Finite Group Databasebeta

← C3×#70037 #11792793

Subgroups — C3×#70037 #11792793

Order 1152.

1381 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5804C211yesmaximal, characteristic, complemented
2C2×C3×#937C211yesmaximal, characteristic, complemented
3C2×C3×#882C211yesmaximal, characteristic, complemented
4C2×C32×#99C211yesmaximal, characteristic, complemented
5C3×#4955C211yesmaximal, characteristic, complemented
6C2×C3×#806C211yesmaximal, characteristic, complemented
7C3×#4527C211yesmaximal, characteristic, complemented
8C3×#2021—31nomaximal
9#70037C311yesmaximal, characteristic, direct product factor
10C24×C3×D3C2211yescharacteristic
11C22×C32×D4C2211yescharacteristic
12C22×C3×#67—21no—
13C22×C3×#67C2211yescharacteristic
14C22×C3×D12—21no—
15C2×C32×C22⋊C4C2211yescharacteristic
16C2×C32×C22⋊C4C2211yescharacteristic
17C3×#953—21no—
18C2×C3×#217C2211yescharacteristic
19C2×C3×#217C2211yescharacteristic
20C3×#939—22no—
21C3×#937—22no—
22C3×#937—22no—
23C3×#937—21no—
24C3×#935—21no—
25C3×#929—21no—
26C2×C3×(C2×D3)⋊C4—21no—
27C2×C3×(C2×D3)⋊C4—21no—
28C2×C3×(C2×D3)⋊C4—22no—
29C3×#882—22no—
30C3×#882—22no—
31C32×#99—22no—
32C3×#806—22no—
33C3×#534—31no—
34C2×C3×#120—31no—
35C2×C3×#120—31no—
36#5804C2×C311yescharacteristic, complemented
37C2×#937C2×C311yescharacteristic, complemented
38C2×#882C2×C311yescharacteristic, complemented
39C2×C3×#99—21no—
40C2×C3×#99—31no—
41C2×C3×#99D311yescharacteristic, complemented
42C2×C3×#99C2×C311yescharacteristic, complemented
43C3×#379—31no—
44#4955C2×C311yescharacteristic, complemented
45C2×#806C2×C311yescharacteristic, complemented
46C3×#342—31no—
47#4527C2×C311yescharacteristic, complemented
48C24×C32D411yescharacteristic, complemented
49C24×C32C2311yescharacteristic
50C23×C3×D3—21no—
51C23×C3×D3—21no—
52C23×C3×D3—21no—
53C23×C3×D3—21no—
54C23×C3×D3—21no—
55C23×C3×D3—21no—
56C23×C3×D3—44no—
57C23×C3×D3D412yescomplemented
58C23×C3×D3D411yescharacteristic, complemented
59C2×C32×D4—21no—
60C2×C32×D4—21no—
61C2×C32×D4—21no—
62C2×C32×D4—21no—
63C2×C32×D4—21no—
64C2×C32×D4—21no—
65C22×C32×C4—21no—
66C22×C32×C4—21no—
67C22×C32×C4D411yescharacteristic, complemented
68C2×C3×#67—24no—
69C2×C3×#67—21no—
70C2×C3×#67—21no—
71C2×C3×#67—21no—
72C2×C3×#67—21no—
73C2×C3×#67—21no—
74C2×C3×#67—21no—
75C2×C3×#67—22no—
76C2×C3×#67—44no—
77C22×C3×Dic3—21no—
78C22×C3×Dic3D411yescharacteristic, complemented
79C22×C3×Dic3D412yescomplemented
80C2×C3×D12—24no—
81C2×C3×D12—44no—
82C32×C22⋊C4—21no—
83C32×C22⋊C4—21no—
84C32×C22⋊C4—21no—
85C32×C22⋊C4D412yescomplemented
86C3×#217—22no—
87C3×#217—21no—
88C3×#217—21no—
89C3×#217—21no—
90C3×#217D412yescomplemented
91C3×(C2×D3)⋊C4—24no—
92C3×(C2×D3)⋊C4—24no—
93C3×(C2×D3)⋊C4—22no—
94C3×(C2×D3)⋊C4—44no—
95C3×Dic3⋊C4—22no—
96#2021—31noSylow
97C25×C3—31no—
98C24×D3C22×C311yescharacteristic
99C22×C3×D4—21no—
100C22×C3×D4—31no—
101C22×C3×D4—61no—
