Finite Group Databasebeta

← #11824444

Subgroups — #11824444

Order 1152.

2109 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64104C211yesmaximal, characteristic, complemented
2C2×C3×#895C211yesmaximal, characteristic, complemented
3C2×#63916C211yesmaximal, characteristic, complemented
4C2×#63911C212yesmaximal, complemented
5C2×#63911C211yesmaximal, characteristic, complemented
6C2×#63909C211yesmaximal, characteristic, complemented
7C2×C4×#626C211yesmaximal, characteristic, complemented
8C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
9#10591395C212yesmaximal, complemented
10#10591391C212yesmaximal, complemented
11#10591383C212yesmaximal, complemented
12#82669—31nomaximal
13#73799—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C4⋊(C3⋊D3)C2212yes—
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C3×D12C2211yescharacteristic
18C22×C3×D12C2212yes—
19C22×C3×C4×D3C2211yescharacteristic
20C22×#626C2212yes—
21C22×#626C2212yes—
22C22×#626C2212yes—
23C22×#626C2211yescharacteristic
24C22×#626C2212yes—
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×#3752C2212yes—
27#64104—24no—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2212yes—
31C2×C3×C4×Dic3C2211yescharacteristic
32C3×#895—24no—
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×#3722C2212yes—
35C2×#3722C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2212yes—
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38#63916—24no—
39#63911—28no—
40#63911—24no—
41#63909—24no—
42C4×#626—24no—
43C3×C3⋊#95C2212yes—
44C2×C3×#121—31no—
45C2×#940—32no—
46C2×#940—31no—
47C2×#938—31no—
48C2×#930—31no—
49C2×C4×#67—31no—
50C2×#895—31no—
51C2×#895—31no—
52C2×#895—31no—
53C2×#895—31no—
54C2×#895—61no—
55C2×#895D311yescharacteristic, complemented
56C2×#874—31no—
57C2×#874—32no—
58C2×C4×D12—31no—
59C3×C4×C4⋊C4—31no—
60#5223—32no—
61Dic3×C4⋊C4D311yescharacteristic, complemented
62#4960—32no—
63#4957—32no—
64#4939—32no—
65#4671—32no—
66#4671—32no—
67C23×C3⋊D3C2312yes—
68C23×C3⋊D3C2311yescharacteristic
69C23×C3×D3C2312yes—
70C23×C3×D3C2311yescharacteristic
71C22×C32×C4C2312yes—
72C22×C32×C4C2311yescharacteristic
73C22×C3⋊Dic3C2311yescharacteristic
74C2×C4⋊(C3⋊D3)—24no—
75C2×C4⋊(C3⋊D3)—24no—
76C2×C4⋊(C3⋊D3)—22no—
77C2×C4⋊(C3⋊D3)—22no—
78C2×C4⋊(C3⋊D3)—22no—
79C2×C4⋊(C3⋊D3)—42no—
80C2×C4×C3⋊D3—22no—
81C2×C4×C3⋊D3—22no—
82C2×C4×C3⋊D3—22no—
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2311yescharacteristic
87C2×C3×D12—24no—
88C2×C3×D12—24no—
89C2×C3×D12—22no—
90C2×C3×D12—22no—
91C2×C3×D12—22no—
92C2×C3×D12—42no—
93C2×C3×C4×D3—22no—
94C2×C3×C4×D3—22no—
95C2×C3×C4×D3—22no—
96C2×#626—22no—
97C2×#626—22no—
98C2×#626—24no—
99C2×#626—24no—
100C2×#626—24no—
101C2×#626—24no—
102C2×#626—24no—
103C2×#626—24no—
