Finite Group Databasebeta

← #13156768

Subgroups — #13156768

Order 1728.

1586 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6290C211yesmaximal, characteristic
2C22×C3×D3×Dic3C211yesmaximal, characteristic, complemented
3C2×#88814C211yesmaximal, characteristic, complemented
4C2×C3×#3722C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
6#11722061C211yesmaximal, characteristic, complemented
7#11722061C211yesmaximal, characteristic, complemented
8#10591711—31nomaximal
9#10591381—31nomaximal
10#10591363—31nomaximal
11C23×C3×C3⋊D3C2211yescharacteristic
12C23×C32×D3C2211yescharacteristic
13C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C3×C3⋊Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C2×#6290—22no—
19C2×#6290—22no—
20C2×#6290C414yescomplemented
21C2×C3×D3×Dic3—22no—
22C2×C3×D3×Dic3—22no—
23C2×C3×D3×Dic3—22no—
24#88814—22no—
25C3×#3722—22no—
26C3×(C2×D3)⋊Dic3—22no—
27C22×#638—31no—
28C23×C3×Dic3—31no—
29C22×C3×C4×D3—31no—
30C22×#625—31no—
31C22×#625—31no—
32C22×#625—61no—
33C22×D3×Dic3D311yescharacteristic, complemented
34C2×C3×#217—31no—
35C2×C3×(C2×D3)⋊C4—31no—
36C2×C3×(C2×D3)⋊C4—31no—
37C2×C3×(C2×D3)⋊C4—31no—
38C2×#3722—31no—
39C2×#3722D311yescharacteristic, complemented
40C2×(C2×D3)⋊Dic3—31no—
41C2×(C2×D3)⋊Dic3—31no—
42C2×(C2×D3)⋊Dic3D311yescharacteristic, complemented
43#63658—31no—
44#63658—31no—
45#63579—31no—
46#63579—31no—
47#63579—31no—
48#63579—31no—
49#63579—61no—
50#63579—61no—
51C23×C33C2311yescharacteristic
52C22×C3×C3⋊D3—21no—
53C22×C3×C3⋊D3—21no—
54C22×C3×C3⋊D3—21no—
55C22×C3×C3⋊D3—21no—
56C22×C3×C3⋊D3—21no—
57C22×C3×C3⋊D3—21no—
58C22×C3×C3⋊D3C2×C412yescomplemented
59C22×C32×D3—21no—
60C22×C32×D3—21no—
61C22×C32×D3—21no—
62C22×C32×D3—21no—
63C22×C32×D3C2×C412yes—
64C22×C32×D3D412yes—
65C22×C32×D3D412yes—
66C2×C3⋊(C3⋊Dic3)—21no—
67C2×C3⋊(C3⋊Dic3)—21no—
68C2×C3⋊(C3⋊Dic3)C2×C412yescomplemented
69C2×C3×C3⋊Dic3—21no—
70C2×C3×C3⋊Dic3—21no—
71C2×C3×C3⋊Dic3—21no—
72C2×C3×C3⋊Dic3—21no—
73C2×C3×C3⋊Dic3—21no—
74C2×C3×C3⋊Dic3D412yescomplemented
75C2×C32×Dic3—21no—
76C2×C32×Dic3—21no—
77C2×C32×Dic3—21no—
78C2×C32×Dic3—21no—
79C2×C32×Dic3—21no—
80C2×C32×Dic3D412yescomplemented
81#6290—28no—
82C3×D3×Dic3—28no—
83#5213—91no—
84#4958—91no—
85#4956—91no—
86C24×C32—31no—
87C23×C3⋊D3C2×D311yescharacteristic
88C23×C3×D3—21no—
89C23×C3×D3—31no—
90C23×C3×D3—31no—
91C23×C3×D3—61no—
92C23×C3×D3C2×D311yescharacteristic
93C23×C3×D3C2×D311yescharacteristic
94C22×C32×C4—31no—
95C22×C32×C4—31no—
96C2×#638—34no—
97C2×#638—62no—
98C2×#638—62no—
99C22×C3⋊Dic3—31no—
100C22×C3⋊Dic3—31no—
101C22×C3⋊Dic3—31no—
102C22×C3⋊Dic3—61no—
103C22×C3⋊Dic3—61no—
104C22×C3⋊Dic3—61no—
105C22×C3⋊Dic3—121no—
106C22×C3⋊Dic3C2×D311yescharacteristic
