Finite Group Databasebeta

← #11805671

Subgroups — #11805671

Order 1152.

1397 conjugacy classes of subgroups.

The subgroup lattice has 694 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
4#10592635C211yesmaximal, characteristic, complemented
5C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
6#10591376C212yesmaximal
7Dic3×(C2×D3)⋊C4C212yesmaximal, complemented
8#10591313C211yesmaximal, characteristic, complemented
9#10591313C211yesmaximal, characteristic, complemented
10#10591305C212yesmaximal, complemented
11#10591269C212yesmaximal, complemented
12#82335—31nomaximal
13#73771—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×C3×(C2×D3)⋊C4C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2212yes—
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—
36#63658C2212yes—
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×C4×C4⋊C4—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#4940—32no—
56C4×(C2×D3)⋊C4—32no—
57#4936—31no—
58#4936—31no—
59#4936—61no—
60C4×C4⋊Dic3D311yescharacteristic, complemented
61#4665—32no—
62#4653—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×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2312yes—
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)—22no—
89C3×(C2×D3)⋊C4C2×C414yes—
90C3×(C2×D3)⋊C4C2×C414yescomplemented
91C3×C4⋊Dic3—22no—
92C3×C4⋊Dic3C2×C414yescomplemented
93C3×C4⋊Dic3D414yescomplemented
94C3×C4×Dic3—42no—
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×C42—32no—
117C2×C3×C42C2×D311yescharacteristic
118C2×C3×C42C2×D311yescharacteristic
119C2×#217—32no—
120C2×#217—32no—
121C2×#217—32no—
122C2×(C2×D3)⋊C4—32no—
123C2×(C2×D3)⋊C4—32no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4C2×D311yescharacteristic
126C2×(C2×D3)⋊C4C2×D311yescharacteristic
127#926—64no—
128C2×C4⋊Dic3—31no—
129C2×C4⋊Dic3—31no—
130C2×C4⋊Dic3—31no—
131C2×C4⋊Dic3—31no—
132C2×C4⋊Dic3—32no—
133C2×C4⋊Dic3—61no—
134C2×C4⋊Dic3—61no—
135C2×C4⋊Dic3—64no—
136C2×C4⋊Dic3C2×D311yescharacteristic
137C2×C4⋊Dic3C2×D311yescharacteristic
138C2×C4⋊Dic3C2×D311yescharacteristic
139C2×Dic3⋊C4—32no—
140C2×C4×Dic3—32no—
141C2×C4×Dic3—32no—
142C2×C4×Dic3C2×D312yes—
143#892—64no—
144D3×C4⋊C4—64no—
145C4×D12Dic318yescomplemented
146C3×#95—32no—
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⋊#95—62no—
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⋊Dic3—22no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3C22×C412yes—
198C2×C3×Dic3C22×C412yes—
199C2×C3×Dic3C2×D414yes—
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—91no—
211#380—91no—
212#380—91no—
213C4×C4⋊C4—31no—
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—32no—
228C22×C3×C4—34no—
229C22×C3×C4—34no—
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—34no—
268C3×C4⋊C4—62no—
269C3×C22⋊C4—34no—
270C3×C22⋊C4—34no—
271C3×C42—24no—
272C3×C42—122no—
