Finite Group Databasebeta

← #11783761

Subgroups — #11783761

Order 1152.

953 conjugacy classes of subgroups.

The subgroup lattice has 739 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#67⋊Dic3C211yesmaximal, characteristic
2C22⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#806C211yesmaximal, characteristic
4#10591705C211yesmaximal, characteristic, complemented
5C2×#63580C211yesmaximal, characteristic
6C3×#4527C211yesmaximal, characteristic, complemented
7#10589186C211yesmaximal, characteristic, complemented
8Dic3×#99—31nomaximal
9#68952—31nomaximal
10C23×C3⋊Dic3C2211yescharacteristic
11C22×C3×#67C2211yescharacteristic
12C22×D3×Dic3C411yescharacteristic, complemented
13C2×C32×C22⋊C4C2211yescharacteristic
14C2×#3757C2211yescharacteristic
15C2×C4×C3⋊Dic3—21no—
16C2×C3×#217C2211yescharacteristic
17C2×C3×#217C2211yescharacteristic
18C2×C3×#217C2211yescharacteristic
19#67⋊Dic3—21no—
20#67⋊Dic3—21no—
21#67⋊Dic3—21no—
22#67⋊Dic3—21no—
23C2×Dic3⋊Dic3C411yescharacteristic, complemented
24C2×(C2×D3)⋊Dic3C411yescharacteristic, complemented
25C2×Dic32—21no—
26C2×Dic32C411yescharacteristic, complemented
27#63658—21no—
28C3×#806C414yescomplemented
29#63580C414yescomplemented
30#63579—21no—
31C2×D4×Dic3—31no—
32C2×#67⋊C4—31no—
33C2×C3×#99—31no—
34C2×#834—31no—
35C2×#806—31no—
36C2×#806D311yescharacteristic
37Dic3×C22⋊C4—31no—
38Dic3×C22⋊C4—31no—
39Dic3×C22⋊C4—31no—
40Dic3×C22⋊C4—31no—
41Dic3×C22⋊C4—61no—
42C3×#342—31no—
43#4527—31no—
44#4527D311yescharacteristic, complemented
45#4526—31no—
46C24×C32C2311yescharacteristic
47C23×C3×D3C2×C411yescharacteristic
48C22×C32×C4—21no—
49C22×C3⋊Dic3—21no—
50C22×C3⋊Dic3—42no—
51C22×C3⋊Dic3C2×C411yescharacteristic
52C22×C3⋊Dic3C2×C411yescharacteristic
53C22×C3⋊Dic3D411yescharacteristic
54C22×C3⋊Dic3D411yescharacteristic
55C22×C3⋊Dic3D411yescharacteristic
56C22×C3⋊Dic3D411yescharacteristic
57C2×C3×#67—21no—
58C2×C3×#67—21no—
59C2×C3×#67—21no—
60C2×C3×#67—21no—
61C2×C3×#67C2×C412yes—
62C2×C3×#67C2×C412yes—
63C22×C3×Dic3—21no—
64C22×C3×Dic3—21no—
65C22×C3×Dic3C2×C411yescharacteristic
66C22×C3×Dic3C2×C411yescharacteristic
67C22×C3×Dic3C2×C411yescharacteristic
68C2×D3×Dic3—21no—
69C2×D3×Dic3—21no—
70C2×D3×Dic3—42no—
71C32×C22⋊C4—21no—
72C32×C22⋊C4C2×C412yescomplemented
73#3757—21no—
74#3757C2×C412yescomplemented
75C4×C3⋊Dic3—42no—
76C3×#217—21no—
77C3×#217—21no—
78C3×#217—21no—
79C3×#217—21no—
80C3×#217C2×C412yescomplemented
81C3×#217C2×C412yescomplemented
82Dic3⋊Dic3—21no—
83Dic3⋊Dic3—21no—
84(C2×D3)⋊Dic3—21no—
85(C2×D3)⋊Dic3—21no—
86Dic32—21no—
87Dic32—21no—
88Dic32—42no—
89C4×#99—91noSylow
90C22×C3×D4—31no—
91C22×#67C2×D311yescharacteristic
92C23×Dic3—31no—
93C23×Dic3—31no—
94C23×Dic3—31no—
