Finite Group Databasebeta

← C3×#74884 #11808990

Subgroups — C3×#74884 #11808990

Order 1152.

3271 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×D4C211yesmaximal, characteristic, complemented
2C23×C3×D12C211yesmaximal, characteristic, complemented
3C2×C3×#937C211yesmaximal, characteristic, complemented
4C2×C3×#882C212yesmaximal, complemented
5C2×C3×#882C211yesmaximal, characteristic, complemented
6C32×#386C211yesmaximal, characteristic, complemented
7C3×#5213C211yesmaximal, characteristic, complemented
8C3×#4960C212yesmaximal, complemented
9C3×#4955C211yesmaximal, characteristic, complemented
10C3×#4671C212yesmaximal, complemented
11C3×#4665C212yesmaximal, complemented
12C3×#2403—31nomaximal
13#74884C311yesmaximal, characteristic, direct product factor
14C24×C3×D3C2211yescharacteristic
15C24×C3×D3C2211yescharacteristic, complemented
16C24×C3×D3C2211yescharacteristic, complemented
17C22×C32×D4C2211yescharacteristic
18C23×C32×C4C2211yescharacteristic, complemented
19C22×C3×#67C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic, complemented
21C22×C3×#67C2212yescomplemented
22C2×C3×D3×D4—24no—
23C2×C3×D3×D4—24no—
24C2×C3×D3×D4—24no—
25C22×C3×D12—28no—
26C22×C3×D12—24no—
27C22×C3×D12C2212yes—
28C22×C3×D12C2211yescharacteristic, complemented
29C22×C3×D12C2212yescomplemented
30C22×C3×D12C2212yescomplemented
31C22×C3×C4×D3C2211yescharacteristic, complemented
32C2×C32×C22⋊C4C2211yescharacteristic, complemented
33C2×C32×C22⋊C4C2212yescomplemented
34C2×C3×#217C2211yescharacteristic, complemented
35C3×#937—24no—
36C2×C3×(C2×D3)⋊C4C2212yescomplemented
37C2×C3×(C2×D3)⋊C4C2212yescomplemented
38C2×C3×(C2×D3)⋊C4C2212yescomplemented
39C2×C3×(C2×D3)⋊C4C2212yescomplemented
40C2×C3×(C2×D3)⋊C4C2212yescomplemented
41C3×#882—24no—
42C3×#882—28no—
43C32×#95C2212yescomplemented
44C3×C3⋊#95C2212yescomplemented
45C23×C3×D4—31no—
46C23×C3×D4—31no—
47C22×D3×D4C2×C311yescharacteristic, complemented
48C23×D12C2×C311yescharacteristic, complemented
49C2×C3×#120—31no—
50C2×C3×#120—32no—
51C2×C3×#120—31no—
52C2×#937C2×C311yescharacteristic, complemented
53C2×#882C2×C312yescomplemented
54C2×#882C2×C311yescharacteristic, complemented
55C3×#392—32no—
56C3×#392—32no—
57C3×#386—21no—
58C3×#386—31no—
59C3×#386—32no—
60C3×#386D311yescharacteristic, complemented
61C3×#386C2×C311yescharacteristic, complemented
62C3×#379—31no—
63#5213C2×C311yescharacteristic, complemented
64#4960C2×C312yescomplemented
65#4955C2×C311yescharacteristic, complemented
66#4671C2×C312yescomplemented
67#4665C2×C312yescomplemented
68C24×C32C2311yescharacteristic
69C24×C32C2311yescharacteristic
70C23×C3×D3—22no—
71C23×C3×D3—22no—
72C23×C3×D3—22no—
73C23×C3×D3—22no—
74C23×C3×D3—24no—
75C23×C3×D3—22no—
76C23×C3×D3—24no—
77C23×C3×D3—22no—
78C23×C3×D3—22no—
79C23×C3×D3—22no—
80C23×C3×D3—24no—
81C23×C3×D3—42no—
82C23×C3×D3—42no—
83C23×C3×D3—42no—
84C23×C3×D3D414yescomplemented
85C23×C3×D3C2311yescharacteristic
86C23×C3×D3C2312yes—
87C23×C3×D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C2×C32×D4—22no—
90C2×C32×D4—22no—
