Finite Group Databasebeta

← #11805673

Subgroups — #11805673

Order 1152.

1417 conjugacy classes of subgroups.

The subgroup lattice has 695 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D12C211yesmaximal, characteristic
2C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C2×#63841C211yesmaximal, characteristic, complemented
4C4×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
5C3×#4936C211yesmaximal, characteristic, complemented
6#10591376C212yesmaximal
7#10591368C212yesmaximal, complemented
8#10591313C211yesmaximal, characteristic, complemented
9#10591313C211yesmaximal, characteristic, complemented
10#10591286C212yesmaximal, complemented
11#10591270C212yesmaximal, complemented
12#82335—31nomaximal
13#74229—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×D3×Dic3C2212yes—
18C2×C32×C42C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C4×C3⋊Dic3C2212yes—
22C2×C3×(C2×D3)⋊C4C2211yescharacteristic
23C2×C3×(C2×D3)⋊C4C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C3×C4×D12C418yescomplemented
28C2×Dic3⋊Dic3C2212yes—
29C2×(C2×D3)⋊Dic3C2212yes—
30C2×(C2×D3)⋊Dic3C2212yes—
31C2×(C2×D3)⋊Dic3C2212yes—
32C2×Dic32C2212yes—
33D3×C4⋊Dic3—24no—
34#63841—24no—
35#63658C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×C4×D4—31no—
41C2×#926—31no—
42C22×C4⋊Dic3—31no—
43C2×#892—31no—
44C2×D3×C4⋊C4—31no—
45C2×C4×D12D311yescharacteristic
46C3×#382—31no—
47#5220—32no—
48#5212—31no—
49#5212—31no—
50#4987—31no—
51#4987—31no—
52#4980—32no—
53#4951—32no—
54Dic3×C22⋊C4—32no—
55#4936D311yescharacteristic, complemented
56C4×C4⋊Dic3—31no—
57C4×C4⋊Dic3—31no—
58C4×C4⋊Dic3—61no—
59#4669—32no—
60#4666—32no—
61#4665—32no—
62#4654—32no—
63C23×C3×D3C2311yescharacteristic
64C23×C3×D3C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3C2312yes—
69C22×C3⋊Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C2×C3×D12—22no—
75C2×C3×D12—22no—
76C2×C3×D12C2×C414yes—
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3—22no—
79C2×C3×C4×D3—22no—
80C2×C3×C4×D3—22no—
81C2×C3×C4×D3C2×C414yes—
82C2×C3×C4×D3C2×C414yescomplemented
83C2×D3×Dic3—24no—
84C2×D3×Dic3—24no—
85C2×D3×Dic3—42no—
86C32×C42C2×C414yescomplemented
87C4⋊(C3⋊Dic3)—22no—
88C4⋊(C3⋊Dic3)D414yescomplemented
89C4×C3⋊Dic3—42no—
90C3×(C2×D3)⋊C4C2×C414yes—
91C3×(C2×D3)⋊C4C2×C414yescomplemented
92C3×C4⋊Dic3—22no—
93C3×C4⋊Dic3—22no—
94C3×C4⋊Dic3C2×C414yescomplemented
95Dic3⋊Dic3—24no—
96(C2×D3)⋊Dic3—24no—
97(C2×D3)⋊Dic3—24no—
98(C2×D3)⋊Dic3—42no—
99Dic32—24no—
100#2352—91noSylow
