Finite Group Databasebeta

← C2×#10595188 #11901521

Subgroups — C2×#10595188 #11901521

Order 1152.

2691 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64144C211yesmaximal, characteristic, complemented
2C2×C3×#940C211yesmaximal, characteristic, complemented
3C2×C3×#939C211yesmaximal, characteristic, complemented
4C2×#63980C211yesmaximal, characteristic, complemented
5C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
6C2×Dic3×#67C211yesmaximal, characteristic, complemented
7C2×#63970C211yesmaximal, characteristic, complemented
8C2×#63970C211yesmaximal, characteristic, complemented
9C2×#63970C211yesmaximal, characteristic, complemented
10C2×#63969C211yesmaximal, characteristic, complemented
11C2×#63961C211yesmaximal, characteristic, complemented
12#10595188C2116yesmaximal, direct product factor
13C2×#63885C211yesmaximal, characteristic, complemented
14C2×#63884C211yesmaximal, characteristic, complemented
15C2×#63877C211yesmaximal, characteristic, complemented
16C2×#63867C211yesmaximal, characteristic, complemented
17C2×#5719—31nomaximal
18C2×#5615—31nomaximal
19C22×C32×D4C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C22×C3×#67C2211yescharacteristic
27C23×C3×Dic3C2211yescharacteristic
28C22×C3×D12C2211yescharacteristic
29C22×#625C2211yescharacteristic
30C22×#625C2211yescharacteristic
31C22×D3×Dic3C2211yescharacteristic
32C22×D3×Dic3C2211yescharacteristic
33C22×D3×Dic3C2211yescharacteristic
34C2×#3757C2211yescharacteristic
35C2×#3757C2211yescharacteristic
36C2×#3757C2211yescharacteristic
37#64144C2218yescomplemented
38C2×#3750C2211yescharacteristic
39C2×#3750C2211yescharacteristic
40C2×C3×#217C2211yescharacteristic
41C3×#940C2218yescomplemented
42C3×#939C2218yescomplemented
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×Dic3⋊C4C2211yescharacteristic
45C2×C3×C4×Dic3C2211yescharacteristic
46#63980C2218yescomplemented
47#67⋊Dic3C2218yescomplemented
48Dic3×#67C2218yescomplemented
49#63970C2218yescomplemented
50#63970C2218yescomplemented
51#63970C2218yescomplemented
52#63969C2218yescomplemented
53C2×#3724C2211yescharacteristic
54C2×#3724C2211yescharacteristic
55C2×Dic3⋊Dic3C2211yescharacteristic
56C2×Dic3⋊Dic3C2211yescharacteristic
57C2×Dic3⋊Dic3C2211yescharacteristic
58#63961C2218yescomplemented
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2211yescharacteristic
61C2×(C2×D3)⋊Dic3C2211yescharacteristic
62C2×(C2×D3)⋊Dic3C2211yescharacteristic
63C2×(C2×D3)⋊Dic3C2211yescharacteristic
64C2×Dic32C2211yescharacteristic
65#63885C2218yescomplemented
66#63884C2218yescomplemented
67#63877C2218yescomplemented
68#63867C2218yescomplemented
69C2×C3×#127—31no—
