Finite Group Databasebeta

← C3×#23938 #10642545

Subgroups — C3×#23938 #10642545

Order 768.

1308 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#529C211yesmaximal, characteristic, complemented
2C2×C3×#452C211yesmaximal, characteristic, complemented
3C2×C3×#449C211yesmaximal, characteristic
4C3×#2297C211yesmaximal, characteristic, complemented
5C3×#2026C211yesmaximal, characteristic, complemented
6C3×#2025C211yesmaximal, characteristic, complemented
7C3×#2015C211yesmaximal, characteristic, complemented
8C3×#2012C211yesmaximal, characteristic, complemented
9C3×#1880C211yesmaximal, characteristic, complemented
10C3×#1879C211yesmaximal, characteristic, complemented
11C3×#1878C211yesmaximal, characteristic, complemented
12C3×#1877C211yesmaximal, characteristic, complemented
13C3×#1875C211yesmaximal, characteristic, complemented
14C3×#1873C211yesmaximal, characteristic, complemented
15C3×#1817C211yesmaximal, characteristic, complemented
16#23938C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×SD16C2211yescharacteristic
21C22×C3×D8C2211yescharacteristic
22C3×#529—24no—
23C3×#529—24no—
24C2×C3×#126—21no—
25C2×C3×#125C2211yescharacteristic
26C2×C3×#124C2211yescharacteristic
27C2×C3×#123—21no—
28C2×C3×C22⋊Q8C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×C4×Q8C2211yescharacteristic
31C2×C3×C4×D4—21no—
32C2×C3×C4×D4C2211yescharacteristic
33C2×C3×#117—21no—
34C2×C3×#117C2211yescharacteristic
35C22×C3×C42C2211yescharacteristic
36C3×#452—24no—
37C3×#449—24no—
38C2×C3×#103C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×C22⋊C8C2211yescharacteristic
47C2×C3×C22⋊C8C2211yescharacteristic
48C3×#391C2211yescharacteristic
49C3×#391C2211yescharacteristic
50C3×#390C2211yescharacteristic
51C3×#390C2211yescharacteristic
52C3×#386—21no—
53C3×#386—21no—
54C3×C4×C22⋊C4—21no—
55C3×C4×C22⋊C4—21no—
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#529C2×C311yescharacteristic, complemented
65C2×#452C2×C311yescharacteristic, complemented
66C2×#449C2×C311yescharacteristic
67#2297C2×C311yescharacteristic, complemented
68#2026C2×C311yescharacteristic, complemented
69#2025C2×C311yescharacteristic, complemented
70#2015C2×C311yescharacteristic, complemented
71#2012C2×C311yescharacteristic, complemented
72#1880C2×C311yescharacteristic, complemented
73#1879C2×C311yescharacteristic, complemented
74#1878C2×C311yescharacteristic, complemented
75#1877C2×C311yescharacteristic, complemented
76#1875C2×C311yescharacteristic, complemented
77#1873C2×C311yescharacteristic, complemented
78#1817C2×C311yescharacteristic, complemented
79C2×C3×#41—22no—
80C2×C3×#41—22no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—41no—
84C2×C3×#41—41no—
85C22×C3×Q8C2311yescharacteristic
86C22×C3×Q8C2311yescharacteristic
87C22×C3×D4—21no—
88C22×C3×D4—21no—
89C22×C3×D4C2311yescharacteristic
90C22×C3×D4C2311yescharacteristic
91C23×C3×C4—21no—
92C23×C3×C4—21no—
93C23×C3×C4D411yescharacteristic
94C23×C3×C4D411yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C2×C3×Q16—22no—
97C2×C3×Q16—22no—
98C2×C3×Q16—41no—
