Finite Group Databasebeta

← #11802718

Subgroups — #11802718

Order 1152.

1903 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3804C211yesmaximal, characteristic
2C22×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
3C2×#63955C211yesmaximal, characteristic, complemented
4#10592912C211yesmaximal, characteristic, complemented
5C3×#5213C211yesmaximal, characteristic, complemented
6#10591711C211yesmaximal, characteristic, complemented
7#10591710C211yesmaximal, characteristic, complemented
8#10591384C212yesmaximal, complemented
9#10591367C212yesmaximal, complemented
10#10591366C212yesmaximal, complemented
11#10591235C212yesmaximal, complemented
12#82186—31nomaximal
13#74662—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×#638C2211yescharacteristic
16C22×C3×#67C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C23×C3×Dic3C2211yescharacteristic
19C22×#627C2211yescharacteristic
20C22×#626C2211yescharacteristic
21C22×#624C2211yescharacteristic
22C2×#3804—24no—
23C2×#3804—24no—
24C2×#3804C418yescomplemented
25C22×D3×Dic3C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3752C2212yes—
28C2×C3×#217C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×Dic3⋊C4—24no—
31C2×C3×Dic3⋊C4C2212yes—
32C2×C3×Dic3⋊C4C2212yes—
33C2×Dic3⋊Dic3C2212yes—
34C2×#3722C2212yes—
35C2×(C2×D3)⋊Dic3C2212yes—
36#63955—24no—
37C2×Dic32C2212yes—
38#63658C2212yes—
39C3×C3⋊#95C2212yes—
40#63579C2212yes—
41#63579C2212yes—
42C22×#237—31no—
43C22×#235—31no—
44C22×C3×C4⋊C4—31no—
45C2×#926—31no—
46C22×Dic3⋊C4D311yescharacteristic, complemented
47C2×#877—31no—
48C3×#386—31no—
49#5220—31no—
50#5213—31no—
51#5213—31no—
52#5213—31no—
53#5213—31no—
54#5213—61no—
55#5213D311yescharacteristic, complemented
56#4988—32no—
57#4987—32no—
58#4987—32no—
59#4973—32no—
60#4958—31no—
61#4957—32no—
62#4942—32no—
63#4667—32no—
64#4646—32no—
65C24×C32C2311yescharacteristic
66C23×C3⋊D3C2311yescharacteristic
67C23×C3×D3C2311yescharacteristic
68C22×C32×C4—22no—
69C22×C32×C4—42no—
70C22×C32×C4C2312yes—
71C2×#638—22no—
72C2×#638—22no—
73C2×#638C2×C414yes—
74C22×C3⋊Dic3C2312yes—
75C22×C3⋊Dic3C2311yescharacteristic
76C2×C3×#67—22no—
77C2×C3×#67—22no—
78C2×C3×#67C2×C414yes—
79C22×C3×Dic3—22no—
80C22×C3×Dic3—42no—
81C22×C3×Dic3C2×C414yes—
82C22×C3×Dic3D414yes—
83C22×C3×Dic3D414yes—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2311yescharacteristic
89C2×#627—22no—
90C2×#627—22no—
91C2×#627C2×C414yescomplemented
92C2×#626—22no—
93C2×#626—22no—
94C2×#626C2×C414yescomplemented
95C2×#624—22no—
96C2×#624—22no—
97C2×#624C2×C414yescomplemented
98#3804—232no—
99C2×D3×Dic3—22no—
