Finite Group Databasebeta

← C3×#24402 #10643009

Subgroups — C3×#24402 #10643009

Order 768.

1358 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#575C211yesmaximal, characteristic, complemented
2C2×C3×#472C211yesmaximal, characteristic, complemented
3C2×C3×#471C211yesmaximal, characteristic, complemented
4C3×#3006C211yesmaximal, characteristic, complemented
5C2×C3×#449C211yesmaximal, characteristic, complemented
6C3×#2880C211yesmaximal, characteristic, complemented
7C3×#2052C211yesmaximal, characteristic, complemented
8C3×#2051C211yesmaximal, characteristic, complemented
9C3×#2019C211yesmaximal, characteristic, complemented
10C3×#2018C211yesmaximal, characteristic, complemented
11C3×#1908C211yesmaximal, characteristic, complemented
12C3×#1907C211yesmaximal, characteristic, complemented
13C3×#1900C211yesmaximal, characteristic, complemented
14C3×#1855C211yesmaximal, characteristic, complemented
15C3×#1785C211yesmaximal, characteristic, complemented
16#24402C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×#41C2211yescharacteristic
19C3×#575—24no—
20C3×#575—24no—
21C2×C3×#137—21no—
22C2×C3×#137C2211yescharacteristic
23C2×C3×#137C2211yescharacteristic
24C2×C3×AGL(1,ℤ/8)—21no—
25C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
26C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
27C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
28C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
29C2×C3×#135—21no—
30C2×C3×#135—21no—
31C22×C3×SD16C2211yescharacteristic, complemented
32C22×C3×D8C2211yescharacteristic, complemented
33C2×C3×#131C2211yescharacteristic
34C2×C3×#131C2211yescharacteristic
35C22×C3×M16C2211yescharacteristic
36C2×C3×#121C2211yescharacteristic
37C3×#472—24no—
38C3×#471—24no—
39C3×#449—21no—
40C3×#449—21no—
41C3×#449—21no—
42C3×#449—21no—
43C3×#449—21no—
44C3×#449—21no—
45C3×#448—21no—
46C3×#447—21no—
47C2×C3×#108C2211yescharacteristic, complemented
48C2×C3×#108C2211yescharacteristic, complemented
49C3×#417C2211yescharacteristic
50C3×#417C2211yescharacteristic
51C2×C3×#103C2211yescharacteristic, complemented
52C2×C3×#102C2211yescharacteristic, complemented
53C2×C3×#101C2211yescharacteristic, complemented
54C2×C3×#101C2211yescharacteristic, complemented
55C2×C3×#100C2211yescharacteristic, complemented
56C2×C3×#100C2211yescharacteristic, complemented
57C2×C3×#100C2211yescharacteristic, complemented
58C2×C3×#100C2211yescharacteristic, complemented
59C3×#408—21no—
60C3×#408—21no—
61C3×#408C2211yescharacteristic
62C3×#408C2211yescharacteristic
63C3×#407—21no—
64C3×#407C2211yescharacteristic
65C3×#407C2211yescharacteristic
66C2×C3×C22⋊C8—21no—
67C2×C3×C22⋊C8C2211yescharacteristic
68C3×#343C2211yescharacteristic, complemented
