Finite Group Databasebeta

← C2×#10596031 #11901256

Subgroups — C2×#10596031 #11901256

Order 1152.

4008 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2C2×#64148C211yesmaximal, characteristic, complemented
3C2×#64146C211yesmaximal, characteristic, complemented
4C2×#64139C211yesmaximal, characteristic, complemented
5C2×#64138C211yesmaximal, characteristic, complemented
6C2×C4×#638C211yesmaximal, characteristic, complemented
7C22×#3752C211yesmaximal, characteristic, complemented
8#10596031C2116yesmaximal, direct product factor
9C2×#64107C211yesmaximal, characteristic, complemented
10C2×#64103C211yesmaximal, characteristic, complemented
11C2×#64094C211yesmaximal, characteristic, complemented
12C2×#64093C211yesmaximal, characteristic, complemented
13C2×#64091C211yesmaximal, characteristic, complemented
14C2×#64087C211yesmaximal, characteristic, complemented
15C2×#64085C211yesmaximal, characteristic, complemented
16C2×#64084C211yesmaximal, characteristic, complemented
17C2×#5560—34nomaximal
18C24×C3⋊D3C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C23×C32×C4C2211yescharacteristic
21C23×C32×C4C2211yescharacteristic, complemented
22C22×#638C2211yescharacteristic
23C22×#638C2211yescharacteristic
24C22×#638C2211yescharacteristic
25C22×#638C2211yescharacteristic, complemented
26C23×C3⋊Dic3C2211yescharacteristic
27C22×C4⋊(C3⋊D3)C2211yescharacteristic
28C22×C4⋊(C3⋊D3)C2211yescharacteristic
29C22×C4×C3⋊D3C2211yescharacteristic, complemented
30C22×#634C2211yescharacteristic, complemented
31C32×C4×D4C2218yescomplemented
32C2×C32×C4⋊C4C2211yescharacteristic, complemented
33C2×C32×C22⋊C4C2211yescharacteristic
34C2×C32×C22⋊C4C2211yescharacteristic, complemented
35C2×C32×C42C2211yescharacteristic, complemented
36C2×#3757C2211yescharacteristic
37C2×#3757C2211yescharacteristic, complemented
38#64148C2218yescomplemented
39#64146C2218yescomplemented
40#64139C2218yescomplemented
41#64138C2218yescomplemented
42C4×#638C2218yescomplemented
43C2×#3752C2211yescharacteristic
44C2×#3752C2211yescharacteristic
45C2×#3752C2211yescharacteristic
46C2×#3752C2211yescharacteristic
47C2×#3752C2211yescharacteristic
48C2×#3752C2211yescharacteristic
49C2×#3752C2211yescharacteristic
50C2×#3752C2211yescharacteristic
51C2×#3752C2218yescomplemented
52C2×#3752C2211yescharacteristic, complemented
53C2×#3752C2211yescharacteristic, complemented
54C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
55C2×#3750C2211yescharacteristic, complemented
56C2×#3750C2211yescharacteristic, complemented
57C2×#3750C2211yescharacteristic, complemented
