Finite Group Databasebeta

← #13156785

Subgroups — #13156785

Order 1728.

946 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic3⋊(C3⋊Dic3)C211yesmaximal, characteristic
2C2×Dic3×C3⋊Dic3C211yesmaximal, characteristic
3C2×C3×#3724C211yesmaximal, characteristic
4#11722082C211yesmaximal, characteristic
5#11722061C211yesmaximal, characteristic
6C3×#63579C211yesmaximal, characteristic
7C3×#63579C211yesmaximal, characteristic
8#10591334—31nomaximal
9#10591271—31nomaximal
10#10591254—31nomaximal
11C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
12C22×C3×C3⋊Dic3C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C32×Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18Dic3⋊(C3⋊Dic3)C414yescomplemented
19Dic3×C3⋊Dic3—22no—
20C3×#3724—22no—
21C2×C4⋊(C3⋊Dic3)—31no—
22C2×C4×C3⋊Dic3—31no—
23C2×C3×Dic3⋊C4—31no—
24C2×C3×Dic3⋊C4—31no—
25C2×#3724D311yescharacteristic
26C2×Dic3⋊Dic3—31no—
27C2×Dic3⋊Dic3—31no—
28C2×Dic3⋊Dic3—61no—
29C2×Dic32—31no—
30C2×Dic32—31no—
31C2×Dic32—61no—
32#63658—31no—
33C3×C3⋊#95—31no—
34C3×C3⋊#95—31no—
35C3×C3⋊#95—31no—
36C3×C3⋊#95—31no—
37#63579—31no—
38#63579—31no—
39#63579—31no—
40#63579—31no—
41#63579—31no—
42#63579—61no—
43#63579D311yescharacteristic
44#63579D311yescharacteristic
45C23×C33C2311yescharacteristic
46C2×C3⋊(C3⋊Dic3)—21no—
47C2×C3⋊(C3⋊Dic3)—21no—
48C2×C3⋊(C3⋊Dic3)C2×C412yes—
49C2×C3×C3⋊Dic3—21no—
50C2×C3×C3⋊Dic3—21no—
51C2×C3×C3⋊Dic3—21no—
52C2×C3×C3⋊Dic3—21no—
53C2×C3×C3⋊Dic3—21no—
54C2×C3×C3⋊Dic3—21no—
55C2×C3×C3⋊Dic3—21no—
56C2×C3×C3⋊Dic3C2×C412yes—
57C2×C3×C3⋊Dic3Q812yes—
58C2×C32×Dic3—21no—
59C2×C32×Dic3—21no—
60C2×C32×Dic3—21no—
61C2×C32×Dic3—21no—
62C2×C32×Dic3—21no—
63C2×C32×Dic3—21no—
64C2×C32×Dic3—21no—
65C2×C32×Dic3C2×C412yes—
66C2×C32×Dic3D412yes—
67#4978—91no—
68#4654—91no—
69#4653—91no—
70C22×C32×C4—31no—
71C22×C32×C4—31no—
72C22×C32×C4—31no—
73C22×C3⋊Dic3—31no—
74C22×C3⋊Dic3—31no—
75C22×C3⋊Dic3—31no—
76C22×C3⋊Dic3—61no—
77C22×C3⋊Dic3—61no—
78C22×C3⋊Dic3—61no—
79C22×C3⋊Dic3—121no—
80C22×C3⋊Dic3C2×D311yescharacteristic
81C22×C3⋊Dic3C2×D311yescharacteristic
82C22×C3⋊Dic3C2×D311yescharacteristic
83C22×C3×Dic3—21no—
84C22×C3×Dic3—21no—
85C22×C3×Dic3—21no—
86C22×C3×Dic3—31no—
87C22×C3×Dic3—31no—
88C22×C3×Dic3—31no—
89C22×C3×Dic3—31no—
90C22×C3×Dic3—31no—
91C22×C3×Dic3—31no—
92C22×C3×Dic3—61no—
93C22×C3×Dic3—61no—
94C22×C3×Dic3—61no—
95C22×C3×Dic3C2×D311yescharacteristic
96C22×C3×Dic3C2×D311yescharacteristic
97C22×C3×Dic3C2×D311yescharacteristic
98C22×C3×Dic3C2×D311yescharacteristic
99C22×C3×Dic3C2×D311yescharacteristic
100C22×C3×Dic3C2×D311yescharacteristic
101C4⋊(C3⋊Dic3)—34no—
102C4×C3⋊Dic3—62no—
103C3×Dic3⋊C4—62no—
104C3×Dic3⋊C4—62no—
105#3724—22no—
106Dic3⋊Dic3—34no—
