Finite Group Databasebeta

← #13156841

Subgroups — #13156841

Order 1728.

994 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88815C211yesmaximal, characteristic
2C2×#88806C211yesmaximal, characteristic
3C2×Dic3⋊(C3⋊Dic3)C211yesmaximal, characteristic
4C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic
5C2×C3×Dic32C211yesmaximal, characteristic
6#11722061C211yesmaximal, characteristic
7C3×#63579C211yesmaximal, characteristic
8#10591327—31nomaximal
9#10591234—31nomaximal
10#10591212—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—
19#88806—22no—
20Dic3⋊(C3⋊Dic3)C414yescomplemented
21C3×Dic3⋊Dic3—22no—
22C3×Dic32—22no—
23C2×C4⋊(C3⋊Dic3)—31no—
24C2×#3750—31no—
25C2×C3×C4⋊Dic3—31no—
26C2×C3×Dic3⋊C4—31no—
27C2×C3×C4×Dic3—31no—
28C2×C3×C4×Dic3—31no—
29C2×#3724—31no—
30C2×#3724—31no—
31C2×#3724—31no—
32C2×#3724—61no—
33C2×Dic3⋊Dic3—31no—
34C2×Dic3⋊Dic3—31no—
35C2×Dic3⋊Dic3—31no—
36C2×Dic3⋊Dic3—31no—
37C2×Dic3⋊Dic3—61no—
38C2×Dic3⋊Dic3D311yescharacteristic
39C2×Dic32D311yescharacteristic
40#63658—31no—
41C3×C3⋊#95—31no—
42C3×C3⋊#95—31no—
43#63579—31no—
44#63579—31no—
45#63579—61no—
46#63579D311yescharacteristic
47C23×C33C2311yescharacteristic
48C2×C3⋊(C3⋊Dic3)—21no—
49C2×C3⋊(C3⋊Dic3)—21no—
50C2×C3⋊(C3⋊Dic3)C2×C412yes—
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⋊Dic3—21no—
57C2×C3×C3⋊Dic3—21no—
58C2×C3×C3⋊Dic3C2×C412yes—
59C2×C3×C3⋊Dic3D412yes—
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—
67C2×C32×Dic3Q812yes—
68C2×C32×Dic3Q812yes—
69#4972—91no—
70#4928—91no—
71#4647—91no—
72C22×C32×C4—31no—
73C22×C32×C4—31no—
74C22×C32×C4—31no—
75C22×C3⋊Dic3—31no—
76C22×C3⋊Dic3—31no—
77C22×C3⋊Dic3—31no—
78C22×C3⋊Dic3—61no—
79C22×C3⋊Dic3—61no—
80C22×C3⋊Dic3—61no—
81C22×C3⋊Dic3—121no—
82C22×C3⋊Dic3C2×D311yescharacteristic
83C22×C3⋊Dic3C2×D311yescharacteristic
84C22×C3⋊Dic3C2×D311yescharacteristic
85C22×C3×Dic3—21no—
86C22×C3×Dic3—21no—
87C22×C3×Dic3—21no—
88C22×C3×Dic3—31no—
89C22×C3×Dic3—31no—
90C22×C3×Dic3—31no—
91C22×C3×Dic3—31no—
92C22×C3×Dic3—31no—
93C22×C3×Dic3—31no—
94C22×C3×Dic3—61no—
95C22×C3×Dic3—61no—
96C22×C3×Dic3—61no—
97C22×C3×Dic3C2×D311yescharacteristic
98C22×C3×Dic3C2×D311yescharacteristic
99C22×C3×Dic3C2×D311yescharacteristic
100C22×C3×Dic3C2×D311yescharacteristic
101C22×C3×Dic3C2×D311yescharacteristic
102C22×C3×Dic3C2×D311yescharacteristic
103C4⋊(C3⋊Dic3)—34no—
104#3750—62no—
105C3×C4⋊Dic3—62no—
106C3×Dic3⋊C4—62no—
107C3×C4×Dic3—62no—
108C3×C4×Dic3—62no—
109#3724—62no—
110#3724—62no—
111#3724—64no—
112#3724—62no—
113Dic3⋊Dic3—22no—
114Dic3⋊Dic3—34no—
115Dic3⋊Dic3—34no—
116Dic3⋊Dic3—64no—
117Dic3⋊Dic3—62no—
118Dic3⋊Dic3—62no—
119Dic32—22no—
120C22×C33C22×C411yescharacteristic
