Finite Group Databasebeta

← C3×#69427 #11773304

Subgroups — C3×#69427 #11773304

Order 1152.

1725 conjugacy classes of subgroups.

The subgroup lattice has 753 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×(C2×D3)⋊C4C212yesmaximal
2C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic
3C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C2×C32×#95C211yesmaximal, characteristic, complemented
5C2×C3×C3⋊#95C212yesmaximal, complemented
6C3×#1439—31nomaximal
7#69427C311yesmaximal, characteristic, direct product factor
8C24×C3×D3C2211yescharacteristic
9C23×C32×C4C2212yes—
10C23×C32×C4C2211yescharacteristic
11C23×C3×Dic3C2211yescharacteristic
12C23×C3×Dic3C2212yes—
13C2×C3×(C2×D3)⋊C4—24no—
14C2×C3×(C2×D3)⋊C4—22no—
15C2×C3×(C2×D3)⋊C4—22no—
16C2×C3×(C2×D3)⋊C4—24no—
17C2×C3×(C2×D3)⋊C4—24no—
18C2×C3×(C2×D3)⋊C4C414yescomplemented
19C2×C3×C4⋊Dic3—22no—
20C2×C3×C4⋊Dic3—24no—
21C32×#95—22no—
22C3×C3⋊#95—24no—
23C22×C3×C4⋊C4—31no—
24C22×C3×C22⋊C4—31no—
25C22×C3×C22⋊C4—32no—
26C22×(C2×D3)⋊C4C2×C312yes—
27C22×(C2×D3)⋊C4C2×C311yescharacteristic
28C22×C4⋊Dic3C2×C311yescharacteristic, complemented
29C2×C3×#95—21no—
30C2×C3×#95—32no—
31C2×C3×#95D311yescharacteristic, complemented
32C2×C3×#95C2×C311yescharacteristic, complemented
33C2×C3⋊#95C2×C312yescomplemented
34C24×C32C2311yescharacteristic
35C23×C3×D3—21no—
36C23×C3×D3—21no—
37C23×C3×D3—22no—
38C23×C3×D3—22no—
39C23×C3×D3—21no—
40C23×C3×D3—21no—
41C23×C3×D3—22no—
42C23×C3×D3—22no—
43C23×C3×D3C2×C412yes—
44C23×C3×D3D412yes—
45C23×C3×D3Q812yes—
46C22×C32×C4—22no—
47C22×C32×C4—22no—
48C22×C32×C4—22no—
49C22×C32×C4—22no—
50C22×C32×C4—22no—
51C22×C32×C4—22no—
52C22×C32×C4—22no—
53C22×C32×C4—22no—
54C22×C32×C4C2×C412yes—
55C22×C32×C4D414yes—
56C22×C32×C4D412yes—
57C22×C32×C4D412yes—
58C22×C3×Dic3—22no—
59C22×C3×Dic3—22no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3—21no—
62C22×C3×Dic3—22no—
63C22×C3×Dic3—22no—
64C22×C3×Dic3—22no—
65C22×C3×Dic3—22no—
66C22×C3×Dic3—22no—
67C22×C3×Dic3—22no—
68C22×C3×Dic3C2×C412yes—
69C22×C3×Dic3D414yes—
70C3×(C2×D3)⋊C4—216no—
71C3×(C2×D3)⋊C4—28no—
72C3×C4⋊Dic3—28no—
73#1439—31noSylow
74C25×C3—31no—
75C24×D3C22×C311yescharacteristic
76C23×C3×C4—22no—
77C23×C3×C4—21no—
78C23×C3×C4—31no—
79C23×C3×C4—32no—
80C23×C3×C4C2×D312yes—
81C23×C3×C4C2×D311yescharacteristic
82C23×C3×C4C22×C312yes—
83C23×C3×C4C22×C311yescharacteristic
84C23×Dic3C22×C311yescharacteristic
85C23×Dic3C22×C312yes—
86C2×C3×C4⋊C4—64no—
87C2×C3×C4⋊C4—62no—
88C2×C3×C22⋊C4—34no—
89C2×C3×C22⋊C4—64no—
90C2×C3×C22⋊C4—64no—
91C2×C3×C22⋊C4—64no—
92C2×C3×C22⋊C4—62no—
93C2×C3×C22⋊C4—62no—
94C2×(C2×D3)⋊C4—24no—
95C2×(C2×D3)⋊C4—24no—
96C2×(C2×D3)⋊C4—22no—
97C2×(C2×D3)⋊C4—22no—
98C2×(C2×D3)⋊C4—24no—
99C2×(C2×D3)⋊C4C3×C414yescomplemented
100C2×C4⋊Dic3—22no—
101C2×C4⋊Dic3—24no—
102C3×#95—24no—
103C3×#95—22no—
104C3×#95—22no—
105C3×#95—64no—
106C3⋊#95—24no—
107C23×C32C22×C411yescharacteristic
108C23×C32C2×D411yescharacteristic
109C23×C32C2×D412yes—
110C23×C32C2×D411yescharacteristic
111C23×C32C2×D412yes—
112C23×C32C2×D411yescharacteristic
113C23×C32C2×Q811yescharacteristic
114C23×C32#4112yes—
115C23×C32#4111yescharacteristic
116C23×C32#4112yes—
117C23×C32#4111yescharacteristic
118C22×C3×D3—22no—
119C22×C3×D3—22no—