91C2×C32×D4D414yescomplemented
92C22×C32×C4—22no—
93C22×C32×C4—24no—
94C22×C32×C4C2312yes—
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2312yes—
97C2×C3×#67—22no—
98C2×C3×#67—22no—
99C2×C3×#67—22no—
100C2×C3×#67—22no—
101C2×C3×#67—24no—
102C2×C3×#67—24no—
103C2×C3×#67—22no—
104C2×C3×#67—42no—
105C2×C3×#67D414yescomplemented
106C22×C3×Dic3C2312yes—
107C22×C3×Dic3C2311yescharacteristic
108C3×D3×D4—232no—
109C2×C3×D12—232no—
110C2×C3×D12—24no—
111C2×C3×D12—24no—
112C2×C3×D12—24no—
113C2×C3×D12—22no—
114C2×C3×D12—24no—
115C2×C3×D12—22no—
116C2×C3×D12—24no—
117C2×C3×D12—22no—
118C2×C3×D12—24no—
119C2×C3×D12—24no—
120C2×C3×D12—42no—
121C2×C3×D12D418yescomplemented
122C2×C3×C4×D3—22no—
123C2×C3×C4×D3—22no—
124C2×C3×C4×D3—22no—
125C32×C22⋊C4—22no—
126C32×C22⋊C4—24no—
127C3×#217—22no—
128C3×(C2×D3)⋊C4—24no—
129C3×(C2×D3)⋊C4—24no—
130C3×(C2×D3)⋊C4—24no—
131C3×(C2×D3)⋊C4—24no—
132C3×(C2×D3)⋊C4—42no—
133#2403—31noSylow
134C25×C3—31no—
135C25×C3—31no—
136C25×C3—31no—
137C24×D3C22×C311yescharacteristic
138C24×D3C22×C311yescharacteristic, complemented
139C24×D3C22×C311yescharacteristic, complemented
140C22×C3×D4—21no—
141C22×C3×D4—31no—
142C22×C3×D4—31no—
143C22×C3×D4—32no—
144C22×C3×D4—32no—
145C22×C3×D4—31no—
146C22×C3×D4—32no—
147C22×C3×D4—32no—
148C22×C3×D4—68no—
149C22×C3×D4—64no—
150C22×C3×D4—64no—
151C22×C3×D4—64no—
152C22×C3×D4—64no—
153C22×C3×D4C2×D311yescharacteristic
154C22×C3×D4C22×C311yescharacteristic
155C23×C3×C4—21no—
156C23×C3×C4—31no—
157C23×C3×C4C2×D311yescharacteristic, complemented
158C23×C3×C4C22×C311yescharacteristic, complemented
159C22×#67C22×C311yescharacteristic
160C22×#67C22×C311yescharacteristic, complemented
161C22×#67C22×C312yescomplemented
162C2×D3×D4—24no—
163C2×D3×D4—24no—
164C2×D3×D4—24no—
165C22×D12—24no—
166C22×D12—28no—
167C22×D12C22×C312yes—
168C22×D12C22×C311yescharacteristic, complemented
169C22×D12C22×C312yescomplemented
170C22×D12C22×C312yescomplemented
171C22×C4×D3C22×C311yescharacteristic, complemented
172C3×#120—64no—
173C3×#120—68no—
174C3×#120—64no—
175C2×C3×C22⋊C4—21no—
176C2×C3×C22⋊C4—22no—
177C2×C3×C22⋊C4—31no—
178C2×C3×C22⋊C4—32no—
179C2×C3×C22⋊C4—32no—
180C2×C3×C22⋊C4—32no—
181C2×C3×C22⋊C4—32no—
182C2×C3×C22⋊C4—32no—
183C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
184C2×C3×C22⋊C4C2×D312yescomplemented
185C2×C3×C22⋊C4C22×C311yescharacteristic, complemented
186C2×C3×C22⋊C4C22×C312yescomplemented
187C2×#217C22×C311yescharacteristic, complemented
188#937—24no—
189C2×(C2×D3)⋊C4C22×C312yescomplemented
190C2×(C2×D3)⋊C4C22×C312yescomplemented
191C2×(C2×D3)⋊C4C22×C312yescomplemented
192C2×(C2×D3)⋊C4C22×C312yescomplemented
193C2×(C2×D3)⋊C4C22×C312yescomplemented
194#882—24no—
195#882—28no—
196C3×#95—22no—
197C3×#95—32no—
198C3×#95C2×D312yescomplemented
199C3×#95C22×C312yescomplemented
200C3⋊#95C22×C312yescomplemented
201C23×C32—22no—
202C23×C32—22no—
203C23×C32—22no—
204C23×C32—21no—
205C23×C32—21no—
206C23×C32—22no—
207C23×C32C2×D412yes—
208C23×C32C2×D412yes—
209C23×C32C2×D412yes—
210C23×C32C2×D412yescomplemented
211C23×C32C2411yescharacteristic
