Finite Group Databasebeta

← C3×#24362 #10642969

Subgroups — C3×#24362 #10642969

Order 768.

1484 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#135C211yesmaximal, characteristic, complemented
2C2×C3×#464C211yesmaximal, characteristic, complemented
3C2×C3×#460C211yesmaximal, characteristic, complemented
4C2×C3×#449C211yesmaximal, characteristic, complemented
5C3×#2431C211yesmaximal, characteristic, complemented
6C3×#2341C211yesmaximal, characteristic, complemented
7C3×#2055C211yesmaximal, characteristic, complemented
8C3×#2054C211yesmaximal, characteristic, complemented
9C3×#2012C211yesmaximal, characteristic, complemented
10C3×#2011C211yesmaximal, characteristic, complemented
11C3×#1893C211yesmaximal, characteristic, complemented
12C3×#1880C211yesmaximal, characteristic, complemented
13C3×#1878C211yesmaximal, characteristic, complemented
14C3×#1850C211yesmaximal, characteristic, complemented
15C3×#1788C211yesmaximal, characteristic, complemented
16#24362C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×#41C2211yescharacteristic
19C2×C3×#135—24no—
20C2×C3×#135—24no—
21C2×C3×#135—24no—
22C22×C3×Q16C2211yescharacteristic
23C22×C3×SD16C2211yescharacteristic
24C22×C3×SD16C2211yescharacteristic
25C22×C3×SD16C2211yescharacteristic
26C22×C3×D8C2211yescharacteristic
27C22×C3×D8C2211yescharacteristic
28C23×C3×C8C2211yescharacteristic
29C2×C3×#127C2211yescharacteristic
30C2×C3×#124C2211yescharacteristic
31C2×C3×#121C2211yescharacteristic
32C2×C3×C4×Q8C2211yescharacteristic
33C2×C3×C4×Q8C2211yescharacteristic
34C3×#464—24no—
35C3×#460—24no—
36C3×#449—24no—
37C2×C3×C4⋊C8C2211yescharacteristic
38C2×C3×C4⋊C8C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×C22⋊C8C2211yescharacteristic
48C3×#392—21no—
49C3×#392—21no—
50C3×#391C2211yescharacteristic
51C3×#390—21no—
52C3×#390—21no—
53C3×#390C2211yescharacteristic
54C3×#390C2211yescharacteristic
55C3×#390C2211yescharacteristic
56C3×#386—21no—
57C3×#386—21no—
58C3×#380—21no—
59C3×#380C2211yescharacteristic
60C3×C4×C22⋊C4—21no—
61C3×C4×C22⋊C4C2211yescharacteristic
62C3×#340C2211yescharacteristic
63C3×#340C2211yescharacteristic
64C3×#336C2211yescharacteristic
65C3×#336C2211yescharacteristic
66C22×#135C2×C311yescharacteristic, complemented
67C2×#464C2×C311yescharacteristic, complemented
68C2×#460C2×C311yescharacteristic, complemented
69C2×#449C2×C311yescharacteristic, complemented
70#2431C2×C311yescharacteristic, complemented
71#2341C2×C311yescharacteristic, complemented
72#2055C2×C311yescharacteristic, complemented
73#2054C2×C311yescharacteristic, complemented
74#2012C2×C311yescharacteristic, complemented
75#2011C2×C311yescharacteristic, complemented
76#1893C2×C311yescharacteristic, complemented
77#1880C2×C311yescharacteristic, complemented
78#1878C2×C311yescharacteristic, complemented
79#1850C2×C311yescharacteristic, complemented
80#1788C2×C311yescharacteristic, complemented
