Finite Group Databasebeta

← #13156802

Subgroups — #13156802

Order 1728.

898 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88815C211yesmaximal, characteristic
2C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic
3C2×C3×Dic32C211yesmaximal, characteristic
4#11722061C211yesmaximal, characteristic
5#11722061C211yesmaximal, characteristic
6#11722061C211yesmaximal, characteristic
7C3×#63579C211yesmaximal, characteristic
8#10591331—31nomaximal
9#10591270—31nomaximal
10#10591201—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
18#88815—22no—
19C3×Dic3⋊Dic3C414yescomplemented
20C3×Dic32—22no—
21C2×C3×C4⋊Dic3—31no—
22C2×C3×Dic3⋊C4—31no—
23C2×C3×C4×Dic3—31no—
24C2×C3×C4×Dic3—31no—
25C2×#3724—31no—
26C2×Dic3⋊Dic3—31no—
27C2×Dic3⋊Dic3—31no—
28C2×Dic3⋊Dic3D311yescharacteristic
29C2×Dic32D311yescharacteristic
30#63658—31no—
31#63658—31no—
32#63658—31no—
33C3×C3⋊#95—31no—
34C3×C3⋊#95—31no—
35#63579—31no—
36#63579—31no—
37#63579—31no—
38#63579—31no—
39#63579—31no—
40#63579—31no—
41#63579—61no—
42#63579—61no—
43#63579—61no—
44#63579D311yescharacteristic
45C23×C33C2311yescharacteristic
46C2×C3⋊(C3⋊Dic3)—21no—
47C2×C3⋊(C3⋊Dic3)—21no—
48C2×C3⋊(C3⋊Dic3)—21no—
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⋊Dic3D412yes—
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×Dic3C2×C412yes—
65C2×C32×Dic3C2×C412yes—
66C2×C32×Dic3Q812yes—
67#4980—91no—
68#4933—91no—
69#4654—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
101C3×C4⋊Dic3—34no—
102C3×Dic3⋊C4—34no—
103C3×C4×Dic3—62no—
104C3×C4×Dic3—62no—
105#3724—62no—
106Dic3⋊Dic3—62no—
107Dic3⋊Dic3—62no—
108Dic3⋊Dic3Dic314yescomplemented
109Dic32—22no—
110C22×C33C22×C411yescharacteristic
111C22×C33C2×D411yescharacteristic
112C22×C33C2×Q811yescharacteristic
113C22×C33#4111yescharacteristic
114C22×C33#4111yescharacteristic
115C22×C33#4111yescharacteristic
116C22×C33#4111yescharacteristic
117C3⋊(C3⋊Dic3)—41no—
118C3×C3⋊Dic3—22no—
119C3×C3⋊Dic3—22no—
120C3×C3⋊Dic3—41no—
121C32×Dic3—22no—
122C32×Dic3—22no—
123C32×Dic3—22no—
124C2×C3×C4⋊C4—91no—
125C2×C3×C42—91no—
126C2×C4⋊Dic3—31no—
127C2×C4⋊Dic3—91no—
128C2×Dic3⋊C4—31no—
129C2×Dic3⋊C4—91no—
130C2×Dic3⋊C4—91no—
131C2×C4×Dic3—31no—
132C2×C4×Dic3—31no—
133C3×#95—91no—
134C3⋊#95—31no—
135C3⋊#95—31no—
136C3⋊#95—91no—
137C3⋊#95—91no—
138C3⋊#95—91no—
139C3⋊#95—91no—
140C3⋊#95—91no—
141C3⋊#95—91no—
142C3⋊#95—91no—
143C3⋊#95—91no—
144C3⋊#95—91no—
145C3⋊#95—181no—
146C3⋊#95—181no—
147C3⋊#95—181no—
148C23×C32—21no—
149C23×C32—21no—
150C23×C32—21no—
151C23×C32—41no—
152C23×C32C22×D311yescharacteristic
153C23×C32C22×D311yescharacteristic
154C23×C32C22×D311yescharacteristic
155C2×C32×C4—32no—
156C2×C32×C4—32no—
157C2×C32×C4—32no—
158C2×C32×C4—61no—
159C2×C32×C4—61no—
160C2×C32×C4—61no—
161C2×C32×C4—61no—
162C2×C32×C4—61no—
163C2×C32×C4—61no—
164C2×C3⋊Dic3—21no—