101C22×C3×D4—31no—
102C23×C3×C4—31no—
103C23×C3×C4—31no—
104C23×Dic3—32no—
105C22×D12C2×D311yescharacteristic
106C22×C4×D3—32no—
107C22×C4×D3C2×D311yescharacteristic
108C22×C4×D3C2×D311yescharacteristic
109C3×C4×D4—38no—
110C2×C3×C4⋊C4—31no—
111C2×C3×C4⋊C4—31no—
112C2×C3×C4⋊C4—31no—
113C2×C3×C22⋊C4—31no—
114C2×C3×C22⋊C4—31no—
115C2×C3×C42—21no—
116C2×C3×C42C2×D311yescharacteristic
117C2×C3×C42C2×D311yescharacteristic
118C2×#217—32no—
119C2×#217—32no—
120C2×#217—32no—
121C2×(C2×D3)⋊C4—32no—
122C2×(C2×D3)⋊C4—32no—
123C2×(C2×D3)⋊C4—32no—
124C2×(C2×D3)⋊C4C2×D311yescharacteristic
125C2×(C2×D3)⋊C4C2×D311yescharacteristic
126#926—64no—
127C2×C4⋊Dic3—31no—
128C2×C4⋊Dic3—31no—
129C2×C4⋊Dic3—31no—
130C2×C4⋊Dic3—31no—
131C2×C4⋊Dic3—32no—
132C2×C4⋊Dic3—61no—
133C2×C4⋊Dic3—61no—
134C2×C4⋊Dic3—64no—
135C2×C4⋊Dic3C2×D311yescharacteristic
136C2×C4⋊Dic3C2×D311yescharacteristic
137C2×C4⋊Dic3C2×D311yescharacteristic
138C2×Dic3⋊C4—32no—
139C2×C4×Dic3—32no—
140C2×C4×Dic3—32no—
141C2×C4×Dic3—32no—
142C2×C4×Dic3—32no—
143C2×C4×Dic3—62no—
144#892—64no—
145D3×C4⋊C4—64no—
146C4×D12Dic318yescomplemented
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—62no—
156C3⋊#95C2×D312yes—
157C3⋊#95C2×D312yes—
158C23×C32C2411yescharacteristic
159C22×C3×D3—21no—
160C22×C3×D3—21no—
161C22×C3×D3—21no—
162C22×C3×D3—21no—
163C22×C3×D3—21no—
164C22×C3×D3—21no—
165C22×C3×D3—21no—
166C22×C3×D3—21no—
167C22×C3×D3—21no—
168C22×C3×D3—21no—
169C22×C3×D3C22×C412yes—
170C22×C3×D3C22×C412yes—
171C22×C3×D3#4112yes—
172C22×C3×D3#4112yes—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4C22×C412yes—
178C2×C32×C4C22×C412yes—
179C2×C32×C4C22×C412yes—
180C2×C32×C4C2×D412yes—
181C2×C32×C4#4112yes—
182C2×C3⋊Dic3—22no—
183C2×C3⋊Dic3—22no—
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3—22no—
187C2×C3⋊Dic3C2×D414yes—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3C22×C412yes—
199C2×C3×Dic3C22×C412yes—
200C3×D12—28no—
201C3×C4×D3—28no—
202C3×C4×D3—28no—
203D3×Dic3—48no—
204C2×C4×D4—31no—
205C2×#117—91no—
206C22×C4⋊C4—91no—
207#388—92no—
208#387—92no—
209#386—92no—
210#382—31no—
211#380—91no—
212#380—91no—
213C4×C4⋊C4—91no—
214C4×C22⋊C4—92no—
215C24×C3—31no—
216C24×C3—31no—
217C23×D3C22×D311yescharacteristic
218C23×D3C22×D311yescharacteristic
219C2×C3×D4—34no—
220C2×C3×D4—62no—
221C2×C3×D4—62no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—31no—
226C22×C3×C4—31no—
227C22×C3×C4—34no—
228C22×C3×C4—34no—
229C22×C3×C4—32no—
230C22×C3×C4—32no—