102C22×C3×D4—61no—
103C22×C3×D4C2×D311yescharacteristic
104C22×C3×D4C22×C311yescharacteristic
105C22×#67—21no—
106C22×#67C22×C311yescharacteristic
107C22×D12—21no—
108C3×#123—61no—
109C3×#123—61no—
110C3×#121—62no—
111C3×#120—62no—
112C3×#120—62no—
113C3×#120—62no—
114C3×#120—61no—
115C3×#120—61no—
116C3×#120—62no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4—31no—
120C2×C3×C22⋊C4—31no—
121C2×C3×C22⋊C4—61no—
122C2×C3×C22⋊C4—61no—
123C2×C3×C22⋊C4—62no—
124C2×C3×C22⋊C4C2×D311yescharacteristic
125C2×C3×C22⋊C4C2×D311yescharacteristic
126C2×C3×C22⋊C4C22×C311yescharacteristic
127C2×C3×C22⋊C4C22×C311yescharacteristic
128#953—21no—
129C2×#217C22×C311yescharacteristic
130C2×#217C22×C311yescharacteristic
131#939—22no—
132#937—22no—
133#937—21no—
134#937—22no—
135#935—21no—
136#929—21no—
137C2×(C2×D3)⋊C4—21no—
138C2×(C2×D3)⋊C4—21no—
139C2×(C2×D3)⋊C4—22no—
140#882—22no—
141#882—22no—
142C3×#99—24no—
143C3×#99—22no—
144C3×#99—22no—
145C3×#99—62no—
146#806—22no—
147C23×C32—21no—
148C23×C32—21no—
149C23×C32—21no—
150C23×C32—42no—
151C23×C32—42no—
152C23×C32C2×D411yescharacteristic
153C23×C32C2×D411yescharacteristic
154C23×C32C2×D411yescharacteristic
155C23×C32C2×D411yescharacteristic
156C23×C32C2×D411yescharacteristic
157C23×C32C2×D411yescharacteristic
158C23×C32#4111yescharacteristic
159C22×C3×D3—24no—
160C22×C3×D3—24no—
161C22×C3×D3—24no—
162C22×C3×D3—22no—
163C22×C3×D3—22no—
164C22×C3×D3—22no—
165C22×C3×D3—21no—
166C22×C3×D3—21no—
167C22×C3×D3—21no—
168C22×C3×D3—44no—
169C22×C3×D3—44no—
170C22×C3×D3—44no—
171C22×C3×D3—44no—
172C22×C3×D3—42no—
173C22×C3×D3—42no—
174C22×C3×D3—42no—
175C22×C3×D3—41no—
176C22×C3×D3—41no—
177C22×C3×D3—41no—
178C22×C3×D3—41no—
179C22×C3×D3—42no—
180C32×D4—41no—
181C32×D4—41no—
182C32×D4—41no—
183C32×D4—41no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4—22no—
188C2×C32×C4—41no—
189C2×C32×C4—42no—
190C2×C32×C4—42no—
191C3×#67—48no—
192C3×#67—41no—
193C3×#67—41no—
194C3×#67—41no—
195C3×#67—41no—
196C3×#67—82no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—42no—
203C2×C3×Dic3—42no—
204C3×D12—48no—
205#534—31no—
206C2×#120—31no—
207C2×#120—31no—
208C2×#99—31no—
209C2×#99C3×D311yescharacteristic, complemented
210#379—31no—
211#342—31no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3—32no—
215C24×C3—31no—
216C24×C3—61no—
217C24×C3—61no—
218C24×C3—61no—
219C24×C3—61no—
220C24×C3—61no—
221C24×C3—61no—
222C24×C3—124no—
223C24×C3D1211yescharacteristic, complemented
224C24×C3C3×D411yescharacteristic, complemented
225C24×C3C22×D311yescharacteristic
226C24×C3C23×C311yescharacteristic
227C23×D3—21no—
228C23×D3—21no—
229C23×D3—21no—
230C23×D3—21no—
231C23×D3—21no—
232C23×D3—21no—
233C23×D3—44no—
234C23×D3C3×D412yescomplemented
235C23×D3C3×D411yescharacteristic, complemented
236C2×C3×D4—22no—
237C2×C3×D4—22no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—41no—
