Finite Group Databasebeta

← C3×#14737 #10633344

Subgroups — C3×#14737 #10633344

Order 768.

2110 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#397C211yesmaximal, characteristic, complemented
2C2×C3×#386C211yesmaximal, characteristic
3C2×C3×#386C211yesmaximal, characteristic
4C2×C3×#386C211yesmaximal, characteristic
5C2×C3×#385C211yesmaximal, characteristic, complemented
6C22×C3×#95C211yesmaximal, characteristic, complemented
7C3×#1445C211yesmaximal, characteristic, complemented
8C3×#1443C211yesmaximal, characteristic, complemented
9C3×#1443C211yesmaximal, characteristic, complemented
10C3×#1442C211yesmaximal, characteristic, complemented
11C3×#1440C211yesmaximal, characteristic, complemented
12C3×#1440C211yesmaximal, characteristic, complemented
13C3×#1439C211yesmaximal, characteristic, complemented
14C3×C22⋊#95C211yesmaximal, characteristic, complemented
15C3×C22⋊#95C211yesmaximal, characteristic, complemented
16#14737C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C24×C3×C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C22⋊C4C2211yescharacteristic
31C22×C3×C22⋊C4C2211yescharacteristic
32C3×#397—24no—
33C3×#386—24no—
34C3×#386—24no—
35C3×#386—24no—
36C3×#385—24no—
37C2×C3×#95—24no—
38C2×C3×#95C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42C2×C3×#95C2211yescharacteristic
43C2×C3×#95C2211yescharacteristic
44C2×C3×#95C2211yescharacteristic
45C2×C3×#95C2211yescharacteristic
46C2×C3×#95C2211yescharacteristic
47C2×C3×#95C2211yescharacteristic
48C2×C3×#95C2211yescharacteristic
49C2×C3×#95C2211yescharacteristic
50C2×C3×#95C2211yescharacteristic
51C2×C3×#95C2211yescharacteristic
52C2×C3×#95C2211yescharacteristic
53C2×C3×#95C2211yescharacteristic
54C2×C3×#95C2211yescharacteristic
55C2×C3×#95C2211yescharacteristic
56C2×C3×#95C2211yescharacteristic
57C2×C3×#95C2211yescharacteristic
58C2×#397C2×C311yescharacteristic, complemented
59C2×#386C2×C311yescharacteristic
60C2×#386C2×C311yescharacteristic
61C2×#386C2×C311yescharacteristic
62C2×#385C2×C311yescharacteristic, complemented
63C22×#95C2×C311yescharacteristic, complemented
64#1445C2×C311yescharacteristic, complemented
65#1443C2×C311yescharacteristic, complemented
66#1443C2×C311yescharacteristic, complemented
67#1442C2×C311yescharacteristic, complemented
68#1440C2×C311yescharacteristic, complemented
69#1440C2×C311yescharacteristic, complemented
70#1439C2×C311yescharacteristic, complemented
71C22⋊#95C2×C311yescharacteristic, complemented
72C22⋊#95C2×C311yescharacteristic, complemented
73C25×C3C2311yescharacteristic
74C25×C3C2311yescharacteristic
75C22×C3×D4—22no—
76C22×C3×D4—22no—
77C22×C3×D4—22no—
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—22no—
81C22×C3×D4D414yes—
82C23×C3×C4—22no—
83C23×C3×C4—22no—
84C23×C3×C4—22no—
85C23×C3×C4—22no—
86C23×C3×C4—22no—
87C23×C3×C4—22no—
88C23×C3×C4—22no—
89C23×C3×C4—22no—
90C23×C3×C4—22no—
91C23×C3×C4—22no—
92C23×C3×C4—22no—
93C23×C3×C4—22no—
94C23×C3×C4—22no—
