Finite Group Databasebeta

← C3×#10591338 #13158411

Subgroups — C3×#10591338 #13158411

Order 1728.

1026 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#627C211yesmaximal, characteristic
2C2×C32×C4⋊Dic3C211yesmaximal, characteristic
3C2×C3×#3724C211yesmaximal, characteristic
4C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic
5C3×#63658C211yesmaximal, characteristic
6C32×C3⋊#95C211yesmaximal, characteristic
7C3×#63579C211yesmaximal, characteristic
8C3×#4979—31nomaximal
9C3×#4656—31nomaximal
10#10591338C311yesmaximal, characteristic, direct product factor
11C22×C33×C4C2211yescharacteristic
12C22×C3×C3⋊Dic3C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C22×C32×Dic3C2211yescharacteristic
15C22×C32×Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C2×C3×#627—22no—
19C2×C3×#627—22no—
20C2×C3×#627—22no—
21C32×C4⋊Dic3—22no—
22C3×#3724—22no—
23C3×Dic3⋊Dic3—22no—
24C22×C3×Dic6—31no—
25C22×C3×Dic6—31no—
26C22×#627C2×C311yescharacteristic
27C2×C32×C4⋊C4—31no—
28C2×C3×C4⋊Dic3—21no—
29C2×C3×C4⋊Dic3—31no—
30C2×C3×C4⋊Dic3D311yescharacteristic
31C2×C3×C4⋊Dic3C2×C311yescharacteristic
32C2×C3×Dic3⋊C4—31no—
33C2×C3×Dic3⋊C4—31no—
34C2×C3×Dic3⋊C4—31no—
35C2×#3724C2×C311yescharacteristic
36C2×Dic3⋊Dic3C2×C311yescharacteristic
37C32×#95—31no—
38#63658C2×C311yescharacteristic
39C3×C3⋊#95—21no—
40C3×C3⋊#95—31no—
41C3×C3⋊#95—31no—
42C3×C3⋊#95—31no—
43C3×C3⋊#95—31no—
44C3×C3⋊#95—61no—
45C3×C3⋊#95D311yescharacteristic
46C3×C3⋊#95C2×C311yescharacteristic
47#63579C2×C311yescharacteristic
48C23×C33C2311yescharacteristic
49C2×C33×C4—21no—
50C2×C33×C4—21no—
51C2×C33×C4Q812yescomplemented
52C2×C3×C3⋊Dic3—21no—
53C2×C3×C3⋊Dic3—21no—
54C2×C3×C3⋊Dic3—21no—
55C2×C3×C3⋊Dic3—21no—
56C2×C3×C3⋊Dic3D412yes—
57C2×C3×C3⋊Dic3Q812yescomplemented
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×Dic3—21no—
66C2×C32×Dic3—21no—
67C2×C32×Dic3D412yes—
68C2×C32×Dic3D412yes—
69C2×C32×Dic3Q812yescomplemented
70C3×#627—28no—
71C3×#395—91no—
72#4979—31no—
73#4656—31no—
74C22×C32×C4—21no—
75C22×C32×C4—21no—
76C22×C32×C4—21no—
77C22×C32×C4—31no—
78C22×C32×C4—31no—
79C22×C32×C4—31no—
80C22×C32×C4—31no—
81C22×C32×C4—41no—
82C22×C32×C4C2×D311yescharacteristic
83C22×C32×C4C2×D311yescharacteristic
84C22×C32×C4C22×C311yescharacteristic
85C22×C3⋊Dic3C22×C311yescharacteristic
86C22×C3⋊Dic3C22×C311yescharacteristic
87C22×C3×Dic3—21no—
88C22×C3×Dic3—21no—
89C22×C3×Dic3—21no—
90C22×C3×Dic3—21no—
91C22×C3×Dic3—31no—
92C22×C3×Dic3—31no—
93C22×C3×Dic3—31no—
94C22×C3×Dic3—31no—
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×Dic3C22×C311yescharacteristic
102C22×C3×Dic3C22×C311yescharacteristic
103C22×C3×Dic3C22×C311yescharacteristic
104C22×C3×Dic3C22×C311yescharacteristic
105C2×C3×Dic6—62no—
106C2×C3×Dic6—62no—
