Finite Group Databasebeta

← C2×#11722963 #13172368

Subgroups — C2×#11722963 #13172368

Order 1728.

2546 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6292C211yesmaximal, characteristic, complemented
2C22×#6291C211yesmaximal, characteristic, complemented
3C22×#6289C211yesmaximal, characteristic, complemented
4C22×C3×#626C211yesmaximal, characteristic, complemented
5C2×#88814C211yesmaximal, characteristic, complemented
6C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
7C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8#11722963C218yesmaximal, direct product factor
9C2×#63958—31nomaximal
10C2×#63916—31nomaximal
11C2×#63910—31nomaximal
12C23×C3⋊(C3⋊D3)C2211yescharacteristic
13C23×C3×C3⋊D3C2211yescharacteristic
14C23×C32×D3C2211yescharacteristic
15C22×C3×C3⋊Dic3C2211yescharacteristic
16C22×C3×C3⋊Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C22×C32×Dic3C2211yescharacteristic
19C2×#6292—24no—
20C2×#6292C2214yescomplemented
21C2×#6291—24no—
22C2×#6291C2214yescomplemented
23C2×#6289—24no—
24C2×#6289C2214yescomplemented
25C2×C3×#626—24no—
26C2×C3×#626C2214yescomplemented
27#88814C2214yescomplemented
28C3×Dic3⋊Dic3C2214yescomplemented
29C3×(C2×D3)⋊Dic3C2214yescomplemented
30C22×#638—31no—
31C22×C4⋊(C3⋊D3)—31no—
32C22×C4×C3⋊D3—31no—
33C22×C3×#67—31no—
34C22×C3×D12—31no—
35C22×#626—31no—
36C22×#626—31no—
37C22×#626—31no—
38C22×#626—31no—
39C22×#626—61no—
40C22×#626—61no—
41C22×#626D311yescharacteristic, complemented
42C22×#624—31no—
43C22×#624—31no—
44C22×#624—61no—
45C2×C3×#217—31no—
46C2×C3×(C2×D3)⋊C4—31no—
47C2×C3×C4⋊Dic3—31no—
48C2×C3×Dic3⋊C4—31no—
49C2×Dic3⋊Dic3D311yescharacteristic, complemented
50C2×#3722—31no—
51C2×(C2×D3)⋊Dic3—31no—
52C2×(C2×D3)⋊Dic3—31no—
53C2×(C2×D3)⋊Dic3D311yescharacteristic, complemented
54#63958—38no—
55#63916—38no—
56#63910—38no—
57C23×C33C2311yescharacteristic
58C22×C3⋊(C3⋊D3)—22no—
59C22×C3⋊(C3⋊D3)—22no—
60C22×C3⋊(C3⋊D3)D414yescomplemented
61C22×C3⋊(C3⋊D3)C2312yes—
62C22×C3×C3⋊D3—22no—
63C22×C3×C3⋊D3—22no—
64C22×C3×C3⋊D3—22no—
65C22×C3×C3⋊D3C2312yes—
66C22×C32×D3—22no—
67C22×C32×D3—22no—
68C22×C32×D3—22no—
69C22×C32×D3C2312yes—
70C2×C3×C3⋊Dic3—22no—
71C2×C3×C3⋊Dic3—22no—
72C2×C3×C3⋊Dic3C2312yes—
73C2×C3×C3⋊Dic3C2312yes—
74C2×C32×Dic3—22no—
75C2×C32×Dic3D414yescomplemented
76C2×C32×Dic3C2312yes—
77C2×C32×Dic3C2312yes—
78#6292—28no—
79#6291—28no—
80#6289—28no—
81C3×#626—28no—
82C2×#938—91no—
83C2×#895—91no—
84C2×#884—91no—
85C24×C32—31no—
