Finite Group Databasebeta

← C2×#11723725 #13178798

Subgroups — C2×#11723725 #13178798

Order 1728.

2442 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#638C211yesmaximal, characteristic, complemented
2C22×C3×#638C211yesmaximal, characteristic, complemented
3C22×#6295C211yesmaximal, characteristic, complemented
4C22×#6294C211yesmaximal, characteristic, complemented
5C2×C3×#3757C211yesmaximal, characteristic, complemented
6#11723725C218yesmaximal, direct product factor
7C2×#88815C211yesmaximal, characteristic, complemented
8C2×#88814C211yesmaximal, characteristic, complemented
9C2×#63971—31nomaximal
10C2×#63970—31nomaximal
11C2×#63958—31nomaximal
12C24×C33C2211yescharacteristic
13C23×C3×C3⋊D3C2211yescharacteristic
14C23×C3×C3⋊D3C2211yescharacteristic
15C2×C3×#638—24no—
16C2×C3×#638—24no—
17C2×C3×#638C2214yescomplemented
18C2×C3×#638C2214yescomplemented
19C22×C3×C3⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊Dic3C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C2×#6295—24no—
24C2×#6295C2214yescomplemented
25C2×#6294—24no—
26C2×#6294C2214yescomplemented
27C3×#3757C2214yescomplemented
28#88815C2214yescomplemented
29#88814C2214yescomplemented
30C22×#638D311yescharacteristic, complemented
31C22×#638D311yescharacteristic, complemented
32C22×C3×#67—31no—
33C22×C3×#67—31no—
34C22×C3×#67—31no—
35C22×C3×#67—31no—
36C22×C3×#67—61no—
37C22×C3×#67—61no—
38C22×#626—31no—
39C22×#626—31no—
40C22×#625—31no—
41C22×#624—31no—
42C22×D3×Dic3—31no—
43C22×D3×Dic3—31no—
44C2×#3757D311yescharacteristic, complemented
45C2×C3×#217—31no—
46C2×C3×#217—31no—
47C2×C3×#217—61no—
48#63971—38no—
49#63970—38no—
50C2×#3724—31no—
51C2×Dic3⋊Dic3—31no—
52C2×Dic3⋊Dic3—31no—
53C2×#3722—31no—
54C2×(C2×D3)⋊Dic3—31no—
55C2×(C2×D3)⋊Dic3—31no—
56#63958—38no—
57C23×C33—22no—
58C23×C33—22no—
59C23×C33—22no—
60C23×C33C2312yes—
61C23×C33C2311yescharacteristic
62C22×C3×C3⋊D3—22no—
63C22×C3×C3⋊D3—22no—
64C22×C3×C3⋊D3—22no—
65C22×C3×C3⋊D3—22no—
66C22×C3×C3⋊D3—22no—
67C22×C3×C3⋊D3D414yescomplemented
68C22×C3×C3⋊D3C2312yes—
69C22×C3×C3⋊D3C2312yes—
70C3×#638—28no—
71C3×#638—28no—
72C2×C3×C3⋊Dic3—22no—
73C2×C3×C3⋊Dic3—22no—
74C2×C3×C3⋊Dic3—22no—
75C2×C3×C3⋊Dic3D414yescomplemented
76C2×C3×C3⋊Dic3C2312yes—
77C2×C3×C3⋊Dic3C2312yes—
78C2×C3×C3⋊Dic3C2312yes—
79C2×C3×C3⋊Dic3C2312yes—
80#6295—28no—
81#6294—28no—
82C2×#939—91no—
83C2×#938—91no—
84C2×#884—91no—
85C24×C32—21no—