100C2×D3×Dic3—22no—
101C2×D3×Dic3C2×C414yescomplemented
102#3757—22no—
103#3752—42no—
104C3×#217—22no—
105C3×(C2×D3)⋊C4—42no—
106C3×Dic3⋊C4—24no—
107C3×Dic3⋊C4—24no—
108Dic3⋊Dic3—24no—
109#3722—42no—
110(C2×D3)⋊Dic3—42no—
111Dic32—24no—
112#2311—91noSylow
113C22×C3×D4—31no—
114C23×C3×C4—21no—
115C23×C3×C4—31no—
116C23×C3×C4—31no—
117C23×C3×C4C2×D311yescharacteristic
118C23×C3×C4C2×D311yescharacteristic
119C22×#67—31no—
120C22×#67—31no—
121C22×#67—31no—
122C22×#67—61no—
123C22×#67C2×D311yescharacteristic
124C23×Dic3—31no—
125C23×Dic3C2×D311yescharacteristic
126C23×Dic3C2×D311yescharacteristic
127C2×#237—38no—
128C2×#237—64no—
129C2×#237—64no—
130C2×#235—38no—
131C2×#235—64no—
132C2×#235—64no—
133C22×D12—31no—
134C22×C4×D3—31no—
135C22×C4×D3—31no—
136C22×C4×D3—31no—
137C22×Dic6—31no—
138C22×Dic6—31no—
139C2×C3×C4⋊C4—32no—
140C2×C3×C4⋊C4—32no—
141C2×C3×C4⋊C4—64no—
142C2×C3×C22⋊C4—31no—
143C2×C3×C22⋊C4—32no—
144C2×#217—31no—
145C2×#217—31no—
146C2×#217—32no—
147C2×#217—61no—
148C2×#217C2×D311yescharacteristic
149C2×(C2×D3)⋊C4—32no—
150C2×(C2×D3)⋊C4—32no—
151C2×(C2×D3)⋊C4—32no—
152C2×(C2×D3)⋊C4—32no—
153C2×(C2×D3)⋊C4—32no—
154C2×(C2×D3)⋊C4—62no—
155C2×(C2×D3)⋊C4C2×D312yes—
156#926—64no—
157C2×C4⋊Dic3—32no—
158C2×Dic3⋊C4—24no—
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4C2×D312yes—
161C2×Dic3⋊C4C2×D312yes—
162C2×C4×Dic3—32no—
163C2×C4×Dic3—32no—
164#877—64no—
165C3×#95—32no—
166C3⋊#95—32no—
167C3⋊#95—32no—
168C3⋊#95—32no—
169C3⋊#95—32no—
170C3⋊#95—32no—
171C3⋊#95—32no—
172C3⋊#95—62no—
173C3⋊#95C2×D312yes—
174C23×C32—22no—
175C23×C32—22no—
176C23×C32C22×C412yes—
177C23×C32C2×D412yes—
178C23×C32C2×D412yes—
179C23×C32C2411yescharacteristic
180C22×C3⋊D3—21no—
181C22×C3⋊D3—21no—
182C22×C3⋊D3—22no—
183C22×C3⋊D3—22no—
184C22×C3⋊D3C22×C412yes—
185C22×C3×D3—21no—
186C22×C3×D3—21no—
187C22×C3×D3—22no—
188C22×C3×D3—22no—
189C22×C3×D3C22×C412yes—
190C2×C32×C4—22no—
191C2×C32×C4—22no—
192C2×C32×C4—22no—
193C2×C32×C4—44no—
194#638—28no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—22no—
198C2×C3⋊Dic3—22no—
199C2×C3⋊Dic3—22no—
200C2×C3⋊Dic3C22×C412yes—
201C3×#67—28no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—44no—
211C2×C3×Dic3C22⋊C4116yescomplemented
212C2×C3×Dic3C22×C412yes—
213C2×C3×Dic3C22×C412yes—
214C2×C3×Dic3C22×C412yes—
215C2×C3×Dic3C2×D412yes—
216C2×C3×Dic3C2×D412yes—
217C2×C3×Dic3C2×D412yes—
218C2×C3×Dic3C2×D412yes—
219#627—28no—
220#626—28no—
221#624—28no—
222D3×Dic3—28no—
223C22×#41—91no—
224C2×#117—91no—
225C22×C4⋊C4—31no—
226#391—92no—
227#390—92no—
228#386—31no—
229#386—91no—
230#386—91no—
231#386—91no—
232#380—92no—