104C2×#626—24no—
105C2×#626—24no—
106C2×#626—42no—
107C2×#626—42no—
108C2×#626—42no—
109C2×#626—42no—
110C2×#626D414yescomplemented
111C32×C4⋊C4D414yescomplemented
112#3752—24no—
113C3×(C2×D3)⋊C4—24no—
114C3×C4⋊Dic3D414yescomplemented
115C3×C4×Dic3—24no—
116C3×C4×Dic3D414yescomplemented
117Dic3⋊Dic3—22no—
118#3722—22no—
119#3722—24no—
120(C2×D3)⋊Dic3—22no—
121(C2×D3)⋊Dic3—24no—
122#2541—91noSylow
123C22×C3×D4—31no—
124C22×C3×D4—32no—
125C23×C3×C4—31no—
126C22×#67—31no—
127C22×#67—32no—
128C22×#67—32no—
129C22×#67—32no—
130C22×#67—32no—
131C22×D12—31no—
132C22×D12—32no—
133C22×D12—31no—
134C22×D12—31no—
135C22×D12—32no—
136C22×D12—32no—
137C22×D12—32no—
138C22×D12—32no—
139C22×D12—32no—
140C22×D12—61no—
141C22×D12—62no—
142C22×D12C2×D311yescharacteristic
143C22×D12C2×D312yes—
144C22×C4×D3—31no—
145C22×C4×D3—31no—
146C22×C4×D3—61no—
147C22×C4×D3C2×D311yescharacteristic
148C3×#121—64no—
149C2×C3×C4⋊C4—21no—
150C2×C3×C4⋊C4—31no—
151C2×C3×C4⋊C4C2×D311yescharacteristic
152C2×C3×C4⋊C4C2×D311yescharacteristic
153C2×C3×C22⋊C4—32no—
154C2×C3×C42—31no—
155C2×C3×C42—32no—
156C2×#217—32no—
157C2×#217—31no—
158#940—68no—
159#940—64no—
160#938—64no—
161#930—64no—
162C4×#67—64no—
163C2×(C2×D3)⋊C4—31no—
164C2×(C2×D3)⋊C4—32no—
165C2×(C2×D3)⋊C4—32no—
166C2×(C2×D3)⋊C4—32no—
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4—32no—
169C2×(C2×D3)⋊C4—32no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—62no—
172C2×(C2×D3)⋊C4C2×D312yes—
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3C2×D311yescharacteristic
175C2×Dic3⋊C4—31no—
176C2×C4×Dic3C2×D312yes—
177C2×C4×Dic3C2×D311yescharacteristic
178#895—24no—
179#895—68no—
180#895—64no—
181#895—64no—
182#895—64no—
183#895—64no—
184#874—64no—
185#874—68no—
186C4×D12—64no—
187C3×#95—32no—
188C3⋊#95C2×D312yes—
189C23×C32C2411yescharacteristic
190C22×C3⋊D3—21no—
191C22×C3⋊D3—21no—
192C22×C3⋊D3—22no—
193C22×C3⋊D3—21no—
194C22×C3⋊D3—21no—
195C22×C3⋊D3—21no—
196C22×C3⋊D3—21no—
197C22×C3⋊D3—22no—
198C22×C3⋊D3—22no—
199C22×C3⋊D3—22no—
200C22×C3⋊D3—22no—
201C22×C3⋊D3—22no—
202C22×C3⋊D3—22no—
203C22×C3⋊D3C2×D412yes—
204C22×C3×D3—21no—
205C22×C3×D3—21no—
206C22×C3×D3—21no—
207C22×C3×D3—21no—
208C22×C3×D3—21no—
209C22×C3×D3—21no—
210C22×C3×D3—22no—
211C22×C3×D3—22no—
212C22×C3×D3—22no—
213C22×C3×D3—22no—
214C22×C3×D3—22no—
215C22×C3×D3—22no—
216C22×C3×D3—22no—
217C22×C3×D3C2×D412yes—
218C2×C32×C4—22no—
219C2×C32×C4—22no—
220C2×C32×C4C2×D412yes—
221C2×C32×C4C2×D412yes—
222C2×C32×C4C2×D414yes—
223C2×C32×C4C2×D412yes—
224C2×C3⋊Dic3—21no—
225C2×C3⋊Dic3—21no—
226C2×C3⋊Dic3—21no—
227C4⋊(C3⋊D3)—48no—
228C4⋊(C3⋊D3)—44no—
229C4×C3⋊D3—44no—
230C2×C3×Dic3—22no—
231C2×C3×Dic3—21no—
232C2×C3×Dic3—21no—
233C2×C3×Dic3—22no—
234C2×C3×Dic3—21no—
235C2×C3×Dic3—21no—
