Finite Group Databasebeta

← #13156808

Subgroups — #13156808

Order 1728.

1098 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88813C211yesmaximal, characteristic, complemented
2C2×(C2×D3)⋊(C3⋊Dic3)C211yesmaximal, characteristic
3C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
4C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
5C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
6#11722061C211yesmaximal, characteristic, complemented
7#11722061C211yesmaximal, characteristic, complemented
8#10591701—31nomaximal
9#10591307—31nomaximal
10#10591285—31nomaximal
11C23×C32×D3C2211yescharacteristic
12C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C3×C3⋊Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18#88813—22no—
19(C2×D3)⋊(C3⋊Dic3)—22no—
20C3×Dic3⋊Dic3—22no—
21C3×(C2×D3)⋊Dic3—22no—
22C3×(C2×D3)⋊Dic3C414yescomplemented
23C2×#3757—31no—
24C2×C3×#217—31no—
25C2×C3×#217—31no—
26C2×C3×(C2×D3)⋊C4—31no—
27C2×C3×(C2×D3)⋊C4—31no—
28C2×C3×C4⋊Dic3—31no—
29C2×C3×Dic3⋊C4—31no—
30C2×Dic3⋊Dic3D311yescharacteristic, complemented
31C2×(C2×D3)⋊Dic3—31no—
32C2×(C2×D3)⋊Dic3—31no—
33C2×(C2×D3)⋊Dic3—61no—
34C2×(C2×D3)⋊Dic3D311yescharacteristic
35C2×(C2×D3)⋊Dic3D311yescharacteristic
36C2×Dic32—31no—
37C2×Dic32—31no—
38C2×Dic32—31no—
39#63658—31no—
40#63658—31no—
41#63579—31no—
42#63579—31no—
43#63579—31no—
44#63579—31no—
45#63579—61no—
46#63579—61no—
47C23×C33C2311yescharacteristic
48C22×C32×D3—21no—
49C22×C32×D3—21no—
50C22×C32×D3—21no—
51C22×C32×D3—21no—
52C22×C32×D3—21no—
53C22×C32×D3—21no—
54C22×C32×D3C2×C412yes—
55C2×C3⋊(C3⋊Dic3)—21no—
56C2×C3⋊(C3⋊Dic3)—21no—
57C2×C3⋊(C3⋊Dic3)—21no—
58C2×C3×C3⋊Dic3—21no—
59C2×C3×C3⋊Dic3—21no—
60C2×C3×C3⋊Dic3—21no—
61C2×C3×C3⋊Dic3—21no—
62C2×C3×C3⋊Dic3—21no—
63C2×C3×C3⋊Dic3—21no—
64C2×C3×C3⋊Dic3C2×C412yes—
65C2×C3×C3⋊Dic3D412yes—
66C2×C3×C3⋊Dic3D412yes—
67C2×C32×Dic3—21no—
68C2×C32×Dic3—21no—
69C2×C32×Dic3—21no—
70C2×C32×Dic3—21no—
71C2×C32×Dic3—21no—
72C2×C32×Dic3C2×C412yes—
73#4990—91no—
74#4951—91no—
75#4944—91no—
76C24×C32—31no—
77C23×C3×D3—21no—
78C23×C3×D3C2×D311yescharacteristic
79C23×C3×D3C2×D311yescharacteristic
80C22×C32×C4—31no—
81C22×C32×C4—31no—
82C22×C3⋊Dic3—31no—
83C22×C3⋊Dic3—31no—
84C22×C3⋊Dic3—31no—
85C22×C3⋊Dic3—61no—
86C22×C3⋊Dic3—61no—
87C22×C3⋊Dic3—61no—
88C22×C3⋊Dic3—121no—
89C22×C3⋊Dic3C2×D311yescharacteristic
90C22×C3⋊Dic3C2×D311yescharacteristic
91C22×C3⋊Dic3C2×D311yescharacteristic
92C22×C3×Dic3—21no—
93C22×C3×Dic3—21no—
94C22×C3×Dic3—31no—
95C22×C3×Dic3—31no—
96C22×C3×Dic3—31no—
97C22×C3×Dic3—31no—
98C22×C3×Dic3—31no—