165C2×C3⋊Dic3—21no—
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—61no—
172C2×C3⋊Dic3—61no—
173C2×C3⋊Dic3—61no—
174C2×C3⋊Dic3—62no—
175C2×C3⋊Dic3—62no—
176C2×C3⋊Dic3—62no—
177C2×C3⋊Dic3—61no—
178C2×C3⋊Dic3—61no—
179C2×C3⋊Dic3—61no—
180C2×C3⋊Dic3—61no—
181C2×C3⋊Dic3—61no—
182C2×C3⋊Dic3—61no—
183C2×C3⋊Dic3—121no—
184C2×C3⋊Dic3—121no—
185C2×C3⋊Dic3—121no—
186C2×C3⋊Dic3—121no—
187C2×C3⋊Dic3—121no—
188C2×C3⋊Dic3—121no—
189C2×C3⋊Dic3—122no—
190C2×C3⋊Dic3—122no—
191C2×C3⋊Dic3—122no—
192C2×C3⋊Dic3C2×Dic312yes—
193C2×C3⋊Dic3#6712yes—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—21no—
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—22no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—32no—
210C2×C3×Dic3—32no—
211C2×C3×Dic3—32no—
212C2×C3×Dic3—32no—
213C2×C3×Dic3—41no—
214C2×C3×Dic3—41no—
215C2×C3×Dic3—41no—
216C2×C3×Dic3—41no—
217C2×C3×Dic3—41no—
218C2×C3×Dic3—41no—
219C2×C3×Dic3—62no—
220C2×C3×Dic3—62no—
221C2×C3×Dic3—61no—
222C2×C3×Dic3—61no—
223C2×C3×Dic3—61no—
224C2×C3×Dic3—61no—
225C2×C3×Dic3—61no—
226C2×C3×Dic3—61no—
227C2×C3×Dic3—61no—
228C2×C3×Dic3—61no—
229C2×C3×Dic3—62no—
230C2×C3×Dic3—61no—
231C2×C3×Dic3—61no—
232C2×C3×Dic3—61no—
233C2×C3×Dic3—61no—
234C2×C3×Dic3—61no—
235C2×C3×Dic3—61no—
236C2×C3×Dic3—121no—
237C2×C3×Dic3—121no—
238C2×C3×Dic3—121no—
239C2×C3×Dic3—121no—
240C2×C3×Dic3—121no—
241C2×C3×Dic3—121no—
242C2×C3×Dic3Dic612yes—
243C2×C3×Dic3Dic612yes—
244C2×C3×Dic3C4×D312yes—
245C2×C3×Dic3C4×D312yes—
246C2×C3×Dic3C2×Dic312yes—
247C2×C3×Dic3C2×Dic312yes—
248#387—271noSylow
249C2×C33#11711yescharacteristic
250C2×C33C4×D411yescharacteristic
251C2×C33C4×Q811yescharacteristic
252C2×C33C22⋊Q811yescharacteristic
253C2×C33#12311yescharacteristic
254C2×C33#12511yescharacteristic
255C2×C33#12611yescharacteristic
256C22×C3×C4—31no—
257C22×C3×C4—31no—
258C22×C3×C4—31no—
259C22×C3×C4—31no—
260C22×C3×C4—31no—
261C22×C3×C4—31no—
262C22×C3×C4—61no—
263C22×C3×C4—61no—
264C22×C3×C4—61no—
265C22×C3×C4—91no—
266C22×C3×C4—91no—
267C22×C3×C4—91no—
268C22×Dic3—31no—
269C22×Dic3—31no—
270C22×Dic3—31no—
271C22×Dic3—31no—
272C22×Dic3—31no—
273C22×Dic3—31no—
274C22×Dic3—61no—
275C22×Dic3—61no—
276C22×Dic3—61no—
277C22×Dic3—91no—
278C22×Dic3—91no—
279C22×Dic3—91no—
280C22×Dic3—181no—
281C22×Dic3—181no—
282C22×Dic3—181no—
283C22×Dic3—361no—
284C22×Dic3D3211yescharacteristic
285C22×Dic3D3211yescharacteristic
286C22×Dic3D3211yescharacteristic
287C3×C4⋊C4—94no—
288C3×C42—182no—
289C4⋊Dic3—34no—
290C4⋊Dic3—182no—
291Dic3⋊C4—34no—
292Dic3⋊C4—182no—
293Dic3⋊C4—182no—
294C4×Dic3—62no—
295C4×Dic3—62no—
296C22×C32—21no—
297C22×C32—21no—
298C22×C32—21no—
299C22×C32—21no—
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—41no—
318C22×C32—41no—
319C22×C32—41no—
320C22×C32—41no—
321C22×C32—41no—
322C22×C32—41no—
323C22×C32—41no—