70C2×C3×#121—31no—
71C2×#940D311yescharacteristic, complemented
72C2×#939—31no—
73C2×#939—31no—
74C2×#939—31no—
75C2×#939—31no—
76C2×#939—31no—
77C2×#939—31no—
78C2×#939D311yescharacteristic, complemented
79C2×#938—31no—
80C2×#938—31no—
81C2×#938—31no—
82C2×#935—31no—
83C2×#935—31no—
84C2×#935—31no—
85C2×#935—31no—
86C2×#935—31no—
87C2×#935—61no—
88C2×D4×Dic3—31no—
89C2×D4×Dic3—31no—
90C2×#929—31no—
91C2×C4×#67—31no—
92#5719—316no—
93#5615—316no—
94C2×#894—31no—
95C2×#889—31no—
96C2×#884—31no—
97C2×#883—31no—
98C2×#67⋊C4—31no—
99C2×#877—31no—
100C2×#872—31no—
101C2×#870—31no—
102C24×C32C2311yescharacteristic
103C24×C32C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C2×C32×D4—42no—
108C2×C32×D4C2314yes—
109C22×C32×C4C2311yescharacteristic
110C22×C3⋊Dic3—42no—
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2311yescharacteristic
114C22×C3⋊Dic3C2311yescharacteristic
115C22×C3⋊Dic3C2314yes—
116C2×C3×#67—24no—
117C2×C3×#67—24no—
118C2×C3×#67—42no—
119C2×C3×#67—42no—
120C2×C3×#67—42no—
121C2×C3×#67—42no—
122C2×C3×#67C2314yes—
123C2×C3×#67C2314yes—
124C2×C3×#67C2314yes—
125C2×C3×#67C2314yes—
126C2×C3×#67C2314yes—
127C2×C3×#67C2314yes—
128C22×C3×Dic3—42no—
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2314yes—
134C22×C3×Dic3C2311yescharacteristic
135C2×C3×D12—42no—
136C2×C3×D12C2314yes—
137C2×#625—42no—
138C2×#625—42no—
139C2×#625C2314yes—
140C2×#625C2314yes—
141C2×D3×Dic3—24no—
142C2×D3×Dic3—42no—
143C2×D3×Dic3—42no—
144C2×D3×Dic3C2314yes—
145C2×D3×Dic3C2314yes—
146C2×D3×Dic3C2314yes—
147#3757C2314yes—
148#3757C2314yes—
149#3757C2314yes—
150#3750C2314yes—
151#3750C2314yes—
152C3×#217C2314yes—
153C3×(C2×D3)⋊C4C2314yes—
154C3×Dic3⋊C4C2314yes—
155C3×C4×Dic3C2314yes—
156#3724C2314yes—
157#3724C2314yes—
158Dic3⋊Dic3C2314yes—
159Dic3⋊Dic3C2314yes—
160Dic3⋊Dic3C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163(C2×D3)⋊Dic3C2314yes—
164(C2×D3)⋊Dic3C2314yes—
165(C2×D3)⋊Dic3C2314yes—
166Dic32C2314yes—
167C2×#540—91noSylow
168C22×C3×D4—21no—
169C22×C3×D4—31no—
170C22×C3×D4—31no—
171C22×C3×D4—31no—
172C22×C3×D4—31no—
173C22×C3×D4—31no—
174C22×C3×D4—31no—
175C22×C3×D4—31no—
176C22×C3×D4C2×D311yescharacteristic
177C22×C3×D4C2×D311yescharacteristic
178C23×C3×C4—31no—
179C22×#67—31no—
180C22×#67—31no—
181C22×#67—31no—
182C22×#67—31no—
183C22×#67C2×D311yescharacteristic
184C22×#67C2×D311yescharacteristic
185C22×#67C2×D311yescharacteristic
186C22×#67C2×D311yescharacteristic
187C22×#67C2×D311yescharacteristic
188C22×#67C2×D311yescharacteristic
189C23×Dic3—31no—
190C23×Dic3—31no—
191C23×Dic3—31no—
192C23×Dic3—31no—
193C23×Dic3—31no—
194C23×Dic3—61no—