233#380—92no—
234C24×C3—21no—
235C24×C3—31no—
236C24×C3C22×D311yescharacteristic
237C24×C3C22×D311yescharacteristic
238C23×D3—31no—
239C23×D3—31no—
240C23×D3—61no—
241C23×D3C22×D311yescharacteristic
242C2×C3×D4—34no—
243C2×C3×D4—62no—
244C2×C3×D4—62no—
245C22×C3×C4—22no—
246C22×C3×C4—22no—
247C22×C3×C4—22no—
248C22×C3×C4—34no—
249C22×C3×C4—34no—
250C22×C3×C4—34no—
251C22×C3×C4—31no—
252C22×C3×C4—31no—
253C22×C3×C4—31no—
254C22×C3×C4—32no—
255C22×C3×C4—32no—
256C22×C3×C4—42no—
257C22×C3×C4—42no—
258C22×C3×C4—42no—
259C22×C3×C4—44no—
260C22×C3×C4—62no—
261C22×C3×C4—122no—
262C22×C3×C4C22×D312yes—
263C22×C3×C4C22×D312yes—
264C2×#67—22no—
265C2×#67—22no—
266C2×#67—34no—
267C2×#67—34no—
268C2×#67—34no—
269C2×#67—64no—
270C2×#67—62no—
271C2×#67—62no—
272C2×#67—62no—
273C2×#67—62no—
274C2×#67—62no—
275C2×#67—62no—
276C2×#67—122no—
277C2×#67—122no—
278C2×#67C4×D314yes—
279C22×Dic3—22no—
280C22×Dic3—31no—
281C22×Dic3—31no—
282C22×Dic3—34no—
283C22×Dic3—32no—
284C22×Dic3—32no—
285C22×Dic3—42no—
286C22×Dic3—61no—
287C22×Dic3—62no—
288C22×Dic3—62no—
289C22×Dic3—62no—
290C22×Dic3C4×D314yes—
291C22×Dic3D1214yes—
292C22×Dic3#6714yes—
293C22×Dic3C22×D312yes—
294C22×Dic3C22×D312yes—
295C22×Dic3C22×D311yescharacteristic
296C22×Dic3C22×D311yescharacteristic
297C22×Dic3C22×D311yescharacteristic
298#237—632no—
299#235—632no—
300C2×D12—34no—
301C2×D12—62no—
302C2×D12—62no—
303C2×C4×D3—34no—
304C2×C4×D3—34no—
305C2×C4×D3—34no—
306C2×C4×D3—62no—
307C2×C4×D3—62no—
308C2×C4×D3—62no—
309C2×C4×D3—62no—
310C2×C4×D3—62no—
311C2×C4×D3—62no—
312C2×Dic6—34no—
313C2×Dic6—34no—
314C2×Dic6—62no—
315C2×Dic6—62no—
316C2×Dic6—62no—
317C2×Dic6—62no—
318C3×C4⋊C4—64no—
319C3×C4⋊C4—64no—
320C3×C22⋊C4—62no—
321C3×C22⋊C4—122no—
322#217—22no—
323#217—62no—
324#217—62no—
325#217—122no—
326#217—122no—
327(C2×D3)⋊C4—42no—
328(C2×D3)⋊C4—122no—
329(C2×D3)⋊C4—122no—
330(C2×D3)⋊C4—122no—
331(C2×D3)⋊C4—122no—
332(C2×D3)⋊C4—122no—
333(C2×D3)⋊C4—124no—
334C4⋊Dic3—64no—
335Dic3⋊C4—24no—
336Dic3⋊C4—24no—
337Dic3⋊C4—64no—
338C4×Dic3—64no—
339C4×Dic3—64no—
340C22×C32—24no—
341C22×C32—22no—
342C22×C32—22no—
343C22×C32—24no—
344C22×C32C2×C22⋊C414yes—
345C22×C32C23×C411yescharacteristic
346C22×C32C22×D411yescharacteristic
347C22×C32C22×D411yescharacteristic
348C22×C32H(5,𝔽2)12yes—
349C22×C322−1+412yes—
350C2×C3⋊D3—22no—
351C2×C3⋊D3—24no—
352C2×C3⋊D3—41no—
353C2×C3⋊D3—41no—
354C2×C3⋊D3—42no—
355C2×C3×D3—22no—
356C2×C3×D3—24no—
357C2×C3×D3—41no—
358C2×C3×D3—41no—
359C2×C3×D3—42no—
360C32×C4—42no—
361C3⋊Dic3—22no—
362C3⋊Dic3—42no—
363C3×Dic3—22no—
364C3×Dic3—42no—
365C3×Dic3—42no—