251C2×C3×D4—41no—
252C2×C3×D4—41no—
253C2×C3×D4—41no—
254C2×C3×D4—64no—
255C2×C3×D4—64no—
256C2×C3×D4—61no—
257C2×C3×D4—61no—
258C2×C3×D4—61no—
259C2×C3×D4—61no—
260C2×C3×D4—61no—
261C2×C3×D4—61no—
262C2×C3×D4—62no—
263C2×C3×D4—124no—
264C2×C3×D4—124no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—31no—
271C22×C3×C4—32no—
272C22×C3×C4—41no—
273C22×C3×C4—41no—
274C22×C3×C4—61no—
275C22×C3×C4D1211yescharacteristic, complemented
276C22×C3×C4C3×D411yescharacteristic, complemented
277C2×#67—24no—
278C2×#67—21no—
279C2×#67—21no—
280C2×#67—21no—
281C2×#67—21no—
282C2×#67—21no—
283C2×#67—21no—
284C2×#67—22no—
285C2×#67—44no—
286C22×Dic3—21no—
287C22×Dic3C3×D411yescharacteristic, complemented
288C22×Dic3C3×D412yescomplemented
289C2×D12—24no—
290C2×D12—44no—
291C3×C4⋊C4—62no—
292C3×C22⋊C4—21no—
293C3×C22⋊C4—21no—
294C3×C22⋊C4—22no—
295C3×C22⋊C4—21no—
296C3×C22⋊C4—21no—
297C3×C22⋊C4—21no—
298C3×C22⋊C4—21no—
299C3×C22⋊C4—22no—
300C3×C22⋊C4—32no—
301C3×C22⋊C4—41no—
302C3×C22⋊C4—41no—
303C3×C22⋊C4—64no—
304C3×C22⋊C4—64no—
305C3×C22⋊C4—62no—
306C3×C22⋊C4—62no—
307C3×C22⋊C4—61no—
308C3×C22⋊C4—61no—
309C3×C22⋊C4—61no—
310C3×C22⋊C4—124no—
311C3×C22⋊C4#6712yescomplemented
312C3×C22⋊C4C3×D412yescomplemented
313#217—22no—
314#217—21no—
315#217—21no—
316#217—21no—
317#217C3×D412yescomplemented
318(C2×D3)⋊C4—24no—
319(C2×D3)⋊C4—24no—
320(C2×D3)⋊C4—22no—
321(C2×D3)⋊C4—44no—
322Dic3⋊C4—22no—
323C22×C32—22no—
324C22×C32—22no—
325C22×C32—22no—
326C22×C32—41no—
327C22×C32—41no—
328C22×C32—41no—
329C22×C32—41no—
330C22×C32—41no—
331C22×C32—42no—
332C22×C32—42no—
333C22×C32—81no—
334C22×C32#12011yescharacteristic
335C22×C32#12011yescharacteristic
336C22×C32#12011yescharacteristic
337C22×C32#12111yescharacteristic
338C22×C32#12111yescharacteristic
339C22×C32#12111yescharacteristic
340C22×C32#12711yescharacteristic
341C2×C3×D3—24no—
342C2×C3×D3—24no—
343C2×C3×D3—24no—
344C2×C3×D3—42no—
345C2×C3×D3—42no—
346C2×C3×D3—44no—
347C2×C3×D3—42no—
348C2×C3×D3—44no—
349C2×C3×D3—44no—
350C2×C3×D3—42no—
351C2×C3×D3—44no—
352C2×C3×D3—42no—
353C2×C3×D3—41no—
354C2×C3×D3—42no—
355C2×C3×D3—81no—
356C32×C4—41no—
357C32×C4—42no—
358C32×C4—81no—
359C3×Dic3—42no—
360C3×Dic3—41no—
361C3×Dic3—42no—
362C25—31no—
363C22×D4—31no—
364C22×D4—61no—
365C22×D4—61no—
366C22×D4C2×C3×D311yescharacteristic
367#123—61no—
368#123—61no—
369#121—62no—
370#120—62no—
371#120—62no—
372#120—62no—
373#120—61no—
374#120—61no—
375#120—62no—
376C2×C22⋊C4—31no—
377C2×C22⋊C4—31no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—62no—
381C2×C22⋊C4C2×C3×D311yescharacteristic
382C2×C22⋊C4C2×C3×D311yescharacteristic
383#99—22no—
384#99—62no—
385C23×C3—22no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—21no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—41no—
400C23×C3—41no—
401C23×C3—42no—
402C23×C3—42no—
403C23×C3—42no—
404C23×C3—42no—
405C23×C3—64no—
