Finite Group Databasebeta

← C2×#10595301 #11900462

Subgroups — C2×#10595301 #11900462

Order 1152.

3973 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic, complemented
2C22×C4×D32C211yesmaximal, characteristic, complemented
3C2×#64147C211yesmaximal, characteristic, complemented
4C2×C3×#938C211yesmaximal, characteristic, complemented
5C2×#63983C212yesmaximal, complemented
6C2×Dic3×#67C212yesmaximal, complemented
7C2×#63969C212yesmaximal, complemented
8C2×#63952C212yesmaximal, complemented
9#10595301C2116yesmaximal, direct product factor
10C2×#63871C211yesmaximal, characteristic, complemented
11C2×#63856C211yesmaximal, characteristic, complemented
12C2×#63841C211yesmaximal, characteristic, complemented
13C2×#5828—31nomaximal
14C2×#5606—31nomaximal
15C23×D32C2211yescharacteristic
16C22×C32×D4C2211yescharacteristic, complemented
17C22×#638C2212yes—
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C3×#67C2212yes—
20C22×C3×#67C2212yes—
21C23×C3×Dic3C2212yescomplemented
22C2×C3×#237—28no—
23C2×C3×#237C2218yescomplemented
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×C3×Dic6C2211yescharacteristic, complemented
27C22×#624C2211yescharacteristic
28C22×D3×Dic3C2211yescharacteristic
29C22×D3×Dic3C2211yescharacteristic
30C2×C4×D32—28no—
31C2×C4×D32C2218yescomplemented
32C2×#3757C2212yescomplemented
33#64147C2218yescomplemented
34C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
35C2×C3×#217C2212yescomplemented
36C3×#938C2218yescomplemented
37C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
38#63983C22116yescomplemented
39Dic3×#67C22116yescomplemented
40#63969C22116yescomplemented
41C2×#3724C2212yescomplemented
42C2×Dic3⋊Dic3C2212yescomplemented
43C2×#3722C2212yes—
44C2×(C2×D3)⋊Dic3C2212yes—
45C2×(C2×D3)⋊Dic3C2212yes—
46C2×Dic32C2212yescomplemented
47#63952C22116yescomplemented
48#63871C2218yescomplemented
49#63856C2218yescomplemented
50#63841C2218yescomplemented
51C22×C3×#41—31no—
52C22×#237D311yescharacteristic, complemented
53C23×C4×D3—31no—
54C23×C4×D3—31no—
55C2×C3×#121—31no—
56#5828—316no—
57C2×#946—31no—
58C2×#946—31no—
59C2×#938—31no—
60C2×#938—31no—
61C2×#938—61no—
62C2×#938D311yescharacteristic, complemented
63C2×#937—32no—
64C2×#937—32no—
65C2×#935—32no—
66C2×D4×Dic3—32no—
67C2×C4×#67—32no—
68C2×C4×#67—32no—
69C2×#926—31no—
70C2×#924—31no—
71#5606—316no—
72C2×#897—31no—
73C2×#892—31no—
74C2×#883—32no—
75C2×#67⋊C4—32no—
76C24×C32C2312yes—
77C23×C3⋊D3C2311yescharacteristic
78C23×C3×D3C2311yescharacteristic
79C23×C3×D3C2311yescharacteristic
80C22×D32—24no—
81C22×D32—24no—
82C22×D32—24no—
83C22×D32C2314yes—
84C2×C32×D4—24no—
85C2×C32×D4C2314yescomplemented