121C22×C33C2×D411yescharacteristic
122C22×C33C2×D411yescharacteristic
123C22×C33C2×Q811yescharacteristic
124C22×C33C2×Q811yescharacteristic
125C22×C33#4111yescharacteristic
126C22×C33#4111yescharacteristic
127C3⋊(C3⋊Dic3)—22no—
128C3×C3⋊Dic3—22no—
129C3×C3⋊Dic3—22no—
130C3×C3⋊Dic3—41no—
131C32×Dic3—22no—
132C32×Dic3—41no—
133C32×Dic3C4⋊C414yescomplemented
134C2×C3×C4⋊C4—91no—
135C2×C3×C42—91no—
136C2×C4⋊Dic3—31no—
137C2×C4⋊Dic3—91no—
138C2×C4⋊Dic3—91no—
139C2×C4⋊Dic3—91no—
140C2×C4⋊Dic3—181no—
141C2×Dic3⋊C4—31no—
142C2×Dic3⋊C4—91no—
143C2×Dic3⋊C4—91no—
144C2×Dic3⋊C4—91no—
145C2×Dic3⋊C4—91no—
146C2×Dic3⋊C4—91no—
147C2×Dic3⋊C4—91no—
148C2×Dic3⋊C4—181no—
149C2×C4×Dic3—31no—
150C2×C4×Dic3—31no—
151C3×#95—91no—
152C3⋊#95—31no—
153C3⋊#95—31no—
154C3⋊#95—91no—
155C3⋊#95—91no—
156C3⋊#95—91no—
157C3⋊#95—181no—
158C23×C32—21no—
159C23×C32—21no—
160C23×C32—21no—
161C23×C32—41no—
162C23×C32C22×D311yescharacteristic
163C23×C32C22×D311yescharacteristic
164C23×C32C22×D311yescharacteristic
165C2×C32×C4—32no—
166C2×C32×C4—32no—
167C2×C32×C4—32no—
168C2×C32×C4—32no—
169C2×C32×C4—61no—
170C2×C32×C4—61no—
171C2×C32×C4—61no—
172C2×C32×C4—61no—
173C2×C32×C4—61no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—21no—
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—32no—
182C2×C3⋊Dic3—32no—
183C2×C3⋊Dic3—32no—
184C2×C3⋊Dic3—62no—
185C2×C3⋊Dic3—62no—
186C2×C3⋊Dic3—62no—
187C2×C3⋊Dic3—61no—
188C2×C3⋊Dic3—61no—
189C2×C3⋊Dic3—62no—
190C2×C3⋊Dic3—62no—
191C2×C3⋊Dic3—61no—
192C2×C3⋊Dic3—61no—
193C2×C3⋊Dic3—61no—
194C2×C3⋊Dic3—61no—
195C2×C3⋊Dic3—122no—
196C2×C3⋊Dic3—121no—
197C2×C3⋊Dic3—121no—
198C2×C3⋊Dic3—121no—
199C2×C3⋊Dic3—121no—
200C2×C3⋊Dic3—122no—
201C2×C3⋊Dic3—122no—
202C2×C3⋊Dic3C4×D312yes—
203C2×C3⋊Dic3D1212yes—
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—22no—
218C2×C3×Dic3—22no—
219C2×C3×Dic3—32no—
220C2×C3×Dic3—32no—
221C2×C3×Dic3—32no—
222C2×C3×Dic3—32no—
223C2×C3×Dic3—41no—
224C2×C3×Dic3—41no—
225C2×C3×Dic3—41no—
226C2×C3×Dic3—41no—
227C2×C3×Dic3—62no—
228C2×C3×Dic3—62no—
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—61no—
236C2×C3×Dic3—61no—
237C2×C3×Dic3—62no—
238C2×C3×Dic3—61no—
239C2×C3×Dic3—61no—
240C2×C3×Dic3—61no—
241C2×C3×Dic3—61no—
242C2×C3×Dic3—61no—
243C2×C3×Dic3—61no—
244C2×C3×Dic3—121no—
245C2×C3×Dic3—121no—
246C2×C3×Dic3—121no—
247C2×C3×Dic3—121no—
248C2×C3×Dic3—121no—
249C2×C3×Dic3—121no—
250C2×C3×Dic3Dic612yes—
251C2×C3×Dic3Dic612yes—
252C2×C3×Dic3Dic612yes—
253C2×C3×Dic3Dic612yes—
254C2×C3×Dic3C4×D312yes—
255C2×C3×Dic3C4×D312yes—
256C2×C3×Dic3#6712yes—
257C2×C3×Dic3#6712yes—
258#389—271noSylow
259C2×C33C2×C4⋊C411yescharacteristic
260C2×C33C4×D411yescharacteristic
261C2×C33C4×Q811yescharacteristic
