Finite Group Databasebeta

← C2×#10595246 #11902438

Subgroups — C2×#10595246 #11902438

Order 1152.

4245 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3830C211yesmaximal, characteristic, complemented
2C22×C3×D3×D4C211yesmaximal, characteristic, complemented
3C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
4C2×#63978C212yesmaximal, complemented
5C2×#63977C212yesmaximal, complemented
6C2×#63962C212yesmaximal, complemented
7C22×(C2×D3)⋊Dic3C212yesmaximal, complemented
8#10595246C2116yesmaximal, direct product factor
9C2×#63916C211yesmaximal, characteristic, complemented
10C2×C4×#626C211yesmaximal, characteristic, complemented
11C2×#63860C211yesmaximal, characteristic, complemented
12C2×#63857C211yesmaximal, characteristic, complemented
13C2×#5806—31nomaximal
14C2×#5554—31nomaximal
15C24×C3×D3C2212yes—
16C22×C32×D4C2211yescharacteristic
17C22×#638C2212yescomplemented
18C23×C3⋊Dic3C2212yescomplemented
19C2×#3830—28no—
20C2×#3830C2218yescomplemented
21C22×C4×C3⋊D3C2211yescharacteristic, complemented
22C22×#634C2211yescharacteristic, complemented
23C22×C3×#67C2212yes—
24C23×C3×Dic3C2212yescomplemented
25C2×C3×D3×D4—28no—
26C2×C3×D3×D4C2218yescomplemented
27C22×C3×D12C2211yescharacteristic
28C22×C3×C4×D3C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#626C2212yescomplemented
31C2×C3×#217C2212yescomplemented
32C3×D4×Dic3C2218yescomplemented
33C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
34C2×C3×C4×Dic3C2211yescharacteristic, complemented
35#63978C22116yescomplemented
36#63977C22116yescomplemented
37C2×Dic3⋊Dic3C2212yescomplemented
38C2×Dic3⋊Dic3C2211yescharacteristic, complemented
39C2×#3722C2211yescharacteristic, complemented
40#63962C22116yescomplemented
41C2×(C2×D3)⋊Dic3C2212yes—
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C22116yescomplemented
44C2×(C2×D3)⋊Dic3C2212yescomplemented
45C2×(C2×D3)⋊Dic3C2212yescomplemented
46C2×(C2×D3)⋊Dic3C2212yescomplemented
47#63916C2218yescomplemented
48C4×#626C2218yescomplemented
49#63860C2218yescomplemented
50#63857C2218yescomplemented
51C23×C3×D4—31no—
52C22×#237—31no—
53C22×#237—31no—
54C22×#237—61no—
55C22×D3×D4D311yescharacteristic, complemented
56C2×C3×C4×D4—31no—
57C2×#953—32no—
58C22×#217—32no—
59#5806—316no—
60C2×#939—32no—
61C2×#938—31no—
62C2×#936—31no—
63C2×#935—32no—
64C2×D4×Dic3D311yescharacteristic, complemented
65C2×#930—32no—
66C2×C4×#67—31no—
67C22×(C2×D3)⋊C4—32no—
68C2×#924—31no—
69#5554—316no—
70C2×#897—31no—
71C2×#895—31no—
72C2×#886—32no—
73C2×#882—32no—
74C2×#875—31no—
75C2×C4×D12—31no—
76C24×C32C2312yes—
77C23×C3⋊D3C2311yescharacteristic
78C23×C3×D3—28no—
79C23×C3×D3—28no—
80C23×C3×D3—44no—
81C23×C3×D3C2312yes—
82C23×C3×D3C2318yes—
83C23×C3×D3C2311yescharacteristic