231C22×C3×C4—62no—
232C22×C3×C4—62no—
233C22×C3×C4—62no—
234C22×C3×C4—62no—
235C22×C3×C4C22×D311yescharacteristic
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C22×C3×C4C22×D311yescharacteristic
239C22×C3×C4C22×D311yescharacteristic
240C22×C3×C4C22×D311yescharacteristic
241C22×Dic3—32no—
242C22×Dic3—32no—
243C22×Dic3—32no—
244C22×Dic3—32no—
245C22×Dic3—62no—
246C22×Dic3—62no—
247C22×Dic3—64no—
248C22×Dic3—64no—
249C22×Dic3—122no—
250C22×Dic3C22×D312yes—
251C22×Dic3C22×D312yes—
252C22×Dic3C22×D311yescharacteristic
253C22×Dic3C22×D311yescharacteristic
254C2×D12—22no—
255C2×D12—22no—
256C2×D12C2×Dic314yes—
257C2×C4×D3—22no—
258C2×C4×D3—22no—
259C2×C4×D3—22no—
260C2×C4×D3—22no—
261C2×C4×D3—64no—
262C2×C4×D3—64no—
263C2×C4×D3—122no—
264C2×C4×D3C2×Dic314yes—
265C2×C4×D3C2×Dic314yescomplemented
266C3×C4⋊C4—34no—
267C3×C4⋊C4—62no—
268C3×C4⋊C4—62no—
269C3×C22⋊C4—34no—
270C3×C22⋊C4—34no—
271C3×C42—24no—
272C3×C42C4×D314yescomplemented
273C3×C42C2×Dic314yescomplemented
274#217—64no—
275#217—64no—
276#217—122no—
277(C2×D3)⋊C4—64no—
278(C2×D3)⋊C4—64no—
279(C2×D3)⋊C4—122no—
280(C2×D3)⋊C4C2×Dic314yes—
281(C2×D3)⋊C4C2×Dic314yescomplemented
282C4⋊Dic3—22no—
283C4⋊Dic3—22no—
284C4⋊Dic3—34no—
285C4⋊Dic3—34no—
286C4⋊Dic3—64no—
287C4⋊Dic3—64no—
288C4⋊Dic3—64no—
289C4⋊Dic3—62no—
290C4⋊Dic3—62no—
291C4⋊Dic3C2×Dic314yescomplemented
292Dic3⋊C4—64no—
293C4×Dic3—64no—
294C4×Dic3—64no—
295C4×Dic3—122no—
296C4×Dic3—122no—
297C4×Dic3—124no—
298C22×C32C23×C411yescharacteristic
299C22×C32C22×D411yescharacteristic
300C22×C32C2×#4111yescharacteristic
301C22×C32C2×#4111yescharacteristic
302C22×C32C2×#4111yescharacteristic
303C22×C32H(5,𝔽2)11yescharacteristic
304C22×C322−1+411yescharacteristic
305C2×C3×D3—22no—
306C2×C3×D3—22no—
307C2×C3×D3—22no—
308C2×C3×D3—22no—
309C2×C3×D3—22no—
310C2×C3×D3—22no—
311C2×C3×D3—22no—
312C2×C3×D3—22no—
313C2×C3×D3—22no—
314C2×C3×D3—41no—
315C2×C3×D3—41no—
316C2×C3×D3—41no—
317C2×C3×D3—41no—
318C2×C3×D3#11714yescomplemented
319C32×C4—22no—
320C32×C4—22no—
321C32×C4C4×D414yes—
322C3⋊Dic3—24no—
323C3⋊Dic3—42no—
324C3×Dic3—22no—
325C3×Dic3—22no—
326C3×Dic3—42no—
327C3×Dic3—42no—
328C22×D4—31no—
329C23×C4—31no—
330C23×C4—31no—
331C23×C4—92no—
332C4×D4—38no—
333#117—184no—
334C2×C4⋊C4—31no—
335C2×C4⋊C4—31no—
336C2×C4⋊C4—31no—
337C2×C4⋊C4—91no—
338C2×C4⋊C4—92no—
339C2×C4⋊C4—91no—
340C2×C4⋊C4—184no—
341C2×C22⋊C4—31no—
342C2×C22⋊C4—31no—
343C2×C22⋊C4—92no—
344C2×C22⋊C4—92no—
345C2×C22⋊C4—92no—
346C2×C42—92no—
347C2×C42—92no—