107C2×C3×Dic6—62no—
108C2×C3×Dic6—62no—
109C2×C3×Dic6—62no—
110C2×C3×Dic6—62no—
111C2×#627—22no—
112C2×#627—22no—
113C2×#627—22no—
114C32×C4⋊C4—62no—
115C3×C4⋊Dic3—24no—
116C3×C4⋊Dic3—22no—
117C3×C4⋊Dic3—22no—
118C3×C4⋊Dic3—62no—
119C3×Dic3⋊C4—62no—
120C3×Dic3⋊C4—62no—
121C3×Dic3⋊C4—62no—
122#3724—22no—
123Dic3⋊Dic3—22no—
124C22×C33C2×D411yescharacteristic
125C22×C33C2×D411yescharacteristic
126C22×C33C2×D411yescharacteristic
127C22×C33C2×Q811yescharacteristic
128C22×C33C2×Q811yescharacteristic
129C22×C33C2×Q811yescharacteristic
130C22×C33#4111yescharacteristic
131C33×C4—22no—
132C3×C3⋊Dic3—22no—
133C3×C3⋊Dic3—22no—
134C32×Dic3—22no—
135C32×Dic3—22no—
136C32×Dic3—22no—
137C32×Dic3—41no—
138C22×C3×Q8—91no—
139C22×Dic6—31no—
140C22×Dic6—31no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C4⋊C4—31no—
143C2×C3×C4⋊C4—61no—
144C2×C3×C4⋊C4—91no—
145C2×C3×C4⋊C4—91no—
146C2×C4⋊Dic3—31no—
147C2×C4⋊Dic3C3×D311yescharacteristic
148C2×Dic3⋊C4—31no—
149C2×Dic3⋊C4—31no—
150C2×Dic3⋊C4—31no—
151C3×#95—31no—
152C3×#95—31no—
153C3×#95—61no—
154C3×#95—91no—
155C3×#95—91no—
156C3⋊#95—31no—
157C3⋊#95—31no—
158C3⋊#95—31no—
159C3⋊#95—31no—
160C3⋊#95—61no—
161C3⋊#95C3×D311yescharacteristic
162C23×C32—21no—
163C23×C32—21no—
164C23×C32—21no—
165C23×C32—41no—
166C23×C32C22×D311yescharacteristic
167C23×C32C22×D311yescharacteristic
168C23×C32C23×C311yescharacteristic
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—22no—
172C2×C32×C4—22no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—22no—
178C2×C32×C4—22no—
179C2×C32×C4—22no—
180C2×C32×C4—32no—
181C2×C32×C4—32no—
182C2×C32×C4—32no—
183C2×C32×C4—42no—
184C2×C32×C4—41no—
185C2×C32×C4—41no—
186C2×C32×C4—41no—
187C2×C32×C4—41no—
188C2×C32×C4—42no—
189C2×C32×C4—42no—
190C2×C32×C4—61no—
191C2×C32×C4—61no—
192C2×C32×C4—61no—
193C2×C32×C4—61no—
194C2×C32×C4—61no—
195C2×C32×C4—61no—
196C2×C32×C4—61no—
197C2×C32×C4—61no—
198C2×C32×C4—61no—
199C2×C32×C4Dic612yescomplemented
200C2×C32×C4Dic612yescomplemented
201C2×C32×C4C3×Q812yescomplemented
202C2×C3⋊Dic3—21no—
203C2×C3⋊Dic3—21no—
204C2×C3⋊Dic3—21no—
205C2×C3⋊Dic3—21no—
206C2×C3⋊Dic3C3×D412yes—
207C2×C3⋊Dic3C3×Q812yescomplemented
208C2×C3×Dic3—21no—
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—21no—
216C2×C3×Dic3—21no—
217C2×C3×Dic3—21no—
218C2×C3×Dic3—21no—
219C2×C3×Dic3—21no—
220C2×C3×Dic3—22no—
221C2×C3×Dic3—21no—
222C2×C3×Dic3—21no—
223C2×C3×Dic3—21no—
224C2×C3×Dic3—21no—
225C2×C3×Dic3—21no—
226C2×C3×Dic3—21no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3—22no—
230C2×C3×Dic3—32no—
231C2×C3×Dic3—32no—
232C2×C3×Dic3—32no—
233C2×C3×Dic3—32no—
234C2×C3×Dic3—41no—
235C2×C3×Dic3—41no—
236C2×C3×Dic3—41no—
237C2×C3×Dic3—41no—
238C2×C3×Dic3—41no—
239C2×C3×Dic3—41no—
240C2×C3×Dic3—41no—
