Finite Group Databasebeta

← #11805662

Subgroups — #11805662

Order 1152.

1437 conjugacy classes of subgroups.

The subgroup lattice has 709 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#67C211yesmaximal, characteristic
2C2×C3×#926C211yesmaximal, characteristic, complemented
3C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
4#10592911C211yesmaximal, characteristic, complemented
5#10591721C212yesmaximal
6#10591702C212yesmaximal, complemented
7Dic3×(C2×D3)⋊C4C212yesmaximal, complemented
8#10591313C211yesmaximal, characteristic, complemented
9Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
10#10591224C211yesmaximal, characteristic, complemented
11#10591201C212yesmaximal, complemented
12#82335—31nomaximal
13#82272—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×C3×#67C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×D3×Dic3C2212yes—
18C2×#3757C2212yes—
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C3×#217C2212yes—
22C2×C3×#217C2211yescharacteristic
23C3×C4×#67C418yescomplemented
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C3×#926—24no—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×C4×Dic3C2212yes—
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×Dic3⋊Dic3C2212yes—
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×Dic32C2212yes—
34D3×C4⋊Dic3—24no—
35#63658C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×C4×D4—31no—
41C2×C3×#117—31no—
42C2×C4×#67D311yescharacteristic
43C2×#926D311yescharacteristic, complemented
44C22×C4⋊Dic3—31no—
45C2×D3×C4⋊C4—31no—
46#5220—32no—
47#5212—31no—
48#5212—31no—
49#5212—31no—
50#5212—61no—
51#4987—31no—
52#4980—32no—
53#4977—31no—
54Dic3×C4⋊C4—31no—
55#4956—32no—
56#4951—32no—
57#4945—32no—
58Dic3×C22⋊C4—32no—
59C4×(C2×D3)⋊C4—32no—
60#4936—31no—
61C4×C4⋊Dic3—31no—
62#4933—32no—
63C24×C32C2311yescharacteristic
64C23×C3×D3C2311yescharacteristic
65C22×C32×C4—22no—
66C22×C32×C4—22no—
67C22×C32×C4C2×C414yescomplemented
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3C2312yes—
71C22×C3⋊Dic3C2312yes—
72C2×C3×#67—22no—
73C2×C3×#67—22no—
74C2×C3×#67C2×C414yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2311yescharacteristic
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2311yescharacteristic
79C22×C3×Dic3C2312yes—
80C2×C3×C4×D3—22no—
81C2×C3×C4×D3—22no—
82C2×C3×C4×D3C2×C414yes—
83C2×D3×Dic3—24no—
84C2×D3×Dic3—24no—
85C2×D3×Dic3—42no—
86#3757—42no—
87C4⋊(C3⋊Dic3)—22no—
88C4⋊(C3⋊Dic3)—22no—
89C3×#217—24no—
90C3×#217C2×C414yescomplemented
91C3×(C2×D3)⋊C4C2×C414yes—
92C3×C4⋊Dic3—22no—
93C3×C4⋊Dic3D414yescomplemented
94C3×Dic3⋊C4C2×C414yescomplemented
95C3×C4×Dic3—24no—