86C24×C32—21no—
87C24×C32—21no—
88C24×C32—41no—
89C24×C32C2×D311yescharacteristic
90C24×C32C2×D311yescharacteristic
91C24×C32C2×D311yescharacteristic
92C23×C3⋊D3C2×D311yescharacteristic
93C23×C3⋊D3C2×D311yescharacteristic
94C23×C3×D3—31no—
95C23×C3×D3—31no—
96C23×C3×D3—31no—
97C23×C3×D3—31no—
98C23×C3×D3—61no—
99C23×C3×D3—61no—
100C2×#638—24no—
101C2×#638—24no—
102C2×#638C2×D314yescomplemented
103C2×#638C2×D314yescomplemented
104C22×C3⋊Dic3C2×D311yescharacteristic
105C22×C3⋊Dic3C2×D311yescharacteristic
106C22×C3⋊Dic3C2×D311yescharacteristic
107C22×C3⋊Dic3C2×D311yescharacteristic
108C2×C3×#67—34no—
109C2×C3×#67—34no—
110C2×C3×#67—34no—
111C2×C3×#67—34no—
112C2×C3×#67—64no—
113C2×C3×#67—64no—
114C2×C3×#67—64no—
115C2×C3×#67—64no—
116C2×C3×#67—64no—
117C2×C3×#67—64no—
118C2×C3×#67—68no—
119C2×C3×#67—68no—
120C22×C3×Dic3—31no—
121C22×C3×Dic3—31no—
122C22×C3×Dic3—31no—
123C22×C3×Dic3—31no—
124C22×C3×Dic3—31no—
125C22×C3×Dic3—31no—
126C22×C3×Dic3—31no—
127C22×C3×Dic3—31no—
128C22×C3×Dic3—61no—
129C22×C3×Dic3—61no—
130C22×C3×Dic3—61no—
131C22×C3×Dic3—61no—
132C2×#626—34no—
133C2×#626—34no—
134C2×#626—64no—
135C2×#626—64no—
136C2×#625—34no—
137C2×#625—64no—
138C2×#624—34no—
139C2×#624—64no—
140C2×D3×Dic3—34no—
141C2×D3×Dic3—34no—
142C2×D3×Dic3—64no—
143C2×D3×Dic3—64no—
144#3757C2×D314yescomplemented
145C3×#217—34no—
146C3×#217—34no—
147C3×#217—64no—
148#3724—34no—
149Dic3⋊Dic3—34no—
150Dic3⋊Dic3—34no—
151#3722—34no—
152(C2×D3)⋊Dic3—34no—
153(C2×D3)⋊Dic3—34no—
154C22×C33—22no—
155C22×C33—22no—
156C22×C33—22no—
157C22×C33—44no—
158C22×C33C2×D412yes—
159C22×C33C2×D412yes—
160C22×C33#4112yes—
161C22×C33C2411yescharacteristic
162C2×C3×C3⋊D3—28no—
163C2×C3×C3⋊D3—22no—
164C2×C3×C3⋊D3—22no—
165C2×C3×C3⋊D3—22no—
166C2×C3×C3⋊D3—22no—
167C2×C3×C3⋊D3—22no—
168C2×C3×C3⋊D3—44no—
169C2×C3×C3⋊D3C2×D414yescomplemented
170C3×C3⋊Dic3—22no—
171C3×C3⋊Dic3—22no—
172C3×C3⋊Dic3—22no—
173C3×C3⋊Dic3C2×D414yescomplemented
174C22×C3×D4—91no—
175C22×C3×D4—91no—
176C22×#67—31no—
177C22×#67—31no—
178C22×#67—31no—
179C22×#67—31no—
180C22×#67—61no—
181C22×#67—61no—
182C22×#67—91no—
183C22×#67—91no—
184C23×Dic3—91no—
185C22×D12—91no—
186C22×C4×D3—91no—
187C22×C4×D3—91no—
188C2×C3×C22⋊C4—91no—
189C2×#217—31no—
190C2×#217—31no—
191C2×#217—61no—
192C2×#217—91no—
193#939—98no—
194#938—98no—
195C2×(C2×D3)⋊C4—91no—
196C2×(C2×D3)⋊C4—91no—
197C2×C4⋊Dic3—91no—
198C2×Dic3⋊C4—91no—