95C23×C3×C4—22no—
96C23×C3×C4—22no—
97C23×C3×C4—41no—
98C23×C3×C4—41no—
99C23×C3×C4—41no—
100C23×C3×C4—41no—
101C23×C3×C4—41no—
102C23×C3×C4—41no—
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C23×C3×C4C2311yescharacteristic
111C23×C3×C4C2311yescharacteristic
112C23×C3×C4C2311yescharacteristic
113C23×C3×C4C2311yescharacteristic
114C23×C3×C4C2311yescharacteristic
115C23×C3×C4C2311yescharacteristic
116C2×C3×C4⋊C4—22no—
117C2×C3×C4⋊C4—22no—
118C2×C3×C4⋊C4—22no—
119C2×C3×C4⋊C4—22no—
120C2×C3×C4⋊C4—41no—
121C2×C3×C4⋊C4—41no—
122C2×C3×C22⋊C4—22no—
123C2×C3×C22⋊C4—22no—
124C2×C3×C22⋊C4—22no—
125C2×C3×C22⋊C4—22no—
126C2×C3×C22⋊C4—22no—
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4—22no—
130C2×C3×C22⋊C4—22no—
131C2×C3×C22⋊C4—22no—
132C2×C3×C22⋊C4—22no—
133C2×C3×C22⋊C4—22no—
134C2×C3×C22⋊C4—22no—
135C2×C3×C22⋊C4—22no—
136C2×C3×C22⋊C4—22no—
137C2×C3×C22⋊C4—22no—
138C2×C3×C22⋊C4—22no—
139C2×C3×C22⋊C4—22no—
140C2×C3×C22⋊C4—22no—
141C2×C3×C22⋊C4—22no—
142C2×C3×C22⋊C4—41no—
143C2×C3×C22⋊C4—41no—
144C2×C3×C22⋊C4—41no—
145C2×C3×C22⋊C4—41no—
146C2×C3×C22⋊C4—41no—
147C2×C3×C22⋊C4—41no—
148C2×C3×C22⋊C4D414yes—
149C3×#95—22no—
150C3×#95—22no—
151C3×#95—22no—
152C3×#95—22no—
153C3×#95—22no—
154C3×#95—22no—
155C3×#95—22no—
156C3×#95—22no—
157C3×#95—22no—
158C3×#95—22no—
159C3×#95—22no—
160C3×#95—22no—
161C3×#95—22no—
162C3×#95—22no—
163C3×#95—22no—
164C3×#95—41no—
165C3×#95—41no—
166C3×#95—41no—
167C3×#95—41no—
168C3×#95D414yescomplemented
169C23×D4C22×C311yescharacteristic
170C24×C4C22×C311yescharacteristic
171C24×C4C22×C311yescharacteristic
172C24×C4C22×C311yescharacteristic
173C22×C4⋊C4C22×C311yescharacteristic
174C22×C4⋊C4C22×C311yescharacteristic
175C22×C22⋊C4C22×C311yescharacteristic
176C22×C22⋊C4C22×C311yescharacteristic
177C22×C22⋊C4C22×C311yescharacteristic
178C22×C22⋊C4C22×C311yescharacteristic
179C22×C22⋊C4C22×C311yescharacteristic
180C22×C22⋊C4C22×C311yescharacteristic
181C22×C22⋊C4C22×C311yescharacteristic
182C22×C22⋊C4C22×C311yescharacteristic
183C22×C22⋊C4C22×C311yescharacteristic
184#397—24no—
185#386—24no—
186#386—24no—
187#386—24no—
188#385—24no—
189C2×#95—24no—
190C2×#95C22×C311yescharacteristic
191C2×#95C22×C311yescharacteristic
192C2×#95C22×C311yescharacteristic
193C2×#95C22×C311yescharacteristic
194C2×#95C22×C311yescharacteristic
195C2×#95C22×C311yescharacteristic
196C2×#95C22×C311yescharacteristic
197C2×#95C22×C311yescharacteristic
198C2×#95C22×C311yescharacteristic
199C2×#95C22×C311yescharacteristic
200C2×#95C22×C311yescharacteristic
201C2×#95C22×C311yescharacteristic
202C2×#95C22×C311yescharacteristic
203C2×#95C22×C311yescharacteristic
204C2×#95C22×C311yescharacteristic
205C2×#95C22×C311yescharacteristic
206C2×#95C22×C311yescharacteristic
207C2×#95C22×C311yescharacteristic
208C2×#95C22×C311yescharacteristic
209C2×#95C22×C311yescharacteristic
210C24×C3—21no—
211C24×C3—21no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3—21no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—21no—