84C2×C32×D4D418yescomplemented
85C2×C32×D4C2314yes—
86C22×C32×C4C2311yescharacteristic
87C2×#638—28no—
88C2×#638C2318yescomplemented
89C22×C3⋊Dic3—28no—
90C22×C3⋊Dic3C2312yes—
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2318yescomplemented
93#3830—232no—
94C2×C4×C3⋊D3—24no—
95C2×C4×C3⋊D3C2314yescomplemented
96C2×#634—24no—
97C2×#634C2314yescomplemented
98C2×C3×#67—28no—
99C2×C3×#67C2318yes—
100C22×C3×Dic3—44no—
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2312yes—
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2318yescomplemented
106C3×D3×D4—232no—
107C2×C3×D12—24no—
108C2×C3×D12C2314yes—
109C2×C3×C4×D3—24no—
110C2×C3×C4×D3C2314yes—
111C2×#626—24no—
112C2×#626—44no—
113C2×#626C2314yes—
114C2×#626C2318yescomplemented
115C3×#217C2318yescomplemented
116C3×C4⋊Dic3C2314yescomplemented
117C3×C4×Dic3C2314yescomplemented
118Dic3⋊Dic3C2318yescomplemented
119Dic3⋊Dic3C2314yescomplemented
120#3722C2314yescomplemented
121(C2×D3)⋊Dic3C2318yes—
122(C2×D3)⋊Dic3C2314yes—
123(C2×D3)⋊Dic3C2318yescomplemented
124(C2×D3)⋊Dic3C2318yescomplemented
125(C2×D3)⋊Dic3C2318yescomplemented
126C2×#546—91noSylow
127C25×C3—32no—
128C24×D3C2×D312yes—
129C22×C3×D4—21no—
130C22×C3×D4—32no—
131C22×C3×D4—38no—
132C22×C3×D4—31no—
133C22×C3×D4—68no—
134C22×C3×D4C2×D311yescharacteristic
135C22×C3×D4C2×D311yescharacteristic
136C23×C3×C4—32no—
137C23×C3×C4—31no—
138C22×#67—32no—
139C22×#67—32no—
140C22×#67—31no—
141C22×#67—32no—
142C22×#67—62no—
143C22×#67C2×D312yes—
144C23×Dic3—32no—
145C23×Dic3—32no—
146C23×Dic3—62no—
147C23×Dic3C2×D312yescomplemented
148C2×#237—38no—
149C2×#237—38no—
150C2×#237—68no—
151C2×#237—616no—
152C2×#237—68no—
153C2×#237—68no—
154C2×D3×D4—28no—
155C2×D3×D4C2×D318yescomplemented
156C22×D12—31no—
157C22×D12—32no—
158C22×D12C2×D311yescharacteristic
159C22×C4×D3—31no—
160C22×C4×D3—31no—
161C22×C4×D3—61no—
162C22×C4×D3C2×D311yescharacteristic
163C22×Dic6—31no—
164C22×Dic6—31no—
165C22×Dic6—61no—
166C3×C4×D4—38no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C22⋊C4—32no—
169C2×C3×C42—31no—
170#953—316no—
171C2×#217—32no—
172C2×#217—31no—
173C2×#217—32no—
174C2×#217—32no—
175C2×#217—32no—
176C2×#217—316no—
177C2×#217C2×D312yescomplemented
178#939—316no—
179#938—38no—
180#936—38no—
181#935—316no—
182D4×Dic3C2×D318yescomplemented
183#930—316no—
184C4×#67—38no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—32no—
187C2×(C2×D3)⋊C4—32no—
188C2×(C2×D3)⋊C4—32no—
189C2×(C2×D3)⋊C4—32no—
190C2×(C2×D3)⋊C4—316no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—31no—
193C2×C4⋊Dic3—31no—
194C2×C4⋊Dic3—32no—
195C2×C4⋊Dic3C2×D311yescharacteristic, complemented
196#924—38no—
197C2×Dic3⋊C4—32no—
198C2×Dic3⋊C4—31no—
