Finite Group Databasebeta

← C2×#10594630 #11902459

Subgroups — C2×#10594630 #11902459

Order 1152.

3961 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3802C211yesmaximal, characteristic, complemented
2C22×#3795C211yesmaximal, characteristic, complemented
3C2×#64106C211yesmaximal, characteristic, complemented
4C2×C3×#895C211yesmaximal, characteristic, complemented
5C2×C3×#893C211yesmaximal, characteristic, complemented
6C2×#63922C212yesmaximal, complemented
7C2×D3×(C2×D3)⋊C4C212yesmaximal, complemented
8C2×#63908C212yesmaximal, complemented
9C2×C4×#626C211yesmaximal, characteristic, complemented
10C2×#63891C212yesmaximal, complemented
11C2×#63860C211yesmaximal, characteristic, complemented
12#10594630C2116yesmaximal, direct product factor
13C2×#5612—31nomaximal
14C2×#5554—31nomaximal
15C23×D32C2212yes—
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×#634C2211yescharacteristic, complemented
18C22×C3×D12C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×D12C2212yescomplemented
21C22×C3×C4×D3C2211yescharacteristic, complemented
22C22×C3×C4×D3C2212yescomplemented
23C22×#626C2211yescharacteristic
24C22×#625C2212yes—
25C22×#625C2212yescomplemented
26C22×D3×Dic3C2212yescomplemented
27C2×#3802—28no—
28C2×#3802C2218yescomplemented
29C2×#3795—28no—
30C2×#3795C2218yescomplemented
31C2×C32×C4⋊C4C2211yescharacteristic, complemented
32C2×#3752C2212yes—
33C2×C4⋊(C3⋊Dic3)C2212yescomplemented
34#64106C2218yescomplemented
35C2×C3×(C2×D3)⋊C4C2212yescomplemented
36C2×C3×(C2×D3)⋊C4C2212yescomplemented
37C2×C3×C4×Dic3C2211yescharacteristic, complemented
38C3×#895C2218yescomplemented
39C3×#893C2218yescomplemented
40C2×Dic3⋊Dic3C2211yescharacteristic, complemented
41C2×#3722C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2212yescomplemented
43C2×(C2×D3)⋊Dic3C2212yescomplemented
44C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
45#63922C22116yescomplemented
46D3×(C2×D3)⋊C4C22116yescomplemented
47#63908C22116yescomplemented
48C4×#626C2218yescomplemented
49#63891C22116yescomplemented
50#63860C2218yescomplemented
51C22×#237—31no—
52C22×D3×D4—31no—
53C22×D3×D4—31no—
54C22×#235—31no—
55C2×C3×#121—31no—
56C2×C3×C4×D4—31no—
57C2×#938—32no—
58C2×#937—32no—
59C2×#936—31no—
60C2×#930—32no—
61C2×C4×#67—31no—
62C22×(C2×D3)⋊C4—32no—
63#5612—316no—
64#5554—316no—
65C2×#897—31no—
66C2×#897—31no—
67C2×#897—61no—
68C2×#895D311yescharacteristic, complemented
69C2×#893D311yescharacteristic, complemented
70C2×#886—32no—
71C2×#883—32no—
72C2×#882—32no—
73C2×D3×C22⋊C4—32no—
74C2×#875—31no—
75C2×C4×D12—31no—
76C23×C3⋊D3C2311yescharacteristic
77C23×C3×D3C2312yes—
78C23×C3×D3C2311yescharacteristic
79C23×C3×D3C2312yes—
80C22×D32—28no—
81C22×D32—28no—
