Finite Group Databasebeta

← D3×#4835 #11858761

Subgroups — D3×#4835 #11858761

Order 1152.

1031 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C42×D32C211yesmaximal, characteristic
2#10592534C211yesmaximal, characteristic, complemented
3C3×#4835C211yesmaximal, characteristic, complemented
4C3×D3×C4⋊C8C211yesmaximal, characteristic, complemented
5D3×(C2×D3)⋊C8C212yesmaximal
6#10590665C212yesmaximal, complemented
7#10590661C212yesmaximal, complemented
8D3×#815C212yesmaximal, complemented
9D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
10#10590263C211yesmaximal, characteristic, complemented
11#10590260C211yesmaximal, characteristic, complemented
12D3×#432—31nomaximal
13C2×#4835—31nomaximal
14C2×C4×D32C411yescharacteristic
15C2×C4×D32C411yescharacteristic
16C2×C4×D32C2211yescharacteristic
17C42×C3⋊D3C2211yescharacteristic
18C2×C3×D3×C8C2212yes—
19C3×C42×D3C2211yescharacteristic
20C3×C42×D3C2211yescharacteristic
21C4×#624C411yescharacteristic
22C4×#624C411yescharacteristic
23C4×#624C2211yescharacteristic
24C4×D3×Dic3C411yescharacteristic
25C4×D3×Dic3C411yescharacteristic
26C4×D3×Dic3C411yescharacteristic
27C4×D3×Dic3C411yescharacteristic
28C4×D3×Dic3C2211yescharacteristic
29C4×D3×Dic3C2211yescharacteristic
30C2×D3×C3⋊C8C2212yes—
31C32×C4⋊C8C2211yescharacteristic, complemented
32#63647C2212yes—
33#63642C2212yescomplemented
34C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
35C3×(C2×D3)⋊C8C2212yes—
36C3×#815C2212yescomplemented
37C3×Dic3⋊C8C2212yescomplemented
38C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
39C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
40Dic3⋊(C3⋊C8)C2212yescomplemented
41#63557C2212yes—
42(C2×D3)⋊(C3⋊C8)C2212yes—
43#63555C2212yescomplemented
44#63554C2212yescomplemented
45C2×C42×D3—31no—
46C2×C42×D3—31no—
47C3×#432—31no—
48C2×C3×C4⋊C8—31no—
49C2×(C2×D3)⋊C8—32no—
50C2×#815—32no—
51#4926—31no—
52C2×C4⋊(C3⋊C8)—31no—
53#4835—31no—
54#4835—31no—
55#4835—31no—
56#4835—32no—
57#4835—32no—
58#4835—31no—
59#4835—31no—
60#4835—61no—
61#4835D311yescharacteristic, direct product factor
62D3×C4⋊C8—31no—
63D3×C4⋊C8D311yescharacteristic, complemented
64D3×C22⋊C8—32no—
65#4719—32no—
66#4705—32no—
67D3×#97—32no—
68C22×D32C2×C411yescharacteristic
69C2×C4×C3⋊D3C2×C411yescharacteristic
70C2×C4×C3⋊D3C2×C411yescharacteristic
71C2×C4×C3⋊D3C2311yescharacteristic
72C2×C3×C4×D3C2×C411yescharacteristic
73C2×C3×C4×D3C2×C411yescharacteristic
74C2×C3×C4×D3C2×C411yescharacteristic
75C2×C3×C4×D3C2×C411yescharacteristic
76C2×C3×C4×D3C2311yescharacteristic
77C2×C3×C4×D3C2311yescharacteristic
78C2×#624C2×C411yescharacteristic
79C2×#624C2×C411yescharacteristic
80C2×#624C2×C411yescharacteristic
81C2×D3×Dic3C2×C411yescharacteristic