107Dic3⋊Dic3—34no—
108Dic3⋊Dic3—64no—
109Dic32—64no—
110Dic32—62no—
111Dic32—62no—
112C22×C33C22×C411yescharacteristic
113C22×C33C2×D411yescharacteristic
114C22×C33C2×Q811yescharacteristic
115C22×C33#4111yescharacteristic
116C22×C33#4111yescharacteristic
117C22×C33#4111yescharacteristic
118C22×C33#4111yescharacteristic
119C3⋊(C3⋊Dic3)—22no—
120C3×C3⋊Dic3—22no—
121C3×C3⋊Dic3—22no—
122C3×C3⋊Dic3—41no—
123C32×Dic3—22no—
124C32×Dic3—22no—
125C32×Dic3—41no—
126C2×C3×C4⋊C4—91no—
127C2×C4⋊Dic3—91no—
128C2×C4⋊Dic3—91no—
129C2×C4⋊Dic3—181no—
130C2×Dic3⋊C4—31no—
131C2×Dic3⋊C4—31no—
132C2×Dic3⋊C4—91no—
133C2×C4×Dic3—91no—
134C2×C4×Dic3—91no—
135C2×C4×Dic3—91no—
136C2×C4×Dic3—181no—
137C3×#95—91no—
138C3×#95—91no—
139C3⋊#95—31no—
140C3⋊#95—31no—
141C3⋊#95—31no—
142C3⋊#95—31no—
143C3⋊#95—91no—
144C3⋊#95—91no—
145C3⋊#95—91no—
146C3⋊#95—91no—
147C3⋊#95—91no—
148C3⋊#95—91no—
149C3⋊#95—181no—
150C23×C32—21no—
151C23×C32—21no—
152C23×C32—21no—
153C23×C32—41no—
154C23×C32C22×D311yescharacteristic
155C23×C32C22×D311yescharacteristic
156C23×C32C22×D311yescharacteristic
157C2×C32×C4—32no—
158C2×C32×C4—32no—
159C2×C32×C4—61no—
160C2×C32×C4—61no—
161C2×C32×C4—61no—
162C2×C32×C4—61no—
163C2×C32×C4—61no—
164C2×C32×C4—61no—
165C2×C32×C4—61no—
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—32no—
174C2×C3⋊Dic3—32no—
175C2×C3⋊Dic3—32no—
176C2×C3⋊Dic3—62no—
177C2×C3⋊Dic3—62no—
178C2×C3⋊Dic3—62no—
179C2×C3⋊Dic3—61no—
180C2×C3⋊Dic3—61no—
181C2×C3⋊Dic3—62no—
182C2×C3⋊Dic3—62no—
183C2×C3⋊Dic3—61no—
184C2×C3⋊Dic3—61no—
185C2×C3⋊Dic3—61no—
186C2×C3⋊Dic3—61no—
187C2×C3⋊Dic3—122no—
188C2×C3⋊Dic3—121no—
189C2×C3⋊Dic3—121no—
190C2×C3⋊Dic3—121no—
191C2×C3⋊Dic3—121no—
192C2×C3⋊Dic3—122no—
193C2×C3⋊Dic3—122no—
194C2×C3⋊Dic3Dic612yes—
195C2×C3⋊Dic3C4×D312yes—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—21no—
205C2×C3×Dic3—21no—
206C2×C3×Dic3—21no—
207C2×C3×Dic3—21no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—21no—
210C2×C3×Dic3—21no—
211C2×C3×Dic3—21no—
212C2×C3×Dic3—21no—
213C2×C3×Dic3—21no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3—22no—
216C2×C3×Dic3—22no—
217C2×C3×Dic3—32no—
218C2×C3×Dic3—32no—
219C2×C3×Dic3—32no—
220C2×C3×Dic3—32no—
221C2×C3×Dic3—41no—
222C2×C3×Dic3—41no—
223C2×C3×Dic3—62no—
224C2×C3×Dic3—62no—
225C2×C3×Dic3—62no—
226C2×C3×Dic3—62no—
227C2×C3×Dic3—61no—
228C2×C3×Dic3—61no—
229C2×C3×Dic3—61no—
230C2×C3×Dic3—61no—
231C2×C3×Dic3—61no—
232C2×C3×Dic3—61no—
233C2×C3×Dic3—61no—
234C2×C3×Dic3—61no—
235C2×C3×Dic3—62no—
236C2×C3×Dic3—61no—
237C2×C3×Dic3—61no—
238C2×C3×Dic3—61no—
239C2×C3×Dic3—61no—
240C2×C3×Dic3—61no—
241C2×C3×Dic3—61no—
242C2×C3×Dic3—121no—
243C2×C3×Dic3—121no—
244C2×C3×Dic3—121no—
245C2×C3×Dic3—121no—
