Finite Group Databasebeta

← C2×#10591111 #11858162

Subgroups — C2×#10591111 #11858162

Order 1152.

1693 conjugacy classes of subgroups.

The subgroup lattice has 679 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic
2C22×#3748C211yesmaximal, characteristic, complemented
3C2×C3×#926C211yesmaximal, characteristic, complemented
4#10591111C218yesmaximal, direct product factor
5C2×#63569C214yesmaximal, complemented
6C2×#5236—31nomaximal
7C2×#5005—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C22×C3×#67—21no—
10C2×C3×#235—21no—
11C2×C3×#235—22no—
12C2×C3×#235—21no—
13C2×C3×#235—22no—
14C2×C3×#235C412yescomplemented
15C2×C3×#235C414yescomplemented
16C2×C3×#235C2212yes—
17C2×C3×#235C2214yes—
18C22×C3×D12C411yescharacteristic, complemented
19C22×C3×C4×D3—21no—
20C22×C3×Dic6C411yescharacteristic, complemented
21C2×#3748—21no—
22C2×#3748—22no—
23C2×#3748C2212yescomplemented
24C2×#3748C2214yescomplemented
25C22×C3⋊(C3⋊C8)—21no—
26C2×C3×#217—21no—
27C3×#926—22no—
28C3×#926C2214yescomplemented
29C2×C3×C4⋊Dic3—21no—
30C2×C3×C4×Dic3C2212yescomplemented
31#63569C22116yescomplemented
32C22×C3×#41—31no—
33C22×#235D311yescharacteristic
34C2×C3×#117—31no—
35C2×#926D311yescharacteristic, complemented
36C22×#208—31no—
37C22×#208—31no—
38C22×#208—61no—
39#5236—38no—
40C2×#837—34no—
41#5005—38no—
42C2×#805—34no—
43C24×C32D411yescharacteristic
44C23×C3×D3—21no—
45C22×C32×C4C2×C411yescharacteristic
46C22×C32×C4C2×C411yescharacteristic
47C22×C32×C4C2×C412yes—
48C22×C32×C4D411yescharacteristic
49C22×C32×C4D412yes—
50C22×C32×C4D411yescharacteristic
51C22×C32×C4D411yescharacteristic
52C22×C32×C4D412yes—
53C22×C32×C4C2311yescharacteristic
54C22×C32×C4C2312yes—
55C2×C3×#67—22no—
56C2×C3×#67—24no—
57C2×C3×#67—22no—
58C2×C3×#67—24no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3—22no—
61C3×#235—24no—
62C3×#235—24no—
63C3×#235—24no—
64C3×#235—22no—
65C3×#235—22no—
66C3×#235—24no—
67C3×#235—24no—
68C3×#235C2×C414yes—
69C3×#235C2×C418yescomplemented
70C3×#235C2314yes—
71C2×C3×D12—22no—
72C2×C3×D12—21no—
73C2×C3×D12C2×C412yes—
74C2×C3×D12C2×C414yescomplemented
75C2×C3×C4×D3—24no—
76C2×C3×C4×D3—22no—
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3—24no—
79C2×C3×Dic6—22no—
80C2×C3×Dic6—21no—
81C2×C3×Dic6C2×C412yes—
82C2×C3×Dic6C2×C414yescomplemented
83#3748—24no—
84#3748—22no—
85#3748C2314yescomplemented
86C2×C3⋊(C3⋊C8)—22no—
87C2×C3⋊(C3⋊C8)—24no—
88C3×#217—24no—
89C3×C4⋊Dic3—24no—
90C3×C4×Dic3—22no—
91C3×C4×Dic3C2314yescomplemented
92C2×#421—91noSylow
93C2×C3×#41—32no—
94C2×C3×#41—34no—
95C2×C3×#41—32no—
96C2×C3×#41—34no—
97C2×C3×#41—61no—
98C2×C3×#41—62no—
99C2×C3×#41—61no—
100C2×C3×#41—62no—
101C22×C3×Q8—31no—
102C22×C3×D4—31no—
103C22×C3×D4—61no—