273C3×C42C4×D314yescomplemented
274C3×C42C2×Dic314yescomplemented
275#217—64no—
276#217—64no—
277#217—122no—
278(C2×D3)⋊C4—64no—
279(C2×D3)⋊C4—64no—
280(C2×D3)⋊C4—122no—
281(C2×D3)⋊C4C2×Dic314yes—
282(C2×D3)⋊C4C2×Dic314yescomplemented
283C4⋊Dic3—22no—
284C4⋊Dic3—62no—
285C4⋊Dic3—62no—
286C4⋊Dic3—62no—
287C4⋊Dic3—62no—
288C4⋊Dic3—64no—
289C4⋊Dic3—122no—
290C4⋊Dic3—122no—
291C4⋊Dic3D1214yescomplemented
292C4⋊Dic3C2×Dic314yescomplemented
293Dic3⋊C4—64no—
294C4×Dic3—42no—
295C4×Dic3—64no—
296C4×Dic3—64no—
297C22×C32C23×C411yescharacteristic
298C22×C32C22×D411yescharacteristic
299C22×C32C2×#4111yescharacteristic
300C22×C32C2×#4111yescharacteristic
301C22×C32C2×#4111yescharacteristic
302C22×C32H(5,𝔽2)11yescharacteristic
303C22×C322−1+411yescharacteristic
304C2×C3×D3—22no—
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—41no—
314C2×C3×D3—41no—
315C2×C3×D3—41no—
316C2×C3×D3—41no—
317C2×C3×D3#11714yescomplemented
318C32×C4—22no—
319C32×C4—22no—
320C32×C4C4×D414yes—
321C3⋊Dic3—42no—
322C3⋊Dic3—42no—
323C3×Dic3—22no—
324C3×Dic3—22no—
325C3×Dic3—24no—
326C3×Dic3—42no—
327C22×D4—31no—
328C23×C4—31no—
329C23×C4—31no—
330C23×C4—92no—
331C4×D4—38no—
332#117—184no—
333C2×C4⋊C4—31no—
334C2×C4⋊C4—31no—
335C2×C4⋊C4—31no—
336C2×C4⋊C4—92no—
337C2×C4⋊C4—91no—
338C2×C4⋊C4—91no—
339C2×C4⋊C4—184no—
340C2×C22⋊C4—31no—
341C2×C22⋊C4—31no—
342C2×C22⋊C4—92no—
343C2×C22⋊C4—92no—
344C2×C22⋊C4—92no—
345C2×C42—32no—
346C2×C42—92no—
347C2×C42D3211yescharacteristic
348#95—32no—
349#95—92no—
350#95—92no—
351#95—92no—
352#95—92no—
353C23×C3—21no—
354C23×C3—32no—
355C23×C3—32no—
356C23×C3—32no—
357C23×C3—32no—
358C23×C3—61no—
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×C3C23×D311yescharacteristic
369C23×C3C23×D311yescharacteristic
370C22×D3—21no—
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#23512yes—
381C22×D3#23512yes—
382C22×D3C22×Dic312yes—
383C22×D3C22×Dic312yes—
384C3×D4—68no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—32no—
399C2×C3×C4—32no—
400C2×C3×C4—34no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—41no—
405C2×C3×C4—61no—
406C2×C3×C4—61no—
407C2×C3×C4—62no—
408C2×C3×C4—61no—
409C2×C3×C4—61no—
410C2×C3×C4—62no—
411C2×C3×C4—68no—
412C2×C3×C4—68no—
413C2×C3×C4—62no—
414C2×C3×C4—62no—
415C2×C3×C4—62no—
416C2×C3×C4C2×C4×D312yes—
417C2×C3×C4C2×C4×D312yes—
418C2×C3×C4C2×C4×D312yes—
419C2×C3×C4C2×D1212yes—
420C2×C3×C4#23512yes—
421C2×C3×C4D3×D412yes—
422C2×C3×C4#23712yes—
423C2×C3×C4C22×Dic312yes—
424C2×C3×C4C22×Dic312yes—
425C2×C3×C4C22×Dic312yes—
426C2×Dic3—21no—
427C2×Dic3—21no—
428C2×Dic3—21no—
429C2×Dic3—21no—
430C2×Dic3—22no—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—62no—
436C2×Dic3—62no—
437C2×Dic3—62no—
438C2×Dic3—62no—
439C2×Dic3—62no—
440C2×Dic3—62no—
441C2×Dic3—62no—
442C2×Dic3—62no—
443C2×Dic3—62no—
444C2×Dic3—62no—
445C2×Dic3—62no—