69C3×#343C2211yescharacteristic, complemented
70C3×#341C2211yescharacteristic, complemented
71C3×#341C2211yescharacteristic, complemented
72C2×#575C2×C311yescharacteristic, complemented
73C2×#472C2×C311yescharacteristic, complemented
74C2×#471C2×C311yescharacteristic, complemented
75#3006C2×C311yescharacteristic, complemented
76C2×#449C2×C311yescharacteristic, complemented
77#2880C2×C311yescharacteristic, complemented
78#2052C2×C311yescharacteristic, complemented
79#2051C2×C311yescharacteristic, complemented
80#2019C2×C311yescharacteristic, complemented
81#2018C2×C311yescharacteristic, complemented
82#1908C2×C311yescharacteristic, complemented
83#1907C2×C311yescharacteristic, complemented
84#1900C2×C311yescharacteristic, complemented
85#1855C2×C311yescharacteristic, complemented
86#1785C2×C311yescharacteristic, complemented
87C2×C3×#41—21no—
88C2×C3×#41—21no—
89C2×C3×#41—22no—
90C2×C3×#41—22no—
91C2×C3×#41—22no—
92C2×C3×#41—22no—
93C2×C3×#41—21no—
94C2×C3×#41—21no—
95C2×C3×#41—21no—
96C2×C3×#41—21no—
97C2×C3×#41—41no—
98C2×C3×#41—41no—
99C2×C3×#41—41no—
100C2×C3×#41—41no—
101C2×C3×#41D411yescharacteristic
102C2×C3×#41D411yescharacteristic
103C2×C3×#41C2311yescharacteristic
104C2×C3×#41C2311yescharacteristic
105C22×C3×Q8D411yescharacteristic
106C22×C3×Q8C2311yescharacteristic
107C22×C3×D4—21no—
108C22×C3×D4—21no—
109C22×C3×D4—21no—
110C22×C3×D4D411yescharacteristic
111C22×C3×D4C2311yescharacteristic
112C22×C3×D4C2311yescharacteristic
113C23×C3×C4—21no—
114C23×C3×C4—21no—
115C23×C3×C4C2311yescharacteristic
116C3×#137—28no—
117C3×#137—22no—
118C3×#137—22no—
119C3×#137—22no—
120C3×#137D414yescomplemented
121C3×AGL(1,ℤ/8)—28no—
122C3×AGL(1,ℤ/8)—22no—
123C3×AGL(1,ℤ/8)—22no—
124C3×AGL(1,ℤ/8)—22no—
125C3×AGL(1,ℤ/8)—22no—
126C3×AGL(1,ℤ/8)—22no—
127C3×AGL(1,ℤ/8)—41no—
128C3×AGL(1,ℤ/8)—41no—
129C3×AGL(1,ℤ/8)D414yescomplemented
130C3×#135—28no—
131C3×#135—28no—
132C2×C3×Q16—21no—
133C2×C3×Q16—21no—
134C2×C3×SD16—21no—
135C2×C3×SD16—21no—
136C2×C3×SD16—21no—
137C2×C3×SD16—21no—
138C2×C3×SD16—22no—
139C2×C3×SD16—21no—
140C2×C3×SD16—21no—
141C2×C3×SD16—21no—
142C2×C3×SD16—21no—
143C2×C3×SD16—41no—
144C2×C3×D8—21no—
145C2×C3×D8—21no—
146C2×C3×D8—22no—
147C2×C3×D8—21no—
148C2×C3×D8—21no—
149C2×C3×D8—21no—
150C2×C3×D8—21no—
151C2×C3×D8—41no—
152C3×#131—22no—
153C3×#131—22no—
154C3×#131—41no—
155C3×#131—41no—
156C2×C3×M16—21no—
157C2×C3×M16—22no—
158C2×C3×M16—22no—
159C2×C3×M16—21no—
160C2×C3×M16—21no—
161C2×C3×M16C2311yescharacteristic
162C2×C3×M16C2311yescharacteristic
163C2×C3×M16C2311yescharacteristic
164C2×C3×M16C2311yescharacteristic
165C2×C3×M16C2311yescharacteristic
166C2×C3×M16C2311yescharacteristic
167C22×C3×C8—21no—
168C22×C3×C8—21no—
169C22×C3×C8—21no—
