Finite Group Databasebeta

← C2×#11722961 #13172366

Subgroups — C2×#11722961 #13172366

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×#6295C211yesmaximal, characteristic, complemented
2C22×#6292C211yesmaximal, characteristic, complemented
3C22×#6292C211yesmaximal, characteristic, complemented
4C22×C3×#624C211yesmaximal, characteristic, complemented
5C2×#88804C211yesmaximal, characteristic, complemented
6C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
7C2×C3×#3722C211yesmaximal, characteristic, complemented
8#11722961C218yesmaximal, direct product factor
9C2×#63910—31nomaximal
10C2×#63909—31nomaximal
11C2×#63906—31nomaximal
12C23×C3⋊(C3⋊D3)C2211yescharacteristic
13C23×C3×C3⋊D3C2211yescharacteristic
14C23×C3×C3⋊D3C2211yescharacteristic
15C22×C3×C3⋊Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C22×C32×Dic3C2211yescharacteristic
19C2×#6295—24no—
20C2×#6295C2214yescomplemented
21C2×#6292—24no—
22C2×#6292—24no—
23C2×#6292C2214yescomplemented
24C2×#6292C2214yescomplemented
25C2×C3×#624—24no—
26C2×C3×#624C2214yescomplemented
27#88804C2214yescomplemented
28C3×Dic3⋊Dic3C2214yescomplemented
29C3×#3722C2214yescomplemented
30C22×C4⋊(C3⋊D3)—31no—
31C22×C4⋊(C3⋊D3)—31no—
32C22×C3×C4×D3—31no—
33C22×C3×C4×D3—31no—
34C22×#626—31no—
35C22×#626—31no—
36C22×#626—31no—
37C22×#626—31no—
38C22×#626—31no—
39C22×#626—31no—
40C22×#626—61no—
41C22×#626—61no—
42C22×#625—31no—
43C22×#624D311yescharacteristic, complemented
44C2×#3752—31no—
45C2×C3×(C2×D3)⋊C4—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×#3722—31no—
52C2×#3722—61no—
53C2×#3722D311yescharacteristic, complemented
54#63910—38no—
55#63909—38no—
56#63906—38no—
57C23×C33C2311yescharacteristic
58C22×C3⋊(C3⋊D3)—22no—
59C22×C3⋊(C3⋊D3)—22no—
60C22×C3⋊(C3⋊D3)—22no—
61C22×C3⋊(C3⋊D3)C2312yes—
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—
70C2×C3×C3⋊Dic3—22no—
71C2×C3×C3⋊Dic3C2312yes—
72C2×C32×Dic3—22no—
73C2×C32×Dic3—22no—
74C2×C32×Dic3D414yescomplemented
75C2×C32×Dic3C2312yes—
76C2×C32×Dic3C2312yes—
77C2×C32×Dic3C2312yes—
78#6295—28no—
79#6292—28no—
80#6292—28no—
81C3×#624—28no—
82C2×#930—91no—
83C2×#895—91no—
84C2×#884—91no—
85C23×C3⋊D3—31no—
86C23×C3⋊D3—31no—
87C23×C3⋊D3—31no—
88C23×C3⋊D3—61no—
89C23×C3⋊D3—61no—
90C23×C3⋊D3—61no—
91C23×C3⋊D3—121no—
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—
100C22×C32×C4—31no—
101C22×C32×C4—31no—
102C22×C32×C4—31no—
103C22×C3⋊Dic3C2×D311yescharacteristic
104C2×C4⋊(C3⋊D3)—34no—
105C2×C4⋊(C3⋊D3)—34no—
106C2×C4⋊(C3⋊D3)—64no—
107C2×C4⋊(C3⋊D3)—64no—