82C2×D3×Dic3C2×C411yescharacteristic
83C2×D3×Dic3C2×C411yescharacteristic
84C2×D3×Dic3C2×C411yescharacteristic
85C2×D3×Dic3C2×C411yescharacteristic
86C2×D3×Dic3C2×C411yescharacteristic
87C4×D32—24no—
88C4×D32—24no—
89C4×D32—22no—
90C4×D32—22no—
91C2×C32×C8C2312yes—
92C32×C42C2311yescharacteristic
93C4×C3⋊Dic3C2×C411yescharacteristic
94C4×C3⋊Dic3C2×C411yescharacteristic
95C4×C3⋊Dic3C2311yescharacteristic
96C2×C3⋊(C3⋊C8)C2312yes—
97C3×C4×Dic3C2×C411yescharacteristic
98C3×C4×Dic3C2×C411yescharacteristic
99C3×C4×Dic3C2×C411yescharacteristic
100C3×C4×Dic3C2×C411yescharacteristic
101C3×C4×Dic3C2311yescharacteristic
102C3×C4×Dic3C2311yescharacteristic
103C2×C3×C3⋊C8C2312yes—
104C2×C3×C3⋊C8C2312yes—
105C3×D3×C8—24no—
106Dic32C2×C411yescharacteristic
107Dic32C2×C411yescharacteristic
108Dic32C2×C411yescharacteristic
109Dic32C2×C411yescharacteristic
110Dic32C2×C411yescharacteristic
111Dic32C2×C411yescharacteristic
112D3×C3⋊C8—24no—
113C2×#432—91noSylow
114C22×C4×D3—31no—
115C22×C4×D3—31no—
116C22×C4×D3—31no—
117C22×C4×D3—31no—
118C22×C4×D3—31no—
119C22×C4×D3—31no—
120C22×C3×C8—32no—
121C2×C3×C42—31no—
122C2×C3×C42—31no—
123C2×C4×Dic3—31no—
124C2×C4×Dic3—31no—
125C2×C4×Dic3—31no—
126C2×C4×Dic3—31no—
127C2×C4×Dic3—31no—
128C2×C4×Dic3—31no—
129C22×C3⋊C8—32no—
130C2×D3×C8—32no—
131C2×D3×C8C2×D312yes—
132C42×D3—31no—
133C42×D3—31no—
134C42×D3—31no—
135C42×D3—31no—
136C42×D3—31no—
137C42×D3—31no—
138C42×D3—31no—
139C42×D3—31no—
140C42×D3—31no—
141C42×D3—31no—
142C42×D3—31no—
143C42×D3—31no—
144C42×D3—31no—
145C42×D3—31no—
146C42×D3—61no—
147C42×D3C2×D311yescharacteristic
148C42×D3C2×D311yescharacteristic
149C3×C4⋊C8—21no—
150C3×C4⋊C8—32no—
151C3×C4⋊C8—31no—
152C3×C4⋊C8—31no—
153C3×C4⋊C8C2×D311yescharacteristic, complemented
154C3×C4⋊C8C2×D311yescharacteristic, complemented
155C3×C22⋊C8—32no—
156C3×#97—32no—
157#830—32no—
158(C2×D3)⋊C8—32no—
159(C2×D3)⋊C8—32no—
160(C2×D3)⋊C8—32no—
161(C2×D3)⋊C8—32no—
162(C2×D3)⋊C8—32no—
163(C2×D3)⋊C8—62no—
164(C2×D3)⋊C8C2×D312yes—
165#815—32no—
166#815—32no—
167#815—32no—
168#815—32no—
169#815—32no—
170#815—62no—
171#815C2×D312yescomplemented
172Dic3⋊C8—32no—
173Dic3⋊C8C2×D312yescomplemented
174C4⋊(C3⋊C8)—31no—
175C4⋊(C3⋊C8)—31no—
176C4⋊(C3⋊C8)—32no—
177C4⋊(C3⋊C8)—61no—
178C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
179C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
180#803—32no—
181C22×C3⋊D3C22×C411yescharacteristic
182C22×C3×D3C22×C411yescharacteristic
183C22×C3×D3C22×C411yescharacteristic
184C2×D32—22no—
185C2×D32—22no—
186C2×D32M1614yes—
187C2×C32×C4C22×C411yescharacteristic
188C2×C32×C4C22×C411yescharacteristic
189C2×C32×C4C2411yescharacteristic
190C2×C3⋊Dic3C22×C411yescharacteristic
191C2×C3⋊Dic3C22×C411yescharacteristic
