Finite Group Databasebeta

← C3×#10591228 #13158076

Subgroups — C3×#10591228 #13158076

Order 1728.

754 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#63658C211yesmaximal, characteristic
2C32×C3⋊#95C211yesmaximal, characteristic
3C32×C3⋊#95C211yesmaximal, characteristic
4C3×#63579C211yesmaximal, characteristic
5C3×#63579C211yesmaximal, characteristic
6C3×#63579C211yesmaximal, characteristic
7C3×#63579C211yesmaximal, characteristic
8C3×C3⋊#401—31nomaximal
9C3×C3⋊#401—31nomaximal
10#10591228C311yesmaximal, 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×#95—31no—
19C32×#95—31no—
20#63658C2×C311yescharacteristic
21C3×C3⋊#95—21no—
22C3×C3⋊#95—21no—
23C3×C3⋊#95—31no—
24C3×C3⋊#95—31no—
25C3×C3⋊#95—31no—
26C3×C3⋊#95—31no—
27C3×C3⋊#95—31no—
28C3×C3⋊#95—31no—
29C3×C3⋊#95—31no—
30C3×C3⋊#95—31no—
31C3×C3⋊#95—31no—
32C3×C3⋊#95—31no—
33C3×C3⋊#95—61no—
34C3×C3⋊#95D311yescharacteristic
35C3×C3⋊#95D311yescharacteristic
36C3×C3⋊#95C2×C311yescharacteristic
37C3×C3⋊#95C2×C311yescharacteristic
38#63579C2×C311yescharacteristic
39#63579C2×C311yescharacteristic
40#63579C2×C311yescharacteristic
41#63579C2×C311yescharacteristic
42C23×C33C2311yescharacteristic
43C2×C33×C4—21no—
44C2×C33×C4—21no—
45C2×C33×C4—21no—
46C2×C3×C3⋊Dic3—21no—
47C2×C3×C3⋊Dic3—21no—
48C2×C3×C3⋊Dic3—21no—
49C2×C3×C3⋊Dic3—21no—
50C2×C3×C3⋊Dic3—21no—
51C2×C3×C3⋊Dic3—21no—
52C2×C32×Dic3—21no—
53C2×C32×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—
64C3×#401—91no—
65C3⋊#401—31no—
66C3⋊#401—31no—
67C22×C32×C4—21no—
68C22×C32×C4—21no—
69C22×C32×C4—21no—
70C22×C32×C4—31no—
71C22×C32×C4—31no—
72C22×C32×C4—31no—
73C22×C32×C4—31no—
74C22×C32×C4—41no—
75C22×C32×C4C2×D311yescharacteristic
76C22×C32×C4C2×D311yescharacteristic
77C22×C32×C4C22×C311yescharacteristic
78C22×C3⋊Dic3C22×C311yescharacteristic
79C22×C3⋊Dic3C22×C311yescharacteristic
80C22×C3×Dic3—21no—
81C22×C3×Dic3—21no—
82C22×C3×Dic3—21no—
83C22×C3×Dic3—21no—
84C22×C3×Dic3—31no—
85C22×C3×Dic3—31no—
86C22×C3×Dic3—31no—
87C22×C3×Dic3—31no—
88C22×C3×Dic3—61no—
89C22×C3×Dic3—61no—
90C22×C3×Dic3C2×D311yescharacteristic
91C22×C3×Dic3C2×D311yescharacteristic
92C22×C3×Dic3C2×D311yescharacteristic
93C22×C3×Dic3C2×D311yescharacteristic
94C22×C3×Dic3C22×C311yescharacteristic
95C22×C3×Dic3C22×C311yescharacteristic
96C22×C3×Dic3C22×C311yescharacteristic
97C22×C3×Dic3C22×C311yescharacteristic
98C22×C33#4111yescharacteristic
99C22×C33#4111yescharacteristic
100C22×C33#4111yescharacteristic
101C22×C33#4111yescharacteristic
102C22×C33#4111yescharacteristic
103C22×C33#4111yescharacteristic
104C22×C33#4111yescharacteristic
105C33×C4—41no—
106C3×C3⋊Dic3—41no—
107C3×C3⋊Dic3—41no—
108C32×Dic3—41no—
109C32×Dic3—41no—
110C32×Dic3—41no—
111C32×Dic3—41no—
112C3×#95—31no—
113C3×#95—31no—
114C3×#95—31no—
115C3×#95—31no—
116C3×#95—61no—
117C3×#95—61no—
118C3×#95—91no—
119C3×#95—91no—
120C3×#95—91no—
121C3×#95—91no—
122C3×#95—91no—
123C3⋊#95—31no—
124C3⋊#95—31no—
125C3⋊#95—31no—
126C3⋊#95—31no—
127C3⋊#95—31no—
128C3⋊#95—31no—
129C3⋊#95—31no—
130C3⋊#95—31no—
131C3⋊#95—31no—
132C3⋊#95—31no—