107C22×C3⋊Dic3C2×D311yescharacteristic
108C22×C3×Dic3—21no—
109C22×C3×Dic3—21no—
110C22×C3×Dic3—31no—
111C22×C3×Dic3—31no—
112C22×C3×Dic3—31no—
113C22×C3×Dic3—31no—
114C22×C3×Dic3—62no—
115C22×C3×Dic3—62no—
116C22×C3×Dic3—62no—
117C22×C3×Dic3—61no—
118C22×C3×Dic3—61no—
119C22×C3×Dic3C2×D311yescharacteristic
120C22×C3×Dic3C2×D311yescharacteristic
121C22×C3×Dic3C2×D311yescharacteristic
122C22×C3×Dic3C2×D311yescharacteristic
123C2×C3×C4×D3—62no—
124C2×C3×C4×D3—62no—
125C2×C3×C4×D3—62no—
126C2×#625—34no—
127C2×#625—34no—
128C2×#625—64no—
129C2×#625—64no—
130C2×#625—64no—
131C2×#625—62no—
132C2×#625—62no—
133C2×#625—62no—
134C2×#625—62no—
135C2×D3×Dic3—22no—
136C2×D3×Dic3—22no—
137C2×D3×Dic3—22no—
138C3×#217—62no—
139C3×(C2×D3)⋊C4—62no—
140C3×(C2×D3)⋊C4—62no—
141C3×(C2×D3)⋊C4—62no—
142#3722—22no—
143#3722—62no—
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—62no—
146(C2×D3)⋊Dic3—62no—
147C22×C33C22×C411yescharacteristic
148C22×C33C2×D411yescharacteristic
149C22×C33C2×D411yescharacteristic
150C22×C33C2×D411yescharacteristic
151C22×C33C2×D411yescharacteristic
152C22×C33#4111yescharacteristic
153C22×C33#4111yescharacteristic
154C2×C3×C3⋊D3—22no—
155C2×C3×C3⋊D3—22no—
156C2×C3×C3⋊D3—22no—
157C2×C3×C3⋊D3—41no—
158C2×C3×C3⋊D3—41no—
159C2×C3×C3⋊D3—41no—
160C2×C3×C3⋊D3—41no—
161C2×C32×D3—22no—
162C2×C32×D3—22no—
163C2×C32×D3—22no—
164C2×C32×D3—22no—
165C2×C32×D3—22no—
166C2×C32×D3—22no—
167C2×C32×D3C22⋊C414yescomplemented
168C3⋊(C3⋊Dic3)—22no—
169C3×C3⋊Dic3—22no—
170C3×C3⋊Dic3—41no—
171C32×Dic3—22no—
172C32×Dic3—41no—
173C23×C3×C4—91no—
174C22×#67—91no—
175C22×#67—91no—
176C22×#67—91no—
177C22×#67—181no—
178C23×Dic3—31no—
179C22×C4×D3—31no—
180C2×C3×C22⋊C4—91no—
181C2×C3×C22⋊C4—91no—
182C2×#217—31no—
183C2×#217—91no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—91no—
188C2×(C2×D3)⋊C4—91no—
189C3⋊#95—91no—
190C3⋊#95—91no—
191C3⋊#95—91no—
192C3⋊#95—91no—
193C3⋊#95—91no—
194C3⋊#95—91no—
195C3⋊#95—181no—
196C3⋊#95—181no—
197C23×C32—21no—
198C23×C32—21no—
199C23×C32—21no—
200C23×C32—32no—
201C23×C32—32no—
202C23×C32—32no—
203C23×C32—41no—
204C23×C32—61no—
205C23×C32—61no—
206C23×C32—61no—
207C23×C32—61no—
208C23×C32C22×D311yescharacteristic
209C23×C32C22×D311yescharacteristic
210C23×C32C22×D311yescharacteristic
211C22×C3⋊D3—21no—
212C22×C3⋊D3—21no—
213C22×C3⋊D3—21no—
214C22×C3⋊D3—21no—
215C22×C3⋊D3—21no—
216C22×C3⋊D3—21no—
217C22×C3⋊D3C4×D312yescomplemented
218C22×C3×D3—21no—
219C22×C3×D3—21no—
220C22×C3×D3—21no—
221C22×C3×D3—21no—
222C22×C3×D3—21no—
223C22×C3×D3—21no—
224C22×C3×D3—21no—
225C22×C3×D3—21no—
226C22×C3×D3—22no—
227C22×C3×D3—22no—
228C22×C3×D3—22no—
229C22×C3×D3—32no—
230C22×C3×D3—32no—
231C22×C3×D3—41no—
232C22×C3×D3—41no—