236C2×C3×Dic3—21no—
237C2×C3×Dic3C2×D412yes—
238C2×C3×Dic3C2×D414yes—
239C2×C3×Dic3C2×D412yes—
240C2×C3×Dic3C2×D412yes—
241C2×C3×Dic3#4112yes—
242C3×D12—48no—
243C3×D12—44no—
244C3×C4×D3—44no—
245#626—28no—
246#626—48no—
247#626—48no—
248#626—48no—
249#626—48no—
250C2×#127—91no—
251C2×#127—92no—
252C2×#121—31no—
253C2×#121—91no—
254C2×#121—91no—
255C2×#121—91no—
256C2×C4×D4—91no—
257#392—92no—
258#392—92no—
259#390—92no—
260C4×C4⋊C4—31no—
261C24×C3—31no—
262C24×C3—32no—
263C23×D3—31no—
264C23×D3—31no—
265C23×D3—32no—
266C23×D3—32no—
267C23×D3—61no—
268C23×D3—62no—
269C23×D3C22×D312yes—
270C23×D3C22×D311yescharacteristic
271C2×C3×D4—64no—
272C2×C3×D4—62no—
273C2×C3×D4—62no—
274C2×C3×D4—64no—
275C2×C3×D4—62no—
276C2×C3×D4—122no—
277C22×C3×C4—21no—
278C22×C3×C4—22no—
279C22×C3×C4—31no—
280C22×C3×C4—31no—
281C22×C3×C4—32no—
282C22×C3×C4—31no—
283C22×C3×C4—62no—
284C22×C3×C4—62no—
285C22×C3×C4—62no—
286C22×C3×C4C22×D312yes—
287C22×C3×C4C22×D312yes—
288C22×C3×C4C22×D311yescharacteristic
289C22×C3×C4C22×D311yescharacteristic
290C2×#67—34no—
291C2×#67—64no—
292C2×#67—64no—
293C2×#67—62no—
294C2×#67—64no—
295C2×#67—64no—
296C2×#67—64no—
297C2×#67—64no—
298C2×#67—64no—
299C2×#67—62no—
300C2×#67—64no—
301C2×#67—122no—
302C2×#67—122no—
303C2×#67—122no—
304C2×#67—122no—
305C22×Dic3—31no—
306C22×Dic3—31no—
307C22×Dic3—61no—
308C22×Dic3C22×D311yescharacteristic
309C22×Dic3C22×D311yescharacteristic
310C22×Dic3C22×D312yes—
311C22×Dic3C22×D311yescharacteristic
312C2×D12—24no—
313C2×D12—22no—
314C2×D12—22no—
315C2×D12—24no—
316C2×D12—22no—
317C2×D12—34no—
318C2×D12—42no—
319C2×D12—62no—
320C2×D12—62no—
321C2×D12—64no—
322C2×D12—64no—
323C2×D12—64no—
324C2×D12—68no—
325C2×D12—64no—
326C2×D12—64no—
327C2×D12—64no—
328C2×D12—64no—
329C2×D12—64no—
330C2×D12—64no—
331C2×D12—64no—
332C2×D12—64no—
333C2×D12—64no—
334C2×D12—62no—
335C2×D12—62no—
336C2×D12—62no—
337C2×D12—62no—
338C2×D12—62no—
339C2×D12—64no—
340C2×D12—62no—
341C2×D12—122no—
342C2×D12—122no—
343C2×D12—124no—
344C2×D12—122no—
345C2×D12—122no—
346C2×D12—124no—
347C2×D12—122no—
348C2×D12—122no—
349C2×D12—122no—
350C2×D12—122no—
351C2×C4×D3—22no—
352C2×C4×D3—22no—
353C2×C4×D3—22no—
354C2×C4×D3—64no—
355C2×C4×D3—62no—
356C2×C4×D3—62no—
357C2×C4×D3—62no—
358C2×C4×D3—62no—
359C2×C4×D3—62no—
360C2×C4×D3—62no—
361C2×C4×D3—122no—
362C2×C4×D3—122no—
363C3×C4⋊C4—24no—
364C3×C4⋊C4—34no—
365C3×C4⋊C4D1214yescomplemented
366C3×C4⋊C4#6714yescomplemented
367C3×C22⋊C4—64no—
368C3×C42—34no—
369C3×C42—64no—
370#217—62no—
371#217—64no—
372(C2×D3)⋊C4—24no—
373(C2×D3)⋊C4—62no—
374(C2×D3)⋊C4—64no—
375(C2×D3)⋊C4—68no—
376(C2×D3)⋊C4—62no—
377(C2×D3)⋊C4—64no—
378(C2×D3)⋊C4—64no—
379(C2×D3)⋊C4—64no—
380(C2×D3)⋊C4—62no—
381(C2×D3)⋊C4—64no—
382C4⋊Dic3—62no—