195C23×Dic3C2×D311yescharacteristic
196C22×D12C2×D311yescharacteristic
197C22×C4×D3—31no—
198C22×C4×D3—31no—
199C22×C4×D3—31no—
200C3×#127—38no—
201C3×#121—38no—
202C2×C3×C4⋊C4—31no—
203C2×C3×C22⋊C4—31no—
204C2×C3×C22⋊C4—31no—
205C2×C3×C42—31no—
206C2×#217—31no—
207C2×#217—31no—
208C2×#217—31no—
209C2×#217—31no—
210C2×#217—31no—
211C2×#217—31no—
212C2×#217—31no—
213C2×#217—31no—
214C2×#217—31no—
215C2×#217—31no—
216C2×#217—31no—
217C2×#217—61no—
218C2×#217—61no—
219C2×#217—61no—
220C2×#217C2×D311yescharacteristic
221#940C2×D318yescomplemented
222#939—38no—
223#939—38no—
224#939—38no—
225#939—38no—
226#939—38no—
227#939—38no—
228#939C2×D318yescomplemented
229#938—38no—
230#938—38no—
231#938—38no—
232#935—38no—
233#935—38no—
234#935—38no—
235#935—38no—
236#935—38no—
237#935—68no—
238D4×Dic3—38no—
239D4×Dic3—38no—
240#929—38no—
241C4×#67—38no—
242C2×(C2×D3)⋊C4—31no—
243C2×(C2×D3)⋊C4—31no—
244C2×(C2×D3)⋊C4—31no—
245C2×(C2×D3)⋊C4—31no—
246C2×(C2×D3)⋊C4—31no—
247C2×(C2×D3)⋊C4C2×D311yescharacteristic
248C2×C4⋊Dic3—31no—
249C2×C4⋊Dic3—31no—
250C2×C4⋊Dic3—31no—
251C2×Dic3⋊C4—31no—
252C2×Dic3⋊C4—31no—
253C2×Dic3⋊C4—31no—
254C2×Dic3⋊C4—31no—
255C2×Dic3⋊C4—31no—
256C2×Dic3⋊C4—31no—
257C2×Dic3⋊C4—31no—
258C2×Dic3⋊C4—31no—
259C2×Dic3⋊C4—31no—
260C2×Dic3⋊C4—31no—
261C2×Dic3⋊C4—31no—
262C2×Dic3⋊C4—61no—
263C2×Dic3⋊C4—61no—
264C2×Dic3⋊C4C2×D311yescharacteristic
265C2×C4×Dic3—31no—
266C2×C4×Dic3—31no—
267C2×C4×Dic3C2×D311yescharacteristic
268#894—38no—
269#889—38no—
270#884—38no—
271#883—38no—
272#67⋊C4—38no—
273#877—38no—
274#872—38no—
275#870—38no—
276C23×C32—22no—
277C23×C32—22no—
278C23×C32—22no—
279C23×C32—22no—
280C23×C32—22no—
281C23×C32—22no—
282C23×C32C2412yes—
283C23×C32C2412yes—
284C23×C32C2411yescharacteristic
285C22×C3×D3—22no—
286C22×C3×D3—22no—
287C22×C3×D3—22no—
288C22×C3×D3—22no—
289C22×C3×D3—22no—
290C22×C3×D3—22no—
291C22×C3×D3—22no—
292C22×C3×D3—22no—
293C22×C3×D3—22no—
294C22×C3×D3C2412yes—
295C22×C3×D3C2412yes—
296C22×C3×D3C2412yes—
297C32×D4—44no—
298C2×C32×C4—22no—
299C2×C32×C4C2412yes—
300C2×C3⋊Dic3—22no—
301C2×C3⋊Dic3—22no—
302C2×C3⋊Dic3—22no—
303C2×C3⋊Dic3—22no—
304C2×C3⋊Dic3—44no—
305C2×C3⋊Dic3C2412yes—
306C2×C3⋊Dic3C2412yes—
307C2×C3⋊Dic3C2412yes—
308C2×C3⋊Dic3C2412yes—
309C3×#67—28no—
310C3×#67—28no—
311C3×#67—44no—
312C3×#67—44no—
313C3×#67—44no—
314C3×#67—44no—
315C2×C3×Dic3—22no—
316C2×C3×Dic3—22no—
317C2×C3×Dic3—22no—
318C2×C3×Dic3—22no—
319C2×C3×Dic3—44no—
320C2×C3×Dic3#4114yes—
321C2×C3×Dic3C2412yes—
322C2×C3×Dic3C2412yes—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2412yes—
326C3×D12—44no—
327#625—44no—
328#625—44no—
329D3×Dic3—28no—
330D3×Dic3—44no—
