Finite Group Databasebeta

← C2×#10593968 #11900788

Subgroups — C2×#10593968 #11900788

Order 1152.

3669 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3798C212yesmaximal, complemented
2C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3C2×C3×C4×D12C211yesmaximal, characteristic, complemented
4C2×C3×C42×D3C211yesmaximal, characteristic, complemented
5C2×#63918C211yesmaximal, characteristic, complemented
6C2×#63911C211yesmaximal, characteristic, complemented
7C2×#63909C211yesmaximal, characteristic, complemented
8C2×#63908C211yesmaximal, characteristic, complemented
9C2×#63906C212yesmaximal, complemented
10C2×C4×#626C212yesmaximal, complemented
11C2×#63852C212yesmaximal, complemented
12#10593968C2116yesmaximal, direct product factor
13C2×#5548—31nomaximal
14C2×#5477—31nomaximal
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×C4×C3⋊D3C2212yes—
17C22×C3×D12C2211yescharacteristic
18C22×C3×C4×D3C2212yes—
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×#627C2212yes—
23C22×#626C2212yes—
24C22×#626C2212yes—
25C22×#626C2212yes—
26C22×#625C2212yes—
27C2×#3798—216no—
28C2×#3798C22116yescomplemented
29C2×C32×C42C2211yescharacteristic
30C2×#3752C2212yes—
31C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
32C4×C4⋊(C3⋊D3)C2218yescomplemented
33C2×C3×(C2×D3)⋊C4C2212yes—
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C2×C3×C4×Dic3C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38C3×C4×D12C2218yescomplemented
39C3×C42×D3C2218yescomplemented
40C2×Dic3⋊Dic3C2212yes—
41C2×#3722C2212yes—
42C2×(C2×D3)⋊Dic3C2212yes—
43#63918C2218yescomplemented
44#63911C2218yescomplemented
45#63909C2218yescomplemented
46#63908C2218yescomplemented
47#63906C22116yescomplemented
48C4×#626C22116yescomplemented
49#63852C22116yescomplemented
50C22×#235—32no—
51C22×#235—32no—
52C2×C3×C4×D4—31no—
53C22×C3×C42—31no—
54C2×#940—31no—
55C2×#938—31no—
56C2×#930—31no—
57C2×#930—32no—
58C2×#930—31no—
59C2×C4×#67—32no—
60#5548—316no—
61C2×#895—31no—
62C2×#888—31no—
63C2×#885—32no—
64C2×#884—32no—
65#5477—316no—
66C2×#875—32no—
67C2×#874—31no—
68C2×C4×D12—32no—
69C2×C4×D12—31no—
70C2×C4×D12—31no—
71C2×C4×D12—61no—
72C2×C4×D12D311yescharacteristic, complemented
73C2×C42×D3D311yescharacteristic, complemented
74C2×#869—31no—
75C23×C3⋊D3C2312yes—
76C23×C3×D3C2312yes—
77C23×C3×D3C2311yescharacteristic
78C22×C32×C4C2311yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2311yescharacteristic
81C22×C3⋊Dic3C2312yes—
82C2×C4⋊(C3⋊D3)—24no—
83C2×C4⋊(C3⋊D3)C2314yes—
84C2×C4×C3⋊D3—28no—
85C2×C4×C3⋊D3C2318yes—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2311yescharacteristic
90C2×C3×D12—24no—
91C2×C3×D12C2314yes—
92C2×C3×C4×D3—28no—
93C2×C3×C4×D3—24no—
94C2×C3×C4×D3—24no—
95C2×C3×C4×D3D418yescomplemented
