Finite Group Databasebeta

← C2×#10595258 #11910187

Subgroups — C2×#10595258 #11910187

Order 1152.

2901 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64147C211yesmaximal, characteristic, complemented
2C2×C3×#939C211yesmaximal, characteristic, complemented
3C2×C3×#937C211yesmaximal, characteristic, complemented
4C2×#63979C211yesmaximal, characteristic, complemented
5C2×#63978C211yesmaximal, characteristic, complemented
6C2×#63977C211yesmaximal, characteristic, complemented
7C2×#63976C211yesmaximal, characteristic, complemented
8C2×#63971C211yesmaximal, characteristic, complemented
9C2×#63970C211yesmaximal, characteristic, complemented
10C2×#63961C211yesmaximal, characteristic, complemented
11C2×#63956C211yesmaximal, characteristic, complemented
12#10595258C2116yesmaximal, direct product factor
13C2×#63912C211yesmaximal, characteristic, complemented
14C2×#63891C211yesmaximal, characteristic, complemented
15C2×#63861C211yesmaximal, characteristic, complemented
16C2×#63853C211yesmaximal, characteristic, complemented
17C2×#5620—31nomaximal
18C2×#5595—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C22×#638C2211yescharacteristic, complemented
23C22×C4×C3⋊D3C2211yescharacteristic, complemented
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C22×C3×#67C2211yescharacteristic
27C22×C3×#67C2211yescharacteristic, complemented
28C23×C3×Dic3C2211yescharacteristic, complemented
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic
31C22×#626C2211yescharacteristic, complemented
32C22×#625C2211yescharacteristic
33C22×#625C2211yescharacteristic
34C22×D3×Dic3C2211yescharacteristic, complemented
35C2×#3757C2211yescharacteristic
36C2×#3757C2211yescharacteristic, complemented
37#64147C2218yescomplemented
38C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
39C2×C3×#217C2211yescharacteristic
40C2×C3×#217C2211yescharacteristic
41C3×#939C2218yescomplemented
42C3×#937C2218yescomplemented
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic
45C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
47#63979C2218yescomplemented
48#63978C2218yescomplemented
49#63977C2218yescomplemented
50#63976C2218yescomplemented
51#63971C2218yescomplemented
52#63970C2218yescomplemented
53C2×#3724C2211yescharacteristic, complemented
54C2×#3724C2211yescharacteristic, complemented
55C2×Dic3⋊Dic3C2211yescharacteristic, complemented
56C2×Dic3⋊Dic3C2211yescharacteristic, complemented
57C2×#3722C2211yescharacteristic, complemented
58#63961C2218yescomplemented
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2211yescharacteristic
61C2×(C2×D3)⋊Dic3C2211yescharacteristic
62C2×(C2×D3)⋊Dic3C2211yescharacteristic
63#63956C2218yescomplemented
64C2×Dic32C2211yescharacteristic, complemented
65#63912C2218yescomplemented
66#63891C2218yescomplemented
67#63861C2218yescomplemented
68#63853C2218yescomplemented
69C2×C3×#121—31no—
70C2×C3×#120—31no—
71C2×#953—31no—
72C2×#953—31no—
73C2×#940—31no—
74C2×#940—31no—
75C2×#939—31no—
76C2×#939—31no—