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41—22no—
87C2×C3×#41—22no—
88C2×C3×#41—41no—
89C2×C3×#41—41no—
90C2×C3×#41—41no—
91C2×C3×#41—41no—
92C2×C3×#41D414yescomplemented
93C22×C3×Q8C2311yescharacteristic
94C22×C3×Q8C2311yescharacteristic
95C22×C3×D4—21no—
96C22×C3×D4—21no—
97C22×C3×D4—21no—
98C22×C3×D4—21no—
99C22×C3×D4—21no—
100C22×C3×D4C2311yescharacteristic
101C22×C3×D4C2311yescharacteristic
102C22×C3×D4C2311yescharacteristic
103C23×C3×C4—21no—
104C23×C3×C4—21no—
105C23×C3×C4C2311yescharacteristic
106C3×#135—232no—
107C2×C3×Q16—22no—
108C2×C3×Q16—22no—
109C2×C3×Q16D414yescomplemented
110C2×C3×SD16—22no—
111C2×C3×SD16—22no—
112C2×C3×SD16—22no—
113C2×C3×SD16—22no—
114C2×C3×SD16—22no—
115C2×C3×SD16—22no—
116C2×C3×SD16—22no—
117C2×C3×SD16—22no—
118C2×C3×SD16D414yescomplemented
119C2×C3×D8—22no—
120C2×C3×D8—22no—
121C2×C3×D8—22no—
122C2×C3×D8—22no—
123C2×C3×D8—41no—
124C2×C3×D8—41no—
125C22×C3×C8—22no—
126C22×C3×C8—22no—
127C22×C3×C8—22no—
128C22×C3×C8C2311yescharacteristic
129C22×C3×C8C2311yescharacteristic
130C22×C3×C8C2311yescharacteristic
131C22×C3×C8C2311yescharacteristic
132C3×#127—22no—
133C3×#127—41no—
134C3×#124—22no—
135C3×#124—41no—
136C3×#121—22no—
137C3×#121—22no—
138C3×C4×Q8—22no—
139C3×C4×Q8—22no—
140C3×C4×Q8—41no—
141C3×C4×Q8—41no—
142C2×C3×C4⋊C4—21no—
143C2×C3×C4⋊C4—21no—
144C2×C3×C4⋊C4C2311yescharacteristic
145C2×C3×C4⋊C4C2311yescharacteristic
146C2×C3×C4⋊C4C2311yescharacteristic
147C2×C3×C22⋊C4—21no—
148C2×C3×C22⋊C4—21no—
149C2×C3×C22⋊C4—21no—
150C2×C3×C22⋊C4—21no—
151C2×C3×C22⋊C4—21no—
152C2×C3×C22⋊C4—21no—
153C2×C3×C22⋊C4—21no—
154C2×C3×C22⋊C4—21no—
155C2×C3×C22⋊C4—21no—
156C2×C3×C22⋊C4—21no—
157C2×C3×C22⋊C4D411yescharacteristic
158C2×C3×C22⋊C4D411yescharacteristic
159C2×C3×C42—21no—
160C2×C3×C42—21no—
161C2×C3×C42C2311yescharacteristic
162C2×C3×C42C2311yescharacteristic
163C3×C4⋊C8—22no—
164C3×C4⋊C8—22no—
165C3×#103—22no—
166C3×#103—22no—
167C3×#103—41no—
168C3×#102—22no—
169C3×#102—22no—
170C3×#102—22no—
171C3×#102—22no—
172C3×#102—41no—
173C3×C22⋊C8—22no—
174C3×#95—21no—
175C3×#95—21no—
176C3×#95—21no—
177C3×#95D411yescharacteristic
178C3×#95D411yescharacteristic
179C22×#41C22×C311yescharacteristic
180C22×#41C22×C311yescharacteristic
181C2×#135—24no—
182C2×#135—24no—
183C2×#135—24no—
184C22×Q16C22×C311yescharacteristic
185C22×SD16C22×C311yescharacteristic
186C22×SD16C22×C311yescharacteristic
187C22×SD16C22×C311yescharacteristic
188C22×D8C22×C311yescharacteristic
189C22×D8C22×C311yescharacteristic
190C23×C8C22×C311yescharacteristic
191C2×#127C22×C311yescharacteristic
192C2×#124C22×C311yescharacteristic
193C2×#121C22×C311yescharacteristic
194C2×C4×Q8C22×C311yescharacteristic
195C2×C4×Q8C22×C311yescharacteristic
196#464—24no—
197#460—24no—
198#449—24no—
199C2×C4⋊C8C22×C311yescharacteristic
200C2×C4⋊C8C22×C311yescharacteristic
201C2×#103C22×C311yescharacteristic
202C2×#103C22×C311yescharacteristic