104C23×C3×C4—21no—
105C23×C3×C4—61no—
106C23×C3×C4C2×D311yescharacteristic
107C23×C3×C4C2×D311yescharacteristic
108C22×#67—21no—
109C2×#235—21no—
110C2×#235—22no—
111C2×#235—21no—
112C2×#235—22no—
113C2×#235Dic312yescomplemented
114C2×#235Dic314yescomplemented
115C2×#235C2×D312yes—
116C2×#235C2×D314yes—
117C22×D12Dic311yescharacteristic, complemented
118C22×C4×D3—21no—
119C22×Dic6Dic311yescharacteristic, complemented
120C3×#117—34no—
121C3×#117—62no—
122C2×C3×C4⋊C4—61no—
123C2×C3×C22⋊C4—61no—
124C2×C3×C42—32no—
125C2×#217—21no—
126#926—22no—
127#926C2×D314yescomplemented
128C2×C4⋊Dic3—21no—
129C2×C4×Dic3C2×D312yescomplemented
130C2×#208—32no—
131C2×#208—32no—
132C2×#208—34no—
133C2×#208—34no—
134C2×#208—62no—
135C2×#208—64no—
136C2×#208—64no—
137C2×#208—62no—
138C2×#208—61no—
139C2×#208—62no—
140C2×#208—61no—
141C2×#208—62no—
142C22×C3⋊C8—62no—
143C22×C3⋊C8—61no—
144C22×C3⋊C8—61no—
145#837—316no—
146#805—316no—
147C23×C32—42no—
148C23×C32C22⋊C411yescharacteristic
149C23×C32C22⋊C411yescharacteristic
150C23×C32C22⋊C412yes—
151C23×C32C2×D411yescharacteristic
152C23×C32C2×D412yes—
153C22×C3×D3—22no—
154C22×C3×D3—24no—
155C22×C3×D3—44no—
156C2×C32×C4C22⋊C412yes—
157C2×C32×C4C22⋊C411yescharacteristic
158C2×C32×C4C22⋊C412yes—
159C2×C32×C4C22⋊C411yescharacteristic
160C2×C32×C4C22⋊C412yes—
161C2×C32×C4C22⋊C412yes—
162C2×C32×C4C22⋊C412yes—
163C2×C32×C4C22×C411yescharacteristic
164C2×C32×C4C22×C412yes—
165C2×C32×C4C22×C411yescharacteristic
166C2×C32×C4C22×C412yes—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D412yes—
169C2×C32×C4C2×D412yes—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D412yes—
173C2×C32×C4C2411yescharacteristic
174C3×#67—24no—
175C3×#67—28no—
176C3×#67—24no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—24no—
179C2×C3×Dic3—24no—
180C2×C3×Dic3—44no—
181C3×D12—22no—
182C3×D12—24no—
183C3×D12C22×C414yes—
184C3×C4×D3—24no—
185C3×C4×D3—28no—
186C3×C4×D3—24no—
187C3×Dic6—22no—
188C3×Dic6—24no—
189C3×Dic6C22×C414yes—
190C3⋊(C3⋊C8)—24no—
191C22×#41—31no—
192C22×M16—91no—
193C2×#117—31no—
194#421—98no—
195C2×#104—94no—
196C24×C3—21no—
197C24×C3—61no—
198C24×C3#6711yescharacteristic
199C24×C3#6711yescharacteristic
200C23×D3—21no—
201C3×#41—34no—
202C3×#41—38no—
203C3×#41—34no—
204C3×#41—64no—
205C3×#41—64no—
206C3×#41—64no—
207C3×#41—64no—
208C3×#41—62no—
209C3×#41—62no—
210C3×#41—64no—
211C2×C3×Q8—32no—
212C2×C3×Q8—34no—
213C2×C3×Q8—62no—
214C2×C3×Q8—61no—
215C2×C3×D4—32no—
216C2×C3×D4—34no—
217C2×C3×D4—62no—
218C2×C3×D4—64no—
219C2×C3×D4—62no—
220C2×C3×D4—64no—
221C2×C3×D4—62no—
222C2×C3×D4—61no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—22no—
226C22×C3×C4—21no—
227C22×C3×C4—22no—
228C22×C3×C4—21no—