383C4⋊Dic3D1214yescomplemented
384Dic3⋊C4—62no—
385C4×Dic3—24no—
386C4×Dic3D1214yescomplemented
387C22×C32C22×D411yescharacteristic
388C22×C32C22×D411yescharacteristic
389C22×C32C22×D411yescharacteristic
390C22×C32C22×D411yescharacteristic
391C22×C32C2×#4111yescharacteristic
392C22×C32H(5,𝔽2)11yescharacteristic
393C22×C32H(5,𝔽2)11yescharacteristic
394C2×C3⋊D3—22no—
395C2×C3⋊D3—22no—
396C2×C3⋊D3—22no—
397C2×C3⋊D3—41no—
398C2×C3⋊D3—41no—
399C2×C3⋊D3—41no—
400C2×C3⋊D3—41no—
401C2×C3⋊D3—42no—
402C2×C3⋊D3—42no—
403C2×C3⋊D3—42no—
404C2×C3⋊D3—42no—
405C2×C3⋊D3—42no—
406C2×C3⋊D3—42no—
407C2×C3⋊D3—42no—
408C2×C3×D3—22no—
409C2×C3×D3—22no—
410C2×C3×D3—22no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—41no—
415C2×C3×D3—42no—
416C2×C3×D3—42no—
417C2×C3×D3—42no—
418C2×C3×D3—42no—
419C2×C3×D3—42no—
420C2×C3×D3—42no—
421C2×C3×D3—42no—
422C32×C4—24no—
423C32×C4#12714yescomplemented
424C3⋊Dic3—41no—
425C3×Dic3—22no—
426C3×Dic3—24no—
427C3×Dic3—41no—
428C3×Dic3#12114yescomplemented
429C22×D4—31no—
430C22×D4—32no—
431C22×D4—91no—
432C22×D4—92no—
433C22×D4—92no—
434C22×D4—92no—
435C22×D4—92no—
436C22×D4—91no—
437C22×D4—92no—
438C23×C4—31no—
439C23×C4—91no—
440#127—184no—
441#127—188no—
442#121—64no—
443#121—184no—
444#121—184no—
445#121—184no—
446C4×D4—184no—
447C2×C4⋊C4—31no—
448C2×C4⋊C4—91no—
449C2×C4⋊C4D3211yescharacteristic
450C2×C22⋊C4—32no—
451C2×C22⋊C4—91no—
452C2×C22⋊C4—92no—
453C2×C22⋊C4—91no—
454C2×C22⋊C4—92no—
455C2×C22⋊C4—92no—
456C2×C42—31no—
457C2×C42—32no—
458#95—32no—
459C23×C3—21no—
460C23×C3—32no—
461C23×C3—61no—
462C23×C3—61no—
463C23×C3—61no—
464C23×C3—61no—
465C23×C3—61no—
466C23×C3—61no—
467C23×C3—62no—
468C23×C3—62no—
469C23×C3—62no—
470C23×C3—62no—
471C23×C3—62no—
472C23×C3—62no—
473C23×C3—62no—
474C23×C3C23×D311yescharacteristic
475C23×C3C23×D311yescharacteristic
476C22×D3—21no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—22no—
483C22×D3—22no—
484C22×D3—22no—
485C22×D3—22no—
486C22×D3—22no—
487C22×D3—22no—
488C22×D3—22no—
489C22×D3—32no—
490C22×D3—32no—
491C22×D3—62no—
492C22×D3—62no—
493C22×D3—62no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—61no—
497C22×D3—61no—
498C22×D3—61no—
499C22×D3—61no—
500C22×D3—61no—
501C22×D3—61no—
502C22×D3—61no—
503C22×D3—61no—
504C22×D3—61no—
505C22×D3—61no—
506C22×D3—64no—
507C22×D3—62no—
508C22×D3—62no—
509C22×D3—62no—
510C22×D3—62no—
511C22×D3—62no—
512C22×D3—62no—
513C22×D3—62no—
514C22×D3—62no—
515C22×D3—62no—
516C22×D3—62no—
517C22×D3—62no—
518C22×D3—62no—
519C22×D3—62no—
520C22×D3—62no—
521C22×D3—121no—
522C22×D3—121no—
523C22×D3—121no—
524C22×D3—121no—
525C22×D3—122no—
526C22×D3—122no—
527C22×D3—122no—
528C22×D3—122no—
529C22×D3—122no—
530C22×D3—122no—
531C22×D3D3×D412yes—
532C3×D4—128no—