120C22×C3×D3—24no—
121C22×C3×D3—24no—
122C22×C3×D3—24no—
123C22×C3×D3—22no—
124C22×C3×D3—22no—
125C22×C3×D3—24no—
126C22×C3×D3—22no—
127C22×C3×D3—24no—
128C22×C3×D3—22no—
129C22×C3×D3—24no—
130C22×C3×D3—41no—
131C22×C3×D3—42no—
132C22×C3×D3—42no—
133C22×C3×D3—42no—
134C22×C3×D3—41no—
135C22×C3×D3—42no—
136C22×C3×D3—41no—
137C22×C3×D3—42no—
138C22×C3×D3—42no—
139C22×C3×D3—41no—
140C22×C3×D3C4⋊C414yescomplemented
141C2×C32×C4—24no—
142C2×C32×C4—24no—
143C2×C32×C4—22no—
144C2×C32×C4—24no—
145C2×C32×C4—22no—
146C2×C32×C4—24no—
147C2×C32×C4—24no—
148C2×C32×C4—42no—
149C2×C32×C4—42no—
150C2×C32×C4—42no—
151C2×C32×C4—42no—
152C2×C32×C4C22⋊C414yescomplemented
153C2×C3×Dic3—22no—
154C2×C3×Dic3—24no—
155C2×C3×Dic3—24no—
156C2×C3×Dic3—24no—
157C2×C3×Dic3—24no—
158C2×C3×Dic3—42no—
159C2×C3×Dic3—42no—
160C2×C3×Dic3—42no—
161C2×C3×Dic3—42no—
162C2×C3×Dic3—41no—
163C2×C3×Dic3—41no—
164C2×C3×Dic3—42no—
165C22×C4⋊C4—31no—
166C22×C22⋊C4—31no—
167C22×C22⋊C4—32no—
168C2×#95—32no—
169C2×#95C3×D311yescharacteristic, complemented
170C24×C3—21no—
171C24×C3—32no—
172C24×C3—32no—
173C24×C3—32no—
174C24×C3—62no—
175C24×C3—61no—
176C24×C3—62no—
177C24×C3—62no—
178C24×C3—62no—
179C24×C3—61no—
180C24×C3—61no—
181C24×C3—61no—
182C24×C3C22×D311yescharacteristic
183C24×C3C23×C311yescharacteristic
184C23×D3—21no—
185C23×D3—22no—
186C23×D3—22no—
187C23×D3—21no—
188C23×D3—22no—
189C23×D3—21no—
190C23×D3—22no—
191C23×D3—21no—
192C23×D3C2×C3×C412yes—
193C23×D3C3×D412yes—
194C23×D3C3×Q812yes—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—24no—
200C22×C3×C4—24no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—24no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—32no—
218C22×C3×C4—34no—
219C22×C3×C4—42no—
220C22×C3×C4—42no—
221C22×C3×C4—42no—
222C22×C3×C4—42no—
223C22×C3×C4—42no—
224C22×C3×C4—42no—
225C22×C3×C4—62no—
226C22×C3×C4—62no—
227C22×C3×C4—62no—
228C22×C3×C4—61no—
229C22×C3×C4—62no—
230C22×C3×C4—62no—
231C22×C3×C4—62no—
232C22×C3×C4—62no—
233C22×C3×C4—62no—
234C22×C3×C4—61no—
235C22×C3×C4C4×D312yes—
236C22×C3×C4D1214yes—
237C22×C3×C4D1212yes—
238C22×C3×C4#6712yes—
239C22×C3×C4C2×C3×C412yes—
240C22×C3×C4C3×D414yes—
241C22×C3×C4C3×D412yes—
242C22×C3×C4C3×D412yes—
243C22×Dic3—22no—
244C22×Dic3—22no—
245C22×Dic3—22no—
246C22×Dic3—22no—
247C22×Dic3—21no—
248C22×Dic3—22no—
249C22×Dic3—22no—
250C22×Dic3—21no—
251C22×Dic3—22no—
252C22×Dic3—22no—
253C22×Dic3C2×C3×C412yes—
254C22×Dic3C3×D414yes—
255C3×C4⋊C4—68no—
256C3×C22⋊C4—616no—
257C3×C22⋊C4—68no—
258(C2×D3)⋊C4—216no—
259(C2×D3)⋊C4—28no—
260C4⋊Dic3—28no—
261C22×C32C2×C22⋊C411yescharacteristic
262C22×C32C2×C4⋊C411yescharacteristic
263C22×C32#11711yescharacteristic
264C22×C32C4×D412yes—
265C22×C32C4×D412yes—
266C22×C32#12012yes—
267C22×C32#12011yescharacteristic
268C22×C32#12111yescharacteristic
269C22×C32#12112yes—
270C22×C32#12112yes—
271C22×C32#12111yescharacteristic
272C22×C32#12112yes—
273C22×C32C22⋊Q812yes—
274C22×C32C22⋊Q811yescharacteristic
275C22×C32C22⋊Q812yes—
276C22×C32C22⋊Q811yescharacteristic
277C22×C32#12312yes—
278C22×C32#12311yescharacteristic
279C22×C32#12312yes—
280C22×C32#12411yescharacteristic
281C22×C32#12412yes—
282C22×C32#12612yes—
283C22×C32#12711yescharacteristic
284C2×C3×D3—24no—