199C2×C4×Dic3C2×D311yescharacteristic, complemented
200#897—38no—
201#895—38no—
202#886—316no—
203#882—316no—
204#875—38no—
205C4×D12—38no—
206C23×C32—24no—
207C23×C32—24no—
208C23×C32C2×D418yes—
209C23×C32C2414yes—
210C23×C32C2411yescharacteristic
211C22×C3⋊D3—22no—
212C22×C3⋊D3—22no—
213C22×C3⋊D3—22no—
214C22×C3⋊D3C2412yes—
215C22×C3×D3—22no—
216C22×C3×D3—22no—
217C22×C3×D3—24no—
218C22×C3×D3—216no—
219C22×C3×D3—24no—
220C22×C3×D3—24no—
221C22×C3×D3—216no—
222C22×C3×D3—48no—
223C22×C3×D3—432no—
224C22×C3×D3#4114yescomplemented
225C22×C3×D3C2414yes—
226C22×C3×D3C2412yes—
227C32×D4C2×D4116yescomplemented
228C2×C32×C4C2×D414yes—
229C2×C32×C4C2412yes—
230#638—216no—
231C2×C3⋊Dic3—24no—
232C2×C3⋊Dic3—22no—
233C2×C3⋊Dic3—216no—
234C2×C3⋊Dic3C2414yes—
235C2×C3⋊Dic3C2412yes—
236C4×C3⋊D3—28no—
237#634—28no—
238C3×#67—216no—
239C2×C3×Dic3—22no—
240C2×C3×Dic3—22no—
241C2×C3×Dic3—24no—
242C2×C3×Dic3—22no—
243C2×C3×Dic3—48no—
244C2×C3×Dic3C2412yes—
245C2×C3×Dic3C2414yes—
246C2×C3×Dic3C2412yes—
247C2×C3×Dic3C2412yes—
248C3×D12—28no—
249C3×C4×D3—28no—
250#626—28no—
251#626—48no—
252C22×#41—91no—
253C23×D4—31no—
254#546—916no—
255C2×#124—91no—
256C2×#123—92no—
257C2×C22⋊Q8—91no—
258C2×#121—91no—
259C2×#121—92no—
260C2×#120—92no—
261C2×C4×D4—31no—
262C2×C4×D4—91no—
263C22×C22⋊C4—92no—
264C24×C3—22no—
265C24×C3—31no—
266C24×C3—32no—
267C24×C3—38no—
268C24×C3—68no—
269C24×C3—68no—
270C24×C3—124no—
271C24×C3C22×D312yes—
272C24×C3C22×D312yes—
273C23×D3—28no—
274C23×D3—28no—
275C23×D3—31no—
276C23×D3—31no—
277C23×D3—44no—
278C23×D3—61no—
279C23×D3C22×D312yes—
280C23×D3C22×D318yes—
281C23×D3C22×D311yescharacteristic
282C2×C3×D4—28no—
283C2×C3×D4—24no—
284C2×C3×D4—38no—
285C2×C3×D4—34no—
286C2×C3×D4—68no—
287C2×C3×D4—632no—
288C2×C3×D4—64no—
289C2×C3×D4D1218yescomplemented
290C2×C3×D4#6718yescomplemented
291C2×C3×D4C22×D314yes—
292C2×C3×D4C22×D314yes—
293C22×C3×C4—21no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—32no—
297C22×C3×C4—31no—
298C22×C3×C4—38no—
299C22×C3×C4—34no—
300C22×C3×C4—64no—
301C22×C3×C4—124no—
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C2×#67—28no—
305C2×#67—38no—
306C2×#67—38no—
307C2×#67—34no—
308C2×#67—38no—
309C2×#67—68no—
310C2×#67—64no—
311C2×#67—616no—
312C2×#67—68no—
313C2×#67—68no—
314C2×#67—124no—
315C2×#67C22×D318yes—
316C22×Dic3—38no—
317C22×Dic3—32no—
318C22×Dic3—31no—
319C22×Dic3—32no—
320C22×Dic3—31no—
321C22×Dic3—38no—
322C22×Dic3—44no—
323C22×Dic3—62no—
324C22×Dic3—61no—
325C22×Dic3—68no—
326C22×Dic3—616no—
327C22×Dic3—68no—
328C22×Dic3—68no—
329C22×Dic3C22×D311yescharacteristic
330C22×Dic3C22×D311yescharacteristic
331C22×Dic3C22×D312yes—
332C22×Dic3C22×D311yescharacteristic
333C22×Dic3C22×D318yescomplemented
334#237—664no—