233C22×C3×D3—41no—
234C22×C3×D3—41no—
235C22×C3×D3—62no—
236C22×C3×D3—62no—
237C22×C3×D3—62no—
238C22×C3×D3—61no—
239C22×C3×D3—61no—
240C22×C3×D3—61no—
241C22×C3×D3—61no—
242C22×C3×D3—61no—
243C22×C3×D3—61no—
244C22×C3×D3—61no—
245C22×C3×D3—61no—
246C22×C3×D3—61no—
247C22×C3×D3—61no—
248C22×C3×D3—61no—
249C22×C3×D3—61no—
250C22×C3×D3—121no—
251C22×C3×D3—121no—
252C22×C3×D3—121no—
253C22×C3×D3—121no—
254C22×C3×D3C4×D312yes—
255C22×C3×D3C4×D312yes—
256C22×C3×D3D1212yes—
257C22×C3×D3D1212yes—
258C22×C3×D3#6712yes—
259C22×C3×D3#6712yes—
260C2×C32×C4—32no—
261C2×C32×C4—61no—
262C2×C32×C4—61no—
263C2×C32×C4—61no—
264C2×C32×C4—61no—
265C2×C32×C4—61no—
266#638—68no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—32no—
273C2×C3⋊Dic3—32no—
274C2×C3⋊Dic3—32no—
275C2×C3⋊Dic3—62no—
276C2×C3⋊Dic3—62no—
277C2×C3⋊Dic3—62no—
278C2×C3⋊Dic3—61no—
279C2×C3⋊Dic3—61no—
280C2×C3⋊Dic3—62no—
281C2×C3⋊Dic3—62no—
282C2×C3⋊Dic3—61no—
283C2×C3⋊Dic3—61no—
284C2×C3⋊Dic3—61no—
285C2×C3⋊Dic3—61no—
286C2×C3⋊Dic3—122no—
287C2×C3⋊Dic3—121no—
288C2×C3⋊Dic3—121no—
289C2×C3⋊Dic3—121no—
290C2×C3⋊Dic3—121no—
291C2×C3⋊Dic3—122no—
292C2×C3⋊Dic3—122no—
293C2×C3⋊Dic3#6712yescomplemented
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—22no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—22no—
306C2×C3×Dic3—32no—
307C2×C3×Dic3—32no—
308C2×C3×Dic3—41no—
309C2×C3×Dic3—41no—
310C2×C3×Dic3—41no—
311C2×C3×Dic3—41no—
312C2×C3×Dic3—62no—
313C2×C3×Dic3—68no—
314C2×C3×Dic3—61no—
315C2×C3×Dic3—61no—
316C2×C3×Dic3—61no—
317C2×C3×Dic3—61no—
318C2×C3×Dic3—62no—
319C2×C3×Dic3—61no—
320C2×C3×Dic3—61no—
321C2×C3×Dic3—61no—
322C2×C3×Dic3—61no—
323C2×C3×Dic3—61no—
324C2×C3×Dic3—61no—
325C2×C3×Dic3—121no—
326C2×C3×Dic3—121no—
327C2×C3×Dic3—121no—
328C2×C3×Dic3—121no—
329C2×C3×Dic3#6712yescomplemented
330C2×C3×Dic3#6712yescomplemented
331C3×C4×D3—68no—
332#625—616no—
333#625—68no—
334#625—68no—
335D3×Dic3—28no—
336#386—271noSylow
337C2×C33C2×C22⋊C411yescharacteristic
338C2×C33C4×D411yescharacteristic
339C2×C33C4×D411yescharacteristic
340C2×C33#12011yescharacteristic
341C2×C33#12111yescharacteristic
342C2×C33#12111yescharacteristic
343C2×C33#12311yescharacteristic
344C3×C3⋊D3—42no—
345C32×D3—24no—
346C24×C3—31no—
347C24×C3—31no—
348C24×C3—61no—
349C24×C3—91no—
350C23×D3—31no—
351C23×D3—31no—
352C23×D3—61no—
353C23×D3D3211yescharacteristic
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—31no—
358C22×C3×C4—61no—
359C22×C3×C4—61no—
360C22×C3×C4—91no—
361C22×C3×C4—91no—
362C22×C3×C4—182no—
363C22×C3×C4—182no—
364C22×C3×C4—182no—
365C2×#67—94no—
366C2×#67—94no—
367C2×#67—94no—
368C2×#67—184no—
369C2×#67—182no—
370C2×#67—182no—
371C2×#67—182no—
372C2×#67—182no—
373C2×#67—184no—
