Finite Group Databasebeta

← C3×#15337 #10633944

Subgroups — C3×#15337 #10633944

Order 768.

1334 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#398C211yesmaximal, characteristic
2C2×C3×#391C211yesmaximal, characteristic
3C2×C3×#391C211yesmaximal, characteristic
4C2×C3×#387C211yesmaximal, characteristic
5C3×#1446C211yesmaximal, characteristic
6C3×#1445C211yesmaximal, characteristic
7C3×#1444C211yesmaximal, characteristic
8C3×#1442C211yesmaximal, characteristic
9C3×#1442C211yesmaximal, characteristic
10C3×#1441C211yesmaximal, characteristic
11C3×#1441C211yesmaximal, characteristic
12C3×#1441C211yesmaximal, characteristic
13C3×#1436C211yesmaximal, characteristic
14C3×#1436C211yesmaximal, characteristic
15C3×C4⋊#95C211yesmaximal, characteristic
16#15337C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×Q8C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C42C2211yescharacteristic
27C22×C3×C42C2211yescharacteristic
28C3×#398—24no—
29C3×#391—24no—
30C3×#391—24no—
31C3×#387—24no—
32C2×C3×#95C2211yescharacteristic
33C2×C3×#95C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
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×#398C2×C311yescharacteristic
57C2×#391C2×C311yescharacteristic
58C2×#391C2×C311yescharacteristic
59C2×#387C2×C311yescharacteristic
60#1446C2×C311yescharacteristic
61#1445C2×C311yescharacteristic
62#1444C2×C311yescharacteristic
63#1442C2×C311yescharacteristic
64#1442C2×C311yescharacteristic
65#1441C2×C311yescharacteristic
66#1441C2×C311yescharacteristic
67#1441C2×C311yescharacteristic
68#1436C2×C311yescharacteristic
69#1436C2×C311yescharacteristic
70C4⋊#95C2×C311yescharacteristic
71C22×C3×Q8—22no—
72C22×C3×Q8—22no—
73C22×C3×Q8—22no—
74C22×C3×Q8—22no—
75C22×C3×Q8—41no—
76C22×C3×Q8—41no—
77C22×C3×Q8Q814yes—
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C2×C3×C4⋊C4—22no—
94C2×C3×C4⋊C4—22no—
95C2×C3×C4⋊C4—22no—
96C2×C3×C4⋊C4—22no—
97C2×C3×C4⋊C4—22no—
98C2×C3×C4⋊C4—22no—
99C2×C3×C4⋊C4—22no—
100C2×C3×C4⋊C4—22no—
101C2×C3×C4⋊C4—22no—
102C2×C3×C4⋊C4—22no—
103C2×C3×C4⋊C4—22no—
104C2×C3×C4⋊C4—22no—
105C2×C3×C4⋊C4—22no—
106C2×C3×C4⋊C4—22no—
107C2×C3×C4⋊C4—22no—
108C2×C3×C4⋊C4—41no—
109C2×C3×C4⋊C4—41no—
110C2×C3×C4⋊C4—41no—
111C2×C3×C4⋊C4—41no—
112C2×C3×C4⋊C4—41no—
113C2×C3×C4⋊C4—41no—
114C2×C3×C4⋊C4—41no—
115C2×C3×C4⋊C4—41no—
116C2×C3×C4⋊C4Q814yescomplemented
117C2×C3×C42—22no—
118C2×C3×C42—22no—
119C2×C3×C42—22no—
120C2×C3×C42—22no—
121C2×C3×C42—41no—
122C2×C3×C42—41no—
123C3×#95—22no—
124C3×#95—22no—
125C3×#95—22no—
126C3×#95—22no—
127C3×#95—22no—
128C3×#95—22no—
129C3×#95—22no—
130C3×#95—22no—
131C3×#95—22no—
132C3×#95—22no—
133C3×#95—22no—
134C3×#95—22no—
135C3×#95—22no—
136C3×#95—22no—
137C3×#95—22no—
138C3×#95—22no—
139C3×#95—41no—
140C3×#95—41no—
141C3×#95—41no—
142C3×#95—41no—
143C3×#95—41no—
144C3×#95—41no—
145C3×#95D414yes—
146C3×#95D414yes—
147C23×Q8C22×C311yescharacteristic
148C22×C4⋊C4C22×C311yescharacteristic
149C22×C4⋊C4C22×C311yescharacteristic
150C22×C4⋊C4C22×C311yescharacteristic
151C22×C4⋊C4C22×C311yescharacteristic
152C22×C4⋊C4C22×C311yescharacteristic
153C22×C4⋊C4C22×C311yescharacteristic
154C22×C4⋊C4C22×C311yescharacteristic
