Finite Group Databasebeta

← #13156853

Subgroups — #13156853

Order 1728.

1522 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6290C211yesmaximal, characteristic
2C2×#88814C211yesmaximal, characteristic, complemented
3C2×#88806C211yesmaximal, characteristic, complemented
4C2×Dic3×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C2×C3×#3722C211yesmaximal, characteristic, complemented
6C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
7C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8#10591704—31nomaximal
9#10591386—31nomaximal
10#10591385—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
21#88814—22no—
22#88806—22no—
23Dic3×C3⋊Dic3—22no—
24C3×#3722—22no—
25C3×(C2×D3)⋊Dic3—22no—
26C3×(C2×D3)⋊Dic3—22no—
27C22×#638—31no—
28C22×#625—31no—
29C22×#625—31no—
30C22×#625—61no—
31C2×#3750—31no—
32C2×C4×C3⋊Dic3—31no—
33C2×C3×#217—31no—
34C2×C3×#217—31no—
35C2×C3×(C2×D3)⋊C4—31no—
36C2×C3×(C2×D3)⋊C4—31no—
37C2×C3×(C2×D3)⋊C4—31no—
38C2×C3×(C2×D3)⋊C4—31no—
39C2×#3724—31no—
40C2×#3724—31no—
41C2×#3724—61no—
42C2×#3722—31no—
43C2×#3722D311yescharacteristic, complemented
44C2×(C2×D3)⋊Dic3—31no—
45C2×(C2×D3)⋊Dic3—31no—
46C2×(C2×D3)⋊Dic3D311yescharacteristic, complemented
47C2×(C2×D3)⋊Dic3D311yescharacteristic, complemented
48C2×Dic32—31no—
49C2×Dic32—31no—
50C2×Dic32—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×C412yes—
59C22×C32×D3—21no—
60C22×C32×D3—21no—
61C22×C32×D3—21no—
62C22×C32×D3—21no—
63C22×C32×D3—21no—
64C22×C32×D3—21no—
65C22×C32×D3C2×C412yes—
66C2×C3⋊(C3⋊Dic3)C2×C412yes—
67C2×C3⋊(C3⋊Dic3)D412yes—
68C2×C3⋊(C3⋊Dic3)D412yes—
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—
82#4957—91no—
83#4957—91no—
84#4957—91no—
85C24×C32—31no—
86C23×C3⋊D3C2×D311yescharacteristic
87C23×C3×D3—21no—
88C23×C3×D3—31no—
89C23×C3×D3—31no—
90C23×C3×D3—61no—
91C23×C3×D3C2×D311yescharacteristic
92C23×C3×D3C2×D311yescharacteristic
93C22×C32×C4—31no—
94C22×C32×C4—31no—
95C2×#638—34no—
96C2×#638—62no—
97C2×#638—62no—
98C22×C3⋊Dic3—31no—
99C22×C3⋊Dic3—31no—
100C22×C3⋊Dic3—31no—
101C22×C3⋊Dic3—61no—
102C22×C3⋊Dic3—61no—
103C22×C3⋊Dic3—61no—
104C22×C3⋊Dic3—121no—
105C22×C3⋊Dic3C2×D311yescharacteristic
106C22×C3⋊Dic3C2×D311yescharacteristic
107C22×C3×Dic3—21no—
108C22×C3×Dic3—21no—
109C22×C3×Dic3—31no—
110C22×C3×Dic3—31no—
111C22×C3×Dic3—31no—
112C22×C3×Dic3—31no—
113C22×C3×Dic3—61no—
114C22×C3×Dic3—61no—
115C22×C3×Dic3C2×D311yescharacteristic
116C22×C3×Dic3C2×D311yescharacteristic
117C22×C3×Dic3C2×D311yescharacteristic
118C22×C3×Dic3C2×D311yescharacteristic
119C2×#625—34no—
120C2×#625—34no—
121C2×#625—62no—
122C2×#625—62no—
123C2×#625—62no—
124C2×#625—62no—
125C2×#625—64no—
126C2×#625—64no—
127C2×#625—64no—
128#3750—62no—
129C4×C3⋊Dic3—62no—