262C2×C33#12111yescharacteristic
263C2×C33C22⋊Q811yescharacteristic
264C2×C33#12511yescharacteristic
265C2×C33C4⋊Q811yescharacteristic
266C22×C3×C4—31no—
267C22×C3×C4—31no—
268C22×C3×C4—31no—
269C22×C3×C4—31no—
270C22×C3×C4—31no—
271C22×C3×C4—31no—
272C22×C3×C4—61no—
273C22×C3×C4—61no—
274C22×C3×C4—61no—
275C22×C3×C4—91no—
276C22×C3×C4—91no—
277C22×C3×C4—91no—
278C22×Dic3—31no—
279C22×Dic3—31no—
280C22×Dic3—31no—
281C22×Dic3—31no—
282C22×Dic3—31no—
283C22×Dic3—31no—
284C22×Dic3—61no—
285C22×Dic3—61no—
286C22×Dic3—61no—
287C22×Dic3—91no—
288C22×Dic3—91no—
289C22×Dic3—91no—
290C22×Dic3—181no—
291C22×Dic3—181no—
292C22×Dic3—181no—
293C22×Dic3—361no—
294C22×Dic3D3211yescharacteristic
295C22×Dic3D3211yescharacteristic
296C22×Dic3D3211yescharacteristic
297C3×C4⋊C4—182no—
298C3×C42—182no—
299C4⋊Dic3—62no—
300C4⋊Dic3—94no—
301C4⋊Dic3—94no—
302C4⋊Dic3—184no—
303C4⋊Dic3—182no—
304Dic3⋊C4—62no—
305Dic3⋊C4—94no—
306Dic3⋊C4—182no—
307Dic3⋊C4—182no—
308Dic3⋊C4—182no—
309Dic3⋊C4—182no—
310Dic3⋊C4—182no—
311Dic3⋊C4—184no—
312C4×Dic3—62no—
313C4×Dic3—62no—
314C22×C32—21no—
315C22×C32—21no—
316C22×C32—21no—
317C22×C32—21no—
318C22×C32—21no—
319C22×C32—21no—
320C22×C32—21no—
321C22×C32—21no—
322C22×C32—21no—
323C22×C32—21no—
324C22×C32—21no—
325C22×C32—21no—
326C22×C32—21no—
327C22×C32—21no—
328C22×C32—21no—
329C22×C32—21no—
330C22×C32—21no—
331C22×C32—21no—
332C22×C32—21no—
333C22×C32—21no—
334C22×C32—21no—
335C22×C32—41no—
336C22×C32—41no—
337C22×C32—41no—
338C22×C32—41no—
339C22×C32—41no—
340C22×C32—41no—
341C22×C32—41no—
342C22×C32C2×Dic611yescharacteristic
343C22×C32C2×Dic611yescharacteristic
344C22×C32C2×Dic611yescharacteristic
345C22×C32C2×Dic611yescharacteristic
346C22×C32C2×C4×D311yescharacteristic
347C22×C32C2×C4×D311yescharacteristic
348C22×C32C2×C4×D311yescharacteristic
349C22×C32C2×D1211yescharacteristic
350C22×C32#23511yescharacteristic
351C22×C32#23511yescharacteristic
352C22×C32#23511yescharacteristic
353C22×C32D3×D411yescharacteristic
354C22×C32D3×D411yescharacteristic
355C22×C32D3×D411yescharacteristic
356C22×C32#23711yescharacteristic
357C22×C32#23711yescharacteristic
358C22×C32D3×Q811yescharacteristic
359C22×C32D3×Q811yescharacteristic
360C22×C32#23911yescharacteristic
361C22×C32C2×#6711yescharacteristic
362C22×C32C2×#6711yescharacteristic
363C32×C4—34no—
364C32×C4—62no—
365C32×C4—121no—
366C3⋊Dic3—22no—
367C3⋊Dic3—22no—
368C3⋊Dic3—41no—
369C3⋊Dic3—62no—
370C3⋊Dic3—64no—
371C3⋊Dic3—62no—
372C3⋊Dic3—62no—
373C3⋊Dic3—122no—
374C3⋊Dic3—122no—
375C3⋊Dic3—124no—
376C3×Dic3—22no—
377C3×Dic3—22no—
378C3×Dic3—24no—
379C3×Dic3—42no—
380C3×Dic3—42no—
381C3×Dic3—41no—
382C3×Dic3—41no—
383C3×Dic3—62no—
384C3×Dic3—62no—