96C2×C3×C4×D3C2318yes—
97C2×C3×C4×D3C2314yes—
98C2×C3×C4×D3C2314yes—
99C2×C3×C4×D3C2314yes—
100C2×#627—28no—
101C2×#627C2318yes—
102C2×#626—28no—
103C2×#626—28no—
104C2×#626—28no—
105C2×#626C2318yes—
106C2×#626C2318yes—
107C2×#626C2318yes—
108C2×#625—28no—
109C2×#625C2318yes—
110#3798—264no—
111C32×C42C2314yes—
112#3752C2318yes—
113C4⋊(C3⋊Dic3)C2314yes—
114C3×(C2×D3)⋊C4C2318yes—
115C3×C4⋊Dic3C2314yes—
116C3×C4×Dic3C2314yes—
117C3×C4×Dic3C2314yes—
118C3×C4×Dic3C2314yes—
119Dic3⋊Dic3C2318yes—
120#3722C2318yes—
121(C2×D3)⋊Dic3C2318yes—
122C2×#532—91noSylow
123C22×C3×D4—31no—
124C23×C3×C4—31no—
125C23×C3×C4—32no—
126C23×C3×C4—31no—
127C23×C3×C4—31no—
128C22×#67—32no—
129C22×#67—32no—
130C22×#67—32no—
131C22×#67—32no—
132C22×#67—32no—
133C2×#235—316no—
134C2×#235—316no—
135C2×#235—616no—
136C2×#235—616no—
137C22×D12—32no—
138C22×D12—32no—
139C22×D12—32no—
140C22×D12—31no—
141C22×D12—31no—
142C22×D12—61no—
143C22×D12C2×D311yescharacteristic
144C22×C4×D3—32no—
145C22×C4×D3—32no—
146C22×C4×D3—62no—
147C22×C4×D3C2×D312yes—
148C22×C4×D3C2×D311yescharacteristic
149C22×C4×D3C2×D311yescharacteristic
150C22×C4×D3C2×D311yescharacteristic
151C22×Dic6—32no—
152C22×Dic6—32no—
153C3×C4×D4—38no—
154C2×C3×C4⋊C4—31no—
155C2×C3×C22⋊C4—32no—
156C2×C3×C42—21no—
157C2×C3×C42—31no—
158C2×C3×C42—31no—
159C2×C3×C42—31no—
160C2×C3×C42—38no—
161C2×C3×C42C2×D311yescharacteristic
162C2×C3×C42C2×D311yescharacteristic
163C2×#217—32no—
164#940—38no—
165#938—38no—
166#930—38no—
167#930—316no—
168#930—38no—
169C4×#67—316no—
170C2×(C2×D3)⋊C4—32no—
171C2×(C2×D3)⋊C4—32no—
172C2×(C2×D3)⋊C4—32no—
173C2×(C2×D3)⋊C4—32no—
174C2×(C2×D3)⋊C4—32no—
175C2×(C2×D3)⋊C4—62no—
176C2×(C2×D3)⋊C4C2×D312yes—
177C2×C4⋊Dic3—31no—
178C2×C4⋊Dic3—31no—
179C2×C4⋊Dic3—32no—
180C2×C4⋊Dic3—61no—
181C2×C4⋊Dic3C2×D311yescharacteristic
182C2×Dic3⋊C4—32no—
183C2×C4×Dic3C2×D311yescharacteristic
184C2×C4×Dic3C2×D311yescharacteristic
185C2×C4×Dic3C2×D311yescharacteristic
186#895—38no—
187#888—38no—
188#885—316no—
189#884—316no—
190#875—316no—
191#874—38no—
192C4×D12—316no—
193C4×D12—38no—
194C4×D12—38no—
195C4×D12—68no—
196C4×D12C2×D318yescomplemented
197C42×D3C2×D318yescomplemented
198#869—38no—
199C23×C32C2411yescharacteristic
200C22×C3⋊D3—24no—
201C22×C3⋊D3—24no—
202C22×C3⋊D3—24no—
203C22×C3⋊D3C2414yes—
204C22×C3×D3—22no—
205C22×C3×D3—22no—
206C22×C3×D3—24no—
207C22×C3×D3—24no—
208C22×C3×D3—24no—
209C22×C3×D3C2×D414yes—
210C22×C3×D3C2414yes—
211C22×C3×D3C2412yes—
212C2×C32×C4—22no—
213C2×C32×C4C2×D414yes—
214C2×C32×C4#4114yescomplemented
215C2×C32×C4C2412yes—
216C2×C32×C4C2412yes—
217C2×C32×C4C2412yes—
218C2×C3⋊Dic3—24no—
219C2×C3⋊Dic3C2414yes—
220C4⋊(C3⋊D3)—28no—
221C4×C3⋊D3—216no—
222C2×C3×Dic3—24no—
223C2×C3×Dic3—22no—
224C2×C3×Dic3C2×D414yes—