406C23×C3—64no—
407C23×C3—64no—
408C23×C3—62no—
409C23×C3—62no—
410C23×C3—62no—
411C23×C3—61no—
412C23×C3—61no—
413C23×C3—61no—
414C23×C3—82no—
415C23×C3—82no—
416C23×C3—122no—
417C23×C3—122no—
418C23×C3—122no—
419C23×C3—122no—
420C23×C3—124no—
421C23×C3—124no—
422C23×C3—124no—
423C23×C3—124no—
424C23×C3—121no—
425C23×C3—121no—
426C23×C3—121no—
427C23×C3—121no—
428C23×C3C2×D1211yescharacteristic
429C23×C3#23511yescharacteristic
430C23×C3D3×D411yescharacteristic
431C23×C3D3×D411yescharacteristic
432C23×C3D3×D411yescharacteristic
433C23×C3D3×D411yescharacteristic
434C23×C3C2×#6711yescharacteristic
435C23×C3C2×C3×D411yescharacteristic
436C23×C3C2×C3×D411yescharacteristic
437C23×C3C2×C3×D411yescharacteristic
438C23×C3C2×C3×D411yescharacteristic
439C23×C3C2×C3×D411yescharacteristic
440C23×C3C2×C3×D411yescharacteristic
441C23×C3C3×#4111yescharacteristic
442C22×D3—24no—
443C22×D3—24no—
444C22×D3—24no—
445C22×D3—22no—
446C22×D3—22no—
447C22×D3—22no—
448C22×D3—21no—
449C22×D3—21no—
450C22×D3—21no—
451C22×D3—44no—
452C22×D3—44no—
453C22×D3—44no—
454C22×D3—44no—
455C22×D3—42no—
456C22×D3—42no—
457C22×D3—42no—
458C22×D3—41no—
459C22×D3—41no—
460C22×D3—41no—
461C22×D3—41no—
462C22×D3—42no—
463C3×D4—42no—
464C3×D4—42no—
465C3×D4—42no—
466C3×D4—42no—
467C3×D4—41no—
468C3×D4—41no—
469C3×D4—41no—
470C3×D4—41no—
471C3×D4—41no—
472C3×D4—41no—
473C3×D4—41no—
474C3×D4—41no—
475C3×D4—128no—
476C3×D4—128no—
477C3×D4—121no—
478C3×D4—121no—
479C3×D4—121no—
480C3×D4—121no—
481C3×D4—242no—
482C2×C3×C4—22no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—22no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—22no—
490C2×C3×C4—21no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—42no—
494C2×C3×C4—42no—
495C2×C3×C4—42no—
496C2×C3×C4—42no—
497C2×C3×C4—42no—
498C2×C3×C4—42no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—62no—
502C2×C3×C4—62no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—82no—
507C2×C3×C4—82no—
508C2×C3×C4—122no—
509C2×C3×C4—122no—
510#67—48no—
511#67—41no—
512#67—41no—
513#67—41no—
514#67—41no—
515#67—82no—
516C2×Dic3—21no—
517C2×Dic3—22no—
518C2×Dic3—21no—
519C2×Dic3—22no—
520C2×Dic3—21no—
521C2×Dic3—42no—
522C2×Dic3—42no—
523D12—48no—
524C2×C32—21no—
525C2×C32—21no—
526C2×C32—21no—
527C2×C32—21no—
528C2×C32—21no—
529C2×C32—21no—
530C2×C32—81no—
531C2×C32#39211yescharacteristic
532C2×C32B(4,𝔽2)12yes—
533C3×D3—44no—
534C3×D3—81no—
535C24—32no—
536C24—31no—
537C24—61no—
538C24—61no—
539C24—61no—
540C24—61no—
541C24—61no—
542C24—61no—
543C24—124no—
544C24C3×D1211yescharacteristic, complemented
545C24C22×C3×D311yescharacteristic
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—64no—
553C2×D4—64no—
554C2×D4—61no—
555C2×D4—61no—
556C2×D4—61no—
557C2×D4—61no—
558C2×D4—61no—
559C2×D4—61no—
560C2×D4—62no—
561C2×D4—124no—
562C2×D4—124no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—31no—