241C2×C3×Dic3—41no—
242C2×C3×Dic3—62no—
243C2×C3×Dic3—62no—
244C2×C3×Dic3—61no—
245C2×C3×Dic3—61no—
246C2×C3×Dic3—61no—
247C2×C3×Dic3—61no—
248C2×C3×Dic3—61no—
249C2×C3×Dic3—61no—
250C2×C3×Dic3—61no—
251C2×C3×Dic3—61no—
252C2×C3×Dic3—121no—
253C2×C3×Dic3—121no—
254C2×C3×Dic3—121no—
255C2×C3×Dic3—121no—
256C2×C3×Dic3Dic612yescomplemented
257C2×C3×Dic3D1212yes—
258C2×C3×Dic3#6712yes—
259C2×C3×Dic3C3×D412yes—
260C2×C3×Dic3C3×D412yes—
261C2×C3×Dic3C3×Q812yescomplemented
262C3×Dic6—68no—
263C3×Dic6—68no—
264#627—28no—
265#395—91noSylow
266C2×C33#12011yescharacteristic
267C2×C33C22⋊Q811yescharacteristic
268C2×C33C22⋊Q811yescharacteristic
269C2×C33C22⋊Q811yescharacteristic
270C2×C33C4⋊Q811yescharacteristic
271C2×C33C4⋊Q811yescharacteristic
272C2×C33C4⋊Q811yescharacteristic
273C2×C3×Q8—182no—
274C2×C3×Q8—182no—
275C2×C3×Q8—182no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—31no—
280C22×C3×C4—31no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—41no—
288C22×C3×C4—61no—
289C22×C3×C4—61no—
290C22×C3×C4—61no—
291C22×C3×C4—61no—
292C22×C3×C4—91no—
293C22×C3×C4—91no—
294C22×C3×C4D3211yescharacteristic
295C22×C3×C4C2×C3×D311yescharacteristic
296C22×C3×C4C2×C3×D311yescharacteristic
297C22×Dic3—31no—
298C22×Dic3—31no—
299C22×Dic3—31no—
300C22×Dic3—31no—
301C22×Dic3—61no—
302C22×Dic3—61no—
303C22×Dic3C2×C3×D311yescharacteristic
304C22×Dic3C2×C3×D311yescharacteristic
305C22×Dic3C2×C3×D311yescharacteristic
306C22×Dic3C2×C3×D311yescharacteristic
307C2×Dic6—62no—
308C2×Dic6—62no—
309C2×Dic6—62no—
310C2×Dic6—62no—
311C2×Dic6—62no—
312C2×Dic6—62no—
313C3×C4⋊C4—62no—
314C3×C4⋊C4—62no—
315C3×C4⋊C4—64no—
316C3×C4⋊C4—182no—
317C3×C4⋊C4—182no—
318C4⋊Dic3—22no—
319C4⋊Dic3—62no—
320Dic3⋊C4—62no—
321Dic3⋊C4—62no—
322Dic3⋊C4—62no—
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—21no—
338C22×C32—21no—
339C22×C32—21no—
340C22×C32—21no—
341C22×C32—21no—
342C22×C32—21no—
343C22×C32—21no—
344C22×C32—41no—
345C22×C32—41no—
346C22×C32—41no—
347C22×C32—41no—
348C22×C32—41no—
349C22×C32—41no—
350C22×C32—41no—
351C22×C32C2×Dic611yescharacteristic
352C22×C32C2×Dic611yescharacteristic
353C22×C32C2×Dic611yescharacteristic
354C22×C32C2×D1211yescharacteristic
355C22×C32#23511yescharacteristic
356C22×C32D3×D411yescharacteristic
357C22×C32D3×D411yescharacteristic
358C22×C32D3×D411yescharacteristic
359C22×C32D3×D411yescharacteristic
360C22×C32#23711yescharacteristic
361C22×C32D3×Q811yescharacteristic
362C22×C32D3×Q811yescharacteristic
363C22×C32D3×Q811yescharacteristic
364C22×C32C2×#6711yescharacteristic
365C22×C32C2×C3×D411yescharacteristic
366C22×C32C2×C3×D411yescharacteristic
367C22×C32C2×C3×D411yescharacteristic
368C22×C32C2×C3×Q811yescharacteristic
369C22×C32C2×C3×Q811yescharacteristic
370C22×C32C2×C3×Q811yescharacteristic
