Finite Group Databasebeta

← #11824503

Subgroups — #11824503

Order 1152.

1513 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64133C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C211yesmaximal, characteristic
3C2×C3×#924C211yesmaximal, characteristic, complemented
4C2×#63866C211yesmaximal, characteristic, complemented
5C2×#63857C211yesmaximal, characteristic, complemented
6C2×#63856C211yesmaximal, characteristic, complemented
7#10591715C212yesmaximal, complemented
8#10591707C212yesmaximal
9#10591303C212yesmaximal, complemented
10Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
11#10591244C212yesmaximal, complemented
12#82780—31nomaximal
13#82379—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×#634C2211yescharacteristic
16C22×C3×#67C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C22×C3×Dic6C2211yescharacteristic
19C2×#3757C2212yes—
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21#64133—24no—
22C2×#3750C2212yes—
23C2×C3×#217C2212yes—
24C2×C3×#217C2211yescharacteristic
25C3×C4×#67—24no—
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C3×#924—24no—
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2212yes—
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×#3724C2212yes—
33C2×Dic3⋊Dic3C2212yes—
34C2×Dic3⋊Dic3C2212yes—
35C2×Dic3⋊Dic3C2212yes—
36C2×(C2×D3)⋊Dic3C2212yes—
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×Dic32C2212yes—
39#63866—24no—
40#63857—24no—
41#63856—24no—
42#63579C2212yes—
43C2×C3×C22⋊Q8—31no—
44C2×C3×C4×D4—31no—
45C2×#946—31no—
46C2×#944—31no—
47C2×C4×#67D311yescharacteristic
48C2×#924—31no—
49C2×#924—31no—
50C2×#924—31no—
51C2×#924—31no—
52C2×#924—61no—
53C2×#924D311yescharacteristic, complemented
54C2×#897—31no—
55C2×#869—31no—
56#5221—32no—
57#4993—32no—
58#4975—32no—
59#4975—32no—
60Dic3×C4⋊C4—31no—
61#4957—32no—
62#4949—32no—
63#4949—32no—
64#4949—32no—
65C4×C4⋊Dic3—31no—
66C24×C32C2311yescharacteristic
67C23×C3×D3C2311yescharacteristic
68C22×C32×C4—22no—
69C22×C32×C4—22no—
70C22×C32×C4—22no—
71C22×C32×C4C2311yescharacteristic
72C22×C32×C4C2311yescharacteristic
73C22×C3⋊Dic3C2312yes—
74C22×C3⋊Dic3C2312yes—
75C2×#634—22no—
76C2×#634—22no—
77C2×#634—22no—
78C2×C3×#67—22no—
79C2×C3×#67—22no—
80C2×C3×#67Q814yescomplemented
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2311yescharacteristic
86C2×C3×C4×D3—22no—
87C2×C3×C4×D3—22no—
88C2×C3×C4×D3—22no—
89C2×C3×Dic6—22no—
90C2×C3×Dic6—22no—
91C2×C3×Dic6—22no—
92#3757—24no—
93C4⋊(C3⋊Dic3)D414yescomplemented
94#3750—24no—
95C3×#217—24no—
96C3×#217—22no—
97C3×(C2×D3)⋊C4—22no—
98C3×C4⋊Dic3D414yescomplemented
99C3×Dic3⋊C4—24no—
100C3×Dic3⋊C4—22no—
101C3×C4×Dic3D414yes—