285C2×C3×D3—28no—
286C2×C3×D3—42no—
287C2×C3×D3—44no—
288C2×C3×D3—42no—
289C2×C3×D3—42no—
290C2×C3×D3—42no—
291C2×C3×D3—44no—
292C2×C3×D3—44no—
293C2×C3×D3—42no—
294C2×C3×D3—42no—
295C32×C4—24no—
296C32×C4—44no—
297C3×Dic3—42no—
298C3×Dic3—44no—
299C25—31no—
300C23×C4—32no—
301C23×C4—31no—
302C23×C4C2×C3×D312yes—
303C23×C4C2×C3×D311yescharacteristic
304C2×C4⋊C4—64no—
305C2×C4⋊C4—62no—
306C2×C22⋊C4—34no—
307C2×C22⋊C4—64no—
308C2×C22⋊C4—64no—
309C2×C22⋊C4—64no—
310C2×C22⋊C4—62no—
311C2×C22⋊C4—62no—
312#95—22no—
313#95—64no—
314C23×C3—21no—
315C23×C3—21no—
316C23×C3—22no—
317C23×C3—22no—
318C23×C3—22no—
319C23×C3—21no—
320C23×C3—22no—
321C23×C3—21no—
322C23×C3—21no—
323C23×C3—21no—
324C23×C3—21no—
325C23×C3—34no—
326C23×C3—64no—
327C23×C3—64no—
328C23×C3—64no—
329C23×C3—64no—
330C23×C3—62no—
331C23×C3—62no—
332C23×C3—64no—
333C23×C3—64no—
334C23×C3—62no—
335C23×C3—62no—
336C23×C3—62no—
337C23×C3—62no—
338C23×C3—121no—
339C23×C3—121no—
340C23×C3—121no—
341C23×C3—122no—
342C23×C3—122no—
343C23×C3—121no—
344C23×C3—122no—
345C23×C3—122no—
346C23×C3—122no—
347C23×C3—122no—
348C23×C3C2×C4×D311yescharacteristic
349C23×C3C2×D1212yes—
350C23×C3C2×D1211yescharacteristic
351C23×C3#23512yes—
352C23×C3D3×D412yes—
353C23×C3D3×D411yescharacteristic
354C23×C3#23712yes—
355C23×C3#23711yescharacteristic
356C23×C3D3×Q811yescharacteristic
357C23×C3#23911yescharacteristic
358C23×C3C2×#6711yescharacteristic
359C23×C3C22×C3×C411yescharacteristic
360C23×C3C2×C3×D411yescharacteristic
361C23×C3C2×C3×D412yes—
362C23×C3C2×C3×D411yescharacteristic
363C23×C3C2×C3×D412yes—
364C23×C3C2×C3×D411yescharacteristic
365C23×C3C2×C3×Q811yescharacteristic
366C23×C3C3×#4112yes—
367C23×C3C3×#4111yescharacteristic
368C23×C3C3×#4112yes—
369C23×C3C3×#4111yescharacteristic
370C22×D3—22no—
371C22×D3—22no—
372C22×D3—24no—
373C22×D3—24no—
374C22×D3—24no—
375C22×D3—22no—
376C22×D3—22no—
377C22×D3—24no—
378C22×D3—22no—
379C22×D3—24no—
380C22×D3—22no—
381C22×D3—24no—
382C22×D3—41no—
383C22×D3—42no—
384C22×D3—42no—
385C22×D3—42no—
386C22×D3—41no—
387C22×D3—42no—
388C22×D3—42no—
389C22×D3—41no—
390C22×D3—42no—
391C22×D3—41no—
392C22×D3C3×C4⋊C414yescomplemented
393C2×C3×C4—24no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—24no—
397C2×C3×C4—24no—
398C2×C3×C4—22no—
399C2×C3×C4—24no—
400C2×C3×C4—22no—
401C2×C3×C4—28no—
402C2×C3×C4—24no—
403C2×C3×C4—24no—
404C2×C3×C4—24no—
405C2×C3×C4—24no—
406C2×C3×C4—24no—
407C2×C3×C4—24no—
408C2×C3×C4—24no—
409C2×C3×C4—44no—
410C2×C3×C4—42no—
411C2×C3×C4—42no—
412C2×C3×C4—44no—
413C2×C3×C4—44no—
414C2×C3×C4—44no—
415C2×C3×C4—44no—
416C2×C3×C4—44no—
417C2×C3×C4—44no—
418C2×C3×C4—44no—
419C2×C3×C4—42no—
420C2×C3×C4—42no—
421C2×C3×C4—42no—
422C2×C3×C4—42no—
423C2×C3×C4—42no—
424C2×C3×C4—42no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4—64no—
428C2×C3×C4—64no—
429C2×C3×C4—64no—
430C2×C3×C4—64no—
431C2×C3×C4—62no—
432C2×C3×C4—122no—
433C2×C3×C4—121no—
434C2×C3×C4—121no—
435C2×C3×C4—122no—
436C2×C3×C4—122no—
437C2×C3×C4—122no—
438C2×C3×C4—122no—
439C2×C3×C4(C2×D3)⋊C414yescomplemented
440C2×C3×C4C3×C22⋊C414yescomplemented
441C2×Dic3—22no—
442C2×Dic3—24no—
443C2×Dic3—24no—
444C2×Dic3—24no—
445C2×Dic3—24no—
446C2×Dic3—42no—
447C2×Dic3—42no—
448C2×Dic3—42no—