95C23×Dic3—61no—
96C22×C4×D3—31no—
97C2×C3×C22⋊C4—21no—
98C2×C3×C22⋊C4—31no—
99C2×C3×C22⋊C4—31no—
100C2×C3×C22⋊C4—31no—
101C2×C3×C22⋊C4C2×D311yescharacteristic
102C2×C3×C22⋊C4C2×D311yescharacteristic
103C2×#217—31no—
104C2×#217—31no—
105C2×#217—31no—
106C2×#217—61no—
107C2×#217C2×D311yescharacteristic
108C2×#217C2×D311yescharacteristic
109C2×#217C2×D311yescharacteristic
110D4×Dic3—61no—
111D4×Dic3—61no—
112D4×Dic3—61no—
113D4×Dic3—61no—
114C2×(C2×D3)⋊C4—31no—
115C2×C4⋊Dic3—31no—
116C2×Dic3⋊C4—31no—
117C2×C4×Dic3—31no—
118C2×C4×Dic3—31no—
119C2×C4×Dic3—61no—
120C2×C4×Dic3—61no—
121C2×C4×Dic3—61no—
122C2×C4×Dic3—61no—
123C2×C4×Dic3—62no—
124#67⋊C4—61no—
125#67⋊C4—61no—
126#67⋊C4—61no—
127#67⋊C4—61no—
128C3×#99—34no—
129#834—34no—
130C3⋊#95—61no—
131C3⋊#95—61no—
132C3⋊#95—61no—
133C3⋊#95—61no—
134C3⋊#95—62no—
135#806—34no—
136#806Dic314yescomplemented
137C23×C32—41no—
138C23×C32—41no—
139C23×C32C22×C411yescharacteristic
140C23×C32C22×C411yescharacteristic
141C23×C32C22×C411yescharacteristic
142C23×C32C2×D411yescharacteristic
143C23×C32C2×D411yescharacteristic
144C23×C32#4111yescharacteristic
145C23×C32#4111yescharacteristic
146C22×C3×D3—21no—
147C22×C3×D3—21no—
148C22×C3×D3—41no—
149C22×C3×D3—41no—
150C22×C3×D3C4212yescomplemented
151C2×C32×C4—22no—
152C2×C32×C4—41no—
153C2×C32×C4—41no—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—41no—
159C2×C3⋊Dic3—41no—
160C2×C3⋊Dic3—41no—
161C2×C3⋊Dic3—41no—
162C2×C3⋊Dic3—41no—
163C2×C3⋊Dic3C22⋊C411yescharacteristic
164C2×C3⋊Dic3C22⋊C411yescharacteristic
165C2×C3⋊Dic3C22⋊C411yescharacteristic
166C2×C3⋊Dic3C22⋊C411yescharacteristic
167C3×#67—22no—
168C3×#67—22no—
169C3×#67—22no—
170C3×#67—22no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—41no—
178C2×C3×Dic3—41no—
179C2×C3×Dic3—41no—
180C2×C3×Dic3—41no—
181C2×C3×Dic3—41no—
182C2×C3×Dic3—41no—
183C2×C3×Dic3C4212yescomplemented
184D3×Dic3—42no—
185D3×Dic3—42no—
186C2×C4×D4—91no—
187C2×#99—31no—
188C2×#99—91no—
189C4×C22⋊C4—91no—
190C4×C22⋊C4—91no—
191#342—31no—
192#342—91no—
193C24×C3—21no—
194C24×C3—31no—
195C24×C3C22×D311yescharacteristic
196C24×C3C22×D311yescharacteristic
197C23×D3C4×D311yescharacteristic
198C2×C3×D4—32no—
199C2×C3×D4—32no—
200C2×C3×D4—61no—
201C2×C3×D4—61no—
202C2×C3×D4—61no—
203C2×C3×D4—61no—
204C22×C3×C4—22no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—31no—
208C22×C3×C4—31no—
209C22×C3×C4—31no—
210C22×C3×C4—61no—
211C22×C3×C4—61no—
212C2×#67—21no—
213C2×#67—21no—
214C2×#67—21no—
215C2×#67—21no—
216C2×#67C4×D312yes—
217C2×#67C2×Dic312yes—
218C22×Dic3—21no—
219C22×Dic3—21no—
220C22×Dic3—31no—
221C22×Dic3—31no—
222C22×Dic3—31no—
223C22×Dic3—31no—
224C22×Dic3—31no—
225C22×Dic3—31no—
226C22×Dic3—31no—
