Finite Group Databasebeta

← #13156755

Subgroups — #13156755

Order 1728.

1290 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#624C211yesmaximal, characteristic
2C2×#88814C211yesmaximal, characteristic
3C2×#88806C211yesmaximal, characteristic, complemented
4C2×#88803C211yesmaximal, characteristic
5C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
6#11722061C211yesmaximal, characteristic, complemented
7C3×#63579C211yesmaximal, characteristic, complemented
8#10591378—31nomaximal
9#10591278—31nomaximal
10#10591277—31nomaximal
11C23×C3×C3⋊D3C2211yescharacteristic
12C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C32×Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C2×C3×#624—22no—
19C2×C3×#624—22no—
20C2×C3×#624—22no—
21#88814—22no—
22#88806—22no—
23#88803C414yescomplemented
24C3×Dic3⋊Dic3—22no—
25C22×C3×C4×D3—31no—
26C22×C3×C4×D3—31no—
27C22×#624D311yescharacteristic
28C2×#3752—31no—
29C2×#3750—31no—
30C2×C3×C4⋊Dic3—31no—
31C2×C3×Dic3⋊C4—31no—
32C2×#3724—31no—
33C2×#3724—31no—
34C2×#3724—61no—
35C2×Dic3⋊Dic3D311yescharacteristic, complemented
36C2×#3722—31no—
37C2×(C2×D3)⋊Dic3—31no—
38C2×(C2×D3)⋊Dic3—31no—
39C2×(C2×D3)⋊Dic3—31no—
40C2×(C2×D3)⋊Dic3—31no—
41C2×(C2×D3)⋊Dic3—61no—
42#63658—31no—
43C3×C3⋊#95—31no—
44C3×C3⋊#95—31no—
45#63579—31no—
46#63579—31no—
47#63579—61no—
48#63579D311yescharacteristic, complemented
49C23×C33C2311yescharacteristic
50C22×C3×C3⋊D3—21no—
51C22×C3×C3⋊D3—21no—
52C22×C3×C3⋊D3—21no—
53C22×C3×C3⋊D3—21no—
54C22×C3×C3⋊D3C2×C412yes—
55C22×C3×C3⋊D3D412yes—
56C22×C3×C3⋊D3Q812yes—
57C2×C3⋊(C3⋊Dic3)—21no—
58C2×C3⋊(C3⋊Dic3)—21no—
59C2×C3⋊(C3⋊Dic3)C2×C412yescomplemented
60C2×C3×C3⋊Dic3—21no—
61C2×C3×C3⋊Dic3—21no—
62C2×C3×C3⋊Dic3—21no—
63C2×C3×C3⋊Dic3—21no—
64C2×C3×C3⋊Dic3—21no—
65C2×C3×C3⋊Dic3—21no—
66C2×C32×Dic3—21no—
67C2×C32×Dic3—21no—
68C2×C32×Dic3—21no—
69C2×C32×Dic3—21no—
70C2×C32×Dic3—21no—
71C2×C32×Dic3—21no—
72C2×C32×Dic3C2×C412yescomplemented
73C2×C32×Dic3D412yes—
74C2×C32×Dic3D412yes—
75C3×#624—28no—
76#5210—91no—
77#4989—91no—
78#4668—91no—
79C23×C3⋊D3C2×D311yescharacteristic
80C23×C3×D3—31no—
81C23×C3×D3—31no—
82C23×C3×D3—61no—
83C22×C32×C4—31no—
84C22×C32×C4—31no—
85C22×C32×C4—31no—
86C22×C3⋊Dic3—31no—
87C22×C3⋊Dic3—31no—
88C22×C3⋊Dic3—31no—
89C22×C3⋊Dic3—61no—
90C22×C3⋊Dic3—61no—
91C22×C3⋊Dic3—61no—
92C22×C3⋊Dic3—121no—
93C22×C3⋊Dic3C2×D311yescharacteristic
94C22×C3⋊Dic3C2×D311yescharacteristic
95C22×C3×Dic3—21no—
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—31no—
99C22×C3×Dic3—31no—
100C22×C3×Dic3—31no—
101C22×C3×Dic3—31no—
102C22×C3×Dic3—61no—
103C22×C3×Dic3—61no—
104C22×C3×Dic3C2×D311yescharacteristic