374C2×#67—184no—
375C2×#67—182no—
376C2×#67—182no—
377C22×Dic3—31no—
378C22×Dic3—31no—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—61no—
382C22×Dic3—61no—
383C22×Dic3—62no—
384C22×Dic3—62no—
385C22×Dic3—62no—
386C22×Dic3—91no—
387C22×Dic3—91no—
388C22×Dic3—91no—
389C22×Dic3—181no—
390C22×Dic3—181no—
391C22×Dic3—181no—
392C22×Dic3—361no—
393C22×Dic3D3211yescharacteristic
394C22×Dic3D3211yescharacteristic
395C2×C4×D3—62no—
396C2×C4×D3—62no—
397C2×C4×D3—62no—
398C3×C22⋊C4—182no—
399C3×C22⋊C4—182no—
400#217—62no—
401#217—182no—
402(C2×D3)⋊C4—62no—
403(C2×D3)⋊C4—62no—
404(C2×D3)⋊C4—62no—
405(C2×D3)⋊C4—182no—
406(C2×D3)⋊C4—182no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32—34no—
429C22×C32—41no—
430C22×C32—41no—
431C22×C32—41no—
432C22×C32—41no—
433C22×C32—41no—
434C22×C32—41no—
435C22×C32—41no—
436C22×C32—62no—
437C22×C32—62no—
438C22×C32—62no—
439C22×C32—62no—
440C22×C32—62no—
441C22×C32—62no—
442C22×C32C2×C4×D311yescharacteristic
443C22×C32C2×C4×D311yescharacteristic
444C22×C32C2×C4×D311yescharacteristic
445C22×C32C2×D1211yescharacteristic
446C22×C32C2×D1211yescharacteristic
447C22×C32#23511yescharacteristic
448C22×C32#23511yescharacteristic
449C22×C32#23511yescharacteristic
450C22×C32D3×D411yescharacteristic
451C22×C32D3×D411yescharacteristic
452C22×C32D3×D411yescharacteristic
453C22×C32D3×D411yescharacteristic
454C22×C32D3×D411yescharacteristic
455C22×C32#23711yescharacteristic
456C22×C32#23711yescharacteristic
457C22×C32#23711yescharacteristic
458C22×C32C2×#6711yescharacteristic
459C22×C32C2×#6711yescharacteristic
460C22×C32C2×#6711yescharacteristic
461C22×C32C2×#6711yescharacteristic
462C22×C32C2×#6711yescharacteristic
463C2×C3⋊D3—22no—
464C2×C3⋊D3—22no—
465C2×C3⋊D3—22no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3×D3—22no—
471C2×C3×D3—22no—
472C2×C3×D3—22no—
473C2×C3×D3—22no—
474C2×C3×D3—22no—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—22no—
482C2×C3×D3—24no—
483C2×C3×D3—42no—
484C2×C3×D3—42no—
485C2×C3×D3—42no—
486C2×C3×D3—42no—
487C2×C3×D3—42no—
488C2×C3×D3—42no—
489C2×C3×D3—64no—
490C2×C3×D3—62no—
491C2×C3×D3—62no—
492C2×C3×D3—62no—
493C2×C3×D3—62no—
494C2×C3×D3—62no—
495C2×C3×D3—62no—
496C2×C3×D3—122no—
497C2×C3×D3—122no—
498C2×C3×D3—122no—
499C2×C3×D3—122no—
500C2×C3×D3—122no—
501C2×C3×D3—122no—
502C2×C3×D3—121no—
503C2×C3×D3—121no—
504C2×C3×D3—121no—
505C2×C3×D3—121no—
506C2×C3×D3—121no—
507C2×C3×D3—121no—
508C2×C3×D3—121no—
509C2×C3×D3—121no—
510C2×C3×D3(C2×D3)⋊C414yescomplemented
511C2×C3×D3(C2×D3)⋊C414yescomplemented
512C32×C4—62no—
513C32×C4—121no—
514C3⋊Dic3—22no—
515C3⋊Dic3—41no—
516C3⋊Dic3—62no—
517C3⋊Dic3—64no—
518C3⋊Dic3—62no—
519C3⋊Dic3—62no—
520C3⋊Dic3—122no—
521C3⋊Dic3—122no—