192C2×C3⋊Dic3C22×C411yescharacteristic
193C4×C3⋊D3—22no—
194C4×C3⋊D3—22no—
195C4×C3⋊D3—21no—
196C4×C3⋊D3—21no—
197C2×C3×Dic3C22×C411yescharacteristic
198C2×C3×Dic3C22×C411yescharacteristic
199C2×C3×Dic3C22×C411yescharacteristic
200C2×C3×Dic3C22×C411yescharacteristic
201C2×C3×Dic3C22×C411yescharacteristic
202C2×C3×Dic3C22×C411yescharacteristic
203C3×C4×D3—22no—
204C3×C4×D3—22no—
205C3×C4×D3—22no—
206C3×C4×D3—21no—
207C3×C4×D3—21no—
208C3×C4×D3M1614yes—
209C3×C4×D3#4112yes—
210C3×C4×D3#4112yes—
211#624—22no—
212#624—22no—
213#624—22no—
214D3×Dic3—22no—
215D3×Dic3—22no—
216D3×Dic3—22no—
217D3×Dic3—22no—
218D3×Dic3—22no—
219D3×Dic3—22no—
220C32×C8—22no—
221C3⋊(C3⋊C8)—22no—
222C3×C3⋊C8—22no—
223C3×C3⋊C8—22no—
224C22×C42—91no—
225#432—31no—
226#432—92no—
227#432—92no—
228#432—91no—
229#432—91no—
230#432—91no—
231C2×C4⋊C8—31no—
232C2×C4⋊C8—91no—
233C2×C22⋊C8—92no—
234C2×#97—92no—
235C23×D3—31no—
236C23×D3—31no—
237C22×C3×C4—31no—
238C22×C3×C4—31no—
239C22×C3×C4—31no—
240C22×C3×C4—31no—
241C22×C3×C4—31no—
242C22×C3×C4—31no—
243C22×Dic3—31no—
244C22×Dic3—31no—
245C22×Dic3—31no—
246C22×Dic3—31no—
247C22×Dic3—31no—
248C22×Dic3—31no—
249C2×C4×D3—31no—
250C2×C4×D3—31no—
251C2×C4×D3—31no—
252C2×C4×D3—31no—
253C2×C4×D3—31no—
254C2×C4×D3—31no—
255C2×C4×D3—31no—
256C2×C4×D3—31no—
257C2×C4×D3—31no—
258C2×C4×D3—31no—
259C2×C4×D3—31no—
260C2×C4×D3—31no—
261C2×C4×D3—31no—
262C2×C4×D3—31no—
263C2×C4×D3—31no—
264C2×C4×D3—31no—
265C2×C4×D3—31no—
266C2×C4×D3—31no—
267C2×C4×D3—61no—
268C2×C4×D3—61no—
269C2×C4×D3—61no—
270C2×C4×D3—64no—
271C2×C4×D3—62no—
272C2×C4×D3—62no—
273C2×C4×D3—64no—
274C2×C4×D3—64no—
275C2×C4×D3—64no—
276C2×C4×D3—62no—
277C2×C4×D3—62no—
278C2×C4×D3C4×D311yescharacteristic
279C2×C4×D3C4×D311yescharacteristic
280C2×C4×D3C4×D311yescharacteristic
281C2×C4×D3C4×D311yescharacteristic
282C2×C4×D3C22×D311yescharacteristic
283C2×C4×D3C22×D311yescharacteristic
284C2×C3×C8—22no—
285C2×C3×C8—32no—
286C2×C3×C8—32no—
287C2×C3×C8—64no—
288C2×C3×C8C22×D312yes—
289C2×C3×C8C22×D312yes—
290C3×C42—21no—
291C3×C42—31no—
292C3×C42—31no—
293C3×C42—31no—
294C3×C42—31no—
295C3×C42—31no—
296C3×C42—31no—
297C3×C42C22×D311yescharacteristic
298C3×C42C22×D311yescharacteristic
299C4×Dic3—31no—
300C4×Dic3—31no—
301C4×Dic3—31no—
302C4×Dic3—31no—
303C4×Dic3—31no—
304C4×Dic3—31no—
305C4×Dic3—31no—
306C4×Dic3—31no—
307C4×Dic3—31no—
308C4×Dic3—31no—
309C4×Dic3—31no—
310C4×Dic3—31no—
311C4×Dic3—31no—
312C4×Dic3—31no—
313C4×Dic3—31no—
314C4×Dic3—31no—
315C4×Dic3—31no—
316C4×Dic3—31no—
317C4×Dic3—61no—
318C4×Dic3—61no—
319C4×Dic3—61no—
320C4×Dic3C4×D311yescharacteristic
321C4×Dic3C4×D311yescharacteristic
322C4×Dic3C4×D311yescharacteristic
323C4×Dic3C4×D311yescharacteristic
324C4×Dic3C22×D311yescharacteristic
