Finite Group Databasebeta

← C2×#10591006 #11857646

Subgroups — C2×#10591006 #11857646

Order 1152.

1585 conjugacy classes of subgroups.

The subgroup lattice has 733 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3795C211yesmaximal, characteristic
2C2×C3×D3×M16C211yesmaximal, characteristic, complemented
3C2×D3×#208C211yesmaximal, characteristic, complemented
4C2×#63651C211yesmaximal, characteristic, complemented
5C2×C3×#823C211yesmaximal, characteristic, complemented
6C2×#63561C211yesmaximal, characteristic, complemented
7C2×#63558C211yesmaximal, characteristic, complemented
8#10591006C218yesmaximal, direct product factor
9C2×#5132—31nomaximal
10C2×#4745—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×#625C412yes—
15C22×D3×Dic3C412yes—
16C2×#3795—21no—
17C2×#3795—22no—
18C2×#3795—21no—
19C2×#3795—21no—
20C2×#3795—21no—
21C2×#3795—22no—
22C2×#3795C414yes—
23C2×#3795C2214yes—
24C2×C32×M16C2211yescharacteristic
25C2×#3748C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28C3×D3×M16—22no—
29C3×D3×M16C2214yescomplemented
30C2×C3×ΓL(1,𝔽25)—21no—
31C2×C3×D3×C8—21no—
32C2×#3711—21no—
33D3×#208—22no—
34D3×#208C2214yescomplemented
35C2×D3×C3⋊C8—21no—
36#63651C2214yescomplemented
37C3×#823C2214yescomplemented
38#63561C2214yescomplemented
39#63558C2214yescomplemented
40C22×#237—31no—
41C22×#235—31no—
42C22×C3×M16—31no—
43C22×#208—31no—
44C2×D3×M16—31no—
45C2×D3×M16D311yescharacteristic, complemented
46C2×C3×#100—31no—
47C2×#833—31no—
48C2×#824—31no—
49C2×#824—31no—
50C2×#824—31no—
51C2×#824—31no—
52C2×#824—61no—
53#5132—38no—
54C2×#823—31no—
55C2×#823D311yescharacteristic, complemented
56#4745—38no—
57C23×C3×D3C2×C412yes—
58C23×C3×D3C2×C411yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3C2×C412yes—
61C2×#634—21no—
62C2×#634—21no—
63C2×#634—21no—
64C2×#634—21no—
65C2×#634C2×C412yes—
66C2×#634C2312yes—
67C22×C3×Dic3C2×C411yescharacteristic
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12—21no—
72C2×C3×D12C2×C412yes—
73C2×C3×D12C2312yes—
74C2×C3×C4×D3C2×C412yes—
75C2×C3×C4×D3D411yescharacteristic
76C2×C3×C4×D3D412yes—
77C2×C3×C4×D3D411yescharacteristic
78C2×C3×C4×D3D411yescharacteristic
79C2×C3×C4×D3D411yescharacteristic
80C2×C3×C4×D3D412yes—
81C2×C3×C4×D3C2312yes—
82C2×#625—22no—
83C2×#625—22no—
84C2×#625—24no—
85C2×#625C2×C418yes—
86C2×D3×Dic3—24no—
87C2×D3×Dic3—22no—
88C2×D3×Dic3—22no—
89C2×D3×Dic3C2×C418yes—
90#3795—24no—
91#3795—24no—
92#3795—24no—
93#3795—24no—
94#3795—24no—
95#3795—24no—
96#3795—24no—
97#3795—24no—
98C32×M16—21no—
99C32×M16C2312yes—
100C2×C32×C8—21no—
101#3748—21no—
102#3748C2312yes—
103C2×C3⋊(C3⋊C8)—21no—
104C3×#208—21no—