77C2×#939—31no—
78C2×#939D311yescharacteristic, complemented
79C2×#938—31no—
80C2×#938—31no—
81C2×#938—31no—
82C2×#938—61no—
83C2×#937—31no—
84C2×#937D311yescharacteristic, complemented
85C2×#935—31no—
86C2×#930—31no—
87C2×#929—31no—
88#5620—316no—
89#5595—316no—
90C2×#898—31no—
91C2×#894—31no—
92C2×#886—31no—
93C2×#884—31no—
94C2×#884—31no—
95C2×#884—31no—
96C2×#883—31no—
97C2×#883—31no—
98C2×#882—31no—
99C2×#879—31no—
100C2×#879—31no—
101C2×#879—31no—
102C24×C32C2311yescharacteristic
103C24×C32C2311yescharacteristic
104C23×C3⋊D3C2311yescharacteristic
105C23×C3×D3—42no—
106C23×C3×D3—42no—
107C23×C3×D3—42no—
108C23×C3×D3C2311yescharacteristic
109C23×C3×D3C2311yescharacteristic
110C23×C3×D3C2311yescharacteristic
111C23×C3×D3C2314yes—
112C2×C32×D4—42no—
113C2×C32×D4C2314yes—
114C22×C32×C4C2311yescharacteristic
115C2×#638—42no—
116C2×#638—42no—
117C2×#638C2314yes—
118C2×#638C2314yescomplemented
119C22×C3⋊Dic3C2311yescharacteristic
120C22×C3⋊Dic3C2311yescharacteristic
121C22×C3⋊Dic3C2311yescharacteristic
122C2×C4×C3⋊D3—42no—
123C2×C4×C3⋊D3C2314yescomplemented
124C2×C3×#67—42no—
125C2×C3×#67—42no—
126C2×C3×#67—42no—
127C2×C3×#67—42no—
128C2×C3×#67C2314yes—
129C2×C3×#67C2314yes—
130C2×C3×#67C2314yes—
131C2×C3×#67C2314yescomplemented
132C22×C3×Dic3—42no—
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2311yescharacteristic
137C22×C3×Dic3C2311yescharacteristic
138C22×C3×Dic3C2314yescomplemented
139C2×#626—42no—
140C2×#626—42no—
141C2×#626—42no—
142C2×#626C2314yes—
143C2×#626C2314yes—
144C2×#626C2314yescomplemented
145C2×#625—42no—
146C2×#625—42no—
147C2×#625C2314yes—
148C2×#625C2314yes—
149C2×D3×Dic3—42no—
150C2×D3×Dic3C2314yescomplemented
151#3757C2314yes—
152#3757C2314yescomplemented
153C4⋊(C3⋊Dic3)C2314yescomplemented
154C3×#217C2314yes—
155C3×#217C2314yes—
156C3×(C2×D3)⋊C4C2314yes—
157C3×(C2×D3)⋊C4C2314yes—
158C3×(C2×D3)⋊C4C2314yescomplemented
159C3×Dic3⋊C4C2314yescomplemented
160#3724C2314yescomplemented
161#3724C2314yescomplemented
162Dic3⋊Dic3C2314yescomplemented
163Dic3⋊Dic3C2314yescomplemented
164#3722C2314yescomplemented
165(C2×D3)⋊Dic3C2314yes—
166(C2×D3)⋊Dic3C2314yes—
167(C2×D3)⋊Dic3C2314yes—
168(C2×D3)⋊Dic3C2314yes—
169Dic32C2314yescomplemented
170C2×#560—91noSylow
171C25×C3—31no—
172C24×D3C2×D311yescharacteristic
173C22×C3×D4—21no—
174C22×C3×D4—31no—
175C22×C3×D4—31no—
176C22×C3×D4—31no—
177C22×C3×D4—31no—
178C22×C3×D4C2×D311yescharacteristic
179C22×C3×D4C2×D311yescharacteristic
180C23×C3×C4—31no—
181C22×#67—31no—
182C22×#67—31no—
183C22×#67—31no—
184C22×#67—31no—
185C22×#67—31no—
186C22×#67—31no—
187C22×#67—31no—
188C22×#67—31no—
189C22×#67—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—61no—
193C22×#67—61no—
194C22×#67C2×D311yescharacteristic
195C22×#67C2×D311yescharacteristic
196C22×#67C2×D311yescharacteristic
197C22×#67C2×D311yescharacteristic, complemented
198C23×Dic3—31no—
199C23×Dic3C2×D311yescharacteristic, complemented
200C22×D12—31no—
201C22×D12—31no—
202C22×D12—31no—
203C22×C4×D3—31no—