325C4×Dic3C22×D311yescharacteristic
326C2×C3⋊C8—32no—
327C2×C3⋊C8—32no—
328C2×C3⋊C8—62no—
329C2×C3⋊C8—64no—
330C2×C3⋊C8C22×D312yes—
331C2×C3⋊C8C22×D312yes—
332D3×C8—24no—
333D3×C8—64no—
334C22×C32C23×C411yescharacteristic
335C2×C3⋊D3—21no—
336C2×C3⋊D3—21no—
337C2×C3⋊D3C2×M1612yes—
338C2×C3×D3—21no—
339C2×C3×D3—21no—
340C2×C3×D3#11712yes—
341C2×C3×D3C2×M1612yes—
342C2×C3×D3C2×M1612yes—
343C2×C3×D3C2×M1612yes—
344D32—28no—
345C32×C4—21no—
346C32×C4C2×M1612yes—
347C32×C4C2×#4111yescharacteristic
348C32×C4C2×#4111yescharacteristic
349C3⋊Dic3—21no—
350C3⋊Dic3—21no—
351C3⋊Dic3—21no—
352C3×Dic3—21no—
353C3×Dic3—21no—
354C3×Dic3—21no—
355C3×Dic3—21no—
356C3×Dic3#11712yes—
357C3×Dic3C2×M1612yes—
358C23×C4—91no—
359C23×C4—91no—
360C23×C4—91no—
361C22×C8—32no—
362C22×C8—92no—
363C2×C42—31no—
364C2×C42—31no—
365C2×C42—91no—
366C2×C42—91no—
367C2×C42—91no—
368C2×C42—91no—
369C2×C42—91no—
370C2×C42—91no—
371C2×C42—91no—
372C2×C42—91no—
373C2×C42—91no—
374C2×C42—91no—
375C4⋊C8—32no—
376C4⋊C8—31no—
377C4⋊C8—31no—
378C4⋊C8—92no—
379C4⋊C8—91no—
380C4⋊C8D3211yescharacteristic, complemented
381C22⋊C8—32no—
382C22⋊C8—92no—
383C22⋊C8—92no—
384C22⋊C8—92no—
385#97—32no—
386#97—92no—
387#97—92no—
388#97—92no—
389C23×C3—31no—
390C23×C3—31no—
391C22×D3—31no—
392C22×D3—31no—
393C22×D3—34no—
394C22×D3—34no—
395C22×D3—61no—
396C22×D3—62no—
397C22×D3—62no—
398C22×D3—62no—
399C22×D3—62no—
400C22×D3C2×C4×D311yescharacteristic
401C22×D3C2×C4×D311yescharacteristic
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—31no—
406C2×C3×C4—31no—
407C2×C3×C4—34no—
408C2×C3×C4—32no—
409C2×C3×C4—32no—
410C2×C3×C4—31no—
411C2×C3×C4—31no—
412C2×C3×C4—31no—
413C2×C3×C4—31no—
414C2×C3×C4—62no—
415C2×C3×C4—62no—
416C2×C3×C4—62no—
417C2×C3×C4—61no—
418C2×C3×C4—61no—
419C2×C3×C4C2×C4×D311yescharacteristic
420C2×C3×C4C2×C4×D311yescharacteristic
421C2×C3×C4C2×C4×D311yescharacteristic
422C2×C3×C4C2×C4×D311yescharacteristic
423C2×C3×C4C23×D311yescharacteristic
424C2×C3×C4C23×D311yescharacteristic
425C2×Dic3—31no—
426C2×Dic3—31no—
427C2×Dic3—31no—
428C2×Dic3—31no—
429C2×Dic3—31no—
430C2×Dic3—31no—
431C2×Dic3—61no—
432C2×Dic3—61no—
433C2×Dic3—61no—
434C2×Dic3—62no—
435C2×Dic3—62no—
436C2×Dic3—62no—
437C2×Dic3—62no—
438C2×Dic3—62no—
439C2×Dic3—62no—
440C2×Dic3C2×C4×D311yescharacteristic
441C2×Dic3C2×C4×D311yescharacteristic
442C2×Dic3C2×C4×D311yescharacteristic
443C2×Dic3C2×C4×D311yescharacteristic
444C2×Dic3C2×C4×D311yescharacteristic
445C2×Dic3C2×C4×D311yescharacteristic
446C4×D3—22no—
447C4×D3—22no—
448C4×D3—22no—
449C4×D3—21no—
450C4×D3—21no—
451C4×D3—62no—
452C4×D3—62no—
453C4×D3—62no—
454C4×D3—62no—
455C4×D3—62no—
456C4×D3—62no—
457C4×D3—62no—
458C4×D3—62no—
459C4×D3—62no—
460C4×D3—62no—