86C23×C3⋊D3—31no—
87C23×C3⋊D3—31no—
88C23×C3⋊D3—31no—
89C23×C3⋊D3—61no—
90C23×C3⋊D3—61no—
91C23×C3⋊D3—61no—
92C23×C3⋊D3—121no—
93C23×C3⋊D3C2×D311yescharacteristic
94C23×C3×D3—21no—
95C23×C3×D3—31no—
96C23×C3×D3—31no—
97C23×C3×D3—61no—
98C23×C3×D3C2×D311yescharacteristic
99C23×C3×D3C2×D311yescharacteristic
100C22×C32×C4—31no—
101C22×C32×C4—31no—
102C2×#638—34no—
103C2×#638—64no—
104C22×C3⋊Dic3C2×D311yescharacteristic
105C22×C3⋊Dic3C2×D311yescharacteristic
106C2×C4⋊(C3⋊D3)—34no—
107C2×C4⋊(C3⋊D3)—64no—
108C2×C4×C3⋊D3—34no—
109C2×C4×C3⋊D3—64no—
110C2×C3×#67—34no—
111C2×C3×#67—64no—
112C22×C3×Dic3—21no—
113C22×C3×Dic3—21no—
114C22×C3×Dic3—31no—
115C22×C3×Dic3—31no—
116C22×C3×Dic3—31no—
117C22×C3×Dic3—31no—
118C22×C3×Dic3—61no—
119C22×C3×Dic3—61no—
120C22×C3×Dic3C2×D311yescharacteristic
121C22×C3×Dic3C2×D311yescharacteristic
122C22×C3×Dic3C2×D311yescharacteristic
123C22×C3×Dic3C2×D311yescharacteristic
124C2×C3×D12—34no—
125C2×C3×D12—64no—
126C2×#626—24no—
127C2×#626—34no—
128C2×#626—34no—
129C2×#626—34no—
130C2×#626—34no—
131C2×#626—64no—
132C2×#626—64no—
133C2×#626—64no—
134C2×#626—68no—
135C2×#626—64no—
136C2×#626—64no—
137C2×#626—64no—
138C2×#626—68no—
139C2×#626C2×D314yescomplemented
140C2×#624—34no—
141C2×#624—34no—
142C2×#624—64no—
143C2×#624—68no—
144C2×#624—64no—
145C2×#624—64no—
146C3×#217—34no—
147C3×(C2×D3)⋊C4—34no—
148C3×C4⋊Dic3—34no—
149C3×Dic3⋊C4—34no—
150Dic3⋊Dic3C2×D314yescomplemented
151#3722—34no—
152(C2×D3)⋊Dic3—34no—
153(C2×D3)⋊Dic3—34no—
154(C2×D3)⋊Dic3C2×D314yescomplemented
155C22×C33C2×D412yes—
156C22×C33C2×D412yes—
157C22×C33#4112yes—
158C22×C33C2411yescharacteristic
159C2×C3⋊(C3⋊D3)—28no—
160C2×C3⋊(C3⋊D3)—22no—
161C2×C3⋊(C3⋊D3)—22no—
162C2×C3⋊(C3⋊D3)C2×D414yescomplemented
163C2×C3×C3⋊D3—22no—
164C2×C3×C3⋊D3—22no—
165C2×C3×C3⋊D3—22no—
166C2×C3×C3⋊D3—44no—
167C2×C32×D3—22no—
168C2×C32×D3—22no—
169C2×C32×D3—22no—
170C2×C32×D3—44no—
171C3×C3⋊Dic3—22no—
172C3×C3⋊Dic3—22no—
173C32×Dic3—22no—
174C32×Dic3C2×D414yescomplemented
175C22×C3×D4—91no—
176C22×#67—31no—
177C22×#67—91no—
178C22×#67—91no—
179C22×#67—91no—
180C22×#67—181no—
181C22×D12—31no—
182C22×D12—91no—
183C22×D12—91no—
184C22×D12—91no—
185C22×D12—181no—
186C22×C4×D3—91no—
187C22×C4×D3—91no—
188C22×C4×D3—91no—
189C22×C4×D3—181no—
190C2×C3×C4⋊C4—91no—
191C2×C3×C22⋊C4—91no—
192C2×#217—31no—
193C2×#217—91no—
194#938—98no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4—91no—
197C2×(C2×D3)⋊C4—91no—
198C2×C4⋊Dic3—31no—