105C3×#208—21no—
106C3×#208C2312yes—
107C3×#208C2312yes—
108C2×C3×C3⋊C8—21no—
109C2×C3×C3⋊C8—21no—
110C3×ΓL(1,𝔽25)—24no—
111C3×D3×C8—24no—
112#3711—24no—
113D3×C3⋊C8—24no—
114C2×#413—91noSylow
115C22×C3×D4—31no—
116C23×C3×C4—31no—
117C22×#67—32no—
118C22×#67—32no—
119C23×Dic3—32no—
120C2×#237—34no—
121C2×#237—34no—
122C2×#237—61no—
123C2×#237—61no—
124C2×#237—62no—
125C2×#237—61no—
126C2×#237—61no—
127C2×#237—62no—
128C2×#235—34no—
129C2×#235—34no—
130C2×#235—61no—
131C2×#235—61no—
132C2×#235—62no—
133C2×#235—61no—
134C2×#235—61no—
135C2×#235—62no—
136C22×D12C2×D311yescharacteristic
137C22×C4×D3—32no—
138C22×C4×D3C2×D311yescharacteristic
139C22×Dic6—31no—
140C22×Dic6—31no—
141C22×Dic6—61no—
142C2×C3×M16—21no—
143C2×C3×M16—31no—
144C2×C3×M16—31no—
145C2×C3×M16—34no—
146C2×C3×M16—61no—
147C2×C3×M16—62no—
148C2×C3×M16C2×D311yescharacteristic
149C2×C3×M16C2×D311yescharacteristic
150C22×C3×C8—61no—
151C2×#208—31no—
152C2×#208—31no—
153C2×#208—34no—
154C2×#208—61no—
155C2×#208—61no—
156C2×#208—62no—
157C2×#208C2×D311yescharacteristic
158C2×#208C2×D311yescharacteristic
159C22×C3⋊C8—61no—
160D3×M16—22no—
161D3×M16—34no—
162D3×M16—62no—
163D3×M16C2×D314yescomplemented
164C2×ΓL(1,𝔽25)—21no—
165C2×ΓL(1,𝔽25)—61no—
166C2×D3×C8—21no—
167C2×D3×C8—61no—
168C3×#100—34no—
169#833—34no—
170#824—34no—
171#824—34no—
172#824—34no—
173#824—34no—
174#824—64no—
175#823—34no—
176#823C2×D314yescomplemented
177C23×C32C22×C411yescharacteristic
178C22×C3×D3—22no—
179C22×C3×D3—22no—
180C22×C3×D3—42no—
181C22×C3×D3—44no—
182C22×C3×D3C22⋊C411yescharacteristic
183C22×C3×D3C22⋊C411yescharacteristic
184C22×C3×D3C22⋊C412yes—
185C22×C3×D3C22×C414yes—
186C22×C3×D3C22×C412yes—
187C2×C32×C4C22×C411yescharacteristic
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2411yescharacteristic
193C2×C3⋊Dic3—22no—
194C2×C3⋊Dic3—22no—
195C2×C3⋊Dic3C22×C414yes—
196#634—22no—
197#634—22no—
198#634—22no—
199#634—22no—
200C2×C3×Dic3C22⋊C412yes—
201C2×C3×Dic3C22⋊C411yescharacteristic
202C2×C3×Dic3C22⋊C411yescharacteristic
203C2×C3×Dic3C22×C412yes—
204C3×D12—22no—
205C3×D12—22no—
206C3×D12—22no—
207C3×D12—22no—
208C3×C4×D3C22⋊C412yes—
209C3×C4×D3C22⋊C412yes—
210C3×C4×D3C22⋊C412yes—
211C3×C4×D3C22⋊C412yes—
212C3×C4×D3C2×D412yes—
213C3×C4×D3C2×D412yes—
214C3×C4×D3C2×D412yes—
215C3×C4×D3C2×D412yes—
216#625—28no—
217#625—28no—
218D3×Dic3—28no—
219D3×Dic3—28no—
220C32×C8—22no—
221C3⋊(C3⋊C8)—22no—
222C3×C3⋊C8—22no—
223C3×C3⋊C8—22no—
224C22×#41—91no—
225C22×M16—31no—
226C22×M16—91no—
227#413—98no—
228C2×#101—91no—
229C2×#101—91no—
230C2×#100—31no—
231C2×#100—91no—
232C24×C3—31no—
233C24×C3—32no—
234C23×D3C4×D312yes—
235C23×D3C4×D311yescharacteristic
