Finite Group Databasebeta

← C2×#10595005 #11900450

Subgroups — C2×#10595005 #11900450

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
1C23×C3×C4×D3C211yesmaximal, characteristic, complemented
2C22×#3799C211yesmaximal, characteristic, complemented
3C2×#64139C211yesmaximal, characteristic, complemented
4C2×C3×#924C211yesmaximal, characteristic, complemented
5C2×#63977C212yesmaximal, complemented
6C2×#63952C212yesmaximal, complemented
7C2×#63909C211yesmaximal, characteristic, complemented
8#10595005C2116yesmaximal, direct product factor
9C2×#63904C212yesmaximal, complemented
10C2×#63856C211yesmaximal, characteristic, complemented
11C2×#63850C212yesmaximal, complemented
12C2×#63841C211yesmaximal, characteristic, complemented
13C2×#5791—31nomaximal
14C2×#5627—31nomaximal
15C24×C3×D3C2211yescharacteristic
16C23×C32×C4C2211yescharacteristic
17C22×#638C2212yes—
18C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
19C23×C3×Dic3C2211yescharacteristic
20C22×C3×C4×D3—28no—
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×C4×D3C2218yescomplemented
26C22×C3×Dic6C2211yescharacteristic, complemented
27C22×#626C2212yes—
28C22×#626C2212yes—
29C22×#624C2212yescomplemented
30C2×#3799—28no—
31C2×#3799C2218yescomplemented
32#64139C2218yescomplemented
33C2×#3752C2212yescomplemented
34C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
35C2×C3×#217C2212yes—
36C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
37C3×#924C2218yescomplemented
38C2×C3×Dic3⋊C4C2212yescomplemented
39#63977C22116yescomplemented
40C2×#3724C2212yescomplemented
41C2×#3722C2212yescomplemented
42C2×(C2×D3)⋊Dic3C2212yes—
43C2×(C2×D3)⋊Dic3C2212yes—
44C2×Dic32C2212yescomplemented
45#63952C22116yescomplemented
46#63909C2218yescomplemented
47#63904C22116yescomplemented
48#63856C2218yescomplemented
49#63850C22116yescomplemented
50#63841C2218yescomplemented
51C24×C3×C4—31no—
52C22×#239—31no—
53C22×#235—31no—
54C23×C4×D3D311yescharacteristic, complemented
55C2×C3×C22⋊Q8—31no—
56C2×#953—32no—
57C2×#946—31no—
58#5791—316no—
59C2×#930—31no—
60C2×#930—31no—
61C2×#930—31no—
62C2×#930—61no—
63C2×#929—32no—
64C2×C4×#67—32no—
65C2×C4×#67—32no—
66C2×#926—31no—
67C2×#924—31no—
68C2×#924D311yescharacteristic, complemented
69#5627—316no—
70C2×#895—31no—
71C2×#894—32no—
72C2×#893—32no—
73C2×#892—31no—
74C2×#882—32no—
75C2×#67⋊C4—32no—
76C24×C32C2311yescharacteristic
77C23×C3⋊D3C2312yes—
78C23×C3×D3—24no—
79C23×C3×D3—24no—
80C23×C3×D3—24no—
81C23×C3×D3C2314yes—
82C23×C3×D3C2311yescharacteristic
83C23×C3×D3C2311yescharacteristic
84C22×C32×C4—24no—
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2314yes—
87C22×C32×C4C2311yescharacteristic