246C2×C3×Dic3C4×D312yes—
247C2×C3×Dic3C4×D312yes—
248C2×C3×Dic3D1212yes—
249C2×C3×Dic3#6712yes—
250#387—271noSylow
251C2×C33#11711yescharacteristic
252C2×C33C4×D411yescharacteristic
253C2×C33C4×Q811yescharacteristic
254C2×C33C22⋊Q811yescharacteristic
255C2×C33#12311yescharacteristic
256C2×C33#12511yescharacteristic
257C2×C33#12611yescharacteristic
258C22×C3×C4—31no—
259C22×C3×C4—31no—
260C22×C3×C4—31no—
261C22×C3×C4—31no—
262C22×C3×C4—31no—
263C22×C3×C4—31no—
264C22×C3×C4—61no—
265C22×C3×C4—61no—
266C22×C3×C4—61no—
267C22×C3×C4—91no—
268C22×C3×C4—91no—
269C22×C3×C4—91no—
270C22×Dic3—31no—
271C22×Dic3—31no—
272C22×Dic3—31no—
273C22×Dic3—31no—
274C22×Dic3—31no—
275C22×Dic3—31no—
276C22×Dic3—61no—
277C22×Dic3—61no—
278C22×Dic3—61no—
279C22×Dic3—91no—
280C22×Dic3—91no—
281C22×Dic3—91no—
282C22×Dic3—181no—
283C22×Dic3—181no—
284C22×Dic3—181no—
285C22×Dic3—361no—
286C22×Dic3D3211yescharacteristic
287C22×Dic3D3211yescharacteristic
288C22×Dic3D3211yescharacteristic
289C3×C4⋊C4—182no—
290C4⋊Dic3—94no—
291C4⋊Dic3—94no—
292C4⋊Dic3—184no—
293Dic3⋊C4—62no—
294Dic3⋊C4—62no—
295Dic3⋊C4—94no—
296C4×Dic3—182no—
297C4×Dic3—182no—
298C4×Dic3—184no—
299C4×Dic3—182no—
300C22×C32—21no—
301C22×C32—21no—
302C22×C32—21no—
303C22×C32—21no—
304C22×C32—21no—
305C22×C32—21no—
306C22×C32—21no—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32—21no—
310C22×C32—21no—
311C22×C32—21no—
312C22×C32—21no—
313C22×C32—21no—
314C22×C32—21no—
315C22×C32—21no—
316C22×C32—21no—
317C22×C32—21no—
318C22×C32—21no—
319C22×C32—21no—
320C22×C32—21no—
321C22×C32—41no—
322C22×C32—41no—
323C22×C32—41no—
324C22×C32—41no—
325C22×C32—41no—
326C22×C32—41no—
327C22×C32—41no—
328C22×C32C2×Dic611yescharacteristic
329C22×C32C2×C4×D311yescharacteristic
330C22×C32C2×C4×D311yescharacteristic
331C22×C32C2×C4×D311yescharacteristic
332C22×C32C2×D1211yescharacteristic
333C22×C32#23511yescharacteristic
334C22×C32#23511yescharacteristic
335C22×C32#23511yescharacteristic
336C22×C32D3×D411yescharacteristic
337C22×C32#23711yescharacteristic
338C22×C32#23711yescharacteristic
339C22×C32#23711yescharacteristic
340C22×C32#23711yescharacteristic
341C22×C32#23711yescharacteristic
342C22×C32#23711yescharacteristic
343C22×C32#23711yescharacteristic
344C22×C32D3×Q811yescharacteristic
345C22×C32D3×Q811yescharacteristic
346C22×C32#23911yescharacteristic
347C22×C32#23911yescharacteristic
348C22×C32C2×#6711yescharacteristic
349C32×C4—62no—
350C32×C4—62no—
351C32×C4—121no—
352C3⋊Dic3—22no—
353C3⋊Dic3—22no—
354C3⋊Dic3—41no—
355C3⋊Dic3—62no—
356C3⋊Dic3—64no—
357C3⋊Dic3—62no—
358C3⋊Dic3—62no—
359C3⋊Dic3—122no—
360C3⋊Dic3—122no—
361C3⋊Dic3—124no—
362C3×Dic3—24no—
363C3×Dic3—24no—
364C3×Dic3—22no—
