Finite Group Databasebeta

← #13156759

Subgroups — #13156759

Order 1728.

1570 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6289C211yesmaximal, characteristic
2C2×#88815C211yesmaximal, characteristic, complemented
3C2×#88804C211yesmaximal, characteristic
4C2×#88804C211yesmaximal, characteristic
5C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
6C3×#63579C211yesmaximal, characteristic, complemented
7C3×#63579C211yesmaximal, characteristic, complemented
8#10591378—31nomaximal
9#10591375—31nomaximal
10#10591290—31nomaximal
11C23×C3⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×C3⋊Dic3C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C32×Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C2×#6289—22no—
19C2×#6289—22no—
20C2×#6289—22no—
21#88815—22no—
22#88804—22no—
23#88804C414yescomplemented
24C3×Dic3⋊Dic3—22no—
25C22×C4×C3⋊D3—31no—
26C22×#624—31no—
27C22×#624—31no—
28C22×#624—61no—
29C2×#3752—31no—
30C2×#3752—31no—
31C2×C3×C4⋊Dic3—31no—
32C2×C3×Dic3⋊C4—31no—
33C2×#3724—31no—
34C2×Dic3⋊Dic3—31no—
35C2×Dic3⋊Dic3—31no—
36C2×Dic3⋊Dic3D311yescharacteristic, complemented
37C2×#3722—31no—
38C2×#3722—31no—
39C2×#3722—31no—
40C2×#3722—31no—
41C2×#3722—61no—
42C2×#3722—61no—
43C3×C3⋊#95—31no—
44C3×C3⋊#95—31no—
45C3×C3⋊#95—31no—
46C3×C3⋊#95—31no—
47#63579D311yescharacteristic, complemented
48#63579D311yescharacteristic, complemented
49C23×C33C2311yescharacteristic
50C22×C3⋊(C3⋊D3)—21no—
51C22×C3⋊(C3⋊D3)—21no—
52C22×C3⋊(C3⋊D3)—21no—
53C22×C3⋊(C3⋊D3)—21no—
54C22×C3⋊(C3⋊D3)C2×C412yes—
55C22×C3⋊(C3⋊D3)D412yes—
56C22×C3⋊(C3⋊D3)Q812yes—
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×C412yescomplemented
65C2×C3×C3⋊Dic3D412yes—
66C2×C32×Dic3—21no—
67C2×C32×Dic3—21no—
68C2×C32×Dic3—21no—
69C2×C32×Dic3—21no—
70C2×C32×Dic3—21no—
71C2×C32×Dic3—21no—
72C2×C32×Dic3—21no—
73C2×C32×Dic3C2×C412yescomplemented
74C2×C32×Dic3D412yes—
75#6289—28no—
76#4989—91no—
77#4668—91no—
78#4668—91no—
79C23×C3⋊D3—31no—
80C23×C3⋊D3—31no—
81C23×C3⋊D3—31no—
82C23×C3⋊D3—61no—
83C23×C3⋊D3—61no—
84C23×C3⋊D3—61no—
85C23×C3⋊D3—121no—
86C22×C32×C4—31no—
87C22×C32×C4—31no—
88C22×C32×C4—31no—
89C22×C3⋊Dic3C2×D311yescharacteristic
90C22×C3⋊Dic3C2×D311yescharacteristic
91C22×C3⋊Dic3C2×D311yescharacteristic
92C2×C4×C3⋊D3—62no—
93C2×C4×C3⋊D3—62no—
94C2×C4×C3⋊D3—62no—
95C22×C3×Dic3—21no—
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—31no—
99C22×C3×Dic3—31no—
100C22×C3×Dic3—31no—
101C22×C3×Dic3—31no—
102C22×C3×Dic3—31no—