102#3724—24no—
103Dic3⋊Dic3—24no—
104Dic3⋊Dic3—24no—
105Dic3⋊Dic3—24no—
106(C2×D3)⋊Dic3—24no—
107(C2×D3)⋊Dic3—24no—
108Dic32—24no—
109#2542—91noSylow
110C22×C3×Q8—31no—
111C22×C3×D4—31no—
112C23×C3×C4—21no—
113C23×C3×C4—31no—
114C23×C3×C4C2×D311yescharacteristic
115C23×C3×C4C2×D311yescharacteristic
116C22×#67C2×D311yescharacteristic
117C22×C4×D3C2×D311yescharacteristic
118C22×Dic6—31no—
119C22×Dic6—31no—
120C22×Dic6—61no—
121C22×Dic6C2×D311yescharacteristic
122C3×C22⋊Q8—64no—
123C3×C4×D4—64no—
124C2×C3×C4⋊C4—31no—
125C2×C3×C4⋊C4—31no—
126C2×C3×C4⋊C4—32no—
127C2×C3×C22⋊C4—31no—
128C2×C3×C22⋊C4—32no—
129C2×C3×C22⋊C4—31no—
130C2×C3×C42—31no—
131C2×#217—32no—
132C2×#217—32no—
133C2×#217—32no—
134C2×#217—32no—
135C2×#217—62no—
136C2×#217C2×D311yescharacteristic
137C2×#217C2×D312yes—
138#946—64no—
139#944—64no—
140C4×#67—24no—
141C2×(C2×D3)⋊C4—32no—
142C2×(C2×D3)⋊C4—32no—
143C2×(C2×D3)⋊C4C2×D311yescharacteristic
144C2×C4⋊Dic3—31no—
145C2×C4⋊Dic3—31no—
146C2×C4⋊Dic3—32no—
147C2×C4⋊Dic3—32no—
148C2×C4⋊Dic3—32no—
149C2×C4⋊Dic3—61no—
150C2×C4⋊Dic3C2×D311yescharacteristic
151#924—24no—
152#924—64no—
153#924—64no—
154#924—64no—
155#924—68no—
156#924—64no—
157C2×Dic3⋊C4—32no—
158C2×Dic3⋊C4—32no—
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4—32no—
161C2×Dic3⋊C4—32no—
162C2×Dic3⋊C4—32no—
163C2×Dic3⋊C4—32no—
164C2×Dic3⋊C4—62no—
165C2×Dic3⋊C4C2×D312yes—
166C2×Dic3⋊C4C2×D311yescharacteristic
167C2×C4×Dic3—32no—
168C2×C4×Dic3—32no—
169C2×C4×Dic3C2×D311yescharacteristic
170#897—64no—
171#869—64no—
172C3⋊#95—32no—
173C3⋊#95—32no—
174C23×C32—21no—
175C23×C32—21no—
176C23×C32—21no—
177C23×C32—21no—
178C23×C32—21no—
179C23×C32—21no—
180C23×C32C2×Q812yes—
181C23×C32C2411yescharacteristic
182C22×C3×D3—21no—
183C22×C3×D3—21no—
184C22×C3×D3—21no—
185C22×C3×D3—21no—
186C22×C3×D3—21no—
187C22×C3×D3—21no—
188C22×C3×D3C2×Q812yes—
189C2×C32×C4—21no—
190C2×C32×C4—21no—
191C2×C32×C4—21no—
192C2×C32×C4—44no—
193C2×C32×C4C2×D412yes—
194C2×C32×C4C2×D412yes—
195C2×C32×C4C2×D412yes—
196C2×C3⋊Dic3—22no—
197C2×C3⋊Dic3—22no—
198C2×C3⋊Dic3—22no—
199C2×C3⋊Dic3—22no—
200C2×C3⋊Dic3—22no—
201C2×C3⋊Dic3C2×D414yes—
202#634—44no—
203C3×#67—28no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—21no—
206C2×C3×Dic3—21no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—21no—
211C2×C3×Dic3—21no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—21no—
214C2×C3×Dic3C2×D414yes—
215C2×C3×Dic3C2×D412yes—
216C2×C3×Dic3C2×D412yes—
217C2×C3×Dic3C2×Q812yes—
218C2×C3×Dic3#4112yes—
219C3×C4×D3—44no—
220C3×Dic6—44no—
221C2×C4⋊Q8—91no—
222C2×C22⋊Q8—31no—
223C2×C22⋊Q8—91no—
224C2×C22⋊Q8—91no—
225C2×C22⋊Q8—91no—
226C2×C4×D4—31no—