236C2×C3×D4—32no—
237C2×C3×D4—32no—
238C2×C3×D4—61no—
239C2×C3×D4—61no—
240C2×C3×D4—61no—
241C2×C3×D4—61no—
242C22×C3×C4—21no—
243C22×C3×C4—31no—
244C22×C3×C4—32no—
245C22×C3×C4—31no—
246C22×C3×C4—32no—
247C22×C3×C4—31no—
248C22×C3×C4—31no—
249C22×C3×C4—32no—
250C22×C3×C4—31no—
251C22×C3×C4—32no—
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D311yescharacteristic
254C2×#67—38no—
255C2×#67—38no—
256C2×#67—62no—
257C2×#67—62no—
258C2×#67—64no—
259C2×#67—62no—
260C2×#67—62no—
261C2×#67—64no—
262C22×Dic3—32no—
263C22×Dic3—32no—
264C22×Dic3—38no—
265C22×Dic3—62no—
266C22×Dic3—64no—
267C22×Dic3—62no—
268C22×Dic3—62no—
269C22×Dic3C4×D311yescharacteristic
270#237—64no—
271#237—64no—
272#237—64no—
273#237—64no—
274#237—64no—
275#237—64no—
276#237—64no—
277#237—64no—
278#235—64no—
279#235—64no—
280#235—64no—
281#235—64no—
282#235—64no—
283#235—64no—
284#235—64no—
285#235—64no—
286C2×D12—21no—
287C2×D12—21no—
288C2×D12—21no—
289C2×D12—21no—
290C2×D12C4×D312yes—
291C2×D12C22×D312yes—
292C2×C4×D3—38no—
293C2×C4×D3—64no—
294C2×C4×D3—62no—
295C2×C4×D3—62no—
296C2×C4×D3C4×D312yes—
297C2×C4×D3D1211yescharacteristic
298C2×C4×D3D1211yescharacteristic
299C2×C4×D3D1212yes—
300C2×C4×D3#6711yescharacteristic
301C2×C4×D3#6711yescharacteristic
302C2×C4×D3#6712yes—
303C2×C4×D3C22×D312yes—
304C2×Dic6—32no—
305C2×Dic6—32no—
306C2×Dic6—32no—
307C2×Dic6—32no—
308C2×Dic6—62no—
309C2×Dic6—62no—
310C2×Dic6—61no—
311C2×Dic6—61no—
312C2×Dic6—61no—
313C2×Dic6—61no—
314C2×Dic6—61no—
315C2×Dic6—61no—
316C2×Dic6—61no—
317C2×Dic6—61no—
318C2×Dic6—121no—
319C2×Dic6—121no—
320C2×Dic6—121no—
321C2×Dic6—121no—
322C3×M16—21no—
323C3×M16—21no—
324C3×M16—22no—
325C3×M16—32no—
326C3×M16—32no—
327C3×M16—41no—
328C3×M16—64no—
329C3×M16—61no—
330C3×M16—61no—
331C3×M16C22×D312yes—
332C3×M16C22×D312yes—
333C2×C3×C8—21no—
334C2×C3×C8—21no—
335C2×C3×C8—41no—
336C2×C3×C8—64no—
337C2×C3×C8—61no—
338C2×C3×C8—61no—
339#208—21no—
340#208—21no—
341#208—32no—
342#208—32no—
343#208—62no—
344#208—64no—
345#208—61no—
346#208—61no—
347#208—121no—
348#208C22×D312yes—
349#208C22×D312yes—
350C2×C3⋊C8—21no—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—64no—
353C2×C3⋊C8—61no—
354C2×C3⋊C8—61no—
355C2×C3⋊C8—121no—
356ΓL(1,𝔽25)—24no—
357ΓL(1,𝔽25)—64no—
358D3×C8—24no—
359D3×C8—64no—
360C22×C32—22no—
361C22×C32C2×C22⋊C411yescharacteristic
362C22×C32C2×C22⋊C411yescharacteristic
363C22×C32C23×C411yescharacteristic
364C2×C3×D3—22no—
365C2×C3×D3—22no—
366C2×C3×D3—24no—
367C2×C3×D3—42no—
368C2×C3×D3—42no—
369C2×C3×D3—44no—
370C2×C3×D3—44no—
371C2×C3×D3—44no—
372C2×C3×D3C2×C22⋊C412yes—
373C2×C3×D3C2×C22⋊C412yes—