99C22×C3×Dic3—31no—
100C22×C3×Dic3—61no—
101C22×C3×Dic3—61no—
102C22×C3×Dic3—61no—
103C22×C3×Dic3C2×D311yescharacteristic
104C22×C3×Dic3C2×D311yescharacteristic
105C22×C3×Dic3C2×D311yescharacteristic
106C22×C3×Dic3C2×D311yescharacteristic
107#3757—62no—
108C3×#217—34no—
109C3×#217—62no—
110C3×(C2×D3)⋊C4—34no—
111C3×(C2×D3)⋊C4—62no—
112C3×C4⋊Dic3—62no—
113C3×Dic3⋊C4—62no—
114Dic3⋊Dic3—22no—
115(C2×D3)⋊Dic3—22no—
116(C2×D3)⋊Dic3—62no—
117(C2×D3)⋊Dic3—62no—
118(C2×D3)⋊Dic3—64no—
119(C2×D3)⋊Dic3Dic314yescomplemented
120Dic32—62no—
121Dic32—62no—
122Dic32—62no—
123C22×C33C22×C411yescharacteristic
124C22×C33C2×D411yescharacteristic
125C22×C33C2×D411yescharacteristic
126C22×C33#4111yescharacteristic
127C22×C33#4111yescharacteristic
128C22×C33#4111yescharacteristic
129C22×C33#4111yescharacteristic
130C2×C32×D3—22no—
131C2×C32×D3—22no—
132C2×C32×D3—22no—
133C2×C32×D3—41no—
134C2×C32×D3—41no—
135C2×C32×D3—41no—
136C2×C32×D3—41no—
137C3⋊(C3⋊Dic3)—41no—
138C3×C3⋊Dic3—22no—
139C3×C3⋊Dic3—22no—
140C3×C3⋊Dic3—22no—
141C32×Dic3—22no—
142C32×Dic3—41no—
143C2×C3×C4⋊C4—91no—
144C2×C3×C22⋊C4—91no—
145C2×C3×C22⋊C4—91no—
146C2×#217—31no—
147C2×#217—31no—
148C2×#217—91no—
149C2×#217—91no—
150C2×#217—181no—
151C2×(C2×D3)⋊C4—31no—
152C2×(C2×D3)⋊C4—31no—
153C2×(C2×D3)⋊C4—91no—
154C2×C4⋊Dic3—31no—
155C2×Dic3⋊C4—31no—
156C2×C4×Dic3—91no—
157C2×C4×Dic3—91no—
158C2×C4×Dic3—91no—
159C3⋊#95—91no—
160C3⋊#95—91no—
161C3⋊#95—91no—
162C3⋊#95—91no—
163C3⋊#95—91no—
164C3⋊#95—91no—
165C3⋊#95—181no—
166C3⋊#95—181no—
167C23×C32—21no—
168C23×C32—21no—
169C23×C32—21no—
170C23×C32—32no—
171C23×C32—41no—
172C23×C32—61no—
173C23×C32—61no—
174C23×C32—61no—
175C23×C32—61no—
176C23×C32—61no—
177C23×C32—61no—
178C23×C32C22×D311yescharacteristic
179C23×C32C22×D311yescharacteristic
180C23×C32C22×D311yescharacteristic
181C22×C3×D3—22no—
182C22×C3×D3—22no—
183C22×C3×D3—21no—
184C22×C3×D3—21no—
185C22×C3×D3—21no—
186C22×C3×D3—21no—
187C22×C3×D3—21no—
188C22×C3×D3—21no—
189C22×C3×D3—21no—
190C22×C3×D3—21no—
191C22×C3×D3—21no—
192C22×C3×D3—21no—
193C22×C3×D3—21no—
194C22×C3×D3—21no—
195C22×C3×D3—22no—
196C22×C3×D3—41no—
197C22×C3×D3—41no—
198C22×C3×D3—41no—
199C22×C3×D3—41no—
200C22×C3×D3C4×D312yes—
201C22×C3×D3C2×Dic312yes—
202C2×C32×C4—32no—
203C2×C32×C4—61no—
204C2×C32×C4—61no—
205C2×C32×C4—61no—
206C2×C32×C4—61no—
207C2×C32×C4—61no—
208C2×C3⋊Dic3—21no—
209C2×C3⋊Dic3—21no—
210C2×C3⋊Dic3—21no—
211C2×C3⋊Dic3—21no—
212C2×C3⋊Dic3—21no—
213C2×C3⋊Dic3—21no—
214C2×C3⋊Dic3—61no—
215C2×C3⋊Dic3—61no—
216C2×C3⋊Dic3—61no—
217C2×C3⋊Dic3—62no—