108C22×C3×Dic3—21no—
109C22×C3×Dic3—21no—
110C22×C3×Dic3—21no—
111C22×C3×Dic3—31no—
112C22×C3×Dic3—31no—
113C22×C3×Dic3—61no—
114C22×C3×Dic3C2×D311yescharacteristic
115C22×C3×Dic3C2×D311yescharacteristic
116C22×C3×Dic3C2×D311yescharacteristic
117C22×C3×Dic3C2×D311yescharacteristic
118C22×C3×Dic3C2×D311yescharacteristic
119C22×C3×Dic3C2×D311yescharacteristic
120C2×C3×C4×D3—34no—
121C2×C3×C4×D3—34no—
122C2×C3×C4×D3—64no—
123C2×C3×C4×D3—64no—
124C2×#626—34no—
125C2×#626—34no—
126C2×#626—34no—
127C2×#626—34no—
128C2×#626—34no—
129C2×#626—34no—
130C2×#626—64no—
131C2×#626—64no—
132C2×#626—64no—
133C2×#626—64no—
134C2×#626—68no—
135C2×#626—68no—
136C2×#626—64no—
137C2×#626—64no—
138C2×#626—64no—
139C2×#626—64no—
140C2×#625—34no—
141C2×#625—64no—
142C2×#624—24no—
143C2×#624C2×D314yescomplemented
144#3752—34no—
145C3×(C2×D3)⋊C4—34no—
146C3×(C2×D3)⋊C4—34no—
147C3×C4⋊Dic3—34no—
148C3×Dic3⋊C4—34no—
149Dic3⋊Dic3C2×D314yescomplemented
150#3722—34no—
151#3722—34no—
152#3722—64no—
153#3722C2×D314yescomplemented
154C22×C33C2×D412yes—
155C22×C33C2×D412yes—
156C22×C33#4112yes—
157C22×C33C2411yescharacteristic
158C2×C3⋊(C3⋊D3)—22no—
159C2×C3⋊(C3⋊D3)—22no—
160C2×C3⋊(C3⋊D3)—22no—
161C2×C3⋊(C3⋊D3)—44no—
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—
171C32×Dic3—22no—
172C32×Dic3—22no—
173C32×Dic3C2×D414yescomplemented
174C23×C3×C4—91no—
175C22×#67—91no—
176C22×#67—91no—
177C22×#67—91no—
178C22×#67—91no—
179C22×D12—91no—
180C22×D12—91no—
181C22×D12—91no—
182C22×D12—91no—
183C22×D12—91no—
184C22×D12—181no—
185C22×D12—181no—
186C22×C4×D3—31no—
187C22×C4×D3—31no—
188C2×C3×C4⋊C4—91no—
189C2×C3×C22⋊C4—91no—
190#930—98no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—91no—
194C2×(C2×D3)⋊C4—91no—
195C2×(C2×D3)⋊C4—91no—
196C2×(C2×D3)⋊C4—181no—
197C2×C4⋊Dic3—31no—
198C2×Dic3⋊C4—31no—
199#895—98no—
200#884—98no—
201C23×C32—21no—
202C23×C32—21no—
203C23×C32—21no—
204C23×C32—41no—
205C23×C32C22×D311yescharacteristic
206C23×C32C22×D311yescharacteristic
207C23×C32C22×D311yescharacteristic
208C22×C3⋊D3—22no—
209C22×C3⋊D3—22no—
210C22×C3⋊D3—22no—
211C22×C3⋊D3—22no—
212C22×C3⋊D3—22no—
213C22×C3⋊D3—32no—
214C22×C3⋊D3—32no—
215C22×C3⋊D3—32no—
216C22×C3⋊D3—62no—
217C22×C3⋊D3—62no—
218C22×C3⋊D3—62no—
219C22×C3⋊D3—62no—
220C22×C3⋊D3—62no—
221C22×C3⋊D3—62no—
222C22×C3⋊D3—64no—
223C22×C3⋊D3—64no—
224C22×C3⋊D3—64no—
225C22×C3⋊D3—62no—
226C22×C3⋊D3—62no—
227C22×C3⋊D3—62no—
228C22×C3⋊D3—62no—
229C22×C3⋊D3—62no—
230C22×C3⋊D3—62no—
231C22×C3⋊D3—122no—
232C22×C3⋊D3—122no—
233C22×C3⋊D3—122no—