385C3×Dic3—62no—
386C3×Dic3—62no—
387C3×Dic3—122no—
388C3×Dic3—122no—
389C3×Dic3—122no—
390C3×Dic3—121no—
391C3×Dic3—121no—
392C3×Dic3Dic3⋊C414yescomplemented
393C3×Dic3Dic3⋊C414yescomplemented
394C2×C4⋊C4—91no—
395C2×C4⋊C4—271no—
396C2×C4⋊C4—271no—
397C2×C4⋊C4—271no—
398C2×C42—91no—
399#95—91no—
400#95—271no—
401C33#38911yescharacteristic, complemented, Sylow
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—41no—
406C23×C3C2×D3211yescharacteristic
407C23×C3C2×D3211yescharacteristic
408C23×C3C2×D3211yescharacteristic
409C2×C3×C4—32no—
410C2×C3×C4—32no—
411C2×C3×C4—32no—
412C2×C3×C4—32no—
413C2×C3×C4—32no—
414C2×C3×C4—32no—
415C2×C3×C4—32no—
416C2×C3×C4—32no—
417C2×C3×C4—62no—
418C2×C3×C4—62no—
419C2×C3×C4—62no—
420C2×C3×C4—62no—
421C2×C3×C4—61no—
422C2×C3×C4—61no—
423C2×C3×C4—61no—
424C2×C3×C4—61no—
425C2×C3×C4—62no—
426C2×C3×C4—61no—
427C2×C3×C4—61no—
428C2×C3×C4—61no—
429C2×C3×C4—61no—
430C2×C3×C4—61no—
431C2×C3×C4—61no—
432C2×C3×C4—92no—
433C2×C3×C4—92no—
434C2×C3×C4—121no—
435C2×C3×C4—121no—
436C2×C3×C4—121no—
437C2×C3×C4—121no—
438C2×C3×C4—181no—
439C2×C3×C4—181no—
440C2×C3×C4—181no—
441C2×C3×C4—181no—
442C2×C3×C4—181no—
443C2×C3×C4—181no—
444C2×C3×C4—181no—
445C2×Dic3—21no—
446C2×Dic3—21no—
447C2×Dic3—21no—
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—32no—
451C2×Dic3—32no—
452C2×Dic3—32no—
453C2×Dic3—32no—
454C2×Dic3—62no—
455C2×Dic3—62no—
456C2×Dic3—61no—
457C2×Dic3—61no—
458C2×Dic3—61no—
459C2×Dic3—61no—
460C2×Dic3—61no—
461C2×Dic3—61no—
462C2×Dic3—61no—
463C2×Dic3—61no—
464C2×Dic3—62no—
465C2×Dic3—61no—
466C2×Dic3—61no—
467C2×Dic3—61no—
468C2×Dic3—61no—
469C2×Dic3—61no—
470C2×Dic3—61no—
471C2×Dic3—92no—
472C2×Dic3—92no—
473C2×Dic3—92no—
474C2×Dic3—121no—
475C2×Dic3—121no—
476C2×Dic3—121no—
477C2×Dic3—121no—
478C2×Dic3—121no—
479C2×Dic3—121no—
480C2×Dic3—182no—
481C2×Dic3—182no—
482C2×Dic3—182no—
483C2×Dic3—182no—
484C2×Dic3—182no—
485C2×Dic3—181no—
486C2×Dic3—181no—
487C2×Dic3—181no—
488C2×Dic3—181no—
489C2×Dic3—181no—
490C2×Dic3—181no—
491C2×Dic3—362no—
492C2×Dic3—361no—
493C2×Dic3—361no—
494C2×Dic3—361no—
495C2×Dic3—361no—
496C2×Dic3—362no—
497C2×Dic3—362no—
498C2×Dic3#62412yes—
499C2×Dic3#62512yes—
500C2×Dic3#62712yes—
501C2×Dic3#62712yes—
502C2×C32—21no—
503C2×C32—21no—
504C2×C32—21no—
505C2×C32—21no—
506C2×C32—21no—
507C2×C32—21no—
508C2×C32—21no—
509C2×C32—21no—
510C2×C32—21no—
511C2×C32—21no—
512C2×C32—21no—
513C2×C32—21no—
514C2×C32—21no—
515C2×C32—21no—
516C2×C32—21no—
517C2×C32—21no—
518C2×C32—21no—
519C2×C32—21no—
520C2×C32—21no—
521C2×C32—21no—
522C2×C32—21no—
523C2×C32—41no—
524C2×C32—41no—
525C2×C32—41no—
526C2×C32—41no—
527C2×C32—41no—
528C2×C32—41no—
529C2×C32—41no—