130C3×#217—62no—
131C3×#217—62no—
132C3×(C2×D3)⋊C4—62no—
133C3×(C2×D3)⋊C4—62no—
134C3×(C2×D3)⋊C4—62no—
135C3×(C2×D3)⋊C4—62no—
136#3724—62no—
137#3724—62no—
138#3724—64no—
139#3722—22no—
140#3722—62no—
141(C2×D3)⋊Dic3—22no—
142(C2×D3)⋊Dic3—22no—
143(C2×D3)⋊Dic3—62no—
144(C2×D3)⋊Dic3—62no—
145Dic32—62no—
146Dic32—62no—
147Dic32—64no—
148C22×C33C22×C411yescharacteristic
149C22×C33C2×D411yescharacteristic
150C22×C33C2×D411yescharacteristic
151C22×C33C2×D411yescharacteristic
152C22×C33C2×D411yescharacteristic
153C22×C33#4111yescharacteristic
154C22×C33#4111yescharacteristic
155C2×C3×C3⋊D3—22no—
156C2×C3×C3⋊D3—22no—
157C2×C3×C3⋊D3—22no—
158C2×C3×C3⋊D3—41no—
159C2×C3×C3⋊D3—41no—
160C2×C3×C3⋊D3—41no—
161C2×C3×C3⋊D3—41no—
162C2×C32×D3—22no—
163C2×C32×D3—22no—
164C2×C32×D3—22no—
165C2×C32×D3—41no—
166C2×C32×D3—41no—
167C2×C32×D3—41no—
168C2×C32×D3—41no—
169C3⋊(C3⋊Dic3)C22⋊C414yescomplemented
170C3×C3⋊Dic3—22no—
171C3×C3⋊Dic3—41no—
172C32×Dic3—22no—
173C32×Dic3—41no—
174C22×#67—91no—
175C22×#67—91no—
176C22×#67—91no—
177C22×#67—181no—
178C2×C3×C22⋊C4—91no—
179C2×C3×C22⋊C4—91no—
180C2×C3×C22⋊C4—91no—
181C2×#217—31no—
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—31no—
188C2×(C2×D3)⋊C4—91no—
189C2×(C2×D3)⋊C4—91no—
190C2×Dic3⋊C4—91no—
191C2×Dic3⋊C4—91no—
192C2×Dic3⋊C4—91no—
193C2×Dic3⋊C4—181no—
194C2×C4×Dic3—91no—
195C2×C4×Dic3—91no—
196C2×C4×Dic3—91no—
197C2×C4×Dic3—181no—
198C23×C32—21no—
199C23×C32—21no—
200C23×C32—21no—
201C23×C32—32no—
202C23×C32—41no—
203C23×C32—61no—
204C23×C32—61no—
205C23×C32—61no—
206C23×C32—61no—
207C23×C32—61no—
208C23×C32—61no—
209C23×C32C22×D311yescharacteristic
210C23×C32C22×D311yescharacteristic
211C23×C32C22×D311yescharacteristic
212C22×C3⋊D3—21no—
213C22×C3⋊D3—21no—
214C22×C3⋊D3—21no—
215C22×C3⋊D3—21no—
216C22×C3⋊D3—21no—
217C22×C3⋊D3—21no—
218C22×C3⋊D3C4×D312yes—
219C22×C3×D3—22no—
220C22×C3×D3—22no—
221C22×C3×D3—21no—
222C22×C3×D3—21no—
223C22×C3×D3—21no—
224C22×C3×D3—21no—
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—21no—
228C22×C3×D3—21no—
229C22×C3×D3—21no—
230C22×C3×D3—21no—
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3—22no—
234C22×C3×D3—32no—
235C22×C3×D3—32no—
236C22×C3×D3—41no—
237C22×C3×D3—41no—
238C22×C3×D3—41no—
239C22×C3×D3—41no—
240C22×C3×D3—62no—
241C22×C3×D3—62no—
242C22×C3×D3—62no—
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—61no—
251C22×C3×D3—61no—
252C22×C3×D3—61no—
253C22×C3×D3—61no—
254C22×C3×D3—61no—
255C22×C3×D3—121no—
256C22×C3×D3—121no—
257C22×C3×D3—121no—
258C22×C3×D3—121no—
259C22×C3×D3C4×D312yes—
260C22×C3×D3C4×D312yes—
261C2×C32×C4—32no—
262C2×C32×C4—61no—
263C2×C32×C4—61no—
264C2×C32×C4—61no—
265C2×C32×C4—61no—
266C2×C32×C4—61no—
267#638—68no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—32no—