88C2×#638—28no—
89C2×#638C2318yes—
90C22×C3⋊Dic3C2312yes—
91C2×C4⋊(C3⋊D3)—24no—
92C2×C4⋊(C3⋊D3)C2314yescomplemented
93C22×C3×Dic3—24no—
94C22×C3×Dic3C2312yes—
95C22×C3×Dic3C2312yes—
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2314yes—
98C22×C3×Dic3C2311yescharacteristic
99C2×C3×C4×D3—24no—
100C2×C3×C4×D3—24no—
101C2×C3×C4×D3—24no—
102C2×C3×C4×D3—232no—
103C2×C3×C4×D3D418yescomplemented
104C2×C3×C4×D3C2314yes—
105C2×C3×C4×D3C2314yes—
106C2×C3×C4×D3C2314yes—
107C2×C3×C4×D3C2314yes—
108C2×C3×Dic6—24no—
109C2×C3×Dic6C2314yescomplemented
110C2×#626—28no—
111C2×#626—28no—
112C2×#626C2318yes—
113C2×#626C2318yes—
114C2×#624—28no—
115C2×#624C2318yescomplemented
116#3799—232no—
117#3752C2318yescomplemented
118C4⋊(C3⋊Dic3)C2314yescomplemented
119C3×#217C2318yes—
120C3×C4⋊Dic3C2314yescomplemented
121C3×Dic3⋊C4C2318yescomplemented
122#3724C2318yescomplemented
123#3722C2318yescomplemented
124(C2×D3)⋊Dic3C2318yes—
125(C2×D3)⋊Dic3C2318yes—
126Dic32C2318yescomplemented
127C2×#525—91noSylow
128C25×C3—31no—
129C24×D3C2×D311yescharacteristic
130C22×C3×Q8—31no—
131C23×C3×C4—21no—
132C23×C3×C4—31no—
133C23×C3×C4—31no—
134C23×C3×C4—31no—
135C23×C3×C4—31no—
136C23×C3×C4—31no—
137C23×C3×C4—38no—
138C23×C3×C4—68no—
139C23×C3×C4C2×D311yescharacteristic
140C23×C3×C4C2×D311yescharacteristic
141C22×#67—32no—
142C22×#67—32no—
143C22×#67—32no—
144C22×#67—32no—
145C22×#67—62no—
146C23×Dic3C2×D311yescharacteristic
147C2×#239—38no—
148C2×#239—68no—
149C2×#235—38no—
150C2×#235—68no—
151C22×D12—32no—
152C22×D12—32no—
153C22×D12—31no—
154C22×D12—31no—
155C22×D12—61no—
156C22×C4×D3—28no—
157C22×C4×D3—32no—
158C22×C4×D3—32no—
159C22×C4×D3C2×D311yescharacteristic
160C22×C4×D3C2×D311yescharacteristic
161C22×C4×D3C2×D311yescharacteristic
162C22×C4×D3C2×D311yescharacteristic
163C22×C4×D3C2×D318yescomplemented
164C22×Dic6C2×D311yescharacteristic, complemented
165C3×C22⋊Q8—38no—
166C2×C3×C4⋊C4—32no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C22⋊C4—32no—
169#953—316no—
170C2×#217—32no—
171C2×#217—32no—
172C2×#217C2×D312yes—
173#946—38no—
174#930—38no—
175#930—38no—
176#930—38no—
177#930—68no—
178#929—316no—
179C4×#67—316no—
180C4×#67—316no—
181C2×(C2×D3)⋊C4—32no—
182C2×(C2×D3)⋊C4—32no—
183C2×(C2×D3)⋊C4—32no—
184C2×(C2×D3)⋊C4—32no—
185C2×(C2×D3)⋊C4—32no—
186C2×(C2×D3)⋊C4—32no—
187C2×(C2×D3)⋊C4—62no—
188#926—38no—
189C2×C4⋊Dic3—31no—
190C2×C4⋊Dic3—31no—
191C2×C4⋊Dic3—61no—
192C2×C4⋊Dic3C2×D311yescharacteristic, complemented
193#924—38no—
194#924C2×D318yescomplemented
195C2×Dic3⋊C4—32no—
196C2×Dic3⋊C4—32no—
197C2×Dic3⋊C4C2×D312yescomplemented
198C2×C4×Dic3—32no—
199C2×C4×Dic3—32no—
200#895—38no—