530C2×C32C4×Dic611yescharacteristic
531C2×C32C4×Dic611yescharacteristic
532C2×C32#86911yescharacteristic
533C2×C32#87011yescharacteristic
534C2×C32C4×D1211yescharacteristic
535C2×C32#87811yescharacteristic
536C2×C32#67⋊C411yescharacteristic
537C2×C32#88411yescharacteristic
538C2×C32#88711yescharacteristic
539C2×C32#88811yescharacteristic
540C2×C32#88811yescharacteristic
541C2×C32#88911yescharacteristic
542C2×C32#89011yescharacteristic
543C2×C32D3×C4⋊C411yescharacteristic
544C2×C32#89311yescharacteristic
545C2×C32C2×Dic3⋊C411yescharacteristic
546C2×C32C2×Dic3⋊C411yescharacteristic
547C2×C32#92411yescharacteristic
548C2×C32#93011yescharacteristic
549C2×C32#93811yescharacteristic
550C2×C32#94611yescharacteristic
551C22×C4—31no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—91no—
555C22×C4—91no—
556C22×C4—91no—
557C22×C4—271no—
558C4⋊C4—182no—
559C4⋊C4—274no—
560C4⋊C4—542no—
561C4⋊C4—542no—
562C42—182no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—21no—
566C22×C3—21no—
567C22×C3—21no—
568C22×C3—21no—
569C22×C3—21no—
570C22×C3—21no—
571C22×C3—21no—
572C22×C3—21no—
573C22×C3—21no—
574C22×C3—21no—
575C22×C3—21no—
576C22×C3—21no—
577C22×C3—21no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3D3×Dic611yescharacteristic
592C22×C3D3×Dic611yescharacteristic
593C22×C3D3×Dic611yescharacteristic
594C22×C3D3×Dic611yescharacteristic
595C22×C3#379511yescharacteristic
596C22×C3#379611yescharacteristic
597C22×C3#379811yescharacteristic
598C22×C3#379911yescharacteristic
599C22×C3C4×D3211yescharacteristic
600C22×C3C4×D3211yescharacteristic
601C22×C3D3×D1211yescharacteristic
602C22×C3D3×D1211yescharacteristic
603C22×C3#380411yescharacteristic
604C22×C3#380411yescharacteristic
605C22×C3C2×#62411yescharacteristic
606C22×C3C2×#62511yescharacteristic
607C22×C3C2×#62711yescharacteristic
608C22×C3C2×#62711yescharacteristic
609C22×C3D3×#6711yescharacteristic
610C22×C3D3×#6711yescharacteristic
611C22×C3#381111yescharacteristic
612C3×C4—34no—
613C3×C4—34no—
614C3×C4—64no—
615C3×C4—62no—
616C3×C4—62no—
617C3×C4—122no—
618C3×C4—122no—
619C3×C4—121no—
620C3×C4—121no—
621C3×C4—182no—
622C3×C4—182no—
623C3×C4—361no—
624Dic3—22no—
625Dic3—41no—
626Dic3—62no—
627Dic3—62no—
628Dic3—62no—
629Dic3—62no—
630Dic3—122no—
631Dic3—122no—
632Dic3—122no—
633Dic3—121no—
634Dic3—121no—
635Dic3—184no—
636Dic3—182no—
637Dic3—182no—
638Dic3—182no—
639Dic3—362no—
640Dic3—362no—
641Dic3—364no—
642Dic3#372414yescomplemented
643C32—21no—
644C32—21no—
645C32—21no—
646C32—41no—
647C32#464711yescharacteristic, complemented
648C32#492811yescharacteristic, complemented
649C32#497211yescharacteristic, complemented
650C23D3311yescharacteristic
651C2×C4—32no—