225C2×C3×Dic3#4114yescomplemented
226C2×C3×Dic3C2412yes—
227C2×C3×Dic3C2414yes—
228C2×C3×Dic3C2412yes—
229C2×C3×Dic3C2412yes—
230C3×D12—28no—
231C3×C4×D3—216no—
232C3×C4×D3—28no—
233C3×C4×D3—28no—
234C3×C4×D3C2×D4116yescomplemented
235#627—216no—
236#626—216no—
237#626—216no—
238#626—216no—
239#625—216no—
240C22×#41—92no—
241#532—916no—
242C2×C4⋊Q8—91no—
243C2×#127—91no—
244C2×#124—92no—
245C2×#121—92no—
246C2×#121—91no—
247C2×#121—91no—
248C2×C4×D4—31no—
249C2×C4×D4—92no—
250C2×C4×D4—91no—
251C22×C42—31no—
252C24×C3—31no—
253C24×C3—32no—
254C23×D3—32no—
255C23×D3—32no—
256C23×D3—62no—
257C23×D3C22×D312yes—
258C23×D3C22×D311yescharacteristic
259C2×C3×D4—34no—
260C2×C3×D4—64no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—31no—
265C22×C3×C4—31no—
266C22×C3×C4—38no—
267C22×C3×C4—34no—
268C22×C3×C4—32no—
269C22×C3×C4—31no—
270C22×C3×C4—38no—
271C22×C3×C4—34no—
272C22×C3×C4—34no—
273C22×C3×C4—64no—
274C22×C3×C4—68no—
275C22×C3×C4—64no—
276C22×C3×C4C22×D311yescharacteristic
277C22×C3×C4C22×D311yescharacteristic
278C22×C3×C4C22×D311yescharacteristic
279C22×C3×C4C22×D311yescharacteristic
280C22×C3×C4C22×D311yescharacteristic
281C22×C3×C4C22×D311yescharacteristic
282C2×#67—38no—
283C2×#67—38no—
284C2×#67—38no—
285C2×#67—38no—
286C2×#67—38no—
287C2×#67—68no—
288C2×#67—68no—
289C2×#67—68no—
290C2×#67—68no—
291C2×#67—68no—
292C22×Dic3—32no—
293C22×Dic3—32no—
294C22×Dic3—62no—
295C22×Dic3C22×D311yescharacteristic
296C22×Dic3C22×D312yes—
297C22×Dic3C22×D311yescharacteristic
298C22×Dic3C22×D311yescharacteristic
299#235—664no—
300#235—664no—
301C2×D12—24no—
302C2×D12—38no—
303C2×D12—38no—
304C2×D12—38no—
305C2×D12—34no—
306C2×D12—34no—
307C2×D12—64no—
308C2×D12—68no—
309C2×D12—68no—
310C2×D12—68no—
311C2×D12—68no—
312C2×D12—64no—
313C2×D12—64no—
314C2×D12C22×D314yes—
315C2×C4×D3—24no—
316C2×C4×D3—28no—
317C2×C4×D3—24no—
318C2×C4×D3—38no—
319C2×C4×D3—38no—
320C2×C4×D3—68no—
321C2×C4×D3—68no—
322C2×C4×D3—68no—
323C2×C4×D3—128no—
324C2×C4×D3D1218yescomplemented
325C2×C4×D3C22×D314yes—
326C2×C4×D3C22×D314yes—
327C2×C4×D3C22×D318yes—
328C2×C4×D3C22×D314yes—
329C2×Dic6—38no—
330C2×Dic6—38no—
331C2×Dic6—68no—
332C2×Dic6—68no—
333C3×C4⋊C4—34no—
334C3×C22⋊C4—38no—
335C3×C42—24no—
336C3×C42—34no—
337C3×C42—34no—
338C3×C42—34no—
339C3×C42C22×D314yes—
340C3×C42C22×D314yes—
341#217—38no—
342(C2×D3)⋊C4—38no—
343(C2×D3)⋊C4—38no—
344(C2×D3)⋊C4—38no—
345(C2×D3)⋊C4—38no—
346(C2×D3)⋊C4—38no—
347(C2×D3)⋊C4—68no—
348(C2×D3)⋊C4C22×D318yes—
349C4⋊Dic3—34no—
350C4⋊Dic3—34no—
351C4⋊Dic3—38no—
352C4⋊Dic3—64no—
353C4⋊Dic3C22×D314yes—
354Dic3⋊C4—38no—
355C4×Dic3C22×D314yes—
356C4×Dic3C22×D314yes—
357C4×Dic3C22×D314yes—
358C22×C32C22×D412yes—
359C22×C32C2×#4112yes—
360C22×C32C2×#4112yes—
361C22×C32C2511yescharacteristic
