Finite Group Databasebeta

← #11824499

Subgroups — #11824499

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×#64106C211yesmaximal, characteristic, complemented
2C2×C3×#897C211yesmaximal, characteristic, complemented
3C2×C4×#626C211yesmaximal, characteristic
4C2×#63871C211yesmaximal, characteristic, complemented
5C2×#63866C211yesmaximal, characteristic, complemented
6C2×#63857C211yesmaximal, characteristic, complemented
7C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
8#10591383C212yesmaximal
9#10591350C212yesmaximal, complemented
10#10591349C212yesmaximal, complemented
11#10591317C212yesmaximal, complemented
12#82780—31nomaximal
13#73800—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×#634C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×C3×Dic6C2211yescharacteristic
18C22×#626C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×#3752C2212yes—
21C2×C4⋊(C3⋊Dic3)C2212yes—
22#64106—24no—
23C2×C3×(C2×D3)⋊C4C2212yes—
24C2×C3×C4⋊Dic3C2212yes—
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2212yes—
27C2×C3×C4×Dic3C2211yescharacteristic
28C3×#897—24no—
29C2×Dic3⋊Dic3C2212yes—
30C2×Dic3⋊Dic3C2212yes—
31C2×Dic3⋊Dic3C2212yes—
32C2×Dic3⋊Dic3C2212yes—
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×#3722C2212yes—
35C2×#3722C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2212yes—
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C4×#626—24no—
39#63871—24no—
40#63866—24no—
41#63857—24no—
42C3×C3⋊#95C2212yes—
43C2×C3×C22⋊Q8—31no—
44C2×#946—31no—
45C2×#944—31no—
46C2×C4×#67—31no—
47C2×#924—31no—
48C2×#897—31no—
49C2×#897—31no—
50C2×#897—31no—
51C2×#897—31no—
52C2×#897—61no—
53C2×#897D311yescharacteristic, complemented
54C2×C4×D12—31no—
55C2×#869—31no—
56C3×C4×C4⋊C4—31no—
57#4993—32no—
58#4975—32no—
59Dic3×C4⋊C4D311yescharacteristic, complemented
60#4957—32no—
61#4949—32no—
62#4939—32no—
63#4935—32no—
64#4677—32no—
65#4677—32no—
66C23×C3⋊D3C2311yescharacteristic
67C23×C3×D3C2311yescharacteristic
68C22×C32×C4C2312yes—
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3C2312yes—
71C22×C3⋊Dic3C2311yescharacteristic
72C2×C4×C3⋊D3—22no—
73C2×C4×C3⋊D3—22no—
74C2×C4×C3⋊D3—22no—
75C2×#634—22no—
76C2×#634—22no—
77C2×#634—22no—
78C22×C3×Dic3C2311yescharacteristic
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2311yescharacteristic
83C2×C3×C4×D3—22no—
84C2×C3×C4×D3—22no—
85C2×C3×C4×D3—22no—
86C2×C3×Dic6—22no—
87C2×C3×Dic6—22no—
88C2×C3×Dic6—22no—
89C2×#626—22no—
90C2×#626—22no—
91C2×#626Q814yescomplemented
92C32×C4⋊C4D414yescomplemented
93#3752—24no—
94C4⋊(C3⋊Dic3)—24no—
95C3×(C2×D3)⋊C4—24no—
96C3×C4⋊Dic3—24no—
97C3×C4⋊Dic3D414yescomplemented
98C3×C4×Dic3—24no—
99C3×C4×Dic3D414yes—