522C3⋊Dic3—124no—
523C3×Dic3—22no—
524C3×Dic3—22no—
525C3×Dic3—42no—
526C3×Dic3—42no—
527C3×Dic3—41no—
528C3×Dic3—41no—
529C3×Dic3—62no—
530C3×Dic3—62no—
531C3×Dic3—122no—
532C3×Dic3—122no—
533C3×Dic3—121no—
534C3×Dic3—121no—
535C22×D4—271no—
536C23×C4—91no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—271no—
540#95—271no—
541#95—271no—
542C33#38611yescharacteristic, complemented, Sylow
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—32no—
547C23×C3—32no—
548C23×C3—32no—
549C23×C3—32no—
550C23×C3—32no—
551C23×C3—32no—
552C23×C3—41no—
553C23×C3—62no—
554C23×C3—62no—
555C23×C3—62no—
556C23×C3—61no—
557C23×C3—61no—
558C23×C3—61no—
559C23×C3—61no—
560C23×C3—61no—
561C23×C3—61no—
562C23×C3—61no—
563C23×C3—61no—
564C23×C3—92no—
565C23×C3—121no—
566C23×C3—121no—
567C23×C3—121no—
568C23×C3—121no—
569C23×C3—181no—
570C23×C3—181no—
571C23×C3—181no—
572C23×C3—181no—
573C23×C3—181no—
574C23×C3—181no—
575C23×C3C2×D3211yescharacteristic
576C23×C3C2×D3211yescharacteristic
577C23×C3C2×D3211yescharacteristic
578C22×D3—21no—
579C22×D3—21no—
580C22×D3—21no—
581C22×D3—21no—
582C22×D3—32no—
583C22×D3—32no—
584C22×D3—62no—
585C22×D3—62no—
586C22×D3—62no—
587C22×D3—61no—
588C22×D3—61no—
589C22×D3—61no—
590C22×D3—61no—
591C22×D3—61no—
592C22×D3—61no—
593C22×D3—61no—
594C22×D3—61no—
595C22×D3—61no—
596C22×D3—61no—
597C22×D3—61no—
598C22×D3—61no—
599C22×D3—121no—
600C22×D3—121no—
601C22×D3—121no—
602C22×D3—121no—
603C22×D3#62412yes—
604C22×D3#62612yes—
605C22×D3#62612yes—
606C2×C3×C4—32no—
607C2×C3×C4—32no—
608C2×C3×C4—62no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
612C2×C3×C4—61no—
613C2×C3×C4—62no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—61no—
620C2×C3×C4—92no—
621C2×C3×C4—121no—
622C2×C3×C4—121no—
623C2×C3×C4—121no—
624C2×C3×C4—121no—
625C2×C3×C4—188no—
626C2×C3×C4—181no—
627C2×C3×C4—181no—
628C2×C3×C4—181no—
629C2×C3×C4—181no—
630C2×C3×C4—181no—
631#67—188no—
632#67—188no—
633#67—1816no—
634#67—188no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3—21no—
639C2×Dic3—21no—
640C2×Dic3—32no—
641C2×Dic3—32no—
642C2×Dic3—62no—
643C2×Dic3—68no—
644C2×Dic3—61no—
645C2×Dic3—61no—
646C2×Dic3—61no—
647C2×Dic3—61no—
648C2×Dic3—62no—
649C2×Dic3—61no—
650C2×Dic3—61no—
651C2×Dic3—61no—
652C2×Dic3—61no—
653C2×Dic3—61no—
654C2×Dic3—61no—
655C2×Dic3—92no—
656C2×Dic3—92no—
657C2×Dic3—92no—
658C2×Dic3—121no—
659C2×Dic3—121no—
660C2×Dic3—121no—
661C2×Dic3—121no—
662C2×Dic3—182no—
663C2×Dic3—182no—
664C2×Dic3—182no—
665C2×Dic3—182no—
666C2×Dic3—182no—
667C2×Dic3—181no—
668C2×Dic3—181no—
669C2×Dic3—181no—
670C2×Dic3—181no—
671C2×Dic3—181no—
672C2×Dic3—181no—
673C2×Dic3—362no—
674C2×Dic3—361no—
675C2×Dic3—361no—
676C2×Dic3—361no—
677C2×Dic3—361no—