335#237—632no—
336#237—632no—
337D3×D4—232no—
338C2×D12—24no—
339C2×D12—34no—
340C2×D12—38no—
341C2×D12—64no—
342C2×D12—124no—
343C2×D12C22×D314yes—
344C2×C4×D3—24no—
345C2×C4×D3—34no—
346C2×C4×D3—34no—
347C2×C4×D3—64no—
348C2×C4×D3—68no—
349C2×C4×D3—64no—
350C2×C4×D3—64no—
351C2×C4×D3C22×D314yes—
352C2×Dic6—34no—
353C2×Dic6—34no—
354C2×Dic6—64no—
355C2×Dic6—68no—
356C2×Dic6—64no—
357C2×Dic6—64no—
358C3×C4⋊C4—34no—
359C3×C22⋊C4—38no—
360C3×C42—34no—
361#217—38no—
362#217—34no—
363#217—38no—
364#217—38no—
365#217—38no—
366#217C22×D318yescomplemented
367(C2×D3)⋊C4—34no—
368(C2×D3)⋊C4—38no—
369(C2×D3)⋊C4—38no—
370(C2×D3)⋊C4—38no—
371(C2×D3)⋊C4—38no—
372(C2×D3)⋊C4—34no—
373(C2×D3)⋊C4—34no—
374C4⋊Dic3—34no—
375C4⋊Dic3—38no—
376C4⋊Dic3C22×D314yescomplemented
377Dic3⋊C4—38no—
378Dic3⋊C4—34no—
379C4×Dic3C22×D314yescomplemented
380C22×C32—216no—
381C22×C32—24no—
382C22×C32—24no—
383C22×C32C22×D418yes—
384C22×C32C22×D412yes—
385C22×C32C2×#4112yes—
386C22×C32H(5,𝔽2)12yes—
387C22×C32C2511yescharacteristic
388C2×C3⋊D3—22no—
389C2×C3⋊D3—22no—
390C2×C3⋊D3—22no—
391C2×C3⋊D3—44no—
392C2×C3×D3—28no—
393C2×C3×D3—22no—
394C2×C3×D3—22no—
395C2×C3×D3—24no—
396C2×C3×D3—24no—
397C2×C3×D3—24no—
398C2×C3×D3—432no—
399C2×C3×D3—48no—
400C2×C3×D3C2×#4114yescomplemented
401C32×C4C22×D414yes—
402C3⋊Dic3—24no—
403C3⋊Dic3—22no—
404C3×Dic3—22no—
405C3×Dic3—22no—
406C3×Dic3—24no—
407C3×Dic3—22no—
408C25—32no—
409C2×#41—98no—
410C2×#41—188no—
411C22×Q8—91no—
412C22×D4—32no—
413C22×D4—38no—
414C22×D4—31no—
415C22×D4—68no—
416C22×D4—91no—
417C22×D4—92no—
418C22×D4—92no—
419C22×D4D3211yescharacteristic
420C23×C4—32no—
421C23×C4—31no—
422C23×C4—92no—
423C23×C4—91no—
424#124—98no—
425#123—916no—
426C22⋊Q8—98no—
427#121—98no—
428#121—916no—
429#120—916no—
430C4×D4—38no—
431C4×D4—98no—
432C2×C4⋊C4—31no—
433C2×C4⋊C4—91no—
434C2×C4⋊C4—92no—
435C2×C22⋊C4—32no—
436C2×C22⋊C4—91no—
437C2×C22⋊C4—91no—
438C2×C22⋊C4—92no—
439C2×C22⋊C4—92no—
440C2×C22⋊C4—92no—
441C2×C22⋊C4—916no—
442C2×C22⋊C4—92no—
443C2×C42—31no—
444C23×C3—24no—
445C23×C3—24no—
446C23×C3—24no—
447C23×C3—24no—
448C23×C3—24no—
449C23×C3—21no—
450C23×C3—28no—
451C23×C3—34no—
452C23×C3—32no—
453C23×C3—34no—
454C23×C3—44no—
455C23×C3—44no—
456C23×C3—616no—
457C23×C3—62no—
458C23×C3—62no—
459C23×C3—616no—
460C23×C3—64no—
461C23×C3—64no—
462C23×C3—64no—
463C23×C3—128no—
464C23×C3—1232no—
465C23×C3C2×D1218yes—
466C23×C3C2×#6718yes—
467C23×C3C23×D314yes—
468C23×C3C23×D314yes—
469C23×C3C23×D311yescharacteristic
470C23×C3C23×D311yescharacteristic
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—24no—
474C22×D3—24no—
475C22×D3—24no—
476C22×D3—216no—
477C22×D3—216no—
478C22×D3—32no—
479C22×D3—32no—
480C22×D3—48no—
481C22×D3—432no—
482C22×D3—62no—