227C22×Dic3—31no—
228C22×Dic3—31no—
229C22×Dic3—31no—
230C22×Dic3—31no—
231C22×Dic3—31no—
232C22×Dic3—61no—
233C22×Dic3—61no—
234C22×Dic3—61no—
235C22×Dic3—61no—
236C22×Dic3—61no—
237C22×Dic3—61no—
238C22×Dic3—61no—
239C22×Dic3—61no—
240C22×Dic3—62no—
241C22×Dic3—61no—
242C22×Dic3—61no—
243C22×Dic3—122no—
244C22×Dic3—122no—
245C22×Dic3—122no—
246C22×Dic3—124no—
247C22×Dic3C4×D311yescharacteristic
248C22×Dic3C4×D311yescharacteristic
249C22×Dic3C4×D311yescharacteristic
250C2×C4×D3—61no—
251C2×C4×D3—61no—
252C2×C4×D3—122no—
253C3×C22⋊C4—22no—
254C3×C22⋊C4—21no—
255C3×C22⋊C4—21no—
256C3×C22⋊C4—22no—
257C3×C22⋊C4—32no—
258C3×C22⋊C4—32no—
259C3×C22⋊C4—61no—
260C3×C22⋊C4—61no—
261C3×C22⋊C4—61no—
262C3×C22⋊C4—61no—
263C3×C22⋊C4C4×D312yescomplemented
264C3×C22⋊C4C2×Dic312yescomplemented
265#217—21no—
266#217—21no—
267#217—21no—
268#217—21no—
269#217—32no—
270#217—32no—
271#217—62no—
272#217—61no—
273#217—61no—
274#217—62no—
275#217—61no—
276#217—61no—
277#217C4×D312yescomplemented
278#217C2×Dic312yescomplemented
279(C2×D3)⋊C4—61no—
280(C2×D3)⋊C4—61no—
281C4⋊Dic3—61no—
282C4⋊Dic3—61no—
283Dic3⋊C4—61no—
284Dic3⋊C4—61no—
285C4×Dic3—61no—
286C4×Dic3—61no—
287C4×Dic3—61no—
288C4×Dic3—61no—
289C4×Dic3—122no—
290C4×Dic3—122no—
291C4×Dic3—122no—
292C4×Dic3—122no—
293C4×Dic3—124no—
294C22×C32—21no—
295C22×C32—21no—
296C22×C32—21no—
297C22×C32—21no—
298C22×C32—21no—
299C22×C32—21no—
300C22×C32—41no—
301C22×C32—41no—
302C22×C32—41no—
303C22×C32—41no—
304C22×C32C2×C4211yescharacteristic
305C22×C32C2×C22⋊C411yescharacteristic
306C22×C32#11711yescharacteristic
307C22×C32C4×D411yescharacteristic
308C22×C32C4×D411yescharacteristic
309C22×C32C4×D411yescharacteristic
310C22×C32C4×D411yescharacteristic
311C2×C3×D3—22no—
312C2×C3×D3—42no—
313C2×C3×D3—41no—
314C2×C3×D3—41no—
315C2×C3×D3—42no—
316C32×C4—42no—
317C3⋊Dic3—21no—
318C3⋊Dic3—21no—
319C3⋊Dic3—21no—
320C3⋊Dic3—42no—
321C3⋊Dic3#9912yescomplemented
322C3×Dic3—22no—
323C3×Dic3—42no—
324C3×Dic3—42no—
325C3×Dic3—41no—
326C3×Dic3—41no—
327C22×D4—31no—
328C23×C4—91no—
329C23×C4—91no—
330C4×D4—181no—
331C4×D4—181no—
332C4×D4—181no—
333C4×D4—181no—
334C2×C4⋊C4—91no—
335C2×C22⋊C4—31no—
336C2×C22⋊C4—31no—
337C2×C22⋊C4—31no—
338C2×C22⋊C4—91no—
339C2×C22⋊C4—91no—
340C2×C22⋊C4D3211yescharacteristic
341C2×C42—91no—
342C2×C42—181no—
343C2×C42—181no—
344#99—34no—
345#99—94no—
346#95—181no—
347#95—181no—
348C23×C3—21no—
349C23×C3—21no—
350C23×C3—21no—
351C23×C3—21no—
352C23×C3—21no—
353C23×C3—21no—
354C23×C3—21no—
355C23×C3—32no—
356C23×C3—41no—
357C23×C3—41no—
358C23×C3—41no—
359C23×C3—41no—
360C23×C3—42no—
361C23×C3—42no—
362C23×C3—61no—
363C23×C3—61no—
364C23×C3—121no—
365C23×C3—121no—
366C23×C3C2×C4×D311yescharacteristic