234C22×C3⋊D3—122no—
235C22×C3⋊D3—122no—
236C22×C3⋊D3—122no—
237C22×C3⋊D3—122no—
238C22×C3⋊D3—124no—
239C22×C3⋊D3—124no—
240C22×C3⋊D3—124no—
241C22×C3⋊D3D1214yescomplemented
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—
268C2×C32×C4—34no—
269C2×C32×C4—32no—
270C2×C32×C4—32no—
271C2×C32×C4—32no—
272C2×C32×C4—62no—
273C2×C32×C4—62no—
274C2×C3⋊Dic3—22no—
275C2×C3⋊Dic3C22×D312yes—
276C4⋊(C3⋊D3)—68no—
277C4⋊(C3⋊D3)—68no—
278C2×C3×Dic3—24no—
279C2×C3×Dic3—22no—
280C2×C3×Dic3—22no—
281C2×C3×Dic3—22no—
282C2×C3×Dic3—22no—
283C2×C3×Dic3—24no—
284C2×C3×Dic3—22no—
285C2×C3×Dic3—22no—
286C2×C3×Dic3—22no—
287C2×C3×Dic3—32no—
288C2×C3×Dic3—32no—
289C2×C3×Dic3—42no—
290C2×C3×Dic3—62no—
291C2×C3×Dic3—62no—
292C2×C3×Dic3—62no—
293C2×C3×Dic3—122no—
294C2×C3×Dic3D1214yescomplemented
295C2×C3×Dic3#6714yescomplemented
296C2×C3×Dic3C22×D312yes—
297C2×C3×Dic3C22×D312yes—
298C2×C3×Dic3C22×D312yes—
299C2×C3×Dic3C22×D312yes—
300C2×C3×Dic3C22×D312yes—
301C2×C3×Dic3C22×D312yes—
302C3×C4×D3—68no—
303C3×C4×D3—68no—
304#626—68no—
305#626—68no—
306#626—616no—
307#626—616no—
308#626—68no—
309#626—68no—
310#626—68no—
311#626—68no—
312#625—68no—
313#624—28no—
314C2×#121—271noSylow
315C2×C33#12114yescomplemented
316C2×C33C22×D411yescharacteristic
317C2×C33C22×D411yescharacteristic
318C2×C33C2×#4111yescharacteristic
319C3⋊(C3⋊D3)—42no—
320C3×C3⋊D3—24no—
321C3×C3⋊D3—42no—
322C24×C3—91no—
323C24×C3—91no—
324C23×D3—31no—
325C23×D3—31no—
326C23×D3—31no—
327C23×D3—31no—
328C23×D3—61no—
329C23×D3—61no—
330C23×D3—91no—
331C23×D3—91no—
332C23×D3—91no—
333C23×D3—181no—
334C23×D3—181no—
335C23×D3—181no—
336C23×D3—361no—
337C22×C3×C4—31no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—61no—
344C22×C3×C4—61no—
345C22×C3×C4—61no—
346C22×C3×C4—94no—
347C22×C3×C4—91no—
348C22×C3×C4—184no—
349C2×#67—94no—
350C2×#67—94no—
351C2×#67—94no—
352C2×#67—94no—
353C2×#67—184no—
354C2×#67—184no—
355C2×#67—184no—
356C2×#67—184no—
357C22×Dic3—31no—
358C22×Dic3—31no—
359C22×Dic3—61no—
360C22×Dic3D3211yescharacteristic
361C22×Dic3D3211yescharacteristic
362C22×Dic3D3211yescharacteristic
363C2×D12—94no—
364C2×D12—94no—
365C2×D12—94no—
366C2×D12—94no—
367C2×D12—94no—
368C2×D12—184no—
369C2×D12—184no—
370C2×D12—184no—
371C2×D12—184no—
372C2×D12—184no—
373C2×D12—184no—
374C2×D12—188no—
375C2×D12—188no—
376C2×D12—184no—
377C2×C4×D3—34no—
378C2×C4×D3—34no—
379C2×C4×D3—64no—
380C2×C4×D3—64no—
381C3×C4⋊C4—94no—
382C3×C22⋊C4—94no—
383(C2×D3)⋊C4—34no—
384(C2×D3)⋊C4—34no—
385(C2×D3)⋊C4—94no—
386(C2×D3)⋊C4—94no—