566C22×C4—32no—
567C22×C4—61no—
568C22×C4C3×D1211yescharacteristic, complemented
569C4⋊C4—62no—
570C22⋊C4—21no—
571C22⋊C4—21no—
572C22⋊C4—21no—
573C22⋊C4—32no—
574C22⋊C4—64no—
575C22⋊C4—64no—
576C22⋊C4—62no—
577C22⋊C4—62no—
578C22⋊C4—61no—
579C22⋊C4—61no—
580C22⋊C4—61no—
581C22⋊C4—124no—
582C22⋊C4C3×#6712yescomplemented
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—42no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—41no—
606C22×C3—41no—
607C22×C3—42no—
608C22×C3—42no—
609C22×C3—42no—
610C22×C3—41no—
611C22×C3—42no—
612C22×C3—41no—
613C22×C3—42no—
614C22×C3—64no—
615C22×C3—64no—
616C22×C3—64no—
617C22×C3—82no—
618C22×C3—81no—
619C22×C3—81no—
620C22×C3—81no—
621C22×C3—81no—
622C22×C3—82no—
623C22×C3—81no—
624C22×C3—81no—
625C22×C3—82no—
626C22×C3—122no—
627C22×C3—124no—
628C22×C3—122no—
629C22×C3—122no—
630C22×C3—124no—
631C22×C3—124no—
632C22×C3—122no—
633C22×C3—122no—
634C22×C3—124no—
635C22×C3—121no—
636C22×C3—122no—
637C22×C3—241no—
638C22×C3#88211yescharacteristic
639C22×C3#88211yescharacteristic
640C22×C3#88411yescharacteristic
641C22×C3#88411yescharacteristic
642C22×C3#93011yescharacteristic
643C22×C3#93711yescharacteristic
644C22×C3#94011yescharacteristic
645C22×C3C3×#12011yescharacteristic
646C22×C3C3×#12011yescharacteristic
647C22×C3C3×#12011yescharacteristic
648C22×C3C3×#12111yescharacteristic
649C22×C3C3×#12111yescharacteristic
650C22×C3C3×#12111yescharacteristic
651C22×C3C3×#12711yescharacteristic
652C2×D3—24no—
653C2×D3—24no—
654C2×D3—24no—
655C2×D3—42no—
656C2×D3—42no—
657C2×D3—44no—
658C2×D3—42no—
659C2×D3—44no—
660C2×D3—44no—
661C2×D3—42no—
662C2×D3—44no—
663C2×D3—42no—
664C2×D3—41no—
665C2×D3—42no—
666C2×D3—81no—
667C3×C4—42no—
668C3×C4—42no—
669C3×C4—42no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—82no—
673C3×C4—81no—
674C3×C4—81no—
675C3×C4—82no—
676C3×C4—122no—
677C3×C4—121no—
678C3×C4—122no—
679Dic3—42no—
680Dic3—41no—
681Dic3—42no—
682C32#202111yescharacteristic, complemented, Sylow
683C23—21no—
684C23—21no—
685C23—21no—
686C23—42no—
687C23—42no—
688C23—64no—
689C23—64no—
690C23—64no—
691C23—62no—
692C23—62no—
693C23—62no—
694C23—61no—
695C23—61no—
696C23—61no—
697C23—122no—
698C23—122no—
699C23—122no—
700C23—122no—
701C23—124no—
702C23—124no—
703C23—124no—
704C23—124no—
705C23—121no—
706C23—121no—
707C23—121no—
708C23—121no—
709C23C2×C3×D1211yescharacteristic
710C23C3×#23511yescharacteristic
711C23C3×D3×D411yescharacteristic
712C23C3×D3×D411yescharacteristic
713C23C3×D3×D411yescharacteristic
714C23C3×D3×D411yescharacteristic
715C23C2×C3×#6711yescharacteristic
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—128no—
721D4—128no—
722D4—121no—
723D4—121no—
724D4—121no—
725D4—121no—
726D4—242no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—62no—
735C2×C4—62no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—122no—