199C2×Dic3⋊C4—31no—
200#895—98no—
201#884—98no—
202C23×C32—21no—
203C23×C32—21no—
204C23×C32—21no—
205C23×C32—32no—
206C23×C32—41no—
207C23×C32—62no—
208C23×C32—62no—
209C23×C32—62no—
210C23×C32C22×D311yescharacteristic
211C23×C32C22×D311yescharacteristic
212C23×C32C22×D311yescharacteristic
213C22×C3⋊D3—22no—
214C22×C3⋊D3—22no—
215C22×C3⋊D3—22no—
216C22×C3⋊D3—34no—
217C22×C3⋊D3—34no—
218C22×C3⋊D3—34no—
219C22×C3⋊D3—32no—
220C22×C3⋊D3—32no—
221C22×C3⋊D3—32no—
222C22×C3⋊D3—64no—
223C22×C3⋊D3—62no—
224C22×C3⋊D3—64no—
225C22×C3⋊D3—64no—
226C22×C3⋊D3—62no—
227C22×C3⋊D3—62no—
228C22×C3⋊D3—62no—
229C22×C3⋊D3—62no—
230C22×C3⋊D3—64no—
231C22×C3⋊D3—64no—
232C22×C3⋊D3—62no—
233C22×C3⋊D3—62no—
234C22×C3⋊D3—62no—
235C22×C3⋊D3—62no—
236C22×C3⋊D3—124no—
237C22×C3⋊D3—122no—
238C22×C3⋊D3—122no—
239C22×C3⋊D3—122no—
240C22×C3⋊D3—122no—
241C22×C3⋊D3—122no—
242C22×C3⋊D3—124no—
243C22×C3⋊D3—124no—
244C22×C3⋊D3C22×D312yes—
245C22×C3×D3—24no—
246C22×C3×D3—22no—
247C22×C3×D3—22no—
248C22×C3×D3—22no—
249C22×C3×D3—22no—
250C22×C3×D3—22no—
251C22×C3×D3—22no—
252C22×C3×D3—22no—
253C22×C3×D3—32no—
254C22×C3×D3—32no—
255C22×C3×D3—42no—
256C22×C3×D3—42no—
257C22×C3×D3—62no—
258C22×C3×D3—64no—
259C22×C3×D3—62no—
260C22×C3×D3—62no—
261C22×C3×D3—62no—
262C22×C3×D3—62no—
263C22×C3×D3—62no—
264C22×C3×D3—62no—
265C22×C3×D3—122no—
266C22×C3×D3—122no—
267C22×C3×D3C22×D312yes—
268C22×C3×D3C22×D312yes—
269C2×C32×C4—34no—
270C2×C32×C4—32no—
271C2×C32×C4—32no—
272C2×C32×C4—62no—
273#638—68no—
274C2×C3⋊Dic3—22no—
275C2×C3⋊Dic3—22no—
276C2×C3⋊Dic3C22×D312yes—
277C2×C3⋊Dic3C22×D312yes—
278C4⋊(C3⋊D3)—68no—
279C4×C3⋊D3—68no—
280C3×#67—68no—
281C2×C3×Dic3—24no—
282C2×C3×Dic3—22no—
283C2×C3×Dic3—22no—
284C2×C3×Dic3—24no—
285C2×C3×Dic3—22no—
286C2×C3×Dic3—22no—
287C2×C3×Dic3—32no—
288C2×C3×Dic3—32no—
289C2×C3×Dic3—32no—
290C2×C3×Dic3—32no—
291C2×C3×Dic3—62no—
292C2×C3×Dic3—62no—
293C2×C3×Dic3—64no—
294C2×C3×Dic3—64no—
295C2×C3×Dic3—62no—
296C2×C3×Dic3—62no—
297C2×C3×Dic3—62no—
298C2×C3×Dic3—62no—
299C2×C3×Dic3D1214yescomplemented
300C2×C3×Dic3#6714yescomplemented
301C2×C3×Dic3C22×D312yes—
302C2×C3×Dic3C22×D312yes—
303C2×C3×Dic3C22×D312yes—
304C2×C3×Dic3C22×D312yes—
305C3×D12—68no—
306#626—28no—
307#626—68no—
308#626—68no—
309#626—616no—
310#626—68no—
311#626—68no—
312#626—616no—
313#624—616no—
314#624—68no—
315#624—68no—
316C2×#121—271noSylow
317C2×C33#12114yescomplemented
318C2×C33C22×D411yescharacteristic
319C2×C33C22×D411yescharacteristic