155C22×C4⋊C4C22×C311yescharacteristic
156C22×C42C22×C311yescharacteristic
157C22×C42C22×C311yescharacteristic
158#398—24no—
159#391—24no—
160#391—24no—
161#387—24no—
162C2×#95C22×C311yescharacteristic
163C2×#95C22×C311yescharacteristic
164C2×#95C22×C311yescharacteristic
165C2×#95C22×C311yescharacteristic
166C2×#95C22×C311yescharacteristic
167C2×#95C22×C311yescharacteristic
168C2×#95C22×C311yescharacteristic
169C2×#95C22×C311yescharacteristic
170C2×#95C22×C311yescharacteristic
171C2×#95C22×C311yescharacteristic
172C2×#95C22×C311yescharacteristic
173C2×#95C22×C311yescharacteristic
174C2×#95C22×C311yescharacteristic
175C2×#95C22×C311yescharacteristic
176C2×#95C22×C311yescharacteristic
177C2×#95C22×C311yescharacteristic
178C2×#95C22×C311yescharacteristic
179C2×#95C22×C311yescharacteristic
180C2×#95C22×C311yescharacteristic
181C2×#95C22×C311yescharacteristic
182C2×#95C22×C311yescharacteristic
183C2×#95C22×C311yescharacteristic
184C2×#95C22×C311yescharacteristic
185C2×#95C22×C311yescharacteristic
186C24×C3C2411yescharacteristic
187C2×C3×Q8—28no—
188C2×C3×Q8—28no—
189C2×C3×Q8—44no—
190C2×C3×Q8—44no—
191C2×C3×Q8—44no—
192C2×C3×Q8—44no—
193C2×C3×Q8—44no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
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×C4C2×D412yes—
283C22×C3×C4C2×D412yes—
284C22×C3×C4C2×D412yes—
285C22×C3×C4C2×D412yes—
286C22×C3×C4C2×D412yes—
287C22×C3×C4C2×D412yes—
288C22×C3×C4C2×Q812yes—
289C22×C3×C4C2×Q812yes—
290C22×C3×C4C2×Q812yes—
291C22×C3×C4C2×Q812yes—
292C22×C3×C4C2×Q812yes—
293C22×C3×C4C2×Q812yes—
294C22×C3×C4#4112yes—
295C22×C3×C4#4112yes—
296C22×C3×C4#4112yes—
297C22×C3×C4#4112yes—
298C22×C3×C4#4112yes—
299C3×C4⋊C4—28no—
300C3×C4⋊C4—44no—
301C3×C4⋊C4—44no—
302C3×C4⋊C4—44no—
303C3×C4⋊C4—44no—
304C3×C4⋊C4—44no—
305C3×C4⋊C4—44no—
306C3×C4⋊C4—44no—
307C3×C42—44no—
308C3×C42—44no—
309C22×Q8—22no—
310C22×Q8—22no—
311C22×Q8—22no—
312C22×Q8—22no—
313C22×Q8—41no—
314C22×Q8—41no—
315C22×Q8C3×Q814yes—
316C23×C4C23×C311yescharacteristic
317C23×C4C23×C311yescharacteristic
318C23×C4C23×C311yescharacteristic
319C23×C4C23×C311yescharacteristic
320C23×C4C23×C311yescharacteristic
321C23×C4C23×C311yescharacteristic
322C23×C4C23×C311yescharacteristic
323C23×C4C23×C311yescharacteristic
324C23×C4C23×C311yescharacteristic
325C23×C4C23×C311yescharacteristic
326C23×C4C23×C311yescharacteristic
327C23×C4C23×C311yescharacteristic
328C23×C4C23×C311yescharacteristic
329C23×C4C23×C311yescharacteristic
330C23×C4C23×C311yescharacteristic
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—41no—
347C2×C4⋊C4—41no—
348C2×C4⋊C4—41no—
349C2×C4⋊C4—41no—
350C2×C4⋊C4—41no—
351C2×C4⋊C4—41no—
352C2×C4⋊C4—41no—
353C2×C4⋊C4—41no—
354C2×C4⋊C4C3×Q814yescomplemented
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—41no—
360C2×C42—41no—
361#95—22no—
362#95—22no—
363#95—22no—
364#95—22no—
365#95—22no—
366#95—22no—
367#95—22no—
368#95—22no—
369#95—22no—
370#95—22no—
371#95—22no—
372#95—22no—
373#95—22no—
374#95—22no—
375#95—22no—
376#95—22no—
377#95—41no—
378#95—41no—
379#95—41no—
380#95—41no—
381#95—41no—
382#95—41no—
383#95C3×D414yes—
384#95C3×D414yes—