374C32×C4C2×C22⋊C411yescharacteristic
375C32×C4C2×C22⋊C411yescharacteristic
376C32×C4C22×D411yescharacteristic
377C32×C4C22×D411yescharacteristic
378C3⋊Dic3—24no—
379C3×Dic3C2×C22⋊C412yes—
380C3×Dic3C2×C22⋊C412yes—
381C2×#41—94no—
382C2×#41—94no—
383C2×#41—181no—
384C2×#41—182no—
385C2×#41—181no—
386C2×#41—181no—
387C2×#41—182no—
388C2×#41—181no—
389C22×Q8—91no—
390C22×D4—31no—
391C22×D4—92no—
392C23×C4—31no—
393C23×C4—92no—
394C2×M16—31no—
395C2×M16—31no—
396C2×M16—34no—
397C2×M16—61no—
398C2×M16—62no—
399C2×M16—94no—
400C2×M16—91no—
401C2×M16—181no—
402C2×M16—182no—
403C2×M16D3211yescharacteristic
404C22×C8—61no—
405C22×C8—181no—
406#101—94no—
407#101—94no—
408#100—34no—
409#100—94no—
410C23×C3—21no—
411C23×C3—31no—
412C23×C3—31no—
413C23×C3—32no—
414C23×C3—32no—
415C23×C3—34no—
416C23×C3—62no—
417C23×C3—62no—
418C23×C3—122no—
419C23×C3—124no—
420C23×C3C2×C4×D311yescharacteristic
421C23×C3C2×C4×D311yescharacteristic
422C22×D3—22no—
423C22×D3—22no—
424C22×D3—42no—
425C22×D3—44no—
426C22×D3(C2×D3)⋊C411yescharacteristic
427C22×D3(C2×D3)⋊C411yescharacteristic
428C22×D3(C2×D3)⋊C412yes—
429C22×D3C2×C4×D314yes—
430C22×D3C2×C4×D312yes—
431C3×D4—62no—
432C3×D4—62no—
433C3×D4—62no—
434C3×D4—62no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—32no—
442C2×C3×C4—31no—
443C2×C3×C4—31no—
444C2×C3×C4—32no—
445C2×C3×C4—32no—
446C2×C3×C4—32no—
447C2×C3×C4—32no—
448C2×C3×C4—32no—
449C2×C3×C4—32no—
450C2×C3×C4—32no—
451C2×C3×C4—32no—
452C2×C3×C4—32no—
453C2×C3×C4C2×C4×D311yescharacteristic
454C2×C3×C4C2×C4×D311yescharacteristic
455C2×C3×C4C2×D1211yescharacteristic
456C2×C3×C4C2×D1211yescharacteristic
457C2×C3×C4D3×D411yescharacteristic
458C2×C3×C4D3×D411yescharacteristic
459C2×C3×C4D3×D411yescharacteristic
460C2×C3×C4D3×D411yescharacteristic
461C2×C3×C4C2×#6711yescharacteristic
462C2×C3×C4C2×#6711yescharacteristic
463C2×C3×C4C23×D311yescharacteristic
464C2×C3×C4C23×D311yescharacteristic
465#67—68no—
466#67—68no—
467#67—68no—
468#67—68no—
469C2×Dic3—34no—
470C2×Dic3—34no—
471C2×Dic3—64no—
472C2×Dic3—62no—
473C2×Dic3—62no—
474C2×Dic3—62no—
475C2×Dic3—62no—
476C2×Dic3—68no—
477C2×Dic3—68no—
478C2×Dic3—122no—
479C2×Dic3—122no—
480C2×Dic3(C2×D3)⋊C412yes—
481C2×Dic3(C2×D3)⋊C411yescharacteristic
482C2×Dic3(C2×D3)⋊C411yescharacteristic
483C2×Dic3C2×C4×D312yes—
484D12—22no—
485D12—22no—
486D12—22no—
487D12—22no—
488C4×D3—68no—
489C4×D3—68no—
490C4×D3(C2×D3)⋊C412yes—
491C4×D3(C2×D3)⋊C412yes—
492C4×D3(C2×D3)⋊C412yes—
493C4×D3(C2×D3)⋊C412yes—
494C4×D3C2×D1212yes—
495C4×D3C2×D1212yes—
496C4×D3C2×#6712yes—
497C4×D3C2×#6712yes—
498Dic6—62no—
499Dic6—62no—
500Dic6—62no—
501Dic6—62no—
502Dic6—62no—
503Dic6—62no—