58C2×#3750C2211yescharacteristic, complemented
59C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
60#64107C2218yescomplemented
61#64103C2218yescomplemented
62#64094C2218yescomplemented
63#64093C2218yescomplemented
64#64091C2218yescomplemented
65#64087C2218yescomplemented
66#64085C2218yescomplemented
67#64084C2218yescomplemented
68C2×C3×C4×D4D314yescomplemented
69C2×#939—34no—
70C2×#937—34no—
71C2×#930—34no—
72C2×#929—34no—
73C2×C4×#67—34no—
74C22×(C2×D3)⋊C4—34no—
75#5560—364no—
76C2×#898—34no—
77C2×#894—34no—
78C2×#885—34no—
79C2×#884—34no—
80C2×#882—34no—
81C2×#878—34no—
82C2×#876—34no—
83C2×#875—34no—
84C24×C32C2311yescharacteristic
85C24×C32C2311yescharacteristic
86C23×C3⋊D3—24no—
87C23×C3⋊D3—42no—
88C23×C3⋊D3—42no—
89C23×C3⋊D3C2311yescharacteristic
90C23×C3⋊D3C2311yescharacteristic
91C23×C3⋊D3C2311yescharacteristic
92C23×C3⋊D3C2314yes—
93C2×C32×D4—24no—
94C2×C32×D4C2314yes—
95C22×C32×C4—42no—
96C22×C32×C4—42no—
97C22×C32×C4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C22×C32×C4C2314yes—
103C22×C32×C4C2314yescomplemented
104C2×#638—24no—
105C2×#638—42no—
106C2×#638—42no—
107C2×#638—42no—
108C2×#638C2314yes—
109C2×#638C2314yes—
110C2×#638C2314yes—
111C2×#638C2314yescomplemented
112C22×C3⋊Dic3—42no—
113C22×C3⋊Dic3C2311yescharacteristic
114C22×C3⋊Dic3C2311yescharacteristic
115C22×C3⋊Dic3C2311yescharacteristic
116C22×C3⋊Dic3C2311yescharacteristic
117C22×C3⋊Dic3C2311yescharacteristic
118C22×C3⋊Dic3C2314yes—
119C2×C4⋊(C3⋊D3)—42no—
120C2×C4⋊(C3⋊D3)—42no—
121C2×C4⋊(C3⋊D3)C2314yes—
122C2×C4⋊(C3⋊D3)C2314yes—
123C2×C4×C3⋊D3—42no—
124C2×C4×C3⋊D3C2314yescomplemented
125C2×#634—42no—
126C2×#634C2314yescomplemented
127C32×C4⋊C4C2314yescomplemented
128C32×C22⋊C4C2314yes—
129C32×C22⋊C4C2314yescomplemented
130C32×C42C2314yescomplemented
131#3757C2314yes—
132#3757C2314yescomplemented
133#3752C2314yes—
134#3752C2314yes—
135#3752C2314yes—
136#3752C2314yes—
137#3752C2314yes—
138#3752C2314yes—
139#3752C2314yes—
140#3752C2314yes—
141#3752C2314yescomplemented
142#3752C2314yescomplemented
143C4⋊(C3⋊Dic3)C2314yescomplemented
144#3750C2314yescomplemented
145#3750C2314yescomplemented
146#3750C2314yescomplemented
147#3750C2314yescomplemented
148C4×C3⋊Dic3C2314yescomplemented
149C2×#538—91noSylow
150C24×D3—34no—
151C22×C3×D4C2×D314yes—
152C23×C3×C4C2×D314yes—
153C23×C3×C4C2×D314yescomplemented
154C22×#67—34no—
155C22×#67—34no—
156C22×#67—34no—
157C22×#67—34no—
158C23×Dic3—34no—
159C22×D12—34no—
160C22×D12—34no—
161C22×C4×D3—34no—
162C22×Dic6—34no—
163C3×C4×D4C2×D3132yescomplemented
164C2×C3×C4⋊C4C2×D314yescomplemented
165C2×C3×C22⋊C4C2×D314yes—
