Finite Group Databasebeta

← C3×#10591235 #13158407

Subgroups — C3×#10591235 #13158407

Order 1728.

1042 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#627C211yesmaximal, characteristic
2C2×C32×Dic3⋊C4C211yesmaximal, characteristic
3C2×C3×Dic32C211yesmaximal, characteristic
4C3×#63658C211yesmaximal, characteristic
5C32×C3⋊#95C211yesmaximal, characteristic
6C3×#63579C211yesmaximal, characteristic
7C3×#63579C211yesmaximal, characteristic
8C3×#4973—31nomaximal
9C3×#4646—31nomaximal
10#10591235C311yesmaximal, 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×#627C414yescomplemented
21C32×Dic3⋊C4—22no—
22C3×Dic32—22no—
23C22×C3×Dic6—31no—
24C22×C3×Dic6—31no—
25C22×#627C2×C311yescharacteristic
26C2×C32×C4⋊C4—31no—
27C2×C3×Dic3⋊C4—21no—
28C2×C3×Dic3⋊C4D311yescharacteristic
29C2×C3×Dic3⋊C4C2×C311yescharacteristic
30C2×C3×C4×Dic3—31no—
31C2×C3×C4×Dic3—31no—
32C2×Dic32C2×C311yescharacteristic
33C32×#95—31no—
34#63658C2×C311yescharacteristic
35C3×C3⋊#95—21no—
36C3×C3⋊#95—31no—
37C3×C3⋊#95—31no—
38C3×C3⋊#95—31no—
39C3×C3⋊#95—31no—
40C3×C3⋊#95—31no—
41C3×C3⋊#95—31no—
42C3×C3⋊#95—61no—
43C3×C3⋊#95D311yescharacteristic
44C3×C3⋊#95C2×C311yescharacteristic
45#63579C2×C311yescharacteristic
46#63579C2×C311yescharacteristic
47C23×C33C2311yescharacteristic
48C2×C33×C4—21no—
49C2×C33×C4—21no—
50C2×C33×C4—21no—
51C2×C3×C3⋊Dic3—21no—
52C2×C3×C3⋊Dic3—21no—
53C2×C3×C3⋊Dic3—21no—
54C2×C3×C3⋊Dic3—21no—
55C2×C3×C3⋊Dic3C2×C412yes—
56C2×C3×C3⋊Dic3Q812yescomplemented
57C2×C32×Dic3—21no—
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×Dic3D412yes—
67C2×C32×Dic3D412yes—
68C2×C32×Dic3Q812yescomplemented
69C3×#627—28no—
70C3×#391—91no—
71#4973—31no—
72#4646—31no—
73C22×C32×C4—21no—
74C22×C32×C4—21no—
75C22×C32×C4—21no—
76C22×C32×C4—31no—
77C22×C32×C4—31no—
78C22×C32×C4—31no—
79C22×C32×C4—31no—
80C22×C32×C4—41no—
81C22×C32×C4C2×D311yescharacteristic
82C22×C32×C4C2×D311yescharacteristic
83C22×C32×C4C22×C311yescharacteristic
84C22×C3⋊Dic3C22×C311yescharacteristic
85C22×C3⋊Dic3C22×C311yescharacteristic
86C22×C3×Dic3—21no—
87C22×C3×Dic3—21no—
88C22×C3×Dic3—21no—
89C22×C3×Dic3—21no—
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×Dic3C2×D311yescharacteristic
97C22×C3×Dic3C2×D311yescharacteristic
98C22×C3×Dic3C2×D311yescharacteristic
99C22×C3×Dic3C2×D311yescharacteristic
100C22×C3×Dic3C22×C311yescharacteristic
101C22×C3×Dic3C22×C311yescharacteristic
102C22×C3×Dic3C22×C311yescharacteristic
103C22×C3×Dic3C22×C311yescharacteristic
104C2×C3×Dic6—34no—
105C2×C3×Dic6—34no—
106C2×C3×Dic6—62no—
107C2×C3×Dic6—62no—
108C2×C3×Dic6—62no—
109C2×C3×Dic6—62no—
110C2×#627—22no—
111C2×#627—22no—
112C2×#627C3×C414yescomplemented
113C32×C4⋊C4—62no—
114C3×Dic3⋊C4—24no—
115C3×Dic3⋊C4—22no—
116C3×Dic3⋊C4—22no—
117C3×C4×Dic3—62no—
118C3×C4×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
127C33×C4—41no—
128C3×C3⋊Dic3—22no—
129C3×C3⋊Dic3—22no—
130C32×Dic3—22no—
131C32×Dic3—22no—
132C32×Dic3—41no—
133C32×Dic3C22⋊C414yes—
134C22×C3×Q8—91no—
