Finite Group Databasebeta

← C2×#10595250 #11901503

Subgroups — C2×#10595250 #11901503

Order 1152.

2733 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64148C211yesmaximal, characteristic, complemented
2C2×C3×#939C211yesmaximal, characteristic, complemented
3C2×C3×#938C211yesmaximal, characteristic, complemented
4C2×#63979C211yesmaximal, characteristic, complemented
5C2×#63978C211yesmaximal, characteristic, complemented
6C2×#63975C211yesmaximal, characteristic, complemented
7C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
8C2×#63970C211yesmaximal, characteristic, complemented
9C2×#63962C211yesmaximal, characteristic, complemented
10C2×#63958C211yesmaximal, characteristic, complemented
11C2×#63955C211yesmaximal, characteristic, complemented
12#10595250C2116yesmaximal, direct product factor
13C2×#63905C211yesmaximal, characteristic, complemented
14C2×#63904C211yesmaximal, characteristic, complemented
15C2×#63890C211yesmaximal, characteristic, complemented
16C2×#63846C211yesmaximal, characteristic, complemented
17C2×#5615—31nomaximal
18C2×#5619—31nomaximal
19C22×C32×D4C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C23×C3⋊Dic3C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C22×C3×#67C2211yescharacteristic
27C23×C3×Dic3C2211yescharacteristic
28C22×C3×C4×D3C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic
31C22×#625C2211yescharacteristic
32C22×#624C2211yescharacteristic
33C22×D3×Dic3C2211yescharacteristic
34C2×#3757C2211yescharacteristic
35#64148C2218yescomplemented
36C2×#3752C2211yescharacteristic
37C2×#3750C2211yescharacteristic
38C2×C3×#217C2211yescharacteristic
39C2×C3×#217C2211yescharacteristic
40C2×C3×#217C2211yescharacteristic
41C3×#939C2218yescomplemented
42C3×#938C2218yescomplemented
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×C4⋊Dic3C2211yescharacteristic
45C2×C3×Dic3⋊C4C2211yescharacteristic
46#63979C2218yescomplemented
47#63978C2218yescomplemented
48#63975C2218yescomplemented
49#67⋊Dic3C2218yescomplemented
50#63970C2218yescomplemented
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×Dic3⋊Dic3C2211yescharacteristic
54C2×Dic3⋊Dic3C2211yescharacteristic
55C2×Dic3⋊Dic3C2211yescharacteristic
56C2×#3722C2211yescharacteristic
57#63962C2218yescomplemented
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2211yescharacteristic
61#63958C2218yescomplemented
62#63955C2218yescomplemented
63C2×Dic32C2211yescharacteristic
64C2×Dic32C2211yescharacteristic
65#63905C2218yescomplemented
66#63904C2218yescomplemented
67#63890C2218yescomplemented