212C22×C3×D3—21no—
213C22×C3×D3—21no—
214C22×C3×D3—22no—
215C22×C3×D3—28no—
216C22×C3×D3—28no—
217C22×C3×D3—28no—
218C22×C3×D3—22no—
219C22×C3×D3—22no—
220C22×C3×D3—22no—
221C22×C3×D3—22no—
222C22×C3×D3—22no—
223C22×C3×D3—22no—
224C22×C3×D3—21no—
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—21no—
228C22×C3×D3—22no—
229C22×C3×D3—22no—
230C22×C3×D3—22no—
231C22×C3×D3—22no—
232C22×C3×D3—28no—
233C22×C3×D3—44no—
234C22×C3×D3—48no—
235C22×C3×D3—48no—
236C22×C3×D3—48no—
237C22×C3×D3—48no—
238C22×C3×D3—48no—
239C22×C3×D3—48no—
240C22×C3×D3—44no—
241C22×C3×D3—44no—
242C22×C3×D3—44no—
243C22×C3×D3—44no—
244C22×C3×D3C2×D412yes—
245C22×C3×D3C2×D414yes—
246C22×C3×D3C2×D412yes—
247C22×C3×D3C2×D412yescomplemented
248C22×C3×D3C2×D414yescomplemented
249C32×D4—28no—
250C2×C32×C4—28no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—22no—
254C2×C32×C4—22no—
255C2×C32×C4—22no—
256C2×C32×C4—22no—
257C2×C32×C4—22no—
258C2×C32×C4C2×D412yescomplemented
259C2×C32×C4C2×D414yescomplemented
260C3×#67—28no—
261C3×#67—28no—
262C3×#67—48no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—22no—
266C2×C3×Dic3—22no—
267C2×C3×Dic3—22no—
268C2×C3×Dic3C2×D412yescomplemented
269C3×D12—216no—
270C3×D12—28no—
271C3×D12—216no—
272C3×D12—48no—
273C3×C4×D3—28no—
274C23×D4—31no—
275C23×D4—31no—
276C2×#120—31no—
277C2×#120—32no—
278C2×#120—31no—
279#392—32no—
280#392—32no—
281#386—31no—
282#386—32no—
283#386C3×D311yescharacteristic, complemented
284#379—31no—
285C24×C3—21no—
286C24×C3—21no—
287C24×C3—31no—
288C24×C3—31no—
289C24×C3—32no—
290C24×C3—31no—
291C24×C3—34no—
292C24×C3—64no—
293C24×C3—64no—
294C24×C3—62no—
295C24×C3—62no—
296C24×C3—64no—
297C24×C3—62no—
298C24×C3—62no—
299C24×C3—62no—
300C24×C3—62no—
301C24×C3—62no—
302C24×C3—62no—
303C24×C3—122no—
304C24×C3—122no—
305C24×C3—122no—
306C24×C3C22×D311yescharacteristic
307C24×C3C22×D311yescharacteristic
308C24×C3C23×C311yescharacteristic
309C24×C3C23×C311yescharacteristic
310C23×D3—22no—
311C23×D3—22no—
312C23×D3—22no—
313C23×D3—22no—
314C23×D3—24no—
315C23×D3—22no—
316C23×D3—24no—
317C23×D3—22no—
318C23×D3—22no—
319C23×D3—22no—
320C23×D3—24no—
321C23×D3—42no—
322C23×D3—42no—
323C23×D3—42no—
324C23×D3C3×D414yescomplemented
325C23×D3C23×C311yescharacteristic
326C23×D3C23×C312yes—
327C23×D3C23×C311yescharacteristic
328C23×D3C23×C311yescharacteristic
329C2×C3×D4—22no—
330C2×C3×D4—22no—
331C2×C3×D4—22no—
332C2×C3×D4—22no—
333C2×C3×D4—24no—
334C2×C3×D4—34no—
335C2×C3×D4—38no—
336C2×C3×D4—42no—
337C2×C3×D4—42no—
338C2×C3×D4—64no—
339C2×C3×D4—64no—
340C2×C3×D4—64no—
341C2×C3×D4—64no—
342C2×C3×D4—62no—
343C2×C3×D4—62no—
344C2×C3×D4—632no—
345C2×C3×D4—64no—
346C2×C3×D4—64no—
347C2×C3×D4—62no—
348C2×C3×D4—632no—
349C2×C3×D4—62no—
350C2×C3×D4—62no—
351C2×C3×D4—62no—
352C2×C3×D4—62no—
353C2×C3×D4—64no—
354C2×C3×D4—64no—
355C2×C3×D4—62no—
356C2×C3×D4—64no—
357C2×C3×D4—122no—
358C2×C3×D4—122no—
359C2×C3×D4D1214yescomplemented
360C2×C3×D4C3×D414yescomplemented
361C22×C3×C4—22no—
362C22×C3×C4—22no—
363C22×C3×C4—24no—
364C22×C3×C4—24no—
365C22×C3×C4—21no—