199C2×Dic3⋊C4—91no—
200#884—98no—
201C23×C32—22no—
202C23×C32—22no—
203C23×C32—22no—
204C23×C32—24no—
205C23×C32—24no—
206C23×C32—24no—
207C23×C32—22no—
208C23×C32—22no—
209C23×C32—22no—
210C23×C32—22no—
211C23×C32—22no—
212C23×C32—22no—
213C23×C32—21no—
214C23×C32—21no—
215C23×C32—21no—
216C23×C32—22no—
217C23×C32—22no—
218C23×C32—22no—
219C23×C32—42no—
220C23×C32—41no—
221C23×C32—42no—
222C23×C32—42no—
223C23×C32—42no—
224C23×C32—42no—
225C23×C32—42no—
226C23×C32—42no—
227C23×C32—44no—
228C23×C32—44no—
229C23×C32—44no—
230C23×C32C22×D312yes—
231C23×C32C22×D312yes—
232C23×C32C22×D312yes—
233C23×C32C22×D311yescharacteristic
234C23×C32C22×D311yescharacteristic
235C23×C32C22×D311yescharacteristic
236C22×C3⋊D3—22no—
237C22×C3⋊D3—22no—
238C22×C3⋊D3—22no—
239C22×C3⋊D3—22no—
240C22×C3⋊D3—22no—
241C22×C3⋊D3#6714yescomplemented
242C22×C3⋊D3C22×D312yes—
243C22×C3⋊D3C22×D312yes—
244C22×C3×D3—34no—
245C22×C3×D3—34no—
246C22×C3×D3—32no—
247C22×C3×D3—32no—
248C22×C3×D3—32no—
249C22×C3×D3—32no—
250C22×C3×D3—64no—
251C22×C3×D3—62no—
252C22×C3×D3—62no—
253C22×C3×D3—62no—
254C22×C3×D3—62no—
255C22×C3×D3—62no—
256C22×C3×D3—62no—
257C22×C3×D3—64no—
258C22×C3×D3—62no—
259C22×C3×D3—62no—
260C22×C3×D3—62no—
261C22×C3×D3—62no—
262C22×C3×D3—62no—
263C22×C3×D3—62no—
264C22×C3×D3—122no—
265C22×C3×D3—122no—
266C22×C3×D3—122no—
267C22×C3×D3—122no—
268#638—28no—
269#638—28no—
270C2×C3⋊Dic3—22no—
271C2×C3⋊Dic3—22no—
272C2×C3⋊Dic3—22no—
273C2×C3⋊Dic3#6714yescomplemented
274C2×C3⋊Dic3C22×D312yes—
275C2×C3⋊Dic3C22×D312yes—
276C2×C3⋊Dic3C22×D312yes—
277C2×C3⋊Dic3C22×D312yes—
278C3×#67—68no—
279C3×#67—68no—
280C3×#67—68no—
281C3×#67—68no—
282C3×#67—616no—
283C3×#67—616no—
284C2×C3×Dic3—34no—
285C2×C3×Dic3—34no—
286C2×C3×Dic3—32no—
287C2×C3×Dic3—32no—
288C2×C3×Dic3—32no—
289C2×C3×Dic3—32no—
290C2×C3×Dic3—32no—
291C2×C3×Dic3—32no—
292C2×C3×Dic3—32no—
293C2×C3×Dic3—32no—
294C2×C3×Dic3—64no—
295C2×C3×Dic3—62no—
296C2×C3×Dic3—62no—
297C2×C3×Dic3—62no—
298C2×C3×Dic3—62no—
299C2×C3×Dic3—64no—
300C2×C3×Dic3—62no—
301C2×C3×Dic3—62no—
302C2×C3×Dic3—62no—
303C2×C3×Dic3—62no—
304C2×C3×Dic3—62no—
305C2×C3×Dic3—62no—
306C2×C3×Dic3—122no—
307C2×C3×Dic3—122no—
308#626—68no—
309#626—68no—
310#625—68no—
311#624—68no—
312D3×Dic3—68no—
313D3×Dic3—68no—
314C2×#121—271noSylow
315C2×C33—42no—
316C2×C33#12114yescomplemented
317C2×C33C22×D411yescharacteristic
318C2×C33C22×D411yescharacteristic
