Finite Group Databasebeta

← C3×#10591231 #13158101

Subgroups — C3×#10591231 #13158101

Order 1728.

1002 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#235C211yesmaximal, characteristic
2C3×#64135C211yesmaximal, characteristic, complemented
3C32×#926C211yesmaximal, characteristic, complemented
4C3×#63580C214yesmaximal, complemented
5C3×#5240—31nomaximal
6C3×#5006—31nomaximal
7#10591231C311yesmaximal, characteristic, direct product factor
8C22×C33×C4C2211yescharacteristic
9C2×C32×#67C2212yes—
10C32×#235—21no—
11C32×#235—21no—
12C32×#235—21no—
13C32×#235—21no—
14C2×C32×D12C411yescharacteristic, complemented
15C2×C32×C4×D3C412yescomplemented
16C2×C32×Dic6C411yescharacteristic, complemented
17C3×#3757C2212yes—
18C3×C4⋊(C3⋊Dic3)—21no—
19C3×C4×C3⋊Dic3—21no—
20C32×#217C2212yes—
21C32×C4⋊Dic3—21no—
22C32×C4×Dic3—21no—
23C2×C32×#41—31no—
24C2×C3×#235—21no—
25C2×C3×#235D311yescharacteristic
26C2×C3×#235C2×C311yescharacteristic
27C32×#117—31no—
28#64135C2×C311yescharacteristic, complemented
29C3×#926—21no—
30C3×#926—31no—
31C3×#926—31no—
32C3×#926—61no—
33C3×#926D311yescharacteristic, complemented
34C3×#926C2×C311yescharacteristic, complemented
35C3×#834—34no—
36C3×#806—34no—
37#63580C2×C314yescomplemented
38C23×C33C2311yescharacteristic
39C22×C32×D3C2×C412yes—
40C2×C33×C4C2×C411yescharacteristic
41C2×C33×C4C2×C411yescharacteristic
42C2×C33×C4D411yescharacteristic
43C2×C33×C4D411yescharacteristic
44C2×C33×C4D411yescharacteristic
45C2×C33×C4D411yescharacteristic
46C2×C3×C3⋊Dic3—22no—
47C32×#67—22no—
48C32×#67—22no—
49C2×C32×Dic3—22no—
50C2×C32×Dic3C2×C412yes—
51C32×D12—21no—
52C32×D12—21no—
53C32×C4×D3—22no—
54C32×C4×D3—22no—
55C32×Dic6—21no—
56C32×Dic6—21no—
57C3×#410—91no—
58#5240—31no—
59#5006—31no—
60C32×#41—61no—
61C32×#41—61no—
62C32×#41—61no—
63C32×#41—61no—
64C2×C32×Q8—31no—
65C2×C32×D4—32no—
66C2×C32×D4—31no—
67C22×C32×C4—21no—
68C22×C32×C4—21no—
69C22×C32×C4—21no—
70C22×C32×C4—32no—
71C22×C32×C4—41no—
72C22×C32×C4C2×D311yescharacteristic
73C22×C32×C4C2×D311yescharacteristic
74C22×C32×C4C22×C311yescharacteristic
75C2×C3×#67—22no—
76C2×C3×#67C2×D312yes—
77C2×C3×#67C22×C312yes—
78C3×#235—22no—
79C3×#235—22no—
80C3×#235—22no—
81C3×#235—22no—
82C3×#235—21no—
83C3×#235—21no—
84C3×#235—21no—
85C3×#235—21no—
86C3×#235—21no—
87C3×#235—21no—
88C3×#235—21no—
89C3×#235—21no—
90C2×C3×D12—21no—
91C2×C3×D12Dic311yescharacteristic, complemented
92C2×C3×D12C3×C411yescharacteristic, complemented
93C2×C3×C4×D3—22no—
94C2×C3×C4×D3Dic312yescomplemented
95C2×C3×C4×D3C3×C412yescomplemented
96C2×C3×Dic6—21no—
97C2×C3×Dic6Dic311yescharacteristic, complemented
98C2×C3×Dic6C3×C411yescharacteristic, complemented