170C22×C3×C8C2311yescharacteristic
171C22×C3×C8C2311yescharacteristic
172C3×#121—21no—
173C3×#121—21no—
174C3×#121—21no—
175C3×#121—21no—
176C2×C3×C4⋊C4C2311yescharacteristic
177C2×C3×C22⋊C4—21no—
178C3×#108—22no—
179C3×#108—22no—
180C3×#103—21no—
181C3×#103—21no—
182C3×#103—21no—
183C3×#103—21no—
184C3×#102—21no—
185C3×#102—21no—
186C3×#102—21no—
187C3×#102—21no—
188C3×#101—22no—
189C3×#101—41no—
190C3×#100—22no—
191C3×#100—22no—
192C3×#100—22no—
193C3×#100—41no—
194C3×C22⋊C8—21no—
195C3×C22⋊C8—21no—
196C3×C22⋊C8—21no—
197C3×C22⋊C8—21no—
198C3×C22⋊C8—21no—
199C3×C22⋊C8—21no—
200C3×C22⋊C8—21no—
201C3×C22⋊C8—21no—
202C3×C22⋊C8D411yescharacteristic
203C3×C22⋊C8D411yescharacteristic
204C3×C22⋊C8D411yescharacteristic
205C3×C22⋊C8D411yescharacteristic
206C22×#41C22×C311yescharacteristic
207C22×#41C22×C311yescharacteristic
208#575—24no—
209#575—24no—
210C2×#137—21no—
211C2×#137C22×C311yescharacteristic
212C2×#137C22×C311yescharacteristic
213C2×AGL(1,ℤ/8)—21no—
214C2×AGL(1,ℤ/8)C22×C311yescharacteristic
215C2×AGL(1,ℤ/8)C22×C311yescharacteristic
216C2×AGL(1,ℤ/8)C22×C311yescharacteristic
217C2×AGL(1,ℤ/8)C22×C311yescharacteristic
218C2×#135—21no—
219C2×#135—21no—
220C22×SD16C22×C311yescharacteristic, complemented
221C22×D8C22×C311yescharacteristic, complemented
222C2×#131C22×C311yescharacteristic
223C2×#131C22×C311yescharacteristic
224C22×M16C22×C311yescharacteristic
225C2×#121C22×C311yescharacteristic
226#472—24no—
227#471—24no—
228#449—21no—
229#449—21no—
230#449—21no—
231#449—21no—
232#449—21no—
233#449—21no—
234#448—21no—
235#447—21no—
236C2×#108C22×C311yescharacteristic, complemented
237C2×#108C22×C311yescharacteristic, complemented
238#417C22×C311yescharacteristic
239#417C22×C311yescharacteristic
240C2×#103C22×C311yescharacteristic, complemented
241C2×#102C22×C311yescharacteristic, complemented
242C2×#101C22×C311yescharacteristic, complemented
243C2×#101C22×C311yescharacteristic, complemented
244C2×#100C22×C311yescharacteristic, complemented
245C2×#100C22×C311yescharacteristic, complemented
246C2×#100C22×C311yescharacteristic, complemented
247C2×#100C22×C311yescharacteristic, complemented
248#408—21no—
249#408—21no—
250#408C22×C311yescharacteristic
251#408C22×C311yescharacteristic
252#407—21no—
253#407C22×C311yescharacteristic
254#407C22×C311yescharacteristic
255C2×C22⋊C8—21no—
256C2×C22⋊C8C22×C311yescharacteristic
257#343C22×C311yescharacteristic, complemented
258#343C22×C311yescharacteristic, complemented
259#341C22×C311yescharacteristic, complemented
260#341C22×C311yescharacteristic, complemented
261C24×C3—21no—
262C24×C3—21no—
263C24×C3—21no—
264C24×C3#4111yescharacteristic
265C3×#41—21no—
266C3×#41—21no—
267C3×#41—24no—
268C3×#41—24no—
269C3×#41—22no—