133C3⋊#95—61no—
134C3⋊#95C3×D311yescharacteristic
135C3⋊#95C3×D311yescharacteristic
136C23×C32—21no—
137C23×C32—21no—
138C23×C32—21no—
139C23×C32—41no—
140C23×C32C22×D311yescharacteristic
141C23×C32C22×D311yescharacteristic
142C23×C32C23×C311yescharacteristic
143C2×C32×C4—21no—
144C2×C32×C4—21no—
145C2×C32×C4—21no—
146C2×C32×C4—22no—
147C2×C32×C4—22no—
148C2×C32×C4—22no—
149C2×C32×C4—21no—
150C2×C32×C4—21no—
151C2×C32×C4—21no—
152C2×C32×C4—21no—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4—41no—
156C2×C32×C4—41no—
157C2×C32×C4—41no—
158C2×C32×C4—41no—
159C2×C32×C4—41no—
160C2×C32×C4—41no—
161C2×C32×C4—42no—
162C2×C32×C4—42no—
163C2×C32×C4—42no—
164C2×C32×C4—61no—
165C2×C32×C4—61no—
166C2×C32×C4—61no—
167C2×C32×C4—61no—
168C2×C32×C4—61no—
169C2×C32×C4—61no—
170C2×C32×C4—61no—
171C2×C32×C4—61no—
172C2×C32×C4—61no—
173C2×C32×C4—61no—
174C2×C32×C4—61no—
175C2×C32×C4—61no—
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—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
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—21no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—21no—
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—41no—
211C2×C3×Dic3—41no—
212C2×C3×Dic3—41no—
213C2×C3×Dic3—41no—
214C2×C3×Dic3—41no—
215C2×C3×Dic3—41no—
216C2×C3×Dic3—41no—
217C2×C3×Dic3—41no—
218C2×C3×Dic3—62no—
219C2×C3×Dic3—62no—
220C2×C3×Dic3—61no—
221C2×C3×Dic3—61no—
222C2×C3×Dic3—61no—
223C2×C3×Dic3—61no—
224C2×C3×Dic3—61no—
225C2×C3×Dic3—61no—
226C2×C3×Dic3—61no—
227C2×C3×Dic3—61no—
228C2×C3×Dic3—61no—
229C2×C3×Dic3—61no—
230C2×C3×Dic3—61no—
231C2×C3×Dic3—61no—
232C2×C3×Dic3—121no—
233C2×C3×Dic3—121no—
234C2×C3×Dic3—121no—
235C2×C3×Dic3—121no—
236#401—91noSylow
237C2×C33#12611yescharacteristic
238C2×C33#12611yescharacteristic
239C2×C33#12611yescharacteristic
240C2×C33#12611yescharacteristic
241C2×C33#12611yescharacteristic
242C2×C33#12611yescharacteristic
243C2×C33#12611yescharacteristic
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—31no—
248C22×C3×C4—31no—
249C22×C3×C4—31no—
250C22×C3×C4—31no—
251C22×C3×C4—31no—
252C22×C3×C4—31no—
253C22×C3×C4—31no—
254C22×C3×C4—31no—
255C22×C3×C4—41no—
256C22×C3×C4—61no—
257C22×C3×C4—61no—
258C22×C3×C4—61no—
259C22×C3×C4—61no—
260C22×C3×C4—91no—
261C22×C3×C4—91no—
262C22×C3×C4D3211yescharacteristic
263C22×C3×C4C2×C3×D311yescharacteristic
264C22×C3×C4C2×C3×D311yescharacteristic
265C22×Dic3—31no—
266C22×Dic3—31no—
267C22×Dic3—31no—
268C22×Dic3—31no—
269C22×Dic3—61no—
270C22×Dic3—61no—
271C22×Dic3C2×C3×D311yescharacteristic
272C22×Dic3C2×C3×D311yescharacteristic
273C22×Dic3C2×C3×D311yescharacteristic
274C22×Dic3C2×C3×D311yescharacteristic
275C22×C32—21no—
276C22×C32—21no—
277C22×C32—21no—
278C22×C32—21no—
279C22×C32—21no—
280C22×C32—21no—
281C22×C32—21no—
282C22×C32—21no—
283C22×C32—21no—
284C22×C32—21no—
285C22×C32—21no—
286C22×C32—21no—
287C22×C32—21no—
288C22×C32—21no—
289C22×C32—21no—
290C22×C32—21no—
291C22×C32—21no—
292C22×C32—21no—
293C22×C32—21no—
294C22×C32—21no—
295C22×C32—21no—
296C22×C32—41no—
297C22×C32—41no—
298C22×C32—41no—