533C3×D4—124no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—24no—
542C2×C3×C4—32no—
543C2×C3×C4—32no—
544C2×C3×C4—32no—
545C2×C3×C4—32no—
546C2×C3×C4—34no—
547C2×C3×C4—42no—
548C2×C3×C4—42no—
549C2×C3×C4—62no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—62no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—124no—
557C2×C3×C4C2×D1212yes—
558C2×C3×C4C2×D1212yes—
559C2×C3×C4C2×D1214yes—
560C2×C3×C4C2×D1212yes—
561C2×C3×C4D3×D412yes—
562C2×C3×C4D3×D412yes—
563C2×C3×C4C2×#6714yes—
564C2×C3×C4C2×#6712yes—
565#67—68no—
566#67—128no—
567#67—128no—
568#67—128no—
569#67—128no—
570C2×Dic3—22no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—22no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—62no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—121no—
585C2×Dic3—121no—
586C2×Dic3C2×D1212yes—
587C2×Dic3C2×D1214yes—
588C2×Dic3C2×D1212yes—
589C2×Dic3D3×D412yes—
590C2×Dic3#23912yes—
591D12—48no—
592D12—44no—
593D12—68no—
594D12—128no—
595D12—128no—
596D12—128no—
597D12—128no—
598D12—1216no—
599D12—128no—
600D12—128no—
601D12—128no—
602D12—124no—
603D12—124no—
604C4×D3—44no—
605C4×D3—128no—
606C4×D3—124no—
607C4×D3—124no—
608C2×C32C2×#12111yescharacteristic
609C2×C32C2×#12711yescharacteristic
610C2×C32#53511yescharacteristic
611C2×C32D4211yescharacteristic
612C2×C32D4211yescharacteristic
613C2×C32#55011yescharacteristic
614C2×C32#55011yescharacteristic
615C3⋊D3—42no—
616C3⋊D3—82no—
617C3×D3—42no—
618C3×D3—82no—
619C24—31no—
620C24—32no—
621C24—91no—
622C24—92no—
623C2×D4—64no—
624C2×D4—62no—
625C2×D4—62no—
626C2×D4—64no—
627C2×D4—62no—
628C2×D4—94no—
629C2×D4—122no—
630C2×D4—184no—
631C2×D4—182no—
632C2×D4—182no—
633C2×D4—184no—
634C2×D4—184no—
635C2×D4—184no—
636C2×D4—184no—
637C2×D4—184no—
638C2×D4—184no—
639C2×D4—184no—
640C2×D4—184no—
641C2×D4—182no—
642C2×D4—182no—
643C2×D4—184no—
644C2×D4—182no—
645C2×D4—362no—
646C2×D4—362no—
647C2×D4—362no—
648C2×D4—362no—
649C2×D4—362no—
650C22×C4—31no—
651C22×C4—31no—
652C22×C4—32no—
653C22×C4—31no—
654C22×C4—62no—
655C22×C4—62no—
656C22×C4—62no—
657C22×C4—91no—
658C22×C4—182no—
659C22×C4—182no—
660C22×C4—182no—
661C22×C4C2×D3212yes—
662C22×C4C2×D3211yescharacteristic
663C4⋊C4—34no—
664C4⋊C4—182no—
665C4⋊C4#62614yescomplemented
666C22⋊C4—64no—
667C22⋊C4—182no—
668C22⋊C4—184no—
669C22⋊C4—182no—
670C22⋊C4—184no—
671C22⋊C4—184no—
672C42—34no—
673C42—64no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—62no—
682C22×C3—62no—
683C22×C3—62no—
684C22×C3—121no—
685C22×C3—121no—
686C22×C3—121no—
687C22×C3—121no—
688C22×C3—122no—
689C22×C3—122no—
690C22×C3—122no—
691C22×C3—122no—
692C22×C3—122no—
693C22×C3—122no—
694C22×C3—122no—
695C22×C3C22×D1211yescharacteristic
696C22×C3C22×D1211yescharacteristic
697C22×C3C22×D1211yescharacteristic