387(C2×D3)⋊C4—94no—
388(C2×D3)⋊C4—184no—
389C4⋊Dic3—34no—
390Dic3⋊C4—34no—
391C22×C32—21no—
392C22×C32—21no—
393C22×C32—21no—
394C22×C32—22no—
395C22×C32—22no—
396C22×C32—22no—
397C22×C32—22no—
398C22×C32—22no—
399C22×C32—22no—
400C22×C32—22no—
401C22×C32—22no—
402C22×C32—22no—
403C22×C32—42no—
404C22×C32—42no—
405C22×C32—42no—
406C22×C32—41no—
407C22×C32C2×D1212yes—
408C22×C32C2×D1212yes—
409C22×C32#23512yes—
410C22×C32#23512yes—
411C22×C32D3×D412yes—
412C22×C32D3×D412yes—
413C22×C32D3×D412yes—
414C22×C32#23912yes—
415C22×C32C2×#6712yes—
416C22×C32C23×D311yescharacteristic
417C22×C32C23×D311yescharacteristic
418C22×C32C23×D311yescharacteristic
419C2×C3⋊D3—22no—
420C2×C3⋊D3—28no—
421C2×C3⋊D3—22no—
422C2×C3⋊D3—22no—
423C2×C3⋊D3—22no—
424C2×C3⋊D3—22no—
425C2×C3⋊D3—44no—
426C2×C3⋊D3—62no—
427C2×C3⋊D3—62no—
428C2×C3⋊D3—62no—
429C2×C3⋊D3—64no—
430C2×C3⋊D3—64no—
431C2×C3⋊D3—64no—
432C2×C3⋊D3—62no—
433C2×C3⋊D3—62no—
434C2×C3⋊D3—62no—
435C2×C3⋊D3—62no—
436C2×C3⋊D3—62no—
437C2×C3⋊D3—62no—
438C2×C3⋊D3—122no—
439C2×C3⋊D3—122no—
440C2×C3⋊D3—122no—
441C2×C3⋊D3—122no—
442C2×C3⋊D3—122no—
443C2×C3⋊D3—122no—
444C2×C3⋊D3—124no—
445C2×C3⋊D3—124no—
446C2×C3⋊D3—124no—
447C2×C3⋊D3—128no—
448C2×C3⋊D3—128no—
449C2×C3⋊D3—128no—
450C2×C3⋊D3—1216no—
451C2×C3⋊D3—124no—
452C2×C3⋊D3—124no—
453C2×C3⋊D3—124no—
454C2×C3⋊D3C2×D1214yescomplemented
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—
479C32×C4—34no—
480C32×C4—62no—
481C32×C4—62no—
482C3⋊Dic3—22no—
483C3×Dic3—24no—
484C3×Dic3—22no—
485C3×Dic3—22no—
486C3×Dic3—22no—
487C3×Dic3—22no—
488C3×Dic3—24no—
489C3×Dic3—42no—
490C3×Dic3—62no—
491C3×Dic3—62no—
492C3×Dic3—122no—
493C3×Dic3C2×D1214yescomplemented
494C3×Dic3C2×#6714yescomplemented
495C22×D4—271no—
496C22×D4—271no—
497C22×D4—271no—
498C23×C4—91no—
499#121—278no—
500C2×C4⋊C4—91no—
501C2×C22⋊C4—91no—
502C2×C22⋊C4—271no—
503C33C2×#12111yescharacteristic, complemented, Sylow
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—41no—
508C23×C3—92no—
509C23×C3—94no—
510C23×C3—92no—
511C23×C3—182no—
512C23×C3—182no—
513C23×C3—182no—
514C23×C3—182no—
515C23×C3—182no—
516C23×C3C2×D3211yescharacteristic
517C23×C3C2×D3211yescharacteristic
518C23×C3C2×D3211yescharacteristic
519C22×D3—32no—
520C22×D3—32no—
521C22×D3—34no—
522C22×D3—34no—
523C22×D3—32no—
524C22×D3—32no—
525C22×D3—64no—
526C22×D3—62no—
527C22×D3—62no—
528C22×D3—62no—
529C22×D3—62no—
530C22×D3—62no—
531C22×D3—62no—
532C22×D3—64no—
533C22×D3—62no—
534C22×D3—62no—
535C22×D3—62no—
536C22×D3—62no—
537C22×D3—62no—