362C2×C3⋊D3—24no—
363C2×C3⋊D3—24no—
364C2×C3⋊D3—24no—
365C2×C3⋊D3—48no—
366C2×C3×D3—28no—
367C2×C3×D3—22no—
368C2×C3×D3—22no—
369C2×C3×D3—24no—
370C2×C3×D3—24no—
371C2×C3×D3—24no—
372C2×C3×D3—48no—
373C2×C3×D3C22×D414yes—
374C32×C4—22no—
375C32×C4C22×D414yes—
376C32×C4C2×#4114yescomplemented
377C3⋊Dic3—24no—
378C3×Dic3—24no—
379C3×Dic3—22no—
380C3×Dic3C22×D414yes—
381C3×Dic3C2×#4114yescomplemented
382C2×#41—916no—
383C2×#41—1816no—
384C22×Q8—92no—
385C22×D4—31no—
386C22×D4—92no—
387C22×D4—92no—
388C22×D4—92no—
389C22×D4—92no—
390C22×D4—91no—
391C23×C4—31no—
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—32no—
395C23×C4—92no—
396C4⋊Q8—98no—
397#127—98no—
398#124—916no—
399#121—916no—
400#121—98no—
401#121—98no—
402C4×D4—38no—
403C4×D4—916no—
404C4×D4—98no—
405C2×C4⋊C4—31no—
406C2×C4⋊C4—92no—
407C2×C4⋊C4—91no—
408C2×C22⋊C4—32no—
409C2×C22⋊C4—92no—
410C2×C22⋊C4—92no—
411C2×C22⋊C4—92no—
412C2×C42—31no—
413C2×C42—31no—
414C2×C42—31no—
415C2×C42—38no—
416C2×C42D3211yescharacteristic
417C23×C3—21no—
418C23×C3—34no—
419C23×C3—32no—
420C23×C3—34no—
421C23×C3—62no—
422C23×C3—62no—
423C23×C3—64no—
424C23×C3—64no—
425C23×C3—64no—
426C23×C3C23×D311yescharacteristic
427C23×C3C23×D311yescharacteristic
428C22×D3—22no—
429C22×D3—22no—
430C22×D3—24no—
431C22×D3—24no—
432C22×D3—24no—
433C22×D3—34no—
434C22×D3—34no—
435C22×D3—64no—
436C22×D3—68no—
437C22×D3—64no—
438C22×D3—64no—
439C22×D3—64no—
440C22×D3—64no—
441C22×D3—64no—
442C22×D3—64no—
443C22×D3—124no—
444C22×D3—124no—
445C22×D3C2×D1214yes—
446C22×D3C23×D314yes—
447C22×D3C23×D312yes—
448C3×D4—68no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—24no—
455C2×C3×C4—24no—
456C2×C3×C4—34no—
457C2×C3×C4—34no—
458C2×C3×C4—32no—
459C2×C3×C4—32no—
460C2×C3×C4—316no—
461C2×C3×C4—34no—
462C2×C3×C4—32no—
463C2×C3×C4—42no—
464C2×C3×C4—68no—
465C2×C3×C4—64no—
466C2×C3×C4—62no—
467C2×C3×C4—616no—
468C2×C3×C4—68no—
469C2×C3×C4C2×D1214yes—
470C2×C3×C4#23514yescomplemented
471C2×C3×C4#23514yescomplemented
472C2×C3×C4D3×D414yes—
473C2×C3×C4C23×D312yes—
474C2×C3×C4C23×D312yes—
475C2×C3×C4C23×D312yes—
476C2×C3×C4C23×D312yes—
477C2×C3×C4C23×D312yes—
478C2×C3×C4C23×D312yes—
479#67—616no—
480#67—616no—
481#67—616no—
482#67—616no—
483#67—616no—
484C2×Dic3—22no—
485C2×Dic3—24no—
486C2×Dic3—34no—
487C2×Dic3—34no—
488C2×Dic3—64no—
489C2×Dic3—64no—
490C2×Dic3—64no—
491C2×Dic3—124no—
492C2×Dic3C2×D1214yes—
493C2×Dic3#23514yescomplemented
494C2×Dic3C23×D312yes—
495C2×Dic3C23×D314yes—
496C2×Dic3C23×D312yes—
497C2×Dic3C23×D312yes—
498D12—28no—
499D12—616no—
500D12—616no—
501D12—616no—
502D12—616no—
503D12—68no—
504D12—68no—
505C4×D3—28no—
506C4×D3—216no—
507C4×D3—28no—
508C4×D3—616no—
509C4×D3—616no—
510C4×D3—1216no—
511C4×D3C2×D12116yescomplemented