698C22×C3C2×D3×D411yescharacteristic
699C22×C3C2×D3×D411yescharacteristic
700C22×C3C2×D3×D411yescharacteristic
701C22×C3C2×D3×D411yescharacteristic
702C22×C3#100411yescharacteristic
703C22×C3C2×#23911yescharacteristic
704C22×C3D3×#4111yescharacteristic
705C22×C3#100911yescharacteristic
706C22×C3#100911yescharacteristic
707C22×C3#100911yescharacteristic
708C22×C3C22×#6711yescharacteristic
709C2×D3—22no—
710C2×D3—22no—
711C2×D3—22no—
712C2×D3—41no—
713C2×D3—41no—
714C2×D3—41no—
715C2×D3—41no—
716C2×D3—42no—
717C2×D3—42no—
718C2×D3—42no—
719C2×D3—42no—
720C2×D3—42no—
721C2×D3—42no—
722C2×D3—42no—
723C2×D3—64no—
724C2×D3—62no—
725C2×D3—62no—
726C2×D3—62no—
727C2×D3—62no—
728C2×D3—62no—
729C2×D3—62no—
730C2×D3—122no—
731C2×D3—122no—
732C2×D3—122no—
733C2×D3—122no—
734C2×D3—122no—
735C2×D3—122no—
736C2×D3—121no—
737C2×D3—121no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—121no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—124no—
745C2×D3—124no—
746C2×D3—124no—
747C2×D3—122no—
748C2×D3—122no—
749C2×D3—122no—
750C2×D3—122no—
751C2×D3—122no—
752C2×D3—122no—
753C2×D3—122no—
754C2×D3—122no—
755C2×D3—122no—
756C2×D3—122no—
757C2×D3—122no—
758C2×D3—122no—
759C2×D3—122no—
760C2×D3—122no—
761C2×D3—242no—
762C2×D3—242no—
763C2×D3—242no—
764C2×D3—242no—
765C3×C4—24no—
766C3×C4—24no—
767C3×C4—24no—
768C3×C4—34no—
769C3×C4—44no—
770C3×C4—62no—
771C3×C4—64no—
772C3×C4—121no—
773C3×C4#87414yescomplemented
774C3×C4#94014yescomplemented
775Dic3—22no—
776Dic3—24no—
777Dic3—41no—
778Dic3—122no—
779Dic3—121no—
780Dic3—121no—
781Dic3#89514yescomplemented
782C32#254111yescharacteristic, complemented, Sylow
783C23—32no—
784C23—61no—
785C23—61no—
786C23—61no—
787C23—61no—
788C23—61no—
789C23—61no—
790C23—62no—
791C23—62no—
792C23—62no—
793C23—62no—
794C23—62no—
795C23—62no—
796C23—62no—
797C23—92no—
798C23—181no—
799C23—181no—
800C23—181no—
801C23—181no—
802C23—181no—
803C23—181no—
804C23—182no—
805C23—182no—
806C23—182no—
807C23—182no—
808C23—182no—
809C23—182no—
810C23—182no—
811C23C22×D3211yescharacteristic
812D4—128no—
813D4—124no—
814D4—188no—
815D4—368no—
816D4—368no—
817D4—368no—
818D4—368no—
819D4—368no—
820D4—364no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—32no—
824C2×C4—32no—
825C2×C4—32no—
826C2×C4—32no—
827C2×C4—34no—
828C2×C4—62no—
829C2×C4—61no—
830C2×C4—62no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—124no—
836C2×C4—181no—
837C2×C4—181no—
838C2×C4—181no—
839C2×C4—364no—
840C2×C4D3×D1212yes—
841C2×C4D3×D1212yes—
842C2×C4C2×#62614yes—
843C2×C4C2×#62612yes—
844C2×C3—21no—
845C2×C3—21no—
846C2×C3—21no—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—122no—
852C2×C3—242no—
853C2×C3C2×#87411yescharacteristic
854C2×C3C2×#89511yescharacteristic