274C2×C3⋊Dic3—32no—
275C2×C3⋊Dic3—32no—
276C2×C3⋊Dic3—32no—
277C2×C3⋊Dic3—32no—
278C2×C3⋊Dic3—32no—
279C2×C3⋊Dic3—32no—
280C2×C3⋊Dic3—32no—
281C2×C3⋊Dic3—32no—
282C2×C3⋊Dic3—62no—
283C2×C3⋊Dic3—62no—
284C2×C3⋊Dic3—62no—
285C2×C3⋊Dic3—62no—
286C2×C3⋊Dic3—62no—
287C2×C3⋊Dic3—62no—
288C2×C3⋊Dic3—62no—
289C2×C3⋊Dic3—62no—
290C2×C3⋊Dic3—62no—
291C2×C3⋊Dic3—122no—
292C2×C3⋊Dic3—122no—
293C2×C3⋊Dic3—122no—
294C2×C3⋊Dic3#6712yescomplemented
295C2×C3×Dic3—22no—
296C2×C3×Dic3—22no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—22no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—32no—
310C2×C3×Dic3—32no—
311C2×C3×Dic3—41no—
312C2×C3×Dic3—41no—
313C2×C3×Dic3—62no—
314C2×C3×Dic3—62no—
315C2×C3×Dic3—62no—
316C2×C3×Dic3—61no—
317C2×C3×Dic3—61no—
318C2×C3×Dic3—61no—
319C2×C3×Dic3—61no—
320C2×C3×Dic3—62no—
321C2×C3×Dic3—61no—
322C2×C3×Dic3—61no—
323C2×C3×Dic3—61no—
324C2×C3×Dic3—61no—
325C2×C3×Dic3—61no—
326C2×C3×Dic3—61no—
327C2×C3×Dic3—121no—
328C2×C3×Dic3—121no—
329C2×C3×Dic3#6712yescomplemented
330C2×C3×Dic3#6712yescomplemented
331#625—68no—
332#625—68no—
333#625—616no—
334#390—271noSylow
335C2×C33C2×C22⋊C411yescharacteristic
336C2×C33C4×D411yescharacteristic
337C2×C33C4×D411yescharacteristic
338C2×C33#12111yescharacteristic
339C2×C33#12111yescharacteristic
340C2×C33#12411yescharacteristic
341C2×C33#12711yescharacteristic
342C3×C3⋊D3—42no—
343C32×D3—42no—
344C24×C3—31no—
345C24×C3—31no—
346C24×C3—61no—
347C24×C3—91no—
348C23×D3—31no—
349C23×D3—31no—
350C23×D3—61no—
351C23×D3D3211yescharacteristic
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—61no—
357C22×C3×C4—61no—
358C22×C3×C4—91no—
359C22×C3×C4—91no—
360C2×#67—94no—
361C2×#67—94no—
362C2×#67—94no—
363C2×#67—184no—
364C2×#67—182no—
365C2×#67—182no—
366C2×#67—182no—
367C2×#67—182no—
368C2×#67—182no—
369C2×#67—182no—
370C2×#67—184no—
371C2×#67—184no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—31no—
375C22×Dic3—31no—
376C22×Dic3—61no—
377C22×Dic3—61no—
378C22×Dic3—91no—
379C22×Dic3—91no—
380C22×Dic3—91no—
381C22×Dic3—181no—
382C22×Dic3—181no—
383C22×Dic3—181no—
384C22×Dic3—361no—
385C22×Dic3D3211yescharacteristic
386C22×Dic3D3211yescharacteristic
387C3×C22⋊C4—182no—
388C3×C22⋊C4—182no—
389C3×C22⋊C4—182no—
390#217—62no—
391#217—62no—
392#217—182no—
393(C2×D3)⋊C4—62no—
394(C2×D3)⋊C4—62no—
395(C2×D3)⋊C4—62no—
396(C2×D3)⋊C4—62no—
397(C2×D3)⋊C4—182no—
398(C2×D3)⋊C4—182no—
399Dic3⋊C4—182no—
400Dic3⋊C4—182no—
401Dic3⋊C4—182no—
402Dic3⋊C4—184no—
403C4×Dic3—182no—
404C4×Dic3—182no—
405C4×Dic3—182no—
406C4×Dic3—184no—
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—41no—
429C22×C32—41no—
430C22×C32—41no—
431C22×C32—41no—
432C22×C32—41no—
433C22×C32—41no—