68#63846C2218yescomplemented
69C2×C3×#121—31no—
70C2×C3×#121—31no—
71C2×#940—31no—
72C2×#940—31no—
73C2×#939—31no—
74C2×#939—31no—
75C2×#939—31no—
76C2×#939—31no—
77C2×#939—61no—
78C2×#939D311yescharacteristic, complemented
79C2×#938—31no—
80C2×#938—31no—
81C2×#938D311yescharacteristic, complemented
82C2×#935—31no—
83C2×D4×Dic3—31no—
84C2×#930—31no—
85C2×#929—31no—
86C2×C4×#67—31no—
87C2×#926—31no—
88#5619—316no—
89#5615—316no—
90C2×#894—31no—
91C2×#893—31no—
92C2×#890—31no—
93C2×#889—31no—
94C2×#886—31no—
95C2×#886—31no—
96C2×#884—31no—
97C2×#883—31no—
98C2×#883—31no—
99C2×#883—31no—
100C2×#67⋊C4—31no—
101C2×#877—31no—
102C24×C32C2311yescharacteristic
103C24×C32C2311yescharacteristic
104C23×C3⋊D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C2×C32×D4—42no—
108C2×C32×D4C2314yes—
109C22×C32×C4C2311yescharacteristic
110C2×#638—42no—
111C2×#638—42no—
112C2×#638C2314yes—
113C2×#638C2314yes—
114C22×C3⋊Dic3—42no—
115C22×C3⋊Dic3C2311yescharacteristic
116C22×C3⋊Dic3C2311yescharacteristic
117C22×C3⋊Dic3C2311yescharacteristic
118C22×C3⋊Dic3C2314yes—
119C2×C3×#67—24no—
120C2×C3×#67—42no—
121C2×C3×#67—42no—
122C2×C3×#67—42no—
123C2×C3×#67C2314yes—
124C2×C3×#67C2314yes—
125C2×C3×#67C2314yes—
126C2×C3×#67C2314yes—
127C22×C3×Dic3—24no—
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2314yes—
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C2×C3×C4×D3—42no—
136C2×C3×C4×D3C2314yes—
137C2×#626—24no—
138C2×#626—42no—
139C2×#626C2314yes—
140C2×#626C2314yes—
141C2×#625—42no—
142C2×#625C2314yes—
143C2×#624—42no—
144C2×#624C2314yes—
145C2×D3×Dic3—42no—
146C2×D3×Dic3C2314yes—
147#3757C2314yes—
148#3752C2314yes—
149#3750C2314yes—
150C3×#217C2314yes—
151C3×#217C2314yes—
152C3×#217C2314yes—
153C3×(C2×D3)⋊C4C2314yes—
154C3×C4⋊Dic3C2314yes—
155C3×Dic3⋊C4C2314yes—
156Dic3⋊Dic3C2314yes—
157Dic3⋊Dic3C2314yes—
158Dic3⋊Dic3C2314yes—
159Dic3⋊Dic3C2314yes—
160Dic3⋊Dic3C2314yes—
161#3722C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163(C2×D3)⋊Dic3C2314yes—
164(C2×D3)⋊Dic3C2314yes—
165Dic32C2314yes—
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×D4C2×D311yescharacteristic
174C22×C3×D4C2×D311yescharacteristic
175C23×C3×C4—31no—
176C23×C3×C4—31no—
177C22×#67—31no—
178C22×#67—31no—
179C22×#67—31no—
180C22×#67—31no—
181C22×#67—31no—
182C22×#67—31no—
183C22×#67—31no—
184C22×#67—31no—
185C22×#67—61no—
186C22×#67—61no—
187C22×#67C2×D311yescharacteristic
188C22×#67C2×D311yescharacteristic
189C22×#67C2×D311yescharacteristic
190C22×#67C2×D311yescharacteristic
191C23×Dic3—31no—
192C23×Dic3—31no—