96C3×C4×Dic3C2×C414yescomplemented
97Dic3⋊Dic3—24no—
98(C2×D3)⋊Dic3—24no—
99Dic32—42no—
100#2352—91noSylow
101C22×C3×D4—31no—
102C23×C3×C4—21no—
103C23×C3×C4—31no—
104C23×C3×C4C2×D311yescharacteristic
105C23×C3×C4C2×D311yescharacteristic
106C22×#67C2×D311yescharacteristic
107C23×Dic3—32no—
108C22×C4×D3—32no—
109C22×C4×D3C2×D311yescharacteristic
110C3×C4×D4—38no—
111C3×#117—64no—
112C2×C3×C4⋊C4—31no—
113C2×C3×C4⋊C4—31no—
114C2×C3×C4⋊C4—31no—
115C2×C3×C22⋊C4—31no—
116C2×C3×C22⋊C4—31no—
117C2×C3×C22⋊C4—32no—
118C2×C3×C42—31no—
119C2×C3×C42—32no—
120C2×#217—32no—
121C2×#217—32no—
122C2×#217—32no—
123C2×#217—62no—
124C2×#217C2×D312yes—
125C2×#217C2×D311yescharacteristic
126C4×#67Dic318yescomplemented
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4C2×D311yescharacteristic
129#926—24no—
130C2×C4⋊Dic3—31no—
131C2×C4⋊Dic3—31no—
132C2×C4⋊Dic3—31no—
133C2×C4⋊Dic3—31no—
134C2×C4⋊Dic3—32no—
135C2×C4⋊Dic3—61no—
136C2×C4⋊Dic3—61no—
137C2×C4⋊Dic3—64no—
138C2×C4⋊Dic3C2×D311yescharacteristic
139C2×C4⋊Dic3C2×D311yescharacteristic
140C2×Dic3⋊C4—32no—
141C2×Dic3⋊C4C2×D311yescharacteristic
142C2×C4×Dic3—32no—
143C2×C4×Dic3—32no—
144C2×C4×Dic3C2×D312yes—
145C2×C4×Dic3C2×D311yescharacteristic
146D3×C4⋊C4—64no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95—32no—
150C3⋊#95—32no—
151C3⋊#95—32no—
152C3⋊#95—32no—
153C3⋊#95—32no—
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95—32no—
157C3⋊#95—62no—
158C23×C32—21no—
159C23×C32—21no—
160C23×C32—21no—
161C23×C32—21no—
162C23×C32—21no—
163C23×C32—21no—
164C23×C32C22×C412yes—
165C23×C32C2411yescharacteristic
166C22×C3×D3—21no—
167C22×C3×D3—21no—
168C22×C3×D3—21no—
169C22×C3×D3—21no—
170C22×C3×D3C22×C412yes—
171C22×C3×D3#4112yes—
172C22×C3×D3#4112yes—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—28no—
176C2×C32×C4C22×C412yes—
177C2×C32×C4C22×C412yes—
178C2×C32×C4C2×D412yes—
179C2×C32×C4#4112yes—
180C2×C3⋊Dic3—22no—
181C2×C3⋊Dic3—22no—
182C2×C3⋊Dic3—22no—
183C2×C3⋊Dic3—22no—
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—22no—
186C3×#67—28no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3C22×C412yes—
199C2×C3×Dic3C22×C412yes—
200C2×C3×Dic3C22×C412yes—
201C2×C3×Dic3C2×D414yes—
202C3×C4×D3—28no—
203D3×Dic3—48no—
204C2×C4×D4—31no—
205C2×#117—31no—
206C22×C4⋊C4—91no—
207#388—92no—
208#387—92no—
209#386—92no—
210#382—91no—
211#380—91no—
212#380—91no—
213C4×C4⋊C4—91no—
214C4×C22⋊C4—92no—
215C24×C3—21no—
216C24×C3—31no—
217C24×C3C22×D311yescharacteristic
218C24×C3C22×D311yescharacteristic
219C23×D3C22×D311yescharacteristic
220C2×C3×D4—34no—
221C2×C3×D4—62no—
222C2×C3×D4—62no—
223C22×C3×C4—22no—