99C32×C4⋊C4—61no—
100C32×C22⋊C4—32no—
101C32×C42—61no—
102#3757C22×C312yes—
103C4⋊(C3⋊Dic3)—21no—
104C4×C3⋊Dic3—21no—
105C3×#217—22no—
106C3×#217—32no—
107C3×#217—32no—
108C3×#217—62no—
109C3×#217C2×D312yes—
110C3×#217C22×C312yes—
111C3×C4⋊Dic3—22no—
112C3×C4⋊Dic3—21no—
113C3×C4⋊Dic3—21no—
114C3×C4⋊Dic3—62no—
115C3×C4⋊Dic3—61no—
116C3×C4⋊Dic3—61no—
117C3×C4×Dic3—22no—
118C3×C4×Dic3—21no—
119C3×C4×Dic3—21no—
120C3×C4×Dic3—62no—
121C3×C4×Dic3—61no—
122C3×C4×Dic3—61no—
123C22×C33—41no—
124C22×C33C22×C411yescharacteristic
125C22×C33C2×D411yescharacteristic
126C22×C33C2×D411yescharacteristic
127C2×C32×D3—22no—
128C2×C32×D3—42no—
129C33×C4C22⋊C411yescharacteristic
130C33×C4C22⋊C411yescharacteristic
131C33×C4C22⋊C411yescharacteristic
132C33×C4C22⋊C411yescharacteristic
133C3×C3⋊Dic3—42no—
134C32×Dic3—22no—
135C32×Dic3—42no—
136C2×C3×#41—31no—
137C2×C3×#41—31no—
138C2×C3×#41—61no—
139C2×#235C3×D311yescharacteristic
140C3×#117—31no—
141C3×#117—31no—
142C3×#117—61no—
143C3×#117—91no—
144#926—31no—
145#926—31no—
146#926—61no—
147#926C3×D311yescharacteristic, complemented
148C3×#99—94no—
149#834—34no—
150#806—34no—
151C23×C32—21no—
152C23×C32—21no—
153C23×C32—21no—
154C23×C32—32no—
155C23×C32—41no—
156C23×C32C22×D311yescharacteristic
157C23×C32C22×D311yescharacteristic
158C23×C32C23×C311yescharacteristic
159C22×C3×D3—22no—
160C22×C3×D3C2×Dic312yes—
161C22×C3×D3C2×C3×C412yes—
162C32×Q8—61no—
163C32×Q8—61no—
164C32×D4—62no—
165C32×D4—62no—
166C32×D4—61no—
167C32×D4—61no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
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—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—32no—
187C2×C32×C4—41no—
188C2×C32×C4—41no—
189C2×C32×C4—41no—
190C2×C32×C4—41no—
191C2×C32×C4—41no—
192C2×C32×C4—41no—
193C2×C32×C4—62no—
194C2×C32×C4—62no—
195C2×C32×C4—62no—
196C2×C32×C4C4×D311yescharacteristic
197C2×C32×C4C4×D311yescharacteristic
198C2×C32×C4D1211yescharacteristic
199C2×C32×C4D1211yescharacteristic
200C2×C32×C4C2×Dic311yescharacteristic
201C2×C32×C4C2×Dic311yescharacteristic
202C2×C32×C4#6711yescharacteristic
203C2×C32×C4#6711yescharacteristic
204C2×C32×C4#6711yescharacteristic
205C2×C32×C4#6711yescharacteristic
206C2×C32×C4#6711yescharacteristic
207C2×C32×C4#6711yescharacteristic
208C2×C32×C4C2×C3×C411yescharacteristic
209C2×C32×C4C2×C3×C411yescharacteristic
210C2×C32×C4C3×D411yescharacteristic
211C2×C32×C4C3×D411yescharacteristic
212C2×C32×C4C3×D411yescharacteristic
213C2×C32×C4C3×D411yescharacteristic
214C2×C3⋊Dic3—22no—
215C3×#67—24no—
216C3×#67—24no—
217C3×#67—22no—
218C3×#67—22no—
219C3×#67—22no—
220C3×#67—22no—