371C22×C32C3×#4111yescharacteristic
372C32×C4—22no—
373C32×C4—24no—
374C32×C4—22no—
375C32×C4—22no—
376C32×C4—42no—
377C32×C4—42no—
378C32×C4—44no—
379C32×C4—62no—
380C32×C4—62no—
381C32×C4—62no—
382C32×C4—121no—
383C3⋊Dic3—22no—
384C3⋊Dic3—22no—
385C3×Dic3—22no—
386C3×Dic3—22no—
387C3×Dic3—22no—
388C3×Dic3—22no—
389C3×Dic3—22no—
390C3×Dic3—22no—
391C3×Dic3—42no—
392C3×Dic3—42no—
393C3×Dic3—42no—
394C3×Dic3—42no—
395C3×Dic3—41no—
396C3×Dic3—41no—
397C3×Dic3—62no—
398C3×Dic3—62no—
399C3×Dic3—62no—
400C3×Dic3—62no—
401C3×Dic3—122no—
402C3×Dic3—122no—
403C22×Q8—91no—
404C2×C4⋊C4—31no—
405C2×C4⋊C4—91no—
406C2×C4⋊C4—91no—
407#95—31no—
408#95—91no—
409#95—91no—
410C33#39511yescharacteristic, complemented, Sylow
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—41no—
415C23×C3C2×D3211yescharacteristic
416C23×C3C22×C3×D311yescharacteristic
417C23×C3C22×C3×D311yescharacteristic
418C3×Q8—188no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—32no—
431C2×C3×C4—32no—
432C2×C3×C4—32no—
433C2×C3×C4—32no—
434C2×C3×C4—32no—
435C2×C3×C4—32no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—42no—
441C2×C3×C4—42no—
442C2×C3×C4—42no—
443C2×C3×C4—62no—
444C2×C3×C4—62no—
445C2×C3×C4—62no—
446C2×C3×C4—61no—
447C2×C3×C4—61no—
448C2×C3×C4—61no—
449C2×C3×C4—61no—
450C2×C3×C4—61no—
451C2×C3×C4—61no—
452C2×C3×C4—61no—
453C2×C3×C4—61no—
454C2×C3×C4—61no—
455C2×C3×C4—61no—
456C2×C3×C4—61no—
457C2×C3×C4—61no—
458C2×C3×C4—62no—
459C2×C3×C4—61no—
460C2×C3×C4—61no—
461C2×C3×C4—61no—
462C2×C3×C4—61no—
463C2×C3×C4—61no—
464C2×C3×C4—61no—
465C2×C3×C4—92no—
466C2×C3×C4—92no—
467C2×C3×C4—121no—
468C2×C3×C4—121no—
469C2×C3×C4—121no—
470C2×C3×C4—121no—
471C2×C3×C4—121no—
472C2×C3×C4—121no—
473C2×C3×C4—121no—
474C2×C3×C4—121no—
475C2×C3×C4—181no—
476C2×C3×C4—181no—
477C2×C3×C4—181no—
478C2×C3×C4—181no—
479C2×C3×C4#62712yescomplemented
480C2×C3×C4C3×Dic612yescomplemented
481C2×C3×C4C3×Dic612yescomplemented
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—32no—
492C2×Dic3—32no—
493C2×Dic3—32no—
494C2×Dic3—32no—
495C2×Dic3—62no—
496C2×Dic3—62no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—61no—
503C2×Dic3—61no—
504C2×Dic3—61no—
505C2×Dic3—121no—
506C2×Dic3—121no—
507C2×Dic3—121no—
508C2×Dic3—121no—
509C2×Dic3C3×Dic612yescomplemented
510C2×Dic3C3×D1212yes—
511C2×Dic3C3×#6712yes—
512Dic6—68no—
513Dic6—68no—
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—21no—
526C2×C32—21no—
527C2×C32—21no—
528C2×C32—21no—
529C2×C32—21no—
530C2×C32—21no—
531C2×C32—21no—
532C2×C32—21no—
533C2×C32—21no—
534C2×C32—21no—
535C2×C32—41no—
536C2×C32—41no—
537C2×C32—41no—
538C2×C32—41no—
539C2×C32—41no—
540C2×C32—41no—
541C2×C32—41no—
542C2×C32#86911yescharacteristic
543C2×C32#87811yescharacteristic