100Dic3⋊Dic3—24no—
101Dic3⋊Dic3—24no—
102Dic3⋊Dic3—24no—
103Dic3⋊Dic3—24no—
104Dic3⋊Dic3—22no—
105#3722—24no—
106#3722—22no—
107(C2×D3)⋊Dic3—24no—
108(C2×D3)⋊Dic3—22no—
109#2542—91noSylow
110C22×C3×Q8—31no—
111C23×C3×C4—31no—
112C22×#67—31no—
113C22×D12—31no—
114C22×C4×D3—31no—
115C22×C4×D3—31no—
116C22×C4×D3—61no—
117C22×C4×D3C2×D311yescharacteristic
118C22×Dic6—31no—
119C22×Dic6—31no—
120C22×Dic6—61no—
121C22×Dic6C2×D311yescharacteristic
122C3×C22⋊Q8—64no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—31no—
125C2×C3×C4⋊C4—32no—
126C2×C3×C4⋊C4C2×D311yescharacteristic
127C2×C3×C4⋊C4C2×D311yescharacteristic
128C2×C3×C22⋊C4—32no—
129C2×C3×C42—31no—
130C2×C3×C42—32no—
131C2×#217—31no—
132C2×#217—32no—
133#946—64no—
134#944—64no—
135C4×#67—64no—
136C2×(C2×D3)⋊C4—31no—
137C2×(C2×D3)⋊C4—32no—
138C2×(C2×D3)⋊C4—32no—
139C2×(C2×D3)⋊C4—32no—
140C2×(C2×D3)⋊C4—31no—
141C2×(C2×D3)⋊C4—32no—
142C2×(C2×D3)⋊C4—32no—
143C2×(C2×D3)⋊C4—31no—
144C2×(C2×D3)⋊C4—62no—
145C2×(C2×D3)⋊C4C2×D312yes—
146C2×C4⋊Dic3—32no—
147C2×C4⋊Dic3—32no—
148C2×C4⋊Dic3—32no—
149C2×C4⋊Dic3—32no—
150C2×C4⋊Dic3—32no—
151C2×C4⋊Dic3—31no—
152C2×C4⋊Dic3—32no—
153C2×C4⋊Dic3—62no—
154C2×C4⋊Dic3C2×D312yes—
155C2×C4⋊Dic3C2×D311yescharacteristic
156#924—64no—
157C2×Dic3⋊C4—32no—
158C2×Dic3⋊C4—32no—
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—32no—
162C2×C4×Dic3C2×D312yes—
163C2×C4×Dic3C2×D311yescharacteristic
164#897—24no—
165#897—68no—
166#897—64no—
167#897—64no—
168#897—64no—
169#897—64no—
170C4×D12—64no—
171#869—64no—
172C3×#95—32no—
173C3⋊#95C2×D312yes—
174C23×C32C2411yescharacteristic
175C22×C3⋊D3—21no—
176C22×C3⋊D3—21no—
177C22×C3⋊D3—21no—
178C22×C3⋊D3—21no—
179C22×C3⋊D3—21no—
180C22×C3⋊D3—21no—
181C22×C3⋊D3C2×Q812yes—
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—22no—
190C2×C32×C4—22no—
191C2×C32×C4C2×D412yes—
192C2×C32×C4C2×D412yes—
193C2×C32×C4C2×D414yes—
194C2×C32×C4C2×D412yes—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—22no—
197C2×C3⋊Dic3—22no—
198C2×C3⋊Dic3—21no—
199C2×C3⋊Dic3—22no—
200C2×C3⋊Dic3—21no—
201C4×C3⋊D3—44no—
202#634—44no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—21no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—21no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—21no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—21no—
211C2×C3×Dic3—21no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3C2×D412yes—
214C2×C3×Dic3C2×D414yes—
215C2×C3×Dic3C2×D412yes—
216C2×C3×Dic3C2×Q812yes—
217C2×C3×Dic3#4112yes—
218C3×C4×D3—44no—
219C3×Dic6—44no—
220#626—28no—
221C2×C4⋊Q8—91no—
222C2×C22⋊Q8—31no—
223C2×C22⋊Q8—91no—
224C2×C22⋊Q8—91no—
225C2×C22⋊Q8—91no—
226C2×C4×D4—91no—
227#399—92no—
228#399—92no—
229#390—92no—