366C3×Dic3C2×C22⋊C414yes—
367C3×Dic3C2×C22⋊C414yes—
368C2×#41—98no—
369C2×#41—184no—
370C2×#41—184no—
371C22×Q8—91no—
372C22×D4—31no—
373C22×D4—91no—
374C22×D4—91no—
375C23×C4—31no—
376C23×C4—31no—
377C23×C4—91no—
378C23×C4—91no—
379C23×C4D3211yescharacteristic
380#117—184no—
381C2×C4⋊C4—32no—
382C2×C4⋊C4—32no—
383C2×C4⋊C4—64no—
384C2×C4⋊C4—92no—
385C2×C22⋊C4—31no—
386C2×C22⋊C4—32no—
387C2×C22⋊C4—91no—
388C2×C22⋊C4—92no—
389C2×C22⋊C4—92no—
390C2×C22⋊C4—92no—
391C2×C42—92no—
392#95—32no—
393#95—92no—
394#95—92no—
395#95—92no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—21no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—32no—
405C23×C3—42no—
406C23×C3—42no—
407C23×C3—61no—
408C23×C3—62no—
409C23×C3—62no—
410C23×C3—61no—
411C23×C3C2×C4×D312yes—
412C23×C3C2×C4×D312yes—
413C23×C3C2×D1212yes—
414C23×C3D3×D412yes—
415C23×C3D3×D412yes—
416C23×C3C2×#6712yes—
417C23×C3C23×D311yescharacteristic
418C23×C3C23×D311yescharacteristic
419C22×D3—21no—
420C22×D3—21no—
421C22×D3—22no—
422C22×D3—22no—
423C22×D3—32no—
424C22×D3—32no—
425C22×D3—62no—
426C22×D3—61no—
427C22×D3—61no—
428C22×D3—61no—
429C22×D3—62no—
430C22×D3—62no—
431C22×D3—62no—
432C22×D3—62no—
433C22×D3—61no—
434C22×D3—122no—
435C22×D3—121no—
436C22×D3—121no—
437C22×D3—122no—
438C22×D3C2×C4×D312yes—
439C3×D4—68no—
440C2×C3×C4—24no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—316no—
448C2×C3×C4—32no—
449C2×C3×C4—32no—
450C2×C3×C4—32no—
451C2×C3×C4—32no—
452C2×C3×C4—32no—
453C2×C3×C4—32no—
454C2×C3×C4—32no—
455C2×C3×C4—42no—
456C2×C3×C4—42no—
457C2×C3×C4—44no—
458C2×C3×C4—44no—
459C2×C3×C4—48no—
460C2×C3×C4—61no—
461C2×C3×C4—61no—
462C2×C3×C4—62no—
463C2×C3×C4—62no—
464C2×C3×C4—62no—
465C2×C3×C4—62no—
466C2×C3×C4—62no—
467C2×C3×C4—62no—
468C2×C3×C4—124no—
469#67—28no—
470#67—68no—
471#67—68no—
472#67—68no—
473#67—128no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—32no—
483C2×Dic3—32no—
484C2×Dic3—44no—
485C2×Dic3—62no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—68no—
491C2×Dic3—62no—
492C2×Dic3—62no—
493C2×Dic3—62no—
494C2×Dic3—62no—
495C2×Dic3—62no—
496C2×Dic3—62no—
497C2×Dic3—121no—
498C2×Dic3—121no—
499C2×Dic3—122no—
500C2×Dic3—122no—
501C2×Dic3—122no—
502C2×Dic3(C2×D3)⋊C4116yescomplemented
503C2×Dic3C2×C4×D312yes—
504C2×Dic3C2×C4×D312yes—
505C2×Dic3C2×C4×D312yes—
506C2×Dic3C2×D1212yes—
507C2×Dic3C2×D1212yes—
508C2×Dic3C2×#6712yes—
509C2×Dic3C2×#6712yes—
510D12—68no—
511C4×D3—68no—
512C4×D3—68no—
513C4×D3—68no—
514Dic6—68no—
515Dic6—68no—
516C2×C32—24no—
517C2×C32C22×C22⋊C411yescharacteristic
518C2×C32#52012yes—
519C2×C32#53511yescharacteristic