86C22×C32×C4C2311yescharacteristic
87C2×#638—28no—
88C2×#638C2318yes—
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2312yes—
91C2×C4×C3⋊D3—24no—
92C2×C4×C3⋊D3C2314yes—
93C2×C3×#67—28no—
94C2×C3×#67—28no—
95C2×C3×#67C2318yes—
96C2×C3×#67C2318yes—
97C22×C3×Dic3—28no—
98C22×C3×Dic3C2312yes—
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2312yes—
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2318yescomplemented
103C3×#237—232no—
104C2×C3×C4×D3—24no—
105C2×C3×C4×D3D418yescomplemented
106C2×C3×C4×D3C2314yes—
107C2×C3×C4×D3C2314yes—
108C2×C3×Dic6—24no—
109C2×C3×Dic6C2314yescomplemented
110C2×#624—24no—
111C2×#624C2314yes—
112C2×D3×Dic3—24no—
113C2×D3×Dic3—24no—
114C2×D3×Dic3C2314yes—
115C2×D3×Dic3C2314yes—
116C4×D32—232no—
117#3757C2318yescomplemented
118C4⋊(C3⋊Dic3)C2314yescomplemented
119C3×#217C2318yescomplemented
120C3×C4⋊Dic3C2314yescomplemented
121#3724C2318yescomplemented
122Dic3⋊Dic3C2318yescomplemented
123#3722C2318yes—
124(C2×D3)⋊Dic3C2318yes—
125(C2×D3)⋊Dic3C2318yes—
126Dic32C2318yescomplemented
127C2×#525—91noSylow
128C24×D3—31no—
129C24×D3—31no—
130C2×C3×#41—38no—
131C2×C3×#41—68no—
132C22×C3×Q8—31no—
133C22×C3×D4—21no—
134C22×C3×D4—32no—
135C22×C3×D4—32no—
136C22×C3×D4C2×D311yescharacteristic, complemented
137C22×C3×D4C2×D311yescharacteristic, complemented
138C23×C3×C4—31no—
139C23×C3×C4—32no—
140C23×C3×C4—31no—
141C22×#67—32no—
142C22×#67—32no—
143C22×#67—62no—
144C22×#67C2×D312yes—
145C22×#67C2×D312yes—
146C23×Dic3—31no—
147C23×Dic3—31no—
148C23×Dic3C2×D312yescomplemented
149C2×#237—28no—
150C2×#237C2×D318yescomplemented
151C22×C4×D3—31no—
152C22×C4×D3—31no—
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C22×C4×D3—31no—
156C22×C4×D3—31no—
157C22×C4×D3—38no—
158C22×C4×D3—38no—
159C22×C4×D3—61no—
160C22×C4×D3—68no—
161C22×C4×D3—68no—
162C22×C4×D3C2×D311yescharacteristic
163C22×C4×D3C2×D311yescharacteristic
164C22×Dic6C2×D311yescharacteristic, complemented
165C3×#121—38no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C22⋊C4—32no—
168C2×#217—32no—
169C2×#217—32no—
170C2×#217—32no—
171C2×#217—32no—
172C2×#217—62no—
173C2×#217C2×D312yescomplemented
174#946—38no—
175#946—38no—
176#938—38no—
177#938—38no—
178#938—68no—
179#938C2×D318yescomplemented
180#937—316no—
181#937—316no—
182#935—316no—
183D4×Dic3—316no—
184C4×#67—316no—
185C4×#67—316no—
186C2×(C2×D3)⋊C4—32no—
187C2×(C2×D3)⋊C4—32no—
188C2×(C2×D3)⋊C4—32no—
189C2×(C2×D3)⋊C4—32no—
190#926—38no—
191C2×C4⋊Dic3—31no—
192C2×C4⋊Dic3—31no—
193C2×C4⋊Dic3—32no—
194C2×C4⋊Dic3—61no—
195C2×C4⋊Dic3C2×D311yescharacteristic, complemented
196#924—38no—
197C2×Dic3⋊C4—32no—
198C2×Dic3⋊C4—32no—
199C2×Dic3⋊C4—32no—