135C22×Dic6—31no—
136C22×Dic6—31no—
137C2×C3×C4⋊C4—31no—
138C2×C3×C4⋊C4—31no—
139C2×C3×C4⋊C4—61no—
140C2×C3×C42—91no—
141C2×Dic3⋊C4C3×D311yescharacteristic
142C2×C4×Dic3—31no—
143C2×C4×Dic3—31no—
144C3×#95—31no—
145C3×#95—31no—
146C3×#95—61no—
147C3×#95—91no—
148C3×#95—91no—
149C3×#95—91no—
150C3⋊#95—31no—
151C3⋊#95—31no—
152C3⋊#95—31no—
153C3⋊#95—31no—
154C3⋊#95—31no—
155C3⋊#95—31no—
156C3⋊#95—61no—
157C3⋊#95C3×D311yescharacteristic
158C23×C32—21no—
159C23×C32—21no—
160C23×C32—21no—
161C23×C32—41no—
162C23×C32C22×D311yescharacteristic
163C23×C32C22×D311yescharacteristic
164C23×C32C23×C311yescharacteristic
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4—22no—
169C2×C32×C4—22no—
170C2×C32×C4—22no—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—32no—
178C2×C32×C4—32no—
179C2×C32×C4—32no—
180C2×C32×C4—32no—
181C2×C32×C4—32no—
182C2×C32×C4—41no—
183C2×C32×C4—41no—
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—42no—
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×C3⋊Dic3—21no—
199C2×C3⋊Dic3—21no—
200C2×C3⋊Dic3—21no—
201C2×C3⋊Dic3—21no—
202C2×C3⋊Dic3C2×C3×C412yes—
203C2×C3⋊Dic3C3×Q812yescomplemented
204C2×C3×Dic3—21no—
205C2×C3×Dic3—21no—
206C2×C3×Dic3—21no—
207C2×C3×Dic3—21no—
208C2×C3×Dic3—21no—
209C2×C3×Dic3—21no—
210C2×C3×Dic3—21no—
211C2×C3×Dic3—21no—
212C2×C3×Dic3—22no—
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—22no—
220C2×C3×Dic3—22no—
221C2×C3×Dic3—22no—
222C2×C3×Dic3—22no—
223C2×C3×Dic3—22no—
224C2×C3×Dic3—32no—
225C2×C3×Dic3—32no—
226C2×C3×Dic3—32no—
227C2×C3×Dic3—32no—
228C2×C3×Dic3—41no—
229C2×C3×Dic3—41no—
230C2×C3×Dic3—41no—
231C2×C3×Dic3—41no—
232C2×C3×Dic3—41no—
233C2×C3×Dic3—41no—
234C2×C3×Dic3—62no—
235C2×C3×Dic3—62no—
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—61no—
243C2×C3×Dic3—61no—
244C2×C3×Dic3—121no—
245C2×C3×Dic3—121no—
246C2×C3×Dic3—121no—
247C2×C3×Dic3—121no—
248C2×C3×Dic3Dic612yescomplemented
249C2×C3×Dic3C4×D312yes—
250C2×C3×Dic3C4×D312yes—
251C2×C3×Dic3D1212yes—
252C2×C3×Dic3#6712yes—
253C2×C3×Dic3C2×C3×C412yes—
254C2×C3×Dic3C2×C3×C412yes—
255C2×C3×Dic3C3×D412yes—
256C2×C3×Dic3C3×D412yes—
257C2×C3×Dic3C3×Q812yescomplemented
258C3×Dic6—68no—
259C3×Dic6—68no—
260#627—28no—
261#391—91noSylow
262C2×C33C2×C22⋊C411yescharacteristic
263C2×C33C4×Q811yescharacteristic
264C2×C33C4×Q811yescharacteristic
265C2×C33C22⋊Q811yescharacteristic
266C2×C33C22⋊Q811yescharacteristic
267C2×C33#12411yescharacteristic
268C2×C33C4⋊Q811yescharacteristic
269C2×C3×Q8—94no—
270C2×C3×Q8—182no—
271C2×C3×Q8—182no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—31no—
276C22×C3×C4—31no—
277C22×C3×C4—31no—
278C22×C3×C4—31no—
279C22×C3×C4—31no—
280C22×C3×C4—31no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—41no—
284C22×C3×C4—61no—
285C22×C3×C4—61no—
286C22×C3×C4—61no—
287C22×C3×C4—61no—
288C22×C3×C4—91no—
289C22×C3×C4—91no—
290C22×C3×C4D3211yescharacteristic
291C22×C3×C4C2×C3×D311yescharacteristic
292C22×C3×C4C2×C3×D311yescharacteristic
293C22×Dic3—31no—