82C22×D32—44no—
83C22×D32C2318yes—
84C22×C32×C4C2312yes—
85C22×C32×C4C2311yescharacteristic
86C22×C3⋊Dic3C2312yes—
87C22×C3⋊Dic3C2311yescharacteristic
88C2×C4×C3⋊D3—24no—
89C2×C4×C3⋊D3C2314yes—
90C2×#634—24no—
91C2×#634C2314yescomplemented
92C22×C3×Dic3C2311yescharacteristic
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C2×C3×D12—24no—
96C2×C3×D12—44no—
97C2×C3×D12D418yescomplemented
98C2×C3×D12C2314yes—
99C2×C3×D12C2314yes—
100C2×C3×D12C2318yescomplemented
101C2×C3×C4×D3—24no—
102C2×C3×C4×D3—44no—
103C2×C3×C4×D3C2314yescomplemented
104C2×C3×C4×D3C2318yescomplemented
105C2×#626—24no—
106C2×#626C2314yes—
107C2×#625—28no—
108C2×#625—28no—
109C2×#625C2318yes—
110C2×#625C2318yescomplemented
111C2×D3×Dic3—28no—
112C2×D3×Dic3C2318yescomplemented
113#3802—232no—
114#3795—232no—
115C32×C4⋊C4C2314yescomplemented
116#3752C2318yes—
117C4⋊(C3⋊Dic3)C2318yescomplemented
118C3×(C2×D3)⋊C4C2318yescomplemented
119C3×(C2×D3)⋊C4C2318yescomplemented
120C3×C4×Dic3C2314yescomplemented
121Dic3⋊Dic3C2314yescomplemented
122#3722C2314yes—
123(C2×D3)⋊Dic3C2318yescomplemented
124(C2×D3)⋊Dic3C2318yescomplemented
125(C2×D3)⋊Dic3C2314yescomplemented
126C2×#546—91noSylow
127C24×D3—32no—
128C24×D3—32no—
129C22×C3×D4—31no—
130C22×C3×D4—31no—
131C22×C3×D4—32no—
132C23×C3×C4—31no—
133C23×C3×C4—32no—
134C22×#67—32no—
135C22×#67—32no—
136C22×#67—32no—
137C22×#67—32no—
138C22×#67—31no—
139C23×Dic3—32no—
140C2×#237—38no—
141C2×#237—68no—
142C2×D3×D4—38no—
143C2×D3×D4—38no—
144C2×D3×D4—68no—
145C2×D3×D4—68no—
146C2×#235—38no—
147C2×#235—68no—
148C22×D12—31no—
149C22×D12C2×D311yescharacteristic
150C22×D12C2×D311yescharacteristic
151C22×D12C2×D312yescomplemented
152C22×C4×D3—32no—
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C22×C4×D3—61no—
156C22×C4×D3C2×D311yescharacteristic, complemented
157C22×C4×D3C2×D312yescomplemented
158C22×Dic6—31no—
159C22×Dic6—31no—
160C22×Dic6—61no—
161C3×#121—38no—
162C3×C4×D4—38no—
163C2×C3×C4⋊C4—21no—
164C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
165C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
166C2×C3×C22⋊C4—32no—
167C2×C3×C22⋊C4—32no—
168C2×C3×C42—31no—
169C2×#217—32no—
170C2×#217—32no—
171C2×#217—31no—
172#938—316no—
173#937—316no—
174#936—38no—
175#930—316no—
176C4×#67—38no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4—32no—
179C2×(C2×D3)⋊C4—32no—
180C2×(C2×D3)⋊C4—32no—
181C2×(C2×D3)⋊C4—32no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—316no—
185C2×(C2×D3)⋊C4—62no—
186C2×(C2×D3)⋊C4C2×D312yescomplemented
187C2×(C2×D3)⋊C4C2×D312yescomplemented
188C2×C4⋊Dic3—32no—
189C2×C4⋊Dic3—32no—
190C2×C4⋊Dic3—31no—
191C2×C4⋊Dic3—62no—
192C2×Dic3⋊C4—31no—
193C2×C4×Dic3C2×D311yescharacteristic, complemented