324C22×C32C2×Dic611yescharacteristic
325C22×C32C2×Dic611yescharacteristic
326C22×C32C2×C4×D311yescharacteristic
327C22×C32C2×C4×D311yescharacteristic
328C22×C32#23511yescharacteristic
329C22×C32#23511yescharacteristic
330C22×C32#23511yescharacteristic
331C22×C32#23511yescharacteristic
332C22×C32#23511yescharacteristic
333C22×C32#23511yescharacteristic
334C22×C32#23511yescharacteristic
335C22×C32D3×D411yescharacteristic
336C22×C32D3×D411yescharacteristic
337C22×C32#23711yescharacteristic
338C22×C32#23711yescharacteristic
339C22×C32#23711yescharacteristic
340C22×C32D3×Q811yescharacteristic
341C22×C32#23911yescharacteristic
342C22×C32#23911yescharacteristic
343C22×C32C22×Dic311yescharacteristic
344C22×C32C2×#6711yescharacteristic
345C32×C4—62no—
346C32×C4—62no—
347C32×C4—62no—
348C3⋊Dic3—22no—
349C3⋊Dic3—22no—
350C3⋊Dic3—41no—
351C3⋊Dic3—122no—
352C3⋊Dic3—122no—
353C3⋊Dic3—122no—
354C3⋊Dic3—124no—
355C3⋊Dic3—121no—
356C3⋊Dic3—121no—
357C3⋊Dic3—121no—
358C3×Dic3—22no—
359C3×Dic3—22no—
360C3×Dic3—22no—
361C3×Dic3—22no—
362C3×Dic3—22no—
363C3×Dic3—22no—
364C3×Dic3—42no—
365C3×Dic3—42no—
366C3×Dic3—42no—
367C3×Dic3—62no—
368C3×Dic3—62no—
369C3×Dic3—62no—
370C3×Dic3—62no—
371C3×Dic3—122no—
372C3×Dic3—122no—
373C3×Dic3—122no—
374C3×Dic3—121no—
375C3×Dic3—121no—
376C2×C4⋊C4—91no—
377C2×C4⋊C4—271no—
378C2×C42—91no—
379#95—91no—
380#95—271no—
381#95—271no—
382#95—271no—
383C33#38711yescharacteristic, complemented, Sylow
384C23×C3—21no—
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—41no—
388C23×C3C2×D3211yescharacteristic
389C23×C3C2×D3211yescharacteristic
390C23×C3C2×D3211yescharacteristic
391C2×C3×C4—32no—
392C2×C3×C4—32no—
393C2×C3×C4—32no—
394C2×C3×C4—32no—
395C2×C3×C4—32no—
396C2×C3×C4—32no—
397C2×C3×C4—62no—
398C2×C3×C4—62no—
399C2×C3×C4—62no—
400C2×C3×C4—61no—
401C2×C3×C4—61no—
402C2×C3×C4—61no—
403C2×C3×C4—61no—
404C2×C3×C4—61no—
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—92no—
413C2×C3×C4—92no—
414C2×C3×C4—121no—
415C2×C3×C4—121no—
416C2×C3×C4—121no—
417C2×C3×C4—121no—
418C2×C3×C4—121no—
419C2×C3×C4—121no—
420C2×C3×C4—181no—
421C2×C3×C4—181no—
422C2×C3×C4—181no—
423C2×C3×C4—181no—
424C2×C3×C4—181no—
425C2×C3×C4—181no—
426C2×C3×C4—181no—
427C2×Dic3—21no—
428C2×Dic3—21no—
429C2×Dic3—21no—
430C2×Dic3—21no—
431C2×Dic3—21no—
432C2×Dic3—21no—
433C2×Dic3—32no—
434C2×Dic3—32no—
435C2×Dic3—32no—
436C2×Dic3—32no—
437C2×Dic3—62no—
438C2×Dic3—62no—
439C2×Dic3—61no—
440C2×Dic3—61no—
441C2×Dic3—61no—
442C2×Dic3—61no—
443C2×Dic3—61no—
444C2×Dic3—61no—
445C2×Dic3—61no—
446C2×Dic3—61no—
447C2×Dic3—62no—
448C2×Dic3—61no—
449C2×Dic3—61no—
450C2×Dic3—61no—
451C2×Dic3—61no—
452C2×Dic3—61no—
453C2×Dic3—61no—
454C2×Dic3—121no—
455C2×Dic3—121no—
456C2×Dic3—121no—
457C2×Dic3—121no—
458C2×Dic3—121no—
459C2×Dic3—121no—
460C2×Dic3—182no—
461C2×Dic3—182no—
462C2×Dic3—182no—