166C2×C3×C22⋊C4C2×D314yescomplemented
167C2×C3×C42C2×D314yescomplemented
168C2×#217—34no—
169C2×#217—34no—
170#939—332no—
171#937—332no—
172#930—332no—
173#929—332no—
174C4×#67—332no—
175C2×(C2×D3)⋊C4—34no—
176C2×(C2×D3)⋊C4—34no—
177C2×(C2×D3)⋊C4—34no—
178C2×(C2×D3)⋊C4—34no—
179C2×(C2×D3)⋊C4—34no—
180C2×(C2×D3)⋊C4—34no—
181C2×(C2×D3)⋊C4—34no—
182C2×(C2×D3)⋊C4—34no—
183C2×(C2×D3)⋊C4—34no—
184C2×(C2×D3)⋊C4—34no—
185C2×(C2×D3)⋊C4—332no—
186C2×C4⋊Dic3—34no—
187C2×Dic3⋊C4—34no—
188C2×Dic3⋊C4—34no—
189C2×Dic3⋊C4—34no—
190C2×Dic3⋊C4—34no—
191C2×C4×Dic3—34no—
192#898—332no—
193#894—332no—
194#885—332no—
195#884—332no—
196#882—332no—
197#878—332no—
198#876—332no—
199#875—332no—
200C23×C32—22no—
201C23×C32—22no—
202C23×C32—22no—
203C23×C32—22no—
204C23×C32—22no—
205C23×C32#4114yes—
206C23×C32C2412yes—
207C23×C32C2412yes—
208C23×C32C2411yescharacteristic
209C22×C3⋊D3—28no—
210C22×C3⋊D3—22no—
211C22×C3⋊D3—22no—
212C22×C3⋊D3—22no—
213C22×C3⋊D3—22no—
214C22×C3⋊D3—22no—
215C22×C3⋊D3—22no—
216C22×C3⋊D3—22no—
217C22×C3⋊D3—22no—
218C22×C3⋊D3—22no—
219C22×C3⋊D3—44no—
220C22×C3⋊D3—44no—
221C22×C3⋊D3—416no—
222C22×C3⋊D3C2412yes—
223C22×C3⋊D3C2412yes—
224C22×C3⋊D3C2412yes—
225C32×D4—28no—
226C2×C32×C4—22no—
227C2×C32×C4—22no—
228C2×C32×C4—22no—
229C2×C32×C4—22no—
230C2×C32×C4—22no—
231C2×C32×C4—44no—
232C2×C32×C4—44no—
233C2×C32×C4C2412yes—
234C2×C32×C4C2412yes—
235C2×C32×C4C2412yes—
236C2×C32×C4C2412yes—
237C2×C32×C4C2412yes—
238#638—28no—
239#638—44no—
240#638—44no—
241#638—44no—
242C2×C3⋊Dic3—22no—
243C2×C3⋊Dic3—22no—
244C2×C3⋊Dic3—22no—
245C2×C3⋊Dic3—22no—
246C2×C3⋊Dic3—22no—
247C2×C3⋊Dic3—44no—
248C2×C3⋊Dic3C2412yes—
249C2×C3⋊Dic3C2412yes—
250C2×C3⋊Dic3C2412yes—
251C2×C3⋊Dic3C2412yes—
252C2×C3⋊Dic3C2412yes—
253C4⋊(C3⋊D3)—44no—
254C4⋊(C3⋊D3)—44no—
255C4×C3⋊D3—44no—
256#634—44no—
257#538—916no—
258C2×#126—91no—
259C2×#126—91no—
260C2×#124—91no—
261C2×#124—91no—
262C2×#123—91no—
263C2×#123—91no—
264C2×C22⋊Q8—91no—
265C2×#121—91no—
266C2×#121—91no—
267C2×#121—91no—
268C2×#120—91no—
269C2×#120—91no—
270C2×C4×D4—91no—
271C2×C4×D4C3⋊D311yescharacteristic, complemented
272C22×C22⋊C4—91no—
273C24×C3C22×D314yes—
274C24×C3C22×D314yes—
275C23×D3—34no—
276C23×D3—34no—
277C23×D3—34no—
278C23×D3—316no—
279C23×D3—616no—
280C23×D3—128no—
281C23×D3—128no—
282C2×C3×D4—216no—
283C2×C3×D4C22×D3116yes—
284C22×C3×C4—48no—
285C22×C3×C4—48no—
286C22×C3×C4C22×D314yes—
287C22×C3×C4C22×D314yes—
288C22×C3×C4C22×D314yes—
289C22×C3×C4C22×D314yes—
290C22×C3×C4C22×D314yes—
291C22×C3×C4C22×D3116yes—
292C22×C3×C4C22×D3116yescomplemented
293C2×#67—316no—
294C2×#67—316no—
295C2×#67—316no—