434C22×C32—41no—
435C22×C32—62no—
436C22×C32—62no—
437C22×C32—62no—
438C22×C32—121no—
439C22×C32—121no—
440C22×C32—121no—
441C22×C32—121no—
442C22×C32C2×C4×D311yescharacteristic
443C22×C32C2×C4×D311yescharacteristic
444C22×C32C2×C4×D311yescharacteristic
445C22×C32#23511yescharacteristic
446C22×C32#23511yescharacteristic
447C22×C32#23511yescharacteristic
448C22×C32D3×D411yescharacteristic
449C22×C32D3×D411yescharacteristic
450C22×C32D3×D411yescharacteristic
451C22×C32D3×D411yescharacteristic
452C22×C32D3×D411yescharacteristic
453C22×C32D3×D411yescharacteristic
454C22×C32D3×D411yescharacteristic
455C22×C32D3×D411yescharacteristic
456C22×C32D3×D411yescharacteristic
457C22×C32#23711yescharacteristic
458C22×C32#23711yescharacteristic
459C22×C32#23711yescharacteristic
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—24no—
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—42no—
478C2×C3×D3—42no—
479C2×C3×D3—42no—
480C2×C3×D3—42no—
481C2×C3×D3—42no—
482C2×C3×D3—42no—
483C2×C3×D3—41no—
484C2×C3×D3—41no—
485C2×C3×D3—41no—
486C2×C3×D3—41no—
487C2×C3×D3—41no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C2×C3×D3—41no—
491C2×C3×D3—64no—
492C2×C3×D3—62no—
493C2×C3×D3—62no—
494C2×C3×D3—62no—
495C2×C3×D3—62no—
496C2×C3×D3—62no—
497C2×C3×D3—62no—
498C2×C3×D3—122no—
499C2×C3×D3—122no—
500C2×C3×D3—122no—
501C2×C3×D3—122no—
502C2×C3×D3—122no—
503C2×C3×D3—122no—
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—121no—
511C2×C3×D3—121no—
512C32×C4—62no—
513C32×C4—121no—
514C3⋊Dic3—22no—
515C3⋊Dic3—34no—
516C3⋊Dic3—34no—
517C3⋊Dic3—34no—
518C3⋊Dic3—41no—
519C3⋊Dic3—64no—
520C3⋊Dic3—64no—
521C3⋊Dic3—64no—
522C3⋊Dic3—124no—
523C3×Dic3—24no—
524C3×Dic3—22no—
525C3×Dic3—22no—
526C3×Dic3—42no—
527C3×Dic3—41no—
528C3×Dic3—41no—
529C3×Dic3—64no—
530C3×Dic3—62no—
531C3×Dic3—62no—
532C3×Dic3—122no—
533C3×Dic3—121no—
534C3×Dic3—121no—
535C22×D4—271no—
536C2×C4⋊C4—271no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—91no—
540C2×C22⋊C4—271no—
541C2×C42—271no—
542C33#39011yescharacteristic, complemented, Sylow
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—32no—
547C23×C3—32no—
548C23×C3—41no—
549C23×C3—62no—
550C23×C3—62no—
551C23×C3—62no—
552C23×C3—61no—
553C23×C3—61no—
554C23×C3—61no—
555C23×C3—61no—
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—21no—
583C22×D3—21no—
584C22×D3—32no—
585C22×D3—32no—
586C22×D3—62no—
587C22×D3—62no—
588C22×D3—62no—
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—61no—
600C22×D3—61no—
601C22×D3—121no—
602C22×D3—121no—
603C22×D3—121no—
604C22×D3—121no—
605C22×D3#62412yes—
606C2×C3×C4—32no—
607C2×C3×C4—32no—
608C2×C3×C4—62no—
609C2×C3×C4—62no—
610C2×C3×C4—62no—
611C2×C3×C4—61no—
612C2×C3×C4—61no—
613C2×C3×C4—61no—