224C22×C3×C4—22no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—24no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—31no—
231C22×C3×C4—31no—
232C22×C3×C4—31no—
233C22×C3×C4—32no—
234C22×C3×C4—34no—
235C22×C3×C4—32no—
236C22×C3×C4—42no—
237C22×C3×C4—42no—
238C22×C3×C4—62no—
239C22×C3×C4—62no—
240C22×C3×C4C4×D314yescomplemented
241C22×C3×C4C2×Dic314yescomplemented
242C22×C3×C4C22×D311yescharacteristic
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D311yescharacteristic
246C2×#67—22no—
247C2×#67—22no—
248C2×#67C2×Dic314yes—
249C22×Dic3—32no—
250C22×Dic3—32no—
251C22×Dic3—32no—
252C22×Dic3—32no—
253C22×Dic3—62no—
254C22×Dic3—62no—
255C22×Dic3—64no—
256C22×Dic3—64no—
257C22×Dic3—122no—
258C22×Dic3C22×D312yes—
259C22×Dic3C22×D311yescharacteristic
260C22×Dic3C22×D311yescharacteristic
261C22×Dic3C22×D311yescharacteristic
262C22×Dic3C22×D312yes—
263C2×C4×D3—22no—
264C2×C4×D3—22no—
265C2×C4×D3—64no—
266C2×C4×D3—64no—
267C2×C4×D3—122no—
268C2×C4×D3C2×Dic314yes—
269C3×C4⋊C4—34no—
270C3×C4⋊C4—34no—
271C3×C4⋊C4—62no—
272C3×C22⋊C4—34no—
273C3×C22⋊C4—34no—
274C3×C22⋊C4—64no—
275C3×C42—34no—
276C3×C42—64no—
277#217—24no—
278#217—64no—
279#217—122no—
280#217—122no—
281#217—124no—
282#217C2×Dic314yescomplemented
283(C2×D3)⋊C4—64no—
284(C2×D3)⋊C4C2×Dic314yes—
285C4⋊Dic3—22no—
286C4⋊Dic3—62no—
287C4⋊Dic3—62no—
288C4⋊Dic3—62no—
289C4⋊Dic3—62no—
290C4⋊Dic3—64no—
291C4⋊Dic3—122no—
292C4⋊Dic3—122no—
293C4⋊Dic3#6714yescomplemented
294Dic3⋊C4—64no—
295Dic3⋊C4C2×Dic314yescomplemented
296C4×Dic3—24no—
297C4×Dic3—122no—
298C4×Dic3—122no—
299C4×Dic3C2×Dic314yescomplemented
300C22×C32—22no—
301C22×C32—22no—
302C22×C32—22no—
303C22×C32—41no—
304C22×C32—41no—
305C22×C32—41no—
306C22×C32—41no—
307C22×C32C23×C411yescharacteristic
308C22×C32C22×D411yescharacteristic
309C22×C32C2×#4111yescharacteristic
310C22×C32C2×#4111yescharacteristic
311C22×C32C2×#4111yescharacteristic
312C22×C32H(5,𝔽2)11yescharacteristic
313C22×C322−1+411yescharacteristic
314C2×C3×D3—22no—
315C2×C3×D3—22no—
316C2×C3×D3—22no—
317C2×C3×D3—22no—
318C2×C3×D3—22no—
319C2×C3×D3—22no—
320C2×C3×D3#11714yescomplemented
321C32×C4—22no—
322C32×C4C4×D414yes—
323C3⋊Dic3—42no—
324C3⋊Dic3—42no—
325C3×Dic3—22no—
326C3×Dic3—22no—
327C3×Dic3—22no—
328C3×Dic3—24no—
329C3×Dic3—42no—
330C22×D4—31no—
331C23×C4—31no—
332C23×C4—92no—
333C23×C4D3211yescharacteristic
334C4×D4—38no—
335#117—64no—
336C2×C4⋊C4—31no—
337C2×C4⋊C4—31no—
338C2×C4⋊C4—31no—
339C2×C4⋊C4—92no—
340C2×C4⋊C4—91no—
341C2×C4⋊C4—91no—
342C2×C4⋊C4—184no—
343C2×C22⋊C4—31no—
344C2×C22⋊C4—31no—
345C2×C22⋊C4—32no—
346C2×C22⋊C4—92no—
347C2×C22⋊C4—92no—
348C2×C42—31no—
349C2×C42—32no—
350C2×C42—92no—
351#95—92no—
352#95—92no—
353#95—92no—
354#95—92no—
