Finite Group Databasebeta

← C3×#10591343 #13158276

Subgroups — C3×#10591343 #13158276

Order 1728.

834 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4⋊Dic3C211yesmaximal, characteristic
2C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic
3C3×#63658C211yesmaximal, characteristic
4C32×C3⋊#95C211yesmaximal, characteristic
5C3×#63579C211yesmaximal, characteristic
6C3×#63579C211yesmaximal, characteristic
7C3×#63579C211yesmaximal, characteristic
8C3×#4986—31nomaximal
9C3×#4660—31nomaximal
10#10591343C311yesmaximal, 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
18C32×C4⋊Dic3—22no—
19C3×Dic3⋊Dic3—22no—
20C2×C32×C4⋊C4—31no—
21C2×C3×C4⋊Dic3—21no—
22C2×C3×C4⋊Dic3—31no—
23C2×C3×C4⋊Dic3D311yescharacteristic
24C2×C3×C4⋊Dic3C2×C311yescharacteristic
25C2×C3×Dic3⋊C4—31no—
26C2×Dic3⋊Dic3C2×C311yescharacteristic
27C32×#95—31no—
28#63658C2×C311yescharacteristic
29C3×C3⋊#95—21no—
30C3×C3⋊#95—31no—
31C3×C3⋊#95—31no—
32C3×C3⋊#95—31no—
33C3×C3⋊#95—31no—
34C3×C3⋊#95—31no—
35C3×C3⋊#95—31no—
36C3×C3⋊#95—31no—
37C3×C3⋊#95—31no—
38C3×C3⋊#95—61no—
39C3×C3⋊#95D311yescharacteristic
40C3×C3⋊#95C2×C311yescharacteristic
41#63579C2×C311yescharacteristic
42#63579C2×C311yescharacteristic
43#63579C2×C311yescharacteristic
44C23×C33C2311yescharacteristic
45C2×C33×C4—21no—
46C2×C33×C4—21no—
47C2×C33×C4Q812yes—
48C2×C3×C3⋊Dic3—21no—
49C2×C3×C3⋊Dic3—21no—
50C2×C3×C3⋊Dic3—21no—
51C2×C3×C3⋊Dic3—21no—
52C2×C3×C3⋊Dic3—21no—
53C2×C3×C3⋊Dic3—21no—
54C2×C32×Dic3—21no—
55C2×C32×Dic3—21no—
56C2×C32×Dic3—21no—
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×Dic3—21no—
65C2×C32×Dic3D412yes—
66C3×#400—91no—
67#4986—31no—
68#4660—31no—
69C22×C32×C4—21no—
70C22×C32×C4—21no—
71C22×C32×C4—21no—
72C22×C32×C4—31no—
73C22×C32×C4—31no—
74C22×C32×C4—31no—
75C22×C32×C4—31no—
76C22×C32×C4—41no—
77C22×C32×C4C2×D311yescharacteristic
78C22×C32×C4C2×D311yescharacteristic
79C22×C32×C4C22×C311yescharacteristic
80C22×C3⋊Dic3C22×C311yescharacteristic
81C22×C3⋊Dic3C22×C311yescharacteristic
82C22×C3×Dic3—21no—
83C22×C3×Dic3—21no—
84C22×C3×Dic3—21no—
85C22×C3×Dic3—21no—
86C22×C3×Dic3—31no—
87C22×C3×Dic3—31no—
88C22×C3×Dic3—31no—
89C22×C3×Dic3—31no—
90C22×C3×Dic3—61no—
91C22×C3×Dic3—61no—
92C22×C3×Dic3C2×D311yescharacteristic
93C22×C3×Dic3C2×D311yescharacteristic
94C22×C3×Dic3C2×D311yescharacteristic
95C22×C3×Dic3C2×D311yescharacteristic
96C22×C3×Dic3C22×C311yescharacteristic
97C22×C3×Dic3C22×C311yescharacteristic
98C22×C3×Dic3C22×C311yescharacteristic
99C22×C3×Dic3C22×C311yescharacteristic
100C32×C4⋊C4—62no—
101C3×C4⋊Dic3—24no—
102C3×C4⋊Dic3—22no—
103C3×C4⋊Dic3—22no—
104C3×C4⋊Dic3—62no—
105C3×Dic3⋊C4—62no—
106Dic3⋊Dic3—22no—
107C22×C33C2×D411yescharacteristic
108C22×C33C2×Q811yescharacteristic
109C22×C33#4111yescharacteristic
110C22×C33#4111yescharacteristic
111C22×C33#4111yescharacteristic
112C22×C33#4111yescharacteristic
113C22×C33#4111yescharacteristic
114C33×C4—22no—
115C3×C3⋊Dic3—41no—
116C3×C3⋊Dic3—41no—
117C32×Dic3—22no—
118C32×Dic3—41no—
119C32×Dic3—41no—
120C32×Dic3—41no—
121C2×C3×C4⋊C4—31no—
122C2×C3×C4⋊C4—31no—
123C2×C3×C4⋊C4—61no—