105C22×C3×Dic3C2×D311yescharacteristic
106C22×C3×Dic3C2×D311yescharacteristic
107C22×C3×Dic3C2×D311yescharacteristic
108C22×C3×Dic3C2×D311yescharacteristic
109C22×C3×Dic3C2×D311yescharacteristic
110C2×C3×C4×D3—62no—
111C2×C3×C4×D3—62no—
112C2×C3×C4×D3—62no—
113C2×C3×C4×D3—62no—
114C2×C3×C4×D3—62no—
115C2×C3×C4×D3—62no—
116C2×#624—22no—
117C2×#624—22no—
118C2×#624—22no—
119#3752—34no—
120#3750—62no—
121C3×C4⋊Dic3—62no—
122C3×Dic3⋊C4—62no—
123#3724—64no—
124#3724—62no—
125#3724—62no—
126Dic3⋊Dic3—22no—
127#3722—62no—
128(C2×D3)⋊Dic3—34no—
129(C2×D3)⋊Dic3—34no—
130(C2×D3)⋊Dic3—64no—
131(C2×D3)⋊Dic3—62no—
132(C2×D3)⋊Dic3—62no—
133C22×C33C22×C411yescharacteristic
134C22×C33C2×D411yescharacteristic
135C22×C33C2×D411yescharacteristic
136C22×C33C2×D411yescharacteristic
137C22×C33C2×Q811yescharacteristic
138C22×C33#4111yescharacteristic
139C22×C33#4111yescharacteristic
140C2×C3×C3⋊D3—22no—
141C2×C3×C3⋊D3—22no—
142C2×C3×C3⋊D3—22no—
143C2×C3×C3⋊D3—22no—
144C2×C3×C3⋊D3—22no—
145C2×C3×C3⋊D3—22no—
146C2×C3×C3⋊D3C4⋊C414yescomplemented
147C3⋊(C3⋊Dic3)—22no—
148C3×C3⋊Dic3—41no—
149C3×C3⋊Dic3—41no—
150C32×Dic3—22no—
151C32×Dic3—22no—
152C32×Dic3—22no—
153C23×C3×C4—91no—
154C22×C4×D3—31no—
155C22×C4×D3—31no—
156C2×C3×C4⋊C4—91no—
157C2×#217—91no—
158C2×#217—91no—
159C2×(C2×D3)⋊C4—91no—
160C2×(C2×D3)⋊C4—91no—
161C2×(C2×D3)⋊C4—91no—
162C2×(C2×D3)⋊C4—91no—
163C2×(C2×D3)⋊C4—181no—
164C2×C4⋊Dic3—31no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—91no—
167C2×Dic3⋊C4—91no—
168C2×Dic3⋊C4—91no—
169C2×Dic3⋊C4—181no—
170C3×#95—91no—
171C3⋊#95—31no—
172C3⋊#95—31no—
173C3⋊#95—91no—
174C3⋊#95—91no—
175C3⋊#95—91no—
176C3⋊#95—181no—
177C23×C32—21no—
178C23×C32—21no—
179C23×C32—21no—
180C23×C32—41no—
181C23×C32C22×D311yescharacteristic
182C23×C32C22×D311yescharacteristic
183C23×C32C22×D311yescharacteristic
184C22×C3⋊D3—21no—
185C22×C3⋊D3—21no—
186C22×C3⋊D3—21no—
187C22×C3⋊D3—21no—
188C22×C3⋊D3Dic612yes—
189C22×C3⋊D3C4×D312yes—
190C22×C3⋊D3#6712yes—
191C22×C3×D3—32no—
192C22×C3×D3—32no—
193C22×C3×D3—32no—
194C22×C3×D3—32no—
195C22×C3×D3—32no—
196C22×C3×D3—32no—
197C22×C3×D3—62no—
198C22×C3×D3—62no—
199C22×C3×D3—62no—
200C22×C3×D3—61no—
201C22×C3×D3—61no—
202C22×C3×D3—61no—
203C22×C3×D3—61no—
204C22×C3×D3—61no—
205C22×C3×D3—61no—
206C22×C3×D3—61no—
207C22×C3×D3—61no—
208C22×C3×D3—121no—
209C22×C3×D3—121no—
210C22×C3×D3—121no—
211C22×C3×D3—121no—
212C2×C32×C4—32no—
213C2×C32×C4—32no—
214C2×C32×C4—32no—
215C2×C32×C4—61no—
216C2×C32×C4—61no—
217C2×C32×C4—61no—
218C2×C32×C4—61no—
219C2×C32×C4—61no—
220C2×C32×C4—61no—
221C2×C3⋊Dic3—21no—
222C2×C3⋊Dic3—21no—