194#897—38no—
195#897—38no—
196#897—68no—
197#895C2×D318yescomplemented
198#893C2×D318yescomplemented
199#886—316no—
200#883—316no—
201#882—316no—
202D3×C22⋊C4—316no—
203#875—38no—
204C4×D12—38no—
205C23×C32C2411yescharacteristic
206C22×C3⋊D3—22no—
207C22×C3⋊D3—22no—
208C22×C3⋊D3#4114yescomplemented
209C22×C3⋊D3C2412yes—
210C22×C3×D3—24no—
211C22×C3×D3—24no—
212C22×C3×D3—24no—
213C22×C3×D3—22no—
214C22×C3×D3—24no—
215C22×C3×D3—22no—
216C22×C3×D3—24no—
217C22×C3×D3—22no—
218C22×C3×D3C2×D418yes—
219C22×C3×D3C2414yes—
220C22×C3×D3C2412yes—
221C22×C3×D3C2414yes—
222C2×D32—216no—
223C2×D32—216no—
224C2×D32—48no—
225C2×D32—432no—
226C2×C32×C4—24no—
227C2×C32×C4C2×D414yes—
228C2×C32×C4C2414yes—
229C2×C32×C4C2412yes—
230C2×C3⋊Dic3—24no—
231C2×C3⋊Dic3—22no—
232C2×C3⋊Dic3C2414yes—
233C2×C3⋊Dic3C2412yes—
234C4×C3⋊D3—28no—
235#634—28no—
236C2×C3×Dic3—22no—
237C2×C3×Dic3—22no—
238C2×C3×Dic3—22no—
239C2×C3×Dic3C2412yes—
240C2×C3×Dic3C2412yes—
241C2×C3×Dic3C2412yes—
242C3×D12—28no—
243C3×D12—48no—
244C3×D12C2×D4116yescomplemented
245C3×C4×D3—28no—
246C3×C4×D3—48no—
247#626—28no—
248#625—216no—
249#625—216no—
250D3×Dic3—216no—
251C22×#41—91no—
252C23×D4—91no—
253#546—916no—
254C2×#124—91no—
255C2×#123—92no—
256C2×C22⋊Q8—91no—
257C2×#121—31no—
258C2×#121—92no—
259C2×#120—92no—
260C2×C4×D4—31no—
261C2×C4×D4—91no—
262C22×C22⋊C4—92no—
263C24×C3—32no—
264C24×C3—32no—
265C24×C3—31no—
266C23×D3—31no—
267C23×D3—31no—
268C23×D3—38no—
269C23×D3—38no—
270C23×D3—61no—
271C23×D3—68no—
272C23×D3—68no—
273C23×D3—68no—
274C23×D3—68no—
275C23×D3—124no—
276C23×D3—124no—
277C23×D3C22×D312yes—
278C23×D3C22×D311yescharacteristic
279C23×D3C22×D312yes—
280C2×C3×D4—38no—
281C2×C3×D4—34no—
282C2×C3×D4—34no—
283C2×C3×D4—38no—
284C2×C3×D4—64no—
285C2×C3×D4—124no—
286C22×C3×C4—21no—
287C22×C3×C4—22no—
288C22×C3×C4—31no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—34no—
292C22×C3×C4—38no—
293C22×C3×C4—64no—
294C22×C3×C4—124no—
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—38no—
303C2×#67—34no—
304C2×#67—64no—
305C2×#67—68no—
306C2×#67—68no—
307C2×#67—68no—
308C2×#67—68no—
309C22×Dic3—31no—
310C22×Dic3—31no—
311C22×Dic3—32no—
312C22×Dic3—32no—
313C22×Dic3—38no—
314C22×Dic3—61no—
315C22×Dic3—62no—
316C22×Dic3—68no—
317C22×Dic3C22×D311yescharacteristic
318C22×Dic3C22×D311yescharacteristic
319C22×Dic3C22×D311yescharacteristic
320#237—632no—
321D3×D4—632no—
322D3×D4—632no—
323#235—632no—
324C2×D12—24no—
325C2×D12—34no—
326C2×D12—44no—
327C2×D12—64no—
328C2×D12D1218yescomplemented
329C2×D12C22×D314yes—
330C2×D12C22×D314yes—
331C2×D12C22×D318yescomplemented
332C2×C4×D3—24no—
333C2×C4×D3—38no—
334C2×C4×D3—34no—
335C2×C4×D3—34no—
336C2×C4×D3—44no—
337C2×C4×D3—64no—