299C22×C32—41no—
300C22×C32—41no—
301C22×C32—41no—
302C22×C32—41no—
303C22×C32#23511yescharacteristic
304C22×C32#23511yescharacteristic
305C22×C32#23511yescharacteristic
306C22×C32#23511yescharacteristic
307C22×C32#23511yescharacteristic
308C22×C32#23511yescharacteristic
309C22×C32#23711yescharacteristic
310C22×C32#23711yescharacteristic
311C22×C32#23711yescharacteristic
312C22×C32#23711yescharacteristic
313C22×C32#23711yescharacteristic
314C22×C32#23711yescharacteristic
315C22×C32#23911yescharacteristic
316C22×C32#23911yescharacteristic
317C22×C32C3×#4111yescharacteristic
318C22×C32C3×#4111yescharacteristic
319C22×C32C3×#4111yescharacteristic
320C22×C32C3×#4111yescharacteristic
321C22×C32C3×#4111yescharacteristic
322C22×C32C3×#4111yescharacteristic
323C22×C32C3×#4111yescharacteristic
324C32×C4—42no—
325C32×C4—42no—
326C32×C4—42no—
327C32×C4—44no—
328C32×C4—41no—
329C32×C4—41no—
330C32×C4—41no—
331C32×C4—121no—
332C32×C4—121no—
333C32×C4—121no—
334C32×C4—121no—
335C3⋊Dic3—41no—
336C3⋊Dic3—41no—
337C3×Dic3—42no—
338C3×Dic3—42no—
339C3×Dic3—42no—
340C3×Dic3—42no—
341C3×Dic3—41no—
342C3×Dic3—41no—
343C3×Dic3—41no—
344C3×Dic3—41no—
345C3×Dic3—41no—
346C3×Dic3—41no—
347C3×Dic3—41no—
348C3×Dic3—41no—
349C3×Dic3—122no—
350C3×Dic3—122no—
351C3×Dic3—121no—
352C3×Dic3—121no—
353C3×Dic3—121no—
354C3×Dic3—121no—
355#95—31no—
356#95—31no—
357#95—91no—
358#95—91no—
359#95—91no—
360#95—91no—
361#95—91no—
362C33#40111yescharacteristic, complemented, Sylow
363C23×C3—21no—
364C23×C3—21no—
365C23×C3—21no—
366C23×C3—41no—
367C23×C3C2×D3211yescharacteristic
368C23×C3C22×C3×D311yescharacteristic
369C23×C3C22×C3×D311yescharacteristic
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—42no—
389C2×C3×C4—42no—
390C2×C3×C4—42no—
391C2×C3×C4—62no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—62no—
395C2×C3×C4—61no—
396C2×C3×C4—61no—
397C2×C3×C4—61no—
398C2×C3×C4—61no—
399C2×C3×C4—61no—
400C2×C3×C4—61no—
401C2×C3×C4—61no—
402C2×C3×C4—61no—
403C2×C3×C4—61no—
404C2×C3×C4—61no—
405C2×C3×C4—61no—
406C2×C3×C4—61no—
407C2×C3×C4—61no—
408C2×C3×C4—61no—
409C2×C3×C4—61no—
410C2×C3×C4—61no—
411C2×C3×C4—61no—
412C2×C3×C4—61no—
413C2×C3×C4—61no—
414C2×C3×C4—61no—
415C2×C3×C4—61no—
416C2×C3×C4—61no—
417C2×C3×C4—61no—
418C2×C3×C4—61no—
419C2×C3×C4—121no—
420C2×C3×C4—121no—
421C2×C3×C4—121no—
422C2×C3×C4—121no—
423C2×C3×C4—121no—
424C2×C3×C4—121no—
425C2×C3×C4—121no—
426C2×C3×C4—121no—
427C2×C3×C4—181no—
428C2×C3×C4—181no—
429C2×C3×C4—181no—
430C2×C3×C4—181no—
431C2×C3×C4—181no—
432C2×C3×C4—181no—
433C2×Dic3—21no—
434C2×Dic3—21no—
435C2×Dic3—21no—
436C2×Dic3—21no—
437C2×Dic3—21no—
438C2×Dic3—21no—
439C2×Dic3—21no—
440C2×Dic3—21no—
441C2×Dic3—21no—
442C2×Dic3—21no—
443C2×Dic3—21no—
444C2×Dic3—21no—
445C2×Dic3—62no—
446C2×Dic3—62no—
447C2×Dic3—61no—
448C2×Dic3—61no—
449C2×Dic3—61no—
450C2×Dic3—61no—
451C2×Dic3—61no—
452C2×Dic3—61no—
453C2×Dic3—61no—
454C2×Dic3—61no—
455C2×Dic3—61no—
456C2×Dic3—61no—
457C2×Dic3—61no—
458C2×Dic3—61no—
459C2×Dic3—121no—
460C2×Dic3—121no—
461C2×Dic3—121no—
462C2×Dic3—121no—
