Finite Group Databasebeta

← C2×#10594889 #11902437

Subgroups — C2×#10594889 #11902437

Order 1152.

4013 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×D12C211yesmaximal, characteristic, complemented
2C22×#3796C211yesmaximal, characteristic, complemented
3C2×C4×#638C211yesmaximal, characteristic, complemented
4C2×C3×#924C211yesmaximal, characteristic, complemented
5C2×#63977C212yesmaximal, complemented
6C2×D3×#217C212yesmaximal, complemented
7C2×#63916C211yesmaximal, characteristic, complemented
8C2×#63898C211yesmaximal, characteristic, complemented
9C2×#63886C212yesmaximal, complemented
10#10594889C2116yesmaximal, direct product factor
11C2×#63884C212yesmaximal, complemented
12C2×#63863C211yesmaximal, characteristic, complemented
13C2×#5806—31nomaximal
14C2×#5630—31nomaximal
15C24×C3×D3C2212yes—
16C23×C32×C4C2211yescharacteristic
17C22×#638C2211yescharacteristic
18C22×C4×C3⋊D3C2211yescharacteristic, complemented
19C22×C3×D12—28no—
20C22×C3×D12C2211yescharacteristic
21C22×C3×D12C2212yes—
22C22×C3×D12C2211yescharacteristic
23C22×C3×D12C2218yescomplemented
24C22×C3×Dic6C2211yescharacteristic, complemented
25C22×#626C2212yescomplemented
26C22×#626C2212yescomplemented
27C22×D3×Dic3C2212yescomplemented
28C22×D3×Dic3C2212yescomplemented
29C2×#3796—28no—
30C2×#3796C2218yescomplemented
31C2×#3757C2211yescharacteristic
32C4×#638C2218yescomplemented
33C2×#3752C2211yescharacteristic, complemented
34C2×#3750C2211yescharacteristic, complemented
35C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
36C2×C3×#217C2212yes—
37C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
38C3×#924C2218yescomplemented
39C2×C3×Dic3⋊C4C2212yescomplemented
40#63977C22116yescomplemented
41D3×#217C22116yescomplemented
42C2×(C2×D3)⋊Dic3C2212yescomplemented
43C2×(C2×D3)⋊Dic3C2212yescomplemented
44C2×(C2×D3)⋊Dic3C2212yescomplemented
45C2×(C2×D3)⋊Dic3C2212yescomplemented
46#63916C2218yescomplemented
47#63898C2218yescomplemented
48#63886C22116yescomplemented
49#63884C22116yescomplemented
50#63863C2218yescomplemented
51C23×C3×D4—31no—
52C22×#239—31no—
53C22×#237—31no—
54C23×D12D311yescharacteristic, complemented
55C2×C3×C22⋊Q8—31no—
56C2×#953—32no—
57C22×#217—32no—
58C2×#947—31no—
59#5806—316no—
60C2×#939—32no—
61C2×#938—31no—
62C2×#936—31no—
63C2×#935—32no—
64C2×D4×Dic3—31no—
65C2×C4×#67—31no—
66C2×C4×#67—31no—
67C2×C4×#67—61no—
68C2×#924D311yescharacteristic, complemented
69#5630—316no—
70C2×#895—32no—
71C2×#895—31no—
72C2×#894—32no—
73C2×#893—31no—
74C2×#882—32no—
75C2×D3×C22⋊C4—32no—
76C24×C32C2311yescharacteristic
77C23×C3⋊D3C2311yescharacteristic
78C23×C3×D3—28no—
79C23×C3×D3—28no—
80C23×C3×D3—44no—
81C23×C3×D3C2312yes—
82C23×C3×D3C2318yes—