223C2×C3⋊Dic3—21no—
224C2×C3⋊Dic3—21no—
225C2×C3⋊Dic3—21no—
226C2×C3⋊Dic3—21no—
227C2×C3⋊Dic3—32no—
228C2×C3⋊Dic3—32no—
229C2×C3⋊Dic3—32no—
230C2×C3⋊Dic3—62no—
231C2×C3⋊Dic3—62no—
232C2×C3⋊Dic3—62no—
233C2×C3⋊Dic3—61no—
234C2×C3⋊Dic3—61no—
235C2×C3⋊Dic3—62no—
236C2×C3⋊Dic3—62no—
237C2×C3⋊Dic3—61no—
238C2×C3⋊Dic3—61no—
239C2×C3⋊Dic3—61no—
240C2×C3⋊Dic3—61no—
241C2×C3⋊Dic3—122no—
242C2×C3⋊Dic3—121no—
243C2×C3⋊Dic3—121no—
244C2×C3⋊Dic3—121no—
245C2×C3⋊Dic3—121no—
246C2×C3⋊Dic3—122no—
247C2×C3⋊Dic3—122no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—22no—
261C2×C3×Dic3—22no—
262C2×C3×Dic3—22no—
263C2×C3×Dic3—41no—
264C2×C3×Dic3—41no—
265C2×C3×Dic3—41no—
266C2×C3×Dic3—41no—
267C2×C3×Dic3—41no—
268C2×C3×Dic3—41no—
269C2×C3×Dic3—62no—
270C2×C3×Dic3—62no—
271C2×C3×Dic3—61no—
272C2×C3×Dic3—61no—
273C2×C3×Dic3—61no—
274C2×C3×Dic3—61no—
275C2×C3×Dic3—61no—
276C2×C3×Dic3—61no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—61no—
279C2×C3×Dic3—61no—
280C2×C3×Dic3—61no—
281C2×C3×Dic3—61no—
282C2×C3×Dic3—61no—
283C2×C3×Dic3—121no—
284C2×C3×Dic3—121no—
285C2×C3×Dic3—121no—
286C2×C3×Dic3—121no—
287C2×C3×Dic3C4×D312yescomplemented
288C2×C3×Dic3C4×D312yescomplemented
289C2×C3×Dic3D1212yes—
290C2×C3×Dic3#6712yes—
291C2×C3×Dic3#6712yes—
292C2×C3×Dic3#6712yes—
293C3×C4×D3—68no—
294C3×C4×D3—68no—
295#624—28no—
296#385—271noSylow
297C2×C33C2×C4⋊C411yescharacteristic
298C2×C33C4×D411yescharacteristic
299C2×C33C4×D411yescharacteristic
300C2×C33#12011yescharacteristic
301C2×C33C22⋊Q811yescharacteristic
302C2×C33C22⋊Q811yescharacteristic
303C2×C33#12311yescharacteristic
304C3×C3⋊D3—24no—
305C24×C3—91no—
306C23×D3—31no—
307C23×D3—31no—
308C23×D3—61no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4—91no—
319C22×C3×C4—91no—
320C22×C3×C4—182no—
321C22×C3×C4—182no—
322C22×C3×C4—182no—
323C22×Dic3—31no—
324C22×Dic3—31no—
325C22×Dic3—31no—
326C22×Dic3—31no—
327C22×Dic3—61no—
328C22×Dic3—61no—
329C22×Dic3—91no—
330C22×Dic3—91no—
331C22×Dic3—91no—
332C22×Dic3—181no—
333C22×Dic3—181no—
334C22×Dic3—181no—
335C22×Dic3—361no—
336C22×Dic3D3211yescharacteristic
337C22×Dic3D3211yescharacteristic
338C22×Dic3D3211yescharacteristic
339C2×C4×D3—62no—
340C2×C4×D3—62no—
341C2×C4×D3—62no—
342C2×C4×D3—62no—
343C2×C4×D3—62no—
344C2×C4×D3—62no—
345C3×C4⋊C4—182no—
346#217—94no—
347#217—182no—
348(C2×D3)⋊C4—94no—
349(C2×D3)⋊C4—94no—
350(C2×D3)⋊C4—184no—
351(C2×D3)⋊C4—182no—
352(C2×D3)⋊C4—182no—
353C4⋊Dic3—62no—
354Dic3⋊C4—62no—
355Dic3⋊C4—182no—
356Dic3⋊C4—182no—
357Dic3⋊C4—184no—
358Dic3⋊C4—182no—
359C22×C32—21no—
360C22×C32—21no—
361C22×C32—21no—
362C22×C32—21no—
363C22×C32—21no—
364C22×C32—21no—