103C22×C3×Dic3—31no—
104C22×C3×Dic3—61no—
105C22×C3×Dic3—61no—
106C22×C3×Dic3—61no—
107C22×C3×Dic3C2×D311yescharacteristic
108C22×C3×Dic3C2×D311yescharacteristic
109C22×C3×Dic3C2×D311yescharacteristic
110C22×C3×Dic3C2×D311yescharacteristic
111C22×C3×Dic3C2×D311yescharacteristic
112C22×C3×Dic3C2×D311yescharacteristic
113C2×#624—62no—
114C2×#624—62no—
115C2×#624—62no—
116C2×#624—62no—
117C2×#624—64no—
118C2×#624—64no—
119C2×#624—64no—
120C2×#624—62no—
121C2×#624—62no—
122#3752—34no—
123#3752—62no—
124C3×C4⋊Dic3—62no—
125C3×Dic3⋊C4—62no—
126#3724—62no—
127Dic3⋊Dic3—22no—
128Dic3⋊Dic3—62no—
129Dic3⋊Dic3—62no—
130#3722—34no—
131#3722—34no—
132#3722—62no—
133#3722—62no—
134#3722—64no—
135#3722—64no—
136C22×C33C22×C411yescharacteristic
137C22×C33C2×D411yescharacteristic
138C22×C33C2×D411yescharacteristic
139C22×C33C2×D411yescharacteristic
140C22×C33C2×Q811yescharacteristic
141C22×C33#4111yescharacteristic
142C22×C33#4111yescharacteristic
143C2×C3⋊(C3⋊D3)—22no—
144C2×C3⋊(C3⋊D3)—22no—
145C2×C3⋊(C3⋊D3)—22no—
146C2×C3⋊(C3⋊D3)—22no—
147C2×C3⋊(C3⋊D3)—22no—
148C2×C3⋊(C3⋊D3)—22no—
149C2×C3⋊(C3⋊D3)C4⋊C414yescomplemented
150C3×C3⋊Dic3—22no—
151C3×C3⋊Dic3—22no—
152C3×C3⋊Dic3—41no—
153C32×Dic3—22no—
154C32×Dic3—22no—
155C32×Dic3—41no—
156C22×C4×D3—91no—
157C22×C4×D3—91no—
158C22×C4×D3—91no—
159C22×C4×D3—181no—
160C2×C3×C4⋊C4—91no—
161C2×(C2×D3)⋊C4—91no—
162C2×(C2×D3)⋊C4—91no—
163C2×(C2×D3)⋊C4—91no—
164C2×(C2×D3)⋊C4—91no—
165C2×(C2×D3)⋊C4—91no—
166C2×(C2×D3)⋊C4—91no—
167C2×(C2×D3)⋊C4—181no—
168C2×(C2×D3)⋊C4—181no—
169C2×C4⋊Dic3—31no—
170C2×C4⋊Dic3—91no—
171C2×Dic3⋊C4—31no—
172C2×Dic3⋊C4—91no—
173C2×Dic3⋊C4—91no—
174C3×#95—91no—
175C3×#95—91no—
176C3⋊#95—31no—
177C3⋊#95—31no—
178C3⋊#95—31no—
179C3⋊#95—31no—
180C23×C32—21no—
181C23×C32—21no—
182C23×C32—21no—
183C23×C32—41no—
184C23×C32C22×D311yescharacteristic
185C23×C32C22×D311yescharacteristic
186C23×C32C22×D311yescharacteristic
187C22×C3⋊D3—32no—
188C22×C3⋊D3—32no—
189C22×C3⋊D3—32no—
190C22×C3⋊D3—32no—
191C22×C3⋊D3—32no—
192C22×C3⋊D3—32no—
193C22×C3⋊D3—32no—
194C22×C3⋊D3—32no—
195C22×C3⋊D3—32no—
196C22×C3⋊D3—62no—
197C22×C3⋊D3—62no—
198C22×C3⋊D3—62no—
199C22×C3⋊D3—62no—
200C22×C3⋊D3—62no—
201C22×C3⋊D3—62no—
202C22×C3⋊D3—62no—
203C22×C3⋊D3—62no—
204C22×C3⋊D3—62no—
205C22×C3⋊D3—61no—
206C22×C3⋊D3—61no—
207C22×C3⋊D3—61no—
208C22×C3⋊D3—61no—
209C22×C3⋊D3—62no—
210C22×C3⋊D3—62no—
211C22×C3⋊D3—62no—
212C22×C3⋊D3—62no—
213C22×C3⋊D3—61no—
214C22×C3⋊D3—61no—
215C22×C3⋊D3—61no—
216C22×C3⋊D3—61no—