99C2×C3×SD16—22no—
100C2×C3×SD16—22no—
101C2×C3×SD16—22no—
102C2×C3×SD16—22no—
103C2×C3×SD16—41no—
104C2×C3×SD16—41no—
105C2×C3×D8—22no—
106C2×C3×D8—22no—
107C2×C3×D8—41no—
108C22×C3×C8C2311yescharacteristic
109C22×C3×C8C2311yescharacteristic
110C22×C3×C8C2311yescharacteristic
111C22×C3×C8C2311yescharacteristic
112C3×#126—28no—
113C3×#125—22no—
114C3×#125—22no—
115C3×#124—22no—
116C3×#124—22no—
117C3×#123—28no—
118C3×C22⋊Q8—22no—
119C3×C22⋊Q8D414yes—
120C3×#121—22no—
121C3×#121D414yes—
122C3×C4×Q8—22no—
123C3×C4×Q8—22no—
124C3×C4×D4—28no—
125C3×C4×D4—22no—
126C3×C4×D4—22no—
127C3×#117—28no—
128C3×#117—41no—
129C3×#117—41no—
130C2×C3×C4⋊C4—21no—
131C2×C3×C4⋊C4—21no—
132C2×C3×C4⋊C4—21no—
133C2×C3×C4⋊C4—21no—
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C4⋊C4C2311yescharacteristic
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C4⋊C4C2311yescharacteristic
138C2×C3×C22⋊C4—21no—
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—21no—
141C2×C3×C22⋊C4—21no—
142C2×C3×C22⋊C4—21no—
143C2×C3×C22⋊C4—21no—
144C2×C3×C22⋊C4—21no—
145C2×C3×C22⋊C4—21no—
146C2×C3×C22⋊C4—21no—
147C2×C3×C22⋊C4—21no—
148C2×C3×C42—22no—
149C2×C3×C42—22no—
150C2×C3×C42—21no—
151C2×C3×C42—21no—
152C2×C3×C42D411yescharacteristic
153C2×C3×C42D411yescharacteristic
154C2×C3×C42C2311yescharacteristic
155C2×C3×C42C2311yescharacteristic
156C3×#103—22no—
157C3×#103—22no—
158C3×#103—41no—
159C3×#103—41no—
160C3×#102—22no—
161C3×#102—22no—
162C3×#102—41no—
163C3×#102—41no—
164C3×C22⋊C8—22no—
165C3×C22⋊C8—22no—
166C3×#95—21no—
167C3×#95—21no—
168C3×#95—21no—
169C3×#95—21no—
170C22×#41C22×C311yescharacteristic
171C22×Q16C22×C311yescharacteristic
172C22×SD16C22×C311yescharacteristic
173C22×SD16C22×C311yescharacteristic
174C22×D8C22×C311yescharacteristic
175#529—24no—
176#529—24no—
177C2×#126—21no—
178C2×#125C22×C311yescharacteristic
179C2×#124C22×C311yescharacteristic
180C2×#123—21no—
181C2×C22⋊Q8C22×C311yescharacteristic
182C2×#121C22×C311yescharacteristic
183C2×C4×Q8C22×C311yescharacteristic
184C2×C4×D4—21no—
185C2×C4×D4C22×C311yescharacteristic
186C2×#117—21no—
187C2×#117C22×C311yescharacteristic
188C22×C42C22×C311yescharacteristic
189#452—24no—
190#449—24no—
191C2×#103C22×C311yescharacteristic
192C2×#103C22×C311yescharacteristic
193C2×#103C22×C311yescharacteristic
194C2×#103C22×C311yescharacteristic
195C2×#102C22×C311yescharacteristic
196C2×#102C22×C311yescharacteristic
197C2×#102C22×C311yescharacteristic
198C2×#102C22×C311yescharacteristic
199C2×C22⋊C8C22×C311yescharacteristic
200C2×C22⋊C8C22×C311yescharacteristic
201#391C22×C311yescharacteristic
202#391C22×C311yescharacteristic
203#390C22×C311yescharacteristic
204#390C22×C311yescharacteristic
205#386—21no—
206#386—21no—
207C4×C22⋊C4—21no—
208C4×C22⋊C4—21no—
209#340C22×C311yescharacteristic
210#340C22×C311yescharacteristic
211#340C22×C311yescharacteristic
212#340C22×C311yescharacteristic
213#336C22×C311yescharacteristic
214#336C22×C311yescharacteristic
215#336C22×C311yescharacteristic
216#336C22×C311yescharacteristic
217C24×C3—21no—
218C24×C3—21no—