221C2×C3×Dic3—24no—
222C2×C3×Dic3—22no—
223C2×C3×Dic3—22no—
224C2×C3×Dic3—22no—
225C2×C3×Dic3—64no—
226C2×C3×Dic3—62no—
227C2×C3×Dic3—62no—
228C2×C3×Dic3C2×Dic312yes—
229C2×C3×Dic3C2×C3×C412yes—
230C3×D12—22no—
231C3×D12—22no—
232C3×D12—21no—
233C3×D12—21no—
234C3×D12—21no—
235C3×D12—21no—
236C3×C4×D3—24no—
237C3×C4×D3—24no—
238C3×C4×D3—22no—
239C3×C4×D3—22no—
240C3×C4×D3—22no—
241C3×C4×D3—22no—
242C3×Dic6—22no—
243C3×Dic6—22no—
244C3×Dic6—21no—
245C3×Dic6—21no—
246C3×Dic6—21no—
247C3×Dic6—21no—
248#410—91noSylow
249C2×C33—21no—
250C2×C33—21no—
251C2×C33—21no—
252C2×C33C2×C22⋊C411yescharacteristic
253C32×D3—42no—
254C3×#41—62no—
255C3×#41—62no—
256C3×#41—62no—
257C3×#41—62no—
258C3×#41—61no—
259C3×#41—61no—
260C3×#41—61no—
261C3×#41—61no—
262C3×#41—61no—
263C3×#41—61no—
264C3×#41—61no—
265C3×#41—61no—
266C2×C3×Q8—31no—
267C2×C3×Q8—31no—
268C2×C3×Q8—61no—
269C2×C3×D4—32no—
270C2×C3×D4—32no—
271C2×C3×D4—31no—
272C2×C3×D4—31no—
273C2×C3×D4—61no—
274C2×C3×D4—62no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—32no—
279C22×C3×C4—32no—
280C22×C3×C4—41no—
281C22×C3×C4—62no—
282C22×C3×C4D3211yescharacteristic
283C22×C3×C4C2×C3×D311yescharacteristic
284C22×C3×C4C2×C3×D311yescharacteristic
285C2×#67C2×C3×D312yes—
286#235—21no—
287#235—21no—
288#235—21no—
289#235—21no—
290C2×D12C3×Dic311yescharacteristic, complemented
291C2×C4×D3C3×Dic312yescomplemented
292C2×Dic6C3×Dic311yescharacteristic, complemented
293C3×C4⋊C4—62no—
294C3×C4⋊C4—61no—
295C3×C4⋊C4—61no—
296C3×C4⋊C4—181no—
297C3×C22⋊C4—32no—
298C3×C22⋊C4—32no—
299C3×C22⋊C4—62no—
300C3×C22⋊C4—92no—
301C3×C42—62no—
302C3×C42—61no—
303C3×C42—61no—
304C3×C42—181no—
305#217—32no—
306#217—32no—
307#217—62no—
308#217C2×C3×D312yes—
309C4⋊Dic3—21no—
310C4⋊Dic3—62no—
311C4⋊Dic3—61no—
312C4⋊Dic3—61no—
313C4×Dic3—21no—
314C4×Dic3—62no—
315C4×Dic3—61no—
316C4×Dic3—61no—
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—41no—
327C22×C32—41no—
328C22×C32—41no—
329C22×C32—41no—
330C22×C32—41no—
331C22×C32—41no—
332C22×C32—42no—
333C22×C32—42no—
334C22×C32—42no—
335C22×C32—44no—
336C22×C32—62no—
337C22×C32—122no—
338C22×C32C2×C4×D311yescharacteristic
339C22×C32C2×D1211yescharacteristic
340C22×C32C22×Dic311yescharacteristic
341C22×C32C2×#6711yescharacteristic
342C22×C32C2×#6711yescharacteristic
343C22×C32C2×#6711yescharacteristic
344C22×C32C22×C3×C411yescharacteristic
345C22×C32C2×C3×D411yescharacteristic
346C22×C32C2×C3×D411yescharacteristic
347C2×C3×D3—24no—
348C2×C3×D3—22no—
349C2×C3×D3—22no—
350C2×C3×D3—44no—
351C2×C3×D3—42no—
352C2×C3×D3—42no—
353C32×C4—21no—
354C32×C4—21no—
355C32×C4—21no—
356C32×C4—21no—
357C32×C4—21no—
358C32×C4—21no—