229C22×C3×C4—22no—
230C22×C3×C4—21no—
231C22×C3×C4—22no—
232C22×C3×C4—21no—
233C22×C3×C4—61no—
234C22×C3×C4—64no—
235C22×C3×C4—62no—
236C22×C3×C4—64no—
237C22×C3×C4—62no—
238C22×C3×C4—62no—
239C22×C3×C4C4×D311yescharacteristic
240C22×C3×C4C4×D311yescharacteristic
241C22×C3×C4C4×D312yes—
242C22×C3×C4D1211yescharacteristic
243C22×C3×C4D1211yescharacteristic
244C22×C3×C4D1212yes—
245C22×C3×C4C2×Dic311yescharacteristic
246C22×C3×C4C2×Dic311yescharacteristic
247C22×C3×C4C2×Dic312yes—
248C22×C3×C4#6711yescharacteristic
249C22×C3×C4#6712yes—
250C22×C3×C4#6711yescharacteristic
251C22×C3×C4#6712yes—
252C22×C3×C4#6711yescharacteristic
253C22×C3×C4#6711yescharacteristic
254C22×C3×C4#6712yes—
255C22×C3×C4C22×D311yescharacteristic
256C22×C3×C4C22×D312yes—
257C22×C3×C4C22×D311yescharacteristic
258C22×C3×C4C22×D312yes—
259C2×#67—22no—
260C2×#67—24no—
261C2×#67—22no—
262C2×#67—24no—
263C22×Dic3—21no—
264C22×Dic3—22no—
265#235—24no—
266#235—24no—
267#235—24no—
268#235—22no—
269#235—24no—
270#235—22no—
271#235—24no—
272#235C2×Dic314yes—
273#235C2×Dic318yescomplemented
274#235C22×D314yes—
275C2×D12—22no—
276C2×D12—21no—
277C2×D12C2×Dic312yes—
278C2×D12C2×Dic314yescomplemented
279C2×C4×D3—24no—
280C2×C4×D3—22no—
281C2×C4×D3—24no—
282C2×C4×D3—22no—
283C2×Dic6—22no—
284C2×Dic6—21no—
285C2×Dic6C2×Dic312yes—
286C2×Dic6C2×Dic314yescomplemented
287C3×C4⋊C4—64no—
288C3×C22⋊C4—64no—
289C3×C42—34no—
290C3×C42—62no—
291#217—24no—
292C4⋊Dic3—24no—
293C4×Dic3—22no—
294C4×Dic3C22×D314yescomplemented
295#208—34no—
296#208—34no—
297#208—64no—
298#208—68no—
299#208—64no—
300#208—64no—
301#208—62no—
302#208—64no—
303#208—62no—
304C2×C3⋊C8—68no—
305C2×C3⋊C8—64no—
306C2×C3⋊C8—64no—
307C2×C3⋊C8—62no—
308C2×C3⋊C8—64no—
309C2×C3⋊C8—62no—
310C22×C32—22no—
311C22×C32—22no—
312C22×C32—22no—
313C22×C32—42no—
314C22×C32—42no—
315C22×C32C2×C22⋊C412yes—
316C22×C32C2×C22⋊C412yes—
317C22×C32C2×C22⋊C411yescharacteristic
318C22×C32C2×C22⋊C411yescharacteristic
319C22×C32C22×D411yescharacteristic
320C2×C3×D3—24no—
321C2×C3×D3—48no—
322C2×C3×D3—44no—
323C32×C4C2×C22⋊C411yescharacteristic
324C32×C4C2×C22⋊C412yes—
325C32×C4C2×C22⋊C411yescharacteristic
326C32×C4C2×C22⋊C412yes—
327C32×C4C23×C411yescharacteristic
328C32×C4C22×D411yescharacteristic
329C3×Dic3—24no—
330C3×Dic3—44no—
331C2×#41—32no—
332C2×#41—34no—
333C2×#41—32no—
334C2×#41—34no—
335C2×#41—61no—
336C2×#41—62no—
337C2×#41—62no—
338C2×#41—61no—
339C22×Q8—31no—
340C22×D4—31no—
341C22×D4—61no—
342C23×C4—61no—
343C23×C4D3211yescharacteristic
344C2×M16—92no—
345C2×M16—94no—
346C2×M16—182no—
347C2×M16—181no—
348C22×C8—181no—
349#117—34no—
350#117—62no—
351C2×C4⋊C4—61no—
352C2×C22⋊C4—61no—
353C2×C42—32no—
354#104—916no—
355C23×C3—21no—
356C23×C3—21no—