124C2×C3×C4⋊C4—91no—
125C2×C4⋊Dic3—31no—
126C2×C4⋊Dic3C3×D311yescharacteristic
127C2×Dic3⋊C4—31no—
128C3×#95—31no—
129C3×#95—31no—
130C3×#95—61no—
131C3×#95—91no—
132C3×#95—91no—
133C3×#95—91no—
134C3×#95—91no—
135C3⋊#95—31no—
136C3⋊#95—31no—
137C3⋊#95—31no—
138C3⋊#95—31no—
139C3⋊#95—31no—
140C3⋊#95—31no—
141C3⋊#95—31no—
142C3⋊#95—31no—
143C3⋊#95—61no—
144C3⋊#95C3×D311yescharacteristic
145C23×C32—21no—
146C23×C32—21no—
147C23×C32—21no—
148C23×C32—41no—
149C23×C32C22×D311yescharacteristic
150C23×C32C22×D311yescharacteristic
151C23×C32C23×C311yescharacteristic
152C2×C32×C4—21no—
153C2×C32×C4—21no—
154C2×C32×C4—22no—
155C2×C32×C4—22no—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4—22no—
161C2×C32×C4—22no—
162C2×C32×C4—22no—
163C2×C32×C4—32no—
164C2×C32×C4—42no—
165C2×C32×C4—41no—
166C2×C32×C4—41no—
167C2×C32×C4—41no—
168C2×C32×C4—41no—
169C2×C32×C4—42no—
170C2×C32×C4—42no—
171C2×C32×C4—61no—
172C2×C32×C4—61no—
173C2×C32×C4—61no—
174C2×C32×C4—61no—
175C2×C32×C4—61no—
176C2×C32×C4—61no—
177C2×C32×C4—61no—
178C2×C32×C4—61no—
179C2×C32×C4—61no—
180C2×C32×C4—61no—
181C2×C32×C4—61no—
182C2×C32×C4Dic612yes—
183C2×C32×C4Dic612yes—
184C2×C32×C4C3×Q812yes—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—21no—
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—21no—
213C2×C3×Dic3—21no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3—21no—
216C2×C3×Dic3—22no—
217C2×C3×Dic3—41no—
218C2×C3×Dic3—41no—
219C2×C3×Dic3—41no—
220C2×C3×Dic3—41no—
221C2×C3×Dic3—41no—
222C2×C3×Dic3—41no—
223C2×C3×Dic3—41no—
224C2×C3×Dic3—41no—
225C2×C3×Dic3—62no—
226C2×C3×Dic3—62no—
227C2×C3×Dic3—61no—
228C2×C3×Dic3—61no—
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—61no—
238C2×C3×Dic3—61no—
239C2×C3×Dic3—121no—
240C2×C3×Dic3—121no—
241C2×C3×Dic3—121no—
242C2×C3×Dic3—121no—
243C2×C3×Dic3#6712yes—
244C2×C3×Dic3C3×D412yes—
245#400—91noSylow
246C2×C33C22⋊Q811yescharacteristic
247C2×C33#12311yescharacteristic
248C2×C33#12411yescharacteristic
249C2×C33#12511yescharacteristic
250C2×C33#12511yescharacteristic
251C2×C33#12611yescharacteristic
252C2×C33#12611yescharacteristic
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—31no—
257C22×C3×C4—31no—
258C22×C3×C4—31no—
259C22×C3×C4—31no—
260C22×C3×C4—31no—
261C22×C3×C4—31no—
262C22×C3×C4—31no—
263C22×C3×C4—31no—
264C22×C3×C4—41no—
265C22×C3×C4—61no—
266C22×C3×C4—61no—
267C22×C3×C4—61no—
268C22×C3×C4—61no—
269C22×C3×C4—91no—
270C22×C3×C4—91no—
271C22×C3×C4D3211yescharacteristic
272C22×C3×C4C2×C3×D311yescharacteristic
273C22×C3×C4C2×C3×D311yescharacteristic
274C22×Dic3—31no—
275C22×Dic3—31no—
276C22×Dic3—31no—
277C22×Dic3—31no—
278C22×Dic3—61no—
279C22×Dic3—61no—
280C22×Dic3C2×C3×D311yescharacteristic
281C22×Dic3C2×C3×D311yescharacteristic
282C22×Dic3C2×C3×D311yescharacteristic
283C22×Dic3C2×C3×D311yescharacteristic
284C3×C4⋊C4—62no—
285C3×C4⋊C4—62no—
286C3×C4⋊C4—64no—
287C3×C4⋊C4—182no—
288C4⋊Dic3—22no—
289C4⋊Dic3—62no—
290Dic3⋊C4—62no—
291C22×C32—21no—
292C22×C32—21no—
293C22×C32—21no—
294C22×C32—21no—
295C22×C32—21no—
296C22×C32—21no—
297C22×C32—21no—