367C23×C3C2×C4×D311yescharacteristic
368C23×C3C2×C4×D311yescharacteristic
369C23×C3C2×C4×D311yescharacteristic
370C23×C3C2×C4×D311yescharacteristic
371C23×C3D3×D411yescharacteristic
372C23×C3D3×D411yescharacteristic
373C23×C3D3×D411yescharacteristic
374C23×C3D3×D411yescharacteristic
375C23×C3#23711yescharacteristic
376C23×C3#23711yescharacteristic
377C23×C3#23711yescharacteristic
378C23×C3#23911yescharacteristic
379C23×C3C22×Dic311yescharacteristic
380C22×D3—21no—
381C22×D3—21no—
382C22×D3—41no—
383C22×D3—41no—
384C22×D3C4×Dic312yescomplemented
385C3×D4—62no—
386C3×D4—62no—
387C3×D4—62no—
388C3×D4—62no—
389C2×C3×C4—24no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—32no—
393C2×C3×C4—42no—
394C2×C3×C4—41no—
395C2×C3×C4—41no—
396C2×C3×C4—42no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—61no—
400C2×C3×C4—61no—
401C2×C3×C4—61no—
402C2×C3×C4—61no—
403C2×C3×C4—62no—
404C2×C3×C4—62no—
405C2×C3×C4—121no—
406C2×C3×C4—121no—
407C2×C3×C4—121no—
408C2×C3×C4—121no—
409C2×C3×C4—121no—
410C2×C3×C4—121no—
411#67—22no—
412#67—22no—
413#67—22no—
414#67—22no—
415C2×Dic3—21no—
416C2×Dic3—21no—
417C2×Dic3—21no—
418C2×Dic3—21no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—31no—
422C2×Dic3—31no—
423C2×Dic3—31no—
424C2×Dic3—31no—
425C2×Dic3—31no—
426C2×Dic3—31no—
427C2×Dic3—31no—
428C2×Dic3—31no—
429C2×Dic3—41no—
430C2×Dic3—41no—
431C2×Dic3—41no—
432C2×Dic3—41no—
433C2×Dic3—41no—
434C2×Dic3—41no—
435C2×Dic3—61no—
436C2×Dic3—61no—
437C2×Dic3—61no—
438C2×Dic3—61no—
439C2×Dic3—62no—
440C2×Dic3—62no—
441C2×Dic3—62no—
442C2×Dic3—62no—
443C2×Dic3—62no—
444C2×Dic3—62no—
445C2×Dic3—64no—
446C2×Dic3—64no—
447C2×Dic3—62no—
448C2×Dic3—62no—
449C2×Dic3—122no—
450C2×Dic3—122no—
451C2×Dic3—122no—
452C2×Dic3—122no—
453C2×Dic3—121no—
454C2×Dic3—121no—
455C2×Dic3—121no—
456C2×Dic3—121no—
457C2×Dic3—121no—
458C2×Dic3—121no—
459C2×Dic3—122no—
460C2×Dic3—122no—
461C2×Dic3—122no—
462C2×Dic3—121no—
463C2×Dic3—121no—
464C2×Dic3—122no—
465C2×Dic3—121no—
466C2×Dic3—121no—
467C2×Dic3—122no—
468C2×Dic3C4×Dic312yescomplemented
469C4×D3—122no—
470C4×D3—122no—
471C2×C32—21no—
472C2×C32—21no—
473C2×C32—21no—
474C2×C32—21no—
475C2×C32—21no—
476C2×C32—21no—
477C2×C32C4×C22⋊C411yescharacteristic
478C2×C32C2×#9911yescharacteristic
479C2×C32#41011yescharacteristic
480C3×D3—42no—
481C24—31no—
482C24C2×D3211yescharacteristic
483C2×D4—32no—
484C2×D4—32no—
485C2×D4—61no—
486C2×D4—61no—
487C2×D4—61no—
488C2×D4—61no—
489C22×C4—21no—
490C22×C4—31no—
491C22×C4—31no—
492C22×C4—31no—
493C22×C4—61no—
494C22×C4—61no—
495C22×C4—91no—
496C22×C4—91no—
497C22×C4—91no—
498C22×C4—91no—
499C22×C4—91no—
500C22×C4—91no—
501C22×C4—181no—
502C22×C4—181no—
503C22×C4—181no—