203C2×#103C22×C311yescharacteristic
204C2×#102C22×C311yescharacteristic
205C2×#102C22×C311yescharacteristic
206C2×#102C22×C311yescharacteristic
207C2×#102C22×C311yescharacteristic
208C2×#102C22×C311yescharacteristic
209C2×C22⋊C8C22×C311yescharacteristic
210#392—21no—
211#392—21no—
212#391C22×C311yescharacteristic
213#390—21no—
214#390—21no—
215#390C22×C311yescharacteristic
216#390C22×C311yescharacteristic
217#390C22×C311yescharacteristic
218#386—21no—
219#386—21no—
220#380—21no—
221#380C22×C311yescharacteristic
222C4×C22⋊C4—21no—
223C4×C22⋊C4C22×C311yescharacteristic
224#340C22×C311yescharacteristic
225#340C22×C311yescharacteristic
226#336C22×C311yescharacteristic
227#336C22×C311yescharacteristic
228C24×C3—21no—
229C24×C3—21no—
230C24×C3—21no—
231C24×C3C2×D411yescharacteristic
232C3×#41—28no—
233C3×#41—28no—
234C3×#41—44no—
235C3×#41—44no—
236C3×#41—44no—
237C3×#41—44no—
238C3×#41—44no—
239C3×#41—44no—
240C2×C3×Q8—21no—
241C2×C3×Q8—21no—
242C2×C3×Q8—21no—
243C2×C3×Q8—21no—
244C2×C3×Q8—21no—
245C2×C3×Q8—21no—
246C2×C3×Q8—21no—
247C2×C3×Q8—21no—
248C2×C3×Q8C2×D412yes—
249C2×C3×Q8C2×D412yes—
250C2×C3×Q8C2×D412yes—
251C2×C3×Q8C2×D412yes—
252C2×C3×D4—24no—
253C2×C3×D4—21no—
254C2×C3×D4—21no—
255C2×C3×D4—21no—
256C2×C3×D4—21no—
257C2×C3×D4—21no—
258C2×C3×D4—21no—
259C2×C3×D4—21no—
260C2×C3×D4—21no—
261C2×C3×D4—21no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4—21no—
265C2×C3×D4—21no—
266C2×C3×D4—21no—
267C2×C3×D4—21no—
268C2×C3×D4—21no—
269C2×C3×D4—42no—
270C2×C3×D4—42no—
271C2×C3×D4—42no—
272C2×C3×D4—42no—
273C2×C3×D4—42no—
274C2×C3×D4—42no—
275C2×C3×D4—42no—
276C2×C3×D4—42no—
277C2×C3×D4—42no—
278C2×C3×D4—42no—
279C2×C3×D4—81no—
280C2×C3×D4—81no—
281C2×C3×D4—81no—
282C2×C3×D4—81no—
283C2×C3×D4C2×D412yes—
284C2×C3×D4C2×D412yes—
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—24no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—42no—
296C22×C3×C4—42no—
297C22×C3×C4—42no—
298C22×C3×C4—42no—
299C22×C3×C4—42no—
300C22×C3×C4C2×D411yescharacteristic
301C22×C3×C4C2×D411yescharacteristic
302C22×C3×C4C2×D411yescharacteristic
303C22×C3×C4C2×D411yescharacteristic
304C22×C3×C4C2×D412yes—
305C22×C3×C4C2×D411yescharacteristic
306C22×C3×C4#4112yes—
307C22×C3×C4C2411yescharacteristic
308C3×Q16—28no—
309C3×SD16—28no—
310C3×SD16—28no—
311C3×SD16—44no—
312C3×D8—28no—
313C3×D8—44no—
314C2×C3×C8—28no—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8—21no—
322C2×C3×C8—21no—
323C2×C3×C8—21no—
324C2×C3×C8—21no—
325C2×C3×C8C2×D412yes—
326C2×C3×C8C2×D412yes—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—42no—
334C3×C4⋊C4—42no—
335C3×C22⋊C4—22no—
336C3×C22⋊C4—41no—
337C3×C22⋊C4—42no—
338C3×C22⋊C4—42no—
339C3×C22⋊C4—42no—
340C3×C22⋊C4—42no—
341C3×C22⋊C4—42no—
342C3×C22⋊C4—81no—
343C3×C22⋊C4—81no—
344C3×C22⋊C4—81no—
345C3×C22⋊C4—81no—
346C3×C22⋊C4—81no—
347C3×C42—21no—
348C3×C42—21no—
349C3×C42—21no—
350C3×C42—21no—
351C3×C42—42no—