217C22×C3⋊D3—61no—
218C22×C3⋊D3—61no—
219C22×C3⋊D3—61no—
220C22×C3⋊D3—61no—
221C22×C3⋊D3—122no—
222C22×C3⋊D3—122no—
223C22×C3⋊D3—122no—
224C22×C3⋊D3—121no—
225C22×C3⋊D3—121no—
226C22×C3⋊D3—121no—
227C22×C3⋊D3—121no—
228C22×C3⋊D3—121no—
229C22×C3⋊D3—121no—
230C22×C3⋊D3—121no—
231C22×C3⋊D3—121no—
232C22×C3⋊D3—122no—
233C22×C3⋊D3—122no—
234C22×C3⋊D3—122no—
235C22×C3⋊D3—122no—
236C2×C32×C4—32no—
237C2×C32×C4—32no—
238C2×C32×C4—61no—
239C2×C32×C4—61no—
240C2×C32×C4—61no—
241C2×C32×C4—61no—
242C2×C32×C4—61no—
243C2×C32×C4—61no—
244C2×C32×C4—61no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3C4×D312yescomplemented
253C2×C3⋊Dic3D1212yes—
254C4×C3⋊D3—68no—
255C2×C3×Dic3—22no—
256C2×C3×Dic3—22no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—22no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—22no—
273C2×C3×Dic3—22no—
274C2×C3×Dic3—32no—
275C2×C3×Dic3—32no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—41no—
279C2×C3×Dic3—41no—
280C2×C3×Dic3—41no—
281C2×C3×Dic3—41no—
282C2×C3×Dic3—62no—
283C2×C3×Dic3—62no—
284C2×C3×Dic3—62no—
285C2×C3×Dic3—62no—
286C2×C3×Dic3—61no—
287C2×C3×Dic3—61no—
288C2×C3×Dic3—61no—
289C2×C3×Dic3—61no—
290C2×C3×Dic3—61no—
291C2×C3×Dic3—61no—
292C2×C3×Dic3—61no—
293C2×C3×Dic3—61no—
294C2×C3×Dic3—62no—
295C2×C3×Dic3—61no—
296C2×C3×Dic3—61no—
297C2×C3×Dic3—61no—
298C2×C3×Dic3—61no—
299C2×C3×Dic3—61no—
300C2×C3×Dic3—61no—
301C2×C3×Dic3—121no—
302C2×C3×Dic3—121no—
303C2×C3×Dic3—121no—
304C2×C3×Dic3—121no—
305C2×C3×Dic3C4×D312yescomplemented
306C2×C3×Dic3C4×D312yescomplemented
307C2×C3×Dic3D1212yes—
308C2×C3×Dic3#6712yes—
309#624—616no—
310#624—68no—
311#624—68no—
312#385—271noSylow
313C2×C33C2×C4⋊C411yescharacteristic
314C2×C33C4×D411yescharacteristic
315C2×C33C4×D411yescharacteristic
316C2×C33#12011yescharacteristic
317C2×C33C22⋊Q811yescharacteristic
318C2×C33C22⋊Q811yescharacteristic
319C2×C33#12311yescharacteristic
320C3⋊(C3⋊D3)—24no—
321C23×D3—91no—
322C23×D3—91no—
323C23×D3—91no—
324C23×D3—181no—
325C23×D3—181no—
326C23×D3—181no—
327C23×D3—361no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—61no—
335C22×C3×C4—61no—
336C22×C3×C4—61no—
337C22×C3×C4—91no—
338C22×C3×C4—91no—
339C22×C3×C4—91no—
340C22×Dic3—31no—
341C22×Dic3—31no—
342C22×Dic3—31no—
343C22×Dic3—31no—
344C22×Dic3—31no—
345C22×Dic3—31no—
346C22×Dic3—61no—
347C22×Dic3—61no—
348C22×Dic3—61no—
349C22×Dic3D3211yescharacteristic
350C22×Dic3D3211yescharacteristic
351C22×Dic3D3211yescharacteristic
352C2×C4×D3—182no—