83C23×C3×D3C2312yes—
84C22×C32×C4—24no—
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2314yes—
87C22×C32×C4C2311yescharacteristic
88C2×#638—24no—
89C2×#638C2314yes—
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C2×C4×C3⋊D3—24no—
94C2×C4×C3⋊D3C2314yescomplemented
95C22×C3×Dic3C2312yes—
96C22×C3×Dic3C2312yes—
97C2×C3×D12—28no—
98C2×C3×D12—24no—
99C2×C3×D12—232no—
100C2×C3×D12D418yescomplemented
101C2×C3×D12C2314yes—
102C2×C3×D12C2318yes—
103C2×C3×D12C2314yes—
104C2×C3×Dic6—24no—
105C2×C3×Dic6C2314yescomplemented
106C2×#626—28no—
107C2×#626—44no—
108C2×#626C2318yescomplemented
109C2×#626C2318yescomplemented
110C2×D3×Dic3—28no—
111C2×D3×Dic3—44no—
112C2×D3×Dic3C2318yescomplemented
113C2×D3×Dic3C2318yescomplemented
114#3796—232no—
115#3757C2314yes—
116#3752C2314yescomplemented
117#3750C2314yescomplemented
118C4×C3⋊Dic3C2314yescomplemented
119C3×#217C2318yes—
120C3×C4⋊Dic3C2314yescomplemented
121C3×Dic3⋊C4C2318yescomplemented
122(C2×D3)⋊Dic3C2318yescomplemented
123(C2×D3)⋊Dic3C2318yescomplemented
124(C2×D3)⋊Dic3C2318yescomplemented
125(C2×D3)⋊Dic3C2318yescomplemented
126C2×#546—91noSylow
127C25×C3—32no—
128C24×D3C2×D312yes—
129C22×C3×Q8—31no—
130C22×C3×D4—31no—
131C22×C3×D4—32no—
132C22×C3×D4—31no—
133C22×C3×D4—38no—
134C22×C3×D4—68no—
135C23×C3×C4—21no—
136C23×C3×C4C2×D311yescharacteristic
137C23×C3×C4C2×D311yescharacteristic
138C22×#67—31no—
139C22×#67—31no—
140C22×#67—32no—
141C22×#67—32no—
142C22×#67—61no—
143C23×Dic3—32no—
144C23×Dic3—32no—
145C2×#239—38no—
146C2×#239—68no—
147C2×#237—38no—
148C2×#237—68no—
149C22×D12—28no—
150C22×D12—32no—
151C22×D12—32no—
152C22×D12C2×D312yes—
153C22×D12C2×D311yescharacteristic
154C22×D12C2×D311yescharacteristic
155C22×D12C2×D318yescomplemented
156C22×C4×D3—32no—
157C22×C4×D3—31no—
158C22×C4×D3—31no—
159C22×C4×D3—32no—
160C22×C4×D3—61no—
161C22×Dic6C2×D311yescharacteristic, complemented
162C3×C22⋊Q8—38no—
163C2×C3×C4⋊C4—32no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C22⋊C4—32no—
166#953—316no—
167C2×#217—31no—
168C2×#217—31no—
169C2×#217—32no—
170C2×#217—32no—
171C2×#217—32no—
172C2×#217—32no—
173C2×#217—316no—
174C2×#217—61no—
175C2×#217C2×D312yes—
176#947—38no—
177#939—316no—
178#938—38no—
179#936—38no—
180#935—316no—
181D4×Dic3—38no—
182C4×#67—38no—
183C4×#67—38no—
184C4×#67—68no—
185C2×(C2×D3)⋊C4—32no—
186C2×(C2×D3)⋊C4—32no—
187C2×(C2×D3)⋊C4—32no—
188C2×(C2×D3)⋊C4—32no—
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—61no—
192C2×C4⋊Dic3C2×D311yescharacteristic, complemented
193#924C2×D318yescomplemented
194C2×Dic3⋊C4—31no—
195C2×Dic3⋊C4—31no—
196C2×Dic3⋊C4—61no—
197C2×Dic3⋊C4C2×D312yescomplemented
198C2×C4×Dic3—31no—
199C2×C4×Dic3—31no—
200C2×C4×Dic3—61no—
201#895—316no—