483C22×D3—64no—
484C22×D3—62no—
485C22×D3—62no—
486C22×D3—62no—
487C22×D3—62no—
488C22×D3—62no—
489C22×D3—62no—
490C22×D3—122no—
491C22×D3—122no—
492C22×D3#23714yescomplemented
493C22×D3C23×D314yes—
494C22×D3C23×D312yes—
495C3×D4—216no—
496C3×D4—616no—
497C3×D4—68no—
498C3×D4C2×D12116yescomplemented
499C3×D4C2×#67116yescomplemented
500C2×C3×C4—22no—
501C2×C3×C4—24no—
502C2×C3×C4—32no—
503C2×C3×C4—32no—
504C2×C3×C4—34no—
505C2×C3×C4—32no—
506C2×C3×C4—62no—
507C2×C3×C4—62no—
508C2×C3×C4—64no—
509C2×C3×C4—62no—
510C2×C3×C4—68no—
511C2×C3×C4—128no—
512C2×C3×C4C2×D1214yes—
513C2×C3×C4C2×#6714yes—
514C2×C3×C4C23×D312yes—
515C2×C3×C4C23×D312yes—
516#67—216no—
517#67—68no—
518#67—632no—
519#67—616no—
520#67—616no—
521#67—128no—
522C2×Dic3—22no—
523C2×Dic3—24no—
524C2×Dic3—22no—
525C2×Dic3—22no—
526C2×Dic3—34no—
527C2×Dic3—32no—
528C2×Dic3—34no—
529C2×Dic3—32no—
530C2×Dic3—48no—
531C2×Dic3—64no—
532C2×Dic3—62no—
533C2×Dic3—68no—
534C2×Dic3—64no—
535C2×Dic3—632no—
536C2×Dic3—64no—
537C2×Dic3—62no—
538C2×Dic3—616no—
539C2×Dic3—64no—
540C2×Dic3—62no—
541C2×Dic3—616no—
542C2×Dic3C23×D312yes—
543C2×Dic3C23×D312yes—
544C2×Dic3C23×D314yes—
545C2×Dic3C23×D312yes—
546D12—28no—
547D12—68no—
548D12—128no—
549C4×D3—28no—
550C4×D3—616no—
551C4×D3—68no—
552C4×D3—68no—
553Dic6—616no—
554Dic6—68no—
555Dic6—68no—
556C2×C32—28no—
557C2×C32#54614yescomplemented
558C2×C32C23×D411yescharacteristic
559C2×C32C22×#4111yescharacteristic
560C2×C32C2×H(5,𝔽2)11yescharacteristic
561C3⋊D3—42no—
562C3×D3—24no—
563C3×D3—44no—
564C24—31no—
565C24—32no—
566C24—38no—
567C24—68no—
568C24—68no—
569C24—91no—
570C24—124no—
571C24C2×D3212yes—
572#41—1832no—
573C2×Q8—94no—
574C2×Q8—184no—
575C2×D4—38no—
576C2×D4—34no—
577C2×D4—68no—
578C2×D4—632no—
579C2×D4—64no—
580C2×D4—94no—
581C2×D4—98no—
582C2×D4—98no—
583C2×D4—184no—
584C2×D4—188no—
585C2×D4—364no—
586C2×D4#62618yescomplemented
587C2×D4C2×D3214yes—
588C22×C4—31no—
589C22×C4—31no—
590C22×C4—32no—
591C22×C4—31no—
592C22×C4—38no—
593C22×C4—34no—
594C22×C4—64no—
595C22×C4—98no—
596C22×C4—91no—
597C22×C4—92no—
598C22×C4—94no—
599C22×C4—124no—
600C22×C4—188no—
601C22×C4—184no—
602C22×C4C2×D3211yescharacteristic
603C4⋊C4—34no—
604C4⋊C4—94no—
605C4⋊C4—98no—
606C22⋊C4—38no—
607C22⋊C4—94no—
608C22⋊C4—94no—
609C22⋊C4—98no—
610C22⋊C4—98no—
611C22⋊C4—98no—
612C22⋊C4—98no—
613C42—34no—
614C22×C3—24no—
615C22×C3—24no—
616C22×C3—24no—
617C22×C3—24no—
618C22×C3—216no—
619C22×C3—216no—
620C22×C3—22no—
621C22×C3—22no—
622C22×C3—22no—
623C22×C3—28no—
624C22×C3—21no—
625C22×C3—34no—
626C22×C3—44no—
627C22×C3—44no—
628C22×C3—416no—
629C22×C3—62no—
630C22×C3—62no—
631C22×C3—68no—
632C22×C3—64no—
633C22×C3—64no—
634C22×C3—64no—
635C22×C3—1232no—
636C22×C3—128no—