357C23×C3—22no—
358C23×C3—21no—
359C23×C3—22no—
360C23×C3—42no—
361C23×C3—42no—
362C23×C3—44no—
363C23×C3—64no—
364C23×C3—62no—
365C23×C3—124no—
366C23×C3(C2×D3)⋊C411yescharacteristic
367C23×C3(C2×D3)⋊C411yescharacteristic
368C23×C3(C2×D3)⋊C412yes—
369C23×C3#21711yescharacteristic
370C23×C3#21711yescharacteristic
371C23×C3#21712yes—
372C23×C3C2×#6711yescharacteristic
373C23×C3C2×#6711yescharacteristic
374C23×C3C2×#6712yes—
375C23×C3C2×#6712yes—
376C22×D3—22no—
377C22×D3—24no—
378C22×D3—44no—
379C3×Q8—34no—
380C3×Q8—62no—
381C3×Q8—64no—
382C3×D4—34no—
383C3×D4—64no—
384C3×D4—68no—
385C3×D4—64no—
386C3×D4—62no—
387C3×D4—64no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—22no—
391C2×C3×C4—21no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—21no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—64no—
407C2×C3×C4—62no—
408C2×C3×C4—64no—
409C2×C3×C4—68no—
410C2×C3×C4—64no—
411C2×C3×C4—64no—
412C2×C3×C4—124no—
413C2×C3×C4(C2×D3)⋊C412yes—
414C2×C3×C4(C2×D3)⋊C411yescharacteristic
415C2×C3×C4(C2×D3)⋊C412yes—
416C2×C3×C4(C2×D3)⋊C411yescharacteristic
417C2×C3×C4(C2×D3)⋊C412yes—
418C2×C3×C4(C2×D3)⋊C412yes—
419C2×C3×C4(C2×D3)⋊C412yes—
420C2×C3×C4#21712yes—
421C2×C3×C4#21711yescharacteristic
422C2×C3×C4#21712yes—
423C2×C3×C4#21711yescharacteristic
424C2×C3×C4#21712yes—
425C2×C3×C4#21712yes—
426C2×C3×C4#21712yes—
427C2×C3×C4C2×C4×D312yes—
428C2×C3×C4C2×C4×D311yescharacteristic
429C2×C3×C4C2×C4×D311yescharacteristic
430C2×C3×C4C2×C4×D312yes—
431C2×C3×C4C2×D1212yes—
432C2×C3×C4C2×D1212yes—
433C2×C3×C4C2×D1211yescharacteristic
434C2×C3×C4C2×D1211yescharacteristic
435C2×C3×C4C22×Dic311yescharacteristic
436C2×C3×C4C22×Dic312yes—
437C2×C3×C4C22×Dic311yescharacteristic
438C2×C3×C4C22×Dic312yes—
439C2×C3×C4C2×#6711yescharacteristic
440C2×C3×C4C2×#6712yes—
441C2×C3×C4C2×#6711yescharacteristic
442C2×C3×C4C2×#6712yes—
443C2×C3×C4C2×#6712yes—
444C2×C3×C4C2×#6712yes—
445C2×C3×C4C2×#6711yescharacteristic
446C2×C3×C4C2×#6711yescharacteristic
447C2×C3×C4C23×D311yescharacteristic
448C2×C3×C4C23×D311yescharacteristic
449#67—24no—
450#67—28no—
451#67—24no—
452C2×Dic3—22no—
453C2×Dic3—24no—
454C2×Dic3—24no—
455C2×Dic3—44no—
456D12—22no—
457D12—24no—
458D12C22×Dic314yes—
459C4×D3—24no—
460C4×D3—28no—
461C4×D3—24no—
462Dic6—22no—
463Dic6—24no—
464Dic6C22×Dic314yes—
465C3⋊C8—68no—
466C3⋊C8—64no—
467C3⋊C8—64no—
468C2×C32—22no—
469C2×C32—21no—
470C2×C32—22no—
471C2×C32—21no—
472C2×C32#42112yescomplemented
473C2×C32C22×C22⋊C411yescharacteristic
474C3×D3—44no—
475C24—61no—
476C24#62511yescharacteristic
477#41—34no—
478#41—34no—
479#41—38no—
480#41—64no—
481#41—64no—
482#41—64no—
483#41—62no—
484#41—64no—
485#41—64no—
486#41—62no—
487C2×Q8—32no—
488C2×Q8—34no—