227#399—92no—
228#399—92no—
229#390—92no—
230#384—92no—
231C4×C4⋊C4—91no—
232C24×C3—21no—
233C24×C3—31no—
234C24×C3C22×D311yescharacteristic
235C24×C3C22×D311yescharacteristic
236C23×D3C22×D311yescharacteristic
237C2×C3×Q8—62no—
238C2×C3×Q8—62no—
239C2×C3×Q8—62no—
240C2×C3×D4—34no—
241C2×C3×D4—62no—
242C2×C3×D4—62no—
243C22×C3×C4—24no—
244C22×C3×C4—22no—
245C22×C3×C4—22no—
246C22×C3×C4—22no—
247C22×C3×C4—22no—
248C22×C3×C4—22no—
249C22×C3×C4—22no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—31no—
253C22×C3×C4—31no—
254C22×C3×C4—32no—
255C22×C3×C4—31no—
256C22×C3×C4—32no—
257C22×C3×C4—42no—
258C22×C3×C4—42no—
259C22×C3×C4—62no—
260C22×C3×C4—62no—
261C22×C3×C4—62no—
262C22×C3×C4C22×D311yescharacteristic
263C22×C3×C4C22×D311yescharacteristic
264C22×C3×C4C22×D311yescharacteristic
265C22×C3×C4C22×D311yescharacteristic
266C2×#67—22no—
267C2×#67—22no—
268C2×#67Dic614yescomplemented
269C22×Dic3—32no—
270C22×Dic3—32no—
271C22×Dic3—32no—
272C22×Dic3—32no—
273C22×Dic3—62no—
274C22×Dic3—62no—
275C22×Dic3C22×D311yescharacteristic
276C22×Dic3C22×D312yes—
277C22×Dic3C22×D311yescharacteristic
278C22×Dic3C22×D312yes—
279C22×Dic3C22×D311yescharacteristic
280C2×C4×D3—22no—
281C2×C4×D3—22no—
282C2×C4×D3—22no—
283C2×Dic6—22no—
284C2×Dic6—22no—
285C2×Dic6—22no—
286C2×Dic6—64no—
287C2×Dic6—62no—
288C2×Dic6—62no—
289C2×Dic6—62no—
290C2×Dic6—62no—
291C2×Dic6—62no—
292C2×Dic6—62no—
293C2×Dic6—122no—
294C2×Dic6—122no—
295C3×C4⋊C4—34no—
296C3×C4⋊C4—62no—
297C3×C4⋊C4—64no—
298C3×C22⋊C4—62no—
299C3×C22⋊C4—62no—
300C3×C22⋊C4—64no—
301C3×C42—34no—
302#217—24no—
303#217—22no—
304#217—64no—
305#217—64no—
306#217—64no—
307#217—68no—
308#217—64no—
309(C2×D3)⋊C4—22no—
310(C2×D3)⋊C4—64no—
311(C2×D3)⋊C4—64no—
312C4⋊Dic3—34no—
313C4⋊Dic3—34no—
314C4⋊Dic3—64no—
315C4⋊Dic3—64no—
316C4⋊Dic3—64no—
317C4⋊Dic3—64no—
318C4⋊Dic3#6714yescomplemented
319Dic3⋊C4—24no—
320Dic3⋊C4—22no—
321Dic3⋊C4—64no—
322Dic3⋊C4—64no—
323Dic3⋊C4—64no—
324Dic3⋊C4—64no—
325Dic3⋊C4—68no—
326Dic3⋊C4—64no—
327Dic3⋊C4—64no—
328Dic3⋊C4—64no—
329C4×Dic3—64no—
330C4×Dic3—64no—
331C4×Dic3#6714yes—
332C22×C32—22no—
333C22×C32—22no—
334C22×C32—22no—
335C22×C32—41no—
336C22×C32—41no—
337C22×C32—41no—
338C22×C32—41no—
339C22×C32C22×D411yescharacteristic
340C22×C32C22×D411yescharacteristic
341C22×C32C22×D411yescharacteristic
342C22×C32C22×Q811yescharacteristic
343C22×C32C2×#4111yescharacteristic
344C22×C322−1+411yescharacteristic
345C22×C322−1+411yescharacteristic
346C2×C3×D3—22no—
347C2×C3×D3—22no—
348C2×C3×D3—22no—
349C2×C3×D3—41no—
350C2×C3×D3—41no—
351C2×C3×D3—41no—
352C2×C3×D3—41no—
353C32×C4—41no—
354C32×C4#12714yes—
355C3⋊Dic3—24no—
356C3⋊Dic3—42no—
