic3C2312yes—
87C22×C3⋊Dic3C2311yescharacteristic
88C2×C4×C3⋊D3D418yescomplemented
89C2×C4×C3⋊D3C2314yes—
90C22×C3×Dic3C2311yescharacteristic
91C22×C3×Dic3C2312yes—
92C22×C3×Dic3C2311yescharacteristic
93C2×C3×D12—28no—
94C2×C3×D12—24no—
95C2×C3×D12C2318yes—
96C2×C3×D12C2314yescomplemented
97C2×C3×C4×D3—24no—
98C2×C3×C4×D3—24no—
99C2×C3×C4×D3C2314yes—
100C2×C3×C4×D3C2314yes—
101C2×C3×Dic6—24no—
102C2×C3×Dic6C2314yescomplemented
103C2×#626—28no—
104C2×#626C2318yes—
105C2×#625—28no—
106C2×#625C2318yes—
107C2×#624—24no—
108C2×#624C2314yes—
109C2×D3×Dic3—28no—
110C2×D3×Dic3—24no—
111C2×D3×Dic3—24no—
112C2×D3×Dic3C2314yes—
113C2×D3×Dic3C2314yes—
114C2×D3×Dic3C2318yescomplemented
115C4×D32—232no—
116#3796—232no—
117C32×C4⋊C4C2314yescomplemented
118#3752C2318yes—
119C4⋊(C3⋊Dic3)C2314yescomplemented
120C4×C3⋊Dic3C2318yescomplemented
121C3×(C2×D3)⋊C4C2318yes—
122C3×(C2×D3)⋊C4C2318yescomplemented
123C3×C4⋊Dic3C2318yescomplemented
124#3724C2318yescomplemented
125(C2×D3)⋊Dic3C2318yes—
126(C2×D3)⋊Dic3C2318yescomplemented
127C2×#525—91noSylow
128C24×D3—31no—
129C24×D3—31no—
130C22×C3×Q8—31no—
131C22×C3×D4—31no—
132C22×C3×D4—32no—
133C23×C3×C4—31no—
134C23×C3×C4—31no—
135C22×#67—32no—
136C22×#67—32no—
137C22×#67—32no—
138C23×Dic3—31no—
139C23×Dic3—31no—
140C23×Dic3—32no—
141C2×#239—38no—
142C2×#239—68no—
143C2×#237—38no—
144C2×#237—68no—
145C22×D12—32no—
146C22×D12C2×D312yes—
147C22×D12C2×D311yescharacteristic, complemented
148C22×C4×D3—31no—
149C22×C4×D3—31no—
150C22×C4×D3—31no—
151C22×C4×D3—31no—
152C22×C4×D3—32no—
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C22×C4×D3—38no—
156C22×C4×D3—38no—
157C22×C4×D3—61no—
158C22×C4×D3—68no—
159C22×C4×D3—68no—
160C22×C4×D3C2×D311yescharacteristic
161C22×C4×D3C2×D311yescharacteristic
162C22×Dic6C2×D311yescharacteristic, complemented
163C3×C22⋊Q8—38no—
164C3×#121—38no—
165C2×C3×C4⋊C4—21no—
166C2×C3×C4⋊C4—32no—
167C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
168C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
169C2×C3×C22⋊C4—32no—
170C2×C3×C22⋊C4—32no—
171C2×#217—32no—
172C2×#217—32no—
173#946—38no—
174#938—38no—
175#937—316no—
176D4×Dic3—316no—
177#930—38no—
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—31no—
186C2×C4⋊Dic3—31no—
187C2×C4⋊Dic3—61no—
188C2×C4⋊Dic3C2×D312yescomplemented
189#924—38no—
190C2×Dic3⋊C4—32no—
191C2×Dic3⋊C4—32no—
192C2×C4×Dic3—32no—
193C2×C4×Dic3—32no—
194C2×C4×Dic3—62no—
195#897C2×D318yescomplemented
196#895C2×D318yescomplemented
197#894—316no—