504Dic6—62no—
505Dic6—62no—
506Dic6—122no—
507Dic6—122no—
508Dic6—122no—
509Dic6—122no—
510C3×C8—22no—
511C3×C8—22no—
512C3×C8—42no—
513C3×C8—62no—
514C3×C8—62no—
515C3⋊C8—22no—
516C3⋊C8—22no—
517C3⋊C8—62no—
518C3⋊C8—62no—
519C3⋊C8—122no—
520C2×C32—21no—
521C2×C32—21no—
522C2×C32#41312yescomplemented
523C2×C32C22×C22⋊C411yescharacteristic
524C3×D3—22no—
525C3×D3—22no—
526C3×D3—44no—
527C24—31no—
528C24—32no—
529#41—184no—
530#41—184no—
531#41—184no—
532#41—184no—
533#41—184no—
534#41—184no—
535#41—184no—
536#41—184no—
537C2×Q8—92no—
538C2×Q8—92no—
539C2×Q8—181no—
540C2×Q8—181no—
541C2×Q8—181no—
542C2×Q8—181no—
543C2×D4—32no—
544C2×D4—32no—
545C2×D4—61no—
546C2×D4—61no—
547C2×D4—61no—
548C2×D4—61no—
549C2×D4—98no—
550C2×D4—184no—
551C2×D4—182no—
552C2×D4—182no—
553C22×C4—31no—
554C22×C4—32no—
555C22×C4—32no—
556C22×C4—31no—
557C22×C4—32no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—32no—
561C22×C4—31no—
562C22×C4—98no—
563C22×C4—92no—
564C22×C4—184no—
565C22×C4—182no—
566C22×C4—182no—
567C22×C4C2×D3211yescharacteristic
568M16—21no—
569M16—32no—
570M16—32no—
571M16—64no—
572M16—61no—
573M16—61no—
574M16—92no—
575M16—184no—
576M16—181no—
577M16C2×D3212yes—
578C2×C8—21no—
579C2×C8—64no—
580C2×C8—61no—
581C2×C8—61no—
582C2×C8—184no—
583C2×C8—181no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—21no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—32no—
590C22×C3—32no—
591C22×C3—42no—
592C22×C3—62no—
593C22×C3—62no—
594C22×C3—64no—
595C22×C3—122no—
596C22×C3—122no—
597C22×C3—124no—
598C22×C3—124no—
599C22×C3—124no—
600C22×C3D3×C22⋊C411yescharacteristic
601C22×C3D3×C22⋊C411yescharacteristic
602C22×C3C2×(C2×D3)⋊C411yescharacteristic
603C22×C3C2×(C2×D3)⋊C411yescharacteristic
604C22×C3C22×C4×D311yescharacteristic
605C22×C3C22×C4×D311yescharacteristic
606C2×D3—22no—
607C2×D3—22no—
608C2×D3—24no—
609C2×D3—42no—
610C2×D3—42no—
611C2×D3—44no—
612C2×D3—44no—
613C2×D3—44no—
614C2×D3C2×(C2×D3)⋊C412yes—
615C2×D3C2×(C2×D3)⋊C412yes—
616C3×C4—21no—
617C3×C4—21no—
618C3×C4—21no—
619C3×C4—21no—
620C3×C4—32no—
621C3×C4—32no—
622C3×C4D3×C22⋊C411yescharacteristic
623C3×C4D3×C22⋊C411yescharacteristic
624C3×C4C2×(C2×D3)⋊C411yescharacteristic
625C3×C4C2×(C2×D3)⋊C411yescharacteristic
626C3×C4C22×D1211yescharacteristic
627C3×C4C2×D3×D411yescharacteristic
628C3×C4C2×D3×D411yescharacteristic
629C3×C4C22×#6711yescharacteristic
630Dic3—64no—
631Dic3—64no—
632Dic3—124no—
633Dic3C2×(C2×D3)⋊C412yes—
634Dic3C2×(C2×D3)⋊C412yes—
635C32C2×#41311yescharacteristic, complemented, Sylow
636C23—31no—
637C23—31no—
638C23—32no—
639C23—32no—
640C23—34no—
641C23—62no—
642C23—62no—
643C23—122no—