446C2×Dic3—62no—
447C2×Dic3—122no—
448C2×Dic3—122no—
449C2×Dic3—122no—
450C2×Dic3—122no—
451C2×Dic3—122no—
452C2×Dic3—122no—
453C2×Dic3—128no—
454C2×Dic3C2×D1214yes—
455C2×Dic3C22×Dic312yes—
456C2×Dic3C22×Dic312yes—
457D12—28no—
458C4×D3—28no—
459C4×D3—28no—
460C4×D3—128no—
461C2×C32C2×#11711yescharacteristic
462C2×C32C2×C4×D411yescharacteristic
463C2×C32#52011yescharacteristic
464C2×C32#54611yescharacteristic
465C2×C32#54811yescharacteristic
466C2×C32#55211yescharacteristic
467C2×C32#55311yescharacteristic
468C3×D3—24no—
469C3×D3—42no—
470C24—31no—
471C24—31no—
472C2×D4—34no—
473C2×D4—62no—
474C2×D4—62no—
475C22×C4—32no—
476C22×C4—31no—
477C22×C4—31no—
478C22×C4—34no—
479C22×C4—34no—
480C22×C4—32no—
481C22×C4—62no—
482C22×C4—62no—
483C22×C4—62no—
484C22×C4—62no—
485C22×C4—92no—
486C22×C4—92no—
487C22×C4—184no—
488C22×C4—184no—
489C22×C4—362no—
490C22×C4C2×D3211yescharacteristic
491C22×C4C2×D3211yescharacteristic
492C22×C4C2×D3211yescharacteristic
493C4⋊C4—34no—
494C4⋊C4—34no—
495C4⋊C4—62no—
496C4⋊C4—184no—
497C4⋊C4—182no—
498C4⋊C4—182no—
499C22⋊C4—34no—
500C22⋊C4—34no—
501C22⋊C4—184no—
502C22⋊C4—184no—
503C22⋊C4—362no—
504C42—122no—
505C42—184no—
506C42D3×Dic314yescomplemented
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—34no—
515C22×C3—62no—
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—121no—
525C22×C3—121no—
526C22×C3—121no—
527C22×C3—121no—
528C22×C3C22×C4×D311yescharacteristic
529C22×C3C22×D1211yescharacteristic
530C22×C3C2×#23511yescharacteristic
531C22×C3C2×#23511yescharacteristic
532C22×C3C2×#23511yescharacteristic
533C22×C3C2×D3×D411yescharacteristic
534C22×C3C2×#23711yescharacteristic
535C22×C3#100411yescharacteristic
536C22×C3#100711yescharacteristic
537C22×C3D3×#4111yescharacteristic
538C22×C3D3×#4111yescharacteristic
539C22×C3#100911yescharacteristic
540C22×C3#101011yescharacteristic
541C22×C3C23×Dic311yescharacteristic
542C2×D3—22no—
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—41no—
552C2×D3—41no—
553C2×D3—41no—
554C2×D3—41no—
555C2×D3#92614yescomplemented
556C3×C4—22no—
557C3×C4—22no—
558C3×C4—22no—
559C3×C4—22no—
560C3×C4—24no—
561C3×C4—42no—
562C3×C4—42no—
563C3×C4—62no—
564C3×C4—62no—
565C3×C4—64no—
566C3×C4—122no—
567C3×C4C4×D1214yes—
568C3×C4D4×Dic314yes—
569Dic3—22no—
570Dic3—22no—
571Dic3—24no—
572Dic3—42no—
573Dic3—122no—
574Dic3—122no—
575Dic3—122no—
576Dic3—122no—
577Dic3—242no—
578Dic3—242no—
579C32#235211yescharacteristic, complemented, Sylow
580C23—32no—
581C23—32no—
582C23—32no—
583C23—32no—
584C23—61no—
585C23—61no—
586C23—61no—
587C23—61no—
588C23—61no—
589C23—61no—
590C23—61no—
591C23—61no—
592C23—61no—
593C23—61no—
594C23C22×D3211yescharacteristic
595D4—68no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—34no—
601C2×C4—32no—
602C2×C4—32no—
603C2×C4—61no—
604C2×C4—61no—
605C2×C4—61no—
606C2×C4—61no—