614C2×C3×C4—61no—
615C2×C3×C4—62no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—61no—
620C2×C3×C4—61no—
621C2×C3×C4—61no—
622C2×C3×C4—92no—
623C2×C3×C4—121no—
624C2×C3×C4—121no—
625C2×C3×C4—181no—
626C2×C3×C4—181no—
627C2×C3×C4—181no—
628C2×C3×C4—181no—
629C2×C3×C4—181no—
630#67—188no—
631#67—188no—
632#67—188no—
633#67—1816no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3—21no—
639C2×Dic3—32no—
640C2×Dic3—32no—
641C2×Dic3—62no—
642C2×Dic3—62no—
643C2×Dic3—62no—
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—92no—
659C2×Dic3—92no—
660C2×Dic3—92no—
661C2×Dic3—92no—
662C2×Dic3—92no—
663C2×Dic3—92no—
664C2×Dic3—121no—
665C2×Dic3—121no—
666C2×Dic3—182no—
667C2×Dic3—182no—
668C2×Dic3—182no—
669C2×Dic3—182no—
670C2×Dic3—182no—
671C2×Dic3—182no—
672C2×Dic3—182no—
673C2×Dic3—182no—
674C2×Dic3—182no—
675C2×Dic3—362no—
676C2×Dic3—362no—
677C2×Dic3—362no—
678C2×Dic3#62512yescomplemented
679C2×C32—21no—
680C2×C32—21no—
681C2×C32—21no—
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—41no—
701C2×C32—41no—
702C2×C32—41no—
703C2×C32—41no—
704C2×C32—41no—
705C2×C32—41no—
706C2×C32—41no—
707C2×C32—122no—
708C2×C32D3×C22⋊C411yescharacteristic
709C2×C32D3×C22⋊C411yescharacteristic
710C2×C32D3×C22⋊C411yescharacteristic
711C2×C32#67⋊C411yescharacteristic
712C2×C32#67⋊C411yescharacteristic
713C2×C32#67⋊C411yescharacteristic
714C2×C32#88411yescharacteristic
715C2×C32#88411yescharacteristic
716C2×C32#88411yescharacteristic
717C2×C32#88511yescharacteristic
718C2×C32#88511yescharacteristic
719C2×C32#88511yescharacteristic
720C2×C32C4×#6711yescharacteristic
721C2×C32C4×#6711yescharacteristic
722C2×C32C4×#6711yescharacteristic
723C2×C32#93911yescharacteristic
724C2×C32#93911yescharacteristic
725C2×C32#93911yescharacteristic
726C2×C32#94011yescharacteristic
727C2×C32#94011yescharacteristic
728C2×C32#94011yescharacteristic
729C3⋊D3—42no—
730C3×D3—44no—
731C3×D3—42no—
732C3×D3—42no—
733C3×D3—124no—
734C3×D3—122no—
735C3×D3—122no—
736C24—31no—
737C24—91no—
738C2×D4—274no—
739C2×D4—542no—
740C2×D4—542no—
741C22×C4—31no—
742C22×C4—31no—
743C22×C4—91no—
744C22×C4—91no—
745C22×C4—271no—
746C4⋊C4—542no—
747C22⋊C4—182no—
748C22⋊C4—182no—
749C22⋊C4—182no—
750C22⋊C4—542no—
751C42—542no—
752C22×C3—21no—
753C22×C3—21no—
754C22×C3—21no—
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—41no—
774C22×C3—41no—
775C22×C3—41no—
776C22×C3—41no—
777C22×C3—41no—
778C22×C3—41no—
779C22×C3—41no—
780C22×C3—64no—
781C22×C3—62no—
782C22×C3—62no—
783C22×C3—62no—
784C22×C3—62no—
785C22×C3—62no—
786C22×C3—62no—
787C22×C3—122no—
788C22×C3—122no—
789C22×C3—122no—
790C22×C3—122no—
791C22×C3—122no—
792C22×C3—122no—
793C22×C3—121no—
794C22×C3—121no—
795C22×C3—121no—
796C22×C3—121no—