652C2×C4—32no—
653C2×C4—32no—
654C2×C4—32no—
655C2×C4—61no—
656C2×C4—61no—
657C2×C4—61no—
658C2×C4—61no—
659C2×C4—61no—
660C2×C4—92no—
661C2×C4—92no—
662C2×C4—181no—
663C2×C4—181no—
664C2×C4—181no—
665C2×C4—181no—
666C2×C4—181no—
667C2×C4—181no—
668C2×C4—181no—
669C2×C4—272no—
670C2×C4—541no—
671C2×C4—541no—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—41no—
694C2×C3—41no—
695C2×C3—41no—
696C2×C3—41no—
697C2×C3—41no—
698C2×C3—41no—
699C2×C3—41no—
700C2×C3#6383711yescharacteristic
701C2×C3#6384011yescharacteristic
702C2×C3#6384411yescharacteristic
703C2×C3#6384611yescharacteristic
704C2×C3#6385611yescharacteristic
705C2×C3#6386711yescharacteristic
706C2×C3#6386911yescharacteristic
707C2×C3D3×Dic3⋊C411yescharacteristic
708C2×C3D3×Dic3⋊C411yescharacteristic
709C2×C3#6388011yescharacteristic
710C2×C3#6388111yescharacteristic
711C2×C3#6388711yescharacteristic
712C2×C3#6389411yescharacteristic
713C2×C3#6390611yescharacteristic
714C2×C3#6390811yescharacteristic
715C2×C3C4×#62711yescharacteristic
716C2×C3#6391811yescharacteristic
717C2×C3#6391811yescharacteristic
718C2×C3#6395811yescharacteristic
719C2×C3#6396411yescharacteristic
720C2×C3C2×#372411yescharacteristic
721C22D3×#62411yescharacteristic
722C22D3×#62511yescharacteristic
723C22#8895511yescharacteristic
724C22D3×#62711yescharacteristic
725C22D3×#62711yescharacteristic
726C22#8896011yescharacteristic
727C22#8896211yescharacteristic
728C4—34no—
729C4—62no—
730C4—121no—
731C4—182no—
732C4—182no—
733C4—361no—
734C4—542no—
735C3—21no—
736C3—21no—
737C3—21no—
738C3—41no—
739C3#1059121211yescharacteristic, complemented
740C3#1059123411yescharacteristic, complemented
741C3#1059132711yescharacteristic, complemented
742C2D3×#372411yescharacteristic
743C2#1172293711yescharacteristic
744C2#1172294211yescharacteristic
745C2#1172295711yescharacteristic
746C2#1172296911yescharacteristic
747C2#1172301211yescharacteristic
748C2#1172303611yescharacteristic
subgroupG/H
center, Frattini, hypercenterC23D33
commutatorC22×C33C22×C4
Fitting, socle, prime radical, cosocleC23×C33C23
hypocenterC33#389
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
20. Dic3⋊(C3⋊Dic3)C4semidirect
133. C32×Dic3C4⋊C4semidirect
392. C3×Dic3Dic3⋊C4semidirect
393. C3×Dic3Dic3⋊C4semidirect
401. C33#389semidirect
642. Dic3#3724semidirect
647. C32#4647semidirect
648. C32#4928semidirect
649. C32#4972semidirect
739. C3#10591212semidirect
740. C3#10591234semidirect
741. C3#10591327semidirect

Maximal subgroups

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

subgroupindex
C2×#888152
C2×#888062
C2×Dic3⋊(C3⋊Dic3)2
C2×C3×Dic3⋊Dic32
C2×C3×Dic322
#117220612
C3×#635792
#105913273
#105912343
#105912123