352C3×C42—42no—
353C2×#41—22no—
354C2×#41—22no—
355C2×#41—22no—
356C2×#41—22no—
357C2×#41—22no—
358C2×#41—22no—
359C2×#41—22no—
360C2×#41—41no—
361C2×#41—41no—
362C2×#41—41no—
363C2×#41—41no—
364C2×#41C3×D414yescomplemented
365C22×Q8C23×C311yescharacteristic
366C22×Q8C23×C311yescharacteristic
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4—21no—
372C22×D4C23×C311yescharacteristic
373C22×D4C23×C311yescharacteristic
374C22×D4C23×C311yescharacteristic
375C23×C4—21no—
376C23×C4—21no—
377C23×C4C23×C311yescharacteristic
378#135—232no—
379C2×Q16—22no—
380C2×Q16—22no—
381C2×Q16C3×D414yescomplemented
382C2×SD16—22no—
383C2×SD16—22no—
384C2×SD16—22no—
385C2×SD16—22no—
386C2×SD16—22no—
387C2×SD16—22no—
388C2×SD16—22no—
389C2×SD16—22no—
390C2×SD16C3×D414yescomplemented
391C2×D8—22no—
392C2×D8—22no—
393C2×D8—22no—
394C2×D8—22no—
395C2×D8—41no—
396C2×D8—41no—
397C22×C8—22no—
398C22×C8—22no—
399C22×C8—22no—
400C22×C8C23×C311yescharacteristic
401C22×C8C23×C311yescharacteristic
402C22×C8C23×C311yescharacteristic
403C22×C8C23×C311yescharacteristic
404#127—22no—
405#127—41no—
406#124—22no—
407#124—41no—
408#121—22no—
409#121—22no—
410C4×Q8—22no—
411C4×Q8—22no—
412C4×Q8—41no—
413C4×Q8—41no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4C23×C311yescharacteristic
417C2×C4⋊C4C23×C311yescharacteristic
418C2×C4⋊C4C23×C311yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4C3×D411yescharacteristic
430C2×C22⋊C4C3×D411yescharacteristic
431C2×C42—21no—
432C2×C42—21no—
433C2×C42C23×C311yescharacteristic
434C2×C42C23×C311yescharacteristic
435C4⋊C8—22no—
436C4⋊C8—22no—
437#103—22no—
438#103—22no—
439#103—41no—
440#102—22no—
441#102—22no—
442#102—22no—
443#102—22no—
444#102—41no—
445C22⋊C8—22no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95C3×D411yescharacteristic
450#95C3×D411yescharacteristic
451C23×C3—21no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—21no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3—41no—
465C23×C3—41no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3#12112yes—
479C23×C3C22×D411yescharacteristic
480C3×Q8—22no—
481C3×Q8—22no—
482C3×Q8—22no—
483C3×Q8—22no—
484C3×Q8—22no—
485C3×Q8—41no—
486C3×Q8—41no—
487C3×Q8#12014yes—
488C3×D4—22no—
489C3×D4—22no—
490C3×D4—22no—
491C3×D4—22no—
492C3×D4—48no—
493C3×D4—48no—
494C3×D4—41no—
495C3×D4—41no—
496C3×D4—41no—
497C3×D4—41no—
498C3×D4—41no—
499C3×D4—41no—
500C3×D4—41no—
501C3×D4—41no—
502C3×D4—84no—
503C3×D4—84no—
504C3×D4—84no—
505C2×C3×C4—22no—
506C2×C3×C4—21no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—22no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—48no—
527C2×C3×C4—48no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4#12112yes—
540C2×C3×C4#13512yescomplemented
541C2×C3×C4C22×D411yescharacteristic
542C2×C3×C4C22×D411yescharacteristic
543C2×C3×C4C22×D411yescharacteristic
544C2×C3×C4C2×#4111yescharacteristic
545C2×C3×C4H(5,𝔽2)11yescharacteristic