220C24×C3—21no—
221C24×C3—21no—
222C24×C3—21no—
223C24×C3—21no—
224C24×C3—21no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3—21no—
230C24×C3—21no—
231C24×C3—21no—
232C24×C3C2×D412yes—
233C24×C3C2×D412yes—
234C24×C3C2×D412yes—
235C24×C3#4112yes—
236C24×C3#4112yes—
237C24×C3#4112yes—
238C24×C3#4112yes—
239C24×C3#4112yes—
240C24×C3C2411yescharacteristic
241C2×C3×D4—28no—
242C2×C3×D4—28no—
243C2×C3×D4—28no—
244C2×C3×D4—44no—
245C2×C3×D4—44no—
246C2×C3×D4—44no—
247C2×C3×D4—44no—
248C22×C3×C4—28no—
249C22×C3×C4—28no—
250C22×C3×C4—28no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—21no—
332C22×C3×C4—21no—
333C22×C3×C4—44no—
334C22×C3×C4—44no—
335C22×C3×C4—44no—
336C22×C3×C4—44no—
337C22×C3×C4—44no—
338C22×C3×C4—44no—
339C22×C3×C4—44no—
340C22×C3×C4—44no—
341C22×C3×C4—44no—
342C22×C3×C4—44no—
343C22×C3×C4—44no—
344C22×C3×C4—44no—
345C22×C3×C4—44no—
346C22×C3×C4—44no—
347C22×C3×C4—44no—
348C22×C3×C4—44no—
349C22×C3×C4—44no—
350C22×C3×C4—44no—
351C22×C3×C4C2×D412yes—
352C22×C3×C4C2×D412yes—
353C22×C3×C4C2×D412yes—
354C22×C3×C4C2×D412yes—
355C22×C3×C4C2×D412yes—
356C22×C3×C4C2×D412yes—
357C22×C3×C4#4112yes—
358C22×C3×C4#4112yes—
359C22×C3×C4#4112yes—
360C3×C4⋊C4—44no—
361C3×C4⋊C4—44no—
362C3×C22⋊C4—28no—
363C3×C22⋊C4—44no—
364C3×C22⋊C4—44no—
365C3×C22⋊C4—44no—
366C3×C22⋊C4—44no—
367C3×C22⋊C4—44no—
368C3×C22⋊C4—44no—
369C3×C22⋊C4—44no—
370C3×C22⋊C4—44no—
371C25C23×C311yescharacteristic
372C25C23×C311yescharacteristic
373C22×D4—22no—
374C22×D4—22no—
375C22×D4—22no—
376C22×D4—22no—
377C22×D4—22no—
378C22×D4—22no—
379C22×D4C3×D414yes—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—41no—
396C23×C4—41no—
397C23×C4—41no—
398C23×C4—41no—
399C23×C4—41no—
400C23×C4—41no—
401C23×C4C23×C311yescharacteristic
402C23×C4C23×C311yescharacteristic
403C23×C4C23×C311yescharacteristic
404C23×C4C23×C311yescharacteristic
405C23×C4C23×C311yescharacteristic
406C23×C4C23×C311yescharacteristic
407C23×C4C23×C311yescharacteristic
408C23×C4C23×C311yescharacteristic
409C23×C4C23×C311yescharacteristic
410C23×C4C23×C311yescharacteristic
411C23×C4C23×C311yescharacteristic
412C23×C4C23×C311yescharacteristic
413C23×C4C23×C311yescharacteristic
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—41no—
419C2×C4⋊C4—41no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—41no—
441C2×C22⋊C4—41no—
442C2×C22⋊C4—41no—
443C2×C22⋊C4—41no—
444C2×C22⋊C4—41no—
445C2×C22⋊C4—41no—
446C2×C22⋊C4C3×D414yes—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—41no—
463#95—41no—
464#95—41no—
465#95—41no—
466#95C3×D414yescomplemented
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—22no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—22no—
489C23×C3—22no—
490C23×C3—22no—
491C23×C3—22no—
492C23×C3—22no—
493C23×C3—22no—
494C23×C3—22no—
495C23×C3—22no—
496C23×C3—22no—
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—22no—
501C23×C3—22no—
502C23×C3—41no—
503C23×C3—41no—