797C22×C3—121no—
798C22×C3—121no—
799C22×C3—121no—
800C22×C3—121no—
801C22×C3—182no—
802C22×C3—182no—
803C22×C3—182no—
804C22×C3—361no—
805C22×C3—361no—
806C22×C3—361no—
807C22×C3—361no—
808C22×C3#379511yescharacteristic
809C22×C3#379511yescharacteristic
810C22×C3#379811yescharacteristic
811C22×C3C4×D3211yescharacteristic
812C22×C3C4×D3211yescharacteristic
813C22×C3#380211yescharacteristic
814C22×C3#380211yescharacteristic
815C22×C3#380211yescharacteristic
816C22×C3#380411yescharacteristic
817C22×C3#380411yescharacteristic
818C22×C3#380511yescharacteristic
819C22×C3C2×#62411yescharacteristic
820C22×C3C2×#62511yescharacteristic
821C22×C3D3×#6711yescharacteristic
822C22×C3D3×#6711yescharacteristic
823C22×C3D3×#6711yescharacteristic
824C22×C3D3×#6711yescharacteristic
825C22×C3#381111yescharacteristic
826C22×C3#381111yescharacteristic
827C22×C3#381111yescharacteristic
828C22×C3#381111yescharacteristic
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—41no—
833C2×D3—41no—
834C2×D3—41no—
835C2×D3—41no—
836C2×D3—64no—
837C2×D3—62no—
838C2×D3—62no—
839C2×D3—62no—
840C2×D3—62no—
841C2×D3—62no—
842C2×D3—62no—
843C2×D3—122no—
844C2×D3—122no—
845C2×D3—122no—
846C2×D3—122no—
847C2×D3—122no—
848C2×D3—122no—
849C2×D3—121no—
850C2×D3—121no—
851C2×D3—121no—
852C2×D3—121no—
853C2×D3—121no—
854C2×D3—121no—
855C2×D3—121no—
856C2×D3—121no—
857C3×C4—64no—
858C3×C4—62no—
859C3×C4—62no—
860C3×C4—122no—
861C3×C4—121no—
862C3×C4—121no—
863C3×C4—182no—
864C3×C4—361no—
865Dic3—22no—
866Dic3—41no—
867Dic3—64no—
868Dic3—62no—
869Dic3—62no—
870Dic3—94no—
871Dic3—94no—
872Dic3—94no—
873Dic3—122no—
874Dic3—121no—
875Dic3—121no—
876Dic3—184no—
877Dic3—184no—
878Dic3—184no—
879Dic3—364no—
880C32—21no—
881C32—21no—
882C32—21no—
883C32—41no—
884C32#495711yescharacteristic, complemented
885C32#495711yescharacteristic, complemented
886C32#495711yescharacteristic, complemented
887C23—32no—
888C23—61no—
889C23—61no—
890C23—61no—
891C23—61no—
892C23—61no—
893C23—61no—
894C23—92no—
895C23—181no—
896C23—181no—
897C23—181no—
898C23—181no—
899C23—181no—
900C23—181no—
901C23D3311yescharacteristic
902D4—548no—
903C2×C4—32no—
904C2×C4—61no—
905C2×C4—61no—
906C2×C4—61no—
907C2×C4—61no—
908C2×C4—61no—
909C2×C4—92no—
910C2×C4—181no—
911C2×C4—181no—
912C2×C4—181no—
913C2×C4—181no—
914C2×C4—181no—
915C2×C4—272no—
916C2×C4—272no—
917C2×C4—272no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
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—41no—
940C2×C3—41no—
941C2×C3—41no—
942C2×C3—41no—
943C2×C3—41no—
944C2×C3—41no—
945C2×C3—41no—
946C2×C3—124no—
947C2×C3—122no—
948C2×C3—122no—
949C2×C3—362no—
950C2×C3#6387911yescharacteristic
951C2×C3#6387911yescharacteristic
952C2×C3#6388511yescharacteristic