546C2×C3×C4H(5,𝔽2)11yescharacteristic
547C3×C8—22no—
548C3×C8—22no—
549C3×C8—41no—
550C3×C8—41no—
551C24—21no—
552C24—21no—
553C24—21no—
554C24C2×C3×D411yescharacteristic
555#41—28no—
556#41—28no—
557#41—44no—
558#41—44no—
559#41—44no—
560#41—44no—
561#41—44no—
562#41—44no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8C2×C3×D412yes—
572C2×Q8C2×C3×D412yes—
573C2×Q8C2×C3×D412yes—
574C2×Q8C2×C3×D412yes—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—81no—
603C2×D4—81no—
604C2×D4—81no—
605C2×D4—81no—
606C2×D4C2×C3×D412yes—
607C2×D4C2×C3×D412yes—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—24no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4C2×C3×D411yescharacteristic
624C22×C4C2×C3×D411yescharacteristic
625C22×C4C2×C3×D411yescharacteristic
626C22×C4C2×C3×D411yescharacteristic
627C22×C4C2×C3×D412yes—
628C22×C4C2×C3×D411yescharacteristic
629C22×C4C3×#4112yes—
630C22×C4C24×C311yescharacteristic
631Q16—28no—
632SD16—28no—
633SD16—28no—
634SD16—44no—
635D8—28no—
636D8—44no—
637C2×C8—28no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8C2×C3×D412yes—
649C2×C8C2×C3×D412yes—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C22⋊C4—22no—
659C22⋊C4—41no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—81no—
666C22⋊C4—81no—
667C22⋊C4—81no—
668C22⋊C4—81no—
669C22⋊C4—81no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—42no—
675C42—42no—
676C22×C3—22no—
677C22×C3—22no—
678C22×C3—22no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—42no—
684C22×C3—42no—
685C22×C3—42no—
686C22×C3—42no—
687C22×C3—42no—
688C22×C3—42no—
689C22×C3—81no—
690C22×C3—81no—
691C22×C3—81no—
692C22×C3—81no—
693C22×C3—81no—
694C22×C3—81no—
695C22×C3—81no—
696C22×C3—81no—
697C22×C3—81no—
698C22×C3—81no—
699C22×C3—81no—
700C22×C3—81no—
701C22×C3—81no—
702C22×C3—81no—
703C22×C3—81no—
704C22×C3C2×#12111yescharacteristic
705C22×C3D4211yescharacteristic
706C22×C3D4211yescharacteristic
707C22×C3C2×#13511yescharacteristic
708C22×C3#57511yescharacteristic
709C22×C3#57611yescharacteristic
710C22×C3#57711yescharacteristic
711C3×C4—22no—
712C3×C4—24no—
713C3×C4—22no—
714C3×C4—42no—
715C3×C4—41no—
716C3×C4—41no—
717C3×C4—41no—
718C3×C4—81no—
719C3×C4—81no—
720C3×C4—81no—
721C3×C4C2×#12011yescharacteristic
722C3×C4#53411yescharacteristic
723C3×C4#54611yescharacteristic
724C3×C4#54611yescharacteristic
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—22no—
732C23—22no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23C3×#12112yes—
753C23C22×C3×D411yescharacteristic
754Q8—22no—
755Q8—22no—
756Q8—22no—
757Q8—22no—
758Q8—22no—
759Q8—41no—
760Q8—41no—
761Q8C3×#12014yes—
762D4—22no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—48no—
767D4—48no—
768D4—41no—
769D4—41no—
770D4—41no—
771D4—41no—
772D4—41no—
773D4—41no—
774D4—41no—
775D4—41no—
776D4—84no—
777D4—84no—
778D4—84no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—48no—