504C23×C3—41no—
505C23×C3—41no—
506C23×C3—41no—
507C23×C3—41no—
508C23×C3—41no—
509C23×C3—41no—
510C23×C3—41no—
511C23×C3—41no—
512C23×C3—41no—
513C23×C3—41no—
514C23×C3—41no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3#12114yes—
531C23×C3#12314yes—
532C23×C3#12314yes—
533C23×C3#12314yes—
534C23×C3#12414yes—
535C23×C3#12614yes—
536C23×C3#12614yes—
537C23×C3C22×D411yescharacteristic
538C23×C3C22×D411yescharacteristic
539C23×C3C22×D411yescharacteristic
540C23×C3C2×#4111yescharacteristic
541C23×C3C2×#4111yescharacteristic
542C23×C3C2×#4111yescharacteristic
543C23×C3C2×#4111yescharacteristic
544C23×C3C2×#4111yescharacteristic
545C23×C3C2×#4111yescharacteristic
546C23×C3C2×#4111yescharacteristic
547C23×C3C2×#4111yescharacteristic
548C23×C3H(5,𝔽2)11yescharacteristic
549C23×C3H(5,𝔽2)11yescharacteristic
550C23×C3H(5,𝔽2)11yescharacteristic
551C23×C32−1+411yescharacteristic
552C3×D4—416no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—416no—
581C2×C3×C4—416no—
582C2×C3×C4—416no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—41no—
626C2×C3×C4—41no—
627C2×C3×C4—41no—
628C2×C3×C4—41no—
629C2×C3×C4—41no—
630C2×C3×C4—41no—
631C2×C3×C4—41no—
632C2×C3×C4—41no—
633C2×C3×C4—41no—
634C2×C3×C4—41no—
635C2×C3×C4—41no—
636C2×C3×C4—41no—
637C2×C3×C4—41no—
638C2×C3×C4—41no—
639C2×C3×C4—41no—
640C2×C3×C4—41no—
641C2×C3×C4—41no—
642C2×C3×C4—41no—
643C2×C3×C4—41no—
644C2×C3×C4—41no—
645C2×C3×C4—41no—
646C2×C3×C4—41no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24C2×C3×D412yes—
670C24C2×C3×D412yes—
671C24C2×C3×D412yes—
672C24C3×#4112yes—
673C24C3×#4112yes—
674C24C3×#4112yes—
675C24C3×#4112yes—
676C24C3×#4112yes—
677C24C24×C311yescharacteristic
678C2×D4—28no—
679C2×D4—28no—
680C2×D4—28no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C22×C4—28no—
686C22×C4—28no—
687C22×C4—28no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4—44no—
785C22×C4—44no—
786C22×C4—44no—
787C22×C4—44no—
788C22×C4C2×C3×D412yes—
789C22×C4C2×C3×D412yes—
790C22×C4C2×C3×D412yes—
791C22×C4C2×C3×D412yes—
792C22×C4C2×C3×D412yes—
793C22×C4C2×C3×D412yes—
794C22×C4C3×#4112yes—
795C22×C4C3×#4112yes—
796C22×C4C3×#4112yes—
797C4⋊C4—44no—
798C4⋊C4—44no—
799C22⋊C4—28no—
800C22⋊C4—44no—
801C22⋊C4—44no—
802C22⋊C4—44no—
803C22⋊C4—44no—
804C22⋊C4—44no—
805C22⋊C4—44no—
806C22⋊C4—44no—
807C22⋊C4—44no—
808C22×C3—24no—
809C22×C3—24no—
810C22×C3—24no—
811C22×C3—24no—
812C22×C3—24no—
813C22×C3—24no—
814C22×C3—24no—
815C22×C3—24no—
816C22×C3—24no—
817C22×C3—24no—
818C22×C3—24no—
819C22×C3—24no—
820C22×C3—24no—
821C22×C3—24no—
822C22×C3—42no—
823C22×C3—42no—
824C22×C3—42no—
825C22×C3—42no—
826C22×C3—42no—
827C22×C3—42no—
828C22×C3—42no—
829C22×C3—81no—
830C22×C3—81no—
831C22×C3—81no—
832C22×C3—81no—
833C22×C3—81no—
834C22×C3—81no—
835C22×C3—81no—
836C22×C3—81no—
837C22×C3#39718yescomplemented
838C22×C3C2×#12111yescharacteristic
839C22×C3C2×#12311yescharacteristic
840C22×C3C2×#12311yescharacteristic