294C22×Dic3—31no—
295C22×Dic3—31no—
296C22×Dic3—31no—
297C22×Dic3—61no—
298C22×Dic3—61no—
299C22×Dic3C2×C3×D311yescharacteristic
300C22×Dic3C2×C3×D311yescharacteristic
301C22×Dic3C2×C3×D311yescharacteristic
302C22×Dic3C2×C3×D311yescharacteristic
303C2×Dic6—34no—
304C2×Dic6—34no—
305C2×Dic6—62no—
306C2×Dic6—62no—
307C2×Dic6—62no—
308C2×Dic6—62no—
309C3×C4⋊C4—62no—
310C3×C4⋊C4—62no—
311C3×C4⋊C4—64no—
312C3×C42—182no—
313Dic3⋊C4—22no—
314C4×Dic3—62no—
315C4×Dic3—62no—
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×C4×D311yescharacteristic
346C22×C32C2×C4×D311yescharacteristic
347C22×C32C2×D1211yescharacteristic
348C22×C32#23511yescharacteristic
349C22×C32D3×D411yescharacteristic
350C22×C32D3×D411yescharacteristic
351C22×C32#23711yescharacteristic
352C22×C32#23711yescharacteristic
353C22×C32#23711yescharacteristic
354C22×C32D3×Q811yescharacteristic
355C22×C32D3×Q811yescharacteristic
356C22×C32D3×Q811yescharacteristic
357C22×C32C2×#6711yescharacteristic
358C22×C32C22×C3×C411yescharacteristic
359C22×C32C2×C3×D411yescharacteristic
360C22×C32C2×C3×D411yescharacteristic
361C22×C32C2×C3×Q811yescharacteristic
362C22×C32C2×C3×Q811yescharacteristic
363C22×C32C3×#4111yescharacteristic
364C22×C32C3×#4111yescharacteristic
365C32×C4—34no—
366C32×C4—42no—
367C32×C4—42no—
368C32×C4—42no—
369C32×C4—44no—
370C32×C4—41no—
371C32×C4—41no—
372C32×C4—41no—
373C32×C4—62no—
374C32×C4—62no—
375C32×C4—121no—
376C3⋊Dic3—22no—
377C3⋊Dic3—22no—
378C3×Dic3—22no—
379C3×Dic3—22no—
380C3×Dic3—22no—
381C3×Dic3—22no—
382C3×Dic3—24no—
383C3×Dic3—42no—
384C3×Dic3—42no—
385C3×Dic3—42no—
386C3×Dic3—41no—
387C3×Dic3—41no—
388C3×Dic3—62no—
389C3×Dic3—62no—
390C3×Dic3—62no—
391C3×Dic3—62no—
392C3×Dic3—122no—
393C3×Dic3—122no—
394C3×Dic3(C2×D3)⋊C414yes—
395C3×Dic3C3×C22⋊C414yes—
396C22×Q8—91no—
397C2×C4⋊C4—31no—
398C2×C42—91no—
399#95—31no—
400#95—91no—
401#95—91no—
402#95—91no—
403C33#39111yescharacteristic, complemented, Sylow
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—41no—
408C23×C3C2×D3211yescharacteristic
409C23×C3C22×C3×D311yescharacteristic
410C23×C3C22×C3×D311yescharacteristic
411C3×Q8—188no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—32no—
425C2×C3×C4—32no—
426C2×C3×C4—32no—
427C2×C3×C4—32no—
428C2×C3×C4—32no—
429C2×C3×C4—32no—
430C2×C3×C4—32no—
431C2×C3×C4—32no—
432C2×C3×C4—32no—
433C2×C3×C4—32no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
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—62no—
447C2×C3×C4—62no—
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—62no—
457C2×C3×C4—61no—
458C2×C3×C4—61no—
459C2×C3×C4—61no—
460C2×C3×C4—61no—
461C2×C3×C4—61no—
462C2×C3×C4—61no—
463C2×C3×C4—92no—
464C2×C3×C4—92no—
465C2×C3×C4—121no—
466C2×C3×C4—121no—
467C2×C3×C4—121no—
468C2×C3×C4—121no—
469C2×C3×C4—121no—
470C2×C3×C4—121no—
471C2×C3×C4—181no—
472C2×C3×C4—181no—
473C2×C3×C4—181no—
474C2×C3×C4—181no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—32no—
483C2×Dic3—32no—
484C2×Dic3—32no—
