Finite Group Databasebeta

← C2×#10595257 #11910189

Subgroups — C2×#10595257 #11910189

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×#64148C211yesmaximal, characteristic, complemented
2C2×C3×#938C211yesmaximal, characteristic, complemented
3C2×C3×#937C211yesmaximal, characteristic, complemented
4C2×#63980C211yesmaximal, characteristic, complemented
5C2×#63979C211yesmaximal, characteristic, complemented
6C2×#63977C211yesmaximal, characteristic, complemented
7C2×#63976C211yesmaximal, characteristic, complemented
8C2×#63962C211yesmaximal, characteristic, complemented
9C2×#63958C211yesmaximal, characteristic, complemented
10C2×#63958C211yesmaximal, characteristic, complemented
11C2×#63956C211yesmaximal, characteristic, complemented
12#10595257C2116yesmaximal, direct product factor
13C2×#63906C211yesmaximal, characteristic, complemented
14C2×#63905C211yesmaximal, characteristic, complemented
15C2×#63858C211yesmaximal, characteristic, complemented
16C2×#63854C211yesmaximal, characteristic, complemented
17C2×#5620—31nomaximal
18C2×#5595—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C22×#638C2211yescharacteristic, complemented
23C23×C3⋊Dic3C2211yescharacteristic, complemented
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C22×C3×#67C2211yescharacteristic
27C22×C3×#67C2211yescharacteristic, complemented
28C22×C3×C4×D3C2211yescharacteristic, complemented
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic
31C22×#626C2211yescharacteristic, complemented
32C22×#625C2211yescharacteristic
33C22×#625C2211yescharacteristic
34C22×#624C2211yescharacteristic, complemented
35C2×#3757C2211yescharacteristic
36#64148C2218yescomplemented
37C2×#3752C2211yescharacteristic, complemented
38C2×#3750C2211yescharacteristic, complemented
39C2×C3×#217C2211yescharacteristic
40C2×C3×#217C2211yescharacteristic
41C2×C3×#217C2211yescharacteristic, complemented
42C3×#938C2218yescomplemented
43C3×#937C2218yescomplemented
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic
45C2×C3×(C2×D3)⋊C4C2211yescharacteristic
46C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
47#63980C2218yescomplemented
48#63979C2218yescomplemented
49#63977C2218yescomplemented
50#63976C2218yescomplemented
51C2×#3724C2211yescharacteristic, complemented
52C2×Dic3⋊Dic3C2211yescharacteristic, complemented
53C2×Dic3⋊Dic3C2211yescharacteristic, complemented
54C2×Dic3⋊Dic3C2211yescharacteristic, complemented
55#63962C2218yescomplemented
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61#63958C2218yescomplemented
62#63958C2218yescomplemented
63#63956C2218yescomplemented
64C2×Dic32C2211yescharacteristic, complemented
65#63906C2218yescomplemented
66#63905C2218yescomplemented
67#63858C2218yescomplemented
68#63854C2218yescomplemented
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×#939—31no—
79C2×#939—61no—
80C2×#938—31no—
81C2×#938—31no—
82C2×#938D311yescharacteristic, complemented
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⋊Dic3—42no—
120C22×C3⋊Dic3C2311yescharacteristic
121C22×C3⋊Dic3C2311yescharacteristic
122C22×C3⋊Dic3C2311yescharacteristic
123C22×C3⋊Dic3C2314yescomplemented
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×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2311yescharacteristic
137C2×C3×C4×D3—42no—
138C2×C3×C4×D3C2314yescomplemented
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×#624—42no—
150C2×#624C2314yescomplemented
151#3757C2314yes—
152#3752C2314yescomplemented
153#3750C2314yescomplemented
154C3×#217C2314yes—
155C3×#217C2314yes—
156C3×#217C2314yescomplemented
157C3×(C2×D3)⋊C4C2314yes—
158C3×(C2×D3)⋊C4C2314yes—