504C22×C4—362no—
505C22×C4—362no—
506C4⋊C4—181no—
507C4⋊C4—181no—
508C22⋊C4—21no—
509C22⋊C4—32no—
510C22⋊C4—32no—
511C22⋊C4—61no—
512C22⋊C4—61no—
513C22⋊C4—61no—
514C22⋊C4—61no—
515C22⋊C4—92no—
516C22⋊C4—181no—
517C22⋊C4—181no—
518C22⋊C4—181no—
519C22⋊C4D3×Dic312yescomplemented
520C42—181no—
521C42—181no—
522C42—362no—
523C42—362no—
524C22×C3—22no—
525C22×C3—22no—
526C22×C3—21no—
527C22×C3—21no—
528C22×C3—21no—
529C22×C3—21no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—21no—
533C22×C3—21no—
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—21no—
537C22×C3—21no—
538C22×C3—21no—
539C22×C3—21no—
540C22×C3—21no—
541C22×C3—21no—
542C22×C3—21no—
543C22×C3—21no—
544C22×C3—21no—
545C22×C3—41no—
546C22×C3—41no—
547C22×C3—41no—
548C22×C3—41no—
549C22×C3—41no—
550C22×C3—41no—
551C22×C3—41no—
552C22×C3—41no—
553C22×C3—41no—
554C22×C3—41no—
555C22×C3—41no—
556C22×C3—41no—
557C22×C3—42no—
558C22×C3—42no—
559C22×C3—42no—
560C22×C3—42no—
561C22×C3—62no—
562C22×C3—122no—
563C22×C3—122no—
564C22×C3—121no—
565C22×C3—121no—
566C22×C3C42×D311yescharacteristic
567C22×C3#87711yescharacteristic
568C22×C3D3×C22⋊C411yescharacteristic
569C22×C3D3×C22⋊C411yescharacteristic
570C22×C3#67⋊C411yescharacteristic
571C22×C3#67⋊C411yescharacteristic
572C22×C3#67⋊C411yescharacteristic
573C22×C3#67⋊C411yescharacteristic
574C22×C3#89211yescharacteristic
575C22×C3#89311yescharacteristic
576C22×C3#89311yescharacteristic
577C22×C3C2×C4×Dic311yescharacteristic
578C22×C3D4×Dic311yescharacteristic
579C22×C3D4×Dic311yescharacteristic
580C2×D3—22no—
581C2×D3—42no—
582C2×D3—41no—
583C2×D3—41no—
584C2×D3—42no—
585C3×C4—44no—
586C3×C4—42no—
587C3×C4—42no—
588C3×C4—62no—
589C3×C4—122no—
590C3×C4—122no—
591C3×C4—121no—
592C3×C4—121no—
593Dic3—22no—
594Dic3—32no—
595Dic3—32no—
596Dic3—42no—
597Dic3—42no—
598Dic3—41no—
599Dic3—41no—
600Dic3—62no—
601Dic3—62no—
602Dic3—61no—
603Dic3—61no—
604Dic3—61no—
605Dic3—61no—
606Dic3—61no—
607Dic3—61no—
608Dic3—121no—
609Dic3—121no—
610Dic3—124no—
611Dic3—122no—
612Dic3—122no—
613C32C4×#9911yescharacteristic, complemented, Sylow
614C23—32no—
615C23—41no—
616C23—41no—
617C23—61no—
618C23—61no—
619C23—121no—
620C23—121no—
621C23#379611yescharacteristic
622C23C4×D3211yescharacteristic
623C23C4×D3211yescharacteristic
624C23#380211yescharacteristic
625C23C2×D3×Dic311yescharacteristic
626C23#380511yescharacteristic
627C23#381111yescharacteristic
628D4—62no—
629D4—62no—
630D4—62no—
631D4—62no—
632C2×C4—22no—
633C2×C4—32no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—61no—
637C2×C4—61no—
638C2×C4—62no—
639C2×C4—62no—
640C2×C4—61no—
641C2×C4—61no—
642C2×C4—91no—
643C2×C4—91no—
644C2×C4—91no—
645C2×C4—91no—
646C2×C4—121no—