365C3×Dic3—22no—
366C3×Dic3—22no—
367C3×Dic3—22no—
368C3×Dic3—42no—
369C3×Dic3—41no—
370C3×Dic3—41no—
371C3×Dic3—64no—
372C3×Dic3—62no—
373C3×Dic3—62no—
374C3×Dic3—62no—
375C3×Dic3—62no—
376C3×Dic3—122no—
377C3×Dic3—122no—
378C3×Dic3—121no—
379C3×Dic3—121no—
380C2×C4⋊C4—91no—
381C2×C4⋊C4—271no—
382C2×C42—271no—
383#95—91no—
384#95—91no—
385#95—271no—
386#95—271no—
387C33#38711yescharacteristic, complemented, Sylow
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—41no—
392C23×C3C2×D3211yescharacteristic
393C23×C3C2×D3211yescharacteristic
394C23×C3C2×D3211yescharacteristic
395C2×C3×C4—32no—
396C2×C3×C4—32no—
397C2×C3×C4—32no—
398C2×C3×C4—32no—
399C2×C3×C4—62no—
400C2×C3×C4—62no—
401C2×C3×C4—62no—
402C2×C3×C4—62no—
403C2×C3×C4—62no—
404C2×C3×C4—62no—
405C2×C3×C4—61no—
406C2×C3×C4—61no—
407C2×C3×C4—61no—
408C2×C3×C4—61no—
409C2×C3×C4—61no—
410C2×C3×C4—61no—
411C2×C3×C4—61no—
412C2×C3×C4—61no—
413C2×C3×C4—62no—
414C2×C3×C4—61no—
415C2×C3×C4—61no—
416C2×C3×C4—61no—
417C2×C3×C4—61no—
418C2×C3×C4—61no—
419C2×C3×C4—61no—
420C2×C3×C4—92no—
421C2×C3×C4—92no—
422C2×C3×C4—121no—
423C2×C3×C4—121no—
424C2×C3×C4—181no—
425C2×C3×C4—181no—
426C2×C3×C4—181no—
427C2×C3×C4—181no—
428C2×C3×C4—181no—
429C2×C3×C4—181no—
430C2×C3×C4—181no—
431C2×Dic3—21no—
432C2×Dic3—21no—
433C2×Dic3—21no—
434C2×Dic3—21no—
435C2×Dic3—21no—
436C2×Dic3—21no—
437C2×Dic3—21no—
438C2×Dic3—32no—
439C2×Dic3—32no—
440C2×Dic3—32no—
441C2×Dic3—32no—
442C2×Dic3—62no—
443C2×Dic3—62no—
444C2×Dic3—62no—
445C2×Dic3—62no—
446C2×Dic3—61no—
447C2×Dic3—61no—
448C2×Dic3—61no—
449C2×Dic3—61no—
450C2×Dic3—61no—
451C2×Dic3—61no—
452C2×Dic3—61no—
453C2×Dic3—61no—
454C2×Dic3—62no—
455C2×Dic3—61no—
456C2×Dic3—61no—
457C2×Dic3—61no—
458C2×Dic3—61no—
459C2×Dic3—61no—
460C2×Dic3—61no—
461C2×Dic3—92no—
462C2×Dic3—92no—
463C2×Dic3—92no—
464C2×Dic3—121no—
465C2×Dic3—121no—
466C2×Dic3—121no—
467C2×Dic3—121no—
468C2×Dic3—182no—
469C2×Dic3—182no—
470C2×Dic3—182no—
471C2×Dic3—182no—
472C2×Dic3—182no—
473C2×Dic3—181no—
474C2×Dic3—181no—
475C2×Dic3—181no—
476C2×Dic3—181no—
477C2×Dic3—181no—
478C2×Dic3—181no—
479C2×Dic3—362no—
480C2×Dic3—361no—
481C2×Dic3—361no—
482C2×Dic3—361no—
483C2×Dic3—361no—
484C2×Dic3—362no—
485C2×Dic3—362no—
486C2×Dic3#62412yes—
487C2×Dic3#62612yes—
488C2×C32—21no—
489C2×C32—21no—
490C2×C32—21no—
491C2×C32—21no—
492C2×C32—21no—
493C2×C32—21no—
494C2×C32—21no—
495C2×C32—21no—
496C2×C32—21no—
497C2×C32—21no—
498C2×C32—21no—
499C2×C32—21no—
500C2×C32—21no—
501C2×C32—21no—
502C2×C32—21no—
503C2×C32—21no—
504C2×C32—21no—
505C2×C32—21no—
506C2×C32—21no—
507C2×C32—21no—
508C2×C32—21no—
509C2×C32—41no—
510C2×C32—41no—
511C2×C32—41no—
512C2×C32—41no—
513C2×C32—41no—
514C2×C32—41no—
