Finite Group Databasebeta

← C2×#10594627 #11900464

Subgroups — C2×#10594627 #11900464

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×C4×D32C211yesmaximal, characteristic, complemented
2C22×#3799C211yesmaximal, characteristic, complemented
3C2×#64104C211yesmaximal, characteristic, complemented
4C2×C3×#897C211yesmaximal, characteristic, complemented
5C2×C3×#892C211yesmaximal, characteristic, complemented
6C2×#63923C212yesmaximal, complemented
7C2×#63909C211yesmaximal, characteristic, complemented
8C2×#63894C212yesmaximal, complemented
9C2×#63890C212yesmaximal, complemented
10C2×#63880C212yesmaximal, complemented
11C2×#63871C211yesmaximal, characteristic, complemented
12#10594627C2116yesmaximal, direct product factor
13C2×#5627—31nomaximal
14C2×#5524—31nomaximal
15C23×D32C2211yescharacteristic
16C22×C4⋊(C3⋊D3)C2212yes—
17C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic, complemented
22C22×#626C2212yes—
23C22×#626C2212yes—
24C22×#624C2211yescharacteristic
25C22×#624C2212yescomplemented
26C22×D3×Dic3C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×C4×D32—28no—
29C2×C4×D32C2218yescomplemented
30C2×#3799—28no—
31C2×#3799C2218yescomplemented
32C2×C32×C4⋊C4C2211yescharacteristic, complemented
33C2×#3752C2212yescomplemented
34#64104C2218yescomplemented
35C2×C3×(C2×D3)⋊C4C2212yes—
36C2×C3×(C2×D3)⋊C4C2212yes—
37C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
38C2×C3×C4⋊Dic3C2212yescomplemented
39C2×C3×C4×Dic3C2212yescomplemented
40C3×#897C2218yescomplemented
41C3×#892C2218yescomplemented
42C2×Dic3⋊Dic3C2212yescomplemented
43C2×#3722C2212yes—
44C2×#3722C2212yescomplemented
45#63923C22116yescomplemented
46#63909C2218yescomplemented
47#63894C22116yescomplemented
48#63890C22116yescomplemented
49#63880C22116yescomplemented
50#63871C2218yescomplemented
51C22×#239—31no—
52C22×#235—31no—
53C23×C4×D3—31no—
54C23×C4×D3—31no—
55C2×C3×C22⋊Q8—31no—
56C2×C3×#117—31no—
57C2×#946—31no—
58C2×#930—31no—
59#5627—316no—
60#5524—316no—
61C2×#897—31no—
62C2×#897D311yescharacteristic, complemented
63C2×#895—31no—
64C2×#895—31no—
65C2×#895—31no—
66C2×#895—61no—
67C2×#894—32no—
68C2×#893—32no—
69C2×#892D311yescharacteristic, complemented
70C2×#886—32no—
71C2×#882—32no—
72C2×#882—32no—
73C2×#67⋊C4—32no—
74C2×C4×D12—32no—
75C2×C4×D12—32no—
76C23×C3⋊D3C2312yes—
77C23×C3⋊D3C2311yescharacteristic
78C23×C3×D3C2311yescharacteristic
79C23×C3×D3C2311yescharacteristic
80C22×D32—24no—
81C22×D32—24no—
82C22×D32—24no—
83C22×D32C2314yes—
84C22×C32×C4C2312yes—
85C22×C32×C4C2311yescharacteristic