359C32×C4—21no—
360C32×C4—21no—
361C32×C4—21no—
362C32×C4—21no—
363C32×C4—21no—
364C32×C4—21no—
365C32×C4—41no—
366C32×C4—41no—
367C32×C4—41no—
368C32×C4—41no—
369C32×C4—62no—
370C32×C4—122no—
371C32×C4(C2×D3)⋊C411yescharacteristic
372C32×C4(C2×D3)⋊C411yescharacteristic
373C32×C4(C2×D3)⋊C411yescharacteristic
374C32×C4(C2×D3)⋊C411yescharacteristic
375C32×C4#21711yescharacteristic
376C32×C4#21711yescharacteristic
377C32×C4#21711yescharacteristic
378C32×C4#21711yescharacteristic
379C32×C4C3×C22⋊C411yescharacteristic
380C32×C4C3×C22⋊C411yescharacteristic
381C32×C4C3×C22⋊C411yescharacteristic
382C32×C4C3×C22⋊C411yescharacteristic
383C3⋊Dic3—42no—
384C3×Dic3—24no—
385C3×Dic3—22no—
386C3×Dic3—22no—
387C3×Dic3—44no—
388C3×Dic3—42no—
389C3×Dic3—42no—
390C3×Dic3—124no—
391C3×Dic3—122no—
392C3×Dic3—122no—
393C2×#41—31no—
394#117—31no—
395#117—91no—
396#99—94no—
397C33#41011yescharacteristic, complemented, Sylow
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—32no—
402C23×C3—32no—
403C23×C3—41no—
404C23×C3—62no—
405C23×C3C2×D3211yescharacteristic
406C23×C3C22×C3×D311yescharacteristic
407C23×C3C22×C3×D311yescharacteristic
408C22×D3C2×C3×Dic312yes—
409C3×Q8—62no—
410C3×Q8—62no—
411C3×Q8—61no—
412C3×Q8—61no—
413C3×Q8—61no—
414C3×Q8—61no—
415C3×D4—62no—
416C3×D4—62no—
417C3×D4—64no—
418C3×D4—64no—
419C3×D4—62no—
420C3×D4—62no—
421C3×D4—62no—
422C3×D4—62no—
423C3×D4—61no—
424C3×D4—61no—
425C3×D4—61no—
426C3×D4—61no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—32no—
446C2×C3×C4—32no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—62no—
454C2×C3×C4—64no—
455C2×C3×C4—64no—
456C2×C3×C4—62no—
457C2×C3×C4—62no—
458C2×C3×C4—62no—
459C2×C3×C4—62no—
460C2×C3×C4—64no—
461C2×C3×C4—62no—
462C2×C3×C4—62no—
463C2×C3×C4—182no—
464C2×C3×C4D3×Dic311yescharacteristic
465C2×C3×C4D3×Dic311yescharacteristic
466C2×C3×C4#62511yescharacteristic
467C2×C3×C4#62511yescharacteristic
468C2×C3×C4#62611yescharacteristic
469C2×C3×C4#62611yescharacteristic
470C2×C3×C4C3×C4×D311yescharacteristic
471C2×C3×C4C3×C4×D311yescharacteristic
472C2×C3×C4C3×D1211yescharacteristic
473C2×C3×C4C3×D1211yescharacteristic
474C2×C3×C4C2×C3×Dic311yescharacteristic
475C2×C3×C4C2×C3×Dic311yescharacteristic
476C2×C3×C4C3×#6711yescharacteristic
477C2×C3×C4C3×#6711yescharacteristic
478C2×C3×C4C3×#6711yescharacteristic
479C2×C3×C4C3×#6711yescharacteristic
480C2×C3×C4C3×#6711yescharacteristic
481C2×C3×C4C3×#6711yescharacteristic
482#67—22no—
483#67—22no—
484C2×Dic3—22no—
485C2×Dic3—64no—
486C2×Dic3—62no—
487C2×Dic3—62no—
488C2×Dic3C2×C3×Dic312yes—
489D12—21no—
490D12—21no—
491C4×D3—22no—
492C4×D3—22no—
493Dic6—21no—
494Dic6—21no—