219C24×C3C2×D411yescharacteristic
220C3×#41—44no—
221C3×#41—44no—
222C3×#41—44no—
223C3×#41—44no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8—21no—
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
234C2×C3×Q8C2×D412yes—
235C2×C3×Q8#4112yes—
236C2×C3×D4—24no—
237C2×C3×D4—24no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—42no—
249C2×C3×D4—42no—
250C2×C3×D4—42no—
251C2×C3×D4—42no—
252C2×C3×D4C2×D412yes—
253C2×C3×D4#4112yes—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—24no—
259C22×C3×C4—24no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—22no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—41no—
270C22×C3×C4—41no—
271C22×C3×C4—41no—
272C22×C3×C4—42no—
273C22×C3×C4—42no—
274C22×C3×C4—42no—
275C22×C3×C4—42no—
276C22×C3×C4C2×D411yescharacteristic
277C22×C3×C4C2×D411yescharacteristic
278C22×C3×C4C2×D411yescharacteristic
279C22×C3×C4C2×D411yescharacteristic
280C22×C3×C4C2×D412yes—
281C22×C3×C4C2×D412yes—
282C22×C3×C4C2×D411yescharacteristic
283C22×C3×C4C2411yescharacteristic
284C3×Q16—44no—
285C3×SD16—44no—
286C3×SD16—44no—
287C3×D8—44no—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C2×C3×C8—21no—
298C2×C3×C8—21no—
299C2×C3×C8—21no—
300C3×C4⋊C4—24no—
301C3×C4⋊C4—24no—
302C3×C4⋊C4—24no—
303C3×C4⋊C4—24no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4C2×D412yes—
311C3×C4⋊C4C2×D412yes—
312C3×C22⋊C4—24no—
313C3×C22⋊C4—24no—
314C3×C22⋊C4—24no—
315C3×C22⋊C4—24no—
316C3×C22⋊C4—24no—
317C3×C22⋊C4—42no—
318C3×C22⋊C4—42no—
319C3×C22⋊C4—42no—
320C3×C22⋊C4—42no—
321C3×C22⋊C4—42no—
322C3×C42—24no—
323C3×C42—22no—
324C3×C42—22no—
325C3×C42—21no—
326C3×C42—21no—
327C3×C42—21no—
328C3×C42—21no—
329C3×C42—42no—
330C2×#41—22no—
331C2×#41—22no—
332C2×#41—22no—
333C2×#41—22no—
334C2×#41—41no—
335C2×#41—41no—
336C22×Q8C23×C311yescharacteristic
337C22×Q8C23×C311yescharacteristic
338C22×D4—21no—
339C22×D4—21no—
340C22×D4C23×C311yescharacteristic
341C22×D4C23×C311yescharacteristic
342C23×C4—21no—
343C23×C4—21no—
344C23×C4C3×D411yescharacteristic
345C23×C4C3×D411yescharacteristic
346C23×C4C23×C311yescharacteristic
347C2×Q16—22no—
348C2×Q16—22no—
349C2×Q16—41no—
350C2×SD16—22no—
351C2×SD16—22no—
352C2×SD16—22no—
353C2×SD16—22no—
354C2×SD16—41no—
355C2×SD16—41no—
356C2×D8—22no—
357C2×D8—22no—
358C2×D8—41no—
359C22×C8C23×C311yescharacteristic
360C22×C8C23×C311yescharacteristic
361C22×C8C23×C311yescharacteristic
362C22×C8C23×C311yescharacteristic
363#126—28no—
364#125—22no—
365#125—22no—
366#124—22no—
367#124—22no—
368#123—28no—
369C22⋊Q8—22no—
370C22⋊Q8C3×D414yes—
371#121—22no—
372#121C3×D414yes—
373C4×Q8—22no—
374C4×Q8—22no—
375C4×D4—28no—
376C4×D4—22no—
377C4×D4—22no—
378#117—28no—
379#117—41no—
380#117—41no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4C23×C311yescharacteristic
386C2×C4⋊C4C23×C311yescharacteristic
387C2×C4⋊C4C23×C311yescharacteristic
388C2×C4⋊C4C23×C311yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C42—21no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—21no—
403C2×C42C3×D411yescharacteristic
404C2×C42C3×D411yescharacteristic