86C22×C3⋊Dic3C2311yescharacteristic
87C2×C4⋊(C3⋊D3)—28no—
88C2×C4⋊(C3⋊D3)—24no—
89C2×C4⋊(C3⋊D3)C2318yes—
90C2×C4⋊(C3⋊D3)C2314yescomplemented
91C2×C4×C3⋊D3—24no—
92C2×C4×C3⋊D3C2314yes—
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2312yes—
96C22×C3×Dic3C2311yescharacteristic
97C2×C3×C4×D3—24no—
98C2×C3×C4×D3D418yescomplemented
99C2×C3×C4×D3C2314yes—
100C2×C3×C4×D3C2314yes—
101C2×C3×Dic6—24no—
102C2×C3×Dic6C2314yescomplemented
103C2×#626—28no—
104C2×#626—28no—
105C2×#626C2318yes—
106C2×#626C2318yes—
107C2×#624—28no—
108C2×#624—24no—
109C2×#624C2314yes—
110C2×#624C2318yescomplemented
111C2×D3×Dic3—24no—
112C2×D3×Dic3—24no—
113C2×D3×Dic3C2314yes—
114C2×D3×Dic3C2314yes—
115C4×D32—232no—
116#3799—232no—
117C32×C4⋊C4C2314yescomplemented
118#3752C2318yescomplemented
119C3×(C2×D3)⋊C4C2318yes—
120C3×(C2×D3)⋊C4C2318yes—
121C3×C4⋊Dic3C2314yescomplemented
122C3×C4⋊Dic3C2318yescomplemented
123C3×C4×Dic3C2318yescomplemented
124Dic3⋊Dic3C2318yescomplemented
125#3722C2318yes—
126#3722C2318yescomplemented
127C2×#525—91noSylow
128C24×D3—31no—
129C24×D3—31no—
130C22×C3×Q8—31no—
131C23×C3×C4—31no—
132C23×C3×C4—31no—
133C22×#67—32no—
134C22×#67—32no—
135C23×Dic3—31no—
136C23×Dic3—31no—
137C2×#239—38no—
138C2×#239—68no—
139C2×#235—38no—
140C2×#235—68no—
141C22×D12—32no—
142C22×D12—32no—
143C22×D12—31no—
144C22×D12—31no—
145C22×D12—32no—
146C22×D12—32no—
147C22×D12—62no—
148C22×D12—61no—
149C22×C4×D3—31no—
150C22×C4×D3—31no—
151C22×C4×D3—31no—
152C22×C4×D3—31no—
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C22×C4×D3—32no—
156C22×C4×D3—32no—
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×C22⋊Q8—38no—
166C3×#117—38no—
167C2×C3×C4⋊C4—21no—
168C2×C3×C4⋊C4—32no—
169C2×C3×C4⋊C4—31no—
170C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
171C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
172C2×C3×C22⋊C4—32no—
173C2×C3×C22⋊C4—32no—
174C2×C3×C42—32no—
175#946—38no—
176#930—38no—
177C2×(C2×D3)⋊C4—32no—
178C2×(C2×D3)⋊C4—32no—
179C2×(C2×D3)⋊C4—32no—
180C2×(C2×D3)⋊C4—32no—
181C2×(C2×D3)⋊C4—32no—
182C2×(C2×D3)⋊C4—32no—
183C2×(C2×D3)⋊C4—62no—
184C2×(C2×D3)⋊C4C2×D312yes—
185C2×(C2×D3)⋊C4C2×D312yes—
186C2×C4⋊Dic3—32no—
187C2×C4⋊Dic3C2×D312yescomplemented
188C2×C4⋊Dic3C2×D311yescharacteristic, complemented
189C2×Dic3⋊C4—32no—
190C2×C4×Dic3C2×D312yescomplemented
191#897—38no—
192#897C2×D318yescomplemented
193#895—38no—
194#895—38no—
195#895—38no—
196#895—68no—
197#894—316no—
198#893—316no—
199#892C2×D318yescomplemented
200#886—316no—
201#882—316no—