515C2×C32—41no—
516C2×C32C4×Dic611yescharacteristic
517C2×C32C4×D1211yescharacteristic
518C2×C32#87711yescharacteristic
519C2×C32#87711yescharacteristic
520C2×C32#87811yescharacteristic
521C2×C32#87911yescharacteristic
522C2×C32#88311yescharacteristic
523C2×C32#88611yescharacteristic
524C2×C32#88711yescharacteristic
525C2×C32#88711yescharacteristic
526C2×C32#88911yescharacteristic
527C2×C32#88911yescharacteristic
528C2×C32#89011yescharacteristic
529C2×C32#89211yescharacteristic
530C2×C32#89311yescharacteristic
531C2×C32#89711yescharacteristic
532C2×C32#89811yescharacteristic
533C2×C32#89811yescharacteristic
534C2×C32C4×#6711yescharacteristic
535C2×C32#93511yescharacteristic
536C2×C32#94611yescharacteristic
537C22×C4—31no—
538C22×C4—31no—
539C22×C4—31no—
540C22×C4—91no—
541C22×C4—91no—
542C22×C4—91no—
543C22×C4—271no—
544C4⋊C4—182no—
545C4⋊C4—274no—
546C42—542no—
547C22×C3—21no—
548C22×C3—21no—
549C22×C3—21no—
550C22×C3—21no—
551C22×C3—21no—
552C22×C3—21no—
553C22×C3—21no—
554C22×C3—21no—
555C22×C3—21no—
556C22×C3—21no—
557C22×C3—21no—
558C22×C3—21no—
559C22×C3—21no—
560C22×C3—21no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—21no—
566C22×C3—21no—
567C22×C3—21no—
568C22×C3—41no—
569C22×C3—41no—
570C22×C3—41no—
571C22×C3—41no—
572C22×C3—41no—
573C22×C3—41no—
574C22×C3—41no—
575C22×C3D3×Dic611yescharacteristic
576C22×C3D3×Dic611yescharacteristic
577C22×C3#379511yescharacteristic
578C22×C3#379611yescharacteristic
579C22×C3#379611yescharacteristic
580C22×C3#379711yescharacteristic
581C22×C3#379811yescharacteristic
582C22×C3#379911yescharacteristic
583C22×C3#379911yescharacteristic
584C22×C3C4×D3211yescharacteristic
585C22×C3C4×D3211yescharacteristic
586C22×C3D3×D1211yescharacteristic
587C22×C3#380411yescharacteristic
588C22×C3#380511yescharacteristic
589C22×C3#380511yescharacteristic
590C22×C3#380511yescharacteristic
591C22×C3#380511yescharacteristic
592C22×C3#380511yescharacteristic
593C22×C3C2×#62411yescharacteristic
594C22×C3C2×#62611yescharacteristic
595C22×C3D3×#6711yescharacteristic
596C3×C4—64no—
597C3×C4—64no—
598C3×C4—62no—
599C3×C4—62no—
600C3×C4—62no—
601C3×C4—62no—
602C3×C4—122no—
603C3×C4—121no—
604C3×C4—121no—
605C3×C4—182no—
606C3×C4—182no—
607C3×C4—361no—
608Dic3—22no—
609Dic3—22no—
610Dic3—41no—
611Dic3—64no—
612Dic3—62no—
613Dic3—62no—
614Dic3—62no—
615Dic3—62no—
616Dic3—122no—
617Dic3—122no—
618Dic3—121no—
619Dic3—121no—
620Dic3—184no—
621Dic3—182no—
622Dic3—182no—
623Dic3—182no—
624Dic3—362no—
625Dic3—362no—
626Dic3—364no—
627C32—21no—
628C32—21no—
629C32—21no—
630C32—41no—
631C32#465311yescharacteristic, complemented
632C32#465411yescharacteristic, complemented
633C32#497811yescharacteristic, complemented