520C2×C32#53611yescharacteristic
521C2×C32#53712yes—
522C3⋊D3—42no—
523C3×D3—42no—
524C24—31no—
525C24—91no—
526C24C2×D3211yescharacteristic
527#41—1832no—
528C2×Q8—94no—
529C2×Q8—182no—
530C2×Q8—182no—
531C2×D4—34no—
532C2×D4—62no—
533C2×D4—62no—
534C2×D4—94no—
535C2×D4—94no—
536C2×D4—182no—
537C2×D4—182no—
538C2×D4—182no—
539C2×D4—182no—
540C22×C4—22no—
541C22×C4—31no—
542C22×C4—31no—
543C22×C4—34no—
544C22×C4—34no—
545C22×C4—34no—
546C22×C4—31no—
547C22×C4—32no—
548C22×C4—32no—
549C22×C4—42no—
550C22×C4—62no—
551C22×C4—94no—
552C22×C4—94no—
553C22×C4—91no—
554C22×C4—92no—
555C22×C4—122no—
556C22×C4—182no—
557C22×C4—182no—
558C22×C4—182no—
559C22×C4—182no—
560C22×C4C2×D3212yes—
561C4⋊C4—64no—
562C4⋊C4—64no—
563C4⋊C4—184no—
564C22⋊C4—62no—
565C22⋊C4—122no—
566C22⋊C4—182no—
567C22⋊C4—362no—
568C22⋊C4—362no—
569C22⋊C4—362no—
570C42—184no—
571C22×C3—22no—
572C22×C3—24no—
573C22×C3—24no—
574C22×C3—24no—
575C22×C3—22no—
576C22×C3—22no—
577C22×C3—22no—
578C22×C3—24no—
579C22×C3—22no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—21no—
583C22×C3—22no—
584C22×C3—24no—
585C22×C3—42no—
586C22×C3—44no—
587C22×C3—42no—
588C22×C3—44no—
589C22×C3—64no—
590C22×C3—62no—
591C22×C3—122no—
592C22×C3—121no—
593C22×C3—121no—
594C22×C3D3×C22⋊C414yes—
595C22×C3C2×(C2×D3)⋊C414yes—
596C22×C3C22×C4×D311yescharacteristic
597C22×C3C22×C4×D311yescharacteristic
598C22×C3C22×D1211yescharacteristic
599C22×C3C2×D3×D411yescharacteristic
600C22×C3C2×D3×D411yescharacteristic
601C22×C3#100412yes—
602C22×C3#100412yes—
603C22×C3#100712yes—
604C22×C3#101012yes—
605C22×C3C22×#6711yescharacteristic
606C2×D3—22no—
607C2×D3—24no—
608C2×D3—41no—
609C2×D3—41no—
610C2×D3—42no—
611C2×D3—62no—
612C2×D3—64no—
613C2×D3—62no—
614C2×D3—64no—
615C2×D3—122no—
616C2×D3—124no—
617C2×D3—121no—
618C2×D3—122no—
619C2×D3—121no—
620C2×D3—121no—
621C2×D3—121no—
622C2×D3—122no—
623C2×D3—241no—
624C2×D3—242no—
625C2×D3—241no—
626C3×C4—34no—
627C3×C4—34no—
628C3×C4—44no—
629C3×C4—42no—
630C3×C4—42no—
631C3×C4—62no—
632C3×C4—122no—
633C3×C4—122no—
634Dic3—22no—
635Dic3—42no—
636Dic3—42no—
637Dic3—62no—
638Dic3—62no—
639Dic3—122no—
640Dic3—122no—
641Dic3—122no—
642Dic3—242no—
643Dic3C2×(C2×D3)⋊C414yes—
644Dic3C2×(C2×D3)⋊C414yes—
645C32#231111yescharacteristic, complemented, Sylow
646C23—22no—
647C23—22no—
648C23—32no—
649C23—62no—
650C23—61no—
651C23—61no—
652C23—62no—
653C23—92no—
654C23—182no—
655C23—181no—
656C23—181no—
657C23—182no—
658C23C4×D3212yes—
659C23D3×D1212yes—
660C23D3×#6712yes—
661C23C22×D3211yescharacteristic
662Q8—188no—
663D4—68no—
664D4—188no—
665D4—188no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—32no—