348C2×C42D3211yescharacteristic
349#95—32no—
350#95—32no—
351#95—92no—
352#95—92no—
353#95—92no—
354C23×C3—21no—
355C23×C3—32no—
356C23×C3—32no—
357C23×C3—32no—
358C23×C3—32no—
359C23×C3—61no—
360C23×C3—61no—
361C23×C3—61no—
362C23×C3—61no—
363C23×C3—61no—
364C23×C3—61no—
365C23×C3—61no—
366C23×C3—61no—
367C23×C3—61no—
368C23×C3—61no—
369C23×C3C23×D311yescharacteristic
370C23×C3C23×D311yescharacteristic
371C22×D3—21no—
372C22×D3—21no—
373C22×D3—21no—
374C22×D3—21no—
375C22×D3—21no—
376C22×D3—21no—
377C22×D3—21no—
378C22×D3—21no—
379C22×D3—21no—
380C22×D3—21no—
381C22×D3#23512yes—
382C22×D3#23512yes—
383C22×D3C22×Dic312yes—
384C22×D3C22×Dic312yes—
385C3×D4—68no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—32no—
402C2×C3×C4—32no—
403C2×C3×C4—41no—
404C2×C3×C4—41no—
405C2×C3×C4—61no—
406C2×C3×C4—61no—
407C2×C3×C4—61no—
408C2×C3×C4—61no—
409C2×C3×C4—68no—
410C2×C3×C4—68no—
411C2×C3×C4—62no—
412C2×C3×C4—62no—
413C2×C3×C4—62no—
414C2×C3×C4—62no—
415C2×C3×C4—62no—
416C2×C3×C4—62no—
417C2×C3×C4C2×C4×D312yes—
418C2×C3×C4C2×C4×D312yes—
419C2×C3×C4C2×C4×D312yes—
420C2×C3×C4D3×D412yes—
421C2×C3×C4D3×D412yes—
422C2×C3×C4#23712yes—
423C2×C3×C4#23912yes—
424C2×C3×C4C22×Dic312yes—
425C2×C3×C4C22×Dic312yes—
426C2×C3×C4C22×Dic312yes—
427C2×Dic3—21no—
428C2×Dic3—21no—
429C2×Dic3—21no—
430C2×Dic3—21no—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—22no—
437C2×Dic3—34no—
438C2×Dic3—34no—
439C2×Dic3—64no—
440C2×Dic3—62no—
441C2×Dic3—62no—
442C2×Dic3—62no—
443C2×Dic3—62no—
444C2×Dic3—64no—
445C2×Dic3—62no—
446C2×Dic3—62no—
447C2×Dic3—62no—
448C2×Dic3—62no—
449C2×Dic3—62no—
450C2×Dic3—62no—
451C2×Dic3—122no—
452C2×Dic3—122no—
453C2×Dic3—122no—
454C2×Dic3—122no—
455C2×Dic3—128no—
456C2×Dic3C22×Dic312yes—
457C2×Dic3C22×Dic312yes—
458D12—28no—
459C4×D3—28no—
460C4×D3—28no—
461C4×D3—128no—
462C2×C32C2×#11711yescharacteristic
463C2×C32C2×C4×D411yescharacteristic
464C2×C32#52011yescharacteristic
465C2×C32#54611yescharacteristic
466C2×C32#54811yescharacteristic
467C2×C32#55211yescharacteristic
468C2×C32#55311yescharacteristic
469C3×D3—24no—
470C3×D3—42no—
471C24—31no—
472C24—31no—
473C2×D4—34no—
474C2×D4—62no—
475C2×D4—62no—
476C22×C4—31no—
477C22×C4—31no—
478C22×C4—34no—
479C22×C4—34no—
480C22×C4—32no—
481C22×C4—32no—
482C22×C4—62no—
483C22×C4—62no—
484C22×C4—62no—
485C22×C4—62no—
486C22×C4—92no—
487C22×C4—92no—
488C22×C4—184no—
489C22×C4—184no—
490C22×C4—362no—
491C22×C4C2×D3211yescharacteristic
492C22×C4C2×D3211yescharacteristic