193C23×Dic3—31no—
194C23×Dic3—61no—
195C23×Dic3C2×D311yescharacteristic
196C22×D12—31no—
197C22×D12—31no—
198C22×C4×D3—31no—
199C22×C4×D3—31no—
200C22×C4×D3—31no—
201C22×C4×D3C2×D311yescharacteristic
202C3×#121—38no—
203C3×#121—38no—
204C2×C3×C4⋊C4—31no—
205C2×C3×C4⋊C4—31no—
206C2×C3×C22⋊C4—31no—
207C2×C3×C22⋊C4—31no—
208C2×C3×C22⋊C4—31no—
209C2×C3×C22⋊C4—31no—
210C2×#217—31no—
211C2×#217—31no—
212C2×#217—31no—
213C2×#217—31no—
214C2×#217—31no—
215C2×#217—61no—
216C2×#217C2×D311yescharacteristic
217C2×#217C2×D311yescharacteristic
218C2×#217C2×D311yescharacteristic
219#940—38no—
220#940—38no—
221#939—38no—
222#939—38no—
223#939—38no—
224#939—38no—
225#939—68no—
226#939C2×D318yescomplemented
227#938—38no—
228#938—38no—
229#938C2×D318yescomplemented
230#935—38no—
231D4×Dic3—38no—
232#930—38no—
233#929—38no—
234C4×#67—38no—
235C2×(C2×D3)⋊C4—31no—
236C2×(C2×D3)⋊C4—31no—
237C2×(C2×D3)⋊C4—31no—
238C2×(C2×D3)⋊C4—31no—
239C2×(C2×D3)⋊C4—31no—
240C2×(C2×D3)⋊C4—31no—
241C2×(C2×D3)⋊C4—31no—
242C2×(C2×D3)⋊C4—61no—
243C2×(C2×D3)⋊C4C2×D311yescharacteristic
244#926—38no—
245C2×C4⋊Dic3—31no—
246C2×C4⋊Dic3—31no—
247C2×C4⋊Dic3—31no—
248C2×C4⋊Dic3—31no—
249C2×C4⋊Dic3—31no—
250C2×C4⋊Dic3C2×D311yescharacteristic
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—61no—
259C2×Dic3⋊C4C2×D311yescharacteristic
260C2×C4×Dic3—31no—
261C2×C4×Dic3—31no—
262C2×C4×Dic3—31no—
263C2×C4×Dic3—31no—
264#894—38no—
265#893—38no—
266#890—38no—
267#889—38no—
268#886—38no—
269#886—38no—
270#884—38no—
271#883—38no—
272#883—38no—
273#883—38no—
274#67⋊C4—38no—
275#877—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⋊D3C2412yes—
289C22×C3×D3—22no—
290C22×C3×D3—22no—
291C22×C3×D3—22no—
292C22×C3×D3—22no—
293C22×C3×D3—22no—
294C22×C3×D3—22no—
295C22×C3×D3C2412yes—
296C22×C3×D3C2412yes—
297C32×D4—44no—
298C2×C32×C4—22no—
299C2×C32×C4C2412yes—
300#638—44no—
301#638—44no—
302C2×C3⋊Dic3—22no—
303C2×C3⋊Dic3—22no—
304C2×C3⋊Dic3—22no—
305C2×C3⋊Dic3—44no—
306C2×C3⋊Dic3C2412yes—
307C2×C3⋊Dic3C2412yes—
308C2×C3⋊Dic3C2412yes—
309C3×#67—28no—
310C3×#67—44no—
311C3×#67—44no—
312C3×#67—44no—
313C2×C3×Dic3—22no—
314C2×C3×Dic3—22no—
315C2×C3×Dic3—22no—
316C2×C3×Dic3—22no—
317C2×C3×Dic3—22no—
318C2×C3×Dic3—28no—
319C2×C3×Dic3#4114yes—
320C2×C3×Dic3C2412yes—
321C2×C3×Dic3C2412yes—
322C2×C3×Dic3C2412yes—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2412yes—
326C3×C4×D3—44no—
327#626—28no—
328#626—44no—
329#625—44no—
330#624—44no—
331D3×Dic3—44no—
332#540—916no—
333C2×#127—91no—
334C2×#125—91no—
335C2×#123—91no—
336C2×#123—91no—