365C22×C32—21no—
366C22×C32—21no—
367C22×C32—21no—
368C22×C32—21no—
369C22×C32—21no—
370C22×C32—21no—
371C22×C32—21no—
372C22×C32—21no—
373C22×C32—21no—
374C22×C32—21no—
375C22×C32—21no—
376C22×C32—21no—
377C22×C32—21no—
378C22×C32—21no—
379C22×C32—21no—
380C22×C32—41no—
381C22×C32—41no—
382C22×C32—41no—
383C22×C32—41no—
384C22×C32—41no—
385C22×C32—41no—
386C22×C32—41no—
387C22×C32C2×Dic611yescharacteristic
388C22×C32C2×C4×D311yescharacteristic
389C22×C32C2×C4×D311yescharacteristic
390C22×C32C2×C4×D311yescharacteristic
391C22×C32C2×D1211yescharacteristic
392C22×C32#23511yescharacteristic
393C22×C32#23511yescharacteristic
394C22×C32#23511yescharacteristic
395C22×C32#23511yescharacteristic
396C22×C32D3×D411yescharacteristic
397C22×C32D3×D411yescharacteristic
398C22×C32D3×D411yescharacteristic
399C22×C32D3×D411yescharacteristic
400C22×C32#23711yescharacteristic
401C22×C32D3×Q811yescharacteristic
402C22×C32D3×Q811yescharacteristic
403C22×C32#23911yescharacteristic
404C22×C32C2×#6711yescharacteristic
405C22×C32C2×#6711yescharacteristic
406C22×C32C2×#6711yescharacteristic
407C22×C32C2×#6711yescharacteristic
408C2×C3⋊D3—22no—
409C2×C3⋊D3—22no—
410C2×C3⋊D3—22no—
411C2×C3⋊D3—22no—
412C2×C3⋊D3—22no—
413C2×C3⋊D3—22no—
414C2×C3⋊D3Dic3⋊C414yescomplemented
415C2×C3×D3—34no—
416C2×C3×D3—34no—
417C2×C3×D3—64no—
418C2×C3×D3—62no—
419C2×C3×D3—62no—
420C2×C3×D3—62no—
421C2×C3×D3—62no—
422C2×C3×D3—62no—
423C2×C3×D3—62no—
424C2×C3×D3—62no—
425C2×C3×D3—62no—
426C2×C3×D3—62no—
427C2×C3×D3—62no—
428C2×C3×D3—62no—
429C2×C3×D3—62no—
430C2×C3×D3—122no—
431C2×C3×D3—122no—
432C2×C3×D3—122no—
433C2×C3×D3—122no—
434C2×C3×D3—122no—
435C2×C3×D3—122no—
436C32×C4—62no—
437C32×C4—62no—
438C32×C4—62no—
439C3⋊Dic3—41no—
440C3⋊Dic3—41no—
441C3⋊Dic3—62no—
442C3⋊Dic3—64no—
443C3⋊Dic3—62no—
444C3⋊Dic3—62no—
445C3⋊Dic3—122no—
446C3⋊Dic3—122no—
447C3⋊Dic3—124no—
448C3×Dic3—22no—
449C3×Dic3—22no—
450C3×Dic3—22no—
451C3×Dic3—22no—
452C3×Dic3—22no—
453C3×Dic3—22no—
454C3×Dic3—42no—
455C3×Dic3—42no—
456C3×Dic3—42no—
457C3×Dic3—122no—
458C3×Dic3—122no—
459C3×Dic3—121no—
460C3×Dic3—121no—
461C3×Dic3—121no—
462C3×Dic3—121no—
463C23×C4—91no—
464C2×C4⋊C4—91no—
465C2×C4⋊C4—271no—
466C2×C22⋊C4—271no—
467C2×C22⋊C4—271no—
468#95—91no—
469#95—271no—
470C33#38511yescharacteristic, complemented, Sylow
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—41no—
475C23×C3—92no—
476C23×C3—92no—
477C23×C3—92no—
478C23×C3—181no—
479C23×C3—181no—
480C23×C3—181no—
481C23×C3—181no—
482C23×C3C2×D3211yescharacteristic
483C23×C3C2×D3211yescharacteristic
484C23×C3C2×D3211yescharacteristic
485C22×D3—32no—