449C2×Dic3—42no—
450C2×Dic3—41no—
451C2×Dic3—41no—
452C2×Dic3—42no—
453C2×C32#38011yescharacteristic
454C2×C32#38512yes—
455C2×C32#38611yescharacteristic
456C2×C32#38812yes—
457C2×C32#39011yescharacteristic
458C2×C32#39211yescharacteristic
459C2×C32#39311yescharacteristic
460C2×C32#39412yes—
461C2×C32#39612yes—
462C2×C32#39711yescharacteristic
463C2×C32#39911yescharacteristic
464C3×D3—44no—
465C24—32no—
466C24—32no—
467C24—32no—
468C24—62no—
469C24—61no—
470C24—62no—
471C24—62no—
472C24—62no—
473C24—61no—
474C24—61no—
475C24—61no—
476C24C22×C3×D311yescharacteristic
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—32no—
486C22×C4—34no—
487C22×C4—62no—
488C22×C4—62no—
489C22×C4—62no—
490C22×C4—61no—
491C22×C4—62no—
492C22×C4—62no—
493C22×C4—62no—
494C22×C4—62no—
495C22×C4—62no—
496C22×C4—61no—
497C22×C4C3×C4×D312yes—
498C22×C4C3×D1214yes—
499C22×C4C3×D1212yes—
500C22×C4C3×#6712yes—
501C4⋊C4—68no—
502C22⋊C4—616no—
503C22⋊C4—68no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—21no—
507C22×C3—22no—
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—22no—
514C22×C3—21no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—21no—
518C22×C3—22no—
519C22×C3—21no—
520C22×C3—22no—
521C22×C3—21no—
522C22×C3—22no—
523C22×C3—21no—
524C22×C3—22no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—68no—
528C22×C3—64no—
529C22×C3—124no—
530C22×C3—122no—
531C22×C3—122no—
532C22×C3—122no—
533C22×C3—122no—
534C22×C3—122no—
535C22×C3—122no—
536C22×C3—124no—
537C22×C3—124no—
538C22×C3C4×D1212yes—
539C22×C3#87411yescharacteristic
540C22×C3#87511yescharacteristic
541C22×C3#67⋊C412yes—
542C22×C3#88212yes—
543C22×C3#88211yescharacteristic
544C22×C3#88312yes—
545C22×C3#88512yes—
546C22×C3#88612yes—
547C22×C3#88611yescharacteristic
548C22×C3D3×C4⋊C411yescharacteristic
549C22×C3#89211yescharacteristic
550C22×C3#89512yes—
551C22×C3#89511yescharacteristic
552C22×C3#89612yes—
553C22×C3#89712yes—
554C22×C3#89711yescharacteristic
555C22×C3#89812yes—
556C22×C3C2×(C2×D3)⋊C411yescharacteristic
557C22×C3#93012yes—
558C22×C3#93811yescharacteristic
559C22×C3#93912yes—
560C22×C3#94611yescharacteristic
561C22×C3C2×C3×C22⋊C411yescharacteristic
562C22×C3C2×C3×C4⋊C411yescharacteristic
563C22×C3C3×#11711yescharacteristic
564C22×C3C3×C4×D412yes—
565C22×C3C3×C4×D412yes—
566C22×C3C3×#12012yes—
567C22×C3C3×#12011yescharacteristic
568C22×C3C3×#12111yescharacteristic
569C22×C3C3×#12112yes—
570C22×C3C3×#12112yes—
571C22×C3C3×#12111yescharacteristic
572C22×C3C3×#12112yes—
573C22×C3C3×C22⋊Q812yes—
574C22×C3C3×C22⋊Q811yescharacteristic
575C22×C3C3×C22⋊Q812yes—
576C22×C3C3×C22⋊Q811yescharacteristic
577C22×C3C3×#12312yes—
578C22×C3C3×#12311yescharacteristic
579C22×C3C3×#12312yes—
580C22×C3C3×#12412yes—
581C22×C3C3×#12411yescharacteristic
582C22×C3C3×#12612yes—
583C22×C3C3×#12711yescharacteristic
584C2×D3—24no—
585C2×D3—28no—
586C2×D3—42no—
587C2×D3—44no—
588C2×D3—42no—
589C2×D3—42no—
590C2×D3—42no—
591C2×D3—44no—
592C2×D3—44no—
593C2×D3—42no—
594C2×D3—42no—
595C3×C4—24no—
596C3×C4—24no—
597C3×C4—44no—
598C3×C4—48no—
599C3×C4—44no—
600C3×C4—44no—
601C3×C4—124no—
602C3×C4—122no—
603Dic3—42no—
604Dic3—44no—
605C32#143911yescharacteristic, complemented, Sylow
606C23—34no—
607C23—64no—
608C23—64no—