353C2×C4×D3—182no—
354C2×C4×D3—182no—
355C2×C4×D3—182no—
356C2×C4×D3—182no—
357C2×C4×D3—182no—
358C2×C4×D3—182no—
359C2×C4×D3—182no—
360C2×C4×D3—184no—
361C2×C4×D3—184no—
362C2×C4×D3—184no—
363C2×C4×D3—182no—
364C3×C4⋊C4—182no—
365(C2×D3)⋊C4—94no—
366(C2×D3)⋊C4—94no—
367(C2×D3)⋊C4—94no—
368(C2×D3)⋊C4—184no—
369(C2×D3)⋊C4—182no—
370(C2×D3)⋊C4—182no—
371(C2×D3)⋊C4—182no—
372(C2×D3)⋊C4—184no—
373C4⋊Dic3—62no—
374C4⋊Dic3—182no—
375Dic3⋊C4—62no—
376Dic3⋊C4—182no—
377Dic3⋊C4—182no—
378C22×C32—21no—
379C22×C32—21no—
380C22×C32—21no—
381C22×C32—21no—
382C22×C32—21no—
383C22×C32—21no—
384C22×C32—21no—
385C22×C32—21no—
386C22×C32—21no—
387C22×C32—21no—
388C22×C32—21no—
389C22×C32—21no—
390C22×C32—21no—
391C22×C32—21no—
392C22×C32—21no—
393C22×C32—21no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—21no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32—41no—
400C22×C32—41no—
401C22×C32—41no—
402C22×C32—41no—
403C22×C32—41no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32C2×C4×D311yescharacteristic
407C22×C32C2×C4×D311yescharacteristic
408C22×C32C2×C4×D311yescharacteristic
409C22×C32C2×D1211yescharacteristic
410C22×C32C2×D1211yescharacteristic
411C22×C32#23511yescharacteristic
412C22×C32#23511yescharacteristic
413C22×C32#23511yescharacteristic
414C22×C32D3×D411yescharacteristic
415C22×C32D3×D411yescharacteristic
416C22×C32D3×D411yescharacteristic
417C22×C32D3×D411yescharacteristic
418C22×C32D3×D411yescharacteristic
419C22×C32D3×D411yescharacteristic
420C22×C32#23711yescharacteristic
421C22×C32#23711yescharacteristic
422C22×C32D3×Q811yescharacteristic
423C22×C32D3×Q811yescharacteristic
424C22×C32D3×Q811yescharacteristic
425C22×C32#23911yescharacteristic
426C22×C32C2×#6711yescharacteristic
427C2×C3⋊D3—34no—
428C2×C3⋊D3—34no—
429C2×C3⋊D3—34no—
430C2×C3⋊D3—64no—
431C2×C3⋊D3—64no—
432C2×C3⋊D3—64no—
433C2×C3⋊D3—62no—
434C2×C3⋊D3—62no—
435C2×C3⋊D3—62no—
436C2×C3⋊D3—62no—
437C2×C3⋊D3—62no—
438C2×C3⋊D3—62no—
439C2×C3⋊D3—64no—
440C2×C3⋊D3—64no—
441C2×C3⋊D3—64no—
442C2×C3⋊D3—64no—
443C2×C3⋊D3—64no—
444C2×C3⋊D3—64no—
445C2×C3⋊D3—62no—
446C2×C3⋊D3—62no—
447C2×C3⋊D3—62no—
448C2×C3⋊D3—62no—
449C2×C3⋊D3—62no—
450C2×C3⋊D3—62no—
451C2×C3⋊D3—62no—
452C2×C3⋊D3—62no—
453C2×C3⋊D3—62no—
454C2×C3⋊D3—62no—
455C2×C3⋊D3—62no—
456C2×C3⋊D3—62no—
457C2×C3⋊D3—124no—
458C2×C3⋊D3—122no—
459C2×C3⋊D3—122no—
460C2×C3⋊D3—122no—
461C2×C3⋊D3—122no—
462C2×C3⋊D3—122no—
463C2×C3⋊D3—122no—
464C2×C3⋊D3—122no—
465C2×C3⋊D3—122no—
466C2×C3⋊D3—122no—
467C2×C3⋊D3—122no—