198#893—316no—
199#892—38no—
200#892—38no—
201#892—68no—
202#883—316no—
203#882—316no—
204#67⋊C4—316no—
205#67⋊C4—316no—
206C23×C32C2411yescharacteristic
207C22×C3⋊D3—22no—
208C22×C3⋊D3—22no—
209C22×C3⋊D3C2×D414yes—
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×D3#4114yescomplemented
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—24no—
232C2×C3⋊Dic3C2×D414yes—
233C2×C3⋊Dic3C2414yes—
234C2×C3⋊Dic3C2412yes—
235C4×C3⋊D3C2×D4116yescomplemented
236C2×C3×Dic3—22no—
237C2×C3×Dic3—22no—
238C2×C3×Dic3—24no—
239C2×C3×Dic3C2414yes—
240C2×C3×Dic3C2412yes—
241C2×C3×Dic3C2412yes—
242C3×D12—216no—
243C3×D12—28no—
244C3×C4×D3—28no—
245C3×C4×D3—28no—
246C3×Dic6—28no—
247#626—216no—
248#625—216no—
249#624—28no—
250D3×Dic3—216no—
251D3×Dic3—28no—
252D3×Dic3—28no—
253C22×#41—91no—
254C24×C4—91no—
255#525—916no—
256C2×#123—92no—
257C2×C22⋊Q8—31no—
258C2×C22⋊Q8—91no—
259C2×#121—31no—
260C2×#121—91no—
261C2×#120—92no—
262C2×C4×D4—92no—
263C2×C4×D4—92no—
264C2×#117—91no—
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×Q8—34no—
283C2×C3×Q8—64no—
284C2×C3×D4—38no—
285C2×C3×D4—34no—
286C2×C3×D4—68no—
287C2×C3×D4—64no—
288C22×C3×C4—21no—
289C22×C3×C4—22no—
290C22×C3×C4—31no—
291C22×C3×C4—32no—
292C22×C3×C4—31no—
293C22×C3×C4—34no—
294C22×C3×C4—34no—
295C22×C3×C4—64no—
296C22×C3×C4—64no—
297C22×C3×C4C22×D312yes—
298C22×C3×C4C22×D312yes—
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C2×#67—38no—
302C2×#67—38no—
303C2×#67—38no—
304C2×#67—68no—
305C2×#67—68no—
306C2×#67—68no—
307C22×Dic3—31no—
308C22×Dic3—31no—
309C22×Dic3—32no—
310C22×Dic3—32no—
311C22×Dic3—34no—
312C22×Dic3—38no—
313C22×Dic3—34no—
314C22×Dic3—61no—
315C22×Dic3—62no—
316C22×Dic3—64no—
317C22×Dic3—64no—
318C22×Dic3—68no—
319C22×Dic3C22×D311yescharacteristic
320C22×Dic3C22×D312yes—
321C22×Dic3C22×D311yescharacteristic
322#239—632no—
323#237—632no—
324C2×D12—28no—
325C2×D12—24no—
326C2×D12—38no—
327C2×D12—68no—
328C2×D12C22×D318yes—
329C2×D12C22×D314yescomplemented
330C2×C4×D3—24no—
331C2×C4×D3—24no—
332C2×C4×D3—38no—
333C2×C4×D3—38no—
334C2×C4×D3—34no—
335C2×C4×D3—34no—
336C2×C4×D3—34no—
337C2×C4×D3—38no—
338C2×C4×D3—34no—
339C2×C4×D3—34no—
340C2×C4×D3—34no—
341C2×C4×D3—64no—
342C2×C4×D3—68no—
343C2×C4×D3—632no—
344C2×C4×D3—632no—
345C2×C4×D3—64no—
346C2×C4×D3—64no—
347C2×C4×D3—64no—
348C2×C4×D3—64no—
349C2×C4×D3—68no—
350C2×C4×D3C22×D314yes—
351C2×C4×D3C22×D314yes—
352C2×Dic6—24no—
353C2×Dic6C22×D314yescomplemented
354C3×C4⋊C4—24no—
355C3×C4⋊C4—38no—