609C23—64no—
610C23—62no—
611C23—62no—
612C23—64no—
613C23—64no—
614C23—62no—
615C23—62no—
616C23—62no—
617C23—62no—
618C23—64no—
619C23—121no—
620C23—122no—
621C23—122no—
622C23—121no—
623C23—122no—
624C23—122no—
625C23—122no—
626C23—122no—
627C23—121no—
628C23—121no—
629C23C2×C3×C4×D311yescharacteristic
630C23C2×C3×D1211yescharacteristic
631C23C2×C3×D1212yes—
632C23C3×#23512yes—
633C23C3×D3×D412yes—
634C23C3×D3×D411yescharacteristic
635C23C3×#23712yes—
636C23C3×#23711yescharacteristic
637C23C3×D3×Q811yescharacteristic
638C23C3×#23911yescharacteristic
639C23C2×C3×#6711yescharacteristic
640C2×C4—24no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—64no—
652C2×C4—64no—
653C2×C4—64no—
654C2×C4—62no—
655C2×C4—64no—
656C2×C4—122no—
657C2×C4—122no—
658C2×C4—122no—
659C2×C4—122no—
660C2×C4—122no—
661C2×C4—121no—
662C2×C4—121no—
663C2×C4C3×(C2×D3)⋊C414yescomplemented
664C2×C3—22no—
665C2×C3—22no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—22no—
673C2×C3—21no—
674C2×C3—22no—
675C2×C3—124no—
676C2×C3#466812yes—
677C2×C3#467012yes—
678C2×C3#467111yescharacteristic
679C2×C3#467311yescharacteristic
680C2×C3#467411yescharacteristic
681C2×C3#467711yescharacteristic
682C2×C3#493911yescharacteristic
683C2×C3#495811yescharacteristic
684C2×C3#496112yes—
685C2×C3#498711yescharacteristic
686C2×C3#499412yes—
687C2×C3C3×#38011yescharacteristic
688C2×C3C3×#38512yes—
689C2×C3C3×#38611yescharacteristic
690C2×C3C3×#38812yes—
691C2×C3C3×#39011yescharacteristic
692C2×C3C3×#39211yescharacteristic
693C2×C3C3×#39311yescharacteristic
694C2×C3C3×#39412yes—
695C2×C3C3×#39612yes—
696C2×C3C3×#39711yescharacteristic
697C2×C3C3×#39911yescharacteristic
698D3—44no—
699C22—68no—
700C22—64no—
701C22—124no—
702C22—122no—
703C22—122no—
704C22—122no—
705C22—122no—
706C22—122no—
707C22—122no—
708C22—124no—
709C22—124no—
710C22C3×C4×D1212yes—
711C22C3×#87411yescharacteristic
712C22C3×#87511yescharacteristic
713C22C3×#67⋊C412yes—
714C22C3×#88212yes—
715C22C3×#88211yescharacteristic
716C22C3×#88312yes—
717C22C3×#88512yes—
718C22C3×#88612yes—
719C22C3×#88611yescharacteristic
720C22C3×D3×C4⋊C411yescharacteristic
721C22C3×#89211yescharacteristic
722C22C3×#89512yes—
723C22C3×#89511yescharacteristic
724C22C3×#89612yes—
725C22C3×#89712yes—
726C22C3×#89711yescharacteristic
727C22C3×#89812yes—
728C22C2×C3×(C2×D3)⋊C411yescharacteristic
729C22C3×#93012yes—
730C22C3×#93811yescharacteristic
731C22C3×#93912yes—
732C22C3×#94611yescharacteristic
733C4—24no—
734C4—44no—
735C4—124no—
736C4—122no—
737C3—21no—
738C3#6942711yescharacteristic, direct product factor
739C3C3×#143911yescharacteristic, complemented
740C2—124no—
741C2C3×#466812yes—
742C2C3×#467012yes—
743C2C3×#467111yescharacteristic
744C2C3×#467311yescharacteristic
745C2C3×#467411yescharacteristic
746C2C3×#467711yescharacteristic
747C2C3×#493911yescharacteristic
748C2C3×#495811yescharacteristic
749C2C3×#496112yes—
750C2C3×#498711yescharacteristic
751C2C3×#499412yes—
subgroupG/H
centerC24×C3C22×D3
commutatorC23×C3C22×C3×C4
FrattiniC24C22×C3×D3
FittingC2×C32×#95C2
socleC24×C32C23
prime radicalC24×C3×D3C22
cosocleC24×C3C23×C3
hypercenterC2×C3×#95D3
hypocenterC3C3×#1439
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C2×C3×#95