202#895—38no—
203#894—316no—
204#893—38no—
205#882—316no—
206D3×C22⋊C4—316no—
207C23×C32—22no—
208C23×C32—22no—
209C23×C32#4114yescomplemented
210C23×C32C2412yes—
211C23×C32C2411yescharacteristic
212C22×C3⋊D3—22no—
213C22×C3⋊D3—22no—
214C22×C3⋊D3—22no—
215C22×C3⋊D3C2412yes—
216C22×C3×D3—24no—
217C22×C3×D3—24no—
218C22×C3×D3—24no—
219C22×C3×D3—24no—
220C22×C3×D3—216no—
221C22×C3×D3—24no—
222C22×C3×D3—216no—
223C22×C3×D3—48no—
224C22×C3×D3—432no—
225C22×C3×D3C2×D418yes—
226C22×C3×D3C2414yes—
227C22×C3×D3C2414yes—
228C2×C32×C4—22no—
229C2×C32×C4—28no—
230C2×C32×C4C2×D414yes—
231C2×C32×C4C2412yes—
232C2×C32×C4C2412yes—
233#638—28no—
234C2×C3⋊Dic3—22no—
235C2×C3⋊Dic3—22no—
236C2×C3⋊Dic3—22no—
237C2×C3⋊Dic3C2412yes—
238C2×C3⋊Dic3C2412yes—
239C2×C3⋊Dic3C2412yes—
240C4×C3⋊D3—28no—
241C2×C3×Dic3—24no—
242C2×C3×Dic3—24no—
243C2×C3×Dic3C2414yes—
244C2×C3×Dic3C2414yes—
245C3×D12—216no—
246C3×D12—28no—
247C3×D12C2×D4116yescomplemented
248C3×Dic6—28no—
249#626—216no—
250#626—48no—
251D3×Dic3—216no—
252D3×Dic3—48no—
253C22×#41—91no—
254C23×D4—31no—
255#546—916no—
256C2×#124—91no—
257C2×#123—92no—
258C2×C22⋊Q8—31no—
259C2×#121—91no—
260C2×#121—92no—
261C2×#120—92no—
262C2×C4×D4—91no—
263C2×C4×D4—91no—
264C22×C22⋊C4—92no—
265C24×C3—21no—
266C24×C3—32no—
267C24×C3—32no—
268C24×C3—38no—
269C24×C3—68no—
270C24×C3—68no—
271C24×C3—124no—
272C24×C3C22×D311yescharacteristic
273C24×C3C22×D311yescharacteristic
274C23×D3—28no—
275C23×D3—28no—
276C23×D3—31no—
277C23×D3—31no—
278C23×D3—44no—
279C23×D3—61no—
280C23×D3C22×D312yes—
281C23×D3C22×D318yes—
282C23×D3C22×D312yes—
283C2×C3×Q8—34no—
284C2×C3×Q8—64no—
285C2×C3×D4—38no—
286C2×C3×D4—34no—
287C2×C3×D4—38no—
288C2×C3×D4—34no—
289C2×C3×D4—632no—
290C2×C3×D4—68no—
291C2×C3×D4—64no—
292C22×C3×C4—24no—
293C22×C3×C4—24no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—24no—
297C22×C3×C4—32no—
298C22×C3×C4—32no—
299C22×C3×C4—44no—
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D314yes—
303C22×C3×C4C22×D314yes—
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C2×#67—34no—
307C2×#67—34no—
308C2×#67—38no—
309C2×#67—38no—
310C2×#67—64no—
311C2×#67—68no—
312C2×#67—68no—
313C2×#67—64no—
314C2×#67—64no—
315C2×#67—124no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—31no—
319C22×Dic3—31no—
320C22×Dic3—31no—
321C22×Dic3—31no—
322C22×Dic3—38no—
323C22×Dic3—38no—
324C22×Dic3—61no—
325C22×Dic3—61no—
326C22×Dic3—61no—
327C22×Dic3—68no—
328C22×Dic3—124no—
329C22×Dic3C22×D312yes—
330C22×Dic3C22×D312yes—
331#239—632no—
332#237—632no—
333C2×D12—28no—
334C2×D12—24no—
335C2×D12—232no—
336C2×D12—38no—
337C2×D12—38no—
338C2×D12—68no—
339C2×D12—124no—
340C2×D12#6718yescomplemented
341C2×D12C22×D318yes—