296C2×#67—316no—
297C2×#67—616no—
298C2×#67—128no—
299C2×#67—128no—
300C2×#67—128no—
301C22×Dic3—34no—
302C22×Dic3—34no—
303C22×Dic3—34no—
304C22×Dic3—34no—
305C22×Dic3—34no—
306C22×Dic3—316no—
307C22×Dic3—128no—
308C2×D12—316no—
309C2×D12—316no—
310C2×D12—128no—
311C2×D12—128no—
312C2×C4×D3—316no—
313C2×C4×D3—128no—
314C2×Dic6—316no—
315C2×Dic6—128no—
316C3×C4⋊C4C22×D3116yescomplemented
317C3×C22⋊C4C22×D3116yes—
318C3×C22⋊C4C22×D3116yescomplemented
319C3×C42C22×D3116yescomplemented
320#217—316no—
321#217—316no—
322(C2×D3)⋊C4—316no—
323(C2×D3)⋊C4—316no—
324(C2×D3)⋊C4—316no—
325(C2×D3)⋊C4—316no—
326(C2×D3)⋊C4—316no—
327(C2×D3)⋊C4—316no—
328(C2×D3)⋊C4—316no—
329(C2×D3)⋊C4—316no—
330(C2×D3)⋊C4—316no—
331(C2×D3)⋊C4—316no—
332C4⋊Dic3—316no—
333Dic3⋊C4—316no—
334Dic3⋊C4—316no—
335Dic3⋊C4—316no—
336Dic3⋊C4—316no—
337C4×Dic3—316no—
338C22×C32—28no—
339C22×C32—22no—
340C22×C32—22no—
341C22×C32—22no—
342C22×C32—22no—
343C22×C32—22no—
344C22×C32—44no—
345C22×C32C2×#4114yes—
346C22×C32C2×#4112yes—
347C22×C32H(5,𝔽2)12yes—
348C22×C32H(5,𝔽2)12yes—
349C22×C32C2511yescharacteristic
350C2×C3⋊D3—22no—
351C2×C3⋊D3—22no—
352C2×C3⋊D3—22no—
353C2×C3⋊D3—22no—
354C2×C3⋊D3—22no—
355C2×C3⋊D3—22no—
356C2×C3⋊D3—22no—
357C2×C3⋊D3—22no—
358C2×C3⋊D3—22no—
359C2×C3⋊D3—416no—
360C2×C3⋊D3—44no—
361C2×C3⋊D3—44no—
362C2×C3⋊D3—44no—
363C32×C4—22no—
364C32×C4—22no—
365C32×C4—22no—
366C32×C4—22no—
367C32×C4—22no—
368C3⋊Dic3—22no—
369C3⋊Dic3—22no—
370C3⋊Dic3—22no—
371C3⋊Dic3—22no—
372C3⋊Dic3—22no—
373C25—91no—
374C22×Q8—91no—
375C22×D4—91no—
376C22×D4—91no—
377C22×D4—91no—
378C22×D4—91no—
379C22×D4—91no—
380C22×D4—91no—
381C22×D4C2×C3⋊D311yescharacteristic
382C23×C4—91no—
383C23×C4—91no—
384C23×C4C2×C3⋊D311yescharacteristic
385C23×C4C2×C3⋊D311yescharacteristic, complemented
386#126—98no—
387#126—98no—
388#124—98no—
389#124—98no—
390#123—98no—
391#123—98no—
392C22⋊Q8—98no—
393#121—98no—
394#121—98no—
395#121—98no—
396#120—98no—
397#120—98no—
398C4×D4—98no—
399C4×D4C2×C3⋊D318yescomplemented
400C2×C4⋊C4—91no—
401C2×C4⋊C4—91no—
402C2×C4⋊C4—91no—
403C2×C4⋊C4—91no—
404C2×C4⋊C4—91no—
405C2×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
406C2×C22⋊C4—91no—
407C2×C22⋊C4—91no—
408C2×C22⋊C4—91no—
409C2×C22⋊C4—91no—
410C2×C22⋊C4—91no—
411C2×C22⋊C4—91no—
412C2×C22⋊C4—98no—
413C2×C22⋊C4—91no—
414C2×C22⋊C4—91no—
415C2×C22⋊C4—91no—
416C2×C22⋊C4—91no—
417C2×C22⋊C4—91no—
418C2×C22⋊C4—91no—
419C2×C22⋊C4C2×C3⋊D311yescharacteristic
420C2×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
421C2×C42—91no—
422C2×C42C2×C3⋊D311yescharacteristic, complemented
423C23×C3—28no—