204C22×C4×D3—31no—
205C22×C4×D3—31no—
206C22×C4×D3—61no—
207C3×#121—38no—
208C3×#120—38no—
209C2×C3×C4⋊C4—31no—
210C2×C3×C22⋊C4—31no—
211C2×C3×C22⋊C4—31no—
212C2×C3×C22⋊C4—31no—
213C2×C3×C22⋊C4—31no—
214C2×C3×C22⋊C4—31no—
215#953—38no—
216#953—38no—
217C2×#217—31no—
218C2×#217—31no—
219C2×#217—31no—
220C2×#217—31no—
221C2×#217—31no—
222C2×#217—31no—
223C2×#217—31no—
224C2×#217—31no—
225C2×#217—61no—
226C2×#217—61no—
227C2×#217C2×D311yescharacteristic
228C2×#217C2×D311yescharacteristic
229#940—38no—
230#940—38no—
231#939—38no—
232#939—38no—
233#939—38no—
234#939C2×D318yescomplemented
235#938—38no—
236#938—38no—
237#938—38no—
238#938—68no—
239#937—38no—
240#937C2×D318yescomplemented
241#935—38no—
242#930—38no—
243#929—38no—
244C2×(C2×D3)⋊C4—31no—
245C2×(C2×D3)⋊C4—31no—
246C2×(C2×D3)⋊C4—31no—
247C2×(C2×D3)⋊C4—31no—
248C2×(C2×D3)⋊C4—31no—
249C2×(C2×D3)⋊C4—31no—
250C2×(C2×D3)⋊C4C2×D311yescharacteristic
251C2×(C2×D3)⋊C4C2×D311yescharacteristic
252C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
253C2×C4⋊Dic3—31no—
254C2×C4⋊Dic3—31no—
255C2×C4⋊Dic3—31no—
256C2×C4⋊Dic3—31no—
257C2×C4⋊Dic3—61no—
258C2×Dic3⋊C4—31no—
259C2×Dic3⋊C4—31no—
260C2×Dic3⋊C4—31no—
261C2×Dic3⋊C4—31no—
262C2×Dic3⋊C4—31no—
263C2×Dic3⋊C4—31no—
264C2×Dic3⋊C4C2×D311yescharacteristic, complemented
265C2×C4×Dic3—31no—
266C2×C4×Dic3—31no—
267#898—38no—
268#894—38no—
269#886—38no—
270#884—38no—
271#884—38no—
272#884—38no—
273#883—38no—
274#883—38no—
275#882—38no—
276#879—38no—
277#879—38no—
278#879—38no—
279C23×C32—22no—
280C23×C32—22no—
281C23×C32—22no—
282C23×C32—22no—
283C23×C32—22no—
284C23×C32—22no—
285C23×C32C2412yes—
286C23×C32C2412yes—
287C23×C32C2411yescharacteristic
288C22×C3⋊D3—22no—
289C22×C3⋊D3—22no—
290C22×C3⋊D3—22no—
291C22×C3⋊D3C2412yes—
292C22×C3×D3—22no—
293C22×C3×D3—22no—
294C22×C3×D3—22no—
295C22×C3×D3—22no—
296C22×C3×D3—22no—
297C22×C3×D3—22no—
298C22×C3×D3—22no—
299C22×C3×D3—22no—
300C22×C3×D3—22no—
301C22×C3×D3—44no—
302C22×C3×D3—44no—
303C22×C3×D3—44no—
304C22×C3×D3—416no—
305C22×C3×D3C2412yes—
306C22×C3×D3C2412yes—
307C22×C3×D3C2412yes—
308C32×D4—44no—
309C2×C32×C4—22no—
310C2×C32×C4C2412yes—
311#638—44no—
312#638—44no—
313C2×C3⋊Dic3—22no—
314C2×C3⋊Dic3—22no—
315C2×C3⋊Dic3—22no—
316C2×C3⋊Dic3C2412yes—
317C2×C3⋊Dic3C2412yes—
318C2×C3⋊Dic3C2412yes—
319C4×C3⋊D3—44no—
320C3×#67—44no—
321C3×#67—44no—
322C3×#67—44no—
323C3×#67—44no—
324C2×C3×Dic3—22no—
325C2×C3×Dic3—22no—
326C2×C3×Dic3—22no—
327C2×C3×Dic3—22no—
328C2×C3×Dic3—22no—
329C2×C3×Dic3—44no—
330C2×C3×Dic3C2412yes—
331C2×C3×Dic3C2412yes—
332C2×C3×Dic3C2412yes—
333C2×C3×Dic3C2412yes—
334C2×C3×Dic3C2412yes—
335#626—44no—
336#626—44no—
337#626—44no—
338#625—44no—
339#625—44no—
340D3×Dic3—44no—
341#560—916no—
342C2×#127—91no—
343C2×#126—91no—
344C2×#126—91no—
345C2×#123—91no—
346C2×#123—91no—
347C2×#123—91no—
348C2×#121—31no—
349C2×#121—91no—
350C2×#121—91no—
351C2×#121—91no—
352C2×#121—91no—
353C2×#121—91no—
354C2×#120—31no—
355C2×#120—91no—
356C2×#120—91no—
357C24×C3—21no—
358C24×C3—21no—