200C2×C4×Dic3—32no—
201C2×C4×Dic3—32no—
202#897—38no—
203#892—38no—
204#883—316no—
205#67⋊C4—316no—
206C23×C32—24no—
207C23×C32—24no—
208C23×C32—24no—
209C23×C32C2414yes—
210C23×C32C2411yescharacteristic
211C22×C3⋊D3—22no—
212C22×C3⋊D3—22no—
213C22×C3⋊D3#4114yescomplemented
214C22×C3⋊D3C2412yes—
215C22×C3×D3—22no—
216C22×C3×D3—22no—
217C22×C3×D3—22no—
218C22×C3×D3—22no—
219C22×C3×D3C2×D414yes—
220C22×C3×D3#4114yescomplemented
221C22×C3×D3C2412yes—
222C22×C3×D3C2412yes—
223C2×D32—232no—
224C2×D32—28no—
225C2×D32—28no—
226C2×D32—28no—
227C32×D4—28no—
228C2×C32×C4C2×D414yes—
229C2×C32×C4C2412yes—
230#638—216no—
231C2×C3⋊Dic3—22no—
232C2×C3⋊Dic3—24no—
233C2×C3⋊Dic3C2414yes—
234C2×C3⋊Dic3C2412yes—
235C4×C3⋊D3—28no—
236C3×#67—216no—
237C3×#67—216no—
238C2×C3×Dic3—22no—
239C2×C3×Dic3—24no—
240C2×C3×Dic3—24no—
241C2×C3×Dic3—216no—
242C2×C3×Dic3C2×D414yes—
243C2×C3×Dic3C2414yes—
244C2×C3×Dic3C2414yes—
245C2×C3×Dic3C2412yes—
246C2×C3×Dic3C2412yes—
247C3×C4×D3—28no—
248C3×C4×D3C2×D4116yescomplemented
249C3×Dic6—28no—
250#624—28no—
251D3×Dic3—28no—
252D3×Dic3—28no—
253C22×#41—31no—
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—91no—
265C24×C3—22no—
266C24×C3—31no—
267C24×C3—31no—
268C24×C3C22×D312yes—
269C24×C3C22×D312yes—
270C23×D3—31no—
271C23×D3—31no—
272C23×D3—34no—
273C23×D3—34no—
274C23×D3—61no—
275C23×D3—64no—
276C23×D3—64no—
277C23×D3—64no—
278C23×D3—64no—
279C23×D3—64no—
280C23×D3—64no—
281C23×D3C22×D311yescharacteristic
282C23×D3C22×D311yescharacteristic
283C3×#41—632no—
284C2×C3×Q8—34no—
285C2×C3×Q8—64no—
286C2×C3×D4—24no—
287C2×C3×D4—24no—
288C2×C3×D4—24no—
289C2×C3×D4—38no—
290C2×C3×D4—38no—
291C2×C3×D4—44no—
292C2×C3×D4—68no—
293C2×C3×D4—68no—
294C2×C3×D4C22×D314yescomplemented
295C2×C3×D4C22×D314yescomplemented
296C22×C3×C4—21no—
297C22×C3×C4—31no—
298C22×C3×C4—38no—
299C22×C3×C4—34no—
300C22×C3×C4—32no—
301C22×C3×C4—32no—
302C22×C3×C4—31no—
303C22×C3×C4—38no—
304C22×C3×C4—34no—
305C22×C3×C4—68no—
306C22×C3×C4—64no—
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C2×#67—28no—
310C2×#67—28no—
311C2×#67—38no—
312C2×#67—38no—
313C2×#67—68no—
314C2×#67—68no—
315C2×#67—68no—
316C2×#67—128no—
317C2×#67C22×D318yes—
318C2×#67C22×D318yes—
319C22×Dic3—28no—
320C22×Dic3—32no—
321C22×Dic3—32no—
322C22×Dic3—31no—
323C22×Dic3—31no—
324C22×Dic3—34no—
325C22×Dic3—34no—
326C22×Dic3—62no—
327C22×Dic3—61no—
328C22×Dic3—64no—
329C22×Dic3—64no—
330C22×Dic3C22×D312yes—
331C22×Dic3C22×D311yescharacteristic
332C22×Dic3C22×D312yes—
333C22×Dic3C22×D311yescharacteristic
334C22×Dic3C22×D318yescomplemented
335#237—232no—
336C2×C4×D3—24no—
337C2×C4×D3—34no—
338C2×C4×D3—34no—
339C2×C4×D3—34no—