202#882—316no—
203#67⋊C4—316no—
204C4×D12—316no—
205C4×D12—316no—
206C23×C32C2411yescharacteristic
207C22×C3⋊D3—22no—
208C22×C3⋊D3—22no—
209C22×C3⋊D3—24no—
210C22×C3⋊D3—24no—
211C22×C3⋊D3—24no—
212C22×C3⋊D3#4114yescomplemented
213C22×C3⋊D3C2414yes—
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—
227C2×C32×C4—24no—
228C2×C32×C4C2×D414yes—
229C2×C32×C4C2414yes—
230C2×C32×C4C2412yes—
231C2×C3⋊Dic3—22no—
232C2×C3⋊Dic3C2412yes—
233C4⋊(C3⋊D3)—216no—
234C4⋊(C3⋊D3)—28no—
235C4×C3⋊D3—28no—
236C2×C3×Dic3—22no—
237C2×C3×Dic3—24no—
238C2×C3×Dic3—24no—
239C2×C3×Dic3C2×D414yes—
240C2×C3×Dic3C2414yes—
241C2×C3×Dic3C2414yes—
242C2×C3×Dic3C2412yes—
243C2×C3×Dic3C2412yes—
244C3×C4×D3—28no—
245C3×C4×D3C2×D4116yescomplemented
246C3×Dic6—28no—
247#626—216no—
248#626—216no—
249#624—216no—
250#624—28no—
251D3×Dic3—28no—
252D3×Dic3—28no—
253C22×#41—91no—
254C24×C4—91no—
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—31no—
265C24×C3—31no—
266C24×C3—31no—
267C23×D3—31no—
268C23×D3—31no—
269C23×D3—32no—
270C23×D3—32no—
271C23×D3—34no—
272C23×D3—34no—
273C23×D3—61no—
274C23×D3—62no—
275C23×D3—64no—
276C23×D3—64no—
277C23×D3—64no—
278C23×D3—64no—
279C23×D3—64no—
280C23×D3—64no—
281C23×D3C22×D311yescharacteristic
282C23×D3C22×D311yescharacteristic
283C2×C3×Q8—34no—
284C2×C3×Q8—64no—
285C22×C3×C4—21no—
286C22×C3×C4—22no—
287C22×C3×C4—31no—
288C22×C3×C4—38no—
289C22×C3×C4—34no—
290C22×C3×C4—32no—
291C22×C3×C4—32no—
292C22×C3×C4—31no—
293C22×C3×C4—34no—
294C22×C3×C4—64no—
295C22×C3×C4C22×D312yes—
296C22×C3×C4C22×D312yes—
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D311yescharacteristic
299C2×#67—38no—
300C2×#67—38no—
301C2×#67—68no—
302C2×#67—68no—
303C22×Dic3—31no—
304C22×Dic3—31no—
305C22×Dic3—34no—
306C22×Dic3—34no—
307C22×Dic3—61no—
308C22×Dic3—64no—
309C22×Dic3—64no—
310C22×Dic3C22×D312yes—
311C22×Dic3C22×D312yes—
312C22×Dic3C22×D311yescharacteristic
313C22×Dic3C22×D311yescharacteristic
314#239—632no—
315#235—632no—
316C2×D12—38no—
317C2×D12—38no—
318C2×D12—38no—
319C2×D12—38no—
320C2×D12—34no—
321C2×D12—34no—
322C2×D12—68no—
323C2×D12—64no—
324C2×D12—68no—
325C2×D12—68no—
326C2×D12—68no—
327C2×D12—68no—
328C2×D12—64no—
329C2×D12—64no—
330C2×D12—124no—
331C2×D12—128no—
332C2×C4×D3—24no—
333C2×C4×D3—34no—
334C2×C4×D3—34no—
335C2×C4×D3—34no—
336C2×C4×D3—34no—
337C2×C4×D3—34no—
338C2×C4×D3—38no—
339C2×C4×D3—38no—
340C2×C4×D3—34no—
341C2×C4×D3—64no—
342C2×C4×D3—632no—
343C2×C4×D3—64no—
344C2×C4×D3—68no—
345C2×C4×D3—64no—
346C2×C4×D3—64no—
347C2×C4×D3—64no—
348C2×C4×D3—64no—