319C2×C33C2×#4111yescharacteristic
320C3×C3⋊D3—24no—
321C3×C3⋊D3—42no—
322C24×C3—21no—
323C24×C3—21no—
324C24×C3—21no—
325C24×C3—41no—
326C24×C3—91no—
327C24×C3—91no—
328C24×C3D3211yescharacteristic
329C24×C3D3211yescharacteristic
330C24×C3D3211yescharacteristic
331C23×D3—31no—
332C23×D3—31no—
333C23×D3—31no—
334C23×D3—31no—
335C23×D3—61no—
336C23×D3—61no—
337C2×C3×D4—94no—
338C2×C3×D4—94no—
339C2×C3×D4—184no—
340C2×C3×D4—184no—
341C22×C3×C4—91no—
342C22×C3×C4—91no—
343C22×C3×C4—91no—
344C22×C3×C4—91no—
345C2×#67—34no—
346C2×#67—34no—
347C2×#67—34no—
348C2×#67—34no—
349C2×#67—64no—
350C2×#67—64no—
351C2×#67—64no—
352C2×#67—64no—
353C2×#67—64no—
354C2×#67—64no—
355C2×#67—68no—
356C2×#67—68no—
357C2×#67—94no—
358C2×#67—94no—
359C2×#67—184no—
360C2×#67—184no—
361C22×Dic3—31no—
362C22×Dic3—31no—
363C22×Dic3—31no—
364C22×Dic3—31no—
365C22×Dic3—31no—
366C22×Dic3—31no—
367C22×Dic3—31no—
368C22×Dic3—31no—
369C22×Dic3—61no—
370C22×Dic3—61no—
371C22×Dic3—61no—
372C22×Dic3—61no—
373C22×Dic3—94no—
374C22×Dic3—184no—
375C2×D12—94no—
376C2×D12—184no—
377C2×C4×D3—94no—
378C2×C4×D3—94no—
379C2×C4×D3—184no—
380C2×C4×D3—184no—
381C3×C22⋊C4—94no—
382#217—34no—
383#217—34no—
384#217—64no—
385#217—94no—
386(C2×D3)⋊C4—94no—
387(C2×D3)⋊C4—94no—
388C4⋊Dic3—94no—
389Dic3⋊C4—94no—
390Dic3⋊C4—94no—
391C22×C32—22no—
392C22×C32—22no—
393C22×C32—22no—
394C22×C32—24no—
395C22×C32—24no—
396C22×C32—24no—
397C22×C32—22no—
398C22×C32—22no—
399C22×C32—22no—
400C22×C32—22no—
401C22×C32—22no—
402C22×C32—22no—
403C22×C32—21no—
404C22×C32—21no—
405C22×C32—21no—
406C22×C32—22no—
407C22×C32—22no—
408C22×C32—22no—
409C22×C32—22no—
410C22×C32—22no—
411C22×C32—22no—
412C22×C32—22no—
413C22×C32—22no—
414C22×C32—22no—
415C22×C32—42no—
416C22×C32—42no—
417C22×C32—42no—
418C22×C32—41no—
419C22×C32—42no—
420C22×C32—42no—
421C22×C32—42no—
422C22×C32—42no—
423C22×C32—42no—
424C22×C32—42no—
425C22×C32—44no—
426C22×C32—44no—
427C22×C32—44no—
428C22×C32—48no—
429C22×C32—48no—
430C22×C32—48no—
431C22×C32—416no—
432C22×C32—44no—
433C22×C32—44no—
434C22×C32—44no—
435C22×C32#23512yes—
436C22×C32D3×D412yes—
437C22×C32D3×D412yes—
438C22×C32D3×D412yes—
439C22×C32D3×D412yes—
440C22×C32#23712yes—
441C22×C32#23712yes—
442C22×C32C2×#6712yes—
443C22×C32C2×#6712yes—
444C22×C32C23×D311yescharacteristic
445C22×C32C23×D311yescharacteristic
446C22×C32C23×D311yescharacteristic
447C2×C3⋊D3—22no—
