Finite Group Databasebeta

← C3×#15690 #10634297

Subgroups — C3×#15690 #10634297

Order 768.

1190 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#400C211yesmaximal, characteristic
2C2×C3×#391C211yesmaximal, characteristic
3C3×#1446C211yesmaximal, characteristic
4C3×#1446C211yesmaximal, characteristic
5C3×#1445C211yesmaximal, characteristic
6C3×#1443C211yesmaximal, characteristic
7C3×#1443C211yesmaximal, characteristic
8C3×#1443C211yesmaximal, characteristic
9C3×#1442C211yesmaximal, characteristic
10C3×#1441C211yesmaximal, characteristic
11C3×#1436C211yesmaximal, characteristic
12C3×#1436C211yesmaximal, characteristic
13C3×#1436C211yesmaximal, characteristic
14C3×C4⋊#95C211yesmaximal, characteristic
15C3×#1434C211yesmaximal, characteristic
16#15690C311yesmaximal, 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×C42C2211yescharacteristic
23C22×C3×C42C2211yescharacteristic
24C3×#400—24no—
25C3×#391—24no—
26C2×C3×#95C2211yescharacteristic
27C2×C3×#95C2211yescharacteristic
28C2×C3×#95C2211yescharacteristic
29C2×C3×#95C2211yescharacteristic
30C2×C3×#95C2211yescharacteristic
31C2×C3×#95C2211yescharacteristic
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×#400C2×C311yescharacteristic
55C2×#391C2×C311yescharacteristic
56#1446C2×C311yescharacteristic
57#1446C2×C311yescharacteristic
58#1445C2×C311yescharacteristic
59#1443C2×C311yescharacteristic
60#1443C2×C311yescharacteristic
61#1443C2×C311yescharacteristic
62#1442C2×C311yescharacteristic
63#1441C2×C311yescharacteristic
64#1436C2×C311yescharacteristic
65#1436C2×C311yescharacteristic
66#1436C2×C311yescharacteristic
67C4⋊#95C2×C311yescharacteristic
68#1434C2×C311yescharacteristic
69C22×C3×Q8—22no—
70C22×C3×Q8—22no—
71C22×C3×Q8—22no—
72C22×C3×Q8—22no—
73C22×C3×Q8—22no—
74C22×C3×Q8—41no—
75C22×C3×Q8—41no—
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
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
91C2×C3×C4⋊C4—22no—
92C2×C3×C4⋊C4—22no—
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—41no—
102C2×C3×C4⋊C4—41no—
103C2×C3×C42—22no—
104C2×C3×C42—22no—
105C2×C3×C42—22no—
106C2×C3×C42—41no—
107C2×C3×C42—41no—
108C2×C3×C42—41no—
109C3×#95—22no—
110C3×#95—22no—
111C3×#95—22no—
112C3×#95—22no—
113C3×#95—22no—
114C3×#95—22no—
115C3×#95—22no—
116C3×#95—22no—
117C3×#95—22no—
118C3×#95—22no—
119C3×#95—22no—
120C3×#95—22no—
121C3×#95—22no—
122C3×#95—22no—
123C3×#95—22no—
124C3×#95—41no—
125C3×#95—41no—
126C3×#95—41no—
127C3×#95—41no—
128C3×#95—41no—
129C3×#95—41no—
130C3×#95—41no—
131C3×#95—41no—
132C3×#95—41no—
133C3×#95—41no—
134C3×#95—41no—
135C3×#95D414yes—
136C3×#95Q814yescomplemented
137C23×Q8C22×C311yescharacteristic
138C22×C4⋊C4C22×C311yescharacteristic
139C22×C4⋊C4C22×C311yescharacteristic
140C22×C4⋊C4C22×C311yescharacteristic
141C22×C4⋊C4C22×C311yescharacteristic
142C22×C42C22×C311yescharacteristic
143C22×C42C22×C311yescharacteristic
144#400—24no—
145#391—24no—
146C2×#95C22×C311yescharacteristic
147C2×#95C22×C311yescharacteristic
148C2×#95C22×C311yescharacteristic
149C2×#95C22×C311yescharacteristic
150C2×#95C22×C311yescharacteristic
151C2×#95C22×C311yescharacteristic
152C2×#95C22×C311yescharacteristic
153C2×#95C22×C311yescharacteristic
154C2×#95C22×C311yescharacteristic
155C2×#95C22×C311yescharacteristic
156C2×#95C22×C311yescharacteristic
157C2×#95C22×C311yescharacteristic
158C2×#95C22×C311yescharacteristic
159C2×#95C22×C311yescharacteristic
160C2×#95C22×C311yescharacteristic
161C2×#95C22×C311yescharacteristic
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
174C24×C3C2411yescharacteristic
175C2×C3×Q8—28no—
176C2×C3×Q8—44no—
177C2×C3×Q8—44no—
178C2×C3×Q8—44no—
179C2×C3×Q8—44no—
180C2×C3×Q8—44no—
181C2×C3×Q8—44no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
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×C4C2×D412yes—
275C22×C3×C4C2×D412yes—
276C22×C3×C4C2×D412yes—
277C22×C3×C4C2×Q812yes—