644C23—124no—
645C23C4×D3211yescharacteristic
646Q8—182no—
647Q8—182no—
648Q8—182no—
649Q8—182no—
650D4—62no—
651D4—62no—
652D4—62no—
653D4—62no—
654D4—188no—
655D4—188no—
656C2×C4—32no—
657C2×C4—32no—
658C2×C4—31no—
659C2×C4—31no—
660C2×C4—32no—
661C2×C4—32no—
662C2×C4—32no—
663C2×C4—32no—
664C2×C4—32no—
665C2×C4—32no—
666C2×C4—32no—
667C2×C4—32no—
668C2×C4—94no—
669C2×C4—188no—
670C2×C4—188no—
671C2×C4—182no—
672C2×C4—182no—
673C2×C4C4×D3211yescharacteristic
674C2×C4D3×D1211yescharacteristic
675C2×C4D3×D1211yescharacteristic
676C2×C4D3×#6711yescharacteristic
677C2×C4D3×#6711yescharacteristic
678C2×C4C22×D3211yescharacteristic
679C8—22no—
680C8—62no—
681C8—62no—
682C8—182no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—22no—
688C2×C3—21no—
689C2×C3—41no—
690C2×C3—41no—
691C2×C3—62no—
692C2×C3—62no—
693C2×C3—124no—
694C2×C3#474512yescomplemented
695C2×C3#513212yescomplemented
696C2×C3C2×D3×C22⋊C411yescharacteristic
697C2×C3C22×(C2×D3)⋊C411yescharacteristic
698D3—22no—
699D3—22no—
700D3—44no—
701C22—22no—
702C22—32no—
703C22—32no—
704C22—62no—
705C22—62no—
706C22—64no—
707C22—122no—
708C22—122no—
709C22—124no—
710C22—124no—
711C22—124no—
712C22D3×(C2×D3)⋊C411yescharacteristic
713C22D3×(C2×D3)⋊C411yescharacteristic
714C22C2×C4×D3211yescharacteristic
715C4—32no—
716C4—32no—
717C4—184no—
718C4D3×(C2×D3)⋊C411yescharacteristic
719C4D3×(C2×D3)⋊C411yescharacteristic
720C4C2×D3×D1211yescharacteristic
721C4C2×D3×#6711yescharacteristic
722C3—21no—
723C3C2×#474511yescharacteristic, complemented
724C3C2×#513211yescharacteristic, complemented
725C2—21no—
726C2—21no—
727C2—62no—
728C2—62no—
729C2—124no—
730C2#1059100612yesdirect product factor
731C2C2×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radicalC22×#3795C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32C2×#413
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×M16C2semidirect
3. C2×D3×#208C2semidirect
4. C2×#63651C2semidirect
5. C2×C3×#823C2semidirect
6. C2×#63561C2semidirect
7. C2×#63558C2semidirect
8. #10591006C2direct (N × H)
29. C3×D3×M16C22semidirect
34. D3×#208C22semidirect
36. #63651C22semidirect
37. C3×#823C22semidirect
38. #63561C22semidirect
39. #63558C22semidirect
45. C2×D3×M16D3semidirect
55. C2×#823D3semidirect
163. D3×M16C2×D3semidirect
176. #823C2×D3semidirect
522. C2×C32#413semidirect
635. C32C2×#413semidirect
694. C2×C3#4745semidirect
695. C2×C3#5132semidirect
723. C3C2×#4745semidirect
724. C3C2×#5132semidirect
730. C2#10591006direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37952
C2×C3×D3×M162
C2×D3×#2082
C2×#636512
C2×C3×#8232
C2×#635612
C2×#635582
#105910062
C2×#51323
C2×#47453