355#95—92no—
356C23×C3—22no—
357C23×C3—22no—
358C23×C3—21no—
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—21no—
362C23×C3—21no—
363C23×C3—21no—
364C23×C3—21no—
365C23×C3—21no—
366C23×C3—21no—
367C23×C3—21no—
368C23×C3—21no—
369C23×C3—21no—
370C23×C3—21no—
371C23×C3—22no—
372C23×C3—32no—
373C23×C3—32no—
374C23×C3—32no—
375C23×C3—41no—
376C23×C3—41no—
377C23×C3—41no—
378C23×C3—41no—
379C23×C3—61no—
380C23×C3—61no—
381C23×C3—61no—
382C23×C3—61no—
383C23×C3C2×C4×D312yes—
384C23×C3C22×Dic312yes—
385C23×C3C23×D311yescharacteristic
386C23×C3C23×D311yescharacteristic
387C22×D3—21no—
388C22×D3—21no—
389C22×D3—21no—
390C22×D3—21no—
391C22×D3#23512yes—
392C22×D3#23512yes—
393C22×D3C22×Dic312yes—
394C3×D4—68no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—28no—
400C2×C3×C4—28no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—32no—
406C2×C3×C4—32no—
407C2×C3×C4—32no—
408C2×C3×C4—34no—
409C2×C3×C4—48no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—62no—
413C2×C3×C4—61no—
414C2×C3×C4—61no—
415C2×C3×C4—61no—
416C2×C3×C4—61no—
417C2×C3×C4—62no—
418C2×C3×C4—61no—
419C2×C3×C4—61no—
420C2×C3×C4—68no—
421C2×C3×C4—62no—
422C2×C3×C4—62no—
423C2×C3×C4—62no—
424C2×C3×C4C2×C4×D312yes—
425C2×C3×C4C2×C4×D312yes—
426C2×C3×C4#23512yes—
427C2×C3×C4D3×D412yes—
428C2×C3×C4#23712yes—
429C2×C3×C4C22×Dic312yes—
430C2×C3×C4C22×Dic312yes—
431C2×C3×C4C2×#6712yes—
432#67—28no—
433C2×Dic3—21no—
434C2×Dic3—21no—
435C2×Dic3—21no—
436C2×Dic3—21no—
437C2×Dic3—22no—
438C2×Dic3—21no—
439C2×Dic3—22no—
440C2×Dic3—21no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—22no—
444C2×Dic3—62no—
445C2×Dic3—62no—
446C2×Dic3—62no—
447C2×Dic3—62no—
448C2×Dic3—62no—
449C2×Dic3—62no—
450C2×Dic3—62no—
451C2×Dic3—62no—
452C2×Dic3—62no—
453C2×Dic3—62no—
454C2×Dic3—62no—
455C2×Dic3—62no—
456C2×Dic3—122no—
457C2×Dic3—122no—
458C2×Dic3—122no—
459C2×Dic3—122no—
460C2×Dic3—122no—
461C2×Dic3—122no—
462C2×Dic3—128no—
463C2×Dic3C22×Dic312yes—
464C2×Dic3C22×Dic312yes—
465C2×Dic3C22×Dic312yes—
466C2×Dic3C2×#6714yes—
467C4×D3—28no—
468C4×D3—128no—
469C2×C32—42no—
470C2×C32C2×#11711yescharacteristic
471C2×C32C2×C4×D411yescharacteristic
472C2×C32#52011yescharacteristic
473C2×C32#54611yescharacteristic
474C2×C32#54811yescharacteristic
475C2×C32#55211yescharacteristic
476C2×C32#55311yescharacteristic
477C3×D3—24no—
478C24—31no—
479C24C2×D3211yescharacteristic
480C2×D4—34no—
481C2×D4—62no—
482C2×D4—62no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—31no—
486C22×C4—31no—
487C22×C4—31no—
488C22×C4—32no—
489C22×C4—34no—
490C22×C4—32no—
491C22×C4—62no—
492C22×C4—62no—
493C22×C4—92no—
494C22×C4—92no—
495C22×C4—184no—