486C22×D3—32no—
487C22×D3—32no—
488C22×D3—32no—
489C22×D3—32no—
490C22×D3—32no—
491C22×D3—62no—
492C22×D3—62no—
493C22×D3—62no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—61no—
497C22×D3—61no—
498C22×D3—61no—
499C22×D3—61no—
500C22×D3—61no—
501C22×D3—61no—
502C22×D3—121no—
503C22×D3—121no—
504C22×D3—121no—
505C22×D3—121no—
506C2×C3×C4—32no—
507C2×C3×C4—32no—
508C2×C3×C4—32no—
509C2×C3×C4—32no—
510C2×C3×C4—32no—
511C2×C3×C4—32no—
512C2×C3×C4—62no—
513C2×C3×C4—62no—
514C2×C3×C4—62no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—121no—
528C2×C3×C4—121no—
529C2×C3×C4—121no—
530C2×C3×C4—121no—
531C2×C3×C4—121no—
532C2×C3×C4—121no—
533C2×C3×C4—188no—
534C2×C3×C4—181no—
535C2×C3×C4—181no—
536C2×C3×C4—181no—
537C2×C3×C4—181no—
538C2×C3×C4—181no—
539C2×C3×C4—181no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—62no—
547C2×Dic3—62no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—92no—
561C2×Dic3—92no—
562C2×Dic3—92no—
563C2×Dic3—121no—
564C2×Dic3—121no—
565C2×Dic3—121no—
566C2×Dic3—121no—
567C2×Dic3—182no—
568C2×Dic3—182no—
569C2×Dic3—182no—
570C2×Dic3—182no—
571C2×Dic3—182no—
572C2×Dic3—181no—
573C2×Dic3—181no—
574C2×Dic3—181no—
575C2×Dic3—181no—
576C2×Dic3—181no—
577C2×Dic3—181no—
578C2×Dic3—362no—
579C2×Dic3—361no—
580C2×Dic3—361no—
581C2×Dic3—361no—
582C2×Dic3—361no—
583C2×Dic3—362no—
584C2×Dic3—362no—
585C2×Dic3#62412yescomplemented
586C2×Dic3#62512yes—
587C2×Dic3#62612yes—
588C4×D3—68no—
589C4×D3—68no—
590C2×C32—21no—
591C2×C32—21no—
592C2×C32—21no—
593C2×C32—21no—
594C2×C32—21no—
595C2×C32—21no—
596C2×C32—21no—
597C2×C32—21no—
598C2×C32—21no—
599C2×C32—21no—
600C2×C32—21no—
601C2×C32—21no—
602C2×C32—21no—
603C2×C32—21no—
604C2×C32—21no—
605C2×C32—21no—
606C2×C32—21no—
607C2×C32—21no—
608C2×C32—21no—
609C2×C32—21no—
610C2×C32—21no—
611C2×C32—41no—
612C2×C32—41no—
613C2×C32—41no—
614C2×C32—41no—
615C2×C32—41no—
616C2×C32—41no—
617C2×C32—41no—
618C2×C32C4×D1211yescharacteristic
619C2×C32#67⋊C411yescharacteristic
620C2×C32#88211yescharacteristic
621C2×C32#88311yescharacteristic
622C2×C32D3×C4⋊C411yescharacteristic
623C2×C32D3×C4⋊C411yescharacteristic
624C2×C32#89311yescharacteristic
625C2×C32#89411yescharacteristic
626C2×C32#89611yescharacteristic
627C2×C32#89611yescharacteristic
628C2×C32#89711yescharacteristic
629C2×C32C2×Dic3⋊C411yescharacteristic
630C2×C32#92411yescharacteristic
631C2×C32#92411yescharacteristic
632C2×C32C4×#6711yescharacteristic
633C2×C32C4×#6711yescharacteristic
634C2×C32C4×#6711yescharacteristic
635C2×C32#92911yescharacteristic
636C2×C32#93711yescharacteristic
637C2×C32#94611yescharacteristic