230#384—92no—
231C4×C4⋊C4—31no—
232C24×C3—31no—
233C23×D3—31no—
234C23×D3—31no—
235C23×D3—61no—
236C23×D3C22×D311yescharacteristic
237C2×C3×Q8—62no—
238C2×C3×Q8—62no—
239C2×C3×Q8—62no—
240C22×C3×C4—21no—
241C22×C3×C4—22no—
242C22×C3×C4—31no—
243C22×C3×C4—31no—
244C22×C3×C4—32no—
245C22×C3×C4—32no—
246C22×C3×C4—31no—
247C22×C3×C4—62no—
248C22×C3×C4—62no—
249C22×C3×C4—62no—
250C22×C3×C4C22×D312yes—
251C22×C3×C4C22×D312yes—
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D311yescharacteristic
254C2×#67—34no—
255C2×#67—62no—
256C2×#67—62no—
257C22×Dic3—31no—
258C22×Dic3—32no—
259C22×Dic3—31no—
260C22×Dic3—32no—
261C22×Dic3—61no—
262C22×Dic3—62no—
263C22×Dic3C22×D311yescharacteristic
264C22×Dic3C22×D312yes—
265C22×Dic3C22×D311yescharacteristic
266C22×Dic3C22×D312yes—
267C22×Dic3C22×D311yescharacteristic
268C2×D12—34no—
269C2×D12—62no—
270C2×D12—62no—
271C2×C4×D3—22no—
272C2×C4×D3—22no—
273C2×C4×D3—22no—
274C2×C4×D3—64no—
275C2×C4×D3—62no—
276C2×C4×D3—62no—
277C2×C4×D3—62no—
278C2×C4×D3—62no—
279C2×C4×D3—62no—
280C2×C4×D3—62no—
281C2×C4×D3—122no—
282C2×C4×D3—122no—
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—24no—
296C3×C4⋊C4—34no—
297C3×C4⋊C4—64no—
298C3×C4⋊C4D1214yescomplemented
299C3×C4⋊C4#6714yescomplemented
300C3×C22⋊C4—64no—
301C3×C42—34no—
302C3×C42—64no—
303#217—64no—
304#217—62no—
305(C2×D3)⋊C4—24no—
306(C2×D3)⋊C4—62no—
307(C2×D3)⋊C4—64no—
308(C2×D3)⋊C4—68no—
309(C2×D3)⋊C4—62no—
310(C2×D3)⋊C4—64no—
311(C2×D3)⋊C4—64no—
312(C2×D3)⋊C4—64no—
313(C2×D3)⋊C4—62no—
314(C2×D3)⋊C4—64no—
315C4⋊Dic3—24no—
316C4⋊Dic3—64no—
317C4⋊Dic3—64no—
318C4⋊Dic3—62no—
319C4⋊Dic3—64no—
320C4⋊Dic3—64no—
321C4⋊Dic3—68no—
322C4⋊Dic3—64no—
323C4⋊Dic3—64no—
324C4⋊Dic3D1214yescomplemented
325Dic3⋊C4—64no—
326Dic3⋊C4—62no—
327Dic3⋊C4—64no—
328Dic3⋊C4—64no—
329Dic3⋊C4—64no—
330C4×Dic3—24no—
331C4×Dic3D1214yes—
332C22×C32C22×D411yescharacteristic
333C22×C32C22×D411yescharacteristic
334C22×C32C22×D411yescharacteristic
335C22×C32C22×Q811yescharacteristic
336C22×C32C2×#4111yescharacteristic
337C22×C322−1+411yescharacteristic
338C22×C322−1+411yescharacteristic
339C2×C3⋊D3—22no—
340C2×C3⋊D3—22no—
341C2×C3⋊D3—22no—
342C2×C3⋊D3—41no—
343C2×C3⋊D3—41no—
344C2×C3⋊D3—41no—
345C2×C3⋊D3—41no—
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—24no—
354C32×C4#12714yes—
355C3⋊Dic3—42no—
356C3⋊Dic3—41no—
357C3×Dic3—22no—
358C3×Dic3—24no—
359C3×Dic3—42no—
360C3×Dic3—41no—
361C3×Dic3C22⋊Q814yescomplemented
362C22×Q8—31no—
363C22×Q8—91no—
364C22×D4—91no—
365C23×C4—31no—
366C23×C4—91no—
367C4⋊Q8—184no—
368C22⋊Q8—64no—
369C22⋊Q8—184no—
370C22⋊Q8—184no—
371C22⋊Q8—184no—
372C4×D4—184no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—32no—
375C2×C4⋊C4—91no—