448C2×C3⋊D3—28no—
449C2×C3⋊D3—22no—
450C2×C3⋊D3—22no—
451C2×C3⋊D3—22no—
452C2×C3⋊D3—22no—
453C2×C3⋊D3—44no—
454C2×C3⋊D3C2×#6714yescomplemented
455C2×C3×D3—34no—
456C2×C3×D3—34no—
457C2×C3×D3—64no—
458C2×C3×D3—68no—
459C2×C3×D3—68no—
460C2×C3×D3—62no—
461C2×C3×D3—62no—
462C2×C3×D3—62no—
463C2×C3×D3—62no—
464C2×C3×D3—64no—
465C2×C3×D3—62no—
466C2×C3×D3—62no—
467C2×C3×D3—62no—
468C2×C3×D3—62no—
469C2×C3×D3—62no—
470C2×C3×D3—62no—
471C2×C3×D3—122no—
472C2×C3×D3—122no—
473C2×C3×D3—128no—
474C2×C3×D3—122no—
475C2×C3×D3—122no—
476C2×C3×D3—128no—
477C2×C3×D3—124no—
478C2×C3×D3—124no—
479C3⋊Dic3—22no—
480C3⋊Dic3—22no—
481C3⋊Dic3—22no—
482C3⋊Dic3C2×#6714yescomplemented
483C3×Dic3—34no—
484C3×Dic3—34no—
485C3×Dic3—64no—
486C3×Dic3—64no—
487C3×Dic3—62no—
488C3×Dic3—62no—
489C3×Dic3—62no—
490C3×Dic3—62no—
491C3×Dic3—62no—
492C3×Dic3—62no—
493C3×Dic3—122no—
494C3×Dic3—122no—
495C22×D4—91no—
496C22×D4—91no—
497C22×D4—271no—
498C23×C4—271no—
499#121—278no—
500C2×C4⋊C4—271no—
501C2×C22⋊C4—91no—
502C2×C22⋊C4—271no—
503C33C2×#12111yescharacteristic, complemented, Sylow
504C23×C3—24no—
505C23×C3—24no—
506C23×C3—24no—
507C23×C3—22no—
508C23×C3—22no—
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—22no—
514C23×C3—22no—
515C23×C3—22no—
516C23×C3—22no—
517C23×C3—22no—
518C23×C3—22no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—42no—
523C23×C3—42no—
524C23×C3—42no—
525C23×C3—42no—
526C23×C3—42no—
527C23×C3—42no—
528C23×C3—44no—
529C23×C3—44no—
530C23×C3—44no—
531C23×C3—42no—
532C23×C3—41no—
533C23×C3—92no—
534C23×C3—94no—
535C23×C3—92no—
536C23×C3—182no—
537C23×C3—182no—
538C23×C3—182no—
539C23×C3—182no—
540C23×C3—182no—
541C23×C3C2×D3212yes—
542C23×C3C2×D3212yes—
543C23×C3C2×D3212yes—
544C23×C3C2×D3211yescharacteristic
545C23×C3C2×D3211yescharacteristic
546C23×C3C2×D3211yescharacteristic
547C22×D3—32no—
548C22×D3—32no—
549C22×D3—34no—
550C22×D3—34no—
551C22×D3—32no—
552C22×D3—32no—
553C22×D3—64no—
554C22×D3—62no—
555C22×D3—62no—
556C22×D3—62no—
557C22×D3—62no—
558C22×D3—62no—
559C22×D3—62no—
560C22×D3—64no—
561C22×D3—62no—
562C22×D3—62no—
563C22×D3—62no—
564C22×D3—62no—
565C22×D3—62no—
566C22×D3—62no—
567C22×D3—122no—
568C22×D3—122no—
569C22×D3—122no—
570C22×D3—122no—
571C3×D4—188no—
572C3×D4—188no—
573C2×C3×C4—92no—
574C2×C3×C4—94no—
575C2×C3×C4—92no—
576C2×C3×C4—92no—
577C2×C3×C4—92no—
578C2×C3×C4—182no—
579C2×C3×C4—182no—
580C2×C3×C4—182no—