356C3×C4⋊C4C22×D314yescomplemented
357C3×C4⋊C4C22×D314yescomplemented
358C3×C22⋊C4—38no—
359C3×C22⋊C4—38no—
360#217—38no—
361#217—38no—
362(C2×D3)⋊C4—38no—
363(C2×D3)⋊C4—38no—
364(C2×D3)⋊C4—38no—
365(C2×D3)⋊C4—38no—
366(C2×D3)⋊C4—68no—
367(C2×D3)⋊C4C22×D318yes—
368(C2×D3)⋊C4C22×D318yescomplemented
369C4⋊Dic3—34no—
370C4⋊Dic3—34no—
371C4⋊Dic3—64no—
372C4⋊Dic3C22×D318yescomplemented
373Dic3⋊C4—38no—
374Dic3⋊C4—38no—
375C4×Dic3—38no—
376C4×Dic3—38no—
377C4×Dic3—68no—
378C22×C32C22×D412yes—
379C22×C32C2×#4112yes—
380C22×C32C2×#4112yes—
381C22×C32C2511yescharacteristic
382C2×C3⋊D3—28no—
383C2×C3⋊D3—22no—
384C2×C3⋊D3—22no—
385C2×C3⋊D3C22×D414yes—
386C2×C3×D3—28no—
387C2×C3×D3—28no—
388C2×C3×D3—22no—
389C2×C3×D3—22no—
390C2×C3×D3—22no—
391C2×C3×D3—22no—
392C2×C3×D3—24no—
393C2×C3×D3—24no—
394C2×C3×D3—24no—
395C2×C3×D3—48no—
396C2×C3×D3C2×#4114yescomplemented
397C2×C3×D3C2×#4114yescomplemented
398D32—232no—
399C32×C4—24no—
400C32×C4C22×D414yes—
401C3⋊Dic3—24no—
402C3⋊Dic3C22×D414yes—
403C3×Dic3—22no—
404C3×Dic3—22no—
405C3×Dic3—24no—
406C25—91no—
407C2×#41—98no—
408C2×#41—188no—
409C22×Q8—31no—
410C22×D4—32no—
411C22×D4—31no—
412C22×D4—92no—
413C22×D4—92no—
414C23×C4—31no—
415C23×C4—31no—
416C23×C4—91no—
417C23×C4—98no—
418C23×C4—91no—
419C23×C4—91no—
420C23×C4—92no—
421C23×C4—91no—
422C23×C4—188no—
423#123—916no—
424C22⋊Q8—38no—
425C22⋊Q8—98no—
426#121—38no—
427#121—98no—
428#120—916no—
429C4×D4—916no—
430C4×D4—916no—
431#117—98no—
432C2×C4⋊C4—32no—
433C2×C4⋊C4—92no—
434C2×C4⋊C4—91no—
435C2×C4⋊C4D3211yescharacteristic, complemented
436C2×C22⋊C4—32no—
437C2×C22⋊C4—32no—
438C2×C22⋊C4—92no—
439C2×C22⋊C4—92no—
440C2×C22⋊C4—92no—
441C2×C42—92no—
442C23×C3—21no—
443C23×C3—34no—
444C23×C3—34no—
445C23×C3—32no—
446C23×C3—32no—
447C23×C3—34no—
448C23×C3—62no—
449C23×C3—62no—
450C23×C3—62no—
451C23×C3—62no—
452C23×C3—64no—
453C23×C3—64no—
454C23×C3—64no—
455C23×C3C23×D311yescharacteristic
456C23×C3C23×D311yescharacteristic
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—24no—
462C22×D3—24no—
463C22×D3—24no—
464C22×D3—34no—
465C22×D3—34no—
466C22×D3—32no—
467C22×D3—32no—
468C22×D3—64no—
469C22×D3—62no—
470C22×D3—68no—
471C22×D3—68no—
472C22×D3—68no—
473C22×D3—68no—
474C22×D3—632no—
475C22×D3—632no—
476C22×D3—62no—
477C22×D3—62no—
478C22×D3—62no—
479C22×D3—62no—
480C22×D3—68no—
481C22×D3—68no—
482C22×D3—122no—
483C22×D3—122no—
484C22×D3#23714yescomplemented
485C22×D3#23914yescomplemented
486C22×D3C23×D314yes—
487C22×D3C23×D312yes—
488C22×D3C23×D312yes—