607C2×C4—62no—
608C2×C4—62no—
609C2×C4—68no—
610C2×C4—68no—
611C2×C4—62no—
612C2×C4—62no—
613C2×C4—62no—
614C2×C4—182no—
615C2×C4—182no—
616C2×C4—182no—
617C2×C4—182no—
618C2×C4—182no—
619C2×C4—182no—
620C2×C4—368no—
621C2×C4#379512yes—
622C2×C4D3×D1212yes—
623C2×C4C2×D3×Dic312yes—
624C2×C4C2×D3×Dic312yes—
625C2×C4C2×D3×Dic312yes—
626C2×C3—21no—
627C2×C3—21no—
628C2×C3—21no—
629C2×C3—21no—
630C2×C3—21no—
631C2×C3—21no—
632C2×C3—21no—
633C2×C3—64no—
634C2×C3—122no—
635C2×C3C2×C4×D1211yescharacteristic
636C2×C3#550411yescharacteristic
637C2×C3D3×#11711yescharacteristic
638C2×C3#554111yescharacteristic
639C2×C3#555011yescharacteristic
640C2×C3#555211yescharacteristic
641C2×C3#555411yescharacteristic
642C2×C3#555811yescharacteristic
643C2×C3#556511yescharacteristic
644C2×C3#557611yescharacteristic
645C2×C3#558111yescharacteristic
646C2×C3C2×#92611yescharacteristic
647C2×C3C2×D4×Dic311yescharacteristic
648C2×C3#582711yescharacteristic
649D3—24no—
650D3—42no—
651C22—34no—
652C22—62no—
653C22—62no—
654C22—62no—
655C22—62no—
656C22—62no—
657C22—62no—
658C22—62no—
659C22—62no—
660C22—62no—
661C22—121no—
662C22—121no—
663C22—121no—
664C22—121no—
665C22C2×#379511yescharacteristic
666C22#6429711yescharacteristic
667C22C2×D3×D1211yescharacteristic
668C22D3×#23511yescharacteristic
669C22D3×#23511yescharacteristic
670C22#6430711yescharacteristic
671C22C22×D3×Dic311yescharacteristic
672C4—22no—
673C4—22no—
674C4—62no—
675C4—62no—
676C4—64no—
677C4—122no—
678C4—362no—
679C4—362no—
680C4Dic3×D1214yes—
681C3—21no—
682C3#7377111yescharacteristic, complemented
683C3#8233511yescharacteristic, complemented
684C2—64no—
685C2—122no—
686C2#1059389911yescharacteristic
687C2#1059391711yescharacteristic
688C2#1059392311yescharacteristic
689C2#1059400311yescharacteristic
690C2C2×Dic3×D1211yescharacteristic
691C2D3×#92611yescharacteristic
692C2#1059498611yescharacteristic
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. #10592635C2semidirect
5. C3×C4×C4⋊Dic3C2semidirect
7. Dic3×(C2×D3)⋊C4C2semidirect
8. #10591313C2semidirect
9. #10591313C2semidirect
10. #10591305C2semidirect
11. #10591269C2semidirect
27. C3×C4×D12C4semidirect
60. C4×C4⋊Dic3D3semidirect
82. C2×C3×C4×D3C2×C4semidirect
86. C32×C42C2×C4semidirect
90. C3×(C2×D3)⋊C4C2×C4semidirect
92. C3×C4⋊Dic3C2×C4semidirect
93. C3×C4⋊Dic3D4semidirect
145. C4×D12Dic3semidirect
265. C2×C4×D3C2×Dic3semidirect
273. C3×C42C4×D3semidirect
274. C3×C42C2×Dic3semidirect
282. (C2×D3)⋊C4C2×Dic3semidirect
291. C4⋊Dic3D12semidirect
292. C4⋊Dic3C2×Dic3semidirect
317. C2×C3×D3#117semidirect
506. C42D3×Dic3semidirect
555. C2×D3#926semidirect
579. C32#2352semidirect
682. C3#73771semidirect
683. 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
#105926352
C3×C4×C4⋊Dic32
#105913762
Dic3×(C2×D3)⋊C42
#105913132
#105913052
#105912692
#823353
#737713