544C2×C32#87811yescharacteristic
545C2×C32#88211yescharacteristic
546C2×C32#88811yescharacteristic
547C2×C32#88811yescharacteristic
548C2×C32#88811yescharacteristic
549C2×C32#88811yescharacteristic
550C2×C32#89611yescharacteristic
551C2×C32#89611yescharacteristic
552C2×C32#89711yescharacteristic
553C2×C32#92411yescharacteristic
554C2×C32#93711yescharacteristic
555C2×C32#94411yescharacteristic
556C2×C32C3×#12011yescharacteristic
557C2×C32C3×C22⋊Q811yescharacteristic
558C2×C32C3×C22⋊Q811yescharacteristic
559C2×C32C3×C22⋊Q811yescharacteristic
560C2×C32C3×C4⋊Q811yescharacteristic
561C2×C32C3×C4⋊Q811yescharacteristic
562C2×C32C3×C4⋊Q811yescharacteristic
563C2×Q8—182no—
564C2×Q8—182no—
565C2×Q8—182no—
566C22×C4—31no—
567C22×C4—31no—
568C22×C4—31no—
569C22×C4—31no—
570C22×C4—91no—
571C22×C4—91no—
572C22×C4C3×D3211yescharacteristic
573C4⋊C4—62no—
574C4⋊C4—182no—
575C4⋊C4—182no—
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—21no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3D3×Dic611yescharacteristic
605C22×C3#379711yescharacteristic
606C22×C3D3×D1211yescharacteristic
607C22×C3#380211yescharacteristic
608C22×C3#380411yescharacteristic
609C22×C3C2×#62711yescharacteristic
610C22×C3D3×#6711yescharacteristic
611C22×C3C2×C3×Dic611yescharacteristic
612C22×C3C2×C3×Dic611yescharacteristic
613C22×C3C2×C3×Dic611yescharacteristic
614C22×C3C2×C3×D1211yescharacteristic
615C22×C3C3×#23511yescharacteristic
616C22×C3C3×D3×D411yescharacteristic
617C22×C3C3×D3×D411yescharacteristic
618C22×C3C3×D3×D411yescharacteristic
619C22×C3C3×D3×D411yescharacteristic
620C22×C3C3×#23711yescharacteristic
621C22×C3C3×D3×Q811yescharacteristic
622C22×C3C3×D3×Q811yescharacteristic
623C22×C3C3×D3×Q811yescharacteristic
624C22×C3C2×C3×#6711yescharacteristic
625C3×C4—24no—
626C3×C4—22no—
627C3×C4—22no—
628C3×C4—22no—
629C3×C4—42no—
630C3×C4—42no—
631C3×C4—44no—
632C3×C4—62no—
633C3×C4—62no—
634C3×C4—62no—
635C3×C4—62no—
636C3×C4—62no—
637C3×C4—62no—
638C3×C4—122no—
639C3×C4—122no—
640C3×C4—122no—
641C3×C4—122no—
642C3×C4—121no—
643C3×C4—121no—
644C3×C4—182no—
645C3×C4—182no—
646Dic3—22no—
647Dic3—22no—
648Dic3—22no—
649Dic3—41no—
650Dic3—62no—
651Dic3—62no—
652Dic3—62no—
653Dic3—62no—
654Dic3—122no—
655Dic3—122no—
656C32—21no—
657C32—21no—
658C32—21no—
659C32—41no—
660C32#465611yescharacteristic, complemented
661C32#497911yescharacteristic, complemented
662C32C3×#39511yescharacteristic, complemented
663C23C2×C3×D3211yescharacteristic
664Q8—188no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—32no—
668C2×C4—32no—
669C2×C4—32no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—92no—
680C2×C4—92no—
681C2×C4—181no—
682C2×C4—181no—
683C2×C4—181no—
684C2×C4—181no—
685C2×C4C3×#62712yescomplemented