366C22×C3×C4—22no—
367C22×C3×C4—22no—
368C22×C3×C4—31no—
369C22×C3×C4—32no—
370C22×C3×C4—44no—
371C22×C3×C4—42no—
372C22×C3×C4—62no—
373C22×C3×C4—62no—
374C22×C3×C4—62no—
375C22×C3×C4C22×D312yes—
376C22×C3×C4C22×D311yescharacteristic
377C22×C3×C4C22×D312yes—
378C22×C3×C4C23×C312yes—
379C22×C3×C4C23×C312yes—
380C22×C3×C4C23×C311yescharacteristic
381C2×#67—22no—
382C2×#67—22no—
383C2×#67—22no—
384C2×#67—22no—
385C2×#67—24no—
386C2×#67—24no—
387C2×#67—22no—
388C2×#67—42no—
389C2×#67C3×D414yescomplemented
390C22×Dic3C23×C312yes—
391C22×Dic3C23×C311yescharacteristic
392D3×D4—232no—
393C2×D12—232no—
394C2×D12—24no—
395C2×D12—24no—
396C2×D12—24no—
397C2×D12—22no—
398C2×D12—24no—
399C2×D12—22no—
400C2×D12—24no—
401C2×D12—22no—
402C2×D12—24no—
403C2×D12—24no—
404C2×D12—42no—
405C2×D12C3×D418yescomplemented
406C2×C4×D3—22no—
407C2×C4×D3—22no—
408C2×C4×D3—22no—
409C3×C22⋊C4—22no—
410C3×C22⋊C4—22no—
411C3×C22⋊C4—24no—
412C3×C22⋊C4—24no—
413C3×C22⋊C4—44no—
414C3×C22⋊C4—42no—
415C3×C22⋊C4—64no—
416C3×C22⋊C4—64no—
417C3×C22⋊C4—62no—
418C3×C22⋊C4—64no—
419C3×C22⋊C4—64no—
420C3×C22⋊C4—122no—
421#217—22no—
422(C2×D3)⋊C4—24no—
423(C2×D3)⋊C4—24no—
424(C2×D3)⋊C4—24no—
425(C2×D3)⋊C4—24no—
426(C2×D3)⋊C4—42no—
427C22×C32—22no—
428C22×C32—22no—
429C22×C32—24no—
430C22×C32—24no—
431C22×C32—22no—
432C22×C32—24no—
433C22×C32—41no—
434C22×C32—41no—
435C22×C32—42no—
436C22×C32#12014yescomplemented
437C22×C32C22×D411yescharacteristic
438C22×C32C22×D411yescharacteristic
439C22×C32C22×D412yes—
440C22×C32C22×D411yescharacteristic
441C22×C32H(5,𝔽2)12yes—
442C2×C3×D3—22no—
443C2×C3×D3—22no—
444C2×C3×D3—24no—
445C2×C3×D3—24no—
446C2×C3×D3—22no—
447C2×C3×D3—24no—
448C2×C3×D3—22no—
449C2×C3×D3—22no—
450C2×C3×D3—22no—
451C2×C3×D3—24no—
452C2×C3×D3—24no—
453C2×C3×D3—24no—
454C2×C3×D3—416no—
455C2×C3×D3—416no—
456C2×C3×D3—416no—
457C2×C3×D3—42no—
458C2×C3×D3—41no—
459C2×C3×D3—42no—
460C2×C3×D3—41no—
461C2×C3×D3—42no—
462C2×C3×D3—42no—
463C2×C3×D3—42no—
464C2×C3×D3—42no—
465C2×C3×D3—42no—
466C2×C3×D3#12014yescomplemented
467C32×C4—22no—
468C32×C4—24no—
469C32×C4—42no—
470C3×Dic3—22no—
471C3×Dic3—42no—
472C25—31no—
473C25—31no—
474C25—31no—
475C22×D4—31no—
476C22×D4—31no—
477C22×D4—32no—
478C22×D4—32no—
479C22×D4—31no—
480C22×D4—32no—
481C22×D4—32no—
482C22×D4—68no—
483C22×D4—64no—
484C22×D4—64no—
485C22×D4—64no—
486C22×D4—64no—
487C22×D4C2×C3×D311yescharacteristic
488C23×C4—31no—
489C23×C4C2×C3×D311yescharacteristic, complemented
490#120—64no—
491#120—68no—
492#120—64no—
493C2×C22⋊C4—31no—
494C2×C22⋊C4—32no—
495C2×C22⋊C4—32no—
496C2×C22⋊C4—32no—
497C2×C22⋊C4—32no—
498C2×C22⋊C4—32no—
499C2×C22⋊C4C2×C3×D311yescharacteristic, complemented
500C2×C22⋊C4C2×C3×D312yescomplemented
501#95—32no—
502#95C2×C3×D312yescomplemented
503C23×C3—22no—
504C23×C3—22no—
505C23×C3—22no—
506C23×C3—22no—
507C23×C3—22no—
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—21no—
513C23×C3—21no—
514C23×C3—22no—
515C23×C3—21no—
516C23×C3—22no—
517C23×C3—22no—
518C23×C3—22no—
519C23×C3—22no—
520C23×C3—34no—
521C23×C3—32no—
522C23×C3—32no—