340C2×C4×D3—34no—
341C2×C4×D3—34no—
342C2×C4×D3—34no—
343C2×C4×D3—64no—
344C2×C4×D3—632no—
345C2×C4×D3—64no—
346C2×C4×D3—64no—
347C2×C4×D3—64no—
348C2×C4×D3—64no—
349C2×C4×D3—64no—
350C2×C4×D3—64no—
351C2×C4×D3—632no—
352C2×C4×D3—124no—
353C2×C4×D3#6718yescomplemented
354C2×C4×D3C22×D314yes—
355C2×C4×D3C22×D314yes—
356C2×Dic6—24no—
357C2×Dic6C22×D314yescomplemented
358C3×C4⋊C4—34no—
359C3×C22⋊C4—38no—
360#217—38no—
361#217—38no—
362#217—38no—
363#217—38no—
364#217—68no—
365#217C22×D318yescomplemented
366(C2×D3)⋊C4—38no—
367(C2×D3)⋊C4—38no—
368(C2×D3)⋊C4—38no—
369(C2×D3)⋊C4—38no—
370C4⋊Dic3—34no—
371C4⋊Dic3—34no—
372C4⋊Dic3—38no—
373C4⋊Dic3—64no—
374C4⋊Dic3C22×D314yescomplemented
375Dic3⋊C4—38no—
376Dic3⋊C4—38no—
377Dic3⋊C4—38no—
378C4×Dic3—38no—
379C4×Dic3—38no—
380C22×C32—24no—
381C22×C32—24no—
382C22×C32—24no—
383C22×C32—48no—
384C22×C32C22×D412yes—
385C22×C32C2×#4112yes—
386C22×C32C2×#4112yes—
387C22×C32C2511yescharacteristic
388C2×C3⋊D3—28no—
389C2×C3⋊D3—22no—
390C2×C3⋊D3—22no—
391C2×C3⋊D3C2×#4114yescomplemented
392C2×C3×D3—28no—
393C2×C3×D3—28no—
394C2×C3×D3—22no—
395C2×C3×D3—22no—
396C2×C3×D3—22no—
397C2×C3×D3—22no—
398C2×C3×D3C22×D414yes—
399C2×C3×D3C2×#4114yescomplemented
400D32—232no—
401C32×C4C22×D414yes—
402C3⋊Dic3—22no—
403C3⋊Dic3—24no—
404C3×Dic3—22no—
405C3×Dic3—24no—
406C3×Dic3—24no—
407C3×Dic3C22×D414yes—
408C25—91no—
409C2×#41—38no—
410C2×#41—68no—
411C22×Q8—31no—
412C22×D4—32no—
413C22×D4—32no—
414C22×D4—92no—
415C22×D4D3211yescharacteristic, complemented
416C23×C4—31no—
417C23×C4—32no—
418C23×C4—31no—
419C23×C4—91no—
420C23×C4—98no—
421C23×C4—91no—
422C23×C4—91no—
423C23×C4—91no—
424C23×C4—188no—
425#123—916no—
426C22⋊Q8—98no—
427C22⋊Q8—98no—
428#121—38no—
429#121—98no—
430#120—916no—
431C4×D4—916no—
432C4×D4—916no—
433#117—98no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—92no—
436C2×C4⋊C4—92no—
437C2×C4⋊C4—91no—
438C2×C22⋊C4—32no—
439C2×C22⋊C4—92no—
440C2×C22⋊C4—92no—
441C2×C22⋊C4—92no—
442C2×C22⋊C4—92no—
443C2×C42—92no—
444C23×C3—24no—
445C23×C3—24no—
446C23×C3—24no—
447C23×C3—24no—
448C23×C3—24no—
449C23×C3—24no—
450C23×C3—24no—
451C23×C3—21no—
452C23×C3—34no—
453C23×C3—34no—
454C23×C3—32no—
455C23×C3—32no—
456C23×C3—44no—
457C23×C3—44no—
458C23×C3—44no—
459C23×C3—62no—
460C23×C3—62no—
461C23×C3—62no—
462C23×C3—62no—
463C23×C3C23×D314yes—
464C23×C3C23×D314yes—
465C23×C3C23×D311yescharacteristic
466C23×C3C23×D311yescharacteristic
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—22no—
470C22×D3—22no—
471C22×D3—34no—
472C22×D3—34no—
473C22×D3—32no—
474C22×D3—32no—
475C22×D3—64no—
476C22×D3—62no—
477C22×D3—68no—
478C22×D3—68no—
479C22×D3—68no—