Complements

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

NH ≅ G/Ntype
3. C22×C3×C4⋊Dic3C2semidirect
4. C2×C32×#95C2semidirect
5. C2×C3×C3⋊#95C2semidirect
7. #69427C3direct (N × H)
18. C2×C3×(C2×D3)⋊C4C4semidirect
28. C22×C4⋊Dic3C2×C3semidirect
31. C2×C3×#95D3semidirect
32. C2×C3×#95C2×C3semidirect
33. C2×C3⋊#95C2×C3semidirect
99. C2×(C2×D3)⋊C4C3×C4semidirect
140. C22×C3×D3C4⋊C4semidirect
152. C2×C32×C4C22⋊C4semidirect
169. C2×#95C3×D3semidirect
392. C22×D3C3×C4⋊C4semidirect
439. C2×C3×C4(C2×D3)⋊C4semidirect
440. C2×C3×C4C3×C22⋊C4semidirect
605. C32#1439semidirect
663. C2×C4C3×(C2×D3)⋊C4semidirect
738. C3#69427direct (N × H)
739. C3C3×#1439semidirect

Maximal subgroups

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

subgroupindex
C22×C3×(C2×D3)⋊C42
C22×C3×C4⋊Dic32
C2×C32×#952
C2×C3×C3⋊#952
C3×#14393
#694273