201#894—316no—
202#893—316no—
203#892—38no—
204#882—316no—
205#67⋊C4—316no—
206C23×C32—22no—
207C23×C32—22no—
208C23×C32#4114yescomplemented
209C23×C32C2412yes—
210C23×C32C2411yescharacteristic
211C22×C3⋊D3—24no—
212C22×C3⋊D3—24no—
213C22×C3⋊D3—24no—
214C22×C3⋊D3C2414yes—
215C22×C3×D3—232no—
216C22×C3×D3—22no—
217C22×C3×D3—22no—
218C22×C3×D3—22no—
219C22×C3×D3—22no—
220C22×C3×D3—28no—
221C22×C3×D3—28no—
222C22×C3×D3—28no—
223C22×C3×D3C2×D414yes—
224C22×C3×D3#4114yescomplemented
225C22×C3×D3C2412yes—
226C22×C3×D3C2412yes—
227C2×C32×C4—22no—
228C2×C32×C4—28no—
229C2×C32×C4C2×D414yes—
230C2×C32×C4C2412yes—
231C2×C32×C4C2412yes—
232#638—216no—
233C2×C3⋊Dic3—24no—
234C2×C3⋊Dic3C2414yes—
235C4⋊(C3⋊D3)—28no—
236C2×C3×Dic3—24no—
237C2×C3×Dic3—22no—
238C2×C3×Dic3—24no—
239C2×C3×Dic3—28no—
240C2×C3×Dic3C2×D414yes—
241C2×C3×Dic3C2414yes—
242C2×C3×Dic3C2414yes—
243C2×C3×Dic3C2412yes—
244C2×C3×Dic3C2412yes—
245C3×C4×D3—28no—
246C3×C4×D3—28no—
247C3×C4×D3—28no—
248C3×C4×D3C2×D4116yescomplemented
249C3×Dic6—28no—
250#626—216no—
251#626—216no—
252#624—216no—
253C22×#41—91no—
254C24×C4—31no—
255#525—916no—
256C2×#123—92no—
257C2×C22⋊Q8—31no—
258C2×C22⋊Q8—91no—
259C2×#121—91no—
260C2×#121—91no—
261C2×#120—92no—
262C2×C4×D4—92no—
263C2×C4×D4—92no—
264C2×#117—91no—
265C24×C3—21no—
266C24×C3—31no—
267C24×C3—31no—
268C24×C3—34no—
269C24×C3—64no—
270C24×C3—64no—
271C24×C3—64no—
272C24×C3C22×D311yescharacteristic
273C24×C3C22×D311yescharacteristic
274C23×D3—24no—
275C23×D3—24no—
276C23×D3—24no—
277C23×D3—32no—
278C23×D3—32no—
279C23×D3—62no—
280C23×D3C22×D314yes—
281C23×D3C22×D311yescharacteristic
282C23×D3C22×D311yescharacteristic
283C2×C3×Q8—34no—
284C2×C3×Q8—64no—
285C22×C3×C4—24no—
286C22×C3×C4—24no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—24no—
290C22×C3×C4—31no—
291C22×C3×C4—38no—
292C22×C3×C4—34no—
293C22×C3×C4—32no—
294C22×C3×C4—31no—
295C22×C3×C4—32no—
296C22×C3×C4—34no—
297C22×C3×C4—34no—
298C22×C3×C4—34no—
299C22×C3×C4—34no—
300C22×C3×C4—44no—
301C22×C3×C4—64no—
302C22×C3×C4—632no—
303C22×C3×C4—64no—
304C22×C3×C4—64no—
305C22×C3×C4—64no—
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D314yes—
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D314yes—
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C2×#67—38no—
313C2×#67—38no—
314C2×#67—38no—
315C2×#67—38no—
316C2×#67—68no—
317C2×#67—68no—
318C2×#67—68no—
319C2×#67—68no—
320C2×#67—68no—
321C2×#67—128no—
322C22×Dic3—24no—
323C22×Dic3—32no—
324C22×Dic3—32no—
325C22×Dic3—62no—
326C22×Dic3C22×D314yes—
327C22×Dic3C22×D312yes—
328C22×Dic3C22×D311yescharacteristic
329C22×Dic3C22×D312yes—
330C22×Dic3C22×D311yescharacteristic