159C3×C4⋊Dic3C2314yescomplemented
160#3724C2314yescomplemented
161Dic3⋊Dic3C2314yescomplemented
162Dic3⋊Dic3C2314yescomplemented
163Dic3⋊Dic3C2314yescomplemented
164(C2×D3)⋊Dic3C2314yes—
165(C2×D3)⋊Dic3C2314yes—
166(C2×D3)⋊Dic3C2314yes—
167(C2×D3)⋊Dic3C2314yes—
168(C2×D3)⋊Dic3C2314yescomplemented
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×Dic3—31no—
200C23×Dic3—61no—
201C22×D12—31no—
202C22×D12—31no—
203C22×D12—31no—
204C22×C4×D3—31no—
205C22×C4×D3—31no—
206C22×C4×D3C2×D311yescharacteristic, complemented
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—61no—
225C2×#217C2×D311yescharacteristic
226C2×#217C2×D311yescharacteristic
227C2×#217C2×D311yescharacteristic, complemented
228#940—38no—
229#940—38no—
230#939—38no—
231#939—38no—
232#939—38no—
233#939—38no—
234#939—68no—
235#938—38no—
236#938—38no—
237#938C2×D318yescomplemented
238#937—38no—
239#937C2×D318yescomplemented
240#935—38no—
241#930—38no—
242#929—38no—
243C2×(C2×D3)⋊C4—31no—
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)⋊C4—61no—
251C2×(C2×D3)⋊C4C2×D311yescharacteristic
252C2×(C2×D3)⋊C4C2×D311yescharacteristic
253C2×C4⋊Dic3—31no—
254C2×C4⋊Dic3—31no—
255C2×C4⋊Dic3—31no—
256C2×C4⋊Dic3C2×D311yescharacteristic, complemented
257C2×Dic3⋊C4—31no—
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⋊C4—61no—
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⋊Dic3—44no—
317C2×C3⋊Dic3C2412yes—
318C2×C3⋊Dic3C2412yes—
319C2×C3⋊Dic3C2412yes—
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×Dic3C2412yes—
330C2×C3×Dic3C2412yes—
331C2×C3×Dic3C2412yes—
332C2×C3×Dic3C2412yes—
333C2×C3×Dic3C2412yes—
334C3×C4×D3—44no—
335#626—44no—
336#626—44no—
337#626—44no—
338#625—44no—
339#625—44no—
340#624—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—34no—
446C22×Dic3—61no—
447C22×Dic3—61no—
448C22×Dic3—61no—
449C22×Dic3—64no—
450C22×Dic3—122no—
451C22×Dic3—122no—
452C22×Dic3—124no—
453C22×Dic3C22×D311yescharacteristic
454C22×Dic3C22×D311yescharacteristic
455C22×Dic3C22×D311yescharacteristic
456C22×Dic3C22×D311yescharacteristic
457C22×Dic3C22×D311yescharacteristic
458C2×D12—34no—
459C2×D12—34no—
460C2×D12—34no—
461C2×D12—122no—
462C2×D12—122no—
463C2×D12—122no—
464C2×C4×D3—34no—
465C2×C4×D3—34no—
466C2×C4×D3—42no—
467C2×C4×D3—122no—
468C2×C4×D3—122no—
469C2×C4×D3C22×D314yescomplemented
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—64no—
484#217C22×D314yes—
485#217C22×D314yes—
486#217C22×D314yescomplemented
487(C2×D3)⋊C4—34no—
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)⋊C4—64no—
495(C2×D3)⋊C4C22×D314yes—
496(C2×D3)⋊C4C22×D314yes—
497C4⋊Dic3—34no—
498C4⋊Dic3—34no—
499C4⋊Dic3—34no—
500C4⋊Dic3C22×D314yescomplemented
501Dic3⋊C4—34no—
502Dic3⋊C4—34no—
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4—34no—
508Dic3⋊C4—64no—
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—24no—
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—22no—
614C23×C3—21no—
615C23×C3—32no—
616C23×C3—32no—
617C23×C3—32no—
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—62no—
659C22×D3—62no—
660C22×D3—62no—
661C22×D3—62no—
662C22×D3—62no—
663C22×D3—62no—
664C22×D3—122no—
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—22no—
678C2×C3×C4—22no—
679C2×C3×C4—22no—
680C2×C3×C4—32no—
681C2×C3×C4—32no—
682C2×C3×C4—32no—
683C2×C3×C4—32no—
684C2×C3×C4—32no—
685C2×C3×C4—42no—
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—62no—
723C2×Dic3—62no—
724C2×Dic3—62no—
725C2×Dic3—64no—
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—124no—
735C2×Dic3—124no—
736C2×Dic3—128no—
737C2×Dic3C23×D312yes—
738C2×Dic3C23×D312yes—
739C2×Dic3C23×D312yes—
740C2×Dic3C23×D312yes—
741C2×Dic3C23×D312yes—