538C22×D3—62no—
539C22×D3—92no—
540C22×D3—92no—
541C22×D3—92no—
542C22×D3—122no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—182no—
547C22×D3—182no—
548C22×D3—182no—
549C22×D3—184no—
550C22×D3—184no—
551C22×D3—184no—
552C22×D3—182no—
553C22×D3—182no—
554C22×D3—182no—
555C22×D3—182no—
556C22×D3—182no—
557C22×D3—182no—
558C22×D3—182no—
559C22×D3—182no—
560C22×D3—182no—
561C22×D3—362no—
562C22×D3—362no—
563C22×D3—362no—
564C22×D3—362no—
565C22×D3—362no—
566C22×D3—362no—
567C22×D3—362no—
568C22×D3—364no—
569C22×D3—364no—
570C22×D3—364no—
571C2×C3×C4—32no—
572C2×C3×C4—32no—
573C2×C3×C4—34no—
574C2×C3×C4—34no—
575C2×C3×C4—32no—
576C2×C3×C4—32no—
577C2×C3×C4—32no—
578C2×C3×C4—32no—
579C2×C3×C4—62no—
580C2×C3×C4—64no—
581C2×C3×C4—62no—
582C2×C3×C4—62no—
583C2×C3×C4—64no—
584C2×C3×C4—62no—
585C2×C3×C4—62no—
586C2×C3×C4—62no—
587C2×C3×C4—62no—
588C2×C3×C4—92no—
589C2×C3×C4—122no—
590C2×C3×C4—188no—
591C2×C3×C4—182no—
592#67—188no—
593#67—188no—
594#67—188no—
595#67—188no—
596C2×Dic3—22no—
597C2×Dic3—22no—
598C2×Dic3—32no—
599C2×Dic3—32no—
600C2×Dic3—62no—
601C2×Dic3—62no—
602C2×Dic3—62no—
603C2×Dic3—122no—
604C2×Dic3#62614yescomplemented
605C2×Dic3C2×D3212yes—
606C2×Dic3C2×D3212yes—
607C2×Dic3C2×D3212yes—
608D12—188no—
609D12—188no—
610D12—188no—
611D12—188no—
612D12—1816no—
613D12—1816no—
614D12—188no—
615C4×D3—68no—
616C4×D3—68no—
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#88414yescomplemented
634C2×C32#89514yescomplemented
635C2×C32#93014yescomplemented
636C2×C32C22×D1211yescharacteristic
637C2×C32C22×D1211yescharacteristic
638C2×C32C2×#23511yescharacteristic
639C2×C32C2×#23511yescharacteristic
640C2×C32C2×D3×D411yescharacteristic
641C2×C32C2×D3×D411yescharacteristic
642C2×C32C2×D3×D411yescharacteristic
643C2×C32C2×#23911yescharacteristic
644C2×C32C22×#6711yescharacteristic
645C3⋊D3—24no—
646C3⋊D3—42no—
647C3⋊D3—124no—
648C3⋊D3—124no—
649C3⋊D3—124no—
650C3⋊D3—128no—
651C3⋊D3—122no—
652C3⋊D3—122no—
653C3⋊D3—122no—
654C3×D3—64no—
655C3×D3—64no—
656C3×D3—124no—
657C3×D3—124no—
658C3×D3—122no—
659C3×D3—122no—
660C24—91no—
661C24—91no—
662C24—271no—
663C2×D4—274no—
664C2×D4—274no—
665C2×D4—274no—
666C2×D4—544no—
667C2×D4—544no—
668C2×D4—544no—
669C22×C4—31no—
670C22×C4—31no—
671C22×C4—31no—
672C22×C4—94no—
673C22×C4—91no—
674C22×C4—184no—
675C4⋊C4—94no—
676C22⋊C4—94no—
677C22⋊C4—274no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
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—41no—
691C22×C3—42no—
692C22×C3—42no—
693C22×C3—42no—