463C2×C32—21no—
464C2×C32—21no—
465C2×C32—21no—
466C2×C32—21no—
467C2×C32—21no—
468C2×C32—21no—
469C2×C32—21no—
470C2×C32—21no—
471C2×C32—21no—
472C2×C32—21no—
473C2×C32—21no—
474C2×C32—21no—
475C2×C32—21no—
476C2×C32—21no—
477C2×C32—21no—
478C2×C32—21no—
479C2×C32—21no—
480C2×C32—21no—
481C2×C32—21no—
482C2×C32—21no—
483C2×C32—21no—
484C2×C32—41no—
485C2×C32—41no—
486C2×C32—41no—
487C2×C32—41no—
488C2×C32—41no—
489C2×C32—41no—
490C2×C32—41no—
491C2×C32#87611yescharacteristic
492C2×C32#87611yescharacteristic
493C2×C32#87911yescharacteristic
494C2×C32#87911yescharacteristic
495C2×C32#87911yescharacteristic
496C2×C32#87911yescharacteristic
497C2×C32#87911yescharacteristic
498C2×C32#87911yescharacteristic
499C2×C32#89811yescharacteristic
500C2×C32#89811yescharacteristic
501C2×C32#89811yescharacteristic
502C2×C32#89811yescharacteristic
503C2×C32#89811yescharacteristic
504C2×C32#89811yescharacteristic
505C2×C32C3×#12611yescharacteristic
506C2×C32C3×#12611yescharacteristic
507C2×C32C3×#12611yescharacteristic
508C2×C32C3×#12611yescharacteristic
509C2×C32C3×#12611yescharacteristic
510C2×C32C3×#12611yescharacteristic
511C2×C32C3×#12611yescharacteristic
512C22×C4—31no—
513C22×C4—31no—
514C22×C4—31no—
515C22×C4—31no—
516C22×C4—91no—
517C22×C4—91no—
518C22×C4C3×D3211yescharacteristic
519C22×C3—21no—
520C22×C3—21no—
521C22×C3—21no—
522C22×C3—21no—
523C22×C3—21no—
524C22×C3—21no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—21no—
528C22×C3—21no—
529C22×C3—21no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—21no—
533C22×C3—21no—
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—21no—
537C22×C3—21no—
538C22×C3—21no—
539C22×C3—21no—
540C22×C3—41no—
541C22×C3—41no—
542C22×C3—41no—
543C22×C3—41no—
544C22×C3—41no—
545C22×C3—41no—
546C22×C3—41no—
547C22×C3#379511yescharacteristic
548C22×C3#379611yescharacteristic
549C22×C3#379811yescharacteristic
550C22×C3#379911yescharacteristic
551C22×C3#380411yescharacteristic
552C22×C3#380411yescharacteristic
553C22×C3#380511yescharacteristic
554C22×C3C3×#23511yescharacteristic
555C22×C3C3×#23511yescharacteristic
556C22×C3C3×#23511yescharacteristic
557C22×C3C3×#23511yescharacteristic
558C22×C3C3×#23511yescharacteristic
559C22×C3C3×#23511yescharacteristic
560C22×C3C3×#23711yescharacteristic
561C22×C3C3×#23711yescharacteristic
562C22×C3C3×#23711yescharacteristic
563C22×C3C3×#23711yescharacteristic
564C22×C3C3×#23711yescharacteristic
565C22×C3C3×#23711yescharacteristic
566C22×C3C3×#23911yescharacteristic
567C22×C3C3×#23911yescharacteristic
568C3×C4—42no—
569C3×C4—42no—
570C3×C4—42no—
571C3×C4—44no—
572C3×C4—41no—
573C3×C4—41no—
574C3×C4—41no—
575C3×C4—122no—
576C3×C4—122no—
577C3×C4—122no—
578C3×C4—122no—
579C3×C4—121no—
580C3×C4—121no—
581C3×C4—121no—
582C3×C4—121no—
583C3×C4—121no—
584C3×C4—121no—
585C3×C4—121no—
586C3×C4—121no—
587C3×C4—361no—
588C3×C4—361no—
589Dic3—41no—
590Dic3—41no—
591Dic3—41no—
592Dic3—41no—
593Dic3—122no—
594Dic3—122no—
595Dic3—121no—
596Dic3—121no—
597Dic3—121no—
598Dic3—121no—
599C32—21no—
600C32—21no—
601C32—21no—