480C22×D3—68no—
481C22×D3—632no—
482C22×D3—632no—
483C22×D3—62no—
484C22×D3—62no—
485C22×D3—62no—
486C22×D3—62no—
487C22×D3—68no—
488C22×D3—68no—
489C22×D3—122no—
490C22×D3—122no—
491C22×D3#23714yescomplemented
492C22×D3C2×#6714yes—
493C22×D3C23×D312yes—
494C22×D3C23×D312yes—
495C3×Q8—68no—
496C3×D4—28no—
497C3×D4—28no—
498C3×D4—48no—
499C3×D4—616no—
500C3×D4—616no—
501C2×C3×C4—22no—
502C2×C3×C4—24no—
503C2×C3×C4—34no—
504C2×C3×C4—32no—
505C2×C3×C4—316no—
506C2×C3×C4—34no—
507C2×C3×C4—34no—
508C2×C3×C4—32no—
509C2×C3×C4—616no—
510C2×C3×C4—64no—
511C2×C3×C4—64no—
512C2×C3×C4—62no—
513C2×C3×C4—68no—
514C2×C3×C4D3×D414yes—
515C2×C3×C4C2×#6714yes—
516C2×C3×C4C23×D312yes—
517C2×C3×C4C23×D312yes—
518#67—216no—
519#67—216no—
520#67—616no—
521#67—616no—
522#67—1216no—
523C2×Dic3—22no—
524C2×Dic3—24no—
525C2×Dic3—24no—
526C2×Dic3—216no—
527C2×Dic3—34no—
528C2×Dic3—34no—
529C2×Dic3—32no—
530C2×Dic3—32no—
531C2×Dic3—64no—
532C2×Dic3—62no—
533C2×Dic3—68no—
534C2×Dic3—62no—
535C2×Dic3—64no—
536C2×Dic3—64no—
537C2×Dic3—62no—
538C2×Dic3—68no—
539C2×Dic3—122no—
540C2×Dic3—124no—
541C2×Dic3C2×#6714yes—
542C2×Dic3C23×D314yes—
543C2×Dic3C23×D312yes—
544C2×Dic3C23×D314yes—
545C2×Dic3C23×D312yes—
546C4×D3—28no—
547C4×D3—68no—
548C4×D3—68no—
549C4×D3—68no—
550C4×D3—68no—
551C4×D3—68no—
552C4×D3—68no—
553C4×D3—128no—
554C4×D3C2×#67116yescomplemented
555Dic6—28no—
556C2×C32—44no—
557C2×C32#52514yescomplemented
558C2×C32C23×D411yescharacteristic
559C2×C32C22×#4111yescharacteristic
560C2×C32C22×#4111yescharacteristic
561C3⋊D3—24no—
562C3×D3—24no—
563C3×D3—24no—
564C24—31no—
565C24—31no—
566C24—94no—
567C24—91no—
568C24—184no—
569C24—184no—
570C24—184no—
571C24C2×D3212yes—
572#41—632no—
573C2×Q8—34no—
574C2×Q8—64no—
575C2×D4—24no—
576C2×D4—38no—
577C2×D4—38no—
578C2×D4—68no—
579C2×D4—68no—
580C2×D4—98no—
581C2×D4—188no—
582C2×D4C2×D3214yescomplemented
583C22×C4—31no—
584C22×C4—34no—
585C22×C4—38no—
586C22×C4—38no—
587C22×C4—32no—
588C22×C4—31no—
589C22×C4—32no—
590C22×C4—34no—
591C22×C4—68no—
592C22×C4—64no—
593C22×C4—94no—
594C22×C4—94no—
595C22×C4—94no—
596C22×C4—92no—
597C22×C4—91no—
598C22×C4—94no—
599C22×C4—184no—
600C22×C4—1832no—
601C22×C4—184no—
602C22×C4—184no—
603C22×C4—184no—
604C22×C4C2×D3211yescharacteristic
605C4⋊C4—34no—
606C4⋊C4—98no—
607C4⋊C4—98no—
608C4⋊C4—94no—
609C22⋊C4—38no—
610C22⋊C4—98no—
611C22⋊C4—98no—
612C22⋊C4—98no—
613C22⋊C4—98no—
614C42—98no—
615C22×C3—24no—
616C22×C3—24no—
617C22×C3—24no—
618C22×C3—24no—
619C22×C3—24no—
620C22×C3—24no—
621C22×C3—22no—
622C22×C3—22no—
623C22×C3—22no—
624C22×C3—21no—
625C22×C3—34no—
626C22×C3—34no—
627C22×C3—44no—
628C22×C3—44no—
629C22×C3—44no—