342C2×D12C22×D314yes—
343C2×D12C22×D314yes—
344C2×C4×D3—38no—
345C2×C4×D3—34no—
346C2×C4×D3—34no—
347C2×C4×D3—38no—
348C2×C4×D3—64no—
349C2×C4×D3—68no—
350C2×C4×D3—64no—
351C2×C4×D3—64no—
352C2×C4×D3—124no—
353C2×C4×D3—124no—
354C2×Dic6—24no—
355C2×Dic6C22×D314yescomplemented
356C3×C4⋊C4—34no—
357C3×C4⋊C4—38no—
358C3×C22⋊C4—38no—
359#217—34no—
360#217—34no—
361#217—38no—
362#217—38no—
363#217—38no—
364#217—38no—
365#217—64no—
366#217C22×D318yes—
367(C2×D3)⋊C4—38no—
368(C2×D3)⋊C4—38no—
369(C2×D3)⋊C4—38no—
370(C2×D3)⋊C4—38no—
371(C2×D3)⋊C4—34no—
372(C2×D3)⋊C4—34no—
373(C2×D3)⋊C4—64no—
374C4⋊Dic3C22×D314yescomplemented
375Dic3⋊C4—34no—
376Dic3⋊C4—34no—
377Dic3⋊C4—64no—
378Dic3⋊C4C22×D318yescomplemented
379C4×Dic3—34no—
380C4×Dic3—34no—
381C4×Dic3—64no—
382C22×C32—28no—
383C22×C32—22no—
384C22×C32—22no—
385C22×C32C22×D412yes—
386C22×C32C2×#4112yes—
387C22×C32C2×#4114yescomplemented
388C22×C32H(5,𝔽2)12yes—
389C22×C32C2511yescharacteristic
390C2×C3⋊D3—22no—
391C2×C3⋊D3—22no—
392C2×C3⋊D3—22no—
393C2×C3⋊D3—44no—
394C2×C3×D3—216no—
395C2×C3×D3—24no—
396C2×C3×D3—24no—
397C2×C3×D3—24no—
398C2×C3×D3—24no—
399C2×C3×D3—24no—
400C2×C3×D3—432no—
401C2×C3×D3—48no—
402C2×C3×D3C22×D418yes—
403C32×C4—22no—
404C32×C4C22×D414yes—
405C3⋊Dic3—22no—
406C3⋊Dic3—22no—
407C3⋊Dic3—22no—
408C3×Dic3—24no—
409C3×Dic3—24no—
410C25—32no—
411C2×#41—98no—
412C2×#41—188no—
413C22×Q8—31no—
414C22×D4—31no—
415C22×D4—32no—
416C22×D4—31no—
417C22×D4—38no—
418C22×D4—68no—
419C22×D4—92no—
420C22×D4—92no—
421C22×D4—91no—
422C23×C4—92no—
423C23×C4—92no—
424C23×C4—91no—
425C23×C4D3211yescharacteristic
426#124—98no—
427#123—916no—
428C22⋊Q8—38no—
429#121—98no—
430#121—916no—
431#120—916no—
432C4×D4—98no—
433C4×D4—98no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—32no—
436C2×C4⋊C4—91no—
437C2×C22⋊C4—32no—
438C2×C22⋊C4—916no—
439C2×C22⋊C4—92no—
440C2×C22⋊C4—92no—
441C2×C22⋊C4—92no—
442C2×C22⋊C4—92no—
443C2×C22⋊C4—91no—
444C2×C22⋊C4—91no—
445C2×C42—91no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3—21no—
452C23×C3—24no—
453C23×C3—38no—
454C23×C3—34no—
455C23×C3—34no—
456C23×C3—42no—
457C23×C3—42no—
458C23×C3—616no—
459C23×C3—64no—
460C23×C3—64no—
461C23×C3—64no—
462C23×C3—64no—
463C23×C3—616no—
464C23×C3—64no—
465C23×C3—128no—
466C23×C3—1232no—
467C23×C3#23714yescomplemented
468C23×C3#23914yescomplemented
469C23×C3C23×D312yes—
470C23×C3C23×D312yes—
471C23×C3C23×D311yescharacteristic
472C23×C3C23×D311yescharacteristic
473C22×D3—24no—
474C22×D3—24no—
475C22×D3—24no—
476C22×D3—216no—
477C22×D3—24no—
478C22×D3—24no—
479C22×D3—216no—
480C22×D3—32no—
481C22×D3—32no—
482C22×D3—48no—
483C22×D3—432no—
484C22×D3—62no—
485C22×D3—64no—
486C22×D3—62no—
487C22×D3—62no—