405C2×C42C23×C311yescharacteristic
406C2×C42C23×C311yescharacteristic
407#103—22no—
408#103—22no—
409#103—41no—
410#103—41no—
411#102—22no—
412#102—22no—
413#102—41no—
414#102—41no—
415C22⋊C8—22no—
416C22⋊C8—22no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—22no—
428C23×C3—22no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3#12012yes—
442C23×C3C22×D411yescharacteristic
443C3×Q8—22no—
444C3×Q8—22no—
445C3×Q8—22no—
446C3×Q8—22no—
447C3×Q8—41no—
448C3×Q8—41no—
449C3×Q8—41no—
450C3×Q8—41no—
451C3×D4—22no—
452C3×D4—22no—
453C3×D4—22no—
454C3×D4—22no—
455C3×D4—48no—
456C3×D4—48no—
457C3×D4—41no—
458C3×D4—41no—
459C3×D4—41no—
460C3×D4—41no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—44no—
483C2×C3×C4—48no—
484C2×C3×C4—48no—
485C2×C3×C4—44no—
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#12012yes—
501C2×C3×C4#13512yes—
502C2×C3×C4C22×D411yescharacteristic
503C2×C3×C4C22×D411yescharacteristic
504C2×C3×C4C2×#4111yescharacteristic
505C2×C3×C4C2×#4111yescharacteristic
506C2×C3×C4H(5,𝔽2)11yescharacteristic
507C2×C3×C4H(5,𝔽2)11yescharacteristic
508C3×C8—41no—
509C3×C8—41no—
510C3×C8—41no—
511C3×C8—41no—
512C24—21no—
513C24—21no—
514C24C2×C3×D411yescharacteristic
515#41—44no—
516#41—44no—
517#41—44no—
518#41—44no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8C2×C3×D412yes—
530C2×Q8C3×#4112yes—
531C2×D4—24no—
532C2×D4—24no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4C2×C3×D412yes—
548C2×D4C3×#4112yes—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4C2×C3×D411yescharacteristic
572C22×C4C2×C3×D411yescharacteristic
573C22×C4C2×C3×D411yescharacteristic
574C22×C4C2×C3×D411yescharacteristic
575C22×C4C2×C3×D412yes—
576C22×C4C2×C3×D412yes—
577C22×C4C2×C3×D411yescharacteristic
578C22×C4C24×C311yescharacteristic
579Q16—44no—
580SD16—44no—
581SD16—44no—
582D8—44no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4C2×C3×D412yes—
606C4⋊C4C2×C3×D412yes—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—24no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C42—24no—
618C42—22no—
619C42—22no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—42no—
625C22×C3—22no—
626C22×C3—22no—
627C22×C3—22no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—42no—
633C22×C3—42no—
634C22×C3—42no—
635C22×C3—42no—
636C22×C3—42no—
637C22×C3—42no—
638C22×C3—81no—
639C22×C3—81no—
640C22×C3—81no—
641C22×C3—81no—
642C22×C3—81no—
643C22×C3—81no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3C2×#12011yescharacteristic
647C22×C3#52511yescharacteristic
648C22×C3#53511yescharacteristic
649C22×C3C2×#13511yescharacteristic
650C22×C3#57511yescharacteristic
651C22×C3#57511yescharacteristic
652C22×C3#57511yescharacteristic
653C3×C4—22no—
654C3×C4—22no—
655C3×C4—42no—
656C3×C4—42no—
657C3×C4—41no—
658C3×C4—42no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—42no—
662C3×C4—81no—
663C3×C4—81no—
664C3×C4#54611yescharacteristic
665C3×C4#54611yescharacteristic
666C3×C4#54611yescharacteristic
667C3×C4#54611yescharacteristic
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—22no—