349C2×C4×D3—64no—
350C2×C4×D3—68no—
351C2×C4×D3—632no—
352C2×C4×D3—124no—
353C2×C4×D3D1218yescomplemented
354C2×C4×D3C22×D314yes—
355C2×C4×D3C22×D314yes—
356C2×Dic6—24no—
357C2×Dic6C22×D314yescomplemented
358C3×C4⋊C4—24no—
359C3×C4⋊C4—38no—
360C3×C4⋊C4—34no—
361C3×C4⋊C4C22×D314yescomplemented
362C3×C4⋊C4C22×D314yescomplemented
363C3×C22⋊C4—38no—
364C3×C22⋊C4—38no—
365C3×C42—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—38no—
371(C2×D3)⋊C4—38no—
372(C2×D3)⋊C4—68no—
373(C2×D3)⋊C4C22×D318yes—
374(C2×D3)⋊C4C22×D318yes—
375C4⋊Dic3—38no—
376C4⋊Dic3C22×D318yescomplemented
377C4⋊Dic3C22×D314yescomplemented
378Dic3⋊C4—38no—
379C4×Dic3C22×D318yescomplemented
380C22×C32C22×D412yes—
381C22×C32C2×#4112yes—
382C22×C32C2×#4112yes—
383C22×C32C2511yescharacteristic
384C2×C3⋊D3—28no—
385C2×C3⋊D3—22no—
386C2×C3⋊D3—22no—
387C2×C3⋊D3—24no—
388C2×C3⋊D3—24no—
389C2×C3⋊D3—24no—
390C2×C3⋊D3—48no—
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×C4—24no—
402C32×C4C22×D414yes—
403C3⋊Dic3—22no—
404C3×Dic3—22no—
405C3×Dic3—24no—
406C3×Dic3—24no—
407C3×Dic3C22×D414yes—
408C25—91no—
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—91no—
419C23×C4—92no—
420C23×C4—98no—
421C23×C4—91no—
422C23×C4—91no—
423C23×C4—91no—
424C23×C4—188no—
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—38no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—32no—
436C2×C4⋊C4—92no—
437C2×C4⋊C4D3211yescharacteristic, complemented
438C2×C22⋊C4—32no—
439C2×C22⋊C4—32no—
440C2×C22⋊C4—92no—
441C2×C22⋊C4—92no—
442C2×C22⋊C4—92no—
443C2×C42—32no—
444C23×C3—21no—
445C23×C3—34no—
446C23×C3—34no—
447C23×C3—32no—
448C23×C3—32no—
449C23×C3—62no—
450C23×C3—62no—
451C23×C3—62no—
452C23×C3—62no—
453C23×C3C23×D311yescharacteristic
454C23×C3C23×D311yescharacteristic
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—34no—
460C22×D3—34no—
461C22×D3—32no—
462C22×D3—32no—
463C22×D3—34no—
464C22×D3—34no—
465C22×D3—64no—
466C22×D3—62no—
467C22×D3—64no—
468C22×D3—68no—
469C22×D3—68no—
470C22×D3—68no—
471C22×D3—68no—
472C22×D3—632no—
473C22×D3—632no—
474C22×D3—62no—
475C22×D3—62no—
476C22×D3—62no—
477C22×D3—62no—
478C22×D3—68no—
479C22×D3—68no—
480C22×D3—64no—
481C22×D3—64no—
482C22×D3—64no—
483C22×D3—64no—
484C22×D3—64no—
485C22×D3—64no—
486C22×D3—122no—
487C22×D3—122no—
488C22×D3—124no—
489C22×D3—124no—
490C22×D3—124no—
491C22×D3C2×D1214yes—
492C22×D3#23914yescomplemented
493C22×D3C23×D312yes—
494C22×D3C23×D312yes—
495C3×Q8—68no—
496C2×C3×C4—24no—
497C2×C3×C4—24no—
498C2×C3×C4—22no—
499C2×C3×C4—24no—