841C22×C3C2×#12311yescharacteristic
842C22×C3#52511yescharacteristic
843C22×C3#52511yescharacteristic
844C22×C3#52511yescharacteristic
845C22×C3C2×#12411yescharacteristic
846C22×C3C2×#12611yescharacteristic
847C22×C3C2×#12611yescharacteristic
848C22×C3#52911yescharacteristic
849C22×C3#52911yescharacteristic
850C22×C3#52911yescharacteristic
851C22×C3#53811yescharacteristic
852C22×C3#53811yescharacteristic
853C22×C3#53811yescharacteristic
854C22×C3#53911yescharacteristic
855C22×C3#53911yescharacteristic
856C22×C3#53911yescharacteristic
857C22×C3D4211yescharacteristic
858C22×C3D4211yescharacteristic
859C22×C3#54611yescharacteristic
860C22×C3#54611yescharacteristic
861C22×C3#54611yescharacteristic
862C22×C3#54611yescharacteristic
863C22×C3#54611yescharacteristic
864C22×C3#54711yescharacteristic
865C22×C3#54711yescharacteristic
866C22×C3#54811yescharacteristic
867C22×C3#55111yescharacteristic
868C22×C3#55111yescharacteristic
869C22×C3#55211yescharacteristic
870C22×C3#55311yescharacteristic
871C22×C3#55311yescharacteristic
872C22×C3#55311yescharacteristic
873C3×C4—42no—
874C3×C4—42no—
875C3×C4—42no—
876C3×C4—42no—
877C3×C4—42no—
878C3×C4—42no—
879C3×C4—42no—
880C3×C4—42no—
881C3×C4—42no—
882C3×C4—81no—
883C3×C4—81no—
884C3×C4—81no—
885C3×C4—81no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23C3×#12114yes—
950C23C3×#12314yes—
951C23C3×#12314yes—
952C23C3×#12314yes—
953C23C3×#12414yes—
954C23C3×#12614yes—
955C23C3×#12614yes—
956C23C22×C3×D411yescharacteristic
957C23C22×C3×D411yescharacteristic
958C23C22×C3×D411yescharacteristic
959C23C2×C3×#4111yescharacteristic
960C23C2×C3×#4111yescharacteristic
961C23C2×C3×#4111yescharacteristic
962C23C2×C3×#4111yescharacteristic
963C23C2×C3×#4111yescharacteristic
964C23C2×C3×#4111yescharacteristic
965C23C2×C3×#4111yescharacteristic
966C23C2×C3×#4111yescharacteristic
967C23C3×H(5,𝔽2)11yescharacteristic
968C23C3×H(5,𝔽2)11yescharacteristic
969C23C3×H(5,𝔽2)11yescharacteristic
970C23C3×2−1+411yescharacteristic
971D4—416no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—416no—
1000C2×C4—416no—
1001C2×C4—416no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C3—28no—
1067C2×C3—82no—
1068C2×C3C2×#39711yescharacteristic
1069C2×C3#241811yescharacteristic
1070C2×C3#241911yescharacteristic
1071C2×C3#242411yescharacteristic
1072C2×C3#242511yescharacteristic
1073C2×C3#244311yescharacteristic
1074C2×C3#244311yescharacteristic
1075C2×C3#244411yescharacteristic
1076C2×C3#244411yescharacteristic
1077C2×C3#247211yescharacteristic
1078C2×C3#248111yescharacteristic
1079C2×C3#248811yescharacteristic
1080C2×C3#251011yescharacteristic
1081C2×C3#264311yescharacteristic
1082C2×C3#285211yescharacteristic
1083C22—24no—
1084C22—24no—
1085C22—24no—
1086C22—24no—
1087C22—24no—
1088C22—24no—
1089C22—24no—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—24no—
1096C22—24no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22C3×#39718yescomplemented