270C3×#41—22no—
271C3×#41—21no—
272C3×#41—21no—
273C3×#41—21no—
274C3×#41—21no—
275C3×#41—42no—
276C3×#41—42no—
277C3×#41—41no—
278C3×#41—41no—
279C3×#41—42no—
280C3×#41—42no—
281C3×#41—42no—
282C3×#41—42no—
283C3×#41—42no—
284C3×#41—42no—
285C3×#41—42no—
286C3×#41—42no—
287C3×#41C2×D412yes—
288C3×#41C2×D412yes—
289C2×C3×Q8—21no—
290C2×C3×Q8—21no—
291C2×C3×Q8—22no—
292C2×C3×Q8—21no—
293C2×C3×Q8—21no—
294C2×C3×Q8—21no—
295C2×C3×Q8—21no—
296C2×C3×Q8—41no—
297C2×C3×Q8C2×D412yes—
298C2×C3×Q8C2×D411yescharacteristic
299C2×C3×Q8C2×D411yescharacteristic
300C2×C3×D4—21no—
301C2×C3×D4—22no—
302C2×C3×D4—21no—
303C2×C3×D4—21no—
304C2×C3×D4—21no—
305C2×C3×D4—21no—
306C2×C3×D4—21no—
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4—21no—
311C2×C3×D4—21no—
312C2×C3×D4—21no—
313C2×C3×D4—21no—
314C2×C3×D4—21no—
315C2×C3×D4—21no—
316C2×C3×D4—21no—
317C2×C3×D4—41no—
318C2×C3×D4—42no—
319C2×C3×D4—42no—
320C2×C3×D4—42no—
321C2×C3×D4—42no—
322C2×C3×D4—41no—
323C2×C3×D4—41no—
324C2×C3×D4—41no—
325C2×C3×D4—41no—
326C2×C3×D4—82no—
327C2×C3×D4C2×D412yes—
328C2×C3×D4C2×D411yescharacteristic
329C2×C3×D4C2×D411yescharacteristic
330C22×C3×C4—21no—
331C22×C3×C4—21no—
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4—21no—
340C22×C3×C4—21no—
341C22×C3×C4—42no—
342C22×C3×C4—42no—
343C22×C3×C4—42no—
344C22×C3×C4—42no—
345C22×C3×C4—41no—
346C22×C3×C4—41no—
347C22×C3×C4C2×D411yescharacteristic
348C22×C3×C4C2×D411yescharacteristic
349C22×C3×C4C2×D411yescharacteristic
350C22×C3×C4C2×D411yescharacteristic
351C22×C3×C4#4111yescharacteristic
352C22×C3×C4C2411yescharacteristic
353C3×Q16—24no—
354C3×Q16—24no—
355C3×SD16—24no—
356C3×SD16—24no—
357C3×SD16—24no—
358C3×SD16—24no—
359C3×SD16—42no—
360C3×SD16—42no—
361C3×SD16—42no—
362C3×SD16—42no—
363C3×D8—24no—
364C3×D8—24no—
365C3×D8—42no—
366C3×D8—42no—
367C3×D8—42no—
368C3×D8—42no—
369C3×M16—24no—
370C3×M16—21no—
371C3×M16—21no—
372C3×M16—21no—
373C3×M16—21no—
374C3×M16—21no—
375C3×M16—21no—
376C3×M16—21no—
377C3×M16—21no—
378C3×M16—21no—
379C3×M16—21no—
380C3×M16—42no—
381C3×M16—42no—
382C3×M16C2×D412yes—
383C3×M16C2×D412yes—
384C2×C3×C8—24no—
385C2×C3×C8—21no—
386C2×C3×C8—21no—
387C2×C3×C8—21no—
388C2×C3×C8—21no—
389C2×C3×C8—21no—
390C2×C3×C8—21no—
391C2×C3×C8—21no—
392C2×C3×C8—21no—
393C2×C3×C8—21no—
394C2×C3×C8—21no—
395C2×C3×C8—42no—
396C2×C3×C8—42no—
397C2×C3×C8C2×D411yescharacteristic
398C2×C3×C8C2×D411yescharacteristic
399C2×C3×C8C2×D411yescharacteristic
400C2×C3×C8C2×D411yescharacteristic
401C3×C4⋊C4—21no—
402C3×C4⋊C4—21no—
403C3×C22⋊C4—41no—
404C3×C22⋊C4—41no—
405C2×#41—21no—
406C2×#41—21no—
407C2×#41—22no—
408C2×#41—22no—
409C2×#41—22no—
410C2×#41—22no—
411C2×#41—21no—
412C2×#41—21no—
413C2×#41—21no—
414C2×#41—21no—
415C2×#41—41no—