512Dic6—616no—
513Dic6—616no—
514C2×C32#53214yescomplemented
515C2×C32C23×D411yescharacteristic
516C2×C32C22×#4111yescharacteristic
517C2×C32C22×#4111yescharacteristic
518C3⋊D3—44no—
519C3×D3—24no—
520C3×D3—44no—
521C24—31no—
522C24—32no—
523C24—92no—
524#41—1864no—
525C2×Q8—98no—
526C2×Q8—188no—
527C2×D4—34no—
528C2×D4—64no—
529C2×D4—98no—
530C2×D4—98no—
531C2×D4—98no—
532C2×D4—98no—
533C2×D4—94no—
534C2×D4—188no—
535C2×D4—188no—
536C2×D4—188no—
537C2×D4—188no—
538C2×D4—184no—
539C22×C4—31no—
540C22×C4—31no—
541C22×C4—34no—
542C22×C4—38no—
543C22×C4—31no—
544C22×C4—32no—
545C22×C4—34no—
546C22×C4—34no—
547C22×C4—38no—
548C22×C4—64no—
549C22×C4—64no—
550C22×C4—68no—
551C22×C4—92no—
552C22×C4—98no—
553C22×C4—188no—
554C22×C4C2×D3211yescharacteristic
555C22×C4C2×D3211yescharacteristic
556C22×C4C2×D3211yescharacteristic
557C4⋊C4—34no—
558C4⋊C4—98no—
559C4⋊C4—94no—
560C22⋊C4—38no—
561C22⋊C4—98no—
562C22⋊C4—98no—
563C22⋊C4—98no—
564C42—34no—
565C42—34no—
566C42—34no—
567C42C2×D3214yes—
568C22×C3—22no—
569C22×C3—22no—
570C22×C3—22no—
571C22×C3—21no—
572C22×C3—34no—
573C22×C3—62no—
574C22×C3—62no—
575C22×C3—68no—
576C22×C3—64no—
577C22×C3—64no—
578C22×C3—64no—
579C22×C3—128no—
580C22×C3C22×D1212yes—
581C22×C3C2×#23512yes—
582C22×C3C2×#23512yes—
583C22×C3C2×#23512yes—
584C22×C3C2×D3×D412yes—
585C22×C3D3×#4112yes—
586C22×C3C24×D311yescharacteristic
587C22×C3C24×D311yescharacteristic
588C2×D3—22no—
589C2×D3—22no—
590C2×D3—28no—
591C2×D3—24no—
592C2×D3—24no—
593C2×D3—24no—
594C2×D3—48no—
595C2×D3—68no—
596C2×D3—64no—
597C2×D3—64no—
598C2×D3—64no—
599C2×D3—64no—
600C2×D3—64no—
601C2×D3—64no—
602C2×D3—124no—
603C2×D3—124no—
604C2×D3—1216no—
605C2×D3—128no—
606C2×D3—128no—
607C2×D3C22×D1214yes—
608C3×C4—22no—
609C3×C4—22no—
610C3×C4—24no—
611C3×C4—24no—
612C3×C4—34no—
613C3×C4—34no—
614C3×C4—42no—
615C3×C4—64no—
616C3×C4—62no—
617C3×C4C22×D1214yes—
618C3×C4C2×#23514yescomplemented
619C3×C4C2×#23514yescomplemented
620C3×C4C2×D3×D414yes—
621Dic3—22no—
622Dic3—24no—
623Dic3—64no—
624Dic3—64no—
625Dic3—124no—
626Dic3C22×D1214yes—
627Dic3C2×#23514yescomplemented
628C32C2×#53211yescharacteristic, complemented, Sylow
629C23—34no—
630C23—32no—
631C23—34no—
632C23—62no—
633C23—62no—
634C23—64no—
635C23—64no—
636C23—64no—
637C23—94no—
638C23—184no—
639C23—184no—
640C23—184no—
641C23C22×D3211yescharacteristic
642Q8—1816no—
643D4—68no—
644D4—1816no—
645D4—1816no—
646D4—1816no—
647D4—1816no—
648D4—188no—
649C2×C4—22no—
650C2×C4—34no—
651C2×C4—34no—
652C2×C4—32no—
653C2×C4—32no—
654C2×C4—316no—
655C2×C4—32no—
656C2×C4—34no—
657C2×C4—68no—
658C2×C4—62no—
659C2×C4—64no—
660C2×C4—68no—
661C2×C4—616no—
662C2×C4—94no—
663C2×C4—184no—
664C2×C4—1816no—
665C2×C4#379814yescomplemented
666C2×C4D3×D1214yes—
667C2×C4C22×D3212yes—