637C22×C3C22×D1218yes—
638C22×C3C22×D1212yes—
639C22×C3C2×#23712yes—
640C22×C3#100412yes—
641C22×C3#100412yes—
642C22×C3D3×#4112yes—
643C22×C3C22×#6718yes—
644C22×C3C22×#6712yes—
645C22×C3C24×D311yescharacteristic
646C22×C3C24×D311yescharacteristic
647C2×D3—22no—
648C2×D3—22no—
649C2×D3—28no—
650C2×D3—24no—
651C2×D3—24no—
652C2×D3—24no—
653C2×D3—432no—
654C2×D3—48no—
655C2×D3—64no—
656C2×D3—62no—
657C2×D3—62no—
658C2×D3—62no—
659C2×D3—62no—
660C2×D3—62no—
661C2×D3—62no—
662C2×D3—122no—
663C2×D3—122no—
664C2×D3—128no—
665C2×D3—124no—
666C2×D3—124no—
667C2×D3C2×#23714yescomplemented
668C3×C4—24no—
669C3×C4—62no—
670C3×C4—62no—
671C3×C4—64no—
672C3×C4—62no—
673C3×C4C22×D1214yes—
674C3×C4C22×#6714yes—
675Dic3—22no—
676Dic3—24no—
677Dic3—22no—
678Dic3—22no—
679Dic3—68no—
680Dic3—64no—
681Dic3—64no—
682Dic3—62no—
683Dic3—64no—
684Dic3—62no—
685C32C2×#54611yescharacteristic, complemented, Sylow
686C23—24no—
687C23—24no—
688C23—34no—
689C23—32no—
690C23—34no—
691C23—616no—
692C23—62no—
693C23—62no—
694C23—64no—
695C23—64no—
696C23—616no—
697C23—64no—
698C23—92no—
699C23—128no—
700C23—1232no—
701C23—182no—
702C23—182no—
703C23—182no—
704C23C2×#62618yes—
705C23C22×D3214yes—
706C23C22×D3211yescharacteristic
707Q8—188no—
708D4—616no—
709D4—68no—
710D4—188no—
711D4—1816no—
712D4—368no—
713D4C2×#626116yescomplemented
714C2×C4—32no—
715C2×C4—32no—
716C2×C4—34no—
717C2×C4—32no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—64no—
721C2×C4—62no—
722C2×C4—68no—
723C2×C4—92no—
724C2×C4—94no—
725C2×C4—128no—
726C2×C4—182no—
727C2×C4—184no—
728C2×C4—1816no—
729C2×C4—188no—
730C2×C4C2×#62614yes—
731C2×C4C22×D3212yes—
732C2×C3—28no—
733C2×C3—28no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—24no—
738C2×C3—48no—
739C2×C3—64no—
740C2×C3—124no—
741C2×C3#555414yescomplemented
742C2×C3#580614yescomplemented
743C2×C3C23×D1211yescharacteristic
744C2×C3C22×#23711yescharacteristic
745C2×C3C2×#100411yescharacteristic
746C2×C3C2×#100411yescharacteristic
747C2×C3C2×D3×#4111yescharacteristic
748C2×C3C23×#6711yescharacteristic
749D3—24no—
750D3—44no—
751D3—124no—
752D3—122no—
753D3—122no—
754C22—24no—
755C22—24no—
756C22—216no—
757C22—34no—
758C22—62no—
759C22—62no—
760C22—68no—
761C22—64no—
762C22—64no—
763C22—64no—
764C22—1232no—
765C22—128no—
766C22—182no—
767C22—182no—
768C22—182no—
769C22—364no—
770C22D3×#23712yes—
771C22#6431312yes—
772C22C22×#62618yes—
773C22C22×#62612yes—
774C22C23×D3211yescharacteristic
775C4—62no—
776C4—62no—
777C4—64no—
778C4—62no—
779C4—182no—
780C4—184no—
781C4C22×#62614yes—
782C3—21no—
783C3C2×#555411yescharacteristic, complemented
784C3C2×#580611yescharacteristic, complemented
785C2—28no—
786C2—64no—
787C2—124no—
788C2—362no—