416C2×#41—41no—
417C2×#41—41no—
418C2×#41—41no—
419C2×#41C3×D411yescharacteristic
420C2×#41C3×D411yescharacteristic
421C2×#41C23×C311yescharacteristic
422C2×#41C23×C311yescharacteristic
423C22×Q8C3×D411yescharacteristic
424C22×Q8C23×C311yescharacteristic
425C22×D4—21no—
426C22×D4—21no—
427C22×D4—21no—
428C22×D4C3×D411yescharacteristic
429C22×D4C23×C311yescharacteristic
430C22×D4C23×C311yescharacteristic
431C23×C4—21no—
432C23×C4—21no—
433C23×C4C23×C311yescharacteristic
434#137—28no—
435#137—22no—
436#137—22no—
437#137—22no—
438#137C3×D414yescomplemented
439AGL(1,ℤ/8)—28no—
440AGL(1,ℤ/8)—22no—
441AGL(1,ℤ/8)—22no—
442AGL(1,ℤ/8)—22no—
443AGL(1,ℤ/8)—22no—
444AGL(1,ℤ/8)—22no—
445AGL(1,ℤ/8)—41no—
446AGL(1,ℤ/8)—41no—
447AGL(1,ℤ/8)C3×D414yescomplemented
448#135—28no—
449#135—28no—
450C2×Q16—21no—
451C2×Q16—21no—
452C2×SD16—21no—
453C2×SD16—21no—
454C2×SD16—21no—
455C2×SD16—21no—
456C2×SD16—22no—
457C2×SD16—21no—
458C2×SD16—21no—
459C2×SD16—21no—
460C2×SD16—21no—
461C2×SD16—41no—
462C2×D8—21no—
463C2×D8—21no—
464C2×D8—22no—
465C2×D8—21no—
466C2×D8—21no—
467C2×D8—21no—
468C2×D8—21no—
469C2×D8—41no—
470#131—22no—
471#131—22no—
472#131—41no—
473#131—41no—
474C2×M16—21no—
475C2×M16—22no—
476C2×M16—22no—
477C2×M16—21no—
478C2×M16—21no—
479C2×M16C23×C311yescharacteristic
480C2×M16C23×C311yescharacteristic
481C2×M16C23×C311yescharacteristic
482C2×M16C23×C311yescharacteristic
483C2×M16C23×C311yescharacteristic
484C2×M16C23×C311yescharacteristic
485C22×C8—21no—
486C22×C8—21no—
487C22×C8—21no—
488C22×C8C23×C311yescharacteristic
489C22×C8C23×C311yescharacteristic
490#121—21no—
491#121—21no—
492#121—21no—
493#121—21no—
494C2×C4⋊C4C23×C311yescharacteristic
495C2×C22⋊C4—21no—
496#108—22no—
497#108—22no—
498#103—21no—
499#103—21no—
500#103—21no—
501#103—21no—
502#102—21no—
503#102—21no—
504#102—21no—
505#102—21no—
506#101—22no—
507#101—41no—
508#100—22no—
509#100—22no—
510#100—22no—
511#100—41no—
512C22⋊C8—21no—
513C22⋊C8—21no—
514C22⋊C8—21no—
515C22⋊C8—21no—
516C22⋊C8—21no—
517C22⋊C8—21no—
518C22⋊C8—21no—
519C22⋊C8—21no—
520C22⋊C8C3×D411yescharacteristic
521C22⋊C8C3×D411yescharacteristic
522C22⋊C8C3×D411yescharacteristic
523C22⋊C8C3×D411yescharacteristic
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—22no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—42no—
532C23×C3—42no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—81no—
539C23×C3—81no—
540C23×C3—81no—
541C23×C3—81no—
542C23×C3—81no—
543C23×C3#12111yescharacteristic
544C23×C3#12111yescharacteristic
545C23×C3C2×#4111yescharacteristic
546C3×Q8—21no—
547C3×Q8—21no—
548C3×Q8—22no—
549C3×Q8—21no—
550C3×Q8—22no—
551C3×Q8—42no—
552C3×Q8—41no—
553C3×Q8—41no—
554C3×Q8#12012yes—
555C3×D4—22no—
556C3×D4—22no—