581#67—68no—
582#67—68no—
583#67—68no—
584#67—68no—
585#67—616no—
586#67—616no—
587#67—188no—
588#67—188no—
589C2×Dic3—32no—
590C2×Dic3—32no—
591C2×Dic3—34no—
592C2×Dic3—34no—
593C2×Dic3—32no—
594C2×Dic3—32no—
595C2×Dic3—32no—
596C2×Dic3—32no—
597C2×Dic3—32no—
598C2×Dic3—32no—
599C2×Dic3—64no—
600C2×Dic3—62no—
601C2×Dic3—62no—
602C2×Dic3—62no—
603C2×Dic3—62no—
604C2×Dic3—64no—
605C2×Dic3—62no—
606C2×Dic3—62no—
607C2×Dic3—62no—
608C2×Dic3—62no—
609C2×Dic3—62no—
610C2×Dic3—62no—
611C2×Dic3—122no—
612C2×Dic3—122no—
613C2×Dic3—188no—
614D12—188no—
615C4×D3—188no—
616C4×D3—188no—
617C2×C32—21no—
618C2×C32—21no—
619C2×C32—21no—
620C2×C32—21no—
621C2×C32—21no—
622C2×C32—21no—
623C2×C32—21no—
624C2×C32—21no—
625C2×C32—21no—
626C2×C32—24no—
627C2×C32—24no—
628C2×C32—24no—
629C2×C32—44no—
630C2×C32—41no—
631C2×C32—41no—
632C2×C32—41no—
633C2×C32—44no—
634C2×C32—44no—
635C2×C32—44no—
636C2×C32—48no—
637C2×C32—42no—
638C2×C32—42no—
639C2×C32—42no—
640C2×C32#88414yescomplemented
641C2×C32#93814yescomplemented
642C2×C32#93914yescomplemented
643C2×C32C2×#23511yescharacteristic
644C2×C32C2×D3×D411yescharacteristic
645C2×C32C2×D3×D411yescharacteristic
646C2×C32C2×D3×D411yescharacteristic
647C2×C32C2×D3×D411yescharacteristic
648C2×C32C2×#23711yescharacteristic
649C2×C32C2×#23711yescharacteristic
650C2×C32C22×#6711yescharacteristic
651C2×C32C22×#6711yescharacteristic
652C3⋊D3—24no—
653C3⋊D3—42no—
654C3×D3—64no—
655C3×D3—64no—
656C3×D3—124no—
657C3×D3—124no—
658C3×D3—122no—
659C3×D3—122no—
660C24—91no—
661C24—91no—
662C24#111311yescharacteristic
663C2×D4—94no—
664C2×D4—94no—
665C2×D4—184no—
666C2×D4—184no—
667C2×D4—274no—
668C2×D4—544no—
669C22×C4—91no—
670C22×C4—91no—
671C22×C4—91no—
672C22×C4—91no—
673C22×C4—274no—
674C22×C4—544no—
675C4⋊C4—274no—
676C22⋊C4—94no—
677C22⋊C4—274no—
678C22×C3—24no—
679C22×C3—24no—
680C22×C3—24no—
681C22×C3—22no—
682C22×C3—22no—
683C22×C3—22no—
684C22×C3—22no—
685C22×C3—22no—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—22no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—22no—
694C22×C3—22no—
695C22×C3—22no—
696C22×C3—22no—
697C22×C3—22no—
698C22×C3—22no—
699C22×C3—22no—
700C22×C3—22no—
701C22×C3—22no—
702C22×C3—42no—
703C22×C3—42no—
704C22×C3—42no—
705C22×C3—42no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—44no—
709C22×C3—44no—
710C22×C3—44no—
711C22×C3—48no—
712C22×C3—48no—
713C22×C3—48no—