496C22×C4—184no—
497C22×C4—362no—
498C22×C4D3×Dic314yescomplemented
499C22×C4C2×D3211yescharacteristic
500C22×C4C2×D3211yescharacteristic
501C4⋊C4—34no—
502C4⋊C4—34no—
503C4⋊C4—62no—
504C4⋊C4—184no—
505C4⋊C4—182no—
506C4⋊C4—182no—
507C22⋊C4—34no—
508C22⋊C4—34no—
509C22⋊C4—64no—
510C22⋊C4—184no—
511C22⋊C4—362no—
512C42—34no—
513C42—64no—
514C42—362no—
515C22×C3—24no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—22no—
519C22×C3—22no—
520C22×C3—22no—
521C22×C3—22no—
522C22×C3—21no—
523C22×C3—21no—
524C22×C3—21no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—21no—
528C22×C3—21no—
529C22×C3—34no—
530C22×C3—42no—
531C22×C3—42no—
532C22×C3—42no—
533C22×C3—42no—
534C22×C3—42no—
535C22×C3—42no—
536C22×C3—41no—
537C22×C3—41no—
538C22×C3—41no—
539C22×C3—41no—
540C22×C3—41no—
541C22×C3—41no—
542C22×C3—41no—
543C22×C3—41no—
544C22×C3—62no—
545C22×C3—62no—
546C22×C3—62no—
547C22×C3—62no—
548C22×C3—62no—
549C22×C3—62no—
550C22×C3C22×C4×D311yescharacteristic
551C22×C3C2×#23511yescharacteristic
552C22×C3C2×#23511yescharacteristic
553C22×C3C2×#23511yescharacteristic
554C22×C3C2×D3×D411yescharacteristic
555C22×C3C2×#23711yescharacteristic
556C22×C3D3×#4111yescharacteristic
557C22×C3D3×#4111yescharacteristic
558C22×C3#100911yescharacteristic
559C22×C3#100911yescharacteristic
560C22×C3#101011yescharacteristic
561C22×C3#101011yescharacteristic
562C22×C3C23×Dic311yescharacteristic
563C22×C3C22×#6711yescharacteristic
564C2×D3—22no—
565C2×D3—22no—
566C2×D3—22no—
567C2×D3—22no—
568C2×D3—22no—
569C2×D3—22no—
570C2×D3#92614yescomplemented
571C3×C4—22no—
572C3×C4—22no—
573C3×C4—24no—
574C3×C4—42no—
575C3×C4—62no—
576C3×C4—62no—
577C3×C4—62no—
578C3×C4—64no—
579C3×C4—122no—
580C3×C4C4×#6714yes—
581C3×C4D4×Dic314yes—
582Dic3—22no—
583Dic3—22no—
584Dic3—22no—
585Dic3—24no—
586Dic3—42no—
587Dic3—122no—
588Dic3—122no—
589Dic3—122no—
590Dic3—122no—
591Dic3—242no—
592Dic3—242no—
593C32#235211yescharacteristic, complemented, Sylow
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—32no—
601C23—32no—
602C23—32no—
603C23—61no—
604C23—61no—
605C23—61no—
606C23—61no—
607C23C2×D3×Dic312yes—
608C23C22×D3211yescharacteristic
609D4—68no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—28no—
613C2×C4—32no—
614C2×C4—32no—
615C2×C4—32no—
616C2×C4—34no—
617C2×C4—61no—
618C2×C4—62no—
619C2×C4—61no—
620C2×C4—61no—
621C2×C4—61no—
622C2×C4—62no—
623C2×C4—61no—
624C2×C4—61no—
625C2×C4—68no—
626C2×C4—62no—
627C2×C4—62no—
628C2×C4—62no—
629C2×C4—182no—
630C2×C4—182no—
631C2×C4—182no—
632C2×C4—182no—
633C2×C4—182no—
634C2×C4—182no—
635C2×C4—368no—
636C2×C4C2×D3×Dic312yes—
637C2×C4C2×D3×Dic312yes—
638C2×C4#380412yes—