1113C22C2×C3×#12111yescharacteristic
1114C22C2×C3×#12311yescharacteristic
1115C22C2×C3×#12311yescharacteristic
1116C22C2×C3×#12311yescharacteristic
1117C22C3×#52511yescharacteristic
1118C22C3×#52511yescharacteristic
1119C22C3×#52511yescharacteristic
1120C22C2×C3×#12411yescharacteristic
1121C22C2×C3×#12611yescharacteristic
1122C22C2×C3×#12611yescharacteristic
1123C22C3×#52911yescharacteristic
1124C22C3×#52911yescharacteristic
1125C22C3×#52911yescharacteristic
1126C22C3×#53811yescharacteristic
1127C22C3×#53811yescharacteristic
1128C22C3×#53811yescharacteristic
1129C22C3×#53911yescharacteristic
1130C22C3×#53911yescharacteristic
1131C22C3×#53911yescharacteristic
1132C22C3×D4211yescharacteristic
1133C22C3×D4211yescharacteristic
1134C22C3×#54611yescharacteristic
1135C22C3×#54611yescharacteristic
1136C22C3×#54611yescharacteristic
1137C22C3×#54611yescharacteristic
1138C22C3×#54611yescharacteristic
1139C22C3×#54711yescharacteristic
1140C22C3×#54711yescharacteristic
1141C22C3×#54811yescharacteristic
1142C22C3×#55111yescharacteristic
1143C22C3×#55111yescharacteristic
1144C22C3×#55211yescharacteristic
1145C22C3×#55311yescharacteristic
1146C22C3×#55311yescharacteristic
1147C22C3×#55311yescharacteristic
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—42no—
1157C4—81no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C3#1473711yescharacteristic, direct product factor, Sylow
1162C2—28no—
1163C2—82no—
1164C2C2×C3×#39711yescharacteristic
1165C2C3×#241811yescharacteristic
1166C2C3×#241911yescharacteristic
1167C2C3×#242411yescharacteristic
1168C2C3×#242511yescharacteristic
1169C2C3×#244311yescharacteristic
1170C2C3×#244311yescharacteristic
1171C2C3×#244411yescharacteristic
1172C2C3×#244411yescharacteristic
1173C2C3×#247211yescharacteristic
1174C2C3×#248111yescharacteristic
1175C2C3×#248811yescharacteristic
1176C2C3×#251011yescharacteristic
1177C2C3×#264311yescharacteristic
1178C2C3×#285211yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC23×C3×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#397C2semidirect
5. C2×C3×#385C2semidirect
6. C22×C3×#95C2semidirect
7. C3×#1445C2semidirect
8. C3×#1443C2semidirect
9. C3×#1443C2semidirect
10. C3×#1442C2semidirect
11. C3×#1440C2semidirect
12. C3×#1440C2semidirect
13. C3×#1439C2semidirect
14. C3×C22⋊#95C2semidirect
15. C3×C22⋊#95C2semidirect
16. #14737C3direct (N × H)
58. C2×#397C2×C3semidirect
62. C2×#385C2×C3semidirect
63. C22×#95C2×C3semidirect
64. #1445C2×C3semidirect
65. #1443C2×C3semidirect
66. #1443C2×C3semidirect
67. #1442C2×C3semidirect
68. #1440C2×C3semidirect
69. #1440C2×C3semidirect
70. #1439C2×C3semidirect
71. C22⋊#95C2×C3semidirect
72. C22⋊#95C2×C3semidirect
168. C3×#95D4semidirect
466. #95C3×D4semidirect
837. C22×C3#397semidirect
1112. C22C3×#397semidirect
1161. C3#14737direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3972
C2×C3×#3862
C2×C3×#3852
C22×C3×#952
C3×#14452
C3×#14432
C3×#14422
C3×#14402
C3×#14392
C3×C22⋊#952
#147373