523C23×C3—32no—
524C23×C3—34no—
525C23×C3—42no—
526C23×C3—42no—
527C23×C3—42no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—42no—
531C23×C3—68no—
532C23×C3—68no—
533C23×C3—68no—
534C23×C3—61no—
535C23×C3—61no—
536C23×C3—62no—
537C23×C3—68no—
538C23×C3—62no—
539C23×C3—61no—
540C23×C3—61no—
541C23×C3—62no—
542C23×C3—62no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—62no—
546C23×C3—62no—
547C23×C3—62no—
548C23×C3—62no—
549C23×C3—62no—
550C23×C3—62no—
551C23×C3—62no—
552C23×C3—124no—
553C23×C3—128no—
554C23×C3—128no—
555C23×C3—128no—
556C23×C3—128no—
557C23×C3—128no—
558C23×C3—124no—
559C23×C3—124no—
560C23×C3—128no—
561C23×C3—124no—
562C23×C3—124no—
563C23×C3C2×D1212yes—
564C23×C3C2×D1212yescomplemented
565C23×C3D3×D412yes—
566C23×C3D3×D412yes—
567C23×C3C2×C3×D412yes—
568C23×C3C2×C3×D412yes—
569C23×C3C2×C3×D412yes—
570C23×C3C2×C3×D412yescomplemented
571C23×C3C23×D311yescharacteristic
572C23×C3C24×C311yescharacteristic
573C22×D3—21no—
574C22×D3—21no—
575C22×D3—22no—
576C22×D3—28no—
577C22×D3—28no—
578C22×D3—28no—
579C22×D3—22no—
580C22×D3—22no—
581C22×D3—22no—
582C22×D3—22no—
583C22×D3—22no—
584C22×D3—22no—
585C22×D3—21no—
586C22×D3—21no—
587C22×D3—21no—
588C22×D3—21no—
589C22×D3—22no—
590C22×D3—22no—
591C22×D3—22no—
592C22×D3—22no—
593C22×D3—28no—
594C22×D3—44no—
595C22×D3—48no—
596C22×D3—48no—
597C22×D3—48no—
598C22×D3—48no—
599C22×D3—48no—
600C22×D3—48no—
601C22×D3—44no—
602C22×D3—44no—
603C22×D3—44no—
604C22×D3—44no—
605C22×D3C2×C3×D412yes—
606C22×D3C2×C3×D414yes—
607C22×D3C2×C3×D412yes—
608C22×D3C2×C3×D412yescomplemented
609C22×D3C2×C3×D414yescomplemented
610C3×D4—28no—
611C3×D4—28no—
612C3×D4—48no—
613C3×D4—616no—
614C3×D4—68no—
615C3×D4—616no—
616C3×D4—68no—
617C3×D4—68no—
618C3×D4—128no—
619C3×D4—128no—
620C2×C3×C4—28no—
621C2×C3×C4—28no—
622C2×C3×C4—22no—
623C2×C3×C4—22no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—22no—
629C2×C3×C4—22no—
630C2×C3×C4—22no—
631C2×C3×C4—22no—
632C2×C3×C4—22no—
633C2×C3×C4—22no—
634C2×C3×C4—22no—
635C2×C3×C4—22no—
636C2×C3×C4—22no—
637C2×C3×C4—24no—
638C2×C3×C4—32no—
639C2×C3×C4—42no—
640C2×C3×C4—42no—
641C2×C3×C4—41no—
642C2×C3×C4—41no—
643C2×C3×C4—48no—
644C2×C3×C4—42no—
645C2×C3×C4—42no—
646C2×C3×C4—42no—
647C2×C3×C4—68no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
650C2×C3×C4—62no—
651C2×C3×C4—62no—
652C2×C3×C4—62no—
653C2×C3×C4C2×D1212yescomplemented
654C2×C3×C4D3×D414yescomplemented
655C2×C3×C4C2×C3×D412yescomplemented
656C2×C3×C4C2×C3×D414yescomplemented
657#67—28no—
658#67—28no—
659#67—48no—
660C2×Dic3—21no—
661C2×Dic3—21no—
662C2×Dic3—22no—
663C2×Dic3—22no—
664C2×Dic3—22no—
665C2×Dic3C2×C3×D412yescomplemented
666D12—216no—
667D12—28no—
668D12—216no—
669D12—48no—
670C4×D3—28no—
671C2×C32—24no—
672C2×C32—42no—
673C2×C32C2×#12011yescharacteristic
674C2×C32C2×#12011yescharacteristic
675C2×C32#53411yescharacteristic
676C2×C32D4212yes—
677C2×C32D4212yes—
678C3×D3—24no—
679C3×D3—42no—
680C3×D3—44no—
681C3×D3—42no—
682C24—31no—
683C24—32no—
684C24—31no—
685C24—31no—
686C24—34no—
687C24—64no—
688C24—64no—