801C2×C4—48no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4C3×#12112yes—
814C2×C4C3×#13512yescomplemented
815C2×C4C22×C3×D411yescharacteristic
816C2×C4C22×C3×D411yescharacteristic
817C2×C4C22×C3×D411yescharacteristic
818C2×C4C2×C3×#4111yescharacteristic
819C2×C4C3×H(5,𝔽2)11yescharacteristic
820C2×C4C3×H(5,𝔽2)11yescharacteristic
821C8—22no—
822C8—22no—
823C8—41no—
824C8—41no—
825C2×C3—42no—
826C2×C3—82no—
827C2×C3—82no—
828C2×C3—161no—
829C2×C3#241011yescharacteristic
830C2×C3#303511yescharacteristic
831C2×C3#304511yescharacteristic
832C2×C3#326811yescharacteristic
833C2×C3#327111yescharacteristic
834C2×C3#328211yescharacteristic
835C2×C3#328711yescharacteristic
836C22—22no—
837C22—22no—
838C22—22no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22C2×C3×#12111yescharacteristic
865C22C3×D4211yescharacteristic
866C22C3×D4211yescharacteristic
867C22C2×C3×#13511yescharacteristic
868C22C3×#57511yescharacteristic
869C22C3×#57611yescharacteristic
870C22C3×#57711yescharacteristic
871C4—22no—
872C4—24no—
873C4—22no—
874C4—42no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—81no—
879C4—81no—
880C4—81no—
881C4C2×C3×#12011yescharacteristic
882C4C3×#53411yescharacteristic
883C4C3×#54611yescharacteristic
884C4C3×#54611yescharacteristic
885C3#2436211yescharacteristic, direct product factor, Sylow
886C2—42no—
887C2—82no—
888C2—82no—
889C2—161no—
890C2C3×#241011yescharacteristic
891C2C3×#303511yescharacteristic
892C2C3×#304511yescharacteristic
893C2C3×#326811yescharacteristic
894C2C3×#327111yescharacteristic
895C2C3×#328211yescharacteristic
896C2C3×#328711yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×#135C2semidirect
2. C2×C3×#464C2semidirect
3. C2×C3×#460C2semidirect
4. C2×C3×#449C2semidirect
5. C3×#2431C2semidirect
6. C3×#2341C2semidirect
7. C3×#2055C2semidirect
8. C3×#2054C2semidirect
9. C3×#2012C2semidirect
10. C3×#2011C2semidirect
11. C3×#1893C2semidirect
12. C3×#1880C2semidirect
13. C3×#1878C2semidirect
14. C3×#1850C2semidirect
15. C3×#1788C2semidirect
16. #24362C3direct (N × H)
66. C22×#135C2×C3semidirect
67. C2×#464C2×C3semidirect
68. C2×#460C2×C3semidirect
69. C2×#449C2×C3semidirect
70. #2431C2×C3semidirect
71. #2341C2×C3semidirect
72. #2055C2×C3semidirect
73. #2054C2×C3semidirect
74. #2012C2×C3semidirect
75. #2011C2×C3semidirect
76. #1893C2×C3semidirect
77. #1880C2×C3semidirect
78. #1878C2×C3semidirect
79. #1850C2×C3semidirect
80. #1788C2×C3semidirect
92. C2×C3×#41D4semidirect
109. C2×C3×Q16D4semidirect
118. C2×C3×SD16D4semidirect
364. C2×#41C3×D4semidirect
381. C2×Q16C3×D4semidirect
390. C2×SD16C3×D4semidirect
540. C2×C3×C4#135semidirect
814. C2×C4C3×#135semidirect
885. C3#24362direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1352
C2×C3×#4642
C2×C3×#4602
C2×C3×#4492
C3×#24312
C3×#23412
C3×#20552
C3×#20542
C3×#20122
C3×#20112
C3×#18932
C3×#18802
C3×#18782
C3×#18502
C3×#17882
#243623