488C22×D3—62no—
489C22×D3—62no—
490C22×D3—62no—
491C22×D3—62no—
492C22×D3—122no—
493C22×D3—122no—
494C22×D3C2×#6718yes—
495C22×D3C23×D314yes—
496C22×D3C23×D314yes—
497C3×Q8—68no—
498C3×D4—316no—
499C3×D4—616no—
500C3×D4—68no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—28no—
504C2×C3×C4—28no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—24no—
508C2×C3×C4—34no—
509C2×C3×C4—34no—
510C2×C3×C4—48no—
511C2×C3×C4—42no—
512C2×C3×C4—64no—
513C2×C3×C4—64no—
514C2×C3×C4D3×D414yes—
515C2×C3×C4C2×#6714yes—
516C2×C3×C4C23×D312yes—
517C2×C3×C4C23×D312yes—
518C2×C3×C4C23×D312yes—
519C2×C3×C4C23×D312yes—
520#67—616no—
521#67—616no—
522#67—68no—
523#67—68no—
524#67—128no—
525C2×Dic3—24no—
526C2×Dic3—24no—
527C2×Dic3—32no—
528C2×Dic3—32no—
529C2×Dic3—32no—
530C2×Dic3—32no—
531C2×Dic3—32no—
532C2×Dic3—32no—
533C2×Dic3—62no—
534C2×Dic3—62no—
535C2×Dic3—62no—
536C2×Dic3—616no—
537C2×Dic3—64no—
538C2×Dic3—62no—
539C2×Dic3—62no—
540C2×Dic3—62no—
541C2×Dic3—62no—
542C2×Dic3—62no—
543C2×Dic3—62no—
544C2×Dic3—122no—
545C2×Dic3—122no—
546C2×Dic3—128no—
547C2×Dic3C23×D314yes—
548C2×Dic3C23×D314yes—
549D12—216no—
550D12—28no—
551D12—616no—
552D12—128no—
553D12C2×#67116yescomplemented
554C4×D3—616no—
555C4×D3—68no—
556C4×D3—68no—
557C4×D3—128no—
558C4×D3—128no—
559Dic6—28no—
560C2×C32—24no—
561C2×C32#54614yescomplemented
562C2×C32C23×D411yescharacteristic
563C2×C32C22×#4111yescharacteristic
564C2×C32C2×H(5,𝔽2)11yescharacteristic
565C3⋊D3—42no—
566C3×D3—28no—
567C3×D3—44no—
568C24—32no—
569C24—32no—
570C24—38no—
571C24—68no—
572C24—68no—
573C24—91no—
574C24—124no—
575C24C2×D3211yescharacteristic
576#41—1832no—
577C2×Q8—34no—
578C2×Q8—64no—
579C2×D4—34no—
580C2×D4—38no—
581C2×D4—34no—
582C2×D4—38no—
583C2×D4—632no—
584C2×D4—68no—
585C2×D4—64no—
586C2×D4—98no—
587C2×D4—98no—
588C2×D4—94no—
589C2×D4—188no—
590C2×D4—184no—
591C2×D4—364no—
592C22×C4—24no—
593C22×C4—32no—
594C22×C4—32no—
595C22×C4—98no—
596C22×C4—98no—
597C22×C4—91no—
598C22×C4—91no—
599C22×C4—91no—
600C22×C4—94no—
601C22×C4—188no—
602C22×C4—184no—
603C22×C4—364no—
604C22×C4C2×D3214yes—
605C22×C4C2×D3211yescharacteristic
606C22×C4C2×D3211yescharacteristic
607C4⋊C4—34no—
608C4⋊C4—38no—
609C4⋊C4—94no—
610C22⋊C4—38no—
611C22⋊C4—98no—
612C22⋊C4—98no—
613C22⋊C4—98no—
614C22⋊C4—98no—
615C22⋊C4—94no—
616C22⋊C4—94no—
617C42—94no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—22no—
621C22×C3—22no—
622C22×C3—28no—
623C22×C3—28no—
624C22×C3—22no—
625C22×C3—24no—
626C22×C3—22no—
627C22×C3—22no—
628C22×C3—21no—
629C22×C3—38no—
630C22×C3—42no—
631C22×C3—42no—
632C22×C3—48no—
633C22×C3—64no—
634C22×C3—64no—
635C22×C3—616no—
636C22×C3—64no—
637C22×C3—64no—
638C22×C3—64no—
639C22×C3—1232no—