489C3×Q8—68no—
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—32no—
498C2×C3×C4—34no—
499C2×C3×C4—32no—
500C2×C3×C4—44no—
501C2×C3×C4—62no—
502C2×C3×C4—62no—
503C2×C3×C4—64no—
504C2×C3×C4—68no—
505C2×C3×C4—68no—
506C2×C3×C4D3×D414yes—
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—24no—
516C2×Dic3—22no—
517C2×Dic3—22no—
518C2×Dic3—34no—
519C2×Dic3—34no—
520C2×Dic3—32no—
521C2×Dic3—32no—
522C2×Dic3—34no—
523C2×Dic3—34no—
524C2×Dic3—64no—
525C2×Dic3—62no—
526C2×Dic3—64no—
527C2×Dic3—68no—
528C2×Dic3—68no—
529C2×Dic3—616no—
530C2×Dic3—64no—
531C2×Dic3—64no—
532C2×Dic3—124no—
533C2×Dic3C23×D312yes—
534C2×Dic3C23×D314yes—
535C2×Dic3C23×D312yes—
536D12—216no—
537D12—28no—
538D12—616no—
539C4×D3—28no—
540C4×D3—28no—
541C4×D3—316no—
542C4×D3—316no—
543C4×D3—616no—
544C4×D3—68no—
545C4×D3—68no—
546C4×D3—68no—
547C4×D3—68no—
548C4×D3—616no—
549Dic6—28no—
550C2×C32#52514yescomplemented
551C2×C32C23×D411yescharacteristic
552C2×C32C22×#4111yescharacteristic
553C2×C32C22×#4111yescharacteristic
554C3⋊D3—24no—
555C3×D3—24no—
556C3×D3—24no—
557C3×D3—44no—
558C24—31no—
559C24—31no—
560C24—32no—
561C24—94no—
562C24—91no—
563C24—184no—
564C24—184no—
565C24—184no—
566#41—1832no—
567C2×Q8—34no—
568C2×Q8—64no—
569C2×D4—38no—
570C2×D4—34no—
571C2×D4—68no—
572C2×D4—64no—
573C2×D4—98no—
574C2×D4—98no—
575C2×D4—188no—
576C2×D4—188no—
577C22×C4—31no—
578C22×C4—32no—
579C22×C4—31no—
580C22×C4—34no—
581C22×C4—34no—
582C22×C4—64no—
583C22×C4—64no—
584C22×C4—94no—
585C22×C4—94no—
586C22×C4—94no—
587C22×C4—98no—
588C22×C4—91no—
589C22×C4—94no—
590C22×C4—98no—
591C22×C4—92no—
592C22×C4—1832no—
593C22×C4—184no—
594C22×C4—184no—
595C22×C4—184no—
596C22×C4—188no—
597C22×C4C2×D3212yes—
598C22×C4C2×D3211yescharacteristic
599C4⋊C4—38no—
600C4⋊C4—98no—
601C4⋊C4—94no—
602C4⋊C4C2×D3214yescomplemented
603C22⋊C4—38no—
604C22⋊C4—38no—
605C22⋊C4—98no—
606C22⋊C4—98no—
607C22⋊C4—98no—
608C42—98no—
609C22×C3—22no—
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—21no—
613C22×C3—34no—
614C22×C3—34no—
615C22×C3—62no—
616C22×C3—62no—
617C22×C3—62no—
618C22×C3—62no—
619C22×C3—68no—
620C22×C3—68no—
621C22×C3—64no—
622C22×C3—64no—
623C22×C3—64no—
624C22×C3—128no—
625C22×C3C2×D3×D412yes—
626C22×C3C2×D3×D412yes—
627C22×C3C2×#23712yes—
628C22×C3C2×#23912yes—
629C22×C3D3×#4112yes—
630C22×C3D3×#4112yes—
631C22×C3C24×D311yescharacteristic
632C22×C3C24×D311yescharacteristic
633C2×D3—22no—
634C2×D3—22no—
635C2×D3—22no—
636C2×D3—22no—
637C2×D3—28no—
638C2×D3—28no—