493C22×C4C2×D3211yescharacteristic
494C4⋊C4—34no—
495C4⋊C4—62no—
496C4⋊C4—62no—
497C4⋊C4—94no—
498C4⋊C4—184no—
499C4⋊C4—182no—
500C22⋊C4—34no—
501C22⋊C4—34no—
502C22⋊C4—184no—
503C22⋊C4—184no—
504C22⋊C4—362no—
505C42—184no—
506C42—362no—
507C42D3×Dic314yescomplemented
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—34no—
516C22×C3—62no—
517C22×C3—62no—
518C22×C3—62no—
519C22×C3—62no—
520C22×C3—62no—
521C22×C3—62no—
522C22×C3—62no—
523C22×C3—62no—
524C22×C3—62no—
525C22×C3—121no—
526C22×C3—121no—
527C22×C3—121no—
528C22×C3—121no—
529C22×C3C22×C4×D311yescharacteristic
530C22×C3C2×#23511yescharacteristic
531C22×C3C2×#23511yescharacteristic
532C22×C3C2×D3×D411yescharacteristic
533C22×C3C2×D3×D411yescharacteristic
534C22×C3C2×#23711yescharacteristic
535C22×C3C2×#23911yescharacteristic
536C22×C3D3×#4111yescharacteristic
537C22×C3D3×#4111yescharacteristic
538C22×C3#100911yescharacteristic
539C22×C3#100911yescharacteristic
540C22×C3#101011yescharacteristic
541C22×C3#101011yescharacteristic
542C22×C3C23×Dic311yescharacteristic
543C2×D3—22no—
544C2×D3—22no—
545C2×D3—22no—
546C2×D3—22no—
547C2×D3—22no—
548C2×D3—22no—
549C2×D3—22no—
550C2×D3—22no—
551C2×D3—22no—
552C2×D3—41no—
553C2×D3—41no—
554C2×D3—41no—
555C2×D3—41no—
556C2×D3#92614yescomplemented
557C3×C4—24no—
558C3×C4—22no—
559C3×C4—22no—
560C3×C4—22no—
561C3×C4—22no—
562C3×C4—24no—
563C3×C4—42no—
564C3×C4—62no—
565C3×C4—62no—
566C3×C4—122no—
567C3×C4—122no—
568C3×C4#89314yes—
569C3×C4D4×Dic314yes—
570Dic3—22no—
571Dic3—22no—
572Dic3—42no—
573Dic3—42no—
574Dic3—64no—
575Dic3—64no—
576Dic3—124no—
577Dic3—124no—
578Dic3—122no—
579Dic3—122no—
580C32#235211yescharacteristic, complemented, Sylow
581C23—32no—
582C23—32no—
583C23—32no—
584C23—32no—
585C23—61no—
586C23—61no—
587C23—61no—
588C23—61no—
589C23—61no—
590C23—61no—
591C23—61no—
592C23—61no—
593C23—61no—
594C23—61no—
595C23C22×D3211yescharacteristic
596D4—68no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—32no—
602C2×C4—32no—
603C2×C4—61no—
604C2×C4—61no—
605C2×C4—61no—
606C2×C4—61no—
607C2×C4—68no—
608C2×C4—68no—
609C2×C4—62no—
610C2×C4—62no—
611C2×C4—62no—
612C2×C4—62no—
613C2×C4—62no—
614C2×C4—62no—
615C2×C4—94no—
616C2×C4—182no—
617C2×C4—182no—
618C2×C4—182no—
619C2×C4—182no—
620C2×C4—182no—
621C2×C4—368no—
622C2×C4#379612yes—
623C2×C4#380212yes—
624C2×C4C2×D3×Dic312yes—
625C2×C4C2×D3×Dic312yes—
626C2×C4C2×D3×Dic312yes—
627C2×C3—21no—
628C2×C3—21no—
629C2×C3—21no—
630C2×C3—21no—
631C2×C3—21no—
632C2×C3—21no—