337C2×#123—91no—
338C2×#123—91no—
339C2×#121—31no—
340C2×#121—31no—
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×C3C22×D311yescharacteristic
353C24×C3C22×D311yescharacteristic
354C24×C3C22×D311yescharacteristic
355C24×C3C22×D311yescharacteristic
356C23×D3—31no—
357C23×D3—31no—
358C23×D3—61no—
359C23×D3C22×D311yescharacteristic
360C23×D3C22×D311yescharacteristic
361C2×C3×D4—24no—
362C2×C3×D4—34no—
363C2×C3×D4—34no—
364C2×C3×D4—34no—
365C2×C3×D4—34no—
366C2×C3×D4—42no—
367C2×C3×D4—42no—
368C2×C3×D4—44no—
369C2×C3×D4—64no—
370C2×C3×D4—122no—
371C2×C3×D4—122no—
372C2×C3×D4—122no—
373C2×C3×D4C22×D314yes—
374C2×C3×D4C22×D314yes—
375C22×C3×C4—21no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—31no—
382C22×C3×C4—34no—
383C22×C3×C4—34no—
384C22×C3×C4—64no—
385C22×C3×C4—122no—
386C22×C3×C4C22×D311yescharacteristic
387C22×C3×C4C22×D311yescharacteristic
388C2×#67—24no—
389C2×#67—34no—
390C2×#67—34no—
391C2×#67—34no—
392C2×#67—34no—
393C2×#67—34no—
394C2×#67—34no—
395C2×#67—34no—
396C2×#67—34no—
397C2×#67—42no—
398C2×#67—42no—
399C2×#67—42no—
400C2×#67—64no—
401C2×#67—64no—
402C2×#67—64no—
403C2×#67—122no—
404C2×#67—122no—
405C2×#67—122no—
406C2×#67—122no—
407C2×#67—122no—
408C2×#67—122no—
409C2×#67—122no—
410C2×#67—124no—
411C2×#67—124no—
412C2×#67C22×D314yes—
413C2×#67C22×D314yes—
414C2×#67C22×D314yes—
415C2×#67C22×D314yes—
416C22×Dic3—24no—
417C22×Dic3—31no—
418C22×Dic3—31no—
419C22×Dic3—31no—
420C22×Dic3—31no—
421C22×Dic3—31no—
422C22×Dic3—31no—
423C22×Dic3—34no—
424C22×Dic3—34no—
425C22×Dic3—34no—
426C22×Dic3—61no—
427C22×Dic3—61no—
428C22×Dic3—61no—
429C22×Dic3—64no—
430C22×Dic3—122no—
431C22×Dic3—122no—
432C22×Dic3—122no—
433C22×Dic3—124no—
434C22×Dic3C22×D314yes—
435C22×Dic3C22×D311yescharacteristic
436C22×Dic3C22×D311yescharacteristic
437C22×Dic3C22×D311yescharacteristic
438C22×Dic3C22×D311yescharacteristic
439C22×Dic3C22×D311yescharacteristic
440C22×Dic3C22×D311yescharacteristic
441C2×D12—34no—
442C2×D12—34no—
443C2×D12—64no—
444C2×D12—122no—
445C2×C4×D3—34no—
446C2×C4×D3—34no—
447C2×C4×D3—34no—
448C2×C4×D3—42no—
449C2×C4×D3—122no—
450C2×C4×D3—122no—
451C2×C4×D3—122no—
452C2×C4×D3C22×D314yes—
453C3×C4⋊C4—34no—
454C3×C4⋊C4—34no—
455C3×C22⋊C4—34no—
456C3×C22⋊C4—34no—
457C3×C22⋊C4—34no—
458C3×C22⋊C4—34no—
459#217—34no—
460#217—34no—
461#217—34no—
462#217—34no—
463#217—34no—
464#217—64no—
465#217C22×D314yes—
466#217C22×D314yes—
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)⋊C4—34no—
474(C2×D3)⋊C4—34no—
475(C2×D3)⋊C4—64no—
476(C2×D3)⋊C4C22×D314yes—
477C4⋊Dic3—34no—