678C2×Dic3—362no—
679C2×Dic3—362no—
680C2×Dic3#62512yescomplemented
681C4×D3—68no—
682C2×C32—21no—
683C2×C32—21no—
684C2×C32—21no—
685C2×C32—21no—
686C2×C32—21no—
687C2×C32—21no—
688C2×C32—21no—
689C2×C32—21no—
690C2×C32—21no—
691C2×C32—21no—
692C2×C32—21no—
693C2×C32—21no—
694C2×C32—21no—
695C2×C32—21no—
696C2×C32—21no—
697C2×C32—21no—
698C2×C32—21no—
699C2×C32—21no—
700C2×C32—21no—
701C2×C32—21no—
702C2×C32—21no—
703C2×C32—41no—
704C2×C32—41no—
705C2×C32—41no—
706C2×C32—41no—
707C2×C32—41no—
708C2×C32—41no—
709C2×C32—41no—
710C2×C32—64no—
711C2×C32D3×C22⋊C411yescharacteristic
712C2×C32#67⋊C411yescharacteristic
713C2×C32#67⋊C411yescharacteristic
714C2×C32#67⋊C411yescharacteristic
715C2×C32#88211yescharacteristic
716C2×C32#88311yescharacteristic
717C2×C32#88411yescharacteristic
718C2×C32#88611yescharacteristic
719C2×C32C2×(C2×D3)⋊C411yescharacteristic
720C2×C32C2×(C2×D3)⋊C411yescharacteristic
721C2×C32C4×#6711yescharacteristic
722C2×C32C4×#6711yescharacteristic
723C2×C32C4×#6711yescharacteristic
724C2×C32#92911yescharacteristic
725C2×C32#93011yescharacteristic
726C2×C32#93011yescharacteristic
727C2×C32#93711yescharacteristic
728C2×C32#93811yescharacteristic
729C2×C32#93911yescharacteristic
730C2×C32#93911yescharacteristic
731C2×C32#95311yescharacteristic
732C3⋊D3—42no—
733C3×D3—24no—
734C3×D3—24no—
735C3×D3—44no—
736C3×D3—124no—
737C3×D3—122no—
738C3×D3—122no—
739C24—31no—
740C24—91no—
741C2×D4—274no—
742C2×D4—542no—
743C2×D4—542no—
744C22×C4—31no—
745C22×C4—31no—
746C22×C4—91no—
747C22×C4—91no—
748C22×C4—182no—
749C22×C4—182no—
750C22×C4—182no—
751C22×C4—271no—
752C22⋊C4—182no—
753C22⋊C4—182no—
754C22⋊C4—542no—
755C22×C3—21no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—21no—
765C22×C3—21no—
766C22×C3—21no—
767C22×C3—21no—
768C22×C3—21no—
769C22×C3—21no—
770C22×C3—21no—
771C22×C3—21no—
772C22×C3—21no—
773C22×C3—21no—
774C22×C3—21no—
775C22×C3—21no—
776C22×C3—34no—
777C22×C3—34no—
778C22×C3—41no—
779C22×C3—41no—
780C22×C3—41no—
781C22×C3—41no—
782C22×C3—41no—
783C22×C3—41no—
784C22×C3—41no—
785C22×C3—64no—
786C22×C3—62no—
787C22×C3—62no—
788C22×C3—62no—
789C22×C3—62no—
790C22×C3—62no—
791C22×C3—62no—
792C22×C3—62no—
793C22×C3—62no—
794C22×C3—62no—
795C22×C3—62no—
796C22×C3—62no—
797C22×C3—62no—
798C22×C3—122no—
799C22×C3—122no—
800C22×C3—122no—
801C22×C3—122no—
802C22×C3—122no—
803C22×C3—122no—
804C22×C3—182no—
805C22×C3—182no—
806C22×C3—182no—
807C22×C3—361no—
808C22×C3—361no—
809C22×C3—361no—
810C22×C3—361no—
811C22×C3#379511yescharacteristic
812C22×C3#379511yescharacteristic
813C22×C3#379811yescharacteristic
814C22×C3C4×D3211yescharacteristic
815C22×C3C4×D3211yescharacteristic
816C22×C3D3×D1211yescharacteristic