630C22×C3—48no—
631C22×C3—48no—
632C22×C3—62no—
633C22×C3—62no—
634C22×C3—62no—
635C22×C3—62no—
636C22×C3—68no—
637C22×C3—68no—
638C22×C3—88no—
639C22×C3C2×D3×D412yes—
640C22×C3C2×#23712yes—
641C22×C3D3×#4112yes—
642C22×C3D3×#4112yes—
643C22×C3D3×#4112yes—
644C22×C3C22×#6712yes—
645C22×C3C24×D311yescharacteristic
646C22×C3C24×D311yescharacteristic
647C2×D3—22no—
648C2×D3—22no—
649C2×D3—22no—
650C2×D3—22no—
651C2×D3—28no—
652C2×D3—28no—
653C2×D3—34no—
654C2×D3—34no—
655C2×D3—64no—
656C2×D3—632no—
657C2×D3—632no—
658C2×D3—62no—
659C2×D3—62no—
660C2×D3—62no—
661C2×D3—62no—
662C2×D3—68no—
663C2×D3—68no—
664C2×D3—122no—
665C2×D3—122no—
666C2×D3—128no—
667C2×D3C2×#23714yescomplemented
668C2×D3C22×#6714yes—
669C3×C4—24no—
670C3×C4—34no—
671C3×C4—64no—
672C3×C4—64no—
673C3×C4—62no—
674C3×C4C2×D3×D414yes—
675C3×C4C22×#6714yes—
676Dic3—22no—
677Dic3—24no—
678Dic3—24no—
679Dic3—62no—
680Dic3—64no—
681Dic3—64no—
682Dic3—62no—
683Dic3—122no—
684Dic3—124no—
685Dic3C22×#6714yes—
686C32C2×#52511yescharacteristic, complemented, Sylow
687C23—24no—
688C23—24no—
689C23—24no—
690C23—34no—
691C23—34no—
692C23—32no—
693C23—32no—
694C23—62no—
695C23—62no—
696C23—62no—
697C23—62no—
698C23—94no—
699C23—92no—
700C23—188no—
701C23—188no—
702C23—188no—
703C23—1832no—
704C23—182no—
705C23—182no—
706C23C22×D3214yes—
707C23C22×D3211yescharacteristic
708Q8—68no—
709D4—28no—
710D4—616no—
711D4—616no—
712D4—1816no—
713C2×C4—34no—
714C2×C4—32no—
715C2×C4—316no—
716C2×C4—34no—
717C2×C4—32no—
718C2×C4—34no—
719C2×C4—616no—
720C2×C4—64no—
721C2×C4—62no—
722C2×C4—64no—
723C2×C4—68no—
724C2×C4—94no—
725C2×C4—92no—
726C2×C4—188no—
727C2×C4—188no—
728C2×C4—188no—
729C2×C4—184no—
730C2×C4—182no—
731C2×C4—188no—
732C2×C4D3×#6714yes—
733C2×C4C22×D3212yes—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—24no—
738C2×C3—44no—
739C2×C3—44no—
740C2×C3—64no—
741C2×C3—64no—
742C2×C3—84no—
743C2×C3#560614yescomplemented
744C2×C3#582814yescomplemented
745C2×C3C22×D3×D411yescharacteristic
746C2×C3C22×#23711yescharacteristic
747C2×C3C2×D3×#4111yescharacteristic
748C2×C3C2×D3×#4111yescharacteristic
749C2×C3C2×D3×#4111yescharacteristic
750C2×C3C23×#6711yescharacteristic
751D3—24no—
752D3—24no—
753D3—64no—
754D3—64no—
755D3—124no—
756C22—24no—
757C22—24no—
758C22—24no—
759C22—34no—
760C22—34no—
761C22—48no—
762C22—62no—
763C22—62no—
764C22—62no—
765C22—62no—
766C22—68no—
767C22—68no—
768C22—94no—
769C22—1832no—
770C22—182no—
771C22—182no—
772C22—188no—
773C22D3×#23712yes—
774C22#6431212yes—
775C22C2×D3×#6712yes—
776C22C23×D3211yescharacteristic
777C4—34no—
778C4—64no—
779C4—62no—
780C4—64no—
781C4—184no—
782C4—182no—
783C4C2×D3×#6714yes—