461C4×D3—62no—
462C4×D3—62no—
463C4×D3—62no—
464C4×D3—62no—
465C4×D3—61no—
466C4×D3—61no—
467C4×D3—61no—
468C4×D3—61no—
469C4×D3—62no—
470C4×D3—62no—
471C4×D3—122no—
472C4×D3—121no—
473C4×D3—121no—
474C4×D3—122no—
475C4×D3ΓL(1,𝔽25)14yes—
476C4×D3#23712yes—
477C4×D3#23912yes—
478C3×C8—22no—
479C3×C8—22no—
480C3×C8—42no—
481C3×C8—62no—
482C3×C8—62no—
483C3⋊C8—22no—
484C3⋊C8—22no—
485C3⋊C8—62no—
486C3⋊C8—62no—
487C3⋊C8—122no—
488C2×C32C2×#11711yescharacteristic
489C2×C32C22×M1611yescharacteristic
490C2×C32C22×M1611yescharacteristic
491C3⋊D3—22no—
492C3×D3—22no—
493C3×D3#43214yescomplemented
494C24—91no—
495C22×C4—31no—
496C22×C4—31no—
497C22×C4—31no—
498C22×C4—31no—
499C22×C4—31no—
500C22×C4—31no—
501C22×C4—91no—
502C22×C4—91no—
503C22×C4—91no—
504C22×C4—91no—
505C22×C4—91no—
506C22×C4—91no—
507C22×C4—91no—
508C22×C4—91no—
509C22×C4—91no—
510C22×C4—91no—
511C22×C4—91no—
512C22×C4—91no—
513C22×C4—184no—
514C22×C4—182no—
515C22×C4—182no—
516C22×C4—184no—
517C2×C8—32no—
518C2×C8—32no—
519C2×C8—64no—
520C2×C8—92no—
521C2×C8—184no—
522C2×C8C2×D3212yes—
523C42—31no—
524C42—31no—
525C42—31no—
526C42—31no—
527C42—31no—
528C42—31no—
529C42—91no—
530C42—91no—
531C42—91no—
532C42—91no—
533C42—91no—
534C42—91no—
535C42—91no—
536C42—91no—
537C42—91no—
538C42C2×D3211yescharacteristic
539C22×C3—21no—
540C22×C3—32no—
541C22×C3—32no—
542C22×C3—32no—
543C22×C3—32no—
544C22×C3—61no—
545C22×C3—61no—
546C22×C3C22×C4×D311yescharacteristic
547C22×C3C22×C4×D311yescharacteristic
548C2×D3—21no—
549C2×D3—21no—
550C2×D3—32no—
551C2×D3—32no—
552C2×D3—62no—
553C2×D3—68no—
554C2×D3—61no—
555C2×D3—61no—
556C2×D3—61no—
557C2×D3—61no—
558C2×D3—68no—
559C2×D3—121no—
560C2×D3—121no—
561C2×D3#89212yes—
562C2×D3C2×ΓL(1,𝔽25)12yes—
563C2×D3D3×M1612yes—
564C2×D3D3×M1612yes—
565C3×C4—21no—
566C3×C4—21no—
567C3×C4—22no—
568C3×C4—21no—
569C3×C4—21no—
570C3×C4—32no—
571C3×C4—32no—
572C3×C4—41no—
573C3×C4—61no—
574C3×C4—61no—
575C3×C4—61no—
576C3×C4—61no—
577C3×C4C2×ΓL(1,𝔽25)12yes—
578C3×C4D3×M1612yes—
579C3×C4C2×#23711yescharacteristic
580C3×C4C2×#23911yescharacteristic
581C3×C4D3×#4111yescharacteristic
582C3×C4D3×#4111yescharacteristic
583Dic3—21no—
584Dic3—21no—
585Dic3—21no—
586Dic3—21no—
587Dic3—61no—
588Dic3—61no—
589Dic3—61no—
590Dic3—61no—
591Dic3—61no—
592Dic3—61no—
593Dic3—121no—
594Dic3—121no—
595Dic3—121no—
596Dic3#89212yes—
597Dic3C2×ΓL(1,𝔽25)12yes—
598C32C2×#43211yescharacteristic, complemented, Sylow
599C23—31no—
600C23—31no—
601C23—94no—
602C23—91no—
603C23—182no—
604C23—182no—
605C2×C4—31no—
606C2×C4—31no—
607C2×C4—34no—
608C2×C4—32no—
609C2×C4—32no—
610C2×C4—31no—
611C2×C4—31no—
612C2×C4—31no—
613C2×C4—31no—
614C2×C4—62no—
615C2×C4—62no—
616C2×C4—62no—
617C2×C4—61no—
618C2×C4—61no—