338C2×C4×D3—68no—
339C2×C4×D3—64no—
340C2×C4×D3—64no—
341C2×C4×D3—124no—
342C2×C4×D3C22×D314yescomplemented
343C2×C4×D3C22×D318yescomplemented
344C2×Dic6—34no—
345C2×Dic6—34no—
346C2×Dic6—64no—
347C2×Dic6—64no—
348C2×Dic6—64no—
349C2×Dic6—124no—
350C3×C4⋊C4—24no—
351C3×C4⋊C4C22×D314yescomplemented
352C3×C4⋊C4C22×D314yescomplemented
353C3×C22⋊C4—38no—
354C3×C22⋊C4—38no—
355C3×C42—34no—
356#217—38no—
357#217—38no—
358#217—34no—
359(C2×D3)⋊C4—34no—
360(C2×D3)⋊C4—38no—
361(C2×D3)⋊C4—38no—
362(C2×D3)⋊C4—38no—
363(C2×D3)⋊C4—38no—
364(C2×D3)⋊C4—34no—
365(C2×D3)⋊C4—34no—
366(C2×D3)⋊C4—68no—
367(C2×D3)⋊C4C22×D318yescomplemented
368(C2×D3)⋊C4C22×D318yescomplemented
369C4⋊Dic3—38no—
370C4⋊Dic3—38no—
371C4⋊Dic3—34no—
372C4⋊Dic3—68no—
373Dic3⋊C4—34no—
374C4×Dic3C22×D314yescomplemented
375C22×C32C22×D412yes—
376C22×C32C2×#4112yes—
377C22×C32H(5,𝔽2)12yes—
378C22×C32C2511yescharacteristic
379C2×C3⋊D3—28no—
380C2×C3⋊D3—22no—
381C2×C3⋊D3—22no—
382C2×C3⋊D3C2×#4114yescomplemented
383C2×C3×D3—216no—
384C2×C3×D3—24no—
385C2×C3×D3—24no—
386C2×C3×D3—22no—
387C2×C3×D3—24no—
388C2×C3×D3—22no—
389C2×C3×D3—24no—
390C2×C3×D3—22no—
391C2×C3×D3—24no—
392C2×C3×D3—48no—
393C2×C3×D3—44no—
394C2×C3×D3C22×D418yes—
395D32—432no—
396C32×C4—24no—
397C32×C4C22×D414yes—
398C3⋊Dic3—24no—
399C3⋊Dic3—22no—
400C3×Dic3—22no—
401C3×Dic3—22no—
402C3×Dic3—22no—
403C25—92no—
404C2×#41—98no—
405C2×#41—188no—
406C22×Q8—91no—
407C22×D4—31no—
408C22×D4—31no—
409C22×D4—32no—
410C22×D4—91no—
411C22×D4—98no—
412C22×D4—92no—
413C22×D4—92no—
414C22×D4—188no—
415C23×C4—31no—
416C23×C4—32no—
417C23×C4—92no—
418C23×C4—91no—
419#124—98no—
420#123—916no—
421C22⋊Q8—98no—
422#121—38no—
423#121—916no—
424#120—916no—
425C4×D4—38no—
426C4×D4—98no—
427C2×C4⋊C4—91no—
428C2×C4⋊C4—92no—
429C2×C4⋊C4D3211yescharacteristic, complemented
430C2×C22⋊C4—32no—
431C2×C22⋊C4—32no—
432C2×C22⋊C4—916no—
433C2×C22⋊C4—91no—
434C2×C22⋊C4—92no—
435C2×C22⋊C4—91no—
436C2×C22⋊C4—92no—
437C2×C22⋊C4—92no—
438C2×C42—31no—
439C23×C3—21no—
440C23×C3—38no—
441C23×C3—34no—
442C23×C3—34no—
443C23×C3—32no—
444C23×C3—64no—
445C23×C3—64no—
446C23×C3—62no—
447C23×C3—64no—
448C23×C3—62no—
449C23×C3—64no—
450C23×C3—62no—
451C23×C3—64no—
452C23×C3C23×D311yescharacteristic
453C23×C3C23×D311yescharacteristic
454C22×D3—24no—
455C22×D3—24no—
456C22×D3—22no—
457C22×D3—24no—
458C22×D3—22no—
459C22×D3—24no—
460C22×D3—22no—
461C22×D3—24no—
462C22×D3—34no—
463C22×D3—34no—
464C22×D3—32no—
465C22×D3—32no—
466C22×D3—64no—
467C22×D3—62no—
468C22×D3—616no—
469C22×D3—616no—
470C22×D3—616no—
471C22×D3—62no—
472C22×D3—62no—
473C22×D3—62no—
474C22×D3—62no—
475C22×D3—616no—
476C22×D3—122no—
477C22×D3—122no—
478C22×D3—128no—
479C22×D3—128no—
480C22×D3—1232no—