278C22×C3×C4C2×Q812yes—
279C22×C3×C4C2×Q812yes—
280C22×C3×C4#4112yes—
281C22×C3×C4#4112yes—
282C22×C3×C4#4112yes—
283C22×C3×C4#4112yes—
284C22×C3×C4#4112yes—
285C22×C3×C4#4112yes—
286C22×C3×C4#4112yes—
287C3×C4⋊C4—44no—
288C3×C4⋊C4—44no—
289C3×C4⋊C4—44no—
290C3×C4⋊C4—44no—
291C3×C42—44no—
292C3×C42—44no—
293C22×Q8—22no—
294C22×Q8—22no—
295C22×Q8—22no—
296C22×Q8—22no—
297C22×Q8—22no—
298C22×Q8—41no—
299C22×Q8—41no—
300C23×C4C23×C311yescharacteristic
301C23×C4C23×C311yescharacteristic
302C23×C4C23×C311yescharacteristic
303C23×C4C23×C311yescharacteristic
304C23×C4C23×C311yescharacteristic
305C23×C4C23×C311yescharacteristic
306C23×C4C23×C311yescharacteristic
307C23×C4C23×C311yescharacteristic
308C23×C4C23×C311yescharacteristic
309C23×C4C23×C311yescharacteristic
310C23×C4C23×C311yescharacteristic
311C23×C4C23×C311yescharacteristic
312C23×C4C23×C311yescharacteristic
313C23×C4C23×C311yescharacteristic
314C23×C4C23×C311yescharacteristic
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—41no—
326C2×C4⋊C4—41no—
327C2×C42—22no—
328C2×C42—22no—
329C2×C42—22no—
330C2×C42—41no—
331C2×C42—41no—
332C2×C42—41no—
333#95—22no—
334#95—22no—
335#95—22no—
336#95—22no—
337#95—22no—
338#95—22no—
339#95—22no—
340#95—22no—
341#95—22no—
342#95—22no—
343#95—22no—
344#95—22no—
345#95—22no—
346#95—22no—
347#95—22no—
348#95—41no—
349#95—41no—
350#95—41no—
351#95—41no—
352#95—41no—
353#95—41no—
354#95—41no—
355#95—41no—
356#95—41no—
357#95—41no—
358#95—41no—
359#95C3×D414yes—
360#95C3×Q814yescomplemented
361C23×C3C22×D411yescharacteristic
362C23×C3C22×Q811yescharacteristic
363C23×C3C2×#4111yescharacteristic
364C23×C3C2×#4111yescharacteristic
365C23×C3C2×#4111yescharacteristic
366C23×C3C2×#4111yescharacteristic
367C23×C3C2×#4111yescharacteristic
368C23×C3C2×#4111yescharacteristic
369C23×C3C2×#4111yescharacteristic
370C23×C3H(5,𝔽2)11yescharacteristic
371C23×C3H(5,𝔽2)11yescharacteristic
372C23×C3H(5,𝔽2)11yescharacteristic
373C23×C32−1+411yescharacteristic
374C23×C32−1+411yescharacteristic
375C23×C32−1+411yescharacteristic
376C3×Q8—416no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
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—41no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
416C2×C3×C4—41no—
417C2×C3×C4—41no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
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#12414yes—
481C2×C3×C4#12614yes—
482C24C24×C311yescharacteristic
483C2×Q8—28no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—44no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
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×C4C2×C3×D412yes—
583C22×C4C2×C3×D412yes—
584C22×C4C2×C3×D412yes—
585C22×C4C2×C3×Q812yes—
586C22×C4C2×C3×Q812yes—
587C22×C4C2×C3×Q812yes—
588C22×C4C3×#4112yes—
589C22×C4C3×#4112yes—
590C22×C4C3×#4112yes—
591C22×C4C3×#4112yes—
592C22×C4C3×#4112yes—
593C22×C4C3×#4112yes—
594C22×C4C3×#4112yes—
595C4⋊C4—44no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C42—44no—
600C42—44no—
601C22×C3#52511yescharacteristic
602C22×C3C2×#12411yescharacteristic
603C22×C3C2×#12611yescharacteristic
604C22×C3#52911yescharacteristic
605C22×C3#53311yescharacteristic
606C22×C3#53311yescharacteristic
607C22×C3#53711yescharacteristic
608C22×C3#53811yescharacteristic
609C22×C3#53811yescharacteristic
610C22×C3#53911yescharacteristic
611C22×C3#54111yescharacteristic
612C22×C3#54111yescharacteristic
613C22×C3#54211yescharacteristic
614C22×C3#54211yescharacteristic
615C22×C3#54411yescharacteristic
616C22×C3#54611yescharacteristic
617C22×C3#54611yescharacteristic
618C22×C3#54711yescharacteristic
619C22×C3D4×Q811yescharacteristic
620C22×C3#55111yescharacteristic
621C22×C3#55111yescharacteristic
622C22×C3#55111yescharacteristic
623C22×C3#55211yescharacteristic
624C22×C3#55211yescharacteristic
625C22×C3#55411yescharacteristic
626C22×C3#55411yescharacteristic
627C22×C3#55611yescharacteristic