320C2×C33C2×#4111yescharacteristic
321C3⋊(C3⋊D3)—24no—
322C3×C3⋊D3—42no—
323C32×D3—42no—
324C24×C3—31no—
325C24×C3—31no—
326C24×C3—61no—
327C24×C3—91no—
328C23×D3—31no—
329C23×D3—31no—
330C23×D3—61no—
331C23×D3—91no—
332C23×D3—91no—
333C23×D3—91no—
334C23×D3—181no—
335C23×D3—181no—
336C23×D3—181no—
337C23×D3—361no—
338C23×D3D3211yescharacteristic
339C2×C3×D4—94no—
340C2×C3×D4—184no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—31no—
345C22×C3×C4—61no—
346C22×C3×C4—61no—
347C22×C3×C4—91no—
348C22×C3×C4—91no—
349C2×#67—34no—
350C2×#67—64no—
351C2×#67—94no—
352C2×#67—94no—
353C2×#67—94no—
354C2×#67—184no—
355C2×#67—184no—
356C2×#67—184no—
357C2×#67—184no—
358C2×#67—188no—
359C22×Dic3—31no—
360C22×Dic3—31no—
361C22×Dic3—31no—
362C22×Dic3—31no—
363C22×Dic3—61no—
364C22×Dic3—61no—
365C22×Dic3D3211yescharacteristic
366C22×Dic3D3211yescharacteristic
367C2×D12—34no—
368C2×D12—64no—
369C2×D12—94no—
370C2×D12—94no—
371C2×D12—94no—
372C2×D12—184no—
373C2×D12—184no—
374C2×D12—184no—
375C2×D12—188no—
376C2×D12—184no—
377C2×C4×D3—94no—
378C2×C4×D3—94no—
379C2×C4×D3—94no—
380C2×C4×D3—184no—
381C2×C4×D3—184no—
382C2×C4×D3—184no—
383C2×C4×D3—188no—
384C2×C4×D3—184no—
385C3×C4⋊C4—94no—
386C3×C22⋊C4—94no—
387#217—34no—
388#217—94no—
389(C2×D3)⋊C4—34no—
390(C2×D3)⋊C4—94no—
391(C2×D3)⋊C4—94no—
392C4⋊Dic3—34no—
393Dic3⋊C4—34no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—21no—
397C22×C32—22no—
398C22×C32—22no—
399C22×C32—22no—
400C22×C32—22no—
401C22×C32—22no—
402C22×C32—22no—
403C22×C32—22no—
404C22×C32—22no—
405C22×C32—22no—
406C22×C32—42no—
407C22×C32—42no—
408C22×C32—42no—
409C22×C32—41no—
410C22×C32—62no—
411C22×C32—62no—
412C22×C32—62no—
413C22×C32—124no—
414C22×C32C2×D1212yes—
415C22×C32#23512yes—
416C22×C32D3×D412yes—
417C22×C32D3×D412yes—
418C22×C32D3×D412yes—
419C22×C32D3×D412yes—
420C22×C32#23712yes—
421C22×C32#23912yes—
422C22×C32C2×#6712yes—
423C22×C32C23×D311yescharacteristic
424C22×C32C23×D311yescharacteristic
425C22×C32C23×D311yescharacteristic
426C2×C3⋊D3—22no—
427C2×C3⋊D3—22no—
428C2×C3⋊D3—22no—
429C2×C3⋊D3—34no—
430C2×C3⋊D3—34no—
431C2×C3⋊D3—34no—
432C2×C3⋊D3—44no—
433C2×C3⋊D3—64no—
434C2×C3⋊D3—64no—
435C2×C3⋊D3—64no—
436C2×C3⋊D3—68no—
437C2×C3⋊D3—62no—
438C2×C3⋊D3—62no—
439C2×C3⋊D3—64no—
440C2×C3⋊D3—64no—
441C2×C3⋊D3—616no—
442C2×C3⋊D3—68no—
443C2×C3⋊D3—68no—
444C2×C3⋊D3—62no—
445C2×C3⋊D3—62no—
446C2×C3⋊D3—62no—
447C2×C3⋊D3—62no—
448C2×C3⋊D3—124no—
449C2×C3⋊D3—122no—
450C2×C3⋊D3—122no—