714C22×C3—416no—
715C22×C3—44no—
716C22×C3—44no—
717C22×C3—44no—
718C22×C3—41no—
719C22×C3—42no—
720C22×C3—42no—
721C22×C3—42no—
722C22×C3—94no—
723C22×C3—182no—
724C22×C3—182no—
725C22×C3—188no—
726C22×C3—182no—
727C22×C3—182no—
728C22×C3—182no—
729C22×C3—364no—
730C22×C3#380412yes—
731C22×C3#380412yes—
732C22×C3#380512yes—
733C22×C3D3×#6712yes—
734C22×C3D3×#6712yes—
735C22×C3D3×#6712yes—
736C22×C3D3×#6712yes—
737C22×C3#381112yes—
738C22×C3#381112yes—
739C22×C3C22×D3211yescharacteristic
740C22×C3C22×D3211yescharacteristic
741C22×C3C22×D3211yescharacteristic
742C2×D3—34no—
743C2×D3—34no—
744C2×D3—64no—
745C2×D3—62no—
746C2×D3—62no—
747C2×D3—62no—
748C2×D3—62no—
749C2×D3—68no—
750C2×D3—68no—
751C2×D3—64no—
752C2×D3—62no—
753C2×D3—62no—
754C2×D3—62no—
755C2×D3—62no—
756C2×D3—62no—
757C2×D3—62no—
758C2×D3—122no—
759C2×D3—122no—
760C2×D3—128no—
761C2×D3—122no—
762C2×D3—122no—
763C2×D3—128no—
764C2×D3—124no—
765C2×D3—124no—
766C3×C4—94no—
767C3×C4—182no—
768C3×C4—182no—
769C3×C4—182no—
770Dic3—34no—
771Dic3—34no—
772Dic3—64no—
773Dic3—64no—
774Dic3—62no—
775Dic3—62no—
776Dic3—62no—
777Dic3—62no—
778Dic3—62no—
779Dic3—62no—
780Dic3—122no—
781Dic3—122no—
782C32—21no—
783C32—21no—
784C32—21no—
785C32—41no—
786C32C2×#88411yescharacteristic, complemented
787C32C2×#93811yescharacteristic, complemented
788C32C2×#93911yescharacteristic, complemented
789C23—22no—
790C23—22no—
791C23—22no—
792C23—92no—
793C23—94no—
794C23—92no—
795C23—182no—
796C23—182no—
797C23—182no—
798C23—182no—
799C23—182no—
800C23C2×#111312yes—
801C23C2×#111311yescharacteristic
802D4—188no—
803D4—188no—
804D4—548no—
805C2×C4—92no—
806C2×C4—94no—
807C2×C4—92no—
808C2×C4—92no—
809C2×C4—92no—
810C2×C4—182no—
811C2×C4—182no—
812C2×C4—182no—
813C2×C4—548no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—24no—
824C2×C3—24no—
825C2×C3—24no—
826C2×C3—44no—
827C2×C3—44no—
828C2×C3—44no—
829C2×C3—48no—
830C2×C3—42no—
831C2×C3—42no—
832C2×C3—42no—
833C2×C3—41no—
834C2×C3—41no—
835C2×C3—41no—
836C2×C3—44no—
837C2×C3—184no—
838C2×C3—362no—
839C2×C3#6395814yescomplemented
840C2×C3#6397014yescomplemented
841C2×C3#6397114yescomplemented
842C2×C3C2×#380411yescharacteristic
843C2×C3C2×#380411yescharacteristic
844C2×C3C2×#380511yescharacteristic
845C2×C3C2×D3×#6711yescharacteristic
846C2×C3C2×D3×#6711yescharacteristic
847C2×C3C2×D3×#6711yescharacteristic
848C2×C3C2×D3×#6711yescharacteristic