359C24×C3—31no—
360C24×C3—31no—
361C24×C3—31no—
362C24×C3—34no—
363C24×C3—122no—
364C24×C3—122no—
365C24×C3—122no—
366C24×C3C22×D311yescharacteristic
367C24×C3C22×D311yescharacteristic
368C24×C3C22×D311yescharacteristic
369C24×C3C22×D311yescharacteristic
370C23×D3—31no—
371C23×D3—31no—
372C23×D3—42no—
373C23×D3—42no—
374C23×D3—42no—
375C23×D3—61no—
376C23×D3C22×D311yescharacteristic
377C23×D3C22×D311yescharacteristic
378C23×D3C22×D311yescharacteristic
379C23×D3C22×D314yes—
380C2×C3×D4—24no—
381C2×C3×D4—34no—
382C2×C3×D4—34no—
383C2×C3×D4—34no—
384C2×C3×D4—34no—
385C2×C3×D4—42no—
386C2×C3×D4—42no—
387C2×C3×D4—44no—
388C2×C3×D4—122no—
389C2×C3×D4—122no—
390C2×C3×D4—122no—
391C2×C3×D4—122no—
392C2×C3×D4C22×D314yes—
393C2×C3×D4C22×D314yes—
394C22×C3×C4—21no—
395C22×C3×C4—31no—
396C22×C3×C4—31no—
397C22×C3×C4—31no—
398C22×C3×C4—31no—
399C22×C3×C4—31no—
400C22×C3×C4—34no—
401C22×C3×C4—122no—
402C22×C3×C4C22×D311yescharacteristic
403C22×C3×C4C22×D311yescharacteristic
404C2×#67—34no—
405C2×#67—34no—
406C2×#67—34no—
407C2×#67—34no—
408C2×#67—34no—
409C2×#67—34no—
410C2×#67—34no—
411C2×#67—34no—
412C2×#67—34no—
413C2×#67—34no—
414C2×#67—34no—
415C2×#67—42no—
416C2×#67—42no—
417C2×#67—42no—
418C2×#67—42no—
419C2×#67—64no—
420C2×#67—64no—
421C2×#67—122no—
422C2×#67—122no—
423C2×#67—122no—
424C2×#67—122no—
425C2×#67—122no—
426C2×#67—122no—
427C2×#67—122no—
428C2×#67—122no—
429C2×#67—122no—
430C2×#67—122no—
431C2×#67—122no—
432C2×#67—124no—
433C2×#67—124no—
434C2×#67C22×D314yes—
435C2×#67C22×D314yes—
436C2×#67C22×D314yes—
437C2×#67C22×D314yescomplemented
438C22×Dic3—31no—
439C22×Dic3—31no—
440C22×Dic3—31no—
441C22×Dic3—31no—
442C22×Dic3—31no—
443C22×Dic3—31no—
444C22×Dic3—34no—
445C22×Dic3—42no—
446C22×Dic3—61no—
447C22×Dic3—61no—
448C22×Dic3—61no—
449C22×Dic3—122no—
450C22×Dic3C22×D311yescharacteristic
451C22×Dic3C22×D311yescharacteristic
452C22×Dic3C22×D311yescharacteristic
453C22×Dic3C22×D311yescharacteristic
454C22×Dic3C22×D311yescharacteristic
455C22×Dic3C22×D314yescomplemented
456C2×D12—34no—
457C2×D12—34no—
458C2×D12—34no—
459C2×D12—122no—
460C2×D12—122no—
461C2×D12—122no—
462C2×C4×D3—34no—
463C2×C4×D3—34no—
464C2×C4×D3—34no—
465C2×C4×D3—64no—
466C2×C4×D3—122no—
467C2×C4×D3—122no—
468C2×C4×D3—122no—
469C2×C4×D3—124no—
470C3×C4⋊C4—34no—
471C3×C22⋊C4—34no—
472C3×C22⋊C4—34no—
473C3×C22⋊C4—34no—
474C3×C22⋊C4—34no—
475C3×C22⋊C4—34no—
476#217—34no—
477#217—34no—
478#217—34no—
479#217—34no—
480#217—34no—
481#217—34no—
482#217—34no—
483#217—34no—
484#217—64no—
485#217—64no—
486#217C22×D314yes—
487#217C22×D314yes—
488(C2×D3)⋊C4—34no—
489(C2×D3)⋊C4—34no—
490(C2×D3)⋊C4—34no—
491(C2×D3)⋊C4—34no—
492(C2×D3)⋊C4—34no—
493(C2×D3)⋊C4—34no—
494(C2×D3)⋊C4C22×D314yes—
495(C2×D3)⋊C4C22×D314yes—
496(C2×D3)⋊C4C22×D314yescomplemented
497C4⋊Dic3—34no—
498C4⋊Dic3—34no—
499C4⋊Dic3—34no—
500C4⋊Dic3—34no—
501C4⋊Dic3—64no—
502Dic3⋊C4—34no—
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4—34no—
508Dic3⋊C4C22×D314yescomplemented
509C4×Dic3—34no—