817C22×C3D3×D1211yescharacteristic
818C22×C3#380211yescharacteristic
819C22×C3#380411yescharacteristic
820C22×C3#380411yescharacteristic
821C22×C3#380511yescharacteristic
822C22×C3C2×#62411yescharacteristic
823C22×C3C2×#62511yescharacteristic
824C22×C3C2×#62611yescharacteristic
825C22×C3C2×#62611yescharacteristic
826C22×C3D3×#6711yescharacteristic
827C22×C3D3×#6711yescharacteristic
828C22×C3D3×#6711yescharacteristic
829C22×C3D3×#6711yescharacteristic
830C22×C3D3×#6711yescharacteristic
831C22×C3D3×#6711yescharacteristic
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—22no—
837C2×D3—22no—
838C2×D3—64no—
839C2×D3—62no—
840C2×D3—62no—
841C2×D3—62no—
842C2×D3—62no—
843C2×D3—62no—
844C2×D3—62no—
845C2×D3—122no—
846C2×D3—122no—
847C2×D3—122no—
848C2×D3—122no—
849C2×D3—122no—
850C2×D3—122no—
851C2×D3—121no—
852C2×D3—121no—
853C2×D3—121no—
854C2×D3—121no—
855C2×D3—121no—
856C2×D3—121no—
857C2×D3—121no—
858C2×D3—121no—
859C2×D3#372214yescomplemented
860C3×C4—62no—
861C3×C4—62no—
862C3×C4—122no—
863C3×C4—122no—
864C3×C4—121no—
865C3×C4—121no—
866C3×C4—182no—
867C3×C4—361no—
868Dic3—22no—
869Dic3—41no—
870Dic3—62no—
871Dic3—62no—
872Dic3—122no—
873Dic3—122no—
874Dic3—121no—
875Dic3—121no—
876Dic3—184no—
877Dic3—182no—
878Dic3—182no—
879Dic3—182no—
880Dic3—362no—
881Dic3—362no—
882Dic3—364no—
883C32—21no—
884C32—21no—
885C32—21no—
886C32—41no—
887C32#495611yescharacteristic, complemented
888C32#495811yescharacteristic, complemented
889C32#521311yescharacteristic, complemented
890C23—32no—
891C23—32no—
892C23—32no—
893C23—61no—
894C23—61no—
895C23—61no—
896C23—61no—
897C23—92no—
898C23—181no—
899C23—181no—
900C23—181no—
901C23—181no—
902C23—181no—
903C23—181no—
904C23D3311yescharacteristic
905D4—548no—
906C2×C4—32no—
907C2×C4—61no—
908C2×C4—61no—
909C2×C4—61no—
910C2×C4—61no—
911C2×C4—61no—
912C2×C4—92no—
913C2×C4—188no—
914C2×C4—181no—
915C2×C4—181no—
916C2×C4—181no—
917C2×C4—181no—
918C2×C4—181no—
919C2×C4—272no—
920C2×C4—541no—
921C2×C4—541no—
922C2×C3—21no—
923C2×C3—21no—
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—21no—
934C2×C3—21no—
935C2×C3—21no—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—21no—
939C2×C3—21no—
940C2×C3—21no—
941C2×C3—21no—
942C2×C3—21no—
943C2×C3—41no—
944C2×C3—41no—
945C2×C3—41no—
946C2×C3—41no—
947C2×C3—41no—
948C2×C3—41no—
949C2×C3—41no—
950C2×C3—64no—
951C2×C3—64no—
952C2×C3—124no—
953C2×C3—362no—
954C2×C3#6387911yescharacteristic
955C2×C3#6387911yescharacteristic
956C2×C3#6388511yescharacteristic
957C2×C3#6389111yescharacteristic
958C2×C3C4×#62511yescharacteristic
959C2×C3#6390211yescharacteristic
960C2×C3#6390511yescharacteristic
961C2×C3#6390611yescharacteristic
962C2×C3#6390811yescharacteristic