357C3×Dic3—22no—
358C3×Dic3—24no—
359C3×Dic3—42no—
360C3×Dic3—41no—
361C3×Dic3C22⋊Q814yescomplemented
362C22×Q8—31no—
363C22×Q8—91no—
364C22×D4—31no—
365C23×C4—31no—
366C23×C4D3211yescharacteristic
367C4⋊Q8—184no—
368C22⋊Q8—64no—
369C22⋊Q8—184no—
370C22⋊Q8—184no—
371C22⋊Q8—184no—
372C4×D4—64no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—32no—
376C2×C4⋊C4—91no—
377C2×C4⋊C4—92no—
378C2×C4⋊C4—92no—
379C2×C4⋊C4—92no—
380C2×C4⋊C4—92no—
381C2×C4⋊C4—92no—
382C2×C22⋊C4—31no—
383C2×C22⋊C4—32no—
384C2×C22⋊C4—31no—
385C2×C22⋊C4—92no—
386C2×C22⋊C4—92no—
387C2×C22⋊C4—92no—
388C2×C42—31no—
389C2×C42—92no—
390#95—92no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—22no—
407C23×C3—32no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—61no—
413C23×C3—61no—
414C23×C3—61no—
415C23×C3—61no—
416C23×C3—61no—
417C23×C3—61no—
418C23×C3C2×Dic612yes—
419C23×C3D3×Q812yes—
420C23×C3C23×D311yescharacteristic
421C23×C3C23×D311yescharacteristic
422C22×D3—21no—
423C22×D3—21no—
424C22×D3—21no—
425C22×D3—21no—
426C22×D3—21no—
427C22×D3—21no—
428C22×D3C2×Dic612yes—
429C3×Q8—124no—
430C3×D4—68no—
431C2×C3×C4—22no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—32no—
442C2×C3×C4—32no—
443C2×C3×C4—32no—
444C2×C3×C4—32no—
445C2×C3×C4—34no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—48no—
449C2×C3×C4—44no—
450C2×C3×C4—44no—
451C2×C3×C4—62no—
452C2×C3×C4—61no—
453C2×C3×C4—62no—
454C2×C3×C4—61no—
455C2×C3×C4—61no—
456C2×C3×C4—62no—
457C2×C3×C4—61no—
458C2×C3×C4—62no—
459C2×C3×C4—61no—
460C2×C3×C4—62no—
461C2×C3×C4—124no—
462C2×C3×C4D3×D412yes—
463C2×C3×C4D3×D412yes—
464C2×C3×C4D3×D412yes—
465C2×C3×C4D3×D412yes—
466C2×C3×C4C2×#6712yes—
467C2×C3×C4C2×#6712yes—
468#67—28no—
469C2×Dic3—22no—
470C2×Dic3—21no—
471C2×Dic3—22no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—21no—
477C2×Dic3—22no—
478C2×Dic3—21no—
479C2×Dic3—34no—
480C2×Dic3—34no—
481C2×Dic3—64no—
482C2×Dic3—62no—
483C2×Dic3—62no—
484C2×Dic3—62no—
485C2×Dic3—62no—
486C2×Dic3—64no—
487C2×Dic3—62no—
488C2×Dic3—62no—
489C2×Dic3—62no—
490C2×Dic3—62no—
491C2×Dic3—62no—
492C2×Dic3—62no—
493C2×Dic3—122no—
494C2×Dic3—122no—
495C2×Dic3—122no—
496C2×Dic3—122no—
497C2×Dic3C2×Dic612yes—
498C2×Dic3#23512yes—
499C2×Dic3C2×#6712yes—
500C2×Dic3C2×#6714yes—
501C2×Dic3C2×#6712yes—
502C4×D3—44no—
503Dic6—44no—
504Dic6—128no—
505Dic6—124no—
506Dic6—124no—
507C2×C32—42no—
508C2×C32C2×C22⋊Q811yescharacteristic
509C2×C32C2×#12711yescharacteristic
510C2×C32#53611yescharacteristic
511C2×C32#54711yescharacteristic
512C2×C32#54711yescharacteristic
513C2×C32D4×Q811yescharacteristic
514C2×C32D4×Q811yescharacteristic
515C3×D3—42no—
516C24—31no—
517C24C2×D3211yescharacteristic