385C23×C3C22×D411yescharacteristic
386C23×C3C22×D411yescharacteristic
387C23×C3C22×Q811yescharacteristic
388C23×C3C22×Q811yescharacteristic
389C23×C3C2×#4111yescharacteristic
390C23×C3C2×#4111yescharacteristic
391C23×C3C2×#4111yescharacteristic
392C23×C3C2×#4111yescharacteristic
393C23×C3C2×#4111yescharacteristic
394C23×C3H(5,𝔽2)11yescharacteristic
395C23×C3H(5,𝔽2)11yescharacteristic
396C23×C3H(5,𝔽2)11yescharacteristic
397C23×C32−1+411yescharacteristic
398C23×C32−1+411yescharacteristic
399C23×C32−1+411yescharacteristic
400C3×Q8—416no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
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—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4C22⋊Q814yes—
504C2×C3×C4C22⋊Q814yes—
505C2×C3×C4C22⋊Q814yes—
506C24C24×C311yescharacteristic
507C2×Q8—28no—
508C2×Q8—28no—
509C2×Q8—44no—
510C2×Q8—44no—
511C2×Q8—44no—
512C2×Q8—44no—
513C2×Q8—44no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4C2×C3×D412yes—
603C22×C4C2×C3×D412yes—
604C22×C4C2×C3×D412yes—
605C22×C4C2×C3×D412yes—
606C22×C4C2×C3×D412yes—
607C22×C4C2×C3×D412yes—
608C22×C4C2×C3×Q812yes—
609C22×C4C2×C3×Q812yes—
610C22×C4C2×C3×Q812yes—
611C22×C4C2×C3×Q812yes—
612C22×C4C2×C3×Q812yes—
613C22×C4C2×C3×Q812yes—
614C22×C4C3×#4112yes—
615C22×C4C3×#4112yes—
616C22×C4C3×#4112yes—
617C22×C4C3×#4112yes—
618C22×C4C3×#4112yes—
619C4⋊C4—28no—
620C4⋊C4—44no—
621C4⋊C4—44no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C42—44no—
628C42—44no—
629C22×C3C2×C22⋊Q811yescharacteristic
630C22×C3C2×C22⋊Q811yescharacteristic
631C22×C3C2×C22⋊Q811yescharacteristic
632C22×C3#52911yescharacteristic
633C22×C3#53211yescharacteristic
634C22×C3#53311yescharacteristic
635C22×C3#53611yescharacteristic
636C22×C3#53711yescharacteristic
637C22×C3#53811yescharacteristic
638C22×C3#54111yescharacteristic
639C22×C3#54211yescharacteristic
640C22×C3#54211yescharacteristic
641C22×C3#54211yescharacteristic
642C22×C3#54311yescharacteristic
643C22×C3#54411yescharacteristic
644C22×C3D4211yescharacteristic
645C22×C3#54611yescharacteristic
646C22×C3#54611yescharacteristic
647C22×C3#54611yescharacteristic
648C22×C3#54711yescharacteristic
649C22×C3#54811yescharacteristic
650C22×C3D4×Q811yescharacteristic
651C22×C3#55111yescharacteristic
652C22×C3#55111yescharacteristic
653C22×C3#55211yescharacteristic
654C22×C3#55211yescharacteristic
655C22×C3#55411yescharacteristic
656C22×C3#55711yescharacteristic
657C22×C3#55711yescharacteristic
658C22×C3#55711yescharacteristic
659C22×C3#55711yescharacteristic
660C22×C3Q8211yescharacteristic
661C22×C3#55911yescharacteristic
662C22×C3#56211yescharacteristic
663C22×C3#56311yescharacteristic
664C3×C4—24no—
665C3×C4—24no—
666C3×C4—24no—
667C3×C4—42no—
668C3×C4—42no—
669C3×C4—42no—
670C3×C4—42no—
671C3×C4—42no—
672C3×C4—42no—
673C3×C4—42no—
674C3×C4—42no—
675C3×C4—81no—
676C3×C4—81no—
677C3×C4—81no—
678C3×C4—81no—
679C23C22×C3×D411yescharacteristic
680C23C22×C3×D411yescharacteristic
681C23C22×C3×Q811yescharacteristic
682C23C22×C3×Q811yescharacteristic
683C23C2×C3×#4111yescharacteristic
684C23C2×C3×#4111yescharacteristic
685C23C2×C3×#4111yescharacteristic
686C23C2×C3×#4111yescharacteristic