489C2×Q8—62no—
490C2×Q8—61no—
491C2×D4—32no—
492C2×D4—34no—
493C2×D4—62no—
494C2×D4—64no—
495C2×D4—62no—
496C2×D4—64no—
497C2×D4—62no—
498C2×D4—61no—
499C22×C4—61no—
500C22×C4—64no—
501C22×C4—62no—
502C22×C4—64no—
503C22×C4—62no—
504C22×C4—62no—
505C22×C4D3×Dic311yescharacteristic
506C22×C4D3×Dic311yescharacteristic
507C22×C4D3×Dic312yes—
508C22×C4#62511yescharacteristic
509C22×C4#62512yes—
510C22×C4#62612yes—
511C22×C4#62611yescharacteristic
512C22×C4#62611yescharacteristic
513C22×C4C2×D3212yes—
514C22×C4C2×D3211yescharacteristic
515M16—94no—
516M16—184no—
517M16—182no—
518C2×C8—184no—
519C2×C8—182no—
520C4⋊C4—64no—
521C22⋊C4—64no—
522C42—34no—
523C42—62no—
524C22×C3—24no—
525C22×C3—22no—
526C22×C3—22no—
527C22×C3—22no—
528C22×C3—22no—
529C22×C3—22no—
530C22×C3—22no—
531C22×C3—21no—
532C22×C3—22no—
533C22×C3—21no—
534C22×C3—22no—
535C22×C3—21no—
536C22×C3—42no—
537C22×C3—42no—
538C22×C3—42no—
539C22×C3—42no—
540C22×C3—42no—
541C22×C3—42no—
542C22×C3—44no—
543C22×C3—44no—
544C22×C3—64no—
545C22×C3—128no—
546C22×C3—124no—
547C22×C3C2×(C2×D3)⋊C412yes—
548C22×C3C2×(C2×D3)⋊C412yes—
549C22×C3C2×(C2×D3)⋊C411yescharacteristic
550C22×C3C2×(C2×D3)⋊C411yescharacteristic
551C22×C3C2×#21712yes—
552C22×C3C2×#21711yescharacteristic
553C22×C3C2×#21712yes—
554C22×C3C2×#21711yescharacteristic
555C22×C3C22×#6711yescharacteristic
556C22×C3C22×#6711yescharacteristic
557C2×D3—24no—
558C2×D3—48no—
559C2×D3—44no—
560C3×C4—21no—
561C3×C4—21no—
562C3×C4—22no—
563C3×C4—21no—
564C3×C4—22no—
565C3×C4—21no—
566C3×C4—64no—
567C3×C4—124no—
568C3×C4C2×(C2×D3)⋊C412yes—
569C3×C4C2×(C2×D3)⋊C411yescharacteristic
570C3×C4C2×(C2×D3)⋊C412yes—
571C3×C4C2×(C2×D3)⋊C411yescharacteristic
572C3×C4C2×#21711yescharacteristic
573C3×C4C2×#21712yes—
574C3×C4C2×#21712yes—
575C3×C4C2×#21711yescharacteristic
576C3×C4C22×C4×D311yescharacteristic
577C3×C4C22×D1211yescharacteristic
578C3×C4C23×Dic311yescharacteristic
579C3×C4C22×#6711yescharacteristic
580Dic3—24no—
581Dic3—44no—
582C32C2×#42111yescharacteristic, complemented, Sylow
583C23—42no—
584C23—64no—
585C23—62no—
586C23—124no—
587C23(C2×D3)⋊Dic311yescharacteristic
588C23(C2×D3)⋊Dic311yescharacteristic
589C23(C2×D3)⋊Dic312yes—
590C23C2×#62511yescharacteristic
591C23C2×#62512yes—
592Q8—34no—
593Q8—62no—
594Q8—64no—
595D4—34no—
596D4—64no—
597D4—64no—
598D4—68no—
599D4—62no—
600D4—64no—
601C2×C4—64no—
602C2×C4—62no—
603C2×C4—64no—
604C2×C4—68no—
605C2×C4—64no—
606C2×C4—64no—
607C2×C4—124no—
608C2×C4(C2×D3)⋊Dic311yescharacteristic
609C2×C4(C2×D3)⋊Dic312yes—
610C2×C4(C2×D3)⋊Dic312yes—
611C2×C4(C2×D3)⋊Dic311yescharacteristic
612C2×C4(C2×D3)⋊Dic312yes—
613C2×C4(C2×D3)⋊Dic312yes—
614C2×C4(C2×D3)⋊Dic312yes—
615C2×C4C2×D3×Dic312yes—