953C2×C3#6388511yescharacteristic
954C2×C3C4×#62511yescharacteristic
955C2×C3#6390211yescharacteristic
956C2×C3#6391211yescharacteristic
957C2×C3#6391311yescharacteristic
958C2×C3#6391411yescharacteristic
959C2×C3#6391511yescharacteristic
960C2×C3#6392111yescharacteristic
961C2×C3#6392111yescharacteristic
962C2×C3#6395211yescharacteristic
963C2×C3#6395211yescharacteristic
964C2×C3#6395311yescharacteristic
965C2×C3#6397111yescharacteristic
966C2×C3#6397111yescharacteristic
967C2×C3#6397411yescharacteristic
968C2×C3#6397911yescharacteristic
969C2×C3#6397911yescharacteristic
970C2×C3#6398011yescharacteristic
971D3—42no—
972D3—124no—
973D3—122no—
974D3—122no—
975C22—62no—
976C22—62no—
977C22—62no—
978C22—121no—
979C22—121no—
980C22—121no—
981C22—121no—
982C22—182no—
983C22—182no—
984C22—182no—
985C22—361no—
986C22—361no—
987C22—361no—
988C22—361no—
989C22D3×#62411yescharacteristic
990C22D3×#62511yescharacteristic
991C22#8895311yescharacteristic
992C22#8895411yescharacteristic
993C22#8895411yescharacteristic
994C22#8896011yescharacteristic
995C22#8896111yescharacteristic
996C4—62no—
997C4—121no—
998C4—182no—
999C4—274no—
1000C4—361no—
1001C3—21no—
1002C3—21no—
1003C3—21no—
1004C3—41no—
1005C3#1059138511yescharacteristic, complemented
1006C3#1059138611yescharacteristic, complemented
1007C3#1059170411yescharacteristic, complemented
1008C2—122no—
1009C2—362no—
1010C2#1172290611yescharacteristic
1011C2#1172293011yescharacteristic
1012C2#1172293611yescharacteristic
1013C2#1172295411yescharacteristic
1014C2#1172296711yescharacteristic
1015C2#1172300911yescharacteristic
1016C2#1172302911yescharacteristic
subgroupG/H
center, Frattini, hypercenterC23D33
commutatorC22×C33C22×C4
Fitting, socle, cosocleC23×C33C23
prime radicalC22×#6290C2
hypocenterC33#390
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C2×#88814C2semidirect
3. C2×#88806C2semidirect
4. C2×Dic3×C3⋊Dic3C2semidirect
5. C2×C3×#3722C2semidirect
6. C2×C3×(C2×D3)⋊Dic3C2semidirect
7. C2×C3×(C2×D3)⋊Dic3C2semidirect
20. C2×#6290C4semidirect
43. C2×#3722D3semidirect
46. C2×(C2×D3)⋊Dic3D3semidirect
47. C2×(C2×D3)⋊Dic3D3semidirect
74. C2×C3×C3⋊Dic3D4semidirect
80. C2×C32×Dic3D4semidirect
169. C3⋊(C3⋊Dic3)C22⋊C4semidirect
294. C2×C3⋊Dic3#67semidirect
329. C2×C3×Dic3#67semidirect
330. C2×C3×Dic3#67semidirect
542. C33#390semidirect
678. C2×Dic3#625semidirect
884. C32#4957semidirect
885. C32#4957semidirect
886. C32#4957semidirect
1005. C3#10591385semidirect
1006. C3#10591386semidirect
1007. C3#10591704semidirect

Maximal subgroups

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

subgroupindex
C22×#62902
C2×#888142
C2×#888062
C2×Dic3×C3⋊Dic32
C2×C3×#37222
C2×C3×(C2×D3)⋊Dic32
#105917043
#105913863
#105913853