331D3×Dic3—44no—
332#540—916no—
333C2×#127—31no—
334C2×#125—91no—
335C2×#123—91no—
336C2×#123—91no—
337C2×#123—91no—
338C2×#123—91no—
339C2×#121—31no—
340C2×#121—91no—
341C2×#121—91no—
342C2×#121—91no—
343C2×#121—91no—
344C2×#121—91no—
345C2×C4×D4—91no—
346C2×C4×D4—91no—
347C2×#117—91no—
348C24×C3—21no—
349C24×C3—21no—
350C24×C3—31no—
351C24×C3—31no—
352C24×C3—31no—
353C24×C3C22×D311yescharacteristic
354C24×C3C22×D311yescharacteristic
355C24×C3C22×D311yescharacteristic
356C24×C3C22×D311yescharacteristic
357C23×D3C22×D311yescharacteristic
358C23×D3C22×D311yescharacteristic
359C23×D3C22×D311yescharacteristic
360C2×C3×D4—24no—
361C2×C3×D4—34no—
362C2×C3×D4—34no—
363C2×C3×D4—34no—
364C2×C3×D4—34no—
365C2×C3×D4—34no—
366C2×C3×D4—34no—
367C2×C3×D4—34no—
368C2×C3×D4—42no—
369C2×C3×D4—42no—
370C2×C3×D4—44no—
371C2×C3×D4—64no—
372C2×C3×D4—64no—
373C2×C3×D4—122no—
374C2×C3×D4—122no—
375C2×C3×D4—122no—
376C2×C3×D4—122no—
377C2×C3×D4—122no—
378C2×C3×D4C22×D314yes—
379C2×C3×D4C22×D314yes—
380C22×C3×C4—21no—
381C22×C3×C4—31no—
382C22×C3×C4—31no—
383C22×C3×C4—31no—
384C22×C3×C4—31no—
385C22×C3×C4—31no—
386C22×C3×C4—34no—
387C22×C3×C4—122no—
388C22×C3×C4C22×D311yescharacteristic
389C22×C3×C4C22×D311yescharacteristic
390C2×#67—24no—
391C2×#67—24no—
392C2×#67—34no—
393C2×#67—34no—
394C2×#67—34no—
395C2×#67—34no—
396C2×#67—42no—
397C2×#67—42no—
398C2×#67—42no—
399C2×#67—42no—
400C2×#67—122no—
401C2×#67—122no—
402C2×#67—122no—
403C2×#67—122no—
404C2×#67C22×D314yes—
405C2×#67C22×D314yes—
406C2×#67C22×D314yes—
407C2×#67C22×D314yes—
408C2×#67C22×D314yes—
409C2×#67C22×D314yes—
410C22×Dic3—31no—
411C22×Dic3—31no—
412C22×Dic3—31no—
413C22×Dic3—31no—
414C22×Dic3—31no—
415C22×Dic3—31no—
416C22×Dic3—31no—
417C22×Dic3—31no—
418C22×Dic3—34no—
419C22×Dic3—34no—
420C22×Dic3—34no—
421C22×Dic3—34no—
422C22×Dic3—34no—
423C22×Dic3—42no—
424C22×Dic3—61no—
425C22×Dic3—61no—
426C22×Dic3—61no—
427C22×Dic3—61no—
428C22×Dic3—64no—
429C22×Dic3—64no—
430C22×Dic3—122no—
431C22×Dic3—122no—
432C22×Dic3—122no—
433C22×Dic3—122no—
434C22×Dic3—124no—
435C22×Dic3C22×D311yescharacteristic
436C22×Dic3C22×D311yescharacteristic
437C22×Dic3C22×D311yescharacteristic
438C22×Dic3C22×D311yescharacteristic
439C22×Dic3C22×D314yes—
440C22×Dic3C22×D311yescharacteristic
441C2×D12—42no—
442C2×D12C22×D314yes—
443C2×C4×D3—34no—
444C2×C4×D3—34no—
445C2×C4×D3—34no—
446C2×C4×D3—64no—
447C2×C4×D3—122no—
448C2×C4×D3—122no—
449C3×C4⋊C4—34no—
450C3×C22⋊C4—34no—
451C3×C22⋊C4—34no—
452C3×C42—34no—
453#217—34no—
454#217—34no—
455#217—34no—
456#217—34no—
457#217—34no—
458#217—34no—
459#217—34no—
460#217—34no—
461#217—34no—
462#217—34no—
463#217—34no—