518C2×Q8—62no—
519C2×Q8—62no—
520C2×Q8—62no—
521C2×Q8—182no—
522C2×Q8—182no—
523C2×Q8—182no—
524C2×D4—34no—
525C2×D4—62no—
526C2×D4—62no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—31no—
531C22×C4—31no—
532C22×C4—32no—
533C22×C4—32no—
534C22×C4—31no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—92no—
539C22×C4—92no—
540C22×C4C2×D3211yescharacteristic
541C22×C4C2×D3211yescharacteristic
542C4⋊C4—34no—
543C4⋊C4—62no—
544C4⋊C4—64no—
545C4⋊C4—94no—
546C4⋊C4—184no—
547C4⋊C4—184no—
548C4⋊C4—184no—
549C4⋊C4—184no—
550C4⋊C4—184no—
551C22⋊C4—62no—
552C22⋊C4—62no—
553C22⋊C4—64no—
554C22⋊C4—184no—
555C22⋊C4—184no—
556C22⋊C4—184no—
557C42—34no—
558C42—184no—
559C22×C3—24no—
560C22×C3—22no—
561C22×C3—22no—
562C22×C3—22no—
563C22×C3—22no—
564C22×C3—22no—
565C22×C3—22no—
566C22×C3—21no—
567C22×C3—21no—
568C22×C3—21no—
569C22×C3—21no—
570C22×C3—21no—
571C22×C3—21no—
572C22×C3—21no—
573C22×C3—42no—
574C22×C3—42no—
575C22×C3—42no—
576C22×C3—42no—
577C22×C3—42no—
578C22×C3—42no—
579C22×C3—41no—
580C22×C3—41no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—62no—
588C22×C3—62no—
589C22×C3—62no—
590C22×C3—121no—
591C22×C3—121no—
592C22×C3—121no—
593C22×C3—121no—
594C22×C3C22×Dic611yescharacteristic
595C22×C3C2×#23511yescharacteristic
596C22×C3C2×D3×D411yescharacteristic
597C22×C3C2×D3×D411yescharacteristic
598C22×C3C2×D3×D411yescharacteristic
599C22×C3C2×D3×D411yescharacteristic
600C22×C3C2×D3×Q811yescharacteristic
601C22×C3#100711yescharacteristic
602C22×C3D3×#4111yescharacteristic
603C22×C3#101011yescharacteristic
604C22×C3#101011yescharacteristic
605C22×C3#101011yescharacteristic
606C22×C3C22×#6711yescharacteristic
607C22×C3C22×#6711yescharacteristic
608C2×D3—22no—
609C2×D3—22no—
610C2×D3—22no—
611C2×D3—41no—
612C2×D3—41no—
613C2×D3—41no—
614C2×D3—41no—
615C3×C4—24no—
616C3×C4—34no—
617C3×C4—42no—
618C3×C4—41no—
619C3×C4—41no—
620C3×C4—64no—
621C3×C4—62no—
622C3×C4—121no—
623C3×C4—122no—
624C3×C4#94014yes—
625C3×C4#94014yes—
626Dic3—24no—
627Dic3—22no—
628Dic3—42no—
629Dic3—41no—
630Dic3—64no—
631Dic3—64no—
632Dic3—124no—
633Dic3—124no—
634Dic3—122no—
635Dic3—122no—
636Dic3#92414yescomplemented
637C32#254211yescharacteristic, complemented, Sylow
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—32no—
645C23—61no—
646C23—61no—
647C23—61no—
648C23—61no—
649C23—61no—
650C23—61no—
651C23D3×Dic612yes—
652C23C22×D3211yescharacteristic
653Q8—124no—
654Q8—364no—
655D4—68no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—32no—
660C2×C4—32no—
661C2×C4—32no—
662C2×C4—32no—
663C2×C4—34no—
664C2×C4—44no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—62no—
668C2×C4—62no—