689C24—62no—
690C24—62no—
691C24—64no—
692C24—62no—
693C24—62no—
694C24—62no—
695C24—62no—
696C24—62no—
697C24—62no—
698C24—122no—
699C24—122no—
700C24—122no—
701C24C22×C3×D311yescharacteristic
702C24C22×C3×D311yescharacteristic
703C2×D4—22no—
704C2×D4—22no—
705C2×D4—34no—
706C2×D4—38no—
707C2×D4—64no—
708C2×D4—64no—
709C2×D4—64no—
710C2×D4—64no—
711C2×D4—62no—
712C2×D4—62no—
713C2×D4—632no—
714C2×D4—64no—
715C2×D4—64no—
716C2×D4—62no—
717C2×D4—632no—
718C2×D4—62no—
719C2×D4—62no—
720C2×D4—62no—
721C2×D4—62no—
722C2×D4—64no—
723C2×D4—64no—
724C2×D4—62no—
725C2×D4—64no—
726C2×D4—122no—
727C2×D4—122no—
728C2×D4C3×D1214yescomplemented
729C22×C4—22no—
730C22×C4—24no—
731C22×C4—31no—
732C22×C4—32no—
733C22×C4—62no—
734C22×C4—62no—
735C22×C4—62no—
736C22×C4C22×C3×D312yes—
737C22×C4C22×C3×D311yescharacteristic
738C22×C4C22×C3×D312yes—
739C22⋊C4—22no—
740C22⋊C4—24no—
741C22⋊C4—64no—
742C22⋊C4—64no—
743C22⋊C4—62no—
744C22⋊C4—64no—
745C22⋊C4—64no—
746C22⋊C4—122no—
747C22×C3—22no—
748C22×C3—24no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—22no—
752C22×C3—24no—
753C22×C3—24no—
754C22×C3—24no—
755C22×C3—22no—
756C22×C3—24no—
757C22×C3—22no—
758C22×C3—24no—
759C22×C3—24no—
760C22×C3—21no—
761C22×C3—22no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—22no—
765C22×C3—34no—
766C22×C3—42no—
767C22×C3—44no—
768C22×C3—44no—
769C22×C3—42no—
770C22×C3—42no—
771C22×C3—44no—
772C22×C3—41no—
773C22×C3—41no—
774C22×C3—41no—
775C22×C3—41no—
776C22×C3—42no—
777C22×C3—42no—
778C22×C3—62no—
779C22×C3—62no—
780C22×C3—64no—
781C22×C3—64no—
782C22×C3—62no—
783C22×C3—62no—
784C22×C3—62no—
785C22×C3—64no—
786C22×C3—64no—
787C22×C3—62no—
788C22×C3—64no—
789C22×C3—64no—
790C22×C3—81no—
791C22×C3—82no—
792C22×C3—81no—
793C22×C3—1216no—
794C22×C3—1216no—
795C22×C3—1216no—
796C22×C3—122no—
797C22×C3—121no—
798C22×C3—122no—
799C22×C3—122no—
800C22×C3—122no—
801C22×C3—122no—
802C22×C3—121no—
803C22×C3—122no—
804C22×C3—122no—
805C22×C3#88214yescomplemented
806C22×C3C3×#12014yescomplemented
807C22×C3C22×D1211yescharacteristic
808C22×C3C2×D3×D411yescharacteristic
809C22×C3C2×D3×D411yescharacteristic
810C22×C3C2×D3×D412yes—
811C22×C3#100912yes—
812C22×C3C22×C3×D411yescharacteristic
813C22×C3C22×C3×D411yescharacteristic
814C22×C3C22×C3×D412yes—
815C22×C3C22×C3×D411yescharacteristic
816C22×C3C3×H(5,𝔽2)12yes—
817C2×D3—22no—
818C2×D3—22no—
819C2×D3—24no—
820C2×D3—24no—
821C2×D3—22no—
822C2×D3—24no—
823C2×D3—22no—
824C2×D3—22no—
825C2×D3—22no—
826C2×D3—24no—
827C2×D3—24no—
828C2×D3—24no—
829C2×D3—416no—
830C2×D3—416no—
831C2×D3—416no—
832C2×D3—42no—
833C2×D3—41no—
834C2×D3—42no—
835C2×D3—41no—
836C2×D3—42no—
837C2×D3—42no—
838C2×D3—42no—
839C2×D3—42no—
840C2×D3—42no—
841C2×D3C3×#12014yescomplemented
842C3×C4—22no—
843C3×C4—24no—
844C3×C4—22no—
845C3×C4—24no—
846C3×C4—44no—
847C3×C4—42no—
848C3×C4—42no—
849C3×C4—42no—
850C3×C4—62no—
851C3×C4—82no—
852C3×C4—122no—
853Dic3—22no—
854Dic3—42no—
855C32#240311yescharacteristic, complemented, Sylow
856C23—22no—
857C23—22no—
858C23—22no—
859C23—21no—
860C23—21no—