463C2×Dic3—181no—
464C2×Dic3—181no—
465C2×Dic3—181no—
466C2×Dic3—181no—
467C2×Dic3—181no—
468C2×Dic3—181no—
469C2×Dic3—181no—
470C2×Dic3—181no—
471C2×Dic3—181no—
472C2×Dic3—361no—
473C2×Dic3—361no—
474C2×Dic3—361no—
475C2×Dic3—361no—
476C2×Dic3—361no—
477C2×Dic3—361no—
478C2×Dic3—362no—
479C2×Dic3—362no—
480C2×Dic3—362no—
481C2×Dic3D3×Dic312yes—
482C2×Dic3D3×Dic312yes—
483C2×Dic3#62712yes—
484C2×C32—21no—
485C2×C32—21no—
486C2×C32—21no—
487C2×C32—21no—
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—41no—
506C2×C32—41no—
507C2×C32—41no—
508C2×C32—41no—
509C2×C32—41no—
510C2×C32—41no—
511C2×C32—41no—
512C2×C32C4×Dic611yescharacteristic
513C2×C32C4×Dic611yescharacteristic
514C2×C32#87011yescharacteristic
515C2×C32#87211yescharacteristic
516C2×C32#87611yescharacteristic
517C2×C32#87711yescharacteristic
518C2×C32#87811yescharacteristic
519C2×C32#88311yescharacteristic
520C2×C32#88911yescharacteristic
521C2×C32#89011yescharacteristic
522C2×C32#89311yescharacteristic
523C2×C32#89411yescharacteristic
524C2×C32#89611yescharacteristic
525C2×C32#89811yescharacteristic
526C2×C32#89811yescharacteristic
527C2×C32#92411yescharacteristic
528C2×C32#92611yescharacteristic
529C2×C32C4×#6711yescharacteristic
530C2×C32#92911yescharacteristic
531C2×C32D4×Dic311yescharacteristic
532C2×C32Q8×Dic311yescharacteristic
533C22×C4—31no—
534C22×C4—31no—
535C22×C4—31no—
536C22×C4—91no—
537C22×C4—91no—
538C22×C4—91no—
539C22×C4—271no—
540C4⋊C4—94no—
541C4⋊C4—542no—
542C42—182no—
543C22×C3—21no—
544C22×C3—21no—
545C22×C3—21no—
546C22×C3—21no—
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—41no—
565C22×C3—41no—
566C22×C3—41no—
567C22×C3—41no—
568C22×C3—41no—
569C22×C3—41no—
570C22×C3—41no—
571C22×C3D3×Dic611yescharacteristic
572C22×C3D3×Dic611yescharacteristic
573C22×C3#379511yescharacteristic
574C22×C3#379611yescharacteristic
575C22×C3#379811yescharacteristic
576C22×C3#379811yescharacteristic
577C22×C3#379811yescharacteristic
578C22×C3#379911yescharacteristic
579C22×C3#379911yescharacteristic
580C22×C3#379911yescharacteristic
581C22×C3C4×D3211yescharacteristic
582C22×C3#380211yescharacteristic
583C22×C3C2×D3×Dic311yescharacteristic
584C22×C3C2×D3×Dic311yescharacteristic
585C22×C3#380411yescharacteristic
586C22×C3#380411yescharacteristic
587C22×C3#380411yescharacteristic
588C22×C3#380411yescharacteristic
589C22×C3C2×#62711yescharacteristic
590C22×C3D3×#6711yescharacteristic
591C22×C3D3×#6711yescharacteristic
592C3×C4—62no—
593C3×C4—62no—
594C3×C4—62no—
595C3×C4—62no—
596C3×C4—62no—
597C3×C4—62no—
598C3×C4—122no—
599C3×C4—122no—
600C3×C4—122no—
601C3×C4—182no—
602C3×C4—182no—
603C3×C4—361no—
604Dic3—22no—
605Dic3—22no—
606Dic3—22no—
607Dic3—62no—
608Dic3—62no—
609Dic3—62no—
610Dic3—62no—
611Dic3—122no—
612Dic3—122no—
613Dic3—122no—
614Dic3—121no—
615Dic3—121no—