424C23×C3—28no—
425C23×C3—28no—
426C23×C3—28no—
427C23×C3—28no—
428C23×C3#235116yes—
429C23×C3C23×D318yes—
430C23×C3C23×D318yes—
431C23×C3C23×D314yes—
432C22×D3—38no—
433C22×D3—38no—
434C22×D3—38no—
435C22×D3—68no—
436C22×D3—632no—
437C22×D3—68no—
438C22×D3—68no—
439C22×D3—68no—
440C22×D3—68no—
441C22×D3—68no—
442C22×D3—68no—
443C22×D3—68no—
444C22×D3—68no—
445C22×D3—1216no—
446C22×D3—1216no—
447C22×D3—1264no—
448C3×D4—232no—
449C2×C3×C4—28no—
450C2×C3×C4—28no—
451C2×C3×C4—28no—
452C2×C3×C4—28no—
453C2×C3×C4—28no—
454C2×C3×C4—416no—
455C2×C3×C4—416no—
456C2×C3×C4C23×D318yes—
457C2×C3×C4C23×D318yes—
458C2×C3×C4C23×D318yes—
459C2×C3×C4C23×D318yes—
460C2×C3×C4C23×D318yes—
461#67—632no—
462#67—1216no—
463#67—1216no—
464#67—1216no—
465C2×Dic3—38no—
466C2×Dic3—38no—
467C2×Dic3—38no—
468C2×Dic3—38no—
469C2×Dic3—38no—
470C2×Dic3—68no—
471C2×Dic3—68no—
472C2×Dic3—68no—
473C2×Dic3—68no—
474C2×Dic3—68no—
475C2×Dic3—1216no—
476D12—1216no—
477D12—1216no—
478C4×D3—1216no—
479Dic6—1216no—
480C2×C32—24no—
481C2×C32—42no—
482C2×C32#53814yescomplemented
483C2×C32C22×#4111yescharacteristic
484C2×C32C2×H(5,𝔽2)11yescharacteristic
485C2×C32C2×H(5,𝔽2)11yescharacteristic
486C3⋊D3—42no—
487C3⋊D3—42no—
488C3⋊D3—42no—
489C24—91no—
490C24—91no—
491C24—91no—
492C24—94no—
493C24—184no—
494C24—362no—
495C24—362no—
496C24C22×C3⋊D311yescharacteristic
497C24C22×C3⋊D311yescharacteristic
498C2×Q8—94no—
499C2×Q8—362no—
500C2×D4—24no—
501C2×D4—94no—
502C2×D4—94no—
503C2×D4—94no—
504C2×D4—94no—
505C2×D4—94no—
506C2×D4—94no—
507C2×D4—184no—
508C2×D4—362no—
509C2×D4—362no—
510C2×D4—362no—
511C2×D4—362no—
512C2×D4—362no—
513C2×D4C22×C3⋊D314yes—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—91no—
517C22×C4—91no—
518C22×C4—91no—
519C22×C4—91no—
520C22×C4—91no—
521C22×C4—94no—
522C22×C4—94no—
523C22×C4—362no—
524C22×C4—362no—
525C22×C4C22×C3⋊D311yescharacteristic
526C22×C4C22×C3⋊D311yescharacteristic
527C22×C4C22×C3⋊D311yescharacteristic
528C22×C4C22×C3⋊D311yescharacteristic
529C22×C4C22×C3⋊D311yescharacteristic
530C22×C4C22×C3⋊D314yes—
531C22×C4C22×C3⋊D314yescomplemented
532C4⋊C4—94no—
533C4⋊C4—94no—
534C4⋊C4—94no—
535C4⋊C4—94no—
536C4⋊C4—94no—
537C4⋊C4C22×C3⋊D314yescomplemented
538C22⋊C4—94no—
539C22⋊C4—94no—
540C22⋊C4—94no—
541C22⋊C4—94no—
542C22⋊C4—94no—
543C22⋊C4—94no—
544C22⋊C4—94no—
545C22⋊C4—94no—
546C22⋊C4—94no—
547C22⋊C4—94no—
548C22⋊C4—94no—
549C22⋊C4—94no—
550C22⋊C4C22×C3⋊D314yes—
551C22⋊C4C22×C3⋊D314yescomplemented
552C42—94no—
553C42C22×C3⋊D314yescomplemented
554C22×C3—28no—
555C22×C3—28no—
556C22×C3—232no—
557C22×C3—28no—
558C22×C3—28no—
559C22×C3—28no—