298C22×C32—21no—
299C22×C32—21no—
300C22×C32—21no—
301C22×C32—21no—
302C22×C32—21no—
303C22×C32—21no—
304C22×C32—21no—
305C22×C32—21no—
306C22×C32—21no—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32—21no—
310C22×C32—21no—
311C22×C32—21no—
312C22×C32—41no—
313C22×C32—41no—
314C22×C32—41no—
315C22×C32—41no—
316C22×C32—41no—
317C22×C32—41no—
318C22×C32—41no—
319C22×C32C2×Dic611yescharacteristic
320C22×C32C2×Dic611yescharacteristic
321C22×C32#23511yescharacteristic
322C22×C32#23511yescharacteristic
323C22×C32#23511yescharacteristic
324C22×C32D3×D411yescharacteristic
325C22×C32#23711yescharacteristic
326C22×C32#23711yescharacteristic
327C22×C32#23711yescharacteristic
328C22×C32#23711yescharacteristic
329C22×C32#23911yescharacteristic
330C22×C32#23911yescharacteristic
331C22×C32#23911yescharacteristic
332C22×C32C2×#6711yescharacteristic
333C22×C32C2×C3×D411yescharacteristic
334C22×C32C2×C3×Q811yescharacteristic
335C22×C32C3×#4111yescharacteristic
336C22×C32C3×#4111yescharacteristic
337C22×C32C3×#4111yescharacteristic
338C22×C32C3×#4111yescharacteristic
339C22×C32C3×#4111yescharacteristic
340C32×C4—22no—
341C32×C4—24no—
342C32×C4—22no—
343C32×C4—22no—
344C32×C4—42no—
345C32×C4—42no—
346C32×C4—44no—
347C32×C4—62no—
348C32×C4—121no—
349C32×C4—121no—
350C32×C4—121no—
351C3⋊Dic3—41no—
352C3⋊Dic3—41no—
353C3×Dic3—22no—
354C3×Dic3—22no—
355C3×Dic3—42no—
356C3×Dic3—42no—
357C3×Dic3—42no—
358C3×Dic3—42no—
359C3×Dic3—41no—
360C3×Dic3—41no—
361C3×Dic3—41no—
362C3×Dic3—41no—
363C3×Dic3—41no—
364C3×Dic3—41no—
365C3×Dic3—122no—
366C3×Dic3—122no—
367C3×Dic3—121no—
368C3×Dic3—121no—
369C3×Dic3—121no—
370C3×Dic3—121no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—91no—
373#95—31no—
374#95—91no—
375#95—91no—
376#95—91no—
377#95—91no—
378C33#40011yescharacteristic, complemented, Sylow
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—41no—
383C23×C3C2×D3211yescharacteristic
384C23×C3C22×C3×D311yescharacteristic
385C23×C3C22×C3×D311yescharacteristic
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—32no—
398C2×C3×C4—32no—
399C2×C3×C4—41no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—42no—
404C2×C3×C4—42no—
405C2×C3×C4—42no—
406C2×C3×C4—62no—
407C2×C3×C4—61no—
408C2×C3×C4—61no—
409C2×C3×C4—61no—
410C2×C3×C4—61no—
411C2×C3×C4—62no—
412C2×C3×C4—62no—
413C2×C3×C4—62no—
414C2×C3×C4—61no—
415C2×C3×C4—61no—
416C2×C3×C4—61no—
417C2×C3×C4—61no—
418C2×C3×C4—61no—
419C2×C3×C4—61no—
420C2×C3×C4—61no—
421C2×C3×C4—61no—
422C2×C3×C4—61no—
423C2×C3×C4—61no—
424C2×C3×C4—61no—
425C2×C3×C4—61no—
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—121no—
433C2×C3×C4—121no—
434C2×C3×C4—121no—
435C2×C3×C4—121no—
436C2×C3×C4—121no—
437C2×C3×C4—121no—
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#62712yes—
447C2×C3×C4C3×Dic612yes—
448C2×C3×C4C3×Dic612yes—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—21no—
453C2×Dic3—21no—
454C2×Dic3—21no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—21no—
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—61no—
471C2×Dic3—61no—