485C2×Dic3—32no—
486C2×Dic3—62no—
487C2×Dic3—62no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—121no—
497C2×Dic3—121no—
498C2×Dic3—121no—
499C2×Dic3—121no—
500C2×Dic3C3×Dic612yescomplemented
501C2×Dic3C3×C4×D312yes—
502C2×Dic3C3×C4×D312yes—
503C2×Dic3C3×D1212yes—
504C2×Dic3C3×#6712yes—
505Dic6—68no—
506Dic6—68no—
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—21no—
526C2×C32—21no—
527C2×C32—21no—
528C2×C32—41no—
529C2×C32—41no—
530C2×C32—41no—
531C2×C32—41no—
532C2×C32—41no—
533C2×C32—41no—
534C2×C32—41no—
535C2×C32C4×Dic611yescharacteristic
536C2×C32#87811yescharacteristic
537C2×C32D3×C22⋊C411yescharacteristic
538C2×C32#88511yescharacteristic
539C2×C32#88711yescharacteristic
540C2×C32#88711yescharacteristic
541C2×C32#88711yescharacteristic
542C2×C32#88811yescharacteristic
543C2×C32#89611yescharacteristic
544C2×C32#89711yescharacteristic
545C2×C32#89711yescharacteristic
546C2×C32C2×(C2×D3)⋊C411yescharacteristic
547C2×C32#93611yescharacteristic
548C2×C32#94411yescharacteristic
549C2×C32C2×C3×C22⋊C411yescharacteristic
550C2×C32C3×C4×Q811yescharacteristic
551C2×C32C3×C4×Q811yescharacteristic
552C2×C32C3×C22⋊Q811yescharacteristic
553C2×C32C3×C22⋊Q811yescharacteristic
554C2×C32C3×#12411yescharacteristic
555C2×C32C3×C4⋊Q811yescharacteristic
556C2×Q8—94no—
557C2×Q8—182no—
558C2×Q8—182no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—91no—
564C22×C4—91no—
565C22×C4C3×D3211yescharacteristic
566C4⋊C4—62no—
567C42—182no—
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—21no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3D3×Dic611yescharacteristic
597C22×C3#379711yescharacteristic
598C22×C3C4×D3211yescharacteristic
599C22×C3D3×D1211yescharacteristic
600C22×C3#380411yescharacteristic
601C22×C3#380511yescharacteristic
602C22×C3D3×#6711yescharacteristic
603C22×C3C2×C3×Dic611yescharacteristic
604C22×C3C2×C3×C4×D311yescharacteristic
605C22×C3C2×C3×C4×D311yescharacteristic
606C22×C3C2×C3×D1211yescharacteristic
607C22×C3C3×#23511yescharacteristic
608C22×C3C3×D3×D411yescharacteristic
609C22×C3C3×D3×D411yescharacteristic
610C22×C3C3×#23711yescharacteristic
611C22×C3C3×#23711yescharacteristic
612C22×C3C3×#23711yescharacteristic
613C22×C3C3×D3×Q811yescharacteristic
614C22×C3C3×D3×Q811yescharacteristic
615C22×C3C3×D3×Q811yescharacteristic
616C22×C3C2×C3×#6711yescharacteristic
617C3×C4—34no—
618C3×C4—34no—
619C3×C4—42no—
620C3×C4—42no—
621C3×C4—42no—
622C3×C4—44no—
623C3×C4—41no—
624C3×C4—41no—
625C3×C4—41no—
626C3×C4—64no—
627C3×C4—62no—
628C3×C4—62no—
629C3×C4—62no—
630C3×C4—62no—
631C3×C4—122no—
632C3×C4—122no—
633C3×C4—122no—
634C3×C4—121no—
635C3×C4—121no—
636C3×C4—182no—
637C3×C4—182no—
638Dic3—22no—
639Dic3—22no—
640Dic3—41no—
641Dic3—62no—
642Dic3—62no—
643Dic3—62no—
644Dic3—62no—
645Dic3—122no—
646Dic3—122no—
647Dic3C3×(C2×D3)⋊C414yes—
648C32—21no—
649C32—21no—
650C32—21no—
651C32—41no—
652C32#464611yescharacteristic, complemented
653C32#497311yescharacteristic, complemented