218C2×C3⋊Dic3—62no—
219C2×C3⋊Dic3—62no—
220C2×C3⋊Dic3—61no—
221C2×C3⋊Dic3—61no—
222C2×C3⋊Dic3—61no—
223C2×C3⋊Dic3—61no—
224C2×C3⋊Dic3—61no—
225C2×C3⋊Dic3—61no—
226C2×C3⋊Dic3—121no—
227C2×C3⋊Dic3—121no—
228C2×C3⋊Dic3—121no—
229C2×C3⋊Dic3—121no—
230C2×C3⋊Dic3—121no—
231C2×C3⋊Dic3—121no—
232C2×C3⋊Dic3—122no—
233C2×C3⋊Dic3—122no—
234C2×C3⋊Dic3—122no—
235C2×C3⋊Dic3C2×Dic312yes—
236C2×C3⋊Dic3#6712yes—
237C2×C3⋊Dic3#6712yes—
238C2×C3×Dic3—21no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—22no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—22no—
250C2×C3×Dic3—32no—
251C2×C3×Dic3—32no—
252C2×C3×Dic3—32no—
253C2×C3×Dic3—32no—
254C2×C3×Dic3—32no—
255C2×C3×Dic3—32no—
256C2×C3×Dic3—41no—
257C2×C3×Dic3—41no—
258C2×C3×Dic3—41no—
259C2×C3×Dic3—41no—
260C2×C3×Dic3—62no—
261C2×C3×Dic3—62no—
262C2×C3×Dic3—62no—
263C2×C3×Dic3—61no—
264C2×C3×Dic3—61no—
265C2×C3×Dic3—61no—
266C2×C3×Dic3—61no—
267C2×C3×Dic3—61no—
268C2×C3×Dic3—61no—
269C2×C3×Dic3—61no—
270C2×C3×Dic3—61no—
271C2×C3×Dic3—61no—
272C2×C3×Dic3—61no—
273C2×C3×Dic3—61no—
274C2×C3×Dic3—61no—
275C2×C3×Dic3—121no—
276C2×C3×Dic3—121no—
277C2×C3×Dic3—121no—
278C2×C3×Dic3—121no—
279C2×C3×Dic3—121no—
280C2×C3×Dic3—121no—
281C2×C3×Dic3C4×D312yes—
282C2×C3×Dic3C2×Dic312yes—
283#388—271noSylow
284C2×C33#11711yescharacteristic
285C2×C33C4×D411yescharacteristic
286C2×C33C4×D411yescharacteristic
287C2×C33#12111yescharacteristic
288C2×C33#12311yescharacteristic
289C2×C33#12411yescharacteristic
290C2×C33#12611yescharacteristic
291C32×D3—42no—
292C24×C3—31no—
293C24×C3—31no—
294C24×C3—61no—
295C23×D3D3211yescharacteristic
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C22×C3×C4—91no—
303C22×C3×C4—91no—
304C22×C3×C4—91no—
305C22×Dic3—31no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—31no—
309C22×Dic3—31no—
310C22×Dic3—31no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3—91no—
315C22×Dic3—91no—
316C22×Dic3—91no—
317C22×Dic3—181no—
318C22×Dic3—181no—
319C22×Dic3—181no—
320C22×Dic3—361no—
321C22×Dic3D3211yescharacteristic
322C22×Dic3D3211yescharacteristic
323C3×C4⋊C4—182no—
324C3×C22⋊C4—94no—
325C3×C22⋊C4—182no—
326#217—34no—
327#217—62no—
328#217—182no—
329#217—182no—
330#217—184no—
331(C2×D3)⋊C4—34no—
332(C2×D3)⋊C4—62no—
333(C2×D3)⋊C4—182no—
334C4⋊Dic3—62no—
335Dic3⋊C4—62no—
336C4×Dic3—182no—
337C4×Dic3—182no—
338C4×Dic3—182no—
339C22×C32—21no—
340C22×C32—21no—
341C22×C32—21no—
342C22×C32—21no—
343C22×C32—21no—
344C22×C32—21no—
345C22×C32—21no—
346C22×C32—21no—
347C22×C32—21no—
348C22×C32—21no—
349C22×C32—21no—
350C22×C32—21no—