602C32—41no—
603C32C3⋊#40111yescharacteristic, complemented
604C32C3⋊#40111yescharacteristic, complemented
605C32C3×#40111yescharacteristic, complemented
606C23C2×C3×D3211yescharacteristic
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—61no—
611C2×C4—61no—
612C2×C4—61no—
613C2×C4—61no—
614C2×C4—61no—
615C2×C4—61no—
616C2×C4—61no—
617C2×C4—61no—
618C2×C4—61no—
619C2×C4—61no—
620C2×C4—61no—
621C2×C4—61no—
622C2×C4—181no—
623C2×C4—181no—
624C2×C4—181no—
625C2×C4—181no—
626C2×C4—181no—
627C2×C4—181no—
628C2×C3—21no—
629C2×C3—21no—
630C2×C3—21no—
631C2×C3—21no—
632C2×C3—21no—
633C2×C3—21no—
634C2×C3—21no—
635C2×C3—21no—
636C2×C3—21no—
637C2×C3—21no—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—21no—
641C2×C3—21no—
642C2×C3—21no—
643C2×C3—21no—
644C2×C3—21no—
645C2×C3—21no—
646C2×C3—21no—
647C2×C3—21no—
648C2×C3—21no—
649C2×C3—41no—
650C2×C3—41no—
651C2×C3—41no—
652C2×C3—41no—
653C2×C3—41no—
654C2×C3—41no—
655C2×C3—41no—
656C2×C3#6384811yescharacteristic
657C2×C3#6385811yescharacteristic
658C2×C3#6385911yescharacteristic
659C2×C3#6386111yescharacteristic
660C2×C3#6386211yescharacteristic
661C2×C3#6386811yescharacteristic
662C2×C3#6395611yescharacteristic
663C2×C3C3×#87611yescharacteristic
664C2×C3C3×#87611yescharacteristic
665C2×C3C3×#87911yescharacteristic
666C2×C3C3×#87911yescharacteristic
667C2×C3C3×#87911yescharacteristic
668C2×C3C3×#87911yescharacteristic
669C2×C3C3×#87911yescharacteristic
670C2×C3C3×#87911yescharacteristic
671C2×C3C3×#89811yescharacteristic
672C2×C3C3×#89811yescharacteristic
673C2×C3C3×#89811yescharacteristic
674C2×C3C3×#89811yescharacteristic
675C2×C3C3×#89811yescharacteristic
676C2×C3C3×#89811yescharacteristic
677C22C3×#379511yescharacteristic
678C22C3×#379611yescharacteristic
679C22C3×#379811yescharacteristic
680C22C3×#379911yescharacteristic
681C22C3×#380411yescharacteristic
682C22C3×#380411yescharacteristic
683C22C3×#380511yescharacteristic
684C4—41no—
685C4—121no—
686C4—121no—
687C4—121no—
688C4—121no—
689C4—361no—
690C4—361no—
691C3—21no—
692C3—21no—
693C3—21no—
694C3—41no—
695C3#1059122811yescharacteristic, direct product factor
696C3C3×C3⋊#40111yescharacteristic, complemented
697C3C3×C3⋊#40111yescharacteristic, complemented
698C2C3×#6384811yescharacteristic
699C2C3×#6385811yescharacteristic
700C2C3×#6385911yescharacteristic
701C2C3×#6386111yescharacteristic
702C2C3×#6386211yescharacteristic
703C2C3×#6386811yescharacteristic
704C2C3×#6395611yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC23×C32C23×C3
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socle, prime radicalC23×C33C23
hypercenterC22×C3×C4D32
hypocenterC32C3×#401
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. #10591228C3direct (N × H)
362. C33#401semidirect
603. C32C3⋊#401semidirect
604. C32C3⋊#401semidirect
605. C32C3×#401semidirect
695. C3#10591228direct (N × H)
696. C3C3×C3⋊#401semidirect
697. C3C3×C3⋊#401semidirect

Maximal subgroups

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

subgroupindex
C3×#636582
C32×C3⋊#952
C3×#635792
C3×C3⋊#4013
#105912283