640C22×C3—128no—
641C22×C3C2×D3×D412yes—
642C22×C3C2×#23712yes—
643C22×C3C2×#23714yescomplemented
644C22×C3#100412yes—
645C22×C3C2×#23912yes—
646C22×C3C2×#23914yescomplemented
647C22×C3#100912yes—
648C22×C3C22×#6712yes—
649C22×C3C24×D311yescharacteristic
650C22×C3C24×D311yescharacteristic
651C2×D3—24no—
652C2×D3—24no—
653C2×D3—216no—
654C2×D3—24no—
655C2×D3—24no—
656C2×D3—24no—
657C2×D3—432no—
658C2×D3—48no—
659C2×D3—64no—
660C2×D3—62no—
661C2×D3—62no—
662C2×D3—62no—
663C2×D3—62no—
664C2×D3—62no—
665C2×D3—62no—
666C2×D3—122no—
667C2×D3—122no—
668C2×D3—128no—
669C2×D3—124no—
670C2×D3—124no—
671C2×D3C22×#6718yes—
672C3×C4—22no—
673C3×C4—22no—
674C3×C4—24no—
675C3×C4—42no—
676C3×C4—64no—
677C3×C4—64no—
678C3×C4C2×D3×D414yes—
679C3×C4C22×#6714yes—
680Dic3—24no—
681Dic3—24no—
682Dic3—64no—
683Dic3—62no—
684Dic3—62no—
685Dic3—62no—
686Dic3—62no—
687Dic3—62no—
688Dic3—62no—
689Dic3—122no—
690Dic3—122no—
691C32C2×#54611yescharacteristic, complemented, Sylow
692C23—22no—
693C23—22no—
694C23—38no—
695C23—34no—
696C23—34no—
697C23—616no—
698C23—64no—
699C23—64no—
700C23—64no—
701C23—616no—
702C23—64no—
703C23—64no—
704C23—92no—
705C23—128no—
706C23—1232no—
707C23—182no—
708C23—182no—
709C23—182no—
710C23#379614yescomplemented
711C23C22×D3212yes—
712C23C22×D3211yescharacteristic
713Q8—68no—
714D4—316no—
715D4—616no—
716D4—68no—
717D4—1816no—
718D4—188no—
719D4—368no—
720C2×C4—22no—
721C2×C4—28no—
722C2×C4—34no—
723C2×C4—34no—
724C2×C4—64no—
725C2×C4—64no—
726C2×C4—92no—
727C2×C4—92no—
728C2×C4—92no—
729C2×C4—1816no—
730C2×C4—182no—
731C2×C4—182no—
732C2×C4—182no—
733C2×C4—188no—
734C2×C4—368no—
735C2×C4D3×#6714yes—
736C2×C4C22×D3212yes—
737C2×C4C22×D3212yes—
738C2×C3—24no—
739C2×C3—24no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—24no—
743C2×C3—21no—
744C2×C3—44no—
745C2×C3—68no—
746C2×C3—124no—
747C2×C3#563014yescomplemented
748C2×C3#580614yescomplemented
749C2×C3C22×D3×D411yescharacteristic
750C2×C3C22×#23711yescharacteristic
751C2×C3C2×#100411yescharacteristic
752C2×C3C22×#23911yescharacteristic
753C2×C3C2×#100911yescharacteristic
754C2×C3C23×#6711yescharacteristic
755D3—28no—
756D3—44no—
757D3—124no—
758D3—122no—
759D3—122no—
760C22—22no—
761C22—28no—
762C22—22no—
763C22—38no—
764C22—64no—
765C22—64no—
766C22—616no—
767C22—64no—
768C22—64no—
769C22—64no—
770C22—1232no—
771C22—128no—
772C22—182no—
773C22—182no—
774C22—182no—
775C22—364no—
776C22C2×#379612yes—
777C22C2×#379614yescomplemented
778C22#6430712yes—
779C22C2×D3×#6712yes—
780C22C23×D3211yescharacteristic
781C4—22no—
782C4—64no—
783C4—64no—
784C4—182no—
785C4—182no—
786C4—182no—
787C4C2×D3×#6714yes—
788C3—21no—
789C3C2×#563011yescharacteristic, complemented