510C4×Dic3—34no—
511C22×C32—22no—
512C22×C32—22no—
513C22×C32—22no—
514C22×C32—22no—
515C22×C32—22no—
516C22×C32—22no—
517C22×C32—44no—
518C22×C32—44no—
519C22×C32H(5,𝔽2)12yes—
520C22×C32H(5,𝔽2)12yes—
521C22×C32H(5,𝔽2)12yes—
522C22×C32C2511yescharacteristic
523C2×C3⋊D3—22no—
524C2×C3⋊D3—22no—
525C2×C3⋊D3—22no—
526C2×C3⋊D3—44no—
527C2×C3×D3—22no—
528C2×C3×D3—22no—
529C2×C3×D3—22no—
530C2×C3×D3—22no—
531C2×C3×D3—22no—
532C2×C3×D3—22no—
533C2×C3×D3—22no—
534C2×C3×D3—22no—
535C2×C3×D3—22no—
536C2×C3×D3—416no—
537C2×C3×D3—44no—
538C2×C3×D3—44no—
539C2×C3×D3—44no—
540C32×C4—22no—
541C3⋊Dic3—22no—
542C3⋊Dic3—22no—
543C3⋊Dic3—22no—
544C3×Dic3—22no—
545C3×Dic3—22no—
546C3×Dic3—22no—
547C3×Dic3—22no—
548C3×Dic3—22no—
549C25—31no—
550C22×D4—31no—
551C22×D4—31no—
552C22×D4—31no—
553C22×D4—31no—
554C22×D4—91no—
555C22×D4—91no—
556C22×D4—91no—
557C22×D4—91no—
558C22×D4—91no—
559C22×D4—91no—
560C22×D4—91no—
561C22×D4D3211yescharacteristic
562C23×C4—31no—
563C23×C4—91no—
564C23×C4—91no—
565#127—98no—
566#126—98no—
567#126—98no—
568#123—98no—
569#123—98no—
570#123—98no—
571#121—38no—
572#121—98no—
573#121—98no—
574#121—98no—
575#121—98no—
576#121—98no—
577#120—38no—
578#120—98no—
579#120—98no—
580C2×C4⋊C4—31no—
581C2×C4⋊C4—91no—
582C2×C4⋊C4—91no—
583C2×C4⋊C4—91no—
584C2×C4⋊C4—91no—
585C2×C4⋊C4—91no—
586C2×C22⋊C4—31no—
587C2×C22⋊C4—31no—
588C2×C22⋊C4—31no—
589C2×C22⋊C4—31no—
590C2×C22⋊C4—31no—
591C2×C22⋊C4—91no—
592C2×C22⋊C4—91no—
593C2×C22⋊C4—91no—
594C2×C22⋊C4—91no—
595C2×C22⋊C4—91no—
596C2×C22⋊C4—91no—
597C2×C22⋊C4—91no—
598C2×C42—91no—
599C23×C3—22no—
600C23×C3—22no—
601C23×C3—22no—
602C23×C3—22no—
603C23×C3—22no—
604C23×C3—22no—
605C23×C3—22no—
606C23×C3—22no—
607C23×C3—22no—
608C23×C3—22no—
609C23×C3—22no—
610C23×C3—22no—
611C23×C3—22no—
612C23×C3—22no—
613C23×C3—21no—
614C23×C3—32no—
615C23×C3—32no—
616C23×C3—32no—
617C23×C3—42no—
618C23×C3—42no—
619C23×C3—42no—
620C23×C3—42no—
621C23×C3—42no—
622C23×C3—42no—
623C23×C3—62no—
624C23×C3—62no—
625C23×C3—62no—
626C23×C3—62no—
627C23×C3—62no—
628C23×C3—62no—
629C23×C3—62no—
630C23×C3—62no—
631C23×C3—62no—
632C23×C3—124no—
633C23×C3—124no—
634C23×C3—124no—
635C23×C3—1216no—
636C23×C3C23×D312yes—
637C23×C3C23×D312yes—
638C23×C3C23×D312yes—
639C23×C3C23×D312yes—
640C23×C3C23×D311yescharacteristic
641C23×C3C23×D311yescharacteristic
642C22×D3—22no—
643C22×D3—22no—
644C22×D3—22no—
645C22×D3—22no—
646C22×D3—22no—
647C22×D3—22no—
648C22×D3—22no—
649C22×D3—22no—
650C22×D3—22no—
651C22×D3—32no—
652C22×D3—32no—
653C22×D3—44no—
654C22×D3—44no—
655C22×D3—44no—
656C22×D3—416no—
657C22×D3—62no—
658C22×D3—64no—
659C22×D3—62no—
660C22×D3—62no—
661C22×D3—62no—
662C22×D3—62no—
663C22×D3—62no—
664C22×D3—62no—
665C22×D3—122no—
666C22×D3—122no—
667C22×D3C23×D312yes—
668C22×D3C23×D312yes—
669C22×D3C23×D312yes—
670C3×D4—44no—
671C3×D4—44no—
672C3×D4—48no—
673C3×D4—124no—
674C3×D4—124no—
675C3×D4—124no—
676C3×D4—124no—
677C2×C3×C4—24no—
678C2×C3×C4—22no—
679C2×C3×C4—22no—
680C2×C3×C4—22no—
681C2×C3×C4—32no—