560C22×C3—416no—
561C22×C3C2×#235116yes—
562C22×C3C2×#23518yes—
563C22×C3#100418yes—
564C22×C3#100918yes—
565C22×C3C24×D314yes—
566C2×D3—68no—
567C2×D3—68no—
568C2×D3—68no—
569C2×D3—68no—
570C2×D3—68no—
571C2×D3—68no—
572C2×D3—68no—
573C2×D3—68no—
574C2×D3—68no—
575C2×D3—1264no—
576C2×D3—1216no—
577C2×D3—1216no—
578C2×D3—1216no—
579C3×C4—28no—
580C3×C4—28no—
581C3×C4—28no—
582C3×C4—28no—
583C3×C4—28no—
584Dic3—68no—
585Dic3—68no—
586Dic3—68no—
587Dic3—68no—
588Dic3—68no—
589C32C2×#53811yescharacteristic, complemented, Sylow
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—92no—
596C23—92no—
597C23—92no—
598C23—182no—
599C23—188no—
600C23—182no—
601C23—182no—
602C23—182no—
603C23—182no—
604C23—182no—
605C23—182no—
606C23—182no—
607C23—182no—
608C23—364no—
609C23—364no—
610C23—3616no—
611C23#382814yes—
612C23C23×C3⋊D312yes—
613C23C23×C3⋊D312yes—
614C23C23×C3⋊D311yescharacteristic
615Q8—364no—
616D4—28no—
617D4—188no—
618D4—364no—
619D4—364no—
620D4—364no—
621D4—364no—
622D4—364no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—44no—
629C2×C4—44no—
630C2×C4—92no—
631C2×C4—92no—
632C2×C4—92no—
633C2×C4—92no—
634C2×C4—92no—
635C2×C4—182no—
636C2×C4—182no—
637C2×C4—182no—
638C2×C4—182no—
639C2×C4—182no—
640C2×C4—364no—
641C2×C4—364no—
642C2×C4C23×C3⋊D312yes—
643C2×C4C23×C3⋊D312yes—
644C2×C4C23×C3⋊D312yes—
645C2×C4C23×C3⋊D312yes—
646C2×C4C23×C3⋊D312yes—
647C2×C3—216no—
648C2×C3—48no—
649C2×C3#5560116yescomplemented
650C2×C3C22×#23514yes—
651C2×C3C2×#100414yes—
652C2×C3C2×#100914yes—
653D3—128no—
654D3—128no—
655D3—128no—
656C22—22no—
657C22—22no—
658C22—28no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—44no—
663C22—182no—
664C22—182no—
665C22—182no—
666C22—182no—
667C22—182no—
668C22—182no—
669C22—182no—
670C22—182no—
671C22—182no—
672C22—3616no—
673C22—364no—
674C22—364no—
675C22—364no—
676C22C2×#382814yes—
677C22C2×#382812yes—
678C22#6436112yes—
679C22#6436612yes—
680C22C24×C3⋊D311yescharacteristic
681C4—22no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—22no—
686C4—182no—
687C4—182no—
688C4—182no—
689C4—182no—
690C4—182no—
691C3C2×#556014yescomplemented
692C2—24no—
693C2—42no—
694C2—362no—
695C2—362no—
696C2—362no—
697C2#1059603114yesdirect product factor
698C2C22×#382811yescharacteristic
699C2C2×#6436111yescharacteristic
700C2C2×#6436611yescharacteristic
subgroupG/H
centerC23C23×C3⋊D3
commutator, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC2×C32×C4×D4C2
socleC23×C32C24
hypercenterC2×C4×D4C3⋊D3
hypocenterC32C2×#538
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D4C2semidirect