628C22×C3#55611yescharacteristic
629C22×C3#55611yescharacteristic
630C22×C3#55611yescharacteristic
631C22×C3#55711yescharacteristic
632C22×C3#55911yescharacteristic
633C22×C3#55911yescharacteristic
634C22×C3#56211yescharacteristic
635C22×C3#56311yescharacteristic
636C3×C4—24no—
637C3×C4—24no—
638C3×C4—42no—
639C3×C4—42no—
640C3×C4—42no—
641C3×C4—42no—
642C3×C4—42no—
643C3×C4—42no—
644C3×C4—42no—
645C3×C4—81no—
646C3×C4—81no—
647C3×C4—81no—
648C3×C4—81no—
649C3×C4—81no—
650C3×C4—81no—
651C23C22×C3×D411yescharacteristic
652C23C22×C3×Q811yescharacteristic
653C23C2×C3×#4111yescharacteristic
654C23C2×C3×#4111yescharacteristic
655C23C2×C3×#4111yescharacteristic
656C23C2×C3×#4111yescharacteristic
657C23C2×C3×#4111yescharacteristic
658C23C2×C3×#4111yescharacteristic
659C23C2×C3×#4111yescharacteristic
660C23C3×H(5,𝔽2)11yescharacteristic
661C23C3×H(5,𝔽2)11yescharacteristic
662C23C3×H(5,𝔽2)11yescharacteristic
663C23C3×2−1+411yescharacteristic
664C23C3×2−1+411yescharacteristic
665C23C3×2−1+411yescharacteristic
666Q8—416no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
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×C4C3×#12414yes—
771C2×C4C3×#12614yes—
772C2×C3#246211yescharacteristic
773C2×C3#248011yescharacteristic
774C2×C3#248811yescharacteristic
775C2×C3#249211yescharacteristic
776C2×C3#251111yescharacteristic
777C2×C3#251411yescharacteristic
778C2×C3#258911yescharacteristic
779C2×C3#259211yescharacteristic
780C2×C3#260511yescharacteristic
781C2×C3#270411yescharacteristic
782C2×C3#271511yescharacteristic
783C2×C3#275111yescharacteristic
784C2×C3#276211yescharacteristic
785C2×C3#279811yescharacteristic
786C2×C3#280511yescharacteristic
787C22C3×#52511yescharacteristic
788C22C2×C3×#12411yescharacteristic
789C22C2×C3×#12611yescharacteristic
790C22C3×#52911yescharacteristic
791C22C3×#53311yescharacteristic
792C22C3×#53311yescharacteristic
793C22C3×#53711yescharacteristic
794C22C3×#53811yescharacteristic
795C22C3×#53811yescharacteristic
796C22C3×#53911yescharacteristic
797C22C3×#54111yescharacteristic
798C22C3×#54111yescharacteristic
799C22C3×#54211yescharacteristic
800C22C3×#54211yescharacteristic
801C22C3×#54411yescharacteristic
802C22C3×#54611yescharacteristic
803C22C3×#54611yescharacteristic
804C22C3×#54711yescharacteristic
805C22C3×D4×Q811yescharacteristic
806C22C3×#55111yescharacteristic
807C22C3×#55111yescharacteristic
808C22C3×#55111yescharacteristic
809C22C3×#55211yescharacteristic
810C22C3×#55211yescharacteristic
811C22C3×#55411yescharacteristic
812C22C3×#55411yescharacteristic
813C22C3×#55611yescharacteristic
814C22C3×#55611yescharacteristic
815C22C3×#55611yescharacteristic
816C22C3×#55611yescharacteristic
817C22C3×#55711yescharacteristic
818C22C3×#55911yescharacteristic
819C22C3×#55911yescharacteristic
820C22C3×#56211yescharacteristic
821C22C3×#56311yescharacteristic
822C4—24no—
823C4—24no—
824C4—42no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—42no—
830C4—42no—
831C4—81no—
832C4—81no—
833C4—81no—
834C4—81no—
835C4—81no—
836C4—81no—
837C3#1569011yescharacteristic, direct product factor, Sylow
838C2C3×#246211yescharacteristic
839C2C3×#248011yescharacteristic
840C2C3×#248811yescharacteristic
841C2C3×#249211yescharacteristic
842C2C3×#251111yescharacteristic
843C2C3×#251411yescharacteristic
844C2C3×#258911yescharacteristic
845C2C3×#259211yescharacteristic
846C2C3×#260511yescharacteristic
847C2C3×#270411yescharacteristic
848C2C3×#271511yescharacteristic
849C2C3×#275111yescharacteristic
850C2C3×#276211yescharacteristic
851C2C3×#279811yescharacteristic
852C2C3×#280511yescharacteristic
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. #15690C3direct (N × H)
136. C3×#95Q8semidirect
360. #95C3×Q8semidirect
837. C3#15690direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4002
C2×C3×#3912
C3×#14462
C3×#14452
C3×#14432
C3×#14422
C3×#14412
C3×#14362
C3×C4⋊#952
C3×#14342
#156903