464#217—64no—
465#217—64no—
466#217—64no—
467#217C22×D314yes—
468(C2×D3)⋊C4—34no—
469(C2×D3)⋊C4—34no—
470(C2×D3)⋊C4—34no—
471(C2×D3)⋊C4—34no—
472(C2×D3)⋊C4—34no—
473(C2×D3)⋊C4C22×D314yes—
474C4⋊Dic3—34no—
475C4⋊Dic3—34no—
476C4⋊Dic3—34no—
477Dic3⋊C4—34no—
478Dic3⋊C4—34no—
479Dic3⋊C4—34no—
480Dic3⋊C4—34no—
481Dic3⋊C4—34no—
482Dic3⋊C4—34no—
483Dic3⋊C4—34no—
484Dic3⋊C4—34no—
485Dic3⋊C4—34no—
486Dic3⋊C4—34no—
487Dic3⋊C4—34no—
488Dic3⋊C4—64no—
489Dic3⋊C4—64no—
490Dic3⋊C4C22×D314yes—
491C4×Dic3—34no—
492C4×Dic3—34no—
493C4×Dic3C22×D314yes—
494C22×C32—22no—
495C22×C32—22no—
496C22×C32—22no—
497C22×C32—22no—
498C22×C32—22no—
499C22×C32—22no—
500C22×C32—44no—
501C22×C32—44no—
502C22×C32C2×#4112yes—
503C22×C32H(5,𝔽2)12yes—
504C22×C32H(5,𝔽2)12yes—
505C22×C32C2511yescharacteristic
506C2×C3×D3—22no—
507C2×C3×D3—22no—
508C2×C3×D3—22no—
509C2×C3×D3—22no—
510C2×C3×D3—22no—
511C2×C3×D3—22no—
512C2×C3×D3—22no—
513C2×C3×D3—22no—
514C2×C3×D3—22no—
515C2×C3×D3—44no—
516C2×C3×D3—44no—
517C2×C3×D3—44no—
518C32×C4—22no—
519C3⋊Dic3—22no—
520C3⋊Dic3—22no—
521C3⋊Dic3—22no—
522C3⋊Dic3—22no—
523C3×Dic3—22no—
524C3×Dic3—22no—
525C3×Dic3—22no—
526C3×Dic3—22no—
527C3×Dic3C2×#4114yes—
528C22×D4—31no—
529C22×D4—31no—
530C22×D4—31no—
531C22×D4—31no—
532C22×D4—31no—
533C22×D4—31no—
534C22×D4—31no—
535C22×D4—91no—
536C22×D4—91no—
537C22×D4D3211yescharacteristic
538C23×C4—31no—
539C23×C4—91no—
540C23×C4—91no—
541C23×C4—91no—
542C23×C4—91no—
543#127—38no—
544#125—98no—
545#123—98no—
546#123—98no—
547#123—98no—
548#123—98no—
549#121—38no—
550#121—98no—
551#121—98no—
552#121—98no—
553#121—98no—
554#121—98no—
555C4×D4—98no—
556C4×D4—98no—
557#117—98no—
558C2×C4⋊C4—31no—
559C2×C4⋊C4—91no—
560C2×C4⋊C4—91no—
561C2×C4⋊C4—91no—
562C2×C4⋊C4—91no—
563C2×C4⋊C4—91no—
564C2×C4⋊C4—91no—
565C2×C4⋊C4—91no—
566C2×C22⋊C4—31no—
567C2×C22⋊C4—31no—
568C2×C22⋊C4—91no—
569C2×C22⋊C4—91no—
570C2×C22⋊C4—91no—
571C2×C22⋊C4—91no—
572C2×C22⋊C4—91no—
573C2×C22⋊C4—91no—
574C2×C22⋊C4—91no—
575C2×C22⋊C4—91no—
576C2×C42—31no—
577C2×C42—91no—
578C23×C3—24no—
579C23×C3—22no—
580C23×C3—22no—
581C23×C3—22no—
582C23×C3—22no—
583C23×C3—22no—
584C23×C3—22no—
585C23×C3—22no—
586C23×C3—22no—
587C23×C3—22no—
588C23×C3—22no—
589C23×C3—22no—
590C23×C3—22no—
591C23×C3—22no—
592C23×C3—22no—
593C23×C3—21no—
594C23×C3—32no—
595C23×C3—32no—
596C23×C3—32no—
597C23×C3—42no—
598C23×C3—42no—
599C23×C3—42no—
600C23×C3—42no—
601C23×C3—42no—
602C23×C3—62no—
603C23×C3—62no—
604C23×C3—62no—
605C23×C3—62no—
606C23×C3—62no—
607C23×C3—62no—
608C23×C3—62no—
609C23×C3—62no—
610C23×C3—62no—
611C23×C3C23×D312yes—
612C23×C3C23×D312yes—
613C23×C3C23×D312yes—