654C32C3×#39111yescharacteristic, complemented
655C23C2×C3×D3211yescharacteristic
656Q8—188no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—32no—
661C2×C4—32no—
662C2×C4—32no—
663C2×C4—32no—
664C2×C4—32no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—92no—
673C2×C4—92no—
674C2×C4—181no—
675C2×C4—181no—
676C2×C4—181no—
677C2×C4—181no—
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—21no—
696C2×C3—21no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—41no—
700C2×C3—41no—
701C2×C3—41no—
702C2×C3—41no—
703C2×C3—41no—
704C2×C3—41no—
705C2×C3—41no—
706C2×C3#6383711yescharacteristic
707C2×C3#6383811yescharacteristic
708C2×C3#6383911yescharacteristic
709C2×C3#6389311yescharacteristic
710C2×C3#6389511yescharacteristic
711C2×C3D3×(C2×D3)⋊C411yescharacteristic
712C2×C3#6395911yescharacteristic
713C2×C3C3×C4×Dic611yescharacteristic
714C2×C3C3×#87811yescharacteristic
715C2×C3C3×D3×C22⋊C411yescharacteristic
716C2×C3C3×#88511yescharacteristic
717C2×C3C3×#88711yescharacteristic
718C2×C3C3×#88711yescharacteristic
719C2×C3C3×#88711yescharacteristic
720C2×C3C3×#88811yescharacteristic
721C2×C3C3×#89611yescharacteristic
722C2×C3C3×#89711yescharacteristic
723C2×C3C3×#89711yescharacteristic
724C2×C3C2×C3×(C2×D3)⋊C411yescharacteristic
725C2×C3C3×#93611yescharacteristic
726C2×C3C3×#94411yescharacteristic
727C22C3×D3×Dic611yescharacteristic
728C22C3×#379711yescharacteristic
729C22C3×C4×D3211yescharacteristic
730C22C3×D3×D1211yescharacteristic
731C22C3×#380411yescharacteristic
732C22C3×#380511yescharacteristic
733C22C3×D3×#6711yescharacteristic
734C4—34no—
735C4—41no—
736C4—62no—
737C4—62no—
738C4—121no—
739C4—182no—
740C4—182no—
741C3—21no—
742C3—21no—
743C3—21no—
744C3—41no—
745C3#1059123511yescharacteristic, direct product factor
746C3C3×#464611yescharacteristic, complemented
747C3C3×#497311yescharacteristic, complemented
748C2C3×#6383711yescharacteristic
749C2C3×#6383811yescharacteristic
750C2C3×#6383911yescharacteristic
751C2C3×#6389311yescharacteristic
752C2C3×#6389511yescharacteristic
753C2C3×D3×(C2×D3)⋊C411yescharacteristic
754C2C3×#6395911yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutatorC22×C32C22×C3×C4
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socle, prime radicalC23×C33C23
cosocleC23×C32C23×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×#391
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
10. #10591235C3direct (N × H)
20. C2×C3×#627C4semidirect
56. C2×C3×C3⋊Dic3Q8semidirect
68. C2×C32×Dic3Q8semidirect
112. C2×#627C3×C4semidirect
203. C2×C3⋊Dic3C3×Q8semidirect
248. C2×C3×Dic3Dic6semidirect
257. C2×C3×Dic3C3×Q8semidirect
403. C33#391semidirect
500. C2×Dic3C3×Dic6semidirect
652. C32#4646semidirect
653. C32#4973semidirect
654. C32C3×#391semidirect
745. C3#10591235direct (N × H)
746. C3C3×#4646semidirect
747. C3C3×#4973semidirect

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×Dic3⋊C42
C2×C3×Dic322
C3×#636582
C32×C3⋊#952
C3×#635792
C3×#49733
C3×#46463
#105912353