481C22×D3—1232no—
482C22×D3C2×D1218yes—
483C22×D3C23×D314yes—
484C22×D3C23×D312yes—
485C22×D3C23×D314yes—
486C3×D4—316no—
487C3×D4—68no—
488C3×D4—128no—
489C2×C3×C4—24no—
490C2×C3×C4—24no—
491C2×C3×C4—22no—
492C2×C3×C4—24no—
493C2×C3×C4—24no—
494C2×C3×C4—32no—
495C2×C3×C4—32no—
496C2×C3×C4—32no—
497C2×C3×C4—44no—
498C2×C3×C4—62no—
499C2×C3×C4—62no—
500C2×C3×C4—62no—
501C2×C3×C4—68no—
502C2×C3×C4—128no—
503C2×C3×C4C2×D1214yes—
504C2×C3×C4D3×D414yes—
505C2×C3×C4C23×D314yes—
506C2×C3×C4C23×D314yes—
507C2×C3×C4C23×D312yes—
508C2×C3×C4C23×D312yes—
509#67—68no—
510#67—616no—
511#67—616no—
512#67—616no—
513#67—616no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—22no—
517C2×Dic3—32no—
518C2×Dic3—32no—
519C2×Dic3—34no—
520C2×Dic3—34no—
521C2×Dic3—62no—
522C2×Dic3—64no—
523C2×Dic3—616no—
524C2×Dic3—64no—
525C2×Dic3—62no—
526C2×Dic3—64no—
527C2×Dic3—62no—
528C2×Dic3—124no—
529C2×Dic3—122no—
530C2×Dic3C23×D312yes—
531C2×Dic3C23×D312yes—
532C2×Dic3C23×D312yes—
533D12—28no—
534D12—48no—
535D12—68no—
536D12C2×D12116yescomplemented
537C4×D3—28no—
538C4×D3—48no—
539C4×D3—616no—
540C4×D3—68no—
541C4×D3—68no—
542C4×D3—128no—
543Dic6—68no—
544Dic6—68no—
545Dic6—128no—
546C2×C32#54614yescomplemented
547C2×C32C23×D411yescharacteristic
548C2×C32C22×#4111yescharacteristic
549C2×C32C2×H(5,𝔽2)11yescharacteristic
550C3⋊D3—24no—
551C3×D3—28no—
552C3×D3—44no—
553C3×D3—42no—
554C24—32no—
555C24—32no—
556C24—31no—
557C24—98no—
558C24—91no—
559C24—188no—
560C24—188no—
561C24—364no—
562#41—1832no—
563C2×Q8—94no—
564C2×Q8—184no—
565C2×D4—34no—
566C2×D4—34no—
567C2×D4—38no—
568C2×D4—38no—
569C2×D4—64no—
570C2×D4—94no—
571C2×D4—98no—
572C2×D4—98no—
573C2×D4—124no—
574C2×D4—184no—
575C2×D4—1832no—
576C2×D4—188no—
577C2×D4—188no—
578C22×C4—31no—
579C22×C4—31no—
580C22×C4—31no—
581C22×C4—34no—
582C22×C4—38no—
583C22×C4—64no—
584C22×C4—98no—
585C22×C4—92no—
586C22×C4—91no—
587C22×C4—94no—
588C22×C4—124no—
589C22×C4—188no—
590C22×C4—184no—
591C22×C4C2×D3212yes—
592C22×C4C2×D3211yescharacteristic
593C4⋊C4—94no—
594C4⋊C4—98no—
595C4⋊C4C2×D3214yescomplemented
596C22⋊C4—38no—
597C22⋊C4—38no—
598C22⋊C4—94no—
599C22⋊C4—98no—
600C22⋊C4—94no—
601C22⋊C4—98no—
602C22⋊C4—98no—
603C42—34no—
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—21no—
608C22×C3—38no—
609C22×C3—64no—
610C22×C3—64no—
611C22×C3—616no—
612C22×C3—62no—
613C22×C3—64no—
614C22×C3—62no—
615C22×C3—64no—
616C22×C3—62no—
617C22×C3—64no—
618C22×C3—128no—
619C22×C3—124no—
620C22×C3C22×D1212yes—
621C22×C3C2×D3×D412yes—
622C22×C3#100412yes—
623C22×C3#100412yes—
624C22×C3D3×#4112yes—
625C22×C3D3×#4112yes—
626C22×C3C24×D311yescharacteristic
627C22×C3C24×D311yescharacteristic
628C2×D3—24no—
629C2×D3—24no—
630C2×D3—216no—