351C22×C32—21no—
352C22×C32—21no—
353C22×C32—21no—
354C22×C32—21no—
355C22×C32—21no—
356C22×C32—21no—
357C22×C32—21no—
358C22×C32—21no—
359C22×C32—21no—
360C22×C32—41no—
361C22×C32—41no—
362C22×C32—41no—
363C22×C32—41no—
364C22×C32—41no—
365C22×C32—41no—
366C22×C32—41no—
367C22×C32—62no—
368C22×C32—62no—
369C22×C32—62no—
370C22×C32—121no—
371C22×C32—121no—
372C22×C32—121no—
373C22×C32—121no—
374C22×C32C2×C4×D311yescharacteristic
375C22×C32C2×C4×D311yescharacteristic
376C22×C32#23511yescharacteristic
377C22×C32#23511yescharacteristic
378C22×C32#23511yescharacteristic
379C22×C32#23511yescharacteristic
380C22×C32D3×D411yescharacteristic
381C22×C32D3×D411yescharacteristic
382C22×C32D3×D411yescharacteristic
383C22×C32D3×D411yescharacteristic
384C22×C32#23711yescharacteristic
385C22×C32#23711yescharacteristic
386C22×C32#23711yescharacteristic
387C22×C32#23711yescharacteristic
388C22×C32#23711yescharacteristic
389C22×C32#23711yescharacteristic
390C22×C32#23911yescharacteristic
391C22×C32#23911yescharacteristic
392C22×C32C22×Dic311yescharacteristic
393C22×C32C2×#6711yescharacteristic
394C22×C32C2×#6711yescharacteristic
395C2×C3×D3—24no—
396C2×C3×D3—22no—
397C2×C3×D3—22no—
398C2×C3×D3—22no—
399C2×C3×D3—22no—
400C2×C3×D3—22no—
401C2×C3×D3—22no—
402C2×C3×D3—42no—
403C2×C3×D3—42no—
404C2×C3×D3—42no—
405C2×C3×D3—42no—
406C2×C3×D3—42no—
407C2×C3×D3—42no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C32×C4—62no—
417C32×C4—121no—
418C3⋊Dic3—22no—
419C3⋊Dic3—22no—
420C3⋊Dic3—22no—
421C3⋊Dic3—122no—
422C3⋊Dic3—122no—
423C3⋊Dic3—122no—
424C3⋊Dic3—124no—
425C3⋊Dic3—121no—
426C3⋊Dic3—121no—
427C3⋊Dic3—121no—
428C3×Dic3—22no—
429C3×Dic3—22no—
430C3×Dic3—42no—
431C3×Dic3—42no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—62no—
435C3×Dic3—62no—
436C3×Dic3—62no—
437C3×Dic3—62no—
438C3×Dic3—62no—
439C3×Dic3—62no—
440C3×Dic3—122no—
441C3×Dic3—122no—
442C3×Dic3—122no—
443C2×C4⋊C4—91no—
444C2×C22⋊C4—91no—
445C2×C22⋊C4—91no—
446C2×C22⋊C4—271no—
447C2×C42—271no—
448#95—271no—
449#95—271no—
450C33#38811yescharacteristic, complemented, Sylow
451C23×C3—21no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—32no—
455C23×C3—32no—
456C23×C3—41no—
457C23×C3—62no—
458C23×C3—62no—
459C23×C3—62no—
460C23×C3—61no—
461C23×C3—61no—
462C23×C3—61no—
463C23×C3—61no—
464C23×C3—61no—
465C23×C3—61no—
466C23×C3—61no—
467C23×C3—61no—
468C23×C3—61no—
469C23×C3—61no—
470C23×C3—61no—
471C23×C3—61no—
472C23×C3—121no—
473C23×C3—121no—
474C23×C3—121no—
475C23×C3—121no—
476C23×C3C2×D3211yescharacteristic
477C23×C3C2×D3211yescharacteristic