675C23—22no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23C3×#12012yes—
689C23C22×C3×D411yescharacteristic
690Q8—22no—
691Q8—22no—
692Q8—22no—
693Q8—22no—
694Q8—41no—
695Q8—41no—
696Q8—41no—
697Q8—41no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—48no—
703D4—48no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—44no—
730C2×C4—48no—
731C2×C4—48no—
732C2×C4—44no—
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×C4C3×#12012yes—
748C2×C4C3×#13512yes—
749C2×C4C22×C3×D411yescharacteristic
750C2×C4C22×C3×D411yescharacteristic
751C2×C4C2×C3×#4111yescharacteristic
752C2×C4C2×C3×#4111yescharacteristic
753C2×C4C3×H(5,𝔽2)11yescharacteristic
754C2×C4C3×H(5,𝔽2)11yescharacteristic
755C8—41no—
756C8—41no—
757C8—41no—
758C8—41no—
759C2×C3—42no—
760C2×C3—82no—
761C2×C3—82no—
762C2×C3#240411yescharacteristic
763C2×C3#300211yescharacteristic
764C2×C3#300511yescharacteristic
765C2×C3#310211yescharacteristic
766C2×C3#311111yescharacteristic
767C2×C3#321211yescharacteristic
768C2×C3#321911yescharacteristic
769C22—22no—
770C22—22no—
771C22—22no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22C2×C3×#12011yescharacteristic
791C22C3×#52511yescharacteristic
792C22C3×#53511yescharacteristic
793C22C2×C3×#13511yescharacteristic
794C22C3×#57511yescharacteristic
795C22C3×#57511yescharacteristic
796C22C3×#57511yescharacteristic
797C4—22no—
798C4—22no—
799C4—42no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—41no—
805C4—42no—
806C4—81no—
807C4—81no—
808C4C3×#54611yescharacteristic
809C4C3×#54611yescharacteristic
810C4C3×#54611yescharacteristic
811C4C3×#54611yescharacteristic
812C3#2393811yescharacteristic, direct product factor, Sylow
813C2—42no—
814C2—82no—
815C2—82no—
816C2C3×#240411yescharacteristic
817C2C3×#300211yescharacteristic
818C2C3×#300511yescharacteristic
819C2C3×#310211yescharacteristic
820C2C3×#311111yescharacteristic
821C2C3×#321211yescharacteristic
822C2C3×#321911yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#449C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C22×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#529C2semidirect
2. C2×C3×#452C2semidirect
4. C3×#2297C2semidirect
5. C3×#2026C2semidirect
6. C3×#2025C2semidirect
7. C3×#2015C2semidirect
8. C3×#2012C2semidirect
9. C3×#1880C2semidirect
10. C3×#1879C2semidirect
11. C3×#1878C2semidirect
12. C3×#1877C2semidirect
13. C3×#1875C2semidirect
14. C3×#1873C2semidirect
15. C3×#1817C2semidirect
16. #23938C3direct (N × H)
64. C2×#529C2×C3semidirect
65. C2×#452C2×C3semidirect
67. #2297C2×C3semidirect
68. #2026C2×C3semidirect
69. #2025C2×C3semidirect
70. #2015C2×C3semidirect
71. #2012C2×C3semidirect
72. #1880C2×C3semidirect
73. #1879C2×C3semidirect
74. #1878C2×C3semidirect
75. #1877C2×C3semidirect
76. #1875C2×C3semidirect
77. #1873C2×C3semidirect
78. #1817C2×C3semidirect
812. C3#23938direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5292
C2×C3×#4522
C2×C3×#4492
C3×#22972
C3×#20262
C3×#20252
C3×#20152
C3×#20122
C3×#18802
C3×#18792
C3×#18782
C3×#18772
C3×#18752
C3×#18732
C3×#18172
#239383