647C2×C4—121no—
648C2×C4—121no—
649C2×C4—121no—
650C2×C4—121no—
651C2×C4—121no—
652C2×C4—182no—
653C2×C4—182no—
654C2×C4—182no—
655C2×C4—182no—
656C2×C4—362no—
657C2×C4—362no—
658C2×C4—361no—
659C2×C4—361no—
660C2×C4—361no—
661C2×C4—361no—
662C2×C4—361no—
663C2×C3—22no—
664C2×C3—22no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—41no—
681C2×C3—41no—
682C2×C3—41no—
683C2×C3—41no—
684C2×C3—122no—
685C2×C3#466611yescharacteristic
686C2×C3#474011yescharacteristic
687C2×C3#474011yescharacteristic
688C2×C3D3×#9911yescharacteristic
689C2×C3D3×#9911yescharacteristic
690C2×C3Dic3×C22⋊C411yescharacteristic
691D3—42no—
692C22—21no—
693C22—21no—
694C22—21no—
695C22—21no—
696C22—21no—
697C22—21no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—62no—
703C22—122no—
704C22—122no—
705C22—121no—
706C22—121no—
707C22C4×D3×Dic311yescharacteristic
708C22#6387811yescharacteristic
709C22#6388111yescharacteristic
710C22#6389811yescharacteristic
711C22#6390211yescharacteristic
712C22#6392111yescharacteristic
713C22#67⋊Dic311yescharacteristic
714C4—42no—
715C4—62no—
716C4—92no—
717C4—122no—
718C4—122no—
719C4—121no—
720C4—121no—
721C4—181no—
722C4—181no—
723C4—181no—
724C4—362no—
725C3—21no—
726C3#6895211yescharacteristic, complemented
727C3Dic3×#9911yescharacteristic, complemented
728C2—21no—
729C2—21no—
730C2—21no—
731C2—21no—
732C2—21no—
733C2—21no—
734C2—122no—
735C2#1059040411yescharacteristic
736C2#1059040611yescharacteristic
737C2#1059136811yescharacteristic
subgroupG/H
centerC22#63921
commutatorC22×C32C2×C42
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×#67C22
cosocleC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32C4×#99
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22⋊C4×C3⋊Dic3C2semidirect
4. #10591705C2semidirect
6. C3×#4527C2semidirect
7. #10589186C2semidirect
12. C22×D3×Dic3C4semidirect
23. C2×Dic3⋊Dic3C4semidirect
24. C2×(C2×D3)⋊Dic3C4semidirect
26. C2×Dic32C4semidirect
28. C3×#806C4semidirect
29. #63580C4semidirect
44. #4527D3semidirect
72. C32×C22⋊C4C2×C4semidirect
74. #3757C2×C4semidirect
80. C3×#217C2×C4semidirect
81. C3×#217C2×C4semidirect
136. #806Dic3semidirect
150. C22×C3×D3C42semidirect
183. C2×C3×Dic3C42semidirect
263. C3×C22⋊C4C4×D3semidirect
264. C3×C22⋊C4C2×Dic3semidirect
277. #217C4×D3semidirect
278. #217C2×Dic3semidirect
321. C3⋊Dic3#99semidirect
384. C22×D3C4×Dic3semidirect
468. C2×Dic3C4×Dic3semidirect
519. C22⋊C4D3×Dic3semidirect
613. C32C4×#99semidirect
726. C3#68952semidirect
727. C3Dic3×#99semidirect

Maximal subgroups

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

subgroupindex
C2×#67⋊Dic32
C22⋊C4×C3⋊Dic32
C2×C3×#8062
#105917052
C2×#635802
C3×#45272
#105891862
Dic3×#993
#689523