478C23×C3C2×D3211yescharacteristic
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—21no—
483C22×D3—21no—
484C22×D3—21no—
485C22×D3D3×Dic312yes—
486C2×C3×C4—32no—
487C2×C3×C4—32no—
488C2×C3×C4—62no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—62no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—92no—
501C2×C3×C4—92no—
502C2×C3×C4—92no—
503C2×C3×C4—121no—
504C2×C3×C4—121no—
505C2×C3×C4—121no—
506C2×C3×C4—121no—
507C2×C3×C4—181no—
508C2×C3×C4—181no—
509C2×C3×C4—181no—
510C2×C3×C4—181no—
511C2×C3×C4—181no—
512C2×C3×C4—181no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—32no—
519C2×Dic3—32no—
520C2×Dic3—32no—
521C2×Dic3—32no—
522C2×Dic3—32no—
523C2×Dic3—32no—
524C2×Dic3—62no—
525C2×Dic3—62no—
526C2×Dic3—62no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—121no—
540C2×Dic3—121no—
541C2×Dic3—121no—
542C2×Dic3—121no—
543C2×Dic3—121no—
544C2×Dic3—121no—
545C2×Dic3—182no—
546C2×Dic3—182no—
547C2×Dic3—182no—
548C2×Dic3—181no—
549C2×Dic3—181no—
550C2×Dic3—181no—
551C2×Dic3—181no—
552C2×Dic3—181no—
553C2×Dic3—181no—
554C2×Dic3—181no—
555C2×Dic3—181no—
556C2×Dic3—181no—
557C2×Dic3—361no—
558C2×Dic3—361no—
559C2×Dic3—361no—
560C2×Dic3—361no—
561C2×Dic3—361no—
562C2×Dic3—361no—
563C2×Dic3—362no—
564C2×Dic3—362no—
565C2×Dic3—362no—
566C2×Dic3D3×Dic312yes—
567C2×C32—21no—
568C2×C32—21no—
569C2×C32—21no—
570C2×C32—21no—
571C2×C32—21no—
572C2×C32—21no—
573C2×C32—21no—
574C2×C32—21no—
575C2×C32—21no—
576C2×C32—21no—
577C2×C32—21no—
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—21no—
581C2×C32—21no—
582C2×C32—21no—
583C2×C32—21no—
584C2×C32—21no—
585C2×C32—21no—
586C2×C32—21no—
587C2×C32—21no—
588C2×C32—41no—
589C2×C32—41no—
590C2×C32—41no—
591C2×C32—41no—
592C2×C32—41no—
593C2×C32—41no—
594C2×C32—41no—
595C2×C32—122no—
596C2×C32#87711yescharacteristic
597C2×C32#87911yescharacteristic
598C2×C32#87911yescharacteristic
599C2×C32#67⋊C411yescharacteristic
600C2×C32#88311yescharacteristic
601C2×C32#88411yescharacteristic
602C2×C32#88511yescharacteristic
603C2×C32#88511yescharacteristic
604C2×C32#89211yescharacteristic
605C2×C32#89311yescharacteristic
606C2×C32#89411yescharacteristic
607C2×C32#89811yescharacteristic
608C2×C32#92611yescharacteristic
609C2×C32C4×#6711yescharacteristic
610C2×C32C4×#6711yescharacteristic
611C2×C32D4×Dic311yescharacteristic
612C2×C32D4×Dic311yescharacteristic
613C2×C32#93511yescharacteristic
614C2×C32#93811yescharacteristic
615C2×C32#93911yescharacteristic
616C2×C32#94711yescharacteristic
617C3×D3—44no—
618C3×D3—42no—
619C3×D3—42no—