478C4⋊Dic3—34no—
479C4⋊Dic3—34no—
480C4⋊Dic3—34no—
481C4⋊Dic3—34no—
482C4⋊Dic3C22×D314yes—
483Dic3⋊C4—34no—
484Dic3⋊C4—34no—
485Dic3⋊C4—34no—
486Dic3⋊C4—34no—
487Dic3⋊C4—34no—
488Dic3⋊C4—34no—
489Dic3⋊C4—34no—
490Dic3⋊C4—64no—
491Dic3⋊C4C22×D314yes—
492C4×Dic3—34no—
493C4×Dic3—34no—
494C4×Dic3—34no—
495C4×Dic3—34no—
496C22×C32—22no—
497C22×C32—22no—
498C22×C32—22no—
499C22×C32—22no—
500C22×C32—22no—
501C22×C32—22no—
502C22×C32—44no—
503C22×C32—44no—
504C22×C32C2×#4112yes—
505C22×C32H(5,𝔽2)12yes—
506C22×C32H(5,𝔽2)12yes—
507C22×C32C2511yescharacteristic
508C2×C3⋊D3—22no—
509C2×C3⋊D3—22no—
510C2×C3⋊D3—22no—
511C2×C3⋊D3—44no—
512C2×C3×D3—22no—
513C2×C3×D3—22no—
514C2×C3×D3—22no—
515C2×C3×D3—22no—
516C2×C3×D3—22no—
517C2×C3×D3—22no—
518C2×C3×D3—44no—
519C2×C3×D3—44no—
520C32×C4—22no—
521C3⋊Dic3—22no—
522C3⋊Dic3—22no—
523C3⋊Dic3—22no—
524C3×Dic3—22no—
525C3×Dic3—22no—
526C3×Dic3—22no—
527C3×Dic3—22no—
528C3×Dic3—22no—
529C3×Dic3C2×#4114yes—
530C22×D4—31no—
531C22×D4—31no—
532C22×D4—31no—
533C22×D4—31no—
534C22×D4—91no—
535C22×D4—91no—
536C22×D4—91no—
537C22×D4—91no—
538C22×D4—91no—
539C22×D4D3211yescharacteristic
540C23×C4—31no—
541C23×C4—31no—
542C23×C4—91no—
543C23×C4—91no—
544C23×C4—91no—
545#127—98no—
546#125—98no—
547#123—98no—
548#123—98no—
549#123—98no—
550#123—98no—
551#121—38no—
552#121—38no—
553#121—98no—
554#121—98no—
555#121—98no—
556#121—98no—
557C4×D4—98no—
558C4×D4—98no—
559#117—98no—
560C2×C4⋊C4—31no—
561C2×C4⋊C4—31no—
562C2×C4⋊C4—91no—
563C2×C4⋊C4—91no—
564C2×C4⋊C4—91no—
565C2×C4⋊C4—91no—
566C2×C4⋊C4—91no—
567C2×C4⋊C4—91no—
568C2×C22⋊C4—31no—
569C2×C22⋊C4—31no—
570C2×C22⋊C4—31no—
571C2×C22⋊C4—31no—
572C2×C22⋊C4—91no—
573C2×C22⋊C4—91no—
574C2×C22⋊C4—91no—
575C2×C22⋊C4—91no—
576C2×C22⋊C4—91no—
577C2×C22⋊C4—91no—
578C2×C42—91no—
579C2×C42—91no—
580C23×C3—24no—
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—22no—
594C23×C3—22no—
595C23×C3—21no—
596C23×C3—32no—
597C23×C3—32no—
598C23×C3—42no—
599C23×C3—42no—
600C23×C3—42no—
601C23×C3—42no—
602C23×C3—42no—
603C23×C3—62no—
604C23×C3—62no—
605C23×C3—62no—
606C23×C3—62no—
607C23×C3—62no—
608C23×C3—62no—
609C23×C3C23×D312yes—
610C23×C3C23×D312yes—
611C23×C3C23×D312yes—
612C23×C3C23×D312yes—
613C23×C3C23×D311yescharacteristic
614C23×C3C23×D311yescharacteristic
615C22×D3—22no—
616C22×D3—22no—
617C22×D3—22no—
618C22×D3—22no—
619C22×D3—22no—
620C22×D3—22no—
621C22×D3—32no—
622C22×D3—32no—
623C22×D3—62no—
624C22×D3—62no—
625C22×D3—62no—
626C22×D3—62no—
627C22×D3—62no—
628C22×D3—62no—
629C22×D3—62no—
630C22×D3—122no—
631C22×D3—122no—