557C3×D4—21no—
558C3×D4—22no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—22no—
562C3×D4—42no—
563C3×D4—42no—
564C3×D4—42no—
565C3×D4—44no—
566C3×D4—44no—
567C3×D4—41no—
568C3×D4—41no—
569C3×D4—41no—
570C3×D4—41no—
571C3×D4—41no—
572C3×D4—41no—
573C3×D4—41no—
574C3×D4—41no—
575C3×D4—82no—
576C3×D4—82no—
577C3×D4#12012yes—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—22no—
593C2×C3×C4—42no—
594C2×C3×C4—42no—
595C2×C3×C4—42no—
596C2×C3×C4—44no—
597C2×C3×C4—44no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—81no—
604C2×C3×C4#12111yescharacteristic
605C2×C3×C4#12111yescharacteristic
606C2×C3×C4C22×D411yescharacteristic
607C2×C3×C4C22×D411yescharacteristic
608C2×C3×C4C22×D411yescharacteristic
609C2×C3×C4C22×D411yescharacteristic
610C2×C3×C4H(5,𝔽2)11yescharacteristic
611C2×C3×C4H(5,𝔽2)11yescharacteristic
612C3×C8—22no—
613C3×C8—22no—
614C3×C8—21no—
615C3×C8—21no—
616C3×C8—21no—
617C3×C8—21no—
618C3×C8—41no—
619C3×C8—41no—
620C3×C8—41no—
621C3×C8—41no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24C3×#4111yescharacteristic
626#41—21no—
627#41—21no—
628#41—24no—
629#41—24no—
630#41—22no—
631#41—22no—
632#41—21no—
633#41—21no—
634#41—21no—
635#41—21no—
636#41—42no—
637#41—42no—
638#41—41no—
639#41—41no—
640#41—42no—
641#41—42no—
642#41—42no—
643#41—42no—
644#41—42no—
645#41—42no—
646#41—42no—
647#41—42no—
648#41C2×C3×D412yes—
649#41C2×C3×D412yes—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—22no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—41no—
658C2×Q8C2×C3×D412yes—
659C2×Q8C2×C3×D411yescharacteristic
660C2×Q8C2×C3×D411yescharacteristic
661C2×D4—21no—
662C2×D4—22no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—41no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—41no—
684C2×D4—41no—
685C2×D4—41no—
686C2×D4—41no—
687C2×D4—82no—
688C2×D4C2×C3×D412yes—
689C2×D4C2×C3×D411yescharacteristic
690C2×D4C2×C3×D411yescharacteristic
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—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—41no—
707C22×C4—41no—
708C22×C4C2×C3×D411yescharacteristic
709C22×C4C2×C3×D411yescharacteristic
710C22×C4C2×C3×D411yescharacteristic
711C22×C4C2×C3×D411yescharacteristic
712C22×C4C3×#4111yescharacteristic
713C22×C4C24×C311yescharacteristic
714Q16—24no—
715Q16—24no—
716SD16—24no—
717SD16—24no—
718SD16—24no—
719SD16—24no—
720SD16—42no—
721SD16—42no—
722SD16—42no—
723SD16—42no—
724D8—24no—
725D8—24no—
726D8—42no—
727D8—42no—
728D8—42no—
729D8—42no—
730M16—24no—
731M16—21no—
732M16—21no—
733M16—21no—
734M16—21no—
735M16—21no—
736M16—21no—
737M16—21no—
738M16—21no—
739M16—21no—
740M16—21no—
741M16—42no—
742M16—42no—
743M16C2×C3×D412yes—
744M16C2×C3×D412yes—