682C2×C3×C4—32no—
683C2×C3×C4—32no—
684C2×C3×C4—32no—
685C2×C3×C4—32no—
686C2×C3×C4—62no—
687C2×C3×C4—62no—
688C2×C3×C4—62no—
689C2×C3×C4—62no—
690C2×C3×C4—62no—
691C2×C3×C4—124no—
692C2×C3×C4C23×D312yes—
693C2×C3×C4C23×D312yes—
694#67—44no—
695#67—44no—
696#67—44no—
697#67—44no—
698#67—124no—
699#67—124no—
700#67—124no—
701#67—124no—
702#67—124no—
703#67—124no—
704#67—124no—
705#67—124no—
706#67—124no—
707#67—124no—
708#67—124no—
709#67—128no—
710#67—128no—
711C2×Dic3—22no—
712C2×Dic3—22no—
713C2×Dic3—22no—
714C2×Dic3—22no—
715C2×Dic3—22no—
716C2×Dic3—32no—
717C2×Dic3—32no—
718C2×Dic3—32no—
719C2×Dic3—32no—
720C2×Dic3—32no—
721C2×Dic3—32no—
722C2×Dic3—44no—
723C2×Dic3—62no—
724C2×Dic3—62no—
725C2×Dic3—62no—
726C2×Dic3—62no—
727C2×Dic3—62no—
728C2×Dic3—62no—
729C2×Dic3—62no—
730C2×Dic3—62no—
731C2×Dic3—62no—
732C2×Dic3—122no—
733C2×Dic3—122no—
734C2×Dic3—122no—
735C2×Dic3—124no—
736C2×Dic3C23×D312yes—
737C2×Dic3C23×D312yes—
738C2×Dic3C23×D312yes—
739C2×Dic3C23×D312yes—
740C2×Dic3C23×D312yes—
741D12—124no—
742D12—124no—
743D12—124no—
744C4×D3—124no—
745C4×D3—124no—
746C4×D3—124no—
747C4×D3—128no—
748C2×C32—42no—
749C2×C32—42no—
750C2×C32#56014yescomplemented
751C2×C32C2×H(5,𝔽2)11yescharacteristic
752C2×C32C2×H(5,𝔽2)11yescharacteristic
753C2×C32C2×H(5,𝔽2)11yescharacteristic
754C3⋊D3—42no—
755C3×D3—42no—
756C3×D3—42no—
757C3×D3—42no—
758C24—31no—
759C24—31no—
760C24—31no—
761C24—34no—
762C24—91no—
763C24—122no—
764C24—122no—
765C24—122no—
766C24C2×D3211yescharacteristic
767C24C2×D3211yescharacteristic
768C2×D4—34no—
769C2×D4—34no—
770C2×D4—34no—
771C2×D4—34no—
772C2×D4—42no—
773C2×D4—94no—
774C2×D4—94no—
775C2×D4—94no—
776C2×D4—94no—
777C2×D4—94no—
778C2×D4—94no—
779C2×D4—94no—
780C2×D4—122no—
781C2×D4—122no—
782C2×D4—122no—
783C2×D4—122no—
784C2×D4—362no—
785C2×D4—362no—
786C2×D4—362no—
787C2×D4—362no—
788C2×D4—362no—
789C2×D4—362no—
790C2×D4—362no—
791C2×D4C2×D3214yes—
792C22×C4—31no—
793C22×C4—31no—
794C22×C4—31no—
795C22×C4—31no—
796C22×C4—31no—
797C22×C4—34no—
798C22×C4—94no—
799C22×C4—91no—
800C22×C4—91no—
801C22×C4—91no—
802C22×C4—94no—
803C22×C4—122no—
804C22×C4—362no—
805C22×C4—362no—
806C22×C4C2×D3211yescharacteristic
807C4⋊C4—34no—
808C4⋊C4—94no—
809C4⋊C4—94no—
810C4⋊C4—94no—
811C4⋊C4—94no—
812C4⋊C4—94no—
813C22⋊C4—34no—
814C22⋊C4—34no—
815C22⋊C4—34no—
816C22⋊C4—34no—
817C22⋊C4—34no—
818C22⋊C4—94no—
819C22⋊C4—94no—
820C22⋊C4—94no—
821C22⋊C4—94no—
822C22⋊C4—94no—
823C22⋊C4—94no—
824C22⋊C4—94no—
825C42—94no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—22no—
831C22×C3—22no—
832C22×C3—22no—
833C22×C3—22no—
834C22×C3—22no—
835C22×C3—22no—
836C22×C3—22no—
837C22×C3—22no—
838C22×C3—22no—
839C22×C3—22no—
840C22×C3—22no—
841C22×C3—21no—
842C22×C3—42no—
843C22×C3—42no—
844C22×C3—42no—
845C22×C3—42no—
846C22×C3—42no—
847C22×C3—42no—
848C22×C3—44no—
849C22×C3—44no—
850C22×C3—44no—
851C22×C3—44no—
852C22×C3—62no—
853C22×C3—62no—
854C22×C3—62no—
855C22×C3—62no—
856C22×C3—62no—
857C22×C3—62no—
858C22×C3—62no—
