Finite Group Databasebeta

← #13156836

Subgroups — #13156836

Order 1728.

1026 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88807C211yesmaximal, characteristic
2C2×Dic3⋊(C3⋊Dic3)C211yesmaximal, characteristic
3C2×Dic3×C3⋊Dic3C211yesmaximal, characteristic
4C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic
5C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic
6#11722082C211yesmaximal, characteristic
7C3×#63579C211yesmaximal, characteristic
8#10591357—31nomaximal
9#10591268—31nomaximal
10#10591234—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#88807—22no—
19Dic3⋊(C3⋊Dic3)—22no—
20Dic3×C3⋊Dic3—22no—
21C3×Dic3⋊Dic3—22no—
22C3×Dic3⋊Dic3C414yescomplemented
23C2×C4⋊(C3⋊Dic3)—31no—
24C2×#3750—31no—
25C2×C4×C3⋊Dic3—31no—
26C2×C3×C4⋊Dic3—31no—
27C2×C3×C4⋊Dic3—31no—
28C2×C3×Dic3⋊C4—31no—
29C2×C3×Dic3⋊C4—31no—
30C2×Dic3⋊Dic3—31no—
31C2×Dic3⋊Dic3—31no—
32C2×Dic3⋊Dic3—31no—
33C2×Dic3⋊Dic3—31no—
34C2×Dic3⋊Dic3—61no—
35C2×Dic3⋊Dic3—61no—
36C2×Dic3⋊Dic3D311yescharacteristic
37C2×Dic3⋊Dic3D311yescharacteristic
38C2×Dic32—31no—
39C2×Dic32—31no—
40C2×Dic32—61no—
41C3×C3⋊#95—31no—
42C3×C3⋊#95—31no—
43#63579—31no—
44#63579—31no—
45#63579—31no—
46#63579D311yescharacteristic
47C23×C33C2311yescharacteristic
48C2×C3⋊(C3⋊Dic3)—21no—
49C2×C3⋊(C3⋊Dic3)—21no—
50C2×C3⋊(C3⋊Dic3)D412yes—
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⋊Dic3Q812yes—
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×Dic3C2×C412yes—
67C2×C32×Dic3D412yes—
68C2×C32×Dic3Q812yes—
69#4984—91no—
70#4972—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)—62no—
104#3750—62no—
105C4×C3⋊Dic3—62no—
106C3×C4⋊Dic3—34no—
107C3×C4⋊Dic3—62no—
108C3×Dic3⋊C4—34no—
109C3×Dic3⋊C4—62no—
110Dic3⋊Dic3—22no—
111Dic3⋊Dic3—62no—
112Dic3⋊Dic3—62no—
113Dic3⋊Dic3—62no—
114Dic3⋊Dic3—62no—
115Dic3⋊Dic3—64no—
116Dic3⋊Dic3—64no—
117Dic3⋊Dic3Dic314yescomplemented
118Dic32—64no—
119Dic32—62no—
120Dic32—62no—
121C22×C33C22×C411yescharacteristic
122C22×C33C2×D411yescharacteristic
123C22×C33C2×D411yescharacteristic
124C22×C33C2×Q811yescharacteristic
125C22×C33C2×Q811yescharacteristic
126C22×C33#4111yescharacteristic
127C22×C33#4111yescharacteristic
128C3⋊(C3⋊Dic3)—22no—
129C3×C3⋊Dic3—22no—
130C3×C3⋊Dic3—22no—
131C3×C3⋊Dic3—41no—
132C32×Dic3—22no—
133C32×Dic3—41no—
134C32×Dic3C4⋊C414yescomplemented
135C2×C3×C4⋊C4—91no—
136C2×C3×C4⋊C4—91no—
137C2×C4⋊Dic3—31no—
138C2×C4⋊Dic3—31no—
139C2×C4⋊Dic3—91no—
140C2×C4⋊Dic3—91no—
141C2×C4⋊Dic3—91no—
142C2×C4⋊Dic3—181no—
143C2×Dic3⋊C4—31no—
144C2×Dic3⋊C4—31no—
145C2×Dic3⋊C4—91no—
146C2×Dic3⋊C4—91no—
147C2×Dic3⋊C4—91no—
148C2×Dic3⋊C4—181no—
149C2×C4×Dic3—91no—
150C2×C4×Dic3—91no—
151C2×C4×Dic3—91no—
152C2×C4×Dic3—181no—
153C3×#95—91no—
154C3⋊#95—31no—
155C3⋊#95—31no—
156C3⋊#95—91no—
157C3⋊#95—91no—
158C3⋊#95—91no—
159C23×C32—21no—
160C23×C32—21no—
161C23×C32—21no—
162C23×C32—41no—
163C23×C32C22×D311yescharacteristic
164C23×C32C22×D311yescharacteristic
165C23×C32C22×D311yescharacteristic