472C2×Dic3—61no—
473C2×Dic3—61no—
474C2×Dic3—121no—
475C2×Dic3—121no—
476C2×Dic3—121no—
477C2×Dic3—121no—
478C2×Dic3C3×#6712yes—
479C2×C32—21no—
480C2×C32—21no—
481C2×C32—21no—
482C2×C32—21no—
483C2×C32—21no—
484C2×C32—21no—
485C2×C32—21no—
486C2×C32—21no—
487C2×C32—21no—
488C2×C32—21no—
489C2×C32—21no—
490C2×C32—21no—
491C2×C32—21no—
492C2×C32—21no—
493C2×C32—21no—
494C2×C32—21no—
495C2×C32—21no—
496C2×C32—21no—
497C2×C32—21no—
498C2×C32—21no—
499C2×C32—21no—
500C2×C32—41no—
501C2×C32—41no—
502C2×C32—41no—
503C2×C32—41no—
504C2×C32—41no—
505C2×C32—41no—
506C2×C32—41no—
507C2×C32#87011yescharacteristic
508C2×C32#87811yescharacteristic
509C2×C32#87911yescharacteristic
510C2×C32#88511yescharacteristic
511C2×C32#89011yescharacteristic
512C2×C32#89011yescharacteristic
513C2×C32#89011yescharacteristic
514C2×C32#89411yescharacteristic
515C2×C32#89811yescharacteristic
516C2×C32#89811yescharacteristic
517C2×C32#89811yescharacteristic
518C2×C32#92411yescharacteristic
519C2×C32#93511yescharacteristic
520C2×C32#94711yescharacteristic
521C2×C32C3×C22⋊Q811yescharacteristic
522C2×C32C3×#12311yescharacteristic
523C2×C32C3×#12411yescharacteristic
524C2×C32C3×#12511yescharacteristic
525C2×C32C3×#12511yescharacteristic
526C2×C32C3×#12611yescharacteristic
527C2×C32C3×#12611yescharacteristic
528C22×C4—31no—
529C22×C4—31no—
530C22×C4—31no—
531C22×C4—31no—
532C22×C4—91no—
533C22×C4—91no—
534C22×C4C3×D3211yescharacteristic
535C4⋊C4—62no—
536C4⋊C4—182no—
537C22×C3—21no—
538C22×C3—21no—
539C22×C3—21no—
540C22×C3—21no—
541C22×C3—21no—
542C22×C3—21no—
543C22×C3—21no—
544C22×C3—21no—
545C22×C3—21no—
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—21no—
549C22×C3—21no—
550C22×C3—21no—
551C22×C3—21no—
552C22×C3—21no—
553C22×C3—21no—
554C22×C3—21no—
555C22×C3—21no—
556C22×C3—21no—
557C22×C3—21no—
558C22×C3—41no—
559C22×C3—41no—
560C22×C3—41no—
561C22×C3—41no—
562C22×C3—41no—
563C22×C3—41no—
564C22×C3—41no—
565C22×C3#379511yescharacteristic
566C22×C3#379611yescharacteristic
567C22×C3#379611yescharacteristic
568C22×C3#379911yescharacteristic
569C22×C3#380411yescharacteristic
570C22×C3C2×#62711yescharacteristic
571C22×C3D3×#6711yescharacteristic
572C22×C3C2×C3×Dic611yescharacteristic
573C22×C3C2×C3×Dic611yescharacteristic
574C22×C3C3×#23511yescharacteristic
575C22×C3C3×#23511yescharacteristic
576C22×C3C3×#23511yescharacteristic
577C22×C3C3×D3×D411yescharacteristic
578C22×C3C3×#23711yescharacteristic
579C22×C3C3×#23711yescharacteristic
580C22×C3C3×#23711yescharacteristic
581C22×C3C3×#23711yescharacteristic
582C22×C3C3×#23911yescharacteristic
583C22×C3C3×#23911yescharacteristic
584C22×C3C3×#23911yescharacteristic
585C22×C3C2×C3×#6711yescharacteristic
586C3×C4—24no—
587C3×C4—22no—
588C3×C4—22no—
589C3×C4—22no—
590C3×C4—42no—
591C3×C4—42no—
592C3×C4—44no—
593C3×C4—62no—
594C3×C4—62no—
595C3×C4—122no—
596C3×C4—122no—
597C3×C4—122no—
598C3×C4—122no—
599C3×C4—121no—
600C3×C4—121no—
601C3×C4—121no—
602C3×C4—121no—
603C3×C4—121no—
604C3×C4—121no—
605C3×C4—361no—
606C3×C4—361no—
607Dic3—22no—
608Dic3—41no—
609Dic3—41no—
610Dic3—41no—