859C22×C3—62no—
860C22×C3—62no—
861C22×C3—84no—
862C22×C3—84no—
863C22×C3—1216no—
864C22×C3—124no—
865C22×C3—124no—
866C22×C3—124no—
867C22×C3#100412yes—
868C22×C3#100412yes—
869C22×C3#100412yes—
870C22×C3#100412yes—
871C22×C3#100412yes—
872C22×C3#100912yes—
873C22×C3C24×D311yescharacteristic
874C22×C3C24×D311yescharacteristic
875C2×D3—22no—
876C2×D3—22no—
877C2×D3—22no—
878C2×D3—22no—
879C2×D3—22no—
880C2×D3—22no—
881C2×D3—22no—
882C2×D3—22no—
883C2×D3—22no—
884C2×D3—416no—
885C2×D3—44no—
886C2×D3—44no—
887C2×D3—44no—
888C2×D3—64no—
889C2×D3—62no—
890C2×D3—62no—
891C2×D3—62no—
892C2×D3—62no—
893C2×D3—62no—
894C2×D3—62no—
895C2×D3—122no—
896C2×D3—122no—
897C2×D3—128no—
898C2×D3—124no—
899C2×D3—124no—
900C3×C4—24no—
901C3×C4—22no—
902C3×C4—22no—
903C3×C4—62no—
904C3×C4—62no—
905C3×C4—62no—
906C3×C4—62no—
907C3×C4—62no—
908Dic3—22no—
909Dic3—22no—
910Dic3—22no—
911Dic3—22no—
912Dic3—22no—
913Dic3—62no—
914Dic3—62no—
915Dic3—62no—
916Dic3—62no—
917Dic3—62no—
918Dic3—62no—
919Dic3—122no—
920Dic3—122no—
921Dic3—122no—
922C32C2×#56011yescharacteristic, complemented, Sylow
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—32no—
930C23—32no—
931C23—32no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—62no—
936C23—62no—
937C23—62no—
938C23—62no—
939C23—62no—
940C23—62no—
941C23—92no—
942C23—124no—
943C23—124no—
944C23—124no—
945C23—1216no—
946C23—182no—
947C23—182no—
948C23—182no—
949C23C22×D3212yes—
950C23C22×D3212yes—
951C23C22×D3211yescharacteristic
952D4—44no—
953D4—124no—
954D4—124no—
955D4—124no—
956D4—124no—
957D4—364no—
958D4—364no—
959D4—364no—
960D4—364no—
961D4—364no—
962D4—364no—
963D4—364no—
964C2×C4—22no—
965C2×C4—32no—
966C2×C4—32no—
967C2×C4—32no—
968C2×C4—32no—
969C2×C4—32no—
970C2×C4—62no—
971C2×C4—62no—
972C2×C4—62no—
973C2×C4—62no—
974C2×C4—62no—
975C2×C4—92no—
976C2×C4—92no—
977C2×C4—92no—
978C2×C4—124no—
979C2×C4—182no—
980C2×C4—182no—
981C2×C4—182no—
982C2×C4—364no—
983C2×C4—364no—
984C2×C4C22×D3212yes—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—24no—
989C2×C3—42no—
990C2×C3—42no—
991C2×C3—42no—
992C2×C3—42no—
993C2×C3—82no—
994C2×C3—82no—
995C2×C3—122no—
996C2×C3—122no—
997C2×C3—122no—
998C2×C3#559514yescomplemented
999C2×C3#562014yescomplemented
1000C2×C3C2×#100411yescharacteristic
1001C2×C3C2×#100411yescharacteristic
1002C2×C3C2×#100411yescharacteristic
1003C2×C3C2×#100411yescharacteristic
1004C2×C3C2×#100411yescharacteristic
1005C2×C3C2×#100911yescharacteristic
1006D3—42no—
1007D3—42no—
1008D3—42no—
1009D3—124no—
1010D3—122no—
1011D3—122no—
1012C22—22no—
1013C22—22no—
1014C22—22no—
1015C22—22no—
1016C22—22no—
1017C22—22no—
1018C22—44no—
1019C22—44no—
1020C22—62no—
1021C22—62no—
1022C22—62no—
1023C22—62no—
1024C22—62no—
1025C22—62no—
1026C22—62no—
1027C22—62no—
1028C22—62no—
1029C22—1216no—
1030C22—124no—
1031C22—124no—
1032C22—124no—
1033C22—182no—
1034C22—182no—
1035C22—182no—
1036C22—364no—
1037C22#6431312yes—
1038C22#6431412yes—
1039C22#6433012yes—
1040C22C23×D3211yescharacteristic