789C2#1059524614yesdirect product factor
790C2C2×D3×#23711yescharacteristic
791C2C2×#6431311yescharacteristic
792C2C23×#62611yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3830C2semidirect
2. C22×C3×D3×D4C2semidirect
3. C2×C3×D4×Dic3C2semidirect
4. C2×#63978C2semidirect
5. C2×#63977C2semidirect
6. C2×#63962C2semidirect
7. C22×(C2×D3)⋊Dic3C2semidirect
8. #10595246C2direct (N × H)
9. C2×#63916C2semidirect
10. C2×C4×#626C2semidirect
11. C2×#63860C2semidirect
12. C2×#63857C2semidirect
17. C22×#638C22semidirect
18. C23×C3⋊Dic3C22semidirect
20. C2×#3830C22semidirect
21. C22×C4×C3⋊D3C22semidirect
22. C22×#634C22semidirect
24. C23×C3×Dic3C22semidirect
26. C2×C3×D3×D4C22semidirect
30. C22×#626C22semidirect
31. C2×C3×#217C22semidirect
32. C3×D4×Dic3C22semidirect
33. C2×C3×C4⋊Dic3C22semidirect
34. C2×C3×C4×Dic3C22semidirect
35. #63978C22semidirect
36. #63977C22semidirect
37. C2×Dic3⋊Dic3C22semidirect
38. C2×Dic3⋊Dic3C22semidirect
39. C2×#3722C22semidirect
40. #63962C22semidirect
43. C2×(C2×D3)⋊Dic3C22semidirect
44. C2×(C2×D3)⋊Dic3C22semidirect
45. C2×(C2×D3)⋊Dic3C22semidirect
46. C2×(C2×D3)⋊Dic3C22semidirect
47. #63916C22semidirect
48. C4×#626C22semidirect
49. #63860C22semidirect
50. #63857C22semidirect
55. C22×D3×D4D3semidirect
64. C2×D4×Dic3D3semidirect
84. C2×C32×D4D4semidirect
88. C2×#638C23semidirect
92. C22×C3⋊Dic3C23semidirect
95. C2×C4×C3⋊D3C23semidirect
97. C2×#634C23semidirect
105. C22×C3×Dic3C23semidirect
114. C2×#626C23semidirect
115. C3×#217C23semidirect
116. C3×C4⋊Dic3C23semidirect
117. C3×C4×Dic3C23semidirect
118. Dic3⋊Dic3C23semidirect
119. Dic3⋊Dic3C23semidirect
120. #3722C23semidirect
123. (C2×D3)⋊Dic3C23semidirect
124. (C2×D3)⋊Dic3C23semidirect
125. (C2×D3)⋊Dic3C23semidirect
147. C23×Dic3C2×D3semidirect
155. C2×D3×D4C2×D3semidirect
177. C2×#217C2×D3semidirect
182. D4×Dic3C2×D3semidirect
195. C2×C4⋊Dic3C2×D3semidirect
199. C2×C4×Dic3C2×D3semidirect
224. C22×C3×D3#41semidirect
227. C32×D4C2×D4semidirect
289. C2×C3×D4D12semidirect
290. C2×C3×D4#67semidirect
333. C22×Dic3C22×D3semidirect
366. #217C22×D3semidirect
376. C4⋊Dic3C22×D3semidirect
379. C4×Dic3C22×D3semidirect
400. C2×C3×D3C2×#41semidirect
492. C22×D3#237semidirect
498. C3×D4C2×D12semidirect
499. C3×D4C2×#67semidirect
557. C2×C32#546semidirect
586. C2×D4#626semidirect
667. C2×D3C2×#237semidirect
685. C32C2×#546semidirect
713. D4C2×#626semidirect
741. C2×C3#5554semidirect
742. C2×C3#5806semidirect
783. C3C2×#5554semidirect
784. C3C2×#5806semidirect
789. C2#10595246direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38302
C22×C3×D3×D42
C2×C3×D4×Dic32
C2×#639782
C2×#639772
C2×#639622
C22×(C2×D3)⋊Dic32
#105952462
C2×#639162
C2×C4×#6262
C2×#638602
C2×#638572
C2×#58063
C2×#55543