632C22×D3—122no—
633C22×D3C23×D312yes—
634C22×D3C23×D312yes—
635C3×D4—44no—
636C3×D4—44no—
637C3×D4—48no—
638C3×D4—68no—
639C3×D4—124no—
640C3×D4—124no—
641C3×D4—124no—
642C2×C3×C4—22no—
643C2×C3×C4—22no—
644C2×C3×C4—22no—
645C2×C3×C4—34no—
646C2×C3×C4—32no—
647C2×C3×C4—32no—
648C2×C3×C4—32no—
649C2×C3×C4—32no—
650C2×C3×C4—32no—
651C2×C3×C4—32no—
652C2×C3×C4—42no—
653C2×C3×C4—68no—
654C2×C3×C4—62no—
655C2×C3×C4—62no—
656C2×C3×C4—62no—
657C2×C3×C4—62no—
658C2×C3×C4—62no—
659C2×C3×C4—124no—
660C2×C3×C4C23×D312yes—
661C2×C3×C4C23×D312yes—
662#67—28no—
663#67—44no—
664#67—44no—
665#67—44no—
666#67—68no—
667#67—124no—
668#67—124no—
669#67—124no—
670#67—124no—
671#67—124no—
672#67—124no—
673#67—124no—
674#67—128no—
675#67—128no—
676C2×Dic3—22no—
677C2×Dic3—22no—
678C2×Dic3—22no—
679C2×Dic3—22no—
680C2×Dic3—22no—
681C2×Dic3—28no—
682C2×Dic3—32no—
683C2×Dic3—32no—
684C2×Dic3—32no—
685C2×Dic3—32no—
686C2×Dic3—32no—
687C2×Dic3—32no—
688C2×Dic3—62no—
689C2×Dic3—62no—
690C2×Dic3—62no—
691C2×Dic3—64no—
692C2×Dic3—62no—
693C2×Dic3—62no—
694C2×Dic3—62no—
695C2×Dic3—62no—
696C2×Dic3—62no—
697C2×Dic3—62no—
698C2×Dic3—122no—
699C2×Dic3—122no—
700C2×Dic3—124no—
701C2×Dic3—124no—
702C2×Dic3—124no—
703C2×Dic3—128no—
704C2×Dic3#23714yes—
705C2×Dic3C23×D312yes—
706C2×Dic3C23×D312yes—
707C2×Dic3C23×D312yes—
708C2×Dic3C23×D312yes—
709C2×Dic3C23×D312yes—
710C2×Dic3C23×D312yes—
711D12—68no—
712D12—124no—
713C4×D3—44no—
714C4×D3—124no—
715C4×D3—124no—
716C4×D3—124no—
717C2×C32—42no—
718C2×C32—42no—
719C2×C32#54014yescomplemented
720C2×C32C22×#4111yescharacteristic
721C2×C32C2×H(5,𝔽2)11yescharacteristic
722C2×C32C2×H(5,𝔽2)11yescharacteristic
723C3⋊D3—42no—
724C3×D3—42no—
725C3×D3—42no—
726C24—31no—
727C24—31no—
728C24—91no—
729C24C2×D3211yescharacteristic
730C24C2×D3211yescharacteristic
731C2×D4—34no—
732C2×D4—34no—
733C2×D4—34no—
734C2×D4—34no—
735C2×D4—42no—
736C2×D4—64no—
737C2×D4—94no—
738C2×D4—94no—
739C2×D4—94no—
740C2×D4—94no—
741C2×D4—94no—
742C2×D4—122no—
743C2×D4—122no—
744C2×D4—122no—
745C2×D4—184no—
746C2×D4—362no—
747C2×D4—362no—
748C2×D4—362no—
749C2×D4—362no—
750C2×D4C2×D3214yes—
751C22×C4—31no—
752C22×C4—34no—
753C22×C4—31no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—34no—
759C22×C4—64no—
760C22×C4—94no—
761C22×C4—94no—
762C22×C4—91no—
763C22×C4—91no—
764C22×C4—91no—
765C22×C4—94no—
766C22×C4—122no—
767C22×C4—362no—
768C22×C4—362no—
769C22×C4—362no—
770C22×C4C2×D3211yescharacteristic
771C4⋊C4—34no—
772C4⋊C4—34no—
773C4⋊C4—94no—
774C4⋊C4—94no—
775C4⋊C4—94no—
776C4⋊C4—94no—
777C4⋊C4—94no—