639C2×C4D3×#6712yes—
640C2×C3—21no—
641C2×C3—21no—
642C2×C3—21no—
643C2×C3—21no—
644C2×C3—21no—
645C2×C3—21no—
646C2×C3—21no—
647C2×C3—44no—
648C2×C3—42no—
649C2×C3—42no—
650C2×C3—64no—
651C2×C3D3×#11711yescharacteristic
652C2×C3#552311yescharacteristic
653C2×C3#552911yescharacteristic
654C2×C3#553011yescharacteristic
655C2×C3#554111yescharacteristic
656C2×C3#555011yescharacteristic
657C2×C3#555211yescharacteristic
658C2×C3#556511yescharacteristic
659C2×C3C2×#92611yescharacteristic
660C2×C3C2×C4×#6711yescharacteristic
661C2×C3C2×D4×Dic311yescharacteristic
662C2×C3#582711yescharacteristic
663C2×C3#582911yescharacteristic
664C2×C3#583111yescharacteristic
665D3—24no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—34no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—62no—
675C22—62no—
676C22—62no—
677C22—62no—
678C22—62no—
679C22—62no—
680C22#6429811yescharacteristic
681C22D3×#23511yescharacteristic
682C22D3×#23511yescharacteristic
683C22#6430811yescharacteristic
684C22C22×D3×Dic311yescharacteristic
685C22C2×#380411yescharacteristic
686C22C2×D3×#6711yescharacteristic
687C4—22no—
688C4—62no—
689C4—62no—
690C4—62no—
691C4—64no—
692C4—122no—
693C4—362no—
694C4—362no—
695C4Dic3×#6714yes—
696C3—21no—
697C3#8227211yescharacteristic, complemented
698C3#8233511yescharacteristic, complemented
699C2—42no—
700C2—64no—
701C2#1059489911yescharacteristic
702C2D3×#92611yescharacteristic
703C2#1059493911yescharacteristic
704C2#1059494611yescharacteristic
705C2#1059499211yescharacteristic
706C2#1059506711yescharacteristic
707C2C2×Dic3×#6711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32#2352
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#926C2semidirect
3. C2×D3×C4⋊Dic3C2semidirect
4. #10592911C2semidirect
6. #10591702C2semidirect
7. Dic3×(C2×D3)⋊C4C2semidirect
8. #10591313C2semidirect
9. Dic3×C4⋊Dic3C2semidirect
10. #10591224C2semidirect
11. #10591201C2semidirect
23. C3×C4×#67C4semidirect
43. C2×#926D3semidirect
67. C22×C32×C4C2×C4semidirect
90. C3×#217C2×C4semidirect
93. C3×C4⋊Dic3D4semidirect
94. C3×Dic3⋊C4C2×C4semidirect
96. C3×C4×Dic3C2×C4semidirect
126. C4×#67Dic3semidirect
240. C22×C3×C4C4×D3semidirect
241. C22×C3×C4C2×Dic3semidirect
282. #217C2×Dic3semidirect
293. C4⋊Dic3#67semidirect
295. Dic3⋊C4C2×Dic3semidirect
299. C4×Dic3C2×Dic3semidirect
320. C2×C3×D3#117semidirect
498. C22×C4D3×Dic3semidirect
570. C2×D3#926semidirect
593. C32#2352semidirect
697. C3#82272semidirect
698. C3#82335semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×#672
C2×C3×#9262
C2×D3×C4⋊Dic32
#105929112
#105917212
#105917022
Dic3×(C2×D3)⋊C42
#105913132
Dic3×C4⋊Dic32
#105912242
#105912012
#823353
#822723