619C2×C4—91no—
620C2×C4—91no—
621C2×C4—91no—
622C2×C4—182no—
623C2×C4—182no—
624C2×C4—182no—
625C2×C4—182no—
626C2×C4—182no—
627C2×C4—182no—
628C2×C4—182no—
629C2×C4—182no—
630C2×C4—182no—
631C2×C4—182no—
632C2×C4—182no—
633C2×C4—181no—
634C2×C4—181no—
635C2×C4C4×D3211yescharacteristic
636C2×C4C4×D3211yescharacteristic
637C2×C4C22×D3211yescharacteristic
638C8—22no—
639C8—62no—
640C8—62no—
641C8—182no—
642C2×C3—21no—
643C2×C3—21no—
644C2×C3—21no—
645C2×C3—34no—
646C2×C3—62no—
647C2×C3C2×#89211yescharacteristic
648C2×C3D3×#11711yescharacteristic
649C2×C3C22×ΓL(1,𝔽25)11yescharacteristic
650C2×C3C2×D3×M1611yescharacteristic
651C2×C3C2×D3×M1611yescharacteristic
652C2×C3C2×D3×M1611yescharacteristic
653D3—22no—
654D3—62no—
655D3—62no—
656D3—122no—
657D3#483514yesdirect product factor
658C22—32no—
659C22—32no—
660C22—32no—
661C22—32no—
662C22—61no—
663C22—61no—
664C22—92no—
665C22—188no—
666C22—181no—
667C22—181no—
668C22C2×C4×D3211yescharacteristic
669C4—21no—
670C4—32no—
671C4—32no—
672C4—61no—
673C4—61no—
674C4—61no—
675C4—61no—
676C4—181no—
677C4—181no—
678C4—181no—
679C4D3×ΓL(1,𝔽25)12yes—
680C4D3×#23711yescharacteristic
681C4D3×#23911yescharacteristic
682C3—21no—
683C3C2×#483511yescharacteristic, complemented
684C3D3×#43211yescharacteristic, complemented
685C2—34no—
686C2—62no—
687C2—182no—
688C2D3×#89211yescharacteristic
689C2C2×D3×ΓL(1,𝔽25)11yescharacteristic
690C2D32×M1611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4⋊C8C22
prime radicalC22×D32C2×C4
cosocleC2×C32×C4C24
hypercenterC4⋊C8D32
hypocenterC32C2×#432
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592534C2semidirect
3. C3×#4835C2semidirect
4. C3×D3×C4⋊C8C2semidirect
6. #10590665C2semidirect
7. #10590661C2semidirect
8. D3×#815C2semidirect
9. D3×C4⋊(C3⋊C8)C2semidirect
10. #10590263C2semidirect
11. #10590260C2semidirect
31. C32×C4⋊C8C22semidirect
33. #63642C22semidirect
34. C4⋊(C3⋊(C3⋊C8))C22semidirect
36. C3×#815C22semidirect
37. C3×Dic3⋊C8C22semidirect
38. C3×C4⋊(C3⋊C8)C22semidirect
39. C3×C4⋊(C3⋊C8)C22semidirect
40. Dic3⋊(C3⋊C8)C22semidirect
43. #63555C22semidirect
44. #63554C22semidirect
61. #4835D3direct (N × H)
63. D3×C4⋊C8D3semidirect
153. C3×C4⋊C8C2×D3semidirect
154. C3×C4⋊C8C2×D3semidirect
171. #815C2×D3semidirect
173. Dic3⋊C8C2×D3semidirect
178. C4⋊(C3⋊C8)C2×D3semidirect
179. C4⋊(C3⋊C8)C2×D3semidirect
380. C4⋊C8D32semidirect
493. C3×D3#432semidirect
598. C32C2×#432semidirect
657. D3#4835direct (N × H)
683. C3C2×#4835semidirect
684. C3D3×#432semidirect

Maximal subgroups

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

subgroupindex
C42×D322
#105925342
C3×#48352
C3×D3×C4⋊C82
D3×(C2×D3)⋊C82
#105906652
#105906612
D3×#8152
D3×C4⋊(C3⋊C8)2
#105902632
#105902602
D3×#4323
C2×#48353