694C22×C3—94no—
695C22×C3—182no—
696C22×C3—182no—
697C22×C3—188no—
698C22×C3—182no—
699C22×C3—182no—
700C22×C3—182no—
701C22×C3—364no—
702C22×C3#379812yes—
703C22×C3#379912yes—
704C22×C3#379912yes—
705C22×C3D3×D1212yes—
706C22×C3D3×D1212yes—
707C22×C3D3×D1212yes—
708C22×C3C2×#62612yes—
709C22×C3D3×#6712yes—
710C22×C3#381112yes—
711C22×C3C22×D3211yescharacteristic
712C22×C3C22×D3211yescharacteristic
713C22×C3C22×D3211yescharacteristic
714C2×D3—34no—
715C2×D3—34no—
716C2×D3—64no—
717C2×D3—62no—
718C2×D3—62no—
719C2×D3—62no—
720C2×D3—62no—
721C2×D3—68no—
722C2×D3—68no—
723C2×D3—64no—
724C2×D3—62no—
725C2×D3—62no—
726C2×D3—62no—
727C2×D3—62no—
728C2×D3—62no—
729C2×D3—62no—
730C2×D3—122no—
731C2×D3—122no—
732C2×D3—128no—
733C2×D3—122no—
734C2×D3—122no—
735C2×D3—128no—
736C2×D3—124no—
737C2×D3—124no—
738C2×D3—184no—
739C2×D3—184no—
740C2×D3—184no—
741C2×D3—182no—
742C2×D3—182no—
743C2×D3—182no—
744C2×D3—182no—
745C2×D3—182no—
746C2×D3—182no—
747C2×D3—182no—
748C2×D3—182no—
749C2×D3—182no—
750C2×D3—362no—
751C2×D3—362no—
752C2×D3—362no—
753C2×D3—362no—
754C2×D3—362no—
755C2×D3—362no—
756C2×D3—364no—
757C2×D3—364no—
758C2×D3—364no—
759C2×D3—368no—
760C2×D3—368no—
761C2×D3—368no—
762C2×D3—3616no—
763C2×D3—364no—
764C2×D3—364no—
765C2×D3—364no—
766C3×C4—34no—
767C3×C4—34no—
768C3×C4—64no—
769C3×C4—64no—
770C3×C4—62no—
771C3×C4—62no—
772C3×C4—62no—
773C3×C4—62no—
774C3×C4—122no—
775C3×C4—182no—
776Dic3—22no—
777Dic3—22no—
778Dic3—62no—
779Dic3—62no—
780Dic3—122no—
781Dic3C2×#62614yescomplemented
782C32—21no—
783C32—21no—
784C32—21no—
785C32—41no—
786C32C2×#88411yescharacteristic, complemented
787C32C2×#89511yescharacteristic, complemented
788C32C2×#93011yescharacteristic, complemented
789C23—92no—
790C23—94no—
791C23—92no—
792C23—182no—
793C23—182no—
794C23—182no—
795C23—182no—
796C23—182no—
797C23—272no—
798C23—542no—
799C23—542no—
800C23—542no—
801C23D3311yescharacteristic
802D4—548no—
803D4—548no—
804D4—548no—
805C2×C4—32no—
806C2×C4—34no—
807C2×C4—32no—
808C2×C4—32no—
809C2×C4—62no—
810C2×C4—62no—
811C2×C4—92no—
812C2×C4—188no—
813C2×C4—182no—
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—41no—
827C2×C3—41no—
828C2×C3—41no—
829C2×C3—44no—
830C2×C3—184no—
831C2×C3—362no—
832C2×C3#6390614yescomplemented
833C2×C3#6390914yescomplemented
834C2×C3#6391014yescomplemented
835C2×C3C2×#379811yescharacteristic
836C2×C3C2×#379911yescharacteristic
837C2×C3C2×#379911yescharacteristic
838C2×C3C2×D3×D1211yescharacteristic
839C2×C3C2×D3×D1211yescharacteristic