638C2×C32#95311yescharacteristic
639C3⋊D3—24no—
640C3×D3—64no—
641C3×D3—64no—
642C3×D3—124no—
643C24—91no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—91no—
648C22×C4—91no—
649C22×C4—182no—
650C22×C4—182no—
651C22×C4—182no—
652C22×C4—271no—
653C4⋊C4—182no—
654C4⋊C4—542no—
655C22⋊C4—274no—
656C22⋊C4—542no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—94no—
686C22×C3—182no—
687C22×C3—182no—
688C22×C3—182no—
689C22×C3—182no—
690C22×C3—182no—
691C22×C3—182no—
692C22×C3D3×Dic611yescharacteristic
693C22×C3D3×Dic611yescharacteristic
694C22×C3#379511yescharacteristic
695C22×C3#379711yescharacteristic
696C22×C3#379811yescharacteristic
697C22×C3#379811yescharacteristic
698C22×C3#379911yescharacteristic
699C22×C3#379911yescharacteristic
700C22×C3C4×D3211yescharacteristic
701C22×C3C4×D3211yescharacteristic
702C22×C3D3×D1211yescharacteristic
703C22×C3#380211yescharacteristic
704C22×C3#380411yescharacteristic
705C22×C3C2×#62411yescharacteristic
706C22×C3C2×#62511yescharacteristic
707C22×C3C2×#62611yescharacteristic
708C22×C3D3×#6711yescharacteristic
709C22×C3D3×#6711yescharacteristic
710C22×C3D3×#6711yescharacteristic
711C22×C3D3×#6711yescharacteristic
712C22×C3D3×#6711yescharacteristic
713C2×D3—34no—
714C2×D3—34no—
715C2×D3—64no—
716C2×D3—62no—
717C2×D3—62no—
718C2×D3—62no—
719C2×D3—62no—
720C2×D3—62no—
721C2×D3—62no—
722C2×D3—62no—
723C2×D3—62no—
724C2×D3—62no—
725C2×D3—62no—
726C2×D3—62no—
727C2×D3—62no—
728C2×D3—122no—
729C2×D3—122no—
730C2×D3—122no—
731C2×D3—122no—
732C2×D3—122no—
733C2×D3—122no—
734C3×C4—62no—
735C3×C4—62no—
736C3×C4—62no—
737C3×C4—62no—
738C3×C4—62no—
739C3×C4—62no—
740C3×C4—122no—
741C3×C4—122no—
742C3×C4—122no—
743C3×C4—361no—
744C3×C4—361no—
745Dic3—22no—
746Dic3—22no—
747Dic3—22no—
748Dic3—122no—
749Dic3—122no—
750Dic3—121no—
751Dic3—121no—
752Dic3—121no—
753Dic3—121no—
754Dic3—184no—
755Dic3—182no—
756Dic3—182no—
757Dic3—182no—
758Dic3—362no—
759Dic3—362no—
760Dic3—364no—
761C32—21no—
762C32—21no—
763C32—21no—
764C32—41no—
765C32#466811yescharacteristic, complemented
766C32#498911yescharacteristic, complemented
767C32#521011yescharacteristic, complemented
768C23—92no—
769C23—92no—
770C23—92no—
771C23—181no—
772C23—181no—
773C23—181no—
774C23—181no—
775C23D3311yescharacteristic
776C2×C4—32no—
777C2×C4—32no—
778C2×C4—32no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—188no—
786C2×C4—181no—
787C2×C4—181no—
788C2×C4—181no—
789C2×C4—181no—
790C2×C4—181no—
791C2×C4—181no—
792C2×C4—272no—
793C2×C4—541no—
794C2×C4—541no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—41no—
817C2×C3—41no—
818C2×C3—41no—
819C2×C3—41no—
820C2×C3—41no—