778C4⋊C4—94no—
779C22⋊C4—34no—
780C22⋊C4—34no—
781C22⋊C4—34no—
782C22⋊C4—34no—
783C22⋊C4—94no—
784C22⋊C4—94no—
785C22⋊C4—94no—
786C22⋊C4—94no—
787C22⋊C4—94no—
788C22⋊C4—94no—
789C42—94no—
790C42—94no—
791C22×C3—24no—
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—22no—
802C22×C3—22no—
803C22×C3—22no—
804C22×C3—22no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—21no—
808C22×C3—42no—
809C22×C3—42no—
810C22×C3—42no—
811C22×C3—42no—
812C22×C3—42no—
813C22×C3—48no—
814C22×C3—44no—
815C22×C3—44no—
816C22×C3—44no—
817C22×C3—44no—
818C22×C3—62no—
819C22×C3—62no—
820C22×C3—62no—
821C22×C3—62no—
822C22×C3—62no—
823C22×C3—62no—
824C22×C3—84no—
825C22×C3—124no—
826C22×C3—124no—
827C22×C3C2×#23712yes—
828C22×C3#100412yes—
829C22×C3#100412yes—
830C22×C3#100412yes—
831C22×C3D3×#4112yes—
832C22×C3#100912yes—
833C22×C3C24×D311yescharacteristic
834C22×C3C24×D311yescharacteristic
835C2×D3—22no—
836C2×D3—22no—
837C2×D3—22no—
838C2×D3—22no—
839C2×D3—22no—
840C2×D3—22no—
841C2×D3—44no—
842C2×D3—44no—
843C2×D3—62no—
844C2×D3—62no—
845C2×D3—62no—
846C2×D3—62no—
847C2×D3—62no—
848C2×D3—62no—
849C2×D3—122no—
850C2×D3—122no—
851C2×D3—122no—
852C2×D3—124no—
853C2×D3—124no—
854C2×D3—244no—
855C3×C4—22no—
856C3×C4—22no—
857C3×C4—34no—
858C3×C4—42no—
859C3×C4—62no—
860C3×C4—62no—
861C3×C4—62no—
862C3×C4—62no—
863C3×C4—62no—
864Dic3—22no—
865Dic3—22no—
866Dic3—22no—
867Dic3—22no—
868Dic3—22no—
869Dic3—64no—
870Dic3—62no—
871Dic3—62no—
872Dic3—62no—
873Dic3—62no—
874Dic3—62no—
875Dic3—62no—
876Dic3—122no—
877Dic3—122no—
878Dic3C2×#23714yes—
879C32C2×#54011yescharacteristic, complemented, Sylow
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—32no—
887C23—32no—
888C23—62no—
889C23—62no—
890C23—62no—
891C23—62no—
892C23—62no—
893C23—62no—
894C23—92no—
895C23—182no—
896C23—182no—
897C23—182no—
898C23C22×D3212yes—
899C23C22×D3212yes—
900C23C22×D3211yescharacteristic
901D4—44no—
902D4—68no—
903D4—124no—
904D4—124no—
905D4—124no—
906D4—188no—
907D4—364no—
908D4—364no—
909D4—364no—
910D4—364no—
911C2×C4—22no—
912C2×C4—34no—
913C2×C4—32no—
914C2×C4—32no—
915C2×C4—32no—
916C2×C4—32no—
917C2×C4—32no—
918C2×C4—32no—
919C2×C4—68no—
920C2×C4—62no—
921C2×C4—62no—
922C2×C4—62no—
923C2×C4—62no—
924C2×C4—62no—
925C2×C4—92no—
926C2×C4—92no—
927C2×C4—92no—
928C2×C4—124no—
929C2×C4—182no—
930C2×C4—182no—
931C2×C4—182no—
932C2×C4—364no—
933C2×C4—364no—
934C2×C4—364no—
935C2×C4C22×D3212yes—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—21no—
939C2×C3—24no—
940C2×C3—44no—
941C2×C3—42no—
942C2×C3—42no—
943C2×C3—42no—