468C2×C3⋊D3—122no—
469C2×C3⋊D3—122no—
470C2×C3⋊D3—124no—
471C2×C3⋊D3—124no—
472C2×C3⋊D3—124no—
473C2×C3⋊D3—124no—
474C2×C3⋊D3—124no—
475C2×C3⋊D3—124no—
476C32×C4—62no—
477C32×C4—62no—
478C32×C4—121no—
479C3⋊Dic3—22no—
480C3⋊Dic3—22no—
481C3⋊Dic3—41no—
482C3×Dic3—24no—
483C3×Dic3—22no—
484C3×Dic3—22no—
485C3×Dic3—22no—
486C3×Dic3—22no—
487C3×Dic3—42no—
488C3×Dic3—42no—
489C3×Dic3—41no—
490C3×Dic3—41no—
491C3×Dic3—64no—
492C3×Dic3—62no—
493C3×Dic3—62no—
494C3×Dic3—62no—
495C3×Dic3—62no—
496C3×Dic3—122no—
497C3×Dic3—122no—
498C3×Dic3—121no—
499C3×Dic3—121no—
500C23×C4—271no—
501C2×C4⋊C4—91no—
502C2×C4⋊C4—271no—
503C2×C22⋊C4—271no—
504C2×C22⋊C4—271no—
505#95—91no—
506#95—91no—
507C33#38511yescharacteristic, complemented, Sylow
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—21no—
511C23×C3—41no—
512C23×C3C2×D3211yescharacteristic
513C23×C3C2×D3211yescharacteristic
514C23×C3C2×D3211yescharacteristic
515C22×D3—92no—
516C22×D3—92no—
517C22×D3—92no—
518C22×D3—92no—
519C22×D3—92no—
520C22×D3—92no—
521C22×D3—92no—
522C22×D3—92no—
523C22×D3—92no—
524C22×D3—182no—
525C22×D3—182no—
526C22×D3—182no—
527C22×D3—182no—
528C22×D3—182no—
529C22×D3—182no—
530C22×D3—182no—
531C22×D3—182no—
532C22×D3—182no—
533C22×D3—182no—
534C22×D3—182no—
535C22×D3—182no—
536C22×D3—182no—
537C22×D3—181no—
538C22×D3—181no—
539C22×D3—181no—
540C22×D3—181no—
541C22×D3—181no—
542C22×D3—181no—
543C22×D3—181no—
544C22×D3—181no—
545C22×D3—181no—
546C22×D3—181no—
547C22×D3—181no—
548C22×D3—181no—
549C22×D3—362no—
550C22×D3—362no—
551C22×D3—362no—
552C22×D3—361no—
553C22×D3—361no—
554C22×D3—361no—
555C22×D3—361no—
556C22×D3—361no—
557C22×D3—361no—
558C22×D3—361no—
559C22×D3—361no—
560C22×D3—362no—
561C22×D3—362no—
562C22×D3—362no—
563C22×D3—362no—
564C2×C3×C4—32no—
565C2×C3×C4—32no—
566C2×C3×C4—32no—
567C2×C3×C4—32no—
568C2×C3×C4—62no—
569C2×C3×C4—62no—
570C2×C3×C4—62no—
571C2×C3×C4—62no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—62no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—92no—
588C2×C3×C4—92no—
589C2×C3×C4—121no—
590C2×C3×C4—121no—
591C2×C3×C4—121no—
592C2×C3×C4—121no—
593C2×C3×C4—181no—
594C2×C3×C4—181no—
595C2×C3×C4—181no—
596C2×C3×C4—181no—
597C2×C3×C4—181no—
598C2×C3×C4—181no—
599C2×C3×C4—181no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—32no—
608C2×Dic3—32no—
609C2×Dic3—32no—
610C2×Dic3—32no—
611C2×Dic3—62no—
612C2×Dic3—62no—
613C2×Dic3—62no—
614C2×Dic3—62no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—61no—