745C2×C8—24no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—42no—
757C2×C8—42no—
758C2×C8C2×C3×D411yescharacteristic
759C2×C8C2×C3×D411yescharacteristic
760C2×C8C2×C3×D411yescharacteristic
761C2×C8C2×C3×D411yescharacteristic
762C4⋊C4—21no—
763C4⋊C4—21no—
764C22⋊C4—41no—
765C22⋊C4—41no—
766C22×C3—21no—
767C22×C3—21no—
768C22×C3—21no—
769C22×C3—21no—
770C22×C3—22no—
771C22×C3—21no—
772C22×C3—21no—
773C22×C3—21no—
774C22×C3—21no—
775C22×C3—41no—
776C22×C3—41no—
777C22×C3—41no—
778C22×C3—42no—
779C22×C3—41no—
780C22×C3—41no—
781C22×C3—81no—
782C22×C3—81no—
783C22×C3—82no—
784C22×C3—82no—
785C22×C3—84no—
786C22×C3—81no—
787C22×C3—81no—
788C22×C3—81no—
789C22×C3—81no—
790C22×C3—81no—
791C22×C3—161no—
792C22×C3—161no—
793C22×C3C2×#12111yescharacteristic
794C22×C3#54611yescharacteristic
795C22×C3#54611yescharacteristic
796C3×C4—21no—
797C3×C4—21no—
798C3×C4—22no—
799C3×C4—41no—
800C3×C4—42no—
801C3×C4—81no—
802C3×C4C2×#12011yescharacteristic
803C3×C4#53411yescharacteristic
804C3×C4D4211yescharacteristic
805C3×C4D4211yescharacteristic
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—22no—
811C23—41no—
812C23—41no—
813C23—42no—
814C23—42no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—81no—
821C23—81no—
822C23—81no—
823C23—81no—
824C23—81no—
825C23C3×#12111yescharacteristic
826C23C3×#12111yescharacteristic
827C23C2×C3×#4111yescharacteristic
828Q8—21no—
829Q8—21no—
830Q8—22no—
831Q8—21no—
832Q8—22no—
833Q8—42no—
834Q8—41no—
835Q8—41no—
836Q8C3×#12012yes—
837D4—22no—
838D4—22no—
839D4—21no—
840D4—22no—
841D4—21no—
842D4—21no—
843D4—22no—
844D4—42no—
845D4—42no—
846D4—42no—
847D4—44no—
848D4—44no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—41no—
857D4—82no—
858D4—82no—
859D4C3×#12012yes—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—22no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—44no—
879C2×C4—44no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—81no—
886C2×C4C3×#12111yescharacteristic
887C2×C4C3×#12111yescharacteristic
888C2×C4C22×C3×D411yescharacteristic
889C2×C4C22×C3×D411yescharacteristic
890C2×C4C22×C3×D411yescharacteristic
891C2×C4C22×C3×D411yescharacteristic
892C2×C4C3×H(5,𝔽2)11yescharacteristic
893C2×C4C3×H(5,𝔽2)11yescharacteristic
894C8—22no—
895C8—22no—
896C8—21no—
897C8—21no—
898C8—21no—
899C8—21no—
900C8—41no—
901C8—41no—
902C8—41no—
903C8—41no—
904C2×C3—21no—
905C2×C3—21no—
906C2×C3—41no—
907C2×C3—41no—
908C2×C3—42no—
909C2×C3—81no—
910C2×C3—82no—
911C2×C3—161no—
912C2×C3#241011yescharacteristic
913C2×C3#306711yescharacteristic
914C2×C3#306811yescharacteristic
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—22no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—42no—
928C22—41no—
929C22—41no—
930C22—81no—
931C22—81no—