611Dic3—122no—
612Dic3—122no—
613Dic3—121no—
614Dic3—121no—
615Dic3—121no—
616Dic3—121no—
617C32—21no—
618C32—21no—
619C32—21no—
620C32—41no—
621C32#466011yescharacteristic, complemented
622C32#498611yescharacteristic, complemented
623C32C3×#40011yescharacteristic, complemented
624C23C2×C3×D3211yescharacteristic
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—32no—
628C2×C4—61no—
629C2×C4—61no—
630C2×C4—61no—
631C2×C4—61no—
632C2×C4—61no—
633C2×C4—61no—
634C2×C4—61no—
635C2×C4—61no—
636C2×C4—61no—
637C2×C4—61no—
638C2×C4—61no—
639C2×C4—181no—
640C2×C4—181no—
641C2×C4—181no—
642C2×C4—181no—
643C2×C4—181no—
644C2×C4—181no—
645C2×C4C3×#62712yes—
646C2×C3—21no—
647C2×C3—21no—
648C2×C3—21no—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—21no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3—21no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—41no—
668C2×C3—41no—
669C2×C3—41no—
670C2×C3—41no—
671C2×C3—41no—
672C2×C3—41no—
673C2×C3—41no—
674C2×C3#6384811yescharacteristic
675C2×C3#6385811yescharacteristic
676C2×C3#6386911yescharacteristic
677C2×C3#6387211yescharacteristic
678C2×C3#6388411yescharacteristic
679C2×C3#6390711yescharacteristic
680C2×C3#6396411yescharacteristic
681C2×C3C3×#87011yescharacteristic
682C2×C3C3×#87811yescharacteristic
683C2×C3C3×#87911yescharacteristic
684C2×C3C3×#88511yescharacteristic
685C2×C3C3×#89011yescharacteristic
686C2×C3C3×#89011yescharacteristic
687C2×C3C3×#89011yescharacteristic
688C2×C3C3×#89411yescharacteristic
689C2×C3C3×#89811yescharacteristic
690C2×C3C3×#89811yescharacteristic
691C2×C3C3×#89811yescharacteristic
692C2×C3C3×#92411yescharacteristic
693C2×C3C3×#93511yescharacteristic
694C2×C3C3×#94711yescharacteristic
695C22C3×#379511yescharacteristic
696C22C3×#379611yescharacteristic
697C22C3×#379611yescharacteristic
698C22C3×#379911yescharacteristic
699C22C3×#380411yescharacteristic
700C22C2×C3×#62711yescharacteristic
701C22C3×D3×#6711yescharacteristic
702C4—22no—
703C4—62no—
704C4—121no—
705C4—121no—
706C4—121no—
707C4—361no—
708C4—361no—
709C3—21no—
710C3—21no—
711C3—21no—
712C3—41no—
713C3#1059134311yescharacteristic, direct product factor
714C3C3×#466011yescharacteristic, complemented
715C3C3×#498611yescharacteristic, complemented
716C2C3×#6384811yescharacteristic
717C2C3×#6385811yescharacteristic
718C2C3×#6386911yescharacteristic
719C2C3×#6387211yescharacteristic
720C2C3×#6388411yescharacteristic
721C2C3×#6390711yescharacteristic
722C2C3×#6396411yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC23×C32C23×C3
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socle, prime radicalC23×C33C23
hypercenterC22×C3×C4D32
hypocenterC32C3×#400
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. #10591343C3direct (N × H)
378. C33#400semidirect
621. C32#4660semidirect
622. C32#4986semidirect
623. C32C3×#400semidirect
713. C3#10591343direct (N × H)
714. C3C3×#4660semidirect
715. C3C3×#4986semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4⋊Dic32
C2×C3×Dic3⋊Dic32
C3×#636582
C32×C3⋊#952
C3×#635792
C3×#49863
C3×#46603
#105913433