451C2×C3⋊D3—122no—
452C2×C3⋊D3—122no—
453C2×C3⋊D3—128no—
454C2×C3⋊D3—128no—
455C2×C3⋊D3—124no—
456C2×C3⋊D3—1216no—
457C2×C3⋊D3—124no—
458C2×C3×D3—24no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—22no—
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3—22no—
465C2×C3×D3—42no—
466C2×C3×D3—42no—
467C2×C3×D3—48no—
468C2×C3×D3—44no—
469C2×C3×D3—44no—
470C2×C3×D3—64no—
471C2×C3×D3—62no—
472C2×C3×D3—62no—
473C2×C3×D3—62no—
474C2×C3×D3—62no—
475C2×C3×D3—62no—
476C2×C3×D3—62no—
477C2×C3×D3—122no—
478C2×C3×D3—122no—
479C2×C3×D3—128no—
480C2×C3×D3—124no—
481C2×C3×D3—124no—
482C32×C4—34no—
483C32×C4—62no—
484C3⋊Dic3—22no—
485C3⋊Dic3—22no—
486C3×Dic3—24no—
487C3×Dic3—22no—
488C3×Dic3—22no—
489C3×Dic3—24no—
490C3×Dic3—64no—
491C3×Dic3—64no—
492C3×Dic3—62no—
493C3×Dic3—62no—
494C3×Dic3—62no—
495C3×Dic3—62no—
496C3×Dic3C2×D1214yescomplemented
497C3×Dic3C2×#6714yescomplemented
498C22×D4—91no—
499C22×D4—271no—
500C22×D4—271no—
501C23×C4—271no—
502#121—278no—
503C2×C4⋊C4—91no—
504C2×C22⋊C4—91no—
505C2×C22⋊C4—271no—
506C33C2×#12111yescharacteristic, complemented, Sylow
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—32no—
511C23×C3—32no—
512C23×C3—41no—
513C23×C3—62no—
514C23×C3—64no—
515C23×C3—62no—
516C23×C3—62no—
517C23×C3—62no—
518C23×C3—62no—
519C23×C3—62no—
520C23×C3—62no—
521C23×C3—92no—
522C23×C3—122no—
523C23×C3—122no—
524C23×C3—182no—
525C23×C3—182no—
526C23×C3—182no—
527C23×C3C2×D3211yescharacteristic
528C23×C3C2×D3211yescharacteristic
529C23×C3C2×D3211yescharacteristic
530C22×D3—22no—
531C22×D3—22no—
532C22×D3—22no—
533C22×D3—32no—
534C22×D3—32no—
535C22×D3—62no—
536C22×D3—64no—
537C22×D3—62no—
538C22×D3—62no—
539C22×D3—62no—
540C22×D3—62no—
541C22×D3—62no—
542C22×D3—62no—
543C22×D3—92no—
544C22×D3—92no—
545C22×D3—92no—
546C22×D3—94no—
547C22×D3—94no—
548C22×D3—94no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—182no—
552C22×D3—184no—
553C22×D3—182no—
554C22×D3—184no—
555C22×D3—182no—
556C22×D3—184no—
557C22×D3—184no—
558C22×D3—184no—
559C22×D3—182no—
560C22×D3—182no—
561C22×D3—182no—
562C22×D3—182no—
563C22×D3—182no—
564C22×D3—182no—
565C22×D3—362no—
566C22×D3—364no—
567C22×D3—362no—
568C22×D3—362no—
569C22×D3—362no—
570C22×D3—362no—
571C22×D3—364no—
572C22×D3—364no—
573C22×D3C2×D3212yes—
574C3×D4—188no—
575C2×C3×C4—32no—
576C2×C3×C4—32no—
577C2×C3×C4—34no—
578C2×C3×C4—34no—
579C2×C3×C4—32no—
580C2×C3×C4—32no—
581C2×C3×C4—62no—
582C2×C3×C4—64no—
583C2×C3×C4—62no—