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—21no—
696C2×C3—21no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—41no—
708C2×C3—41no—
709C2×C3—41no—
710C2×C3—41no—
711C2×C3—41no—
712C2×C3—41no—
713C2×C3—41no—
714C2×C3#6383911yescharacteristic
715C2×C3#6389511yescharacteristic
716C2×C3#6389911yescharacteristic
717C2×C3#6391811yescharacteristic
718C2×C3#6391911yescharacteristic
719C2×C3#6392211yescharacteristic
720C2×C3#6396411yescharacteristic
721C2×C3C3×#86911yescharacteristic
722C2×C3C3×#87811yescharacteristic
723C2×C3C3×#87811yescharacteristic
724C2×C3C3×#88211yescharacteristic
725C2×C3C3×#88811yescharacteristic
726C2×C3C3×#88811yescharacteristic
727C2×C3C3×#88811yescharacteristic
728C2×C3C3×#88811yescharacteristic
729C2×C3C3×#89611yescharacteristic
730C2×C3C3×#89611yescharacteristic
731C2×C3C3×#89711yescharacteristic
732C2×C3C3×#92411yescharacteristic
733C2×C3C3×#93711yescharacteristic
734C2×C3C3×#94411yescharacteristic
735C22C3×D3×Dic611yescharacteristic
736C22C3×#379711yescharacteristic
737C22C3×D3×D1211yescharacteristic
738C22C3×#380211yescharacteristic
739C22C3×#380411yescharacteristic
740C22C2×C3×#62711yescharacteristic
741C22C3×D3×#6711yescharacteristic
742C4—22no—
743C4—62no—
744C4—62no—
745C4—62no—
746C4—121no—
747C4—182no—
748C4—182no—
749C3—21no—
750C3—21no—
751C3—21no—
752C3—41no—
753C3#1059133811yescharacteristic, direct product factor
754C3C3×#465611yescharacteristic, complemented
755C3C3×#497911yescharacteristic, complemented
756C2C3×#6383911yescharacteristic
757C2C3×#6389511yescharacteristic
758C2C3×#6389911yescharacteristic
759C2C3×#6391811yescharacteristic
760C2C3×#6391911yescharacteristic
761C2C3×#6392211yescharacteristic
762C2C3×#6396411yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC23×C32C23×C3
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socle, prime radicalC23×C33C23
hypercenterC22×C3×C4D32
hypocenterC32C3×#395
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
10. #10591338C3direct (N × H)
51. C2×C33×C4Q8semidirect
57. C2×C3×C3⋊Dic3Q8semidirect
69. C2×C32×Dic3Q8semidirect
199. C2×C32×C4Dic6semidirect
200. C2×C32×C4Dic6semidirect
201. C2×C32×C4C3×Q8semidirect
207. C2×C3⋊Dic3C3×Q8semidirect
256. C2×C3×Dic3Dic6semidirect
261. C2×C3×Dic3C3×Q8semidirect
410. C33#395semidirect
479. C2×C3×C4#627semidirect
480. C2×C3×C4C3×Dic6semidirect
481. C2×C3×C4C3×Dic6semidirect
509. C2×Dic3C3×Dic6semidirect
660. C32#4656semidirect
661. C32#4979semidirect
662. C32C3×#395semidirect
685. C2×C4C3×#627semidirect
753. C3#10591338direct (N × H)
754. C3C3×#4656semidirect
755. C3C3×#4979semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#6272
C2×C32×C4⋊Dic32
C2×C3×#37242
C2×C3×Dic3⋊Dic32
C3×#636582
C32×C3⋊#952
C3×#635792
C3×#49793
C3×#46563
#105913383