166C2×C32×C4—32no—
167C2×C32×C4—32no—
168C2×C32×C4—32no—
169C2×C32×C4—32no—
170C2×C32×C4—61no—
171C2×C32×C4—61no—
172C2×C32×C4—61no—
173C2×C32×C4—61no—
174C2×C32×C4—61no—
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—21no—
182C2×C3⋊Dic3—32no—
183C2×C3⋊Dic3—32no—
184C2×C3⋊Dic3—32no—
185C2×C3⋊Dic3—62no—
186C2×C3⋊Dic3—62no—
187C2×C3⋊Dic3—62no—
188C2×C3⋊Dic3—61no—
189C2×C3⋊Dic3—61no—
190C2×C3⋊Dic3—62no—
191C2×C3⋊Dic3—62no—
192C2×C3⋊Dic3—61no—
193C2×C3⋊Dic3—61no—
194C2×C3⋊Dic3—61no—
195C2×C3⋊Dic3—61no—
196C2×C3⋊Dic3—122no—
197C2×C3⋊Dic3—121no—
198C2×C3⋊Dic3—121no—
199C2×C3⋊Dic3—121no—
200C2×C3⋊Dic3—121no—
201C2×C3⋊Dic3—122no—
202C2×C3⋊Dic3—122no—
203C2×C3⋊Dic3Dic612yes—
204C2×C3⋊Dic3C2×Dic312yes—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—21no—
208C2×C3×Dic3—21no—
209C2×C3×Dic3—21no—
210C2×C3×Dic3—21no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—21no—
213C2×C3×Dic3—21no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3—21no—
216C2×C3×Dic3—21no—
217C2×C3×Dic3—21no—
218C2×C3×Dic3—22no—
219C2×C3×Dic3—22no—
220C2×C3×Dic3—22no—
221C2×C3×Dic3—22no—
222C2×C3×Dic3—32no—
223C2×C3×Dic3—32no—
224C2×C3×Dic3—32no—
225C2×C3×Dic3—32no—
226C2×C3×Dic3—41no—
227C2×C3×Dic3—41no—
228C2×C3×Dic3—62no—
229C2×C3×Dic3—62no—
230C2×C3×Dic3—62no—
231C2×C3×Dic3—62no—
232C2×C3×Dic3—62no—
233C2×C3×Dic3—62no—
234C2×C3×Dic3—61no—
235C2×C3×Dic3—61no—
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—62no—
243C2×C3×Dic3—61no—
244C2×C3×Dic3—61no—
245C2×C3×Dic3—61no—
246C2×C3×Dic3—61no—
247C2×C3×Dic3—61no—
248C2×C3×Dic3—61no—
249C2×C3×Dic3—121no—
250C2×C3×Dic3—121no—
251C2×C3×Dic3Dic612yes—
252C2×C3×Dic3Dic612yes—
253C2×C3×Dic3C4×D312yes—
254C2×C3×Dic3C4×D312yes—
255C2×C3×Dic3D1212yes—
256C2×C3×Dic3C2×Dic312yes—
257C2×C3×Dic3C2×Dic312yes—
258C2×C3×Dic3#6712yes—
259#389—271noSylow
260C2×C33C2×C4⋊C411yescharacteristic
261C2×C33C4×D411yescharacteristic
262C2×C33C4×Q811yescharacteristic
263C2×C33#12111yescharacteristic
264C2×C33C22⋊Q811yescharacteristic
265C2×C33#12511yescharacteristic
266C2×C33C4⋊Q811yescharacteristic
267C22×C3×C4—31no—
268C22×C3×C4—31no—
269C22×C3×C4—31no—
270C22×C3×C4—31no—
271C22×C3×C4—31no—
272C22×C3×C4—31no—
273C22×C3×C4—61no—
274C22×C3×C4—61no—
275C22×C3×C4—61no—
276C22×C3×C4—91no—
277C22×C3×C4—91no—
278C22×C3×C4—91no—
279C22×Dic3—31no—
280C22×Dic3—31no—
281C22×Dic3—31no—
282C22×Dic3—31no—
283C22×Dic3—31no—
284C22×Dic3—31no—
285C22×Dic3—61no—
286C22×Dic3—61no—
287C22×Dic3—61no—
288C22×Dic3—91no—
289C22×Dic3—91no—
290C22×Dic3—91no—
291C22×Dic3—181no—
292C22×Dic3—181no—
293C22×Dic3—181no—
294C22×Dic3—361no—
295C22×Dic3D3211yescharacteristic
296C22×Dic3D3211yescharacteristic
297C22×Dic3D3211yescharacteristic
298C3×C4⋊C4—94no—
299C3×C4⋊C4—182no—
300C4⋊Dic3—34no—
301C4⋊Dic3—62no—
302C4⋊Dic3—182no—
303C4⋊Dic3—182no—
304C4⋊Dic3—182no—
305C4⋊Dic3—184no—
306Dic3⋊C4—34no—
307Dic3⋊C4—62no—
308Dic3⋊C4—182no—
309Dic3⋊C4—182no—
310Dic3⋊C4—182no—
311Dic3⋊C4—184no—