687C23C2×C3×#4111yescharacteristic
688C23C3×H(5,𝔽2)11yescharacteristic
689C23C3×H(5,𝔽2)11yescharacteristic
690C23C3×H(5,𝔽2)11yescharacteristic
691C23C3×2−1+411yescharacteristic
692C23C3×2−1+411yescharacteristic
693C23C3×2−1+411yescharacteristic
694Q8—416no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4C3×C22⋊Q814yes—
798C2×C4C3×C22⋊Q814yes—
799C2×C4C3×C22⋊Q814yes—
800C2×C3#243711yescharacteristic
801C2×C3#243811yescharacteristic
802C2×C3#245111yescharacteristic
803C2×C3#245211yescharacteristic
804C2×C3#245311yescharacteristic
805C2×C3#252011yescharacteristic
806C2×C3#255711yescharacteristic
807C2×C3#256511yescharacteristic
808C2×C3#258211yescharacteristic
809C2×C3#267211yescharacteristic
810C2×C3#270211yescharacteristic
811C2×C3#271311yescharacteristic
812C2×C3#275411yescharacteristic
813C2×C3#279911yescharacteristic
814C2×C3#280611yescharacteristic
815C22C2×C3×C22⋊Q811yescharacteristic
816C22C2×C3×C22⋊Q811yescharacteristic
817C22C2×C3×C22⋊Q811yescharacteristic
818C22C3×#52911yescharacteristic
819C22C3×#53211yescharacteristic
820C22C3×#53311yescharacteristic
821C22C3×#53611yescharacteristic
822C22C3×#53711yescharacteristic
823C22C3×#53811yescharacteristic
824C22C3×#54111yescharacteristic
825C22C3×#54211yescharacteristic
826C22C3×#54211yescharacteristic
827C22C3×#54211yescharacteristic
828C22C3×#54311yescharacteristic
829C22C3×#54411yescharacteristic
830C22C3×D4211yescharacteristic
831C22C3×#54611yescharacteristic
832C22C3×#54611yescharacteristic
833C22C3×#54611yescharacteristic
834C22C3×#54711yescharacteristic
835C22C3×#54811yescharacteristic
836C22C3×D4×Q811yescharacteristic
837C22C3×#55111yescharacteristic
838C22C3×#55111yescharacteristic
839C22C3×#55211yescharacteristic
840C22C3×#55211yescharacteristic
841C22C3×#55411yescharacteristic
842C22C3×#55711yescharacteristic
843C22C3×#55711yescharacteristic
844C22C3×#55711yescharacteristic
845C22C3×#55711yescharacteristic
846C22C3×Q8211yescharacteristic
847C22C3×#55911yescharacteristic
848C22C3×#56211yescharacteristic
849C22C3×#56311yescharacteristic
850C4—24no—
851C4—24no—
852C4—24no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—81no—
862C4—81no—
863C4—81no—
864C4—81no—
865C3#1533711yescharacteristic, direct product factor, Sylow
866C2C3×#243711yescharacteristic
867C2C3×#243811yescharacteristic
868C2C3×#245111yescharacteristic
869C2C3×#245211yescharacteristic
870C2C3×#245311yescharacteristic
871C2C3×#252011yescharacteristic
872C2C3×#255711yescharacteristic
873C2C3×#256511yescharacteristic
874C2C3×#258211yescharacteristic
875C2C3×#267211yescharacteristic
876C2C3×#270211yescharacteristic
877C2C3×#271311yescharacteristic
878C2C3×#275411yescharacteristic
879C2C3×#279911yescharacteristic
880C2C3×#280611yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C3C24
commutator, Frattini, cosocleC24C24×C3
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
16. #15337C3direct (N × H)
116. C2×C3×C4⋊C4Q8semidirect
354. C2×C4⋊C4C3×Q8semidirect
865. C3#15337direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3982
C2×C3×#3912
C2×C3×#3872
C3×#14462
C3×#14452
C3×#14442
C3×#14422
C3×#14412
C3×#14362
C3×C4⋊#952
#153373