668C2×C4C22×D3212yes—
669C2×C4C22×D3212yes—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—24no—
674C2×C3—64no—
675C2×C3—124no—
676C2×C3#547714yescomplemented
677C2×C3#554814yescomplemented
678C2×C3C23×D1211yescharacteristic
679C2×C3C22×#23511yescharacteristic
680C2×C3C22×#23511yescharacteristic
681C2×C3C22×#23511yescharacteristic
682C2×C3C22×D3×D411yescharacteristic
683C2×C3C2×D3×#4111yescharacteristic
684D3—24no—
685D3—44no—
686D3—128no—
687D3—124no—
688D3—124no—
689C22—34no—
690C22—62no—
691C22—62no—
692C22—68no—
693C22—64no—
694C22—64no—
695C22—64no—
696C22—128no—
697C22—184no—
698C22—184no—
699C22—184no—
700C22—368no—
701C22C2×#379812yes—
702C22C2×D3×D1212yes—
703C22D3×#23512yes—
704C22C23×D3211yescharacteristic
705C4—22no—
706C4—34no—
707C4—34no—
708C4—62no—
709C4—64no—
710C4—184no—
711C4C2×#379814yescomplemented
712C4C2×D3×D1214yes—
713C3—21no—
714C3C2×#547711yescharacteristic, complemented
715C3C2×#554811yescharacteristic, complemented
716C2—64no—
717C2—124no—
718C2—364no—
719C2#1059396814yesdirect product factor
720C2C22×#379811yescharacteristic
721C2C22×D3×D1211yescharacteristic
722C2C2×D3×#23511yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C22×#3798C2semidirect
2. C2×C4×C4⋊(C3⋊D3)C2semidirect
3. C2×C3×C4×D12C2semidirect
4. C2×C3×C42×D3C2semidirect
5. C2×#63918C2semidirect
6. C2×#63911C2semidirect
7. C2×#63909C2semidirect
8. C2×#63908C2semidirect
9. C2×#63906C2semidirect
10. C2×C4×#626C2semidirect
11. C2×#63852C2semidirect
12. #10593968C2direct (N × H)
28. C2×#3798C22semidirect
32. C4×C4⋊(C3⋊D3)C22semidirect
38. C3×C4×D12C22semidirect
39. C3×C42×D3C22semidirect
43. #63918C22semidirect
44. #63911C22semidirect
45. #63909C22semidirect
46. #63908C22semidirect
47. #63906C22semidirect
48. C4×#626C22semidirect
49. #63852C22semidirect
72. C2×C4×D12D3semidirect
73. C2×C42×D3D3semidirect
95. C2×C3×C4×D3D4semidirect
196. C4×D12C2×D3semidirect
197. C42×D3C2×D3semidirect
214. C2×C32×C4#41semidirect
225. C2×C3×Dic3#41semidirect
234. C3×C4×D3C2×D4semidirect
324. C2×C4×D3D12semidirect
376. C32×C4C2×#41semidirect
381. C3×Dic3C2×#41semidirect
470. C2×C3×C4#235semidirect
471. C2×C3×C4#235semidirect
493. C2×Dic3#235semidirect
511. C4×D3C2×D12semidirect
514. C2×C32#532semidirect
618. C3×C4C2×#235semidirect
619. C3×C4C2×#235semidirect
627. Dic3C2×#235semidirect
628. C32C2×#532semidirect
665. C2×C4#3798semidirect
676. C2×C3#5477semidirect
677. C2×C3#5548semidirect
711. C4C2×#3798semidirect
714. C3C2×#5477semidirect
715. C3C2×#5548semidirect
719. C2#10593968direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37982
C2×C4×C4⋊(C3⋊D3)2
C2×C3×C4×D122
C2×C3×C42×D32
C2×#639182
C2×#639112
C2×#639092
C2×#639082
C2×#639062
C2×C4×#6262
C2×#638522
#105939682
C2×#55483
C2×#54773