618C2×Dic3—61no—
619C2×Dic3—61no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—61no—
623C2×Dic3—62no—
624C2×Dic3—61no—
625C2×Dic3—61no—
626C2×Dic3—61no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—121no—
631C2×Dic3—121no—
632C2×Dic3—121no—
633C2×Dic3—121no—
634C2×Dic3#62412yescomplemented
635C2×Dic3#62612yes—
636C4×D3—188no—
637C4×D3—1816no—
638C4×D3—188no—
639C4×D3—188no—
640C2×C32—21no—
641C2×C32—21no—
642C2×C32—21no—
643C2×C32—21no—
644C2×C32—21no—
645C2×C32—21no—
646C2×C32—21no—
647C2×C32—21no—
648C2×C32—21no—
649C2×C32—21no—
650C2×C32—21no—
651C2×C32—21no—
652C2×C32—21no—
653C2×C32—21no—
654C2×C32—21no—
655C2×C32—21no—
656C2×C32—21no—
657C2×C32—21no—
658C2×C32—21no—
659C2×C32—21no—
660C2×C32—21no—
661C2×C32—41no—
662C2×C32—41no—
663C2×C32—41no—
664C2×C32—41no—
665C2×C32—41no—
666C2×C32—41no—
667C2×C32—41no—
668C2×C32C4×D1211yescharacteristic
669C2×C32C4×D1211yescharacteristic
670C2×C32#67⋊C411yescharacteristic
671C2×C32#67⋊C411yescharacteristic
672C2×C32#88211yescharacteristic
673C2×C32#88211yescharacteristic
674C2×C32#88311yescharacteristic
675C2×C32#88311yescharacteristic
676C2×C32D3×C4⋊C411yescharacteristic
677C2×C32D3×C4⋊C411yescharacteristic
678C2×C32D3×C4⋊C411yescharacteristic
679C2×C32#89311yescharacteristic
680C2×C32#89411yescharacteristic
681C2×C32#89611yescharacteristic
682C2×C32#89611yescharacteristic
683C2×C32#89611yescharacteristic
684C2×C32#89711yescharacteristic
685C2×C32#89711yescharacteristic
686C2×C32C4×#6711yescharacteristic
687C2×C32#93711yescharacteristic
688C2×C32#94611yescharacteristic
689C3⋊D3—64no—
690C3⋊D3—68no—
691C3⋊D3—64no—
692C3⋊D3—64no—
693C3⋊D3—124no—
694C3⋊D3—124no—
695C3⋊D3—128no—
696C24—271no—
697C22×C4—31no—
698C22×C4—31no—
699C22×C4—31no—
700C22×C4—91no—
701C22×C4—91no—
702C22×C4—91no—
703C22×C4—542no—
704C22×C4—542no—
705C22×C4—542no—
706C4⋊C4—182no—
707C4⋊C4—542no—
708C22⋊C4—274no—
709C22⋊C4—542no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3#379611yescharacteristic
739C22×C3#379711yescharacteristic
740C22×C3#379711yescharacteristic
741C22×C3#379711yescharacteristic
742C22×C3#379811yescharacteristic
743C22×C3#379911yescharacteristic
744C22×C3C4×D3211yescharacteristic
745C22×C3C4×D3211yescharacteristic
746C22×C3D3×D1211yescharacteristic
747C22×C3D3×D1211yescharacteristic
748C22×C3D3×D1211yescharacteristic
749C22×C3#380211yescharacteristic
750C22×C3#380411yescharacteristic
751C22×C3#380411yescharacteristic
752C22×C3#380411yescharacteristic