849C2×C3C2×#381111yescharacteristic
850C2×C3C2×#381111yescharacteristic
851D3—64no—
852D3—64no—
853D3—124no—
854D3—124no—
855D3—122no—
856D3—122no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—44no—
861C22—94no—
862C22—182no—
863C22—182no—
864C22—188no—
865C22—182no—
866C22—182no—
867C22—182no—
868C22—364no—
869C22#8904612yes—
870C22#8904912yes—
871C22#8904912yes—
872C22C22×#111311yescharacteristic
873C4—94no—
874C4—182no—
875C4—182no—
876C4—182no—
877C3—21no—
878C3—21no—
879C3—21no—
880C3—41no—
881C3C2×#6395811yescharacteristic, complemented
882C3C2×#6397011yescharacteristic, complemented
883C3C2×#6397111yescharacteristic, complemented
884C2—42no—
885C2—184no—
886C2—362no—
887C2#1172372514yesdirect product factor
888C2C2×#8904611yescharacteristic
889C2C2×#8904911yescharacteristic
890C2C2×#8904911yescharacteristic
subgroupG/H
centerC23C2×#1113
commutator, cosocleC22×C33C24
FrattiniC22C22×#1113
FittingC24×C33C22
socleC23×C33C23
hypercenterC24#1113
hypocenterC33C2×#121
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C22×C3×#638C2semidirect
2. C22×C3×#638C2semidirect
3. C22×#6295C2semidirect
4. C22×#6294C2semidirect
5. C2×C3×#3757C2semidirect
6. #11723725C2direct (N × H)
7. C2×#88815C2semidirect
8. C2×#88814C2semidirect
17. C2×C3×#638C22semidirect
18. C2×C3×#638C22semidirect
24. C2×#6295C22semidirect
26. C2×#6294C22semidirect
27. C3×#3757C22semidirect
28. #88815C22semidirect
29. #88814C22semidirect
30. C22×#638D3semidirect
31. C22×#638D3semidirect
44. C2×#3757D3semidirect
67. C22×C3×C3⋊D3D4semidirect
75. C2×C3×C3⋊Dic3D4semidirect
102. C2×#638C2×D3semidirect
103. C2×#638C2×D3semidirect
144. #3757C2×D3semidirect
169. C2×C3×C3⋊D3C2×D4semidirect
173. C3×C3⋊Dic3C2×D4semidirect
241. C22×C3⋊D3#67semidirect
273. C2×C3⋊Dic3#67semidirect
316. C2×C33#121semidirect
454. C2×C3⋊D3C2×#67semidirect
482. C3⋊Dic3C2×#67semidirect
503. C33C2×#121semidirect
640. C2×C32#884semidirect
641. C2×C32#938semidirect
642. C2×C32#939semidirect
786. C32C2×#884semidirect
787. C32C2×#938semidirect
788. C32C2×#939semidirect
839. C2×C3#63958semidirect
840. C2×C3#63970semidirect
841. C2×C3#63971semidirect
881. C3C2×#63958semidirect
882. C3C2×#63970semidirect
883. C3C2×#63971semidirect
887. C2#11723725direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#6382
C22×#62952
C22×#62942
C2×C3×#37572
#117237252
C2×#888152
C2×#888142
C2×#639713
C2×#639703
C2×#639583