614C23×C3C23×D312yes—
615C23×C3C23×D311yescharacteristic
616C23×C3C23×D311yescharacteristic
617C22×D3—22no—
618C22×D3—22no—
619C22×D3—22no—
620C22×D3—22no—
621C22×D3—22no—
622C22×D3—22no—
623C22×D3—22no—
624C22×D3—22no—
625C22×D3—22no—
626C22×D3C23×D312yes—
627C22×D3C23×D312yes—
628C22×D3C23×D312yes—
629C3×D4—44no—
630C3×D4—44no—
631C3×D4—48no—
632C3×D4—68no—
633C3×D4—68no—
634C3×D4—124no—
635C3×D4—124no—
636C3×D4—124no—
637C3×D4—124no—
638C3×D4—124no—
639C2×C3×C4—22no—
640C2×C3×C4—22no—
641C2×C3×C4—22no—
642C2×C3×C4—34no—
643C2×C3×C4—32no—
644C2×C3×C4—32no—
645C2×C3×C4—32no—
646C2×C3×C4—32no—
647C2×C3×C4—32no—
648C2×C3×C4—42no—
649C2×C3×C4—62no—
650C2×C3×C4—62no—
651C2×C3×C4—62no—
652C2×C3×C4—62no—
653C2×C3×C4—124no—
654C2×C3×C4C23×D312yes—
655C2×C3×C4C23×D312yes—
656#67—28no—
657#67—28no—
658#67—44no—
659#67—44no—
660#67—44no—
661#67—44no—
662#67—124no—
663#67—124no—
664#67—124no—
665#67—124no—
666C2×Dic3—22no—
667C2×Dic3—22no—
668C2×Dic3—22no—
669C2×Dic3—22no—
670C2×Dic3—32no—
671C2×Dic3—32no—
672C2×Dic3—32no—
673C2×Dic3—32no—
674C2×Dic3—32no—
675C2×Dic3—32no—
676C2×Dic3—32no—
677C2×Dic3—32no—
678C2×Dic3—44no—
679C2×Dic3—62no—
680C2×Dic3—62no—
681C2×Dic3—62no—
682C2×Dic3—62no—
683C2×Dic3—62no—
684C2×Dic3—62no—
685C2×Dic3—62no—
686C2×Dic3—62no—
687C2×Dic3—62no—
688C2×Dic3—62no—
689C2×Dic3—62no—
690C2×Dic3—62no—
691C2×Dic3—68no—
692C2×Dic3—122no—
693C2×Dic3—122no—
694C2×Dic3—122no—
695C2×Dic3—122no—
696C2×Dic3—124no—
697C2×Dic3—124no—
698C2×Dic3—124no—
699C2×Dic3—124no—
700C2×Dic3—128no—
701C2×Dic3#23714yes—
702C2×Dic3C23×D312yes—
703C2×Dic3C23×D312yes—
704C2×Dic3C23×D312yes—
705C2×Dic3C23×D312yes—
706C2×Dic3C23×D312yes—
707D12—44no—
708C4×D3—68no—
709C4×D3—124no—
710C4×D3—124no—
711C2×C32—42no—
712C2×C32—42no—
713C2×C32#54014yescomplemented
714C2×C32C22×#4111yescharacteristic
715C2×C32C2×H(5,𝔽2)11yescharacteristic
716C2×C32C2×H(5,𝔽2)11yescharacteristic
717C3×D3—42no—
718C3×D3—42no—
719C3×D3—42no—
720C24—31no—
721C24—31no—
722C24—31no—
723C24C2×D3211yescharacteristic
724C24C2×D3211yescharacteristic
725C2×D4—34no—
726C2×D4—34no—
727C2×D4—34no—
728C2×D4—34no—
729C2×D4—34no—
730C2×D4—34no—
731C2×D4—34no—
732C2×D4—42no—
733C2×D4—64no—
734C2×D4—64no—
735C2×D4—94no—
736C2×D4—94no—
737C2×D4—122no—
738C2×D4—122no—
739C2×D4—122no—
740C2×D4—122no—
741C2×D4—122no—
742C2×D4—362no—
743C2×D4—362no—
744C2×D4C2×D3214yes—
745C22×C4—31no—
746C22×C4—31no—
747C22×C4—31no—
748C22×C4—31no—
749C22×C4—31no—
750C22×C4—34no—
751C22×C4—94no—
752C22×C4—94no—
753C22×C4—94no—
754C22×C4—91no—
755C22×C4—91no—
756C22×C4—91no—
757C22×C4—91no—
758C22×C4—94no—
759C22×C4—122no—
760C22×C4—184no—
761C22×C4—362no—