376C2×C4⋊C4—92no—
377C2×C4⋊C4—92no—
378C2×C4⋊C4—92no—
379C2×C4⋊C4—92no—
380C2×C4⋊C4—92no—
381C2×C4⋊C4D3211yescharacteristic
382C2×C22⋊C4—32no—
383C2×C22⋊C4—91no—
384C2×C22⋊C4—92no—
385C2×C22⋊C4—91no—
386C2×C22⋊C4—92no—
387C2×C22⋊C4—92no—
388C2×C42—31no—
389C2×C42—32no—
390#95—32no—
391C23×C3—21no—
392C23×C3—32no—
393C23×C3—61no—
394C23×C3—61no—
395C23×C3—61no—
396C23×C3—61no—
397C23×C3—61no—
398C23×C3—61no—
399C23×C3C23×D311yescharacteristic
400C23×C3C23×D311yescharacteristic
401C22×D3—21no—
402C22×D3—21no—
403C22×D3—21no—
404C22×D3—21no—
405C22×D3—21no—
406C22×D3—21no—
407C22×D3—32no—
408C22×D3—32no—
409C22×D3—62no—
410C22×D3—62no—
411C22×D3—62no—
412C22×D3—61no—
413C22×D3—61no—
414C22×D3—61no—
415C22×D3—61no—
416C22×D3—61no—
417C22×D3—61no—
418C22×D3—61no—
419C22×D3—61no—
420C22×D3—61no—
421C22×D3—61no—
422C22×D3—61no—
423C22×D3—61no—
424C22×D3—121no—
425C22×D3—121no—
426C22×D3—121no—
427C22×D3—121no—
428C22×D3D3×Q812yes—
429C3×Q8—124no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—24no—
438C2×C3×C4—32no—
439C2×C3×C4—32no—
440C2×C3×C4—32no—
441C2×C3×C4—32no—
442C2×C3×C4—34no—
443C2×C3×C4—42no—
444C2×C3×C4—42no—
445C2×C3×C4—61no—
446C2×C3×C4—62no—
447C2×C3×C4—62no—
448C2×C3×C4—61no—
449C2×C3×C4—61no—
450C2×C3×C4—62no—
451C2×C3×C4—61no—
452C2×C3×C4—62no—
453C2×C3×C4—62no—
454C2×C3×C4—61no—
455C2×C3×C4—124no—
456C2×C3×C4C2×D1212yes—
457C2×C3×C4C2×D1212yes—
458C2×C3×C4C2×D1214yes—
459C2×C3×C4C2×D1212yes—
460C2×C3×C4D3×D412yes—
461C2×C3×C4D3×D412yes—
462C2×C3×C4C2×#6714yes—
463C2×C3×C4C2×#6712yes—
464#67—68no—
465C2×Dic3—22no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3—21no—
471C2×Dic3—22no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—22no—
475C2×Dic3—62no—
476C2×Dic3—64no—
477C2×Dic3—62no—
478C2×Dic3—61no—
479C2×Dic3—62no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—62no—
483C2×Dic3—62no—
484C2×Dic3—61no—
485C2×Dic3—62no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—62no—
489C2×Dic3—122no—
490C2×Dic3—122no—
491C2×Dic3—121no—
492C2×Dic3—121no—
493C2×Dic3C2×D1212yes—
494C2×Dic3C2×D1214yes—
495C2×Dic3C2×D1212yes—
496C2×Dic3#23712yes—
497C2×Dic3D3×Q812yes—
498D12—68no—
499C4×D3—44no—
500C4×D3—128no—
501C4×D3—124no—
502C4×D3—124no—
503Dic6—44no—
504Dic6—128no—
505Dic6—124no—
506Dic6—124no—
507C2×C32C2×C22⋊Q811yescharacteristic
508C2×C32C2×#12711yescharacteristic
509C2×C32#53611yescharacteristic
510C2×C32#54711yescharacteristic
511C2×C32#54711yescharacteristic
512C2×C32D4×Q811yescharacteristic
513C2×C32D4×Q811yescharacteristic
514C3⋊D3—42no—
515C3×D3—42no—
516C24—31no—
517C24—91no—
518C2×Q8—62no—
519C2×Q8—62no—
520C2×Q8—62no—
521C2×Q8—182no—
522C2×Q8—182no—
523C2×Q8—182no—
524C2×D4—94no—