861C23—22no—
862C23—34no—
863C23—32no—
864C23—32no—
865C23—34no—
866C23—32no—
867C23—68no—
868C23—68no—
869C23—68no—
870C23—61no—
871C23—61no—
872C23—62no—
873C23—68no—
874C23—62no—
875C23—61no—
876C23—61no—
877C23—62no—
878C23—62no—
879C23—61no—
880C23—61no—
881C23—62no—
882C23—62no—
883C23—62no—
884C23—62no—
885C23—62no—
886C23—62no—
887C23—62no—
888C23—124no—
889C23—128no—
890C23—128no—
891C23—128no—
892C23—128no—
893C23—128no—
894C23—124no—
895C23—124no—
896C23—128no—
897C23—124no—
898C23—124no—
899C23C2×C3×D1212yes—
900C23C2×C3×D1212yescomplemented
901C23C3×D3×D412yes—
902C23C3×D3×D412yes—
903C23C23×C3×D311yescharacteristic
904D4—28no—
905D4—616no—
906D4—68no—
907D4—616no—
908D4—68no—
909D4—68no—
910D4—128no—
911D4—128no—
912C2×C4—28no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—32no—
921C2×C4—68no—
922C2×C4—61no—
923C2×C4—61no—
924C2×C4—62no—
925C2×C4—62no—
926C2×C4—62no—
927C2×C4C2×C3×D1212yescomplemented
928C2×C4C3×D3×D414yescomplemented
929C2×C3—24no—
930C2×C3—24no—
931C2×C3—21no—
932C2×C3—22no—
933C2×C3—21no—
934C2×C3—22no—
935C2×C3—21no—
936C2×C3—44no—
937C2×C3—42no—
938C2×C3—42no—
939C2×C3—64no—
940C2×C3—82no—
941C2×C3—122no—
942C2×C3—122no—
943C2×C3—124no—
944C2×C3C2×#88211yescharacteristic
945C2×C3D4×D1212yes—
946C2×C3D3×#12011yescharacteristic
947C2×C3#560912yes—
948C2×C3#565311yescharacteristic
949C2×C3C2×C3×#12011yescharacteristic
950C2×C3C2×C3×#12011yescharacteristic
951C2×C3C3×#53411yescharacteristic
952C2×C3C3×D4212yes—
953C2×C3C3×D4212yes—
954D3—24no—
955D3—42no—
956D3—44no—
957D3—42no—
958C22—24no—
959C22—22no—
960C22—24no—
961C22—22no—
962C22—22no—
963C22—24no—
964C22—34no—
965C22—41no—
966C22—42no—
967C22—41no—
968C22—62no—
969C22—64no—
970C22—64no—
971C22—62no—
972C22—62no—
973C22—62no—
974C22—64no—
975C22—64no—
976C22—62no—
977C22—64no—
978C22—64no—
979C22—62no—
980C22—1216no—
981C22—1216no—
982C22—1216no—
983C22—122no—
984C22—122no—
985C22—122no—
986C22—122no—
987C22—121no—
988C22—122no—
989C22—122no—
990C22—122no—
991C22—121no—
992C22C3×#88214yescomplemented
993C22C22×C3×D1211yescharacteristic
994C22C2×C3×D3×D411yescharacteristic
995C22C2×C3×D3×D411yescharacteristic
996C22C2×C3×D3×D412yes—
997C22C3×#100912yes—
998C4—22no—
999C4—24no—
1000C4—42no—
1001C4—62no—
1002C4—122no—
1003C3—21no—
1004C3#7488411yescharacteristic, direct product factor
1005C3C3×#240311yescharacteristic, complemented
1006C2—24no—
1007C2—42no—
1008C2—64no—
1009C2—122no—
1010C2—122no—
1011C2—124no—
1012C2C2×C3×#88211yescharacteristic
1013C2C3×D4×D1212yes—
1014C2C3×D3×#12011yescharacteristic
1015C2C3×#560912yes—
1016C2C3×#565311yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#386C2
socleC23×C32C24
hypercenterC3×#386D3
hypocenterC3C3×#2403
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#386

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×D4C2semidirect
2. C23×C3×D12C2semidirect
3. C2×C3×#937C2semidirect
4. C2×C3×#882C2semidirect
5. C2×C3×#882C2semidirect
6. C32×#386C2semidirect
7. C3×#5213C2semidirect
8. C3×#4960C2semidirect
9. C3×#4955C2semidirect