620C24—31no—
621C22×C4—31no—
622C22×C4—31no—
623C22×C4—91no—
624C22×C4—91no—
625C22×C4—91no—
626C22×C4—271no—
627C4⋊C4—182no—
628C22⋊C4—94no—
629C22⋊C4—182no—
630C22⋊C4—542no—
631C42—542no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—64no—
661C22×C3—62no—
662C22×C3—62no—
663C22×C3—62no—
664C22×C3—62no—
665C22×C3—62no—
666C22×C3—62no—
667C22×C3—122no—
668C22×C3—122no—
669C22×C3—122no—
670C22×C3—122no—
671C22×C3—122no—
672C22×C3—122no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3—121no—
676C22×C3—121no—
677C22×C3—121no—
678C22×C3—121no—
679C22×C3—121no—
680C22×C3—121no—
681C22×C3#379511yescharacteristic
682C22×C3#379511yescharacteristic
683C22×C3#379611yescharacteristic
684C22×C3#379611yescharacteristic
685C22×C3#379911yescharacteristic
686C22×C3#379911yescharacteristic
687C22×C3C4×D3211yescharacteristic
688C22×C3#380211yescharacteristic
689C22×C3C2×D3×Dic311yescharacteristic
690C22×C3C2×D3×Dic311yescharacteristic
691C22×C3#380411yescharacteristic
692C22×C3#380411yescharacteristic
693C22×C3#380411yescharacteristic
694C22×C3#380411yescharacteristic
695C22×C3#380511yescharacteristic
696C22×C3#380511yescharacteristic
697C22×C3D3×#6711yescharacteristic
698C22×C3D3×#6711yescharacteristic
699C22×C3D3×#6711yescharacteristic
700C22×C3D3×#6711yescharacteristic
701C22×C3#381111yescharacteristic
702C2×D3—22no—
703C2×D3—22no—
704C2×D3—22no—
705C2×D3—41no—
706C2×D3—41no—
707C2×D3—41no—
708C2×D3—41no—
709C3×C4—62no—
710C3×C4—62no—
711C3×C4—122no—
712C3×C4—122no—
713C3×C4—121no—
714C3×C4—121no—
715C3×C4—182no—
716C3×C4—182no—
717C3×C4—182no—
718Dic3—22no—
719Dic3—41no—
720Dic3—62no—
721Dic3—62no—
722Dic3—62no—
723Dic3—62no—
724Dic3—62no—
725Dic3—62no—
726Dic3—122no—
727Dic3—122no—
728Dic3—122no—
729Dic3—362no—
730Dic3—362no—
731Dic3—362no—
732Dic3—364no—
733Dic3—361no—
734Dic3—361no—
735Dic3—361no—
736C32—21no—
737C32—21no—
738C32—21no—
739C32—41no—
740C32#494411yescharacteristic, complemented
741C32#495111yescharacteristic, complemented
742C32#499011yescharacteristic, complemented
743C23—32no—
744C23—61no—
745C23—61no—
746C23—61no—
747C23—61no—
748C23—61no—
749C23—61no—
750C23D3311yescharacteristic
751C2×C4—32no—
752C2×C4—61no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—92no—
758C2×C4—92no—
759C2×C4—92no—
760C2×C4—181no—
761C2×C4—181no—
762C2×C4—181no—
763C2×C4—181no—
764C2×C4—181no—
765C2×C4—181no—
766C2×C4—541no—
767C2×C4—541no—
768C2×C4—541no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—21no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—21no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—41no—