634C23D3311yescharacteristic
635C2×C4—32no—
636C2×C4—32no—
637C2×C4—61no—
638C2×C4—61no—
639C2×C4—61no—
640C2×C4—61no—
641C2×C4—61no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—92no—
645C2×C4—92no—
646C2×C4—181no—
647C2×C4—181no—
648C2×C4—181no—
649C2×C4—181no—
650C2×C4—181no—
651C2×C4—181no—
652C2×C4—181no—
653C2×C4—272no—
654C2×C4—541no—
655C2×C4—541no—
656C2×C3—21no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3—21no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—21no—
677C2×C3—41no—
678C2×C3—41no—
679C2×C3—41no—
680C2×C3—41no—
681C2×C3—41no—
682C2×C3—41no—
683C2×C3—41no—
684C2×C3#6383711yescharacteristic
685C2×C3#6383811yescharacteristic
686C2×C3#6384411yescharacteristic
687C2×C3#6384511yescharacteristic
688C2×C3#6384511yescharacteristic
689C2×C3#6384811yescharacteristic
690C2×C3#6386111yescharacteristic
691C2×C3#6386211yescharacteristic
692C2×C3#6387011yescharacteristic
693C2×C3#6387111yescharacteristic
694C2×C3#6387811yescharacteristic
695C2×C3#6387811yescharacteristic
696C2×C3#6388711yescharacteristic
697C2×C3#6389111yescharacteristic
698C2×C3#6389311yescharacteristic
699C2×C3#6389411yescharacteristic
700C2×C3C4×#62611yescharacteristic
701C2×C3#6390411yescharacteristic
702C2×C3#6395711yescharacteristic
703C2×C3#6396211yescharacteristic
704C2×C3#6396911yescharacteristic
705C22D3×#62411yescharacteristic
706C22D3×#62611yescharacteristic
707C22#8895711yescharacteristic
708C22#8896111yescharacteristic
709C22#8896311yescharacteristic
710C22#8896411yescharacteristic
711C22#8896511yescharacteristic
712C4—62no—
713C4—62no—
714C4—121no—
715C4—182no—
716C4—182no—
717C4—361no—
718C4—542no—
719C3—21no—
720C3—21no—
721C3—21no—
722C3—41no—
723C3#1059125411yescharacteristic, complemented
724C3#1059127111yescharacteristic, complemented
725C3#1059133411yescharacteristic, complemented
726C2#1172291711yescharacteristic
727C2#1172293311yescharacteristic
728C2#1172294311yescharacteristic
729C2#1172297411yescharacteristic
730C2#1172298911yescharacteristic
731C2#1172301811yescharacteristic
732C2#1172302711yescharacteristic
subgroupG/H
center, Frattini, hypercenterC23D33
commutatorC22×C33C22×C4
Fitting, socle, prime radical, cosocleC23×C33C23
hypocenterC33#387
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
18. Dic3⋊(C3⋊Dic3)C4semidirect
387. C33#387semidirect
631. C32#4653semidirect
632. C32#4654semidirect
633. C32#4978semidirect
723. C3#10591254semidirect
724. C3#10591271semidirect
725. C3#10591334semidirect

Maximal subgroups

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

subgroupindex
C2×Dic3⋊(C3⋊Dic3)2
C2×Dic3×C3⋊Dic32
C2×C3×#37242
#117220822
#117220612
C3×#635792
#105913343
#105912713
#105912543