639C2×D3—24no—
640C2×D3—24no—
641C2×D3—24no—
642C2×D3—34no—
643C2×D3—34no—
644C2×D3—48no—
645C2×D3—64no—
646C2×D3—632no—
647C2×D3—632no—
648C2×D3—62no—
649C2×D3—62no—
650C2×D3—62no—
651C2×D3—62no—
652C2×D3—68no—
653C2×D3—68no—
654C2×D3—122no—
655C2×D3—128no—
656C2×D3—122no—
657C2×D3C2×#23714yescomplemented
658C2×D3C2×#23914yescomplemented
659C3×C4—24no—
660C3×C4—24no—
661C3×C4—24no—
662C3×C4—44no—
663C3×C4—62no—
664C3×C4—62no—
665C3×C4—64no—
666C3×C4C2×D3×D414yes—
667C3×C4C2×D3×D414yes—
668Dic3—24no—
669Dic3—22no—
670Dic3—22no—
671Dic3—34no—
672Dic3—34no—
673Dic3—64no—
674Dic3—64no—
675Dic3—64no—
676Dic3—124no—
677C32C2×#52511yescharacteristic, complemented, Sylow
678C23—34no—
679C23—34no—
680C23—32no—
681C23—32no—
682C23—34no—
683C23—62no—
684C23—62no—
685C23—62no—
686C23—62no—
687C23—64no—
688C23—64no—
689C23—64no—
690C23—94no—
691C23—92no—
692C23—188no—
693C23—188no—
694C23—188no—
695C23—1832no—
696C23—182no—
697C23—182no—
698C23C22×D3211yescharacteristic
699Q8—68no—
700D4—616no—
701D4—68no—
702D4—1816no—
703D4—1816no—
704C2×C4—24no—
705C2×C4—32no—
706C2×C4—34no—
707C2×C4—32no—
708C2×C4—62no—
709C2×C4—62no—
710C2×C4—64no—
711C2×C4—68no—
712C2×C4—68no—
713C2×C4—94no—
714C2×C4—92no—
715C2×C4—916no—
716C2×C4—94no—
717C2×C4—188no—
718C2×C4—188no—
719C2×C4—188no—
720C2×C4—1816no—
721C2×C4—184no—
722C2×C4#380214yes—
723C2×C4C22×D3214yes—
724C2×C4C22×D3212yes—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—24no—
728C2×C3—21no—
729C2×C3—64no—
730C2×C3—64no—
731C2×C3—124no—
732C2×C3#560614yescomplemented
733C2×C3#562714yescomplemented
734C2×C3C22×D3×D411yescharacteristic
735C2×C3C22×D3×D411yescharacteristic
736C2×C3C22×#23711yescharacteristic
737C2×C3C22×#23911yescharacteristic
738C2×C3C2×D3×#4111yescharacteristic
739C2×C3C2×D3×#4111yescharacteristic
740D3—24no—
741D3—24no—
742D3—44no—
743D3—64no—
744D3—64no—
745D3—124no—
746C22—34no—
747C22—34no—
748C22—62no—
749C22—62no—
750C22—62no—
751C22—68no—
752C22—68no—
753C22—62no—
754C22—64no—
755C22—64no—
756C22—64no—
757C22—94no—
758C22—128no—
759C22—1832no—
760C22—182no—
761C22—188no—
762C22—182no—
763C22C2×#380212yes—
764C22D3×#23712yes—
765C22D3×#23912yes—
766C22C23×D3211yescharacteristic
767C4—24no—
768C4—62no—
769C4—62no—
770C4—64no—
771C4—94no—
772C4—184no—
773C4C2×#380214yes—
774C3—21no—
775C3C2×#560611yescharacteristic, complemented
776C3C2×#562711yescharacteristic, complemented
777C2—64no—
778C2—64no—
779C2—124no—
780C2—184no—
781C2#1059463214yesdirect product factor