840C2×C3C2×D3×D1211yescharacteristic
841C2×C3C22×#62611yescharacteristic
842C2×C3C2×D3×#6711yescharacteristic
843C2×C3C2×#381111yescharacteristic
844D3—64no—
845D3—64no—
846D3—124no—
847D3—124no—
848D3—122no—
849D3—122no—
850D3—364no—
851D3—364no—
852D3—364no—
853D3—368no—
854D3—362no—
855D3—362no—
856D3—362no—
857C22—94no—
858C22—182no—
859C22—182no—
860C22—188no—
861C22—182no—
862C22—182no—
863C22—182no—
864C22—364no—
865C22—542no—
866C22—542no—
867C22—542no—
868C22—1084no—
869C22D3×#62612yes—
870C22#8895512yes—
871C22#8896512yes—
872C22C2×D3311yescharacteristic
873C4—34no—
874C4—62no—
875C4—62no—
876C4—182no—
877C3—21no—
878C3—21no—
879C3—21no—
880C3—41no—
881C3C2×#6390611yescharacteristic, complemented
882C3C2×#6390911yescharacteristic, complemented
883C3C2×#6391011yescharacteristic, complemented
884C2—184no—
885C2—362no—
886C2—1082no—
887C2#1172296114yesdirect product factor
888C2C2×D3×#62611yescharacteristic
889C2C2×#8895511yescharacteristic
890C2C2×#8896511yescharacteristic
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×#6295C2semidirect
2. C22×#6292C2semidirect
3. C22×#6292C2semidirect
4. C22×C3×#624C2semidirect
5. C2×#88804C2semidirect
6. C2×C3×Dic3⋊Dic3C2semidirect
7. C2×C3×#3722C2semidirect
8. #11722961C2direct (N × H)
20. C2×#6295C22semidirect
23. C2×#6292C22semidirect
24. C2×#6292C22semidirect
26. C2×C3×#624C22semidirect
27. #88804C22semidirect
28. C3×Dic3⋊Dic3C22semidirect
29. C3×#3722C22semidirect
43. C22×#624D3semidirect
49. C2×Dic3⋊Dic3D3semidirect
53. C2×#3722D3semidirect
67. C22×C3×C3⋊D3D4semidirect
74. C2×C32×Dic3D4semidirect
143. C2×#624C2×D3semidirect
149. Dic3⋊Dic3C2×D3semidirect
153. #3722C2×D3semidirect
169. C2×C3×C3⋊D3C2×D4semidirect
173. C32×Dic3C2×D4semidirect
241. C22×C3⋊D3D12semidirect
294. C2×C3×Dic3D12semidirect
295. C2×C3×Dic3#67semidirect
315. C2×C33#121semidirect
454. C2×C3⋊D3C2×D12semidirect
493. C3×Dic3C2×D12semidirect
494. C3×Dic3C2×#67semidirect
503. C33C2×#121semidirect
604. C2×Dic3#626semidirect
633. C2×C32#884semidirect
634. C2×C32#895semidirect
635. C2×C32#930semidirect
781. Dic3C2×#626semidirect
786. C32C2×#884semidirect
787. C32C2×#895semidirect
788. C32C2×#930semidirect
832. C2×C3#63906semidirect
833. C2×C3#63909semidirect
834. C2×C3#63910semidirect
881. C3C2×#63906semidirect
882. C3C2×#63909semidirect
883. C3C2×#63910semidirect
887. C2#11722961direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#62952
C22×#62922
C22×C3×#6242
C2×#888042
C2×C3×Dic3⋊Dic32
C2×C3×#37222
#117229612
C2×#639103
C2×#639093
C2×#639063