784C3—21no—
785C3C2×#560611yescharacteristic, complemented
786C3C2×#582811yescharacteristic, complemented
787C2—44no—
788C2—64no—
789C2—64no—
790C2—184no—
791C2#1059530114yesdirect product factor
792C2C2×D3×#23711yescharacteristic
793C2C2×#6431211yescharacteristic
794C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#237C2semidirect
2. C22×C4×D32C2semidirect
3. C2×#64147C2semidirect
4. C2×C3×#938C2semidirect
5. C2×#63983C2semidirect
6. C2×Dic3×#67C2semidirect
7. C2×#63969C2semidirect
8. C2×#63952C2semidirect
9. #10595301C2direct (N × H)
10. C2×#63871C2semidirect
11. C2×#63856C2semidirect
12. C2×#63841C2semidirect
16. C22×C32×D4C22semidirect
21. C23×C3×Dic3C22semidirect
23. C2×C3×#237C22semidirect
26. C22×C3×Dic6C22semidirect
31. C2×C4×D32C22semidirect
32. C2×#3757C22semidirect
33. #64147C22semidirect
34. C2×C4⋊(C3⋊Dic3)C22semidirect
35. C2×C3×#217C22semidirect
36. C3×#938C22semidirect
37. C2×C3×C4⋊Dic3C22semidirect
38. #63983C22semidirect
39. Dic3×#67C22semidirect
40. #63969C22semidirect
41. C2×#3724C22semidirect
42. C2×Dic3⋊Dic3C22semidirect
46. C2×Dic32C22semidirect
47. #63952C22semidirect
48. #63871C22semidirect
49. #63856C22semidirect
50. #63841C22semidirect
52. C22×#237D3semidirect
62. C2×#938D3semidirect
85. C2×C32×D4C23semidirect
102. C22×C3×Dic3C23semidirect
105. C2×C3×C4×D3D4semidirect
109. C2×C3×Dic6C23semidirect
117. #3757C23semidirect
118. C4⋊(C3⋊Dic3)C23semidirect
119. C3×#217C23semidirect
120. C3×C4⋊Dic3C23semidirect
121. #3724C23semidirect
122. Dic3⋊Dic3C23semidirect
126. Dic32C23semidirect
136. C22×C3×D4C2×D3semidirect
137. C22×C3×D4C2×D3semidirect
148. C23×Dic3C2×D3semidirect
150. C2×#237C2×D3semidirect
164. C22×Dic6C2×D3semidirect
173. C2×#217C2×D3semidirect
179. #938C2×D3semidirect
195. C2×C4⋊Dic3C2×D3semidirect
213. C22×C3⋊D3#41semidirect
220. C22×C3×D3#41semidirect
248. C3×C4×D3C2×D4semidirect
294. C2×C3×D4C22×D3semidirect
295. C2×C3×D4C22×D3semidirect
334. C22×Dic3C22×D3semidirect
353. C2×C4×D3#67semidirect
357. C2×Dic6C22×D3semidirect
365. #217C22×D3semidirect
374. C4⋊Dic3C22×D3semidirect
391. C2×C3⋊D3C2×#41semidirect
399. C2×C3×D3C2×#41semidirect
415. C22×D4D32semidirect
491. C22×D3#237semidirect
554. C4×D3C2×#67semidirect
557. C2×C32#525semidirect
582. C2×D4C2×D32semidirect
667. C2×D3C2×#237semidirect
686. C32C2×#525semidirect
743. C2×C3#5606semidirect
744. C2×C3#5828semidirect
785. C3C2×#5606semidirect
786. C3C2×#5828semidirect
791. C2#10595301direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C22×C4×D322
C2×#641472
C2×C3×#9382
C2×#639832
C2×Dic3×#672
C2×#639692
C2×#639522
#105953012
C2×#638712
C2×#638562
C2×#638412
C2×#58283
C2×#56063