782C2C22×#380211yescharacteristic
783C2C2×D3×#23711yescharacteristic
784C2C2×D3×#23911yescharacteristic
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×#3796C2semidirect
3. C2×#64101C2semidirect
4. C2×C3×#897C2semidirect
5. C2×C3×#895C2semidirect
6. C2×#63922C2semidirect
7. C2×#63908C2semidirect
8. C2×#63902C2semidirect
9. C2×#63898C2semidirect
10. C2×#63856C2semidirect
11. C2×#63854C2semidirect
12. #10594632C2direct (N × H)
18. C22×C3×D12C22semidirect
21. C22×C3×Dic6C22semidirect
27. C22×D3×Dic3C22semidirect
29. C2×C4×D32C22semidirect
31. C2×#3796C22semidirect
32. C2×C32×C4⋊C4C22semidirect
34. C2×C4⋊(C3⋊Dic3)C22semidirect
35. C2×C4×C3⋊Dic3C22semidirect
36. #64101C22semidirect
38. C2×C3×(C2×D3)⋊C4C22semidirect
39. C2×C3×C4⋊Dic3C22semidirect
40. C3×#897C22semidirect
41. C3×#895C22semidirect
42. C2×#3724C22semidirect
44. C2×(C2×D3)⋊Dic3C22semidirect
45. #63922C22semidirect
46. #63908C22semidirect
47. #63902C22semidirect
48. #63898C22semidirect
49. #63856C22semidirect
50. #63854C22semidirect
65. C2×#897D3semidirect
66. C2×#895D3semidirect
88. C2×C4×C3⋊D3D4semidirect
96. C2×C3×D12C23semidirect
102. C2×C3×Dic6C23semidirect
114. C2×D3×Dic3C23semidirect
117. C32×C4⋊C4C23semidirect
119. C4⋊(C3⋊Dic3)C23semidirect
120. C4×C3⋊Dic3C23semidirect
122. C3×(C2×D3)⋊C4C23semidirect
123. C3×C4⋊Dic3C23semidirect
124. #3724C23semidirect
126. (C2×D3)⋊Dic3C23semidirect
147. C22×D12C2×D3semidirect
162. C22×Dic6C2×D3semidirect
167. C2×C3×C4⋊C4C2×D3semidirect
168. C2×C3×C4⋊C4C2×D3semidirect
184. C2×(C2×D3)⋊C4C2×D3semidirect
188. C2×C4⋊Dic3C2×D3semidirect
195. #897C2×D3semidirect
196. #895C2×D3semidirect
218. C22×C3×D3#41semidirect
219. C22×C3×D3#41semidirect
235. C4×C3⋊D3C2×D4semidirect
329. C2×D12C22×D3semidirect
353. C2×Dic6C22×D3semidirect
356. C3×C4⋊C4C22×D3semidirect
357. C3×C4⋊C4C22×D3semidirect
368. (C2×D3)⋊C4C22×D3semidirect
372. C4⋊Dic3C22×D3semidirect
396. C2×C3×D3C2×#41semidirect
397. C2×C3×D3C2×#41semidirect
435. C2×C4⋊C4D32semidirect
484. C22×D3#237semidirect
485. C22×D3#239semidirect
550. C2×C32#525semidirect
602. C4⋊C4C2×D32semidirect
657. C2×D3C2×#237semidirect
658. C2×D3C2×#239semidirect
677. C32C2×#525semidirect
732. C2×C3#5606semidirect
733. C2×C3#5627semidirect
775. C3C2×#5606semidirect
776. C3C2×#5627semidirect
781. C2#10594632direct (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×#37962
C2×#641012
C2×C3×#8972
C2×C3×#8952
C2×#639222
C2×#639082
C2×#639022
C2×#638982
C2×#638562
C2×#638542
#105946322
C2×#56273
C2×#56063