631C2×D3—22no—
632C2×D3—24no—
633C2×D3—22no—
634C2×D3—24no—
635C2×D3—22no—
636C2×D3—24no—
637C2×D3—34no—
638C2×D3—34no—
639C2×D3—48no—
640C2×D3—44no—
641C2×D3—64no—
642C2×D3—62no—
643C2×D3—62no—
644C2×D3—62no—
645C2×D3—62no—
646C2×D3—68no—
647C2×D3—68no—
648C2×D3—122no—
649C2×D3—122no—
650C2×D3—128no—
651C2×D3—1232no—
652C2×D3—1232no—
653C2×D3C22×D1218yes—
654C3×C4—24no—
655C3×C4—24no—
656C3×C4—24no—
657C3×C4—44no—
658C3×C4—62no—
659C3×C4—62no—
660C3×C4—62no—
661C3×C4C22×D1214yes—
662C3×C4C2×D3×D414yes—
663Dic3—22no—
664Dic3—22no—
665Dic3—22no—
666Dic3—64no—
667Dic3—62no—
668Dic3—64no—
669Dic3—62no—
670Dic3—124no—
671Dic3—122no—
672C32C2×#54611yescharacteristic, complemented, Sylow
673C23—38no—
674C23—34no—
675C23—34no—
676C23—32no—
677C23—64no—
678C23—64no—
679C23—62no—
680C23—64no—
681C23—62no—
682C23—64no—
683C23—62no—
684C23—64no—
685C23—94no—
686C23—92no—
687C23—1816no—
688C23—1816no—
689C23—182no—
690C23—182no—
691C23—368no—
692C23—3632no—
693C23C22×D3211yescharacteristic
694Q8—188no—
695D4—316no—
696D4—68no—
697D4—128no—
698D4—188no—
699D4—1816no—
700D4—1816no—
701C2×C4—24no—
702C2×C4—32no—
703C2×C4—32no—
704C2×C4—32no—
705C2×C4—62no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—68no—
709C2×C4—94no—
710C2×C4—92no—
711C2×C4—128no—
712C2×C4—1816no—
713C2×C4—182no—
714C2×C4—184no—
715C2×C4—188no—
716C2×C4D3×D1214yes—
717C2×C4C22×D3214yes—
718C2×C4C22×D3212yes—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—24no—
722C2×C3—21no—
723C2×C3—68no—
724C2×C3—124no—
725C2×C3—122no—
726C2×C3#555414yescomplemented
727C2×C3#561214yescomplemented
728C2×C3C23×D1211yescharacteristic
729C2×C3C22×D3×D411yescharacteristic
730C2×C3C2×#100411yescharacteristic
731C2×C3C2×#100411yescharacteristic
732C2×C3C2×D3×#4111yescharacteristic
733C2×C3C2×D3×#4111yescharacteristic
734D3—28no—
735D3—44no—
736D3—42no—
737D3—64no—
738D3—64no—
739D3—124no—
740C22—38no—
741C22—64no—
742C22—616no—
743C22—64no—
744C22—62no—
745C22—64no—
746C22—62no—
747C22—64no—
748C22—62no—
749C22—64no—
750C22—94no—
751C22—128no—
752C22—124no—
753C22—182no—
754C22—182no—
755C22—188no—
756C22—3632no—
757C22C2×D3×D1212yes—
758C22#6431312yes—
759C22#6431912yes—
760C22C23×D3211yescharacteristic
761C4—24no—
762C4—62no—
763C4—62no—
764C4—62no—
765C4—182no—
766C4—184no—
767C4C2×D3×D1214yes—
768C3—21no—
769C3C2×#555411yescharacteristic, complemented
770C3C2×#561211yescharacteristic, complemented
771C2—68no—
772C2—124no—
773C2—122no—
774C2—184no—
775C2#1059463014yesdirect product factor
776C2C22×D3×D1211yescharacteristic
777C2C2×#6431311yescharacteristic
778C2C2×#6431911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#546
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×#3802C2semidirect