500C2×C3×C4—24no—
501C2×C3×C4—34no—
502C2×C3×C4—32no—
503C2×C3×C4—316no—
504C2×C3×C4—34no—
505C2×C3×C4—34no—
506C2×C3×C4—32no—
507C2×C3×C4—44no—
508C2×C3×C4—62no—
509C2×C3×C4—64no—
510C2×C3×C4—64no—
511C2×C3×C4—68no—
512C2×C3×C4C2×D1214yes—
513C2×C3×C4D3×D414yes—
514C2×C3×C4C23×D314yes—
515C2×C3×C4C23×D314yes—
516C2×C3×C4C23×D312yes—
517C2×C3×C4C23×D312yes—
518#67—616no—
519#67—616no—
520C2×Dic3—24no—
521C2×Dic3—22no—
522C2×Dic3—24no—
523C2×Dic3—32no—
524C2×Dic3—32no—
525C2×Dic3—62no—
526C2×Dic3—68no—
527C2×Dic3—62no—
528C2×Dic3—62no—
529C2×Dic3—68no—
530C2×Dic3—122no—
531C2×Dic3C2×D1214yes—
532C2×Dic3C23×D314yes—
533C2×Dic3C23×D314yes—
534C2×Dic3C23×D312yes—
535C2×Dic3C23×D312yes—
536D12—616no—
537D12—616no—
538D12—616no—
539D12—616no—
540D12—68no—
541D12—68no—
542D12—128no—
543D12—1216no—
544C4×D3—28no—
545C4×D3—68no—
546C4×D3—616no—
547C4×D3—68no—
548C4×D3—68no—
549C4×D3—68no—
550C4×D3—68no—
551C4×D3—68no—
552C4×D3—616no—
553C4×D3—128no—
554C4×D3C2×D12116yescomplemented
555Dic6—28no—
556C2×C32#52514yescomplemented
557C2×C32C23×D411yescharacteristic
558C2×C32C22×#4111yescharacteristic
559C2×C32C22×#4111yescharacteristic
560C3⋊D3—24no—
561C3⋊D3—44no—
562C3×D3—24no—
563C3×D3—24no—
564C24—31no—
565C24—31no—
566C24—94no—
567C24—91no—
568C24—92no—
569C24—184no—
570C24—184no—
571C24—184no—
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—31no—
584C22×C4—34no—
585C22×C4—38no—
586C22×C4—32no—
587C22×C4—32no—
588C22×C4—31no—
589C22×C4—34no—
590C22×C4—64no—
591C22×C4—94no—
592C22×C4—98no—
593C22×C4—94no—
594C22×C4—94no—
595C22×C4—91no—
596C22×C4—94no—
597C22×C4—184no—
598C22×C4—1832no—
599C22×C4—188no—
600C22×C4—184no—
601C22×C4—184no—
602C22×C4—184no—
603C22×C4C2×D3212yes—
604C22×C4C2×D3211yescharacteristic
605C4⋊C4—34no—
606C4⋊C4—38no—
607C4⋊C4—98no—
608C4⋊C4C2×D3214yescomplemented
609C22⋊C4—38no—
610C22⋊C4—38no—
611C22⋊C4—98no—
612C22⋊C4—98no—
613C22⋊C4—98no—
614C42—38no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—22no—
618C22×C3—21no—
619C22×C3—34no—
620C22×C3—34no—
621C22×C3—62no—
622C22×C3—62no—
623C22×C3—62no—
624C22×C3—62no—
625C22×C3—68no—
626C22×C3—68no—
627C22×C3C22×D1212yes—
628C22×C3C2×D3×D412yes—
629C22×C3C2×#23912yes—
630C22×C3D3×#4112yes—
631C22×C3D3×#4112yes—
632C22×C3D3×#4112yes—
633C22×C3C24×D311yescharacteristic
634C22×C3C24×D311yescharacteristic
635C2×D3—22no—
636C2×D3—22no—
637C2×D3—22no—
638C2×D3—22no—
639C2×D3—28no—
640C2×D3—28no—
641C2×D3—34no—
642C2×D3—34no—
643C2×D3—64no—
644C2×D3—632no—
645C2×D3—632no—
646C2×D3—62no—
647C2×D3—62no—