742D12—124no—
743D12—124no—
744D12—124no—
745C4×D3—44no—
746C4×D3—124no—
747C4×D3—124no—
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—24no—
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—22no—
842C22×C3—21no—
843C22×C3—42no—
844C22×C3—42no—
845C22×C3—42no—
846C22×C3—42no—
847C22×C3—42no—
848C22×C3—48no—
849C22×C3—44no—
850C22×C3—44no—
851C22×C3—44no—
852C22×C3—44no—
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—62no—
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—62no—
889C2×D3—62no—
890C2×D3—62no—
891C2×D3—62no—
892C2×D3—62no—
893C2×D3—62no—
894C2×D3—122no—
895C2×D3—122no—
896C2×D3—122no—
897C2×D3—124no—
898C2×D3—124no—
899C2×D3—244no—
900C3×C4—22no—
901C3×C4—22no—
902C3×C4—42no—
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—64no—
914Dic3—62no—
915Dic3—62no—
916Dic3—62no—
917Dic3—62no—
918Dic3—62no—
919Dic3—62no—
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—44no—
990C2×C3—42no—
991C2×C3—42no—
992C2×C3—42no—
993C2×C3—42no—
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—122no—
1010D3—122no—
1011D3—242no—
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#1059525714yesdirect 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×#64148C2semidirect
2. C2×C3×#938C2semidirect
3. C2×C3×#937C2semidirect
4. C2×#63980C2semidirect
5. C2×#63979C2semidirect
6. C2×#63977C2semidirect
7. C2×#63976C2semidirect
8. C2×#63962C2semidirect
9. C2×#63958C2semidirect
10. C2×#63958C2semidirect
11. C2×#63956C2semidirect
12. #10595257C2direct (N × H)
13. C2×#63906C2semidirect
14. C2×#63905C2semidirect
15. C2×#63858C2semidirect
16. C2×#63854C2semidirect
22. C22×#638C22semidirect
23. C23×C3⋊Dic3C22semidirect
27. C22×C3×#67C22semidirect
28. C22×C3×C4×D3C22semidirect
31. C22×#626C22semidirect
34. C22×#624C22semidirect
36. #64148C22semidirect
37. C2×#3752C22semidirect
38. C2×#3750C22semidirect
41. C2×C3×#217C22semidirect
42. C3×#938C22semidirect
43. C3×#937C22semidirect
46. C2×C3×C4⋊Dic3C22semidirect
47. #63980C22semidirect
48. #63979C22semidirect
49. #63977C22semidirect
50. #63976C22semidirect
51. C2×#3724C22semidirect
52. C2×Dic3⋊Dic3C22semidirect
53. C2×Dic3⋊Dic3C22semidirect
54. C2×Dic3⋊Dic3C22semidirect
55. #63962C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. #63958C22semidirect
62. #63958C22semidirect
63. #63956C22semidirect
64. C2×Dic32C22semidirect
65. #63906C22semidirect
66. #63905C22semidirect
67. #63858C22semidirect
68. #63854C22semidirect
82. C2×#938D3semidirect
84. C2×#937D3semidirect
118. C2×#638C23semidirect
123. C22×C3⋊Dic3C23semidirect
131. C2×C3×#67C23semidirect
138. C2×C3×C4×D3C23semidirect
144. C2×#626C23semidirect
150. C2×#624C23semidirect
152. #3752C23semidirect
153. #3750C23semidirect
156. C3×#217C23semidirect
159. C3×C4⋊Dic3C23semidirect
160. #3724C23semidirect
161. Dic3⋊Dic3C23semidirect
162. Dic3⋊Dic3C23semidirect
163. Dic3⋊Dic3C23semidirect
168. (C2×D3)⋊Dic3C23semidirect
169. Dic32C23semidirect
197. C22×#67C2×D3semidirect
206. C22×C4×D3C2×D3semidirect
227. C2×#217C2×D3semidirect
237. #938C2×D3semidirect
239. #937C2×D3semidirect
256. C2×C4⋊Dic3C2×D3semidirect
437. C2×#67C22×D3semidirect
469. C2×C4×D3C22×D3semidirect
486. #217C22×D3semidirect
500. C4⋊Dic3C22×D3semidirect
750. C2×C32#560semidirect
922. C32C2×#560semidirect
998. C2×C3#5595semidirect
999. C2×C3#5620semidirect
1051. C3C2×#5595semidirect
1052. C3C2×#5620semidirect
1059. C2#10595257direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641482
C2×C3×#9382
C2×C3×#9372
C2×#639802
C2×#639792
C2×#639772
C2×#639762
C2×#639622
C2×#639582
C2×#639562
#105952572
C2×#639062
C2×#639052
C2×#638582
C2×#638542
C2×#56203
C2×#55953