312C4×Dic3—182no—
313C4×Dic3—182no—
314C4×Dic3—184no—
315C4×Dic3—182no—
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—21no—
336C22×C32—21no—
337C22×C32—41no—
338C22×C32—41no—
339C22×C32—41no—
340C22×C32—41no—
341C22×C32—41no—
342C22×C32—41no—
343C22×C32—41no—
344C22×C32C2×Dic611yescharacteristic
345C22×C32C2×Dic611yescharacteristic
346C22×C32C2×Dic611yescharacteristic
347C22×C32C2×C4×D311yescharacteristic
348C22×C32C2×C4×D311yescharacteristic
349C22×C32C2×D1211yescharacteristic
350C22×C32#23511yescharacteristic
351C22×C32D3×D411yescharacteristic
352C22×C32D3×D411yescharacteristic
353C22×C32D3×D411yescharacteristic
354C22×C32D3×D411yescharacteristic
355C22×C32#23711yescharacteristic
356C22×C32#23711yescharacteristic
357C22×C32#23711yescharacteristic
358C22×C32D3×Q811yescharacteristic
359C22×C32D3×Q811yescharacteristic
360C22×C32D3×Q811yescharacteristic
361C22×C32#23911yescharacteristic
362C22×C32#23911yescharacteristic
363C22×C32C22×Dic311yescharacteristic
364C22×C32C2×#6711yescharacteristic
365C32×C4—34no—
366C32×C4—62no—
367C32×C4—121no—
368C3⋊Dic3—22no—
369C3⋊Dic3—22no—
370C3⋊Dic3—41no—
371C3⋊Dic3—62no—
372C3⋊Dic3—64no—
373C3⋊Dic3—62no—
374C3⋊Dic3—62no—
375C3⋊Dic3—122no—
376C3⋊Dic3—122no—
377C3⋊Dic3—124no—
378C3×Dic3—24no—
379C3×Dic3—22no—
380C3×Dic3—22no—
381C3×Dic3—24no—
382C3×Dic3—42no—
383C3×Dic3—41no—
384C3×Dic3—41no—
385C3×Dic3—64no—
386C3×Dic3—64no—
387C3×Dic3—62no—
388C3×Dic3—62no—
389C3×Dic3—62no—
390C3×Dic3—62no—
391C3×Dic3—122no—
392C3×Dic3—121no—
393C3×Dic3—121no—
394C3×Dic3Dic3⋊C414yescomplemented
395C3×Dic3C4⋊Dic314yescomplemented
396C2×C4⋊C4—91no—
397C2×C4⋊C4—91no—
398C2×C4⋊C4—271no—
399C2×C4⋊C4—271no—
400C2×C42—271no—
401#95—91no—
402#95—271no—
403C33#38911yescharacteristic, complemented, Sylow
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—41no—
408C23×C3C2×D3211yescharacteristic
409C23×C3C2×D3211yescharacteristic
410C23×C3C2×D3211yescharacteristic
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—32no—
418C2×C3×C4—32no—
419C2×C3×C4—62no—
420C2×C3×C4—62no—
421C2×C3×C4—62no—
422C2×C3×C4—62no—
423C2×C3×C4—62no—
424C2×C3×C4—62no—
425C2×C3×C4—61no—
426C2×C3×C4—61no—
427C2×C3×C4—61no—
428C2×C3×C4—61no—
429C2×C3×C4—62no—
430C2×C3×C4—61no—
431C2×C3×C4—61no—
432C2×C3×C4—61no—
433C2×C3×C4—61no—
434C2×C3×C4—61no—
435C2×C3×C4—61no—
436C2×C3×C4—92no—
437C2×C3×C4—92no—
438C2×C3×C4—121no—
439C2×C3×C4—121no—
440C2×C3×C4—181no—
441C2×C3×C4—181no—
442C2×C3×C4—181no—
443C2×C3×C4—181no—
444C2×C3×C4—181no—
445C2×C3×C4—181no—
446C2×C3×C4—181no—
447C2×Dic3—21no—
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—32no—
453C2×Dic3—32no—
454C2×Dic3—32no—
455C2×Dic3—32no—
456C2×Dic3—62no—
457C2×Dic3—62no—
458C2×Dic3—62no—
459C2×Dic3—62no—
460C2×Dic3—62no—
461C2×Dic3—62no—
462C2×Dic3—61no—
463C2×Dic3—61no—
464C2×Dic3—61no—
465C2×Dic3—61no—
466C2×Dic3—61no—
467C2×Dic3—61no—
468C2×Dic3—61no—
469C2×Dic3—61no—
470C2×Dic3—62no—
471C2×Dic3—61no—
472C2×Dic3—61no—