616Dic3—362no—
617Dic3—362no—
618Dic3—362no—
619Dic3—364no—
620Dic3—361no—
621Dic3—361no—
622Dic3—361no—
623C32—21no—
624C32—21no—
625C32—21no—
626C32—41no—
627C32#465411yescharacteristic, complemented
628C32#493311yescharacteristic, complemented
629C32#498011yescharacteristic, complemented
630C23D3311yescharacteristic
631C2×C4—32no—
632C2×C4—32no—
633C2×C4—32no—
634C2×C4—61no—
635C2×C4—61no—
636C2×C4—61no—
637C2×C4—61no—
638C2×C4—61no—
639C2×C4—61no—
640C2×C4—92no—
641C2×C4—92no—
642C2×C4—181no—
643C2×C4—181no—
644C2×C4—181no—
645C2×C4—181no—
646C2×C4—181no—
647C2×C4—181no—
648C2×C4—181no—
649C2×C4—541no—
650C2×C4—541no—
651C2×C4—541no—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—21no—
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—41no—
674C2×C3—41no—
675C2×C3—41no—
676C2×C3—41no—
677C2×C3—41no—
678C2×C3—41no—
679C2×C3—41no—
680C2×C3Dic3×Dic611yescharacteristic
681C2×C3Dic3×Dic611yescharacteristic
682C2×C3#6384611yescharacteristic
683C2×C3#6384811yescharacteristic
684C2×C3#6385011yescharacteristic
685C2×C3#6385111yescharacteristic
686C2×C3#6385411yescharacteristic
687C2×C3#6385511yescharacteristic
688C2×C3#6386711yescharacteristic
689C2×C3#6386811yescharacteristic
690C2×C3#6386811yescharacteristic
691C2×C3#6386911yescharacteristic
692C2×C3#6387711yescharacteristic
693C2×C3#6389811yescharacteristic
694C2×C3#6389911yescharacteristic
695C2×C3#6390411yescharacteristic
696C2×C3#6390511yescharacteristic
697C2×C3C4×#62711yescharacteristic
698C2×C3#6395511yescharacteristic
699C2×C3#6396411yescharacteristic
700C2×C3Dic3×#6711yescharacteristic
701C22D32×Dic311yescharacteristic
702C22#8895311yescharacteristic
703C22D3×#62711yescharacteristic
704C22#8895911yescharacteristic
705C22#8896011yescharacteristic
706C22#8896211yescharacteristic
707C22#8896511yescharacteristic
708C4—62no—
709C4—62no—
710C4—62no—
711C4—182no—
712C4—182no—
713C4—361no—
714C4—1081no—
715C3—21no—
716C3—21no—
717C3—21no—
718C3—41no—
719C3#1059120111yescharacteristic, complemented
720C3#1059127011yescharacteristic, complemented
721C3#1059133111yescharacteristic, complemented
722C2#1172291311yescharacteristic
723C2#1172292711yescharacteristic
724C2Dic3×#62711yescharacteristic
725C2#1172297811yescharacteristic
726C2#1172299511yescharacteristic
727C2#1172301211yescharacteristic
728C2#1172302111yescharacteristic
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
19. C3×Dic3⋊Dic3C4semidirect
108. Dic3⋊Dic3Dic3semidirect
383. C33#387semidirect
627. C32#4654semidirect
628. C32#4933semidirect
629. C32#4980semidirect
719. C3#10591201semidirect
720. C3#10591270semidirect
721. C3#10591331semidirect

Maximal subgroups

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

subgroupindex
C2×#888152
C2×C3×Dic3⋊Dic32
C2×C3×Dic322
#117220612
C3×#635792
#105913313
#105912703
#105912013