584C2×C3×C4—64no—
585C2×C3×C4—62no—
586C2×C3×C4—62no—
587C2×C3×C4—92no—
588C2×C3×C4—92no—
589C2×C3×C4—182no—
590C2×C3×C4—182no—
591#67—68no—
592#67—188no—
593#67—188no—
594#67—188no—
595#67—1816no—
596C2×Dic3—22no—
597C2×Dic3—32no—
598C2×Dic3—32no—
599C2×Dic3—32no—
600C2×Dic3—32no—
601C2×Dic3—62no—
602C2×Dic3—62no—
603C2×Dic3—64no—
604C2×Dic3—64no—
605C2×Dic3—62no—
606C2×Dic3—62no—
607C2×Dic3—62no—
608C2×Dic3—62no—
609C2×Dic3#62614yescomplemented
610C2×Dic3C2×D3212yes—
611C2×Dic3C2×D3212yes—
612D12—68no—
613D12—188no—
614D12—188no—
615D12—1816no—
616D12—188no—
617C4×D3—188no—
618C4×D3—188no—
619C4×D3—1816no—
620C4×D3—188no—
621C2×C32—21no—
622C2×C32—21no—
623C2×C32—21no—
624C2×C32—21no—
625C2×C32—21no—
626C2×C32—21no—
627C2×C32—21no—
628C2×C32—21no—
629C2×C32—21no—
630C2×C32—24no—
631C2×C32—24no—
632C2×C32—24no—
633C2×C32—44no—
634C2×C32—41no—
635C2×C32—41no—
636C2×C32—41no—
637C2×C32—122no—
638C2×C32#88414yescomplemented
639C2×C32#89514yescomplemented
640C2×C32#93814yescomplemented
641C2×C32C22×D1211yescharacteristic
642C2×C32C2×#23511yescharacteristic
643C2×C32C2×D3×D411yescharacteristic
644C2×C32C2×D3×D411yescharacteristic
645C2×C32C2×D3×D411yescharacteristic
646C2×C32C2×D3×D411yescharacteristic
647C2×C32C2×#23711yescharacteristic
648C2×C32C2×#23911yescharacteristic
649C2×C32C22×#6711yescharacteristic
650C3⋊D3—42no—
651C3⋊D3—64no—
652C3⋊D3—68no—
653C3⋊D3—64no—
654C3⋊D3—64no—
655C3⋊D3—124no—
656C3⋊D3—124no—
657C3⋊D3—128no—
658C3×D3—44no—
659C3×D3—42no—
660C3×D3—42no—
661C3×D3—124no—
662C3×D3—122no—
663C3×D3—122no—
664C24—31no—
665C24—91no—
666C24—271no—
667C2×D4—94no—
668C2×D4—184no—
669C2×D4—274no—
670C2×D4—274no—
671C2×D4—544no—
672C2×D4—544no—
673C22×C4—31no—
674C22×C4—31no—
675C22×C4—91no—
676C22×C4—91no—
677C22×C4—274no—
678C22×C4—544no—
679C4⋊C4—94no—
680C22⋊C4—94no—
681C22⋊C4—274no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—22no—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—22no—
690C22×C3—22no—
691C22×C3—22no—
692C22×C3—22no—
693C22×C3—22no—
694C22×C3—41no—
695C22×C3—42no—
696C22×C3—42no—
697C22×C3—42no—
698C22×C3—64no—
699C22×C3—62no—
700C22×C3—62no—
701C22×C3—62no—
702C22×C3—62no—
703C22×C3—62no—
704C22×C3—62no—
705C22×C3—122no—
706C22×C3—122no—
707C22×C3—128no—
708C22×C3—124no—
709C22×C3—124no—
710C22×C3—182no—
711C22×C3—182no—
712C22×C3—182no—
713C22×C3—364no—
714C22×C3#379612yes—
715C22×C3#379912yes—
716C22×C3D3×D1212yes—
717C22×C3#380212yes—
718C22×C3#380412yes—