473C2×Dic3—61no—
474C2×Dic3—61no—
475C2×Dic3—61no—
476C2×Dic3—61no—
477C2×Dic3—92no—
478C2×Dic3—92no—
479C2×Dic3—92no—
480C2×Dic3—121no—
481C2×Dic3—121no—
482C2×Dic3—182no—
483C2×Dic3—182no—
484C2×Dic3—182no—
485C2×Dic3—182no—
486C2×Dic3—182no—
487C2×Dic3—181no—
488C2×Dic3—181no—
489C2×Dic3—181no—
490C2×Dic3—181no—
491C2×Dic3—181no—
492C2×Dic3—181no—
493C2×Dic3—362no—
494C2×Dic3—361no—
495C2×Dic3—361no—
496C2×Dic3—361no—
497C2×Dic3—361no—
498C2×Dic3—362no—
499C2×Dic3—362no—
500C2×Dic3D3×Dic312yes—
501C2×Dic3D3×Dic312yes—
502C2×Dic3#62612yes—
503C2×Dic3#62712yes—
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—21no—
524C2×C32—21no—
525C2×C32—41no—
526C2×C32—41no—
527C2×C32—41no—
528C2×C32—41no—
529C2×C32—41no—
530C2×C32—41no—
531C2×C32—41no—
532C2×C32C4×Dic611yescharacteristic
533C2×C32#87811yescharacteristic
534C2×C32#67⋊C411yescharacteristic
535C2×C32#88411yescharacteristic
536C2×C32#88711yescharacteristic
537C2×C32#88811yescharacteristic
538C2×C32#88811yescharacteristic
539C2×C32#88811yescharacteristic
540C2×C32#88911yescharacteristic
541C2×C32#89011yescharacteristic
542C2×C32#89011yescharacteristic
543C2×C32D3×C4⋊C411yescharacteristic
544C2×C32#89311yescharacteristic
545C2×C32#89511yescharacteristic
546C2×C32#89711yescharacteristic
547C2×C32C2×Dic3⋊C411yescharacteristic
548C2×C32C2×C4⋊Dic311yescharacteristic
549C2×C32D4×Dic311yescharacteristic
550C2×C32#93811yescharacteristic
551C2×C32Q8×Dic311yescharacteristic
552C2×C32#94611yescharacteristic
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—31no—
556C22×C4—91no—
557C22×C4—91no—
558C22×C4—91no—
559C22×C4—271no—
560C4⋊C4—94no—
561C4⋊C4—182no—
562C4⋊C4—542no—
563C4⋊C4—542no—
564C42—542no—
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—21no—
585C22×C3—21no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—41no—
593C22×C3D3×Dic611yescharacteristic
594C22×C3D3×Dic611yescharacteristic
595C22×C3D3×Dic611yescharacteristic
596C22×C3D3×Dic611yescharacteristic
597C22×C3#379611yescharacteristic
598C22×C3#379611yescharacteristic
599C22×C3#379611yescharacteristic
600C22×C3#379711yescharacteristic
601C22×C3#379911yescharacteristic
602C22×C3C4×D3211yescharacteristic
603C22×C3D3×D1211yescharacteristic
604C22×C3#380211yescharacteristic
605C22×C3C2×D3×Dic311yescharacteristic
606C22×C3C2×D3×Dic311yescharacteristic
607C22×C3#380411yescharacteristic
608C22×C3#380511yescharacteristic
609C22×C3C2×#62611yescharacteristic
610C22×C3C2×#62711yescharacteristic
611C22×C3D3×#6711yescharacteristic
612C22×C3#381111yescharacteristic
613C22×C3#381111yescharacteristic
614C3×C4—34no—
615C3×C4—34no—
616C3×C4—64no—
617C3×C4—64no—
618C3×C4—62no—
619C3×C4—62no—
620C3×C4—122no—
621C3×C4—121no—
622C3×C4—121no—
623C3×C4—182no—
624C3×C4—182no—
625C3×C4—361no—
626Dic3—22no—
627Dic3—41no—
628Dic3—64no—
629Dic3—64no—
630Dic3—62no—
631Dic3—62no—
632Dic3—62no—
633Dic3—62no—
634Dic3—122no—
635Dic3—121no—
636Dic3—121no—
637Dic3—184no—
638Dic3—182no—