331#239—632no—
332#235—632no—
333C2×D12—38no—
334C2×D12—38no—
335C2×D12—34no—
336C2×D12—34no—
337C2×D12—64no—
338C2×D12—68no—
339C2×D12—68no—
340C2×D12—64no—
341C2×D12—64no—
342C2×D12—124no—
343C2×C4×D3—24no—
344C2×C4×D3—24no—
345C2×C4×D3—24no—
346C2×C4×D3—232no—
347C2×C4×D3—38no—
348C2×C4×D3—38no—
349C2×C4×D3—68no—
350C2×C4×D3—68no—
351C2×C4×D3#6718yescomplemented
352C2×C4×D3C22×D314yes—
353C2×C4×D3C22×D314yes—
354C2×C4×D3C22×D314yes—
355C2×C4×D3C22×D314yes—
356C2×Dic6—24no—
357C2×Dic6C22×D314yescomplemented
358C3×C4⋊C4—34no—
359C3×C4⋊C4—38no—
360C3×C22⋊C4—38no—
361#217—38no—
362#217—38no—
363#217C22×D318yes—
364(C2×D3)⋊C4—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—38no—
370(C2×D3)⋊C4—68no—
371C4⋊Dic3—34no—
372C4⋊Dic3—34no—
373C4⋊Dic3—64no—
374C4⋊Dic3C22×D314yescomplemented
375Dic3⋊C4—38no—
376Dic3⋊C4—38no—
377Dic3⋊C4C22×D318yescomplemented
378C4×Dic3—38no—
379C4×Dic3—38no—
380C22×C32—28no—
381C22×C32—22no—
382C22×C32—22no—
383C22×C32C22×D412yes—
384C22×C32C2×#4112yes—
385C22×C32C2×#4112yes—
386C22×C32C2×#4114yescomplemented
387C22×C32C2511yescharacteristic
388C2×C3⋊D3—24no—
389C2×C3⋊D3—24no—
390C2×C3⋊D3—24no—
391C2×C3⋊D3—48no—
392C2×C3×D3—232no—
393C2×C3×D3—28no—
394C2×C3×D3—28no—
395C2×C3×D3—22no—
396C2×C3×D3—22no—
397C2×C3×D3—22no—
398C2×C3×D3—22no—
399C2×C3×D3C22×D414yes—
400C2×C3×D3C2×#4114yescomplemented
401C32×C4—22no—
402C32×C4C22×D414yes—
403C3⋊Dic3—24no—
404C3×Dic3—24no—
405C3×Dic3—22no—
406C3×Dic3—24no—
407C3×Dic3C22×D414yes—
408C25—31no—
409C2×#41—98no—
410C2×#41—188no—
411C22×Q8—31no—
412C22×D4—92no—
413C22×D4—92no—
414C22×D4—92no—
415C22×D4—91no—
416C23×C4—31no—
417C23×C4—31no—
418C23×C4—31no—
419C23×C4—31no—
420C23×C4—31no—
421C23×C4—38no—
422C23×C4—68no—
423C23×C4—92no—
424C23×C4D3211yescharacteristic
425#123—916no—
426C22⋊Q8—38no—
427C22⋊Q8—98no—
428#121—98no—
429#121—98no—
430#120—916no—
431C4×D4—916no—
432C4×D4—916no—
433#117—98no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—32no—
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—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—21no—
450C23×C3—24no—
451C23×C3—34no—
452C23×C3—34no—
453C23×C3—32no—
454C23×C3—32no—
455C23×C3—42no—
456C23×C3—42no—
457C23×C3—68no—
458C23×C3—68no—
459C23×C3—632no—
460C23×C3—62no—
461C23×C3—62no—
462C23×C3—62no—
463C23×C3—68no—
464C23×C3—62no—
465C23×C3#23514yescomplemented
466C23×C3#23914yescomplemented
467C23×C3C23×D312yes—
468C23×C3C23×D312yes—
469C23×C3C23×D311yescharacteristic
470C23×C3C23×D311yescharacteristic
471C22×D3—232no—
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—28no—
476C22×D3—22no—
477C22×D3—28no—
478C22×D3—28no—