944C2×C3—42no—
945C2×C3—82no—
946C2×C3—122no—
947C2×C3—122no—
948C2×C3#561514yescomplemented
949C2×C3#561914yescomplemented
950C2×C3C22×#23711yescharacteristic
951C2×C3C2×#100411yescharacteristic
952C2×C3C2×#100411yescharacteristic
953C2×C3C2×#100411yescharacteristic
954C2×C3C2×D3×#4111yescharacteristic
955C2×C3C2×#100911yescharacteristic
956D3—42no—
957D3—42no—
958D3—122no—
959D3—122no—
960D3—242no—
961C22—22no—
962C22—22no—
963C22—22no—
964C22—22no—
965C22—22no—
966C22—22no—
967C22—44no—
968C22—44no—
969C22—62no—
970C22—62no—
971C22—62no—
972C22—62no—
973C22—62no—
974C22—62no—
975C22—124no—
976C22—124no—
977C22—182no—
978C22—182no—
979C22—182no—
980C22—364no—
981C22D3×#23712yes—
982C22#6431412yes—
983C22#6433012yes—
984C22C23×D3211yescharacteristic
985C4—22no—
986C4—34no—
987C4—62no—
988C4—62no—
989C4—62no—
990C4—62no—
991C4—62no—
992C4—182no—
993C4—182no—
994C4—182no—
995C3—21no—
996C3C2×#561911yescharacteristic, complemented
997C3C2×#561511yescharacteristic, complemented
998C2—42no—
999C2—42no—
1000C2—122no—
1001C2—122no—
1002C2—362no—
1003C2#1059525014yesdirect product factor
1004C2C2×D3×#23711yescharacteristic
1005C2C2×#6431411yescharacteristic
1006C2C2×#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×#64148C2semidirect
2. C2×C3×#939C2semidirect
3. C2×C3×#938C2semidirect
4. C2×#63979C2semidirect
5. C2×#63978C2semidirect
6. C2×#63975C2semidirect
7. C2×#67⋊Dic3C2semidirect
8. C2×#63970C2semidirect
9. C2×#63962C2semidirect
10. C2×#63958C2semidirect
11. C2×#63955C2semidirect
12. #10595250C2direct (N × H)
13. C2×#63905C2semidirect
14. C2×#63904C2semidirect
15. C2×#63890C2semidirect
16. C2×#63846C2semidirect
35. #64148C22semidirect
41. C3×#939C22semidirect
42. C3×#938C22semidirect
46. #63979C22semidirect
47. #63978C22semidirect
48. #63975C22semidirect
49. #67⋊Dic3C22semidirect
50. #63970C22semidirect
57. #63962C22semidirect
61. #63958C22semidirect
62. #63955C22semidirect
65. #63905C22semidirect
66. #63904C22semidirect
67. #63890C22semidirect
68. #63846C22semidirect
78. C2×#939D3semidirect
81. C2×#938D3semidirect
226. #939C2×D3semidirect
229. #938C2×D3semidirect
719. C2×C32#540semidirect
879. C32C2×#540semidirect
948. C2×C3#5615semidirect
949. C2×C3#5619semidirect
996. C3C2×#5619semidirect
997. C3C2×#5615semidirect
1003. C2#10595250direct (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×#9392
C2×C3×#9382
C2×#639792
C2×#639782
C2×#639752
C2×#67⋊Dic32
C2×#639702
C2×#639622
C2×#639582
C2×#639552
#105952502
C2×#639052
C2×#639042
C2×#638902
C2×#638462
C2×#56153
C2×#56193