719C22×C3C2×#62612yes—
720C22×C3D3×#6712yes—
721C22×C3#381112yes—
722C22×C3#381112yes—
723C22×C3C22×D3211yescharacteristic
724C22×C3C22×D3211yescharacteristic
725C22×C3C22×D3211yescharacteristic
726C2×D3—22no—
727C2×D3—22no—
728C2×D3—22no—
729C2×D3—44no—
730C2×D3—64no—
731C2×D3—62no—
732C2×D3—62no—
733C2×D3—62no—
734C2×D3—62no—
735C2×D3—62no—
736C2×D3—62no—
737C2×D3—94no—
738C2×D3—94no—
739C2×D3—94no—
740C2×D3—122no—
741C2×D3—122no—
742C2×D3—128no—
743C2×D3—124no—
744C2×D3—124no—
745C2×D3—184no—
746C2×D3—184no—
747C2×D3—184no—
748C2×D3—184no—
749C2×D3—184no—
750C2×D3—1816no—
751C2×D3—182no—
752C2×D3—182no—
753C2×D3—182no—
754C2×D3—182no—
755C2×D3—182no—
756C2×D3—182no—
757C2×D3—188no—
758C2×D3—188no—
759C2×D3—188no—
760C2×D3—364no—
761C2×D3—362no—
762C2×D3—362no—
763C2×D3—362no—
764C2×D3—362no—
765C2×D3—368no—
766C2×D3—368no—
767C2×D3—364no—
768C2×D3—364no—
769C2×D3—3616no—
770C3×C4—34no—
771C3×C4—34no—
772C3×C4—64no—
773C3×C4—64no—
774C3×C4—62no—
775C3×C4—62no—
776C3×C4—182no—
777C3×C4—182no—
778Dic3—22no—
779Dic3—64no—
780Dic3—64no—
781Dic3—62no—
782Dic3—62no—
783Dic3—62no—
784Dic3—62no—
785Dic3C2×#62614yescomplemented
786C32—21no—
787C32—21no—
788C32—21no—
789C32—41no—
790C32C2×#88411yescharacteristic, complemented
791C32C2×#89511yescharacteristic, complemented
792C32C2×#93811yescharacteristic, complemented
793C23—32no—
794C23—62no—
795C23—62no—
796C23—62no—
797C23—92no—
798C23—182no—
799C23—182no—
800C23—182no—
801C23—272no—
802C23—274no—
803C23—542no—
804C23—542no—
805C23D3311yescharacteristic
806D4—188no—
807D4—548no—
808D4—548no—
809C2×C4—32no—
810C2×C4—34no—
811C2×C4—32no—
812C2×C4—62no—
813C2×C4—92no—
814C2×C4—92no—
815C2×C4—182no—
816C2×C4—182no—
817C2×C4—548no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—21no—
824C2×C3—21no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—24no—
828C2×C3—24no—
829C2×C3—24no—
830C2×C3—41no—
831C2×C3—41no—
832C2×C3—41no—
833C2×C3—44no—
834C2×C3—124no—
835C2×C3—122no—
836C2×C3—122no—
837C2×C3—362no—
838C2×C3#6391014yescomplemented
839C2×C3#6391614yescomplemented
840C2×C3#6395814yescomplemented
841C2×C3C2×#379611yescharacteristic
842C2×C3C2×#379911yescharacteristic
843C2×C3C2×D3×D1211yescharacteristic
844C2×C3C2×#380211yescharacteristic
845C2×C3C2×#380411yescharacteristic
846C2×C3C22×#62611yescharacteristic
847C2×C3C2×D3×#6711yescharacteristic
848C2×C3C2×#381111yescharacteristic
849C2×C3C2×#381111yescharacteristic
850D3—42no—
851D3—124no—