648C2×D3—62no—
649C2×D3—62no—
650C2×D3—68no—
651C2×D3—68no—
652C2×D3—64no—
653C2×D3—64no—
654C2×D3—64no—
655C2×D3—64no—
656C2×D3—64no—
657C2×D3—64no—
658C2×D3—122no—
659C2×D3—128no—
660C2×D3—122no—
661C2×D3—124no—
662C2×D3—124no—
663C2×D3—124no—
664C2×D3—128no—
665C2×D3—128no—
666C2×D3—248no—
667C2×D3C22×D1214yes—
668C2×D3C2×#23914yescomplemented
669C3×C4—24no—
670C3×C4—24no—
671C3×C4—24no—
672C3×C4—34no—
673C3×C4—44no—
674C3×C4—62no—
675C3×C4—64no—
676C3×C4—64no—
677C3×C4C22×D1214yes—
678C3×C4C2×D3×D414yes—
679Dic3—24no—
680Dic3—22no—
681Dic3—24no—
682Dic3—62no—
683Dic3—62no—
684Dic3—122no—
685Dic3C22×D1214yes—
686C32C2×#52511yescharacteristic, complemented, Sylow
687C23—34no—
688C23—34no—
689C23—32no—
690C23—32no—
691C23—62no—
692C23—62no—
693C23—62no—
694C23—62no—
695C23—94no—
696C23—92no—
697C23—94no—
698C23—188no—
699C23—188no—
700C23—188no—
701C23—1832no—
702C23—182no—
703C23—182no—
704C23—184no—
705C23—184no—
706C23—184no—
707C23C22×D3211yescharacteristic
708Q8—68no—
709D4—1816no—
710D4—1816no—
711D4—1816no—
712D4—188no—
713C2×C4—24no—
714C2×C4—34no—
715C2×C4—32no—
716C2×C4—316no—
717C2×C4—34no—
718C2×C4—34no—
719C2×C4—32no—
720C2×C4—62no—
721C2×C4—64no—
722C2×C4—64no—
723C2×C4—68no—
724C2×C4—92no—
725C2×C4—188no—
726C2×C4—1816no—
727C2×C4—188no—
728C2×C4—188no—
729C2×C4—182no—
730C2×C4—188no—
731C2×C4D3×D1214yes—
732C2×C4C22×D3214yes—
733C2×C4C22×D3212yes—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—24no—
737C2×C3—21no—
738C2×C3—64no—
739C2×C3—64no—
740C2×C3#552414yescomplemented
741C2×C3#562714yescomplemented
742C2×C3C23×D1211yescharacteristic
743C2×C3C22×D3×D411yescharacteristic
744C2×C3C22×#23911yescharacteristic
745C2×C3C2×D3×#4111yescharacteristic
746C2×C3C2×D3×#4111yescharacteristic
747C2×C3C2×D3×#4111yescharacteristic
748D3—24no—
749D3—24no—
750D3—64no—
751D3—64no—
752D3—124no—
753D3—124no—
754D3—124no—
755D3—244no—
756C22—34no—
757C22—34no—
758C22—62no—
759C22—62no—
760C22—62no—
761C22—68no—
762C22—68no—
763C22—62no—
764C22—94no—
765C22—1832no—
766C22—182no—
767C22—188no—
768C22—182no—
769C22—184no—
770C22—184no—
771C22—184no—
772C22—368no—
773C22C2×D3×D1212yes—
774C22#6431212yes—
775C22D3×#23912yes—
776C22C23×D3211yescharacteristic
777C4—24no—
778C4—34no—
779C4—62no—
780C4—64no—
781C4—64no—
782C4—182no—
783C4C2×D3×D1214yes—
784C3—21no—
785C3C2×#552411yescharacteristic, complemented
786C3C2×#562711yescharacteristic, complemented
787C2—64no—
788C2—64no—
789C2—184no—
790C2—364no—
791C2#1059462714yesdirect product factor