791C2×C3—41no—
792C2×C3—41no—
793C2×C3—41no—
794C2×C3—41no—
795C2×C3—41no—
796C2×C3—41no—
797C2×C3—124no—
798C2×C3—122no—
799C2×C3—122no—
800C2×C3#6384111yescharacteristic
801C2×C3#6385411yescharacteristic
802C2×C3#6385811yescharacteristic
803C2×C3#6386111yescharacteristic
804C2×C3#6387811yescharacteristic
805C2×C3#6387911yescharacteristic
806C2×C3#6388411yescharacteristic
807C2×C3#6388511yescharacteristic
808C2×C3#6389811yescharacteristic
809C2×C3#6390411yescharacteristic
810C2×C3#6390711yescharacteristic
811C2×C3#6390711yescharacteristic
812C2×C3#6395311yescharacteristic
813C2×C3#6395511yescharacteristic
814C2×C3#6395611yescharacteristic
815C2×C3#6395811yescharacteristic
816C2×C3#6396911yescharacteristic
817C2×C3#6397011yescharacteristic
818C2×C3Dic3×#6711yescharacteristic
819C2×C3Dic3×#6711yescharacteristic
820C2×C3#67⋊Dic311yescharacteristic
821D3—42no—
822C22—62no—
823C22—62no—
824C22—62no—
825C22—121no—
826C22—121no—
827C22—121no—
828C22—121no—
829C22D32×Dic311yescharacteristic
830C22#8895211yescharacteristic
831C22#8895311yescharacteristic
832C22#8896111yescharacteristic
833C22#8896111yescharacteristic
834C22#8896211yescharacteristic
835C22#8896211yescharacteristic
836C4—62no—
837C4—121no—
838C4—182no—
839C4—182no—
840C4—182no—
841C4—1081no—
842C3—21no—
843C3—21no—
844C3—21no—
845C3—41no—
846C3#1059128511yescharacteristic, complemented
847C3#1059130711yescharacteristic, complemented
848C3#1059170111yescharacteristic, complemented
849C2—122no—
850C2#1172291411yescharacteristic
851C2#1172292411yescharacteristic
852C2#1172292711yescharacteristic
853C2#1172296511yescharacteristic
854C2#1172299411yescharacteristic
855C2#1172300511yescharacteristic
856C2#1172302611yescharacteristic
subgroupG/H
center, Frattini, hypercenterC23D33
commutatorC22×C33C22×C4
Fitting, socle, cosocleC23×C33C23
prime radicalC23×C32×D3C22
hypocenterC33#388
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×#88813C2semidirect
3. C2×C3×Dic3⋊Dic3C2semidirect
6. #11722061C2semidirect
7. #11722061C2semidirect
22. C3×(C2×D3)⋊Dic3C4semidirect
30. C2×Dic3⋊Dic3D3semidirect
119. (C2×D3)⋊Dic3Dic3semidirect
450. C33#388semidirect
740. C32#4944semidirect
741. C32#4951semidirect
742. C32#4990semidirect
846. C3#10591285semidirect
847. C3#10591307semidirect
848. C3#10591701semidirect

Maximal subgroups

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

subgroupindex
C2×#888132
C2×(C2×D3)⋊(C3⋊Dic3)2
C2×C3×Dic3⋊Dic32
C2×C3×(C2×D3)⋊Dic32
#117220612
#105917013
#105913073
#105912853