669C2×C4—61no—
670C2×C4—62no—
671C2×C4—61no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—61no—
675C2×C4—94no—
676C2×C4—124no—
677C2×C4—182no—
678C2×C4—182no—
679C2×C4—182no—
680C2×C4—182no—
681C2×C4—182no—
682C2×C4D3×#6712yes—
683C2×C4D3×#6712yes—
684C2×C4#381112yes—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—44no—
693C2×C3—42no—
694C2×C3—42no—
695C2×C3—122no—
696C2×C3D4×Dic611yescharacteristic
697C2×C3D4×Dic611yescharacteristic
698C2×C3#555111yescharacteristic
699C2×C3#555111yescharacteristic
700C2×C3D3×C22⋊Q811yescharacteristic
701C2×C3#562811yescharacteristic
702C2×C3#563111yescharacteristic
703C2×C3#563211yescharacteristic
704C2×C3C2×#92411yescharacteristic
705C2×C3C2×#94011yescharacteristic
706C2×C3C2×#94011yescharacteristic
707C2×C3Q8×#6711yescharacteristic
708C2×C3#582411yescharacteristic
709C2×C3#582511yescharacteristic
710D3—42no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—62no—
719C22—62no—
720C22—62no—
721C22—121no—
722C22—121no—
723C22—121no—
724C22—121no—
725C22C2×D3×Dic611yescharacteristic
726C22#6429711yescharacteristic
727C22#6429811yescharacteristic
728C22D3×#23511yescharacteristic
729C22C2×D3×#6711yescharacteristic
730C22C2×D3×#6711yescharacteristic
731C22C2×#381111yescharacteristic
732C4—34no—
733C4—41no—
734C4—62no—
735C4—64no—
736C4—121no—
737C4—122no—
738C4—184no—
739C4—362no—
740C4#6397914yes—
741C3—21no—
742C3#8237911yescharacteristic, complemented
743C3#8278011yescharacteristic, complemented
744C2—42no—
745C2—122no—
746C2#1059483411yescharacteristic
747C2D3×#92411yescharacteristic
748C2#1059488411yescharacteristic
749C2#1059488711yescharacteristic
750C2Dic6×#6711yescharacteristic
751C2#1059491511yescharacteristic
752C2C2×#6397911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC23×C32×C4C22
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32#2542
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#64133C2semidirect
3. C2×C3×#924C2semidirect
4. C2×#63866C2semidirect
5. C2×#63857C2semidirect
6. C2×#63856C2semidirect
7. #10591715C2semidirect
9. #10591303C2semidirect
10. Dic3×C4⋊Dic3C2semidirect
11. #10591244C2semidirect
53. C2×#924D3semidirect
80. C2×C3×#67Q8semidirect
93. C4⋊(C3⋊Dic3)D4semidirect
98. C3×C4⋊Dic3D4semidirect
268. C2×#67Dic6semidirect
318. C4⋊Dic3#67semidirect
361. C3×Dic3C22⋊Q8semidirect
636. Dic3#924semidirect
637. C32#2542semidirect
742. C3#82379semidirect
743. C3#82780semidirect

Maximal subgroups

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

subgroupindex
C2×#641332
C2×C3×C4×#672
C2×C3×#9242
C2×#638662
C2×#638572
C2×#638562
#105917152
#105917072
#105913032
Dic3×C4⋊Dic32
#105912442
#827803
#823793