792C2C22×D3×D1211yescharacteristic
793C2C2×#6431211yescharacteristic
794C2C2×D3×#23911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#525
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×C4×D32C2semidirect
2. C22×#3799C2semidirect
3. C2×#64104C2semidirect
4. C2×C3×#897C2semidirect
5. C2×C3×#892C2semidirect
6. C2×#63923C2semidirect
7. C2×#63909C2semidirect
8. C2×#63894C2semidirect
9. C2×#63890C2semidirect
10. C2×#63880C2semidirect
11. C2×#63871C2semidirect
12. #10594627C2direct (N × H)
17. C22×C4⋊(C3⋊D3)C22semidirect
21. C22×C3×Dic6C22semidirect
25. C22×#624C22semidirect
29. C2×C4×D32C22semidirect
31. C2×#3799C22semidirect
32. C2×C32×C4⋊C4C22semidirect
33. C2×#3752C22semidirect
34. #64104C22semidirect
37. C2×C3×C4⋊Dic3C22semidirect
38. C2×C3×C4⋊Dic3C22semidirect
39. C2×C3×C4×Dic3C22semidirect
40. C3×#897C22semidirect
41. C3×#892C22semidirect
42. C2×Dic3⋊Dic3C22semidirect
44. C2×#3722C22semidirect
45. #63923C22semidirect
46. #63909C22semidirect
47. #63894C22semidirect
48. #63890C22semidirect
49. #63880C22semidirect
50. #63871C22semidirect
62. C2×#897D3semidirect
69. C2×#892D3semidirect
90. C2×C4⋊(C3⋊D3)C23semidirect
98. C2×C3×C4×D3D4semidirect
102. C2×C3×Dic6C23semidirect
110. C2×#624C23semidirect
117. C32×C4⋊C4C23semidirect
118. #3752C23semidirect
121. C3×C4⋊Dic3C23semidirect
122. C3×C4⋊Dic3C23semidirect
123. C3×C4×Dic3C23semidirect
124. Dic3⋊Dic3C23semidirect
126. #3722C23semidirect
164. C22×Dic6C2×D3semidirect
170. C2×C3×C4⋊C4C2×D3semidirect
171. C2×C3×C4⋊C4C2×D3semidirect
187. C2×C4⋊Dic3C2×D3semidirect
188. C2×C4⋊Dic3C2×D3semidirect
190. C2×C4×Dic3C2×D3semidirect
192. #897C2×D3semidirect
199. #892C2×D3semidirect
212. C22×C3⋊D3#41semidirect
220. C22×C3×D3#41semidirect
245. C3×C4×D3C2×D4semidirect
353. C2×C4×D3D12semidirect
357. C2×Dic6C22×D3semidirect
361. C3×C4⋊C4C22×D3semidirect
362. C3×C4⋊C4C22×D3semidirect
376. C4⋊Dic3C22×D3semidirect
377. C4⋊Dic3C22×D3semidirect
379. C4×Dic3C22×D3semidirect
391. C2×C3⋊D3C2×#41semidirect
399. C2×C3×D3C2×#41semidirect
437. C2×C4⋊C4D32semidirect
492. C22×D3#239semidirect
554. C4×D3C2×D12semidirect
556. C2×C32#525semidirect
608. C4⋊C4C2×D32semidirect
668. C2×D3C2×#239semidirect
686. C32C2×#525semidirect
740. C2×C3#5524semidirect
741. C2×C3#5627semidirect
785. C3C2×#5524semidirect
786. C3C2×#5627semidirect
791. C2#10594627direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D322
C22×#37992
C2×#641042
C2×C3×#8972
C2×C3×#8922
C2×#639232
C2×#639092
C2×#638942
C2×#638902
C2×#638802
C2×#638712
#105946272
C2×#56273
C2×#55243