2. C22×#3795C2semidirect
3. C2×#64106C2semidirect
4. C2×C3×#895C2semidirect
5. C2×C3×#893C2semidirect
6. C2×#63922C2semidirect
7. C2×D3×(C2×D3)⋊C4C2semidirect
8. C2×#63908C2semidirect
9. C2×C4×#626C2semidirect
10. C2×#63891C2semidirect
11. C2×#63860C2semidirect
12. #10594630C2direct (N × H)
17. C22×#634C22semidirect
20. C22×C3×D12C22semidirect
21. C22×C3×C4×D3C22semidirect
22. C22×C3×C4×D3C22semidirect
25. C22×#625C22semidirect
26. C22×D3×Dic3C22semidirect
28. C2×#3802C22semidirect
30. C2×#3795C22semidirect
31. C2×C32×C4⋊C4C22semidirect
33. C2×C4⋊(C3⋊Dic3)C22semidirect
34. #64106C22semidirect
35. C2×C3×(C2×D3)⋊C4C22semidirect
36. C2×C3×(C2×D3)⋊C4C22semidirect
37. C2×C3×C4×Dic3C22semidirect
38. C3×#895C22semidirect
39. C3×#893C22semidirect
40. C2×Dic3⋊Dic3C22semidirect
42. C2×(C2×D3)⋊Dic3C22semidirect
43. C2×(C2×D3)⋊Dic3C22semidirect
44. C2×(C2×D3)⋊Dic3C22semidirect
45. #63922C22semidirect
46. D3×(C2×D3)⋊C4C22semidirect
47. #63908C22semidirect
48. C4×#626C22semidirect
49. #63891C22semidirect
50. #63860C22semidirect
68. C2×#895D3semidirect
69. C2×#893D3semidirect
91. C2×#634C23semidirect
97. C2×C3×D12D4semidirect
100. C2×C3×D12C23semidirect
103. C2×C3×C4×D3C23semidirect
104. C2×C3×C4×D3C23semidirect
110. C2×#625C23semidirect
112. C2×D3×Dic3C23semidirect
115. C32×C4⋊C4C23semidirect
117. C4⋊(C3⋊Dic3)C23semidirect
118. C3×(C2×D3)⋊C4C23semidirect
119. C3×(C2×D3)⋊C4C23semidirect
120. C3×C4×Dic3C23semidirect
121. Dic3⋊Dic3C23semidirect
123. (C2×D3)⋊Dic3C23semidirect
124. (C2×D3)⋊Dic3C23semidirect
125. (C2×D3)⋊Dic3C23semidirect
151. C22×D12C2×D3semidirect
156. C22×C4×D3C2×D3semidirect
157. C22×C4×D3C2×D3semidirect
164. C2×C3×C4⋊C4C2×D3semidirect
165. C2×C3×C4⋊C4C2×D3semidirect
186. C2×(C2×D3)⋊C4C2×D3semidirect
187. C2×(C2×D3)⋊C4C2×D3semidirect
193. C2×C4×Dic3C2×D3semidirect
197. #895C2×D3semidirect
198. #893C2×D3semidirect
208. C22×C3⋊D3#41semidirect
244. C3×D12C2×D4semidirect
328. C2×D12D12semidirect
331. C2×D12C22×D3semidirect
342. C2×C4×D3C22×D3semidirect
343. C2×C4×D3C22×D3semidirect
351. C3×C4⋊C4C22×D3semidirect
352. C3×C4⋊C4C22×D3semidirect
367. (C2×D3)⋊C4C22×D3semidirect
368. (C2×D3)⋊C4C22×D3semidirect
374. C4×Dic3C22×D3semidirect
382. C2×C3⋊D3C2×#41semidirect
429. C2×C4⋊C4D32semidirect
536. D12C2×D12semidirect
546. C2×C32#546semidirect
595. C4⋊C4C2×D32semidirect
672. C32C2×#546semidirect
726. C2×C3#5554semidirect
727. C2×C3#5612semidirect
769. C3C2×#5554semidirect
770. C3C2×#5612semidirect
775. C2#10594630direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38022
C22×#37952
C2×#641062
C2×C3×#8952
C2×C3×#8932
C2×#639222
C2×D3×(C2×D3)⋊C42
C2×#639082
C2×C4×#6262
C2×#638912
C2×#638602
#105946302
C2×#56123
C2×#55543