963C2×C3D3×(C2×D3)⋊C411yescharacteristic
964C2×C3D3×(C2×D3)⋊C411yescharacteristic
965C2×C3#6392211yescharacteristic
966C2×C3#6395211yescharacteristic
967C2×C3#6395211yescharacteristic
968C2×C3C2×#372211yescharacteristic
969C2×C3#6396611yescharacteristic
970C2×C3#6397011yescharacteristic
971C2×C3#6397611yescharacteristic
972C2×C3#6397711yescharacteristic
973C2×C3#6397811yescharacteristic
974C2×C3#6397811yescharacteristic
975D3—24no—
976D3—124no—
977D3—122no—
978D3—122no—
979C22—34no—
980C22—62no—
981C22—62no—
982C22—62no—
983C22—62no—
984C22—62no—
985C22—62no—
986C22—182no—
987C22—182no—
988C22—182no—
989C22—361no—
990C22—361no—
991C22—361no—
992C22—361no—
993C22D3×#62411yescharacteristic
994C22D3×#62511yescharacteristic
995C22D3×#62611yescharacteristic
996C22D3×#62611yescharacteristic
997C22#8895311yescharacteristic
998C22#8896011yescharacteristic
999C22#8896111yescharacteristic
1000C4—62no—
1001C4—121no—
1002C4—182no—
1003C4—361no—
1004C4—542no—
1005C3—21no—
1006C3—21no—
1007C3—21no—
1008C3—41no—
1009C3#1059136311yescharacteristic, complemented
1010C3#1059138111yescharacteristic, complemented
1011C3#1059171111yescharacteristic, complemented
1012C2—64no—
1013C2—362no—
1014C2D3×#372211yescharacteristic
1015C2#1172293011yescharacteristic
1016C2#1172293611yescharacteristic
1017C2#1172294711yescharacteristic
1018C2#1172295611yescharacteristic
1019C2#1172296011yescharacteristic
1020C2#1172298811yescharacteristic
subgroupG/H
center, Frattini, hypercenterC23D33
commutatorC22×C33C22×C4
Fitting, socle, cosocleC23×C33C23
prime radicalC22×#6290C2
hypocenterC33#386
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C22×C3×D3×Dic3C2semidirect
3. C2×#88814C2semidirect
4. C2×C3×#3722C2semidirect
5. C2×C3×(C2×D3)⋊Dic3C2semidirect
6. #11722061C2semidirect
7. #11722061C2semidirect
20. C2×#6290C4semidirect
33. C22×D3×Dic3D3semidirect
39. C2×#3722D3semidirect
42. C2×(C2×D3)⋊Dic3D3semidirect
58. C22×C3×C3⋊D3C2×C4semidirect
68. C2×C3⋊(C3⋊Dic3)C2×C4semidirect
74. C2×C3×C3⋊Dic3D4semidirect
80. C2×C32×Dic3D4semidirect
167. C2×C32×D3C22⋊C4semidirect
217. C22×C3⋊D3C4×D3semidirect
293. C2×C3⋊Dic3#67semidirect
329. C2×C3×Dic3#67semidirect
330. C2×C3×Dic3#67semidirect
510. C2×C3×D3(C2×D3)⋊C4semidirect
511. C2×C3×D3(C2×D3)⋊C4semidirect
542. C33#386semidirect
680. C2×Dic3#625semidirect
859. C2×D3#3722semidirect
887. C32#4956semidirect
888. C32#4958semidirect
889. C32#5213semidirect
1009. C3#10591363semidirect
1010. C3#10591381semidirect
1011. C3#10591711semidirect

Maximal subgroups

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

subgroupindex
C22×#62902
C22×C3×D3×Dic32
C2×#888142
C2×C3×#37222
C2×C3×(C2×D3)⋊Dic32
#117220612
#105917113
#105913813
#105913633