479C22×D3—34no—
480C22×D3—34no—
481C22×D3—64no—
482C22×D3—64no—
483C22×D3—64no—
484C22×D3—64no—
485C22×D3—64no—
486C22×D3—64no—
487C22×D3—64no—
488C22×D3—124no—
489C22×D3—124no—
490C22×D3—124no—
491C22×D3#23514yescomplemented
492C22×D3C2×#6714yes—
493C22×D3C23×D312yes—
494C22×D3C23×D312yes—
495C3×Q8—68no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—28no—
499C2×C3×C4—28no—
500C2×C3×C4—22no—
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—32no—
508C2×C3×C4—34no—
509C2×C3×C4—48no—
510C2×C3×C4—42no—
511C2×C3×C4—68no—
512C2×C3×C4—68no—
513C2×C3×C4—68no—
514C2×C3×C4—64no—
515C2×C3×C4—62no—
516C2×C3×C4—64no—
517C2×C3×C4—68no—
518C2×C3×C4D3×D414yes—
519C2×C3×C4C2×#6714yes—
520C2×C3×C4C23×D312yes—
521C2×C3×C4C23×D312yes—
522C2×C3×C4C23×D312yes—
523C2×C3×C4C23×D312yes—
524#67—616no—
525#67—616no—
526#67—616no—
527#67—616no—
528#67—1216no—
529C2×Dic3—24no—
530C2×Dic3—24no—
531C2×Dic3—22no—
532C2×Dic3—28no—
533C2×Dic3—34no—
534C2×Dic3—34no—
535C2×Dic3—64no—
536C2×Dic3—64no—
537C2×Dic3—64no—
538C2×Dic3—124no—
539C2×Dic3C2×#6714yes—
540C2×Dic3C23×D314yes—
541C2×Dic3C23×D312yes—
542C2×Dic3C23×D314yes—
543C2×Dic3C23×D312yes—
544D12—616no—
545D12—616no—
546D12—68no—
547D12—68no—
548D12—128no—
549C4×D3—28no—
550C4×D3—28no—
551C4×D3—28no—
552C4×D3—616no—
553C4×D3—616no—
554C4×D3C2×#67116yescomplemented
555Dic6—28no—
556C2×C32—24no—
557C2×C32#52514yescomplemented
558C2×C32C23×D411yescharacteristic
559C2×C32C22×#4111yescharacteristic
560C2×C32C22×#4111yescharacteristic
561C3⋊D3—44no—
562C3×D3—24no—
563C3×D3—24no—
564C24—31no—
565C24—31no—
566C24—34no—
567C24—64no—
568C24—64no—
569C24—64no—
570C24—92no—
571C24C2×D3211yescharacteristic
572#41—1832no—
573C2×Q8—34no—
574C2×Q8—64no—
575C2×D4—98no—
576C2×D4—98no—
577C2×D4—98no—
578C2×D4—94no—
579C2×D4—188no—
580C2×D4—188no—
581C2×D4—188no—
582C2×D4—184no—
583C22×C4—24no—
584C22×C4—31no—
585C22×C4—34no—
586C22×C4—38no—
587C22×C4—34no—
588C22×C4—32no—
589C22×C4—32no—
590C22×C4—31no—
591C22×C4—34no—
592C22×C4—34no—
593C22×C4—34no—
594C22×C4—64no—
595C22×C4—632no—
596C22×C4—64no—
597C22×C4—64no—
598C22×C4—64no—
599C22×C4—98no—
600C22×C4—92no—
601C22×C4—188no—
602C22×C4C2×D3214yes—
603C22×C4C2×D3211yescharacteristic
604C22×C4C2×D3211yescharacteristic
605C4⋊C4—34no—
606C4⋊C4—38no—
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—22no—
616C22×C3—22no—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—28no—
620C22×C3—28no—
621C22×C3—22no—
622C22×C3—24no—
623C22×C3—22no—
624C22×C3—22no—
625C22×C3—21no—
626C22×C3—34no—
627C22×C3—34no—
628C22×C3—42no—
629C22×C3—42no—
630C22×C3—48no—
631C22×C3—632no—
632C22×C3—62no—
633C22×C3—62no—
634C22×C3—62no—