762C22×C4—362no—
763C22×C4—362no—
764C22×C4C2×D3211yescharacteristic
765C4⋊C4—34no—
766C4⋊C4—94no—
767C4⋊C4—94no—
768C4⋊C4—94no—
769C4⋊C4—94no—
770C4⋊C4—94no—
771C4⋊C4—94no—
772C4⋊C4—94no—
773C22⋊C4—34no—
774C22⋊C4—34no—
775C22⋊C4—94no—
776C22⋊C4—94no—
777C22⋊C4—94no—
778C22⋊C4—94no—
779C22⋊C4—94no—
780C22⋊C4—94no—
781C22⋊C4—94no—
782C22⋊C4—94no—
783C42—34no—
784C42—94no—
785C22×C3—24no—
786C22×C3—22no—
787C22×C3—22no—
788C22×C3—22no—
789C22×C3—22no—
790C22×C3—22no—
791C22×C3—22no—
792C22×C3—22no—
793C22×C3—22no—
794C22×C3—22no—
795C22×C3—22no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—21no—
802C22×C3—42no—
803C22×C3—42no—
804C22×C3—42no—
805C22×C3—42no—
806C22×C3—42no—
807C22×C3—48no—
808C22×C3—44no—
809C22×C3—44no—
810C22×C3—44no—
811C22×C3—44no—
812C22×C3—62no—
813C22×C3—62no—
814C22×C3—62no—
815C22×C3—62no—
816C22×C3—62no—
817C22×C3—62no—
818C22×C3—62no—
819C22×C3—62no—
820C22×C3—62no—
821C22×C3—84no—
822C22×C3—124no—
823C22×C3—124no—
824C22×C3—124no—
825C22×C3C2×#23712yes—
826C22×C3#100412yes—
827C22×C3#100412yes—
828C22×C3#100412yes—
829C22×C3#100412yes—
830C22×C3D3×#4112yes—
831C22×C3C24×D311yescharacteristic
832C22×C3C24×D311yescharacteristic
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—22no—
837C2×D3—22no—
838C2×D3—22no—
839C2×D3—22no—
840C2×D3—22no—
841C2×D3—22no—
842C2×D3—44no—
843C2×D3—44no—
844C2×D3—44no—
845C3×C4—22no—
846C3×C4—22no—
847C3×C4—34no—
848C3×C4—42no—
849C3×C4—62no—
850C3×C4—62no—
851C3×C4—62no—
852C3×C4—62no—
853Dic3—22no—
854Dic3—22no—
855Dic3—22no—
856Dic3—22no—
857Dic3—62no—
858Dic3—62no—
859Dic3—62no—
860Dic3—62no—
861Dic3—62no—
862Dic3—62no—
863Dic3—62no—
864Dic3—62no—
865Dic3—122no—
866Dic3—122no—
867Dic3—122no—
868Dic3—122no—
869Dic3C2×#23714yes—
870C32C2×#54011yescharacteristic, complemented, Sylow
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—32no—
878C23—32no—
879C23—32no—
880C23—62no—
881C23—62no—
882C23—62no—
883C23—62no—
884C23—62no—
885C23—62no—
886C23—62no—
887C23—62no—
888C23—62no—
889C23C22×D3212yes—
890C23C22×D3212yes—
891C23C22×D3211yescharacteristic
892D4—44no—
893D4—68no—
894D4—68no—
895D4—124no—
896D4—124no—
897D4—124no—
898D4—124no—
899D4—124no—
900D4—364no—
901D4—364no—
902C2×C4—22no—
903C2×C4—34no—
904C2×C4—32no—
905C2×C4—32no—
906C2×C4—32no—
907C2×C4—32no—
908C2×C4—32no—
909C2×C4—62no—
910C2×C4—62no—
911C2×C4—62no—
912C2×C4—62no—
913C2×C4—92no—
914C2×C4—92no—
915C2×C4—92no—
916C2×C4—92no—
917C2×C4—124no—
918C2×C4—188no—
919C2×C4—182no—
920C2×C4—182no—
921C2×C4—182no—
922C2×C4—182no—
923C2×C4—364no—
924C2×C4—364no—
925C2×C4—364no—
926C2×C4C22×D3212yes—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—24no—