740C2×C4—122no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—22no—
755C2×C3—41no—
756C2×C3—41no—
757C2×C3—41no—
758C2×C3—41no—
759C2×C3—41no—
760C2×C3—41no—
761C2×C3—82no—
762C2×C3—81no—
763C2×C3—81no—
764C2×C3—124no—
765C2×C3—241no—
766C2×C3#474112yes—
767C2×C3#496011yescharacteristic
768C2×C3C3×#39211yescharacteristic
769C2×C3C3×B(4,𝔽2)12yes—
770D3—44no—
771D3—81no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—42no—
780C22—41no—
781C22—42no—
782C22—64no—
783C22—64no—
784C22—64no—
785C22—81no—
786C22—122no—
787C22—124no—
788C22—122no—
789C22—122no—
790C22—124no—
791C22—124no—
792C22—122no—
793C22—122no—
794C22—124no—
795C22—121no—
796C22—122no—
797C22—241no—
798C22C3×#88211yescharacteristic
799C22C3×#88211yescharacteristic
800C22C3×#88411yescharacteristic
801C22C3×#88411yescharacteristic
802C22C3×#93011yescharacteristic
803C22C3×#93711yescharacteristic
804C22C3×#94011yescharacteristic
805C4—42no—
806C4—41no—
807C4—81no—
808C4—122no—
809C4—121no—
810C4—122no—
811C3—21no—
812C3#7003711yescharacteristic, direct product factor
813C3C3×#202111yescharacteristic, complemented
814C2—21no—
815C2—21no—
816C2—21no—
817C2—21no—
818C2—21no—
819C2—21no—
820C2—81no—
821C2—124no—
822C2—241no—
823C2C3×#474112yes—
824C2C3×#496011yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC24×C3C23×C3
FrattiniC24C22×C3×D3
FittingC2×C32×#99C2
socleC22×C32#120
hypercenterC2×C3×#99D3
hypocenterC3C3×#2021
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C2×C3×#99

Complements

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

NH ≅ G/Ntype
1. C3×#5804C2semidirect
2. C2×C3×#937C2semidirect
3. C2×C3×#882C2semidirect
4. C2×C32×#99C2semidirect
5. C3×#4955C2semidirect
6. C2×C3×#806C2semidirect
7. C3×#4527C2semidirect
9. #70037C3direct (N × H)
36. #5804C2×C3semidirect
37. C2×#937C2×C3semidirect
38. C2×#882C2×C3semidirect
41. C2×C3×#99D3semidirect
42. C2×C3×#99C2×C3semidirect
44. #4955C2×C3semidirect
45. C2×#806C2×C3semidirect
47. #4527C2×C3semidirect
48. C24×C32D4semidirect
57. C23×C3×D3D4semidirect
58. C23×C3×D3D4semidirect
67. C22×C32×C4D4semidirect
78. C22×C3×Dic3D4semidirect
79. C22×C3×Dic3D4semidirect
85. C32×C22⋊C4D4semidirect
90. C3×#217D4semidirect
209. C2×#99C3×D3semidirect
223. C24×C3D12semidirect
224. C24×C3C3×D4semidirect
234. C23×D3C3×D4semidirect
235. C23×D3C3×D4semidirect
275. C22×C3×C4D12semidirect
276. C22×C3×C4C3×D4semidirect
287. C22×Dic3C3×D4semidirect
288. C22×Dic3C3×D4semidirect
311. C3×C22⋊C4#67semidirect
312. C3×C22⋊C4C3×D4semidirect
317. #217C3×D4semidirect
544. C24C3×D12semidirect
568. C22×C4C3×D12semidirect
582. C22⋊C4C3×#67semidirect
682. C32#2021semidirect
812. C3#70037direct (N × H)
813. C3C3×#2021semidirect

Maximal subgroups

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

subgroupindex
C3×#58042
C2×C3×#9372
C2×C3×#8822
C2×C32×#992
C3×#49552
C2×C3×#8062
C3×#45272
C3×#20213
#700373