1041C4—22no—
1042C4—62no—
1043C4—62no—
1044C4—62no—
1045C4—62no—
1046C4—62no—
1047C4—182no—
1048C4—182no—
1049C4—182no—
1050C3—21no—
1051C3C2×#559511yescharacteristic, complemented
1052C3C2×#562011yescharacteristic, complemented
1053C2—42no—
1054C2—42no—
1055C2—122no—
1056C2—122no—
1057C2—122no—
1058C2—362no—
1059C2#1059525814yesdirect product factor
1060C2C2×#6431311yescharacteristic
1061C2C2×#6431411yescharacteristic
1062C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#560
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64147C2semidirect
2. C2×C3×#939C2semidirect
3. C2×C3×#937C2semidirect
4. C2×#63979C2semidirect
5. C2×#63978C2semidirect
6. C2×#63977C2semidirect
7. C2×#63976C2semidirect
8. C2×#63971C2semidirect
9. C2×#63970C2semidirect
10. C2×#63961C2semidirect
11. C2×#63956C2semidirect
12. #10595258C2direct (N × H)
13. C2×#63912C2semidirect
14. C2×#63891C2semidirect
15. C2×#63861C2semidirect
16. C2×#63853C2semidirect
22. C22×#638C22semidirect
23. C22×C4×C3⋊D3C22semidirect
27. C22×C3×#67C22semidirect
28. C23×C3×Dic3C22semidirect
31. C22×#626C22semidirect
34. C22×D3×Dic3C22semidirect
36. C2×#3757C22semidirect
37. #64147C22semidirect
38. C2×C4⋊(C3⋊Dic3)C22semidirect
41. C3×#939C22semidirect
42. C3×#937C22semidirect
45. C2×C3×(C2×D3)⋊C4C22semidirect
46. C2×C3×Dic3⋊C4C22semidirect
47. #63979C22semidirect
48. #63978C22semidirect
49. #63977C22semidirect
50. #63976C22semidirect
51. #63971C22semidirect
52. #63970C22semidirect
53. C2×#3724C22semidirect
54. C2×#3724C22semidirect
55. C2×Dic3⋊Dic3C22semidirect
56. C2×Dic3⋊Dic3C22semidirect
57. C2×#3722C22semidirect
58. #63961C22semidirect
63. #63956C22semidirect
64. C2×Dic32C22semidirect
65. #63912C22semidirect
66. #63891C22semidirect
67. #63861C22semidirect
68. #63853C22semidirect
78. C2×#939D3semidirect
84. C2×#937D3semidirect
118. C2×#638C23semidirect
123. C2×C4×C3⋊D3C23semidirect
131. C2×C3×#67C23semidirect
138. C22×C3×Dic3C23semidirect
144. C2×#626C23semidirect
150. C2×D3×Dic3C23semidirect
152. #3757C23semidirect
153. C4⋊(C3⋊Dic3)C23semidirect
158. C3×(C2×D3)⋊C4C23semidirect
159. C3×Dic3⋊C4C23semidirect
160. #3724C23semidirect
161. #3724C23semidirect
162. Dic3⋊Dic3C23semidirect
163. Dic3⋊Dic3C23semidirect
164. #3722C23semidirect
169. Dic32C23semidirect
197. C22×#67C2×D3semidirect
199. C23×Dic3C2×D3semidirect
234. #939C2×D3semidirect
240. #937C2×D3semidirect
252. C2×(C2×D3)⋊C4C2×D3semidirect
264. C2×Dic3⋊C4C2×D3semidirect
437. C2×#67C22×D3semidirect
455. C22×Dic3C22×D3semidirect
496. (C2×D3)⋊C4C22×D3semidirect
508. Dic3⋊C4C22×D3semidirect
750. C2×C32#560semidirect
922. C32C2×#560semidirect
998. C2×C3#5595semidirect
999. C2×C3#5620semidirect
1051. C3C2×#5595semidirect
1052. C3C2×#5620semidirect
1059. C2#10595258direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641472
C2×C3×#9392
C2×C3×#9372
C2×#639792
C2×#639782
C2×#639772
C2×#639762
C2×#639712
C2×#639702
C2×#639612
C2×#639562
#105952582
C2×#639122
C2×#638912
C2×#638612
C2×#638532
C2×#56203
C2×#55953