525C2×D4—182no—
526C2×D4—182no—
527C22×C4—31no—
528C22×C4—31no—
529C22×C4—32no—
530C22×C4—32no—
531C22×C4—31no—
532C22×C4—62no—
533C22×C4—62no—
534C22×C4—62no—
535C22×C4—92no—
536C22×C4—91no—
537C22×C4—182no—
538C22×C4—182no—
539C22×C4—182no—
540C22×C4C2×D3212yes—
541C22×C4C2×D3211yescharacteristic
542C4⋊C4—34no—
543C4⋊C4—64no—
544C4⋊C4—182no—
545C4⋊C4—184no—
546C4⋊C4—184no—
547C4⋊C4—184no—
548C4⋊C4—184no—
549C4⋊C4—184no—
550C4⋊C4#62614yescomplemented
551C22⋊C4—64no—
552C22⋊C4—182no—
553C22⋊C4—184no—
554C22⋊C4—182no—
555C22⋊C4—184no—
556C22⋊C4—184no—
557C42—34no—
558C42—64no—
559C22×C3—21no—
560C22×C3—21no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—21no—
566C22×C3—62no—
567C22×C3—62no—
568C22×C3—62no—
569C22×C3—121no—
570C22×C3—121no—
571C22×C3—121no—
572C22×C3—121no—
573C22×C3C22×D1211yescharacteristic
574C22×C3C22×D1211yescharacteristic
575C22×C3C22×D1211yescharacteristic
576C22×C3C2×D3×D411yescharacteristic
577C22×C3C2×D3×D411yescharacteristic
578C22×C3C2×#23711yescharacteristic
579C22×C3C2×D3×Q811yescharacteristic
580C22×C3C2×D3×Q811yescharacteristic
581C22×C3#100711yescharacteristic
582C22×C3D3×#4111yescharacteristic
583C22×C3#101011yescharacteristic
584C22×C3#101011yescharacteristic
585C22×C3#101011yescharacteristic
586C22×C3C22×#6711yescharacteristic
587C2×D3—22no—
588C2×D3—22no—
589C2×D3—22no—
590C2×D3—41no—
591C2×D3—41no—
592C2×D3—41no—
593C2×D3—41no—
594C2×D3—64no—
595C2×D3—62no—
596C2×D3—62no—
597C2×D3—62no—
598C2×D3—62no—
599C2×D3—62no—
600C2×D3—62no—
601C2×D3—122no—
602C2×D3—122no—
603C2×D3—122no—
604C2×D3—122no—
605C2×D3—122no—
606C2×D3—122no—
607C2×D3—121no—
608C2×D3—121no—
609C2×D3—121no—
610C2×D3—121no—
611C2×D3—121no—
612C2×D3—121no—
613C2×D3—121no—
614C2×D3—121no—
615C3×C4—24no—
616C3×C4—24no—
617C3×C4—24no—
618C3×C4—34no—
619C3×C4—44no—
620C3×C4—62no—
621C3×C4—64no—
622C3×C4—121no—
623C3×C4—122no—
624C3×C4#87414yes—
625C3×C4#94014yes—
626Dic3—22no—
627Dic3—24no—
628Dic3—42no—
629Dic3—41no—
630Dic3—124no—
631Dic3—122no—
632Dic3—122no—
633Dic3—121no—
634Dic3—122no—
635Dic3—121no—
636Dic3#89714yescomplemented
637C32#254211yescharacteristic, complemented, Sylow
638C23—32no—
639C23—61no—
640C23—61no—
641C23—61no—
642C23—61no—
643C23—61no—
644C23—61no—
645C23—92no—
646C23—181no—
647C23—181no—
648C23—181no—
649C23—181no—
650C23—181no—
651C23—181no—
652C23C22×D3211yescharacteristic
653Q8—124no—
654Q8—364no—
655D4—188no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—32no—
659C2×C4—32no—
660C2×C4—32no—
661C2×C4—32no—
662C2×C4—34no—
663C2×C4—61no—
664C2×C4—62no—
665C2×C4—61no—
666C2×C4—62no—
667C2×C4—61no—
668C2×C4—62no—
669C2×C4—61no—
670C2×C4—62no—
671C2×C4—62no—
672C2×C4—61no—
673C2×C4—124no—