2. C2×#64148C2semidirect
3. C2×#64146C2semidirect
4. C2×#64139C2semidirect
5. C2×#64138C2semidirect
6. C2×C4×#638C2semidirect
7. C22×#3752C2semidirect
8. #10596031C2direct (N × H)
9. C2×#64107C2semidirect
10. C2×#64103C2semidirect
11. C2×#64094C2semidirect
12. C2×#64093C2semidirect
13. C2×#64091C2semidirect
14. C2×#64087C2semidirect
15. C2×#64085C2semidirect
16. C2×#64084C2semidirect
21. C23×C32×C4C22semidirect
25. C22×#638C22semidirect
29. C22×C4×C3⋊D3C22semidirect
30. C22×#634C22semidirect
31. C32×C4×D4C22semidirect
32. C2×C32×C4⋊C4C22semidirect
34. C2×C32×C22⋊C4C22semidirect
35. C2×C32×C42C22semidirect
37. C2×#3757C22semidirect
38. #64148C22semidirect
39. #64146C22semidirect
40. #64139C22semidirect
41. #64138C22semidirect
42. C4×#638C22semidirect
51. C2×#3752C22semidirect
52. C2×#3752C22semidirect
53. C2×#3752C22semidirect
54. C2×C4⋊(C3⋊Dic3)C22semidirect
55. C2×#3750C22semidirect
56. C2×#3750C22semidirect
57. C2×#3750C22semidirect
58. C2×#3750C22semidirect
59. C2×C4×C3⋊Dic3C22semidirect
60. #64107C22semidirect
61. #64103C22semidirect
62. #64094C22semidirect
63. #64093C22semidirect
64. #64091C22semidirect
65. #64087C22semidirect
66. #64085C22semidirect
67. #64084C22semidirect
68. C2×C3×C4×D4D3semidirect
103. C22×C32×C4C23semidirect
111. C2×#638C23semidirect
124. C2×C4×C3⋊D3C23semidirect
126. C2×#634C23semidirect
127. C32×C4⋊C4C23semidirect
129. C32×C22⋊C4C23semidirect
130. C32×C42C23semidirect
132. #3757C23semidirect
141. #3752C23semidirect
142. #3752C23semidirect
143. C4⋊(C3⋊Dic3)C23semidirect
144. #3750C23semidirect
145. #3750C23semidirect
146. #3750C23semidirect
147. #3750C23semidirect
148. C4×C3⋊Dic3C23semidirect
153. C23×C3×C4C2×D3semidirect
163. C3×C4×D4C2×D3semidirect
164. C2×C3×C4⋊C4C2×D3semidirect
166. C2×C3×C22⋊C4C2×D3semidirect
167. C2×C3×C42C2×D3semidirect
271. C2×C4×D4C3⋊D3semidirect
292. C22×C3×C4C22×D3semidirect
316. C3×C4⋊C4C22×D3semidirect
318. C3×C22⋊C4C22×D3semidirect
319. C3×C42C22×D3semidirect
385. C23×C4C2×C3⋊D3semidirect
399. C4×D4C2×C3⋊D3semidirect
405. C2×C4⋊C4C2×C3⋊D3semidirect
420. C2×C22⋊C4C2×C3⋊D3semidirect
422. C2×C42C2×C3⋊D3semidirect
482. C2×C32#538semidirect
531. C22×C4C22×C3⋊D3semidirect
537. C4⋊C4C22×C3⋊D3semidirect
551. C22⋊C4C22×C3⋊D3semidirect
553. C42C22×C3⋊D3semidirect
589. C32C2×#538semidirect
649. C2×C3#5560semidirect
691. C3C2×#5560semidirect
697. C2#10596031direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×#641482
C2×#641462
C2×#641392
C2×#641382
C2×C4×#6382
C22×#37522
#105960312
C2×#641072
C2×#641032
C2×#640942
C2×#640932
C2×#640912
C2×#640872
C2×#640852
C2×#640842
C2×#55603