931C2×C3—44no—
932C2×C3—42no—
933C2×C3—42no—
934C2×C3—42no—
935C2×C3—42no—
936C2×C3—82no—
937C2×C3—122no—
938C2×C3—122no—
939C2×C3—122no—
940C2×C3#561514yescomplemented
941C2×C3#571914yescomplemented
942C2×C3C22×#23711yescharacteristic
943C2×C3C2×#100411yescharacteristic
944C2×C3C2×#100411yescharacteristic
945C2×C3C2×#100411yescharacteristic
946C2×C3C2×#100411yescharacteristic
947C2×C3C2×D3×#4111yescharacteristic
948D3—42no—
949D3—42no—
950D3—42no—
951C22—22no—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—44no—
958C22—44no—
959C22—62no—
960C22—62no—
961C22—62no—
962C22—62no—
963C22—62no—
964C22—62no—
965C22—62no—
966C22—62no—
967C22—62no—
968C22—124no—
969C22—124no—
970C22—124no—
971C22D3×#23712yes—
972C22#6431312yes—
973C22#6433012yes—
974C22C23×D3211yescharacteristic
975C4—22no—
976C4—34no—
977C4—62no—
978C4—62no—
979C4—62no—
980C4—62no—
981C4—182no—
982C4—182no—
983C4—182no—
984C4—182no—
985C3—21no—
986C3C2×#561511yescharacteristic, complemented
987C3C2×#571911yescharacteristic, complemented
988C2—42no—
989C2—42no—
990C2—122no—
991C2—122no—
992C2—122no—
993C2#1059518814yesdirect product factor
994C2C2×D3×#23711yescharacteristic
995C2C2×#6431311yescharacteristic
996C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#540
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64144C2semidirect
2. C2×C3×#940C2semidirect
3. C2×C3×#939C2semidirect
4. C2×#63980C2semidirect
5. C2×#67⋊Dic3C2semidirect
6. C2×Dic3×#67C2semidirect
7. C2×#63970C2semidirect
8. C2×#63970C2semidirect
9. C2×#63970C2semidirect
10. C2×#63969C2semidirect
11. C2×#63961C2semidirect
12. #10595188C2direct (N × H)
13. C2×#63885C2semidirect
14. C2×#63884C2semidirect
15. C2×#63877C2semidirect
16. C2×#63867C2semidirect
37. #64144C22semidirect
41. C3×#940C22semidirect
42. C3×#939C22semidirect
46. #63980C22semidirect
47. #67⋊Dic3C22semidirect
48. Dic3×#67C22semidirect
49. #63970C22semidirect
50. #63970C22semidirect
51. #63970C22semidirect
52. #63969C22semidirect
58. #63961C22semidirect
65. #63885C22semidirect
66. #63884C22semidirect
67. #63877C22semidirect
68. #63867C22semidirect
71. C2×#940D3semidirect
78. C2×#939D3semidirect
221. #940C2×D3semidirect
228. #939C2×D3semidirect
713. C2×C32#540semidirect
870. C32C2×#540semidirect
940. C2×C3#5615semidirect
941. C2×C3#5719semidirect
986. C3C2×#5615semidirect
987. C3C2×#5719semidirect
993. C2#10595188direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641442
C2×C3×#9402
C2×C3×#9392
C2×#639802
C2×#67⋊Dic32
C2×Dic3×#672
C2×#639702
C2×#639692
C2×#639612
#105951882
C2×#638852
C2×#638842
C2×#638772
C2×#638672
C2×#57193
C2×#56153