674C2×C4—181no—
675C2×C4—182no—
676C2×C4—181no—
677C2×C4—182no—
678C2×C4—182no—
679C2×C4—181no—
680C2×C4—364no—
681C2×C4D3×D1212yes—
682C2×C4D3×D1212yes—
683C2×C4C2×#62614yes—
684C2×C4C2×#62612yes—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—122no—
693C2×C3C2×#87411yescharacteristic
694C2×C3C2×#89711yescharacteristic
695C2×C3#552611yescharacteristic
696C2×C3#555511yescharacteristic
697C2×C3#555511yescharacteristic
698C2×C3Q8×D1211yescharacteristic
699C2×C3Q8×D1211yescharacteristic
700C2×C3D3×C22⋊Q811yescharacteristic
701C2×C3#562811yescharacteristic
702C2×C3#563111yescharacteristic
703C2×C3#563211yescharacteristic
704C2×C3C2×#94011yescharacteristic
705C2×C3Q8×#6711yescharacteristic
706C2×C3#582411yescharacteristic
707D3—42no—
708D3—124no—
709D3—122no—
710D3—122no—
711C22—62no—
712C22—62no—
713C22—62no—
714C22—121no—
715C22—121no—
716C22—121no—
717C22—121no—
718C22—182no—
719C22—182no—
720C22—182no—
721C22—361no—
722C22—361no—
723C22—361no—
724C22—361no—
725C22C2×D3×D1211yescharacteristic
726C22C2×D3×D1211yescharacteristic
727C22#6430911yescharacteristic
728C22D3×#23711yescharacteristic
729C22#6431511yescharacteristic
730C22D32×Q811yescharacteristic
731C22C22×#62611yescharacteristic
732C4—24no—
733C4—34no—
734C4—62no—
735C4—64no—
736C4—121no—
737C4—122no—
738C4—361no—
739C4—362no—
740C4#6391114yes—
741C3—21no—
742C3#7380011yescharacteristic, complemented
743C3#8278011yescharacteristic, complemented
744C2—122no—
745C2—362no—
746C2#1059438011yescharacteristic
747C2#1059438111yescharacteristic
748C2#1059438311yescharacteristic
749C2D3×#89711yescharacteristic
750C2C2×#6391111yescharacteristic
751C2#1059524811yescharacteristic
752C2Q8×#62611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC22×#626C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2542
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×#64106C2semidirect
2. C2×C3×#897C2semidirect
4. C2×#63871C2semidirect
5. C2×#63866C2semidirect
6. C2×#63857C2semidirect
7. C3×Dic3×C4⋊C4C2semidirect
9. #10591350C2semidirect
10. #10591349C2semidirect
11. #10591317C2semidirect
53. C2×#897D3semidirect
59. Dic3×C4⋊C4D3semidirect
91. C2×#626Q8semidirect
92. C32×C4⋊C4D4semidirect
97. C3×C4⋊Dic3D4semidirect
298. C3×C4⋊C4D12semidirect
299. C3×C4⋊C4#67semidirect
324. C4⋊Dic3D12semidirect
361. C3×Dic3C22⋊Q8semidirect
550. C4⋊C4#626semidirect
636. Dic3#897semidirect
637. C32#2542semidirect
742. C3#73800semidirect
743. C3#82780semidirect

Maximal subgroups

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

subgroupindex
C2×#641062
C2×C3×#8972
C2×C4×#6262
C2×#638712
C2×#638662
C2×#638572
C3×Dic3×C4⋊C42
#105913832
#105913502
#105913492
#105913172
#827803
#738003