753C22×C3C2×#62411yescharacteristic
754C22×C3C2×#62611yescharacteristic
755C22×C3D3×#6711yescharacteristic
756C22×C3#381111yescharacteristic
757C22×C3#381111yescharacteristic
758C22×C3#381111yescharacteristic
759C2×D3—94no—
760C2×D3—94no—
761C2×D3—94no—
762C2×D3—184no—
763C2×D3—184no—
764C2×D3—184no—
765C2×D3—184no—
766C2×D3—184no—
767C2×D3—184no—
768C2×D3—184no—
769C2×D3—184no—
770C2×D3—184no—
771C2×D3—182no—
772C2×D3—182no—
773C2×D3—182no—
774C2×D3—182no—
775C2×D3—182no—
776C2×D3—182no—
777C2×D3—182no—
778C2×D3—182no—
779C2×D3—182no—
780C2×D3—182no—
781C2×D3—182no—
782C2×D3—182no—
783C2×D3—182no—
784C2×D3—182no—
785C2×D3—182no—
786C2×D3—182no—
787C2×D3—182no—
788C2×D3—182no—
789C2×D3—364no—
790C2×D3—362no—
791C2×D3—362no—
792C2×D3—362no—
793C2×D3—362no—
794C2×D3—362no—
795C2×D3—362no—
796C2×D3—362no—
797C2×D3—362no—
798C2×D3—362no—
799C2×D3—362no—
800C2×D3—362no—
801C2×D3—362no—
802C2×D3—364no—
803C2×D3—364no—
804C2×D3—364no—
805C2×D3—364no—
806C2×D3—364no—
807C2×D3—364no—
808C3×C4—64no—
809C3×C4—62no—
810C3×C4—62no—
811C3×C4—62no—
812C3×C4—62no—
813C3×C4—122no—
814C3×C4—122no—
815C3×C4—121no—
816C3×C4—121no—
817C3×C4—182no—
818C3×C4—182no—
819C3×C4—361no—
820Dic3—22no—
821Dic3—22no—
822Dic3—41no—
823Dic3—64no—
824Dic3—62no—
825Dic3—62no—
826Dic3—62no—
827Dic3—62no—
828Dic3—122no—
829Dic3—122no—
830Dic3—121no—
831Dic3—121no—
832C32—21no—
833C32—21no—
834C32—21no—
835C32—41no—
836C32#466811yescharacteristic, complemented
837C32#466811yescharacteristic, complemented
838C32#498911yescharacteristic, complemented
839C23—272no—
840C23—272no—
841C23—272no—
842C23—541no—
843C23—541no—
844C23—541no—
845C23—541no—
846C23D3311yescharacteristic
847C2×C4—32no—
848C2×C4—32no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—92no—
857C2×C4—92no—
858C2×C4—181no—
859C2×C4—181no—
860C2×C4—181no—
861C2×C4—181no—
862C2×C4—181no—
863C2×C4—181no—
864C2×C4—181no—
865C2×C4—548no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—21no—
870C2×C3—21no—
871C2×C3—21no—
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—21no—
879C2×C3—21no—
880C2×C3—21no—
881C2×C3—21no—
882C2×C3—21no—
883C2×C3—21no—
884C2×C3—21no—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—41no—
888C2×C3—41no—
889C2×C3—41no—
890C2×C3—41no—
891C2×C3—41no—
892C2×C3—41no—
893C2×C3—41no—
894C2×C3#6385311yescharacteristic
895C2×C3#6385411yescharacteristic
896C2×C3#6386511yescharacteristic
897C2×C3#6387111yescharacteristic
898C2×C3#6388011yescharacteristic