10. C3×#4671C2semidirect
11. C3×#4665C2semidirect
13. #74884C3direct (N × H)
15. C24×C3×D3C22semidirect
16. C24×C3×D3C22semidirect
18. C23×C32×C4C22semidirect
20. C22×C3×#67C22semidirect
21. C22×C3×#67C22semidirect
28. C22×C3×D12C22semidirect
29. C22×C3×D12C22semidirect
30. C22×C3×D12C22semidirect
31. C22×C3×C4×D3C22semidirect
32. C2×C32×C22⋊C4C22semidirect
33. C2×C32×C22⋊C4C22semidirect
34. C2×C3×#217C22semidirect
36. C2×C3×(C2×D3)⋊C4C22semidirect
37. C2×C3×(C2×D3)⋊C4C22semidirect
38. C2×C3×(C2×D3)⋊C4C22semidirect
39. C2×C3×(C2×D3)⋊C4C22semidirect
40. C2×C3×(C2×D3)⋊C4C22semidirect
43. C32×#95C22semidirect
44. C3×C3⋊#95C22semidirect
47. C22×D3×D4C2×C3semidirect
48. C23×D12C2×C3semidirect
52. C2×#937C2×C3semidirect
53. C2×#882C2×C3semidirect
54. C2×#882C2×C3semidirect
60. C3×#386D3semidirect
61. C3×#386C2×C3semidirect
63. #5213C2×C3semidirect
64. #4960C2×C3semidirect
65. #4955C2×C3semidirect
66. #4671C2×C3semidirect
67. #4665C2×C3semidirect
84. C23×C3×D3D4semidirect
91. C2×C32×D4D4semidirect
105. C2×C3×#67D4semidirect
121. C2×C3×D12D4semidirect
138. C24×D3C22×C3semidirect
139. C24×D3C22×C3semidirect
157. C23×C3×C4C2×D3semidirect
158. C23×C3×C4C22×C3semidirect
160. C22×#67C22×C3semidirect
161. C22×#67C22×C3semidirect
168. C22×D12C22×C3semidirect
169. C22×D12C22×C3semidirect
170. C22×D12C22×C3semidirect
171. C22×C4×D3C22×C3semidirect
183. C2×C3×C22⋊C4C2×D3semidirect
184. C2×C3×C22⋊C4C2×D3semidirect
185. C2×C3×C22⋊C4C22×C3semidirect
186. C2×C3×C22⋊C4C22×C3semidirect
187. C2×#217C22×C3semidirect
189. C2×(C2×D3)⋊C4C22×C3semidirect
190. C2×(C2×D3)⋊C4C22×C3semidirect
191. C2×(C2×D3)⋊C4C22×C3semidirect
192. C2×(C2×D3)⋊C4C22×C3semidirect
193. C2×(C2×D3)⋊C4C22×C3semidirect
198. C3×#95C2×D3semidirect
199. C3×#95C22×C3semidirect
200. C3⋊#95C22×C3semidirect
210. C23×C32C2×D4semidirect
247. C22×C3×D3C2×D4semidirect
248. C22×C3×D3C2×D4semidirect
258. C2×C32×C4C2×D4semidirect
259. C2×C32×C4C2×D4semidirect
268. C2×C3×Dic3C2×D4semidirect
283. #386C3×D3semidirect
324. C23×D3C3×D4semidirect
359. C2×C3×D4D12semidirect
360. C2×C3×D4C3×D4semidirect
389. C2×#67C3×D4semidirect
405. C2×D12C3×D4semidirect
436. C22×C32#120semidirect
466. C2×C3×D3#120semidirect
489. C23×C4C2×C3×D3semidirect
499. C2×C22⋊C4C2×C3×D3semidirect
500. C2×C22⋊C4C2×C3×D3semidirect
502. #95C2×C3×D3semidirect
564. C23×C3C2×D12semidirect
570. C23×C3C2×C3×D4semidirect
608. C22×D3C2×C3×D4semidirect
609. C22×D3C2×C3×D4semidirect
653. C2×C3×C4C2×D12semidirect
654. C2×C3×C4D3×D4semidirect
655. C2×C3×C4C2×C3×D4semidirect
656. C2×C3×C4C2×C3×D4semidirect
665. C2×Dic3C2×C3×D4semidirect
728. C2×D4C3×D12semidirect
805. C22×C3#882semidirect
806. C22×C3C3×#120semidirect
841. C2×D3C3×#120semidirect
855. C32#2403semidirect
900. C23C2×C3×D12semidirect
927. C2×C4C2×C3×D12semidirect
928. C2×C4C3×D3×D4semidirect
992. C22C3×#882semidirect
1004. C3#74884direct (N × H)
1005. C3C3×#2403semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×D42
C23×C3×D122
C2×C3×#9372
C2×C3×#8822
C32×#3862
C3×#52132
C3×#49602
C3×#49552
C3×#46712
C3×#46652
C3×#24033
#748843