670C2×C4—32no—
671C2×C4—32no—
672C2×C4—32no—
673C2×C4—32no—
674C2×C4—32no—
675C2×C4—316no—
676C2×C4—32no—
677C2×C4—44no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—62no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—92no—
687C2×C4—124no—
688C2×C4—188no—
689C2×C4—188no—
690C2×C4—181no—
691C2×C4—181no—
692C2×C4—182no—
693C2×C4—182no—
694C2×C4—182no—
695C2×C3—24no—
696C2×C3—24no—
697C2×C3—22no—
698C2×C3—21no—
699C2×C3—22no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—44no—
703C2×C3—122no—
704C2×C3C2×D3×C22⋊C411yescharacteristic
705C2×C3#550412yes—
706C2×C3#551012yes—
707C2×C3#554612yes—
708C2×C3#559211yescharacteristic
709C2×C3#559712yes—
710C2×C3#564811yescharacteristic
711C2×C3C22×(C2×D3)⋊C411yescharacteristic
712C2×C3#580511yescharacteristic
713C2×C3#581611yescharacteristic
714D3—42no—
715D3—122no—
716D3—122no—
717D3—242no—
718C22—24no—
719C22—22no—
720C22—24no—
721C22—22no—
722C22—64no—
723C22—62no—
724C22—121no—
725C22—122no—
726C22—121no—
727C22—184no—
728C22—182no—
729C22—361no—
730C22—362no—
731C22—361no—
732C22D3×(C2×D3)⋊C414yes—
733C22#6429712yes—
734C22C2×C4×D3211yescharacteristic
735C22C2×D3×D1211yescharacteristic
736C22C2×D3×#6711yescharacteristic
737C22#6433012yes—
738C4—34no—
739C4—34no—
740C4—42no—
741C4—62no—
742C4—122no—
743C4—122no—
744C4—182no—
745C4—362no—
746C3—21no—
747C3#7466211yescharacteristic, complemented
748C3#8218611yescharacteristic, complemented
749C2—24no—
750C2—122no—
751C2—362no—
752C2#1059487412yes—
753C2#1059489711yescharacteristic
754C2#1059491112yes—
755C2C2×D3×(C2×D3)⋊C411yescharacteristic
756C2#1059551311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×#3804C2
hypercenterC23×C4D32
hypocenterC32#2311
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×Dic3⋊C4C2semidirect
3. C2×#63955C2semidirect
4. #10592912C2semidirect
5. C3×#5213C2semidirect
6. #10591711C2semidirect
7. #10591710C2semidirect
8. #10591384C2semidirect
9. #10591367C2semidirect
10. #10591366C2semidirect
11. #10591235C2semidirect
24. C2×#3804C4semidirect
46. C22×Dic3⋊C4D3semidirect
55. #5213D3semidirect
91. C2×#627C2×C4semidirect
94. C2×#626C2×C4semidirect
97. C2×#624C2×C4semidirect
101. C2×D3×Dic3C2×C4semidirect
211. C2×C3×Dic3C22⋊C4semidirect
502. C2×Dic3(C2×D3)⋊C4semidirect
645. C32#2311semidirect
747. C3#74662semidirect
748. C3#82186semidirect

Maximal subgroups

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

subgroupindex
C22×#38042
C22×C3×Dic3⋊C42
C2×#639552
#105929122
C3×#52132
#105917112
#105917102
#105913842
#105913672
#105913662
#105912352
#821863
#746623