639Dic3—182no—
640Dic3—182no—
641Dic3—362no—
642Dic3—362no—
643Dic3—364no—
644Dic3Dic3⋊Dic314yescomplemented
645C32—21no—
646C32—21no—
647C32—21no—
648C32—41no—
649C32#464711yescharacteristic, complemented
650C32#497211yescharacteristic, complemented
651C32#498411yescharacteristic, complemented
652C23D3311yescharacteristic
653C2×C4—32no—
654C2×C4—32no—
655C2×C4—32no—
656C2×C4—32no—
657C2×C4—61no—
658C2×C4—61no—
659C2×C4—61no—
660C2×C4—61no—
661C2×C4—61no—
662C2×C4—92no—
663C2×C4—92no—
664C2×C4—181no—
665C2×C4—181no—
666C2×C4—181no—
667C2×C4—181no—
668C2×C4—181no—
669C2×C4—181no—
670C2×C4—181no—
671C2×C4—272no—
672C2×C4—541no—
673C2×C4—541no—
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—21no—
694C2×C3—21no—
695C2×C3—41no—
696C2×C3—41no—
697C2×C3—41no—
698C2×C3—41no—
699C2×C3—41no—
700C2×C3—41no—
701C2×C3—41no—
702C2×C3#6383711yescharacteristic
703C2×C3#6384011yescharacteristic
704C2×C3#6384011yescharacteristic
705C2×C3Dic3×Dic611yescharacteristic
706C2×C3#6384311yescharacteristic
707C2×C3#6384511yescharacteristic
708C2×C3#6384611yescharacteristic
709C2×C3#6387111yescharacteristic
710C2×C3#6387211yescharacteristic
711C2×C3D3×Dic3⋊C411yescharacteristic
712C2×C3#6388111yescharacteristic
713C2×C3#6388711yescharacteristic
714C2×C3D3×C4⋊Dic311yescharacteristic
715C2×C3#6389311yescharacteristic
716C2×C3#6389811yescharacteristic
717C2×C3#6391011yescharacteristic
718C2×C3#6391611yescharacteristic
719C2×C3#6391911yescharacteristic
720C2×C3#6395811yescharacteristic
721C2×C3C2×Dic3⋊Dic311yescharacteristic
722C2×C3#67⋊Dic311yescharacteristic
723C22D32×Dic311yescharacteristic
724C22D3×#62611yescharacteristic
725C22#8895411yescharacteristic
726C22D3×#62711yescharacteristic
727C22#8895711yescharacteristic
728C22#8896211yescharacteristic
729C22#8896411yescharacteristic
730C4—34no—
731C4—62no—
732C4—121no—
733C4—182no—
734C4—182no—
735C4—361no—
736C4—542no—
737C3—21no—
738C3—21no—
739C3—21no—
740C3—41no—
741C3#1059123411yescharacteristic, complemented
742C3#1059126811yescharacteristic, complemented
743C3#1059135711yescharacteristic, complemented
744C2D3×Dic3⋊Dic311yescharacteristic
745C2#1172292911yescharacteristic
746C2#1172294011yescharacteristic
747C2#1172296311yescharacteristic
748C2#1172297411yescharacteristic
749C2#1172301311yescharacteristic
750C2#1172303711yescharacteristic
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
22. C3×Dic3⋊Dic3C4semidirect
117. Dic3⋊Dic3Dic3semidirect
134. C32×Dic3C4⋊C4semidirect
394. C3×Dic3Dic3⋊C4semidirect
395. C3×Dic3C4⋊Dic3semidirect
403. C33#389semidirect
644. Dic3Dic3⋊Dic3semidirect
649. C32#4647semidirect
650. C32#4972semidirect
651. C32#4984semidirect
741. C3#10591234semidirect
742. C3#10591268semidirect
743. C3#10591357semidirect

Maximal subgroups

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

subgroupindex
C2×#888072
C2×Dic3⋊(C3⋊Dic3)2
C2×Dic3×C3⋊Dic32
C2×C3×Dic3⋊Dic32
#117220822
C3×#635792
#105913573
#105912683
#105912343