633C2×C3—21no—
634C2×C3—64no—
635C2×C3—122no—
636C2×C3C2×#89311yescharacteristic
637C2×C3D3×#11711yescharacteristic
638C2×C3#552311yescharacteristic
639C2×C3#554111yescharacteristic
640C2×C3#555011yescharacteristic
641C2×C3#555211yescharacteristic
642C2×C3#556511yescharacteristic
643C2×C3#567611yescharacteristic
644C2×C3#567711yescharacteristic
645C2×C3#569411yescharacteristic
646C2×C3#569511yescharacteristic
647C2×C3C2×#92611yescharacteristic
648C2×C3C2×D4×Dic311yescharacteristic
649C2×C3#582711yescharacteristic
650D3—24no—
651D3—42no—
652C22—34no—
653C22—62no—
654C22—62no—
655C22—62no—
656C22—62no—
657C22—62no—
658C22—62no—
659C22—62no—
660C22—62no—
661C22—62no—
662C22—121no—
663C22—121no—
664C22—121no—
665C22—121no—
666C22C2×#379611yescharacteristic
667C22#6429811yescharacteristic
668C22C2×#380211yescharacteristic
669C22D3×#23511yescharacteristic
670C22D3×#23511yescharacteristic
671C22#6430811yescharacteristic
672C22C22×D3×Dic311yescharacteristic
673C4—22no—
674C4—22no—
675C4—62no—
676C4—62no—
677C4—122no—
678C4—122no—
679C4—184no—
680C4—362no—
681C4#6389814yes—
682C3—21no—
683C3#7422911yescharacteristic, complemented
684C3#8233511yescharacteristic, complemented
685C2—64no—
686C2—122no—
687C2#1059390511yescharacteristic
688C2#1059392011yescharacteristic
689C2#1059392511yescharacteristic
690C2#1059400711yescharacteristic
691C2C2×#6389811yescharacteristic
692C2D3×#92611yescharacteristic
693C2#1059499211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32#2352
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×D3×C4⋊Dic3C2semidirect
3. C2×#63841C2semidirect
4. C4×C4⋊(C3⋊Dic3)C2semidirect
5. C3×#4936C2semidirect
7. #10591368C2semidirect
8. #10591313C2semidirect
9. #10591313C2semidirect
10. #10591286C2semidirect
11. #10591270C2semidirect
27. C3×C4×D12C4semidirect
55. #4936D3semidirect
82. C2×C3×C4×D3C2×C4semidirect
86. C32×C42C2×C4semidirect
88. C4⋊(C3⋊Dic3)D4semidirect
91. C3×(C2×D3)⋊C4C2×C4semidirect
94. C3×C4⋊Dic3C2×C4semidirect
146. C4×D12Dic3semidirect
265. C2×C4×D3C2×Dic3semidirect
272. C3×C42C4×D3semidirect
273. C3×C42C2×Dic3semidirect
281. (C2×D3)⋊C4C2×Dic3semidirect
291. C4⋊Dic3C2×Dic3semidirect
318. C2×C3×D3#117semidirect
507. C42D3×Dic3semidirect
556. C2×D3#926semidirect
580. C32#2352semidirect
683. C3#74229semidirect
684. 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×D122
C2×D3×C4⋊Dic32
C2×#638412
C4×C4⋊(C3⋊Dic3)2
C3×#49362
#105913762
#105913682
#105913132
#105912862
#105912702
#823353
#742293