495C2×C32—21no—
496C2×C32—21no—
497C2×C32—21no—
498C2×C32—22no—
499C2×C32—22no—
500C2×C32—22no—
501C2×C32—21no—
502C2×C32—21no—
503C2×C32—21no—
504C2×C32—21no—
505C2×C32—21no—
506C2×C32—21no—
507C2×C32—21no—
508C2×C32—21no—
509C2×C32—21no—
510C2×C32—41no—
511C2×C32—41no—
512C2×C32—41no—
513C2×C32—41no—
514C2×C32—41no—
515C2×C32—41no—
516C2×C32—41no—
517C2×C32—42no—
518C2×C32—42no—
519C2×C32—42no—
520C2×C32—122no—
521C2×C32C2×(C2×D3)⋊C411yescharacteristic
522C2×C32C2×#21711yescharacteristic
523C2×C32C2×C3×C22⋊C411yescharacteristic
524C3×D3—44no—
525C3×D3—42no—
526C3×D3—42no—
527#41—61no—
528#41—61no—
529#41—61no—
530#41—61no—
531C2×Q8—31no—
532C2×D4—32no—
533C2×D4—31no—
534C22×C4—32no—
535C22×C4C3×D3211yescharacteristic
536C4⋊C4—61no—
537C4⋊C4—181no—
538C22⋊C4—32no—
539C22⋊C4—92no—
540C42—61no—
541C42—181no—
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—41no—
552C22×C3—41no—
553C22×C3—41no—
554C22×C3—42no—
555C22×C3—42no—
556C22×C3—42no—
557C22×C3—44no—
558C22×C3—41no—
559C22×C3—41no—
560C22×C3—41no—
561C22×C3—64no—
562C22×C3—62no—
563C22×C3—62no—
564C22×C3—122no—
565C22×C3—122no—
566C22×C3—124no—
567C22×C3C2×D3×Dic311yescharacteristic
568C22×C3C2×#62511yescharacteristic
569C22×C3C2×#62611yescharacteristic
570C22×C3C2×C3×C4×D311yescharacteristic
571C22×C3C2×C3×D1211yescharacteristic
572C22×C3C22×C3×Dic311yescharacteristic
573C22×C3C2×C3×#6711yescharacteristic
574C22×C3C2×C3×#6711yescharacteristic
575C22×C3C2×C3×#6711yescharacteristic
576C2×D3—22no—
577C2×D3—42no—
578C3×C4—21no—
579C3×C4—21no—
580C3×C4—21no—
581C3×C4—21no—
582C3×C4—21no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—21no—
590C3×C4—41no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—41no—
594C3×C4—64no—
595C3×C4—62no—
596C3×C4—62no—
597C3×C4—124no—
598C3×C4—122no—
599C3×C4—122no—
600C3×C4—362no—
601C3×C4(C2×D3)⋊Dic311yescharacteristic
602C3×C4(C2×D3)⋊Dic311yescharacteristic
603C3×C4(C2×D3)⋊Dic311yescharacteristic
604C3×C4(C2×D3)⋊Dic311yescharacteristic
605C3×C4C3×(C2×D3)⋊C411yescharacteristic
606C3×C4C3×(C2×D3)⋊C411yescharacteristic
607C3×C4C3×(C2×D3)⋊C411yescharacteristic
608C3×C4C3×(C2×D3)⋊C411yescharacteristic
609C3×C4C3×#21711yescharacteristic
610C3×C4C3×#21711yescharacteristic
611C3×C4C3×#21711yescharacteristic
612C3×C4C3×#21711yescharacteristic
613Dic3—22no—
614Dic3—42no—
615Dic3—124no—
616Dic3—122no—
617Dic3—122no—
618C32—21no—
619C32—21no—
620C32—21no—
621C32—41no—
622C32#500611yescharacteristic, complemented
623C32#524011yescharacteristic, complemented
624C32C3×#41011yescharacteristic, complemented
625C23—32no—
626C23C2×C3×D3211yescharacteristic
627Q8—61no—
628Q8—61no—
629D4—62no—