635C22×C3—62no—
636C22×C3—68no—
637C22×C3—68no—
638C22×C3C2×#23512yes—
639C22×C3C2×#23512yes—
640C22×C3C2×#23514yescomplemented
641C22×C3C2×D3×D412yes—
642C22×C3C2×#23912yes—
643C22×C3C2×#23914yescomplemented
644C22×C3D3×#4112yes—
645C22×C3C22×#6712yes—
646C22×C3C24×D311yescharacteristic
647C22×C3C24×D311yescharacteristic
648C2×D3—232no—
649C2×D3—22no—
650C2×D3—22no—
651C2×D3—22no—
652C2×D3—22no—
653C2×D3—28no—
654C2×D3—28no—
655C2×D3—64no—
656C2×D3—64no—
657C2×D3—64no—
658C2×D3—64no—
659C2×D3—64no—
660C2×D3—64no—
661C2×D3—124no—
662C2×D3—124no—
663C2×D3—124no—
664C2×D3—128no—
665C2×D3—128no—
666C2×D3—248no—
667C2×D3C2×#23514yescomplemented
668C2×D3C22×#6714yes—
669C3×C4—22no—
670C3×C4—22no—
671C3×C4—24no—
672C3×C4—34no—
673C3×C4—42no—
674C3×C4—64no—
675C3×C4—62no—
676C3×C4—64no—
677C3×C4C2×D3×D414yes—
678C3×C4C22×#6714yes—
679Dic3—24no—
680Dic3—24no—
681Dic3—22no—
682Dic3—64no—
683Dic3—64no—
684Dic3—124no—
685Dic3C22×#6714yes—
686C32C2×#52511yescharacteristic, complemented, Sylow
687C23—22no—
688C23—22no—
689C23—34no—
690C23—34no—
691C23—32no—
692C23—32no—
693C23—68no—
694C23—68no—
695C23—632no—
696C23—62no—
697C23—62no—
698C23—68no—
699C23—62no—
700C23—62no—
701C23—94no—
702C23—184no—
703C23—184no—
704C23—184no—
705C23#379914yescomplemented
706C23C22×D3212yes—
707C23C22×D3211yescharacteristic
708Q8—68no—
709D4—1816no—
710D4—1816no—
711D4—1816no—
712D4—188no—
713C2×C4—22no—
714C2×C4—28no—
715C2×C4—34no—
716C2×C4—32no—
717C2×C4—316no—
718C2×C4—34no—
719C2×C4—34no—
720C2×C4—32no—
721C2×C4—68no—
722C2×C4—68no—
723C2×C4—68no—
724C2×C4—64no—
725C2×C4—62no—
726C2×C4—64no—
727C2×C4—68no—
728C2×C4—94no—
729C2×C4—1816no—
730C2×C4—184no—
731C2×C4D3×#6714yes—
732C2×C4C22×D3212yes—
733C2×C4C22×D3212yes—
734C2×C3—24no—
735C2×C3—24no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—24no—
740C2×C3—44no—
741C2×C3—64no—
742C2×C3—64no—
743C2×C3#562714yescomplemented
744C2×C3#579114yescomplemented
745C2×C3C22×#23511yescharacteristic
746C2×C3C22×#23511yescharacteristic
747C2×C3C22×D3×D411yescharacteristic
748C2×C3C22×#23911yescharacteristic
749C2×C3C2×D3×#4111yescharacteristic
750C2×C3C23×#6711yescharacteristic
751D3—24no—
752D3—24no—
753D3—124no—
754D3—124no—
755D3—244no—
756C22—22no—
757C22—22no—
758C22—28no—
759C22—34no—
760C22—34no—
761C22—632no—
762C22—62no—
763C22—62no—
764C22—62no—
765C22—62no—
766C22—68no—
767C22—68no—
768C22—184no—
769C22—184no—
770C22—184no—
771C22—368no—
772C22C2×#379912yes—
773C22C2×#379914yescomplemented
774C22D3×#23512yes—
775C22C2×D3×#6712yes—
776C22C23×D3211yescharacteristic
777C4—22no—
778C4—34no—
779C4—64no—
780C4—62no—
781C4—64no—
782C4—184no—
783C4C2×D3×#6714yes—