899C2×C3#6388011yescharacteristic
900C2×C3#6388111yescharacteristic
901C2×C3#6388311yescharacteristic
902C2×C3#6388311yescharacteristic
903C2×C3#6388811yescharacteristic
904C2×C3#6389411yescharacteristic
905C2×C3#6389511yescharacteristic
906C2×C3#6389511yescharacteristic
907C2×C3#6389511yescharacteristic
908C2×C3#6390011yescharacteristic
909C2×C3C4×#62611yescharacteristic
910C2×C3#6392211yescharacteristic
911C2×C3#6392311yescharacteristic
912C2×C3#6395211yescharacteristic
913C2×C3#6397511yescharacteristic
914C2×C3#6398111yescharacteristic
915D3—188no—
916D3—184no—
917D3—184no—
918D3—184no—
919D3—364no—
920D3—364no—
921D3—368no—
922C22—274no—
923C22—542no—
924C22—542no—
925C22—542no—
926C22—542no—
927C22—542no—
928C22—542no—
929C22D3×#62411yescharacteristic
930C22D3×#62611yescharacteristic
931C22#8895411yescharacteristic
932C22#8895511yescharacteristic
933C22#8895811yescharacteristic
934C22#8895911yescharacteristic
935C22#8896211yescharacteristic
936C4—62no—
937C4—62no—
938C4—121no—
939C4—182no—
940C4—182no—
941C4—361no—
942C3—21no—
943C3—21no—
944C3—21no—
945C3—41no—
946C3#1059129011yescharacteristic, complemented
947C3#1059137511yescharacteristic, complemented
948C3#1059137811yescharacteristic, complemented
949C2—544no—
950C2#1172291211yescharacteristic
951C2#1172293211yescharacteristic
952C2#1172293711yescharacteristic
953C2#1172295011yescharacteristic
954C2#1172297311yescharacteristic
955C2#1172298211yescharacteristic
956C2#1172299611yescharacteristic
subgroupG/H
center, Frattini, hypercenterC23D33
commutatorC22×C33C22×C4
Fitting, socle, cosocleC23×C33C23
prime radicalC23×C3⋊(C3⋊D3)C22
hypocenterC33#385
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C2×#88815C2semidirect
5. C2×C3×Dic3⋊Dic3C2semidirect
6. C3×#63579C2semidirect
7. C3×#63579C2semidirect
23. #88804C4semidirect
36. C2×Dic3⋊Dic3D3semidirect
47. #63579D3semidirect
48. #63579D3semidirect
64. C2×C3×C3⋊Dic3C2×C4semidirect
73. C2×C32×Dic3C2×C4semidirect
149. C2×C3⋊(C3⋊D3)C4⋊C4semidirect
252. C2×C3⋊Dic3C4×D3semidirect
305. C2×C3×Dic3C4×D3semidirect
306. C2×C3×Dic3C4×D3semidirect
507. C33#385semidirect
634. C2×Dic3#624semidirect
836. C32#4668semidirect
837. C32#4668semidirect
838. C32#4989semidirect
946. C3#10591290semidirect
947. C3#10591375semidirect
948. C3#10591378semidirect

Maximal subgroups

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

subgroupindex
C22×#62892
C2×#888152
C2×#888042
C2×C3×Dic3⋊Dic32
C3×#635792
#105913783
#105913753
#105912903