630D4—62no—
631D4—61no—
632D4—61no—
633C2×C4—32no—
634C2×C4—62no—
635C2×C4—62no—
636C2×C4—62no—
637C2×C4—182no—
638C2×C4C3×D3×Dic311yescharacteristic
639C2×C4C3×D3×Dic311yescharacteristic
640C2×C4C3×#62511yescharacteristic
641C2×C4C3×#62511yescharacteristic
642C2×C4C3×#62611yescharacteristic
643C2×C4C3×#62611yescharacteristic
644C2×C3—22no—
645C2×C3—22no—
646C2×C3—22no—
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—41no—
660C2×C3—41no—
661C2×C3—41no—
662C2×C3—41no—
663C2×C3—41no—
664C2×C3—41no—
665C2×C3—42no—
666C2×C3—42no—
667C2×C3—42no—
668C2×C3—41no—
669C2×C3—124no—
670C2×C3—122no—
671C2×C3—122no—
672C2×C3C2×(C2×D3)⋊Dic311yescharacteristic
673C2×C3C2×C3×(C2×D3)⋊C411yescharacteristic
674C2×C3C2×C3×#21711yescharacteristic
675D3—42no—
676C22—41no—
677C22—62no—
678C22—122no—
679C22C2×C3×D3×Dic311yescharacteristic
680C22C2×C3×#62511yescharacteristic
681C22C2×C3×#62611yescharacteristic
682C4—62no—
683C4—122no—
684C4—362no—
685C4C3×(C2×D3)⋊Dic311yescharacteristic
686C4C3×(C2×D3)⋊Dic311yescharacteristic
687C4C3×(C2×D3)⋊Dic311yescharacteristic
688C4C3×(C2×D3)⋊Dic311yescharacteristic
689C3—21no—
690C3—21no—
691C3—21no—
692C3—41no—
693C3#1059123111yescharacteristic, direct product factor
694C3C3×#500611yescharacteristic, complemented
695C3C3×#524011yescharacteristic, complemented
696C2—21no—
697C2—21no—
698C2—21no—
699C2—122no—
700C2C2×C3×(C2×D3)⋊Dic311yescharacteristic
subgroupG/H
centerC3×C4(C2×D3)⋊Dic3
commutatorC22×C32C22×C3×C4
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socleC2×C33C2×C22⋊C4
prime radicalC2×C32×#235C2
cosocleC23×C32C23×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×#410
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C3×C4 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
2. C3×#64135C2semidirect
3. C32×#926C2semidirect
4. C3×#63580C2semidirect
7. #10591231C3direct (N × H)
14. C2×C32×D12C4semidirect
15. C2×C32×C4×D3C4semidirect
16. C2×C32×Dic6C4semidirect
28. #64135C2×C3semidirect
33. C3×#926D3semidirect
34. C3×#926C2×C3semidirect
37. #63580C2×C3semidirect
91. C2×C3×D12Dic3semidirect
92. C2×C3×D12C3×C4semidirect
94. C2×C3×C4×D3Dic3semidirect
95. C2×C3×C4×D3C3×C4semidirect
97. C2×C3×Dic6Dic3semidirect
98. C2×C3×Dic6C3×C4semidirect
147. #926C3×D3semidirect
290. C2×D12C3×Dic3semidirect
291. C2×C4×D3C3×Dic3semidirect
292. C2×Dic6C3×Dic3semidirect
397. C33#410semidirect
622. C32#5006semidirect
623. C32#5240semidirect
624. C32C3×#410semidirect
693. C3#10591231direct (N × H)
694. C3C3×#5006semidirect
695. C3C3×#5240semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#2352
C3×#641352
C32×#9262
C3×#635802
C3×#52403
C3×#50063
#105912313