784C3—21no—
785C3C2×#562711yescharacteristic, complemented
786C3C2×#579111yescharacteristic, complemented
787C2—24no—
788C2—64no—
789C2—64no—
790C2—364no—
791C2#1059500514yesdirect product factor
792C2C22×#379911yescharacteristic
793C2C2×D3×#23511yescharacteristic
794C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#525
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×C4×D3C2semidirect
2. C22×#3799C2semidirect
3. C2×#64139C2semidirect
4. C2×C3×#924C2semidirect
5. C2×#63977C2semidirect
6. C2×#63952C2semidirect
7. C2×#63909C2semidirect
8. #10595005C2direct (N × H)
9. C2×#63904C2semidirect
10. C2×#63856C2semidirect
11. C2×#63850C2semidirect
12. C2×#63841C2semidirect
18. C22×C4⋊(C3⋊D3)C22semidirect
25. C22×C3×C4×D3C22semidirect
26. C22×C3×Dic6C22semidirect
29. C22×#624C22semidirect
31. C2×#3799C22semidirect
32. #64139C22semidirect
33. C2×#3752C22semidirect
34. C2×C4⋊(C3⋊Dic3)C22semidirect
36. C2×C3×C4⋊Dic3C22semidirect
37. C3×#924C22semidirect
38. C2×C3×Dic3⋊C4C22semidirect
39. #63977C22semidirect
40. C2×#3724C22semidirect
41. C2×#3722C22semidirect
44. C2×Dic32C22semidirect
45. #63952C22semidirect
46. #63909C22semidirect
47. #63904C22semidirect
48. #63856C22semidirect
49. #63850C22semidirect
50. #63841C22semidirect
54. C23×C4×D3D3semidirect
68. C2×#924D3semidirect
92. C2×C4⋊(C3⋊D3)C23semidirect
103. C2×C3×C4×D3D4semidirect
109. C2×C3×Dic6C23semidirect
115. C2×#624C23semidirect
117. #3752C23semidirect
118. C4⋊(C3⋊Dic3)C23semidirect
120. C3×C4⋊Dic3C23semidirect
121. C3×Dic3⋊C4C23semidirect
122. #3724C23semidirect
123. #3722C23semidirect
126. Dic32C23semidirect
163. C22×C4×D3C2×D3semidirect
164. C22×Dic6C2×D3semidirect
192. C2×C4⋊Dic3C2×D3semidirect
194. #924C2×D3semidirect
197. C2×Dic3⋊C4C2×D3semidirect
208. C23×C32#41semidirect
224. C22×C3×D3#41semidirect
248. C3×C4×D3C2×D4semidirect
351. C2×C4×D3#67semidirect
357. C2×Dic6C22×D3semidirect
374. C4⋊Dic3C22×D3semidirect
377. Dic3⋊C4C22×D3semidirect
386. C22×C32C2×#41semidirect
400. C2×C3×D3C2×#41semidirect
465. C23×C3#235semidirect
466. C23×C3#239semidirect
491. C22×D3#235semidirect
554. C4×D3C2×#67semidirect
557. C2×C32#525semidirect
640. C22×C3C2×#235semidirect
643. C22×C3C2×#239semidirect
667. C2×D3C2×#235semidirect
686. C32C2×#525semidirect
705. C23#3799semidirect
743. C2×C3#5627semidirect
744. C2×C3#5791semidirect
773. C22C2×#3799semidirect
785. C3C2×#5627semidirect
786. C3C2×#5791semidirect
791. C2#10595005direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C4×D32
C22×#37992
C2×#641392
C2×C3×#9242
C2×#639772
C2×#639522
C2×#639092
#105950052
C2×#639042
C2×#638562
C2×#638502
C2×#638412
C2×#57913
C2×#56273