855C2×C3#552511yescharacteristic
856C2×C3D4×D1211yescharacteristic
857C2×C3D4×D1211yescharacteristic
858C2×C3#557711yescharacteristic
859C2×C3#557711yescharacteristic
860C2×C3#559911yescharacteristic
861C2×C3D3×#12111yescharacteristic
862C2×C3#560711yescharacteristic
863C2×C3#560911yescharacteristic
864C2×C3D4×#6711yescharacteristic
865C2×C3C2×#94011yescharacteristic
866C2×C3#583411yescharacteristic
867D3—42no—
868D3—82no—
869D3—124no—
870D3—122no—
871D3—122no—
872D3—244no—
873D3—242no—
874D3—242no—
875C22—62no—
876C22—62no—
877C22—62no—
878C22—121no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—122no—
883C22—122no—
884C22—122no—
885C22—122no—
886C22—122no—
887C22—122no—
888C22—122no—
889C22—182no—
890C22—182no—
891C22—182no—
892C22—361no—
893C22—361no—
894C22—361no—
895C22—361no—
896C22—362no—
897C22—362no—
898C22—362no—
899C22—362no—
900C22—362no—
901C22—362no—
902C22—362no—
903C22C2×D3×D1211yescharacteristic
904C22C2×D3×D1211yescharacteristic
905C22D32×D411yescharacteristic
906C22#6431411yescharacteristic
907C22D3×#23911yescharacteristic
908C22#6432011yescharacteristic
909C22C22×#62611yescharacteristic
910C4—24no—
911C4—34no—
912C4—64no—
913C4—62no—
914C4—121no—
915C4—361no—
916C4#6391114yescomplemented
917C3—21no—
918C3#7379911yescharacteristic, complemented
919C3#8266911yescharacteristic, complemented
920C2—122no—
921C2—242no—
922C2—362no—
923C2—722no—
924C2#1059452411yescharacteristic
925C2D3×#89511yescharacteristic
926C2#1059462111yescharacteristic
927C2#1059462811yescharacteristic
928C2C2×#6391111yescharacteristic
929C2D4×#62611yescharacteristic
930C2#1059541011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2541
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64104C2semidirect
2. C2×C3×#895C2semidirect
3. C2×#63916C2semidirect
4. C2×#63911C2semidirect
5. C2×#63911C2semidirect
6. C2×#63909C2semidirect
7. C2×C4×#626C2semidirect
8. C3×Dic3×C4⋊C4C2semidirect
9. #10591395C2semidirect
10. #10591391C2semidirect
11. #10591383C2semidirect
55. C2×#895D3semidirect
61. Dic3×C4⋊C4D3semidirect
110. C2×#626D4semidirect
111. C32×C4⋊C4D4semidirect
114. C3×C4⋊Dic3D4semidirect
116. C3×C4×Dic3D4semidirect
365. C3×C4⋊C4D12semidirect
366. C3×C4⋊C4#67semidirect
383. C4⋊Dic3D12semidirect
386. C4×Dic3D12semidirect
423. C32×C4#127semidirect
428. C3×Dic3#121semidirect
665. C4⋊C4#626semidirect
773. C3×C4#874semidirect
774. C3×C4#940semidirect
781. Dic3#895semidirect
782. C32#2541semidirect
916. C4#63911semidirect
918. C3#73799semidirect
919. C3#82669semidirect

Maximal subgroups

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

subgroupindex
C2×#641042
C2×C3×#8952
C2×#639162
C2×#639112
C2×#639092
C2×C4×#6262
C3×Dic3×C4⋊C42
#105913952
#105913912
#105913832
#826693
#737993