790C3C2×#580611yescharacteristic, complemented
791C2—24no—
792C2—68no—
793C2—124no—
794C2—362no—
795C2#1059488914yesdirect product factor
796C2C22×#379611yescharacteristic
797C2C2×#6430711yescharacteristic
798C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×C3×D12C2semidirect
2. C22×#3796C2semidirect
3. C2×C4×#638C2semidirect
4. C2×C3×#924C2semidirect
5. C2×#63977C2semidirect
6. C2×D3×#217C2semidirect
7. C2×#63916C2semidirect
8. C2×#63898C2semidirect
9. C2×#63886C2semidirect
10. #10594889C2direct (N × H)
11. C2×#63884C2semidirect
12. C2×#63863C2semidirect
18. C22×C4×C3⋊D3C22semidirect
23. C22×C3×D12C22semidirect
24. C22×C3×Dic6C22semidirect
25. C22×#626C22semidirect
26. C22×#626C22semidirect
27. C22×D3×Dic3C22semidirect
28. C22×D3×Dic3C22semidirect
30. C2×#3796C22semidirect
32. C4×#638C22semidirect
33. C2×#3752C22semidirect
34. C2×#3750C22semidirect
35. C2×C4×C3⋊Dic3C22semidirect
37. C2×C3×C4⋊Dic3C22semidirect
38. C3×#924C22semidirect
39. C2×C3×Dic3⋊C4C22semidirect
40. #63977C22semidirect
41. D3×#217C22semidirect
42. C2×(C2×D3)⋊Dic3C22semidirect
43. C2×(C2×D3)⋊Dic3C22semidirect
44. C2×(C2×D3)⋊Dic3C22semidirect
45. C2×(C2×D3)⋊Dic3C22semidirect
46. #63916C22semidirect
47. #63898C22semidirect
48. #63886C22semidirect
49. #63884C22semidirect
50. #63863C22semidirect
54. C23×D12D3semidirect
68. C2×#924D3semidirect
94. C2×C4×C3⋊D3C23semidirect
100. C2×C3×D12D4semidirect
105. C2×C3×Dic6C23semidirect
108. C2×#626C23semidirect
109. C2×#626C23semidirect
112. C2×D3×Dic3C23semidirect
113. C2×D3×Dic3C23semidirect
116. #3752C23semidirect
117. #3750C23semidirect
118. C4×C3⋊Dic3C23semidirect
120. C3×C4⋊Dic3C23semidirect
121. C3×Dic3⋊C4C23semidirect
122. (C2×D3)⋊Dic3C23semidirect
123. (C2×D3)⋊Dic3C23semidirect
124. (C2×D3)⋊Dic3C23semidirect
125. (C2×D3)⋊Dic3C23semidirect
155. C22×D12C2×D3semidirect
161. C22×Dic6C2×D3semidirect
192. C2×C4⋊Dic3C2×D3semidirect
193. #924C2×D3semidirect
197. C2×Dic3⋊C4C2×D3semidirect
209. C23×C32#41semidirect
247. C3×D12C2×D4semidirect
340. C2×D12#67semidirect
355. C2×Dic6C22×D3semidirect
374. C4⋊Dic3C22×D3semidirect
378. Dic3⋊C4C22×D3semidirect
387. C22×C32C2×#41semidirect
467. C23×C3#237semidirect
468. C23×C3#239semidirect
553. D12C2×#67semidirect
561. C2×C32#546semidirect
643. C22×C3C2×#237semidirect
646. C22×C3C2×#239semidirect
691. C32C2×#546semidirect
710. C23#3796semidirect
747. C2×C3#5630semidirect
748. C2×C3#5806semidirect
777. C22C2×#3796semidirect
789. C3C2×#5630semidirect
790. C3C2×#5806semidirect
795. C2#10594889direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×D122
C22×#37962
C2×C4×#6382
C2×C3×#9242
C2×#639772
C2×D3×#2172
C2×#639162
C2×#638982
C2×#638862
#105948892
C2×#638842
C2×#638632
C2×#58063
C2×#56303