821C2×C3—41no—
822C2×C3—41no—
823C2×C3—184no—
824C2×C3#6385011yescharacteristic
825C2×C3#6385111yescharacteristic
826C2×C3#6385111yescharacteristic
827C2×C3#6385411yescharacteristic
828C2×C3#6385611yescharacteristic
829C2×C3#6385711yescharacteristic
830C2×C3D3×Dic3⋊C411yescharacteristic
831C2×C3D3×Dic3⋊C411yescharacteristic
832C2×C3#6387911yescharacteristic
833C2×C3#6388811yescharacteristic
834C2×C3#6389411yescharacteristic
835C2×C3#6389511yescharacteristic
836C2×C3#6390011yescharacteristic
837C2×C3C4×#62511yescharacteristic
838C2×C3C4×#62611yescharacteristic
839C2×C3#6390411yescharacteristic
840C2×C3#6390511yescharacteristic
841C2×C3#6392211yescharacteristic
842C2×C3#6395211yescharacteristic
843C2×C3#6397611yescharacteristic
844C2×C3#6397711yescharacteristic
845D3—64no—
846D3—64no—
847D3—124no—
848C22—94no—
849C22—182no—
850C22—182no—
851C22—182no—
852C22—182no—
853C22—182no—
854C22—182no—
855C22D3×#62411yescharacteristic
856C22D3×#62511yescharacteristic
857C22D3×#62611yescharacteristic
858C22#8895311yescharacteristic
859C22#8895711yescharacteristic
860C22#8896011yescharacteristic
861C22#8896511yescharacteristic
862C4—62no—
863C4—62no—
864C4—62no—
865C4—361no—
866C4—361no—
867C4—542no—
868C3—21no—
869C3—21no—
870C3—21no—
871C3—41no—
872C3#1059127711yescharacteristic, complemented
873C3#1059127811yescharacteristic, complemented
874C3#1059137811yescharacteristic, complemented
875C2—184no—
876C2#1172291111yescharacteristic
877C2#1172293011yescharacteristic
878C2#1172293311yescharacteristic
879C2#1172294711yescharacteristic
880C2#1172297011yescharacteristic
881C2#1172297211yescharacteristic
882C2#1172299511yescharacteristic
subgroupG/H
center, Frattini, hypercenterC23D33
commutatorC22×C33C22×C4
Fitting, socle, cosocleC23×C33C23
prime radicalC23×C3×C3⋊D3C22
hypocenterC33#385
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
3. C2×#88806C2semidirect
5. C2×C3×Dic3⋊Dic3C2semidirect
6. #11722061C2semidirect
7. C3×#63579C2semidirect
23. #88803C4semidirect
35. C2×Dic3⋊Dic3D3semidirect
48. #63579D3semidirect
59. C2×C3⋊(C3⋊Dic3)C2×C4semidirect
72. C2×C32×Dic3C2×C4semidirect
146. C2×C3×C3⋊D3C4⋊C4semidirect
287. C2×C3×Dic3C4×D3semidirect
288. C2×C3×Dic3C4×D3semidirect
414. C2×C3⋊D3Dic3⋊C4semidirect
470. C33#385semidirect
585. C2×Dic3#624semidirect
765. C32#4668semidirect
766. C32#4989semidirect
767. C32#5210semidirect
872. C3#10591277semidirect
873. C3#10591278semidirect
874. C3#10591378semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#6242
C2×#888142
C2×#888062
C2×#888032
C2×C3×Dic3⋊Dic32
#117220612
C3×#635792
#105913783
#105912783
#105912773