616C2×C4C2×D3×Dic311yescharacteristic
617C2×C4C2×D3×Dic312yes—
618C2×C4C2×D3×Dic311yescharacteristic
619C2×C4C2×#62511yescharacteristic
620C2×C4C2×#62512yes—
621C2×C4C2×#62612yes—
622C2×C4C2×#62612yes—
623C2×C4C2×#62611yescharacteristic
624C2×C4C2×#62611yescharacteristic
625C2×C4C22×D3211yescharacteristic
626C8—184no—
627C2×C3—24no—
628C2×C3—21no—
629C2×C3—22no—
630C2×C3—22no—
631C2×C3—21no—
632C2×C3—21no—
633C2×C3—22no—
634C2×C3—22no—
635C2×C3—21no—
636C2×C3—22no—
637C2×C3—21no—
638C2×C3—41no—
639C2×C3—42no—
640C2×C3—41no—
641C2×C3—124no—
642C2×C3#500512yescomplemented
643C2×C3#523612yescomplemented
644C2×C3C22×(C2×D3)⋊C411yescharacteristic
645C2×C3C22×#21711yescharacteristic
646D3—44no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—42no—
651C22—42no—
652C22—64no—
653C22—128no—
654C22—124no—
655C22C2×(C2×D3)⋊Dic312yes—
656C22C2×(C2×D3)⋊Dic312yes—
657C22C2×(C2×D3)⋊Dic311yescharacteristic
658C22C2×(C2×D3)⋊Dic311yescharacteristic
659C22C22×#62511yescharacteristic
660C4—64no—
661C4—124no—
662C4C2×(C2×D3)⋊Dic312yes—
663C4C2×(C2×D3)⋊Dic311yescharacteristic
664C4C2×(C2×D3)⋊Dic311yescharacteristic
665C4C2×(C2×D3)⋊Dic312yes—
666C4C22×D3×Dic311yescharacteristic
667C4C22×#62611yescharacteristic
668C3—21no—
669C3C2×#500511yescharacteristic, complemented
670C3C2×#523611yescharacteristic, complemented
671C2—21no—
672C2—22no—
673C2—22no—
674C2—21no—
675C2—124no—
676C2#1059111112yesdirect product factor
677C2C22×(C2×D3)⋊Dic311yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×#235C2
cosocleC2×C32×C4C24
hypercenterC23×C4D32
hypocenterC32C2×#421
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×#3748C2semidirect
3. C2×C3×#926C2semidirect
4. #10591111C2direct (N × H)
5. C2×#63569C2semidirect
14. C2×C3×#235C4semidirect
15. C2×C3×#235C4semidirect
18. C22×C3×D12C4semidirect
20. C22×C3×Dic6C4semidirect
23. C2×#3748C22semidirect
24. C2×#3748C22semidirect
28. C3×#926C22semidirect
30. C2×C3×C4×Dic3C22semidirect
31. #63569C22semidirect
35. C2×#926D3semidirect
69. C3×#235C2×C4semidirect
74. C2×C3×D12C2×C4semidirect
82. C2×C3×Dic6C2×C4semidirect
85. #3748C23semidirect
91. C3×C4×Dic3C23semidirect
113. C2×#235Dic3semidirect
114. C2×#235Dic3semidirect
117. C22×D12Dic3semidirect
119. C22×Dic6Dic3semidirect
127. #926C2×D3semidirect
129. C2×C4×Dic3C2×D3semidirect
273. #235C2×Dic3semidirect
278. C2×D12C2×Dic3semidirect
286. C2×Dic6C2×Dic3semidirect
294. C4×Dic3C22×D3semidirect
472. C2×C32#421semidirect
582. C32C2×#421semidirect
642. C2×C3#5005semidirect
643. C2×C3#5236semidirect
669. C3C2×#5005semidirect
670. C3C2×#5236semidirect
676. C2#10591111direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C22×#37482
C2×C3×#9262
#105911112
C2×#635692
C2×#52363
C2×#50053