852D3—122no—
853D3—122no—
854D3—188no—
855D3—184no—
856D3—184no—
857D3—184no—
858D3—364no—
859D3—364no—
860D3—368no—
861C22—62no—
862C22—62no—
863C22—62no—
864C22—124no—
865C22—182no—
866C22—182no—
867C22—182no—
868C22—274no—
869C22—364no—
870C22—542no—
871C22—542no—
872C22—548no—
873C22D3×#62612yes—
874C22#8895412yes—
875C22#8896212yes—
876C22C2×D3311yescharacteristic
877C4—34no—
878C4—62no—
879C4—182no—
880C4—182no—
881C3—21no—
882C3—21no—
883C3—21no—
884C3—41no—
885C3C2×#6391011yescharacteristic, complemented
886C3C2×#6391611yescharacteristic, complemented
887C3C2×#6395811yescharacteristic, complemented
888C2—122no—
889C2—362no—
890C2—544no—
891C2#1172296314yesdirect product factor
892C2C2×D3×#62611yescharacteristic
893C2C2×#8895411yescharacteristic
894C2C2×#8896211yescharacteristic
subgroupG/H
center, hypercenterC23D33
commutator, cosocleC22×C33C24
FrattiniC22C2×D33
Fitting, socleC23×C33C23
hypocenterC33C2×#121
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C22×#6292C2semidirect
2. C22×#6291C2semidirect
3. C22×#6289C2semidirect
4. C22×C3×#626C2semidirect
5. C2×#88814C2semidirect
6. C2×C3×Dic3⋊Dic3C2semidirect
7. C2×C3×(C2×D3)⋊Dic3C2semidirect
8. #11722963C2direct (N × H)
20. C2×#6292C22semidirect
22. C2×#6291C22semidirect
24. C2×#6289C22semidirect
26. C2×C3×#626C22semidirect
27. #88814C22semidirect
28. C3×Dic3⋊Dic3C22semidirect
29. C3×(C2×D3)⋊Dic3C22semidirect
41. C22×#626D3semidirect
49. C2×Dic3⋊Dic3D3semidirect
53. C2×(C2×D3)⋊Dic3D3semidirect
60. C22×C3⋊(C3⋊D3)D4semidirect
75. C2×C32×Dic3D4semidirect
139. C2×#626C2×D3semidirect
150. Dic3⋊Dic3C2×D3semidirect
154. (C2×D3)⋊Dic3C2×D3semidirect
162. C2×C3⋊(C3⋊D3)C2×D4semidirect
174. C32×Dic3C2×D4semidirect
299. C2×C3×Dic3D12semidirect
300. C2×C3×Dic3#67semidirect
317. C2×C33#121semidirect
496. C3×Dic3C2×D12semidirect
497. C3×Dic3C2×#67semidirect
506. C33C2×#121semidirect
609. C2×Dic3#626semidirect
638. C2×C32#884semidirect
639. C2×C32#895semidirect
640. C2×C32#938semidirect
785. Dic3C2×#626semidirect
790. C32C2×#884semidirect
791. C32C2×#895semidirect
792. C32C2×#938semidirect
838. C2×C3#63910semidirect
839. C2×C3#63916semidirect
840. C2×C3#63958semidirect
885. C3C2×#63910semidirect
886. C3C2×#63916semidirect
887. C3C2×#63958semidirect
891. C2#11722963direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#62922
C22×#62912
C22×#62892
C22×C3×#6262
C2×#888142
C2×C3×Dic3⋊Dic32
C2×C3×(C2×D3)⋊Dic32
#117229632
C2×#639583
C2×#639163
C2×#639103