932C22—82no—
933C22—82no—
934C22—84no—
935C22—81no—
936C22—81no—
937C22—81no—
938C22—81no—
939C22—81no—
940C22—161no—
941C22—161no—
942C22C2×C3×#12111yescharacteristic
943C22C3×#54611yescharacteristic
944C22C3×#54611yescharacteristic
945C4—21no—
946C4—21no—
947C4—22no—
948C4—41no—
949C4—42no—
950C4—81no—
951C4C2×C3×#12011yescharacteristic
952C4C3×#53411yescharacteristic
953C4C3×D4211yescharacteristic
954C4C3×D4211yescharacteristic
955C3#2440211yescharacteristic, direct product factor, Sylow
956C2—21no—
957C2—21no—
958C2—41no—
959C2—41no—
960C2—42no—
961C2—81no—
962C2—82no—
963C2—161no—
964C2C3×#241011yescharacteristic
965C2C3×#306711yescharacteristic
966C2C3×#306811yescharacteristic
subgroupG/H
center, socleC22×C3C2×#121
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#575C2semidirect
2. C2×C3×#472C2semidirect
3. C2×C3×#471C2semidirect
4. C3×#3006C2semidirect
5. C2×C3×#449C2semidirect
6. C3×#2880C2semidirect
7. C3×#2052C2semidirect
8. C3×#2051C2semidirect
9. C3×#2019C2semidirect
10. C3×#2018C2semidirect
11. C3×#1908C2semidirect
12. C3×#1907C2semidirect
13. C3×#1900C2semidirect
14. C3×#1855C2semidirect
15. C3×#1785C2semidirect
16. #24402C3direct (N × H)
31. C22×C3×SD16C22semidirect
32. C22×C3×D8C22semidirect
47. C2×C3×#108C22semidirect
48. C2×C3×#108C22semidirect
51. C2×C3×#103C22semidirect
52. C2×C3×#102C22semidirect
53. C2×C3×#101C22semidirect
54. C2×C3×#101C22semidirect
55. C2×C3×#100C22semidirect
56. C2×C3×#100C22semidirect
57. C2×C3×#100C22semidirect
58. C2×C3×#100C22semidirect
68. C3×#343C22semidirect
69. C3×#343C22semidirect
70. C3×#341C22semidirect
71. C3×#341C22semidirect
72. C2×#575C2×C3semidirect
73. C2×#472C2×C3semidirect
74. C2×#471C2×C3semidirect
75. #3006C2×C3semidirect
76. C2×#449C2×C3semidirect
77. #2880C2×C3semidirect
78. #2052C2×C3semidirect
79. #2051C2×C3semidirect
80. #2019C2×C3semidirect
81. #2018C2×C3semidirect
82. #1908C2×C3semidirect
83. #1907C2×C3semidirect
84. #1900C2×C3semidirect
85. #1855C2×C3semidirect
86. #1785C2×C3semidirect
120. C3×#137D4semidirect
129. C3×AGL(1,ℤ/8)D4semidirect
220. C22×SD16C22×C3semidirect
221. C22×D8C22×C3semidirect
236. C2×#108C22×C3semidirect
237. C2×#108C22×C3semidirect
240. C2×#103C22×C3semidirect
241. C2×#102C22×C3semidirect
242. C2×#101C22×C3semidirect
243. C2×#101C22×C3semidirect
244. C2×#100C22×C3semidirect
245. C2×#100C22×C3semidirect
246. C2×#100C22×C3semidirect
247. C2×#100C22×C3semidirect
257. #343C22×C3semidirect
258. #343C22×C3semidirect
259. #341C22×C3semidirect
260. #341C22×C3semidirect
438. #137C3×D4semidirect
447. AGL(1,ℤ/8)C3×D4semidirect
955. C3#24402direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5752
C2×C3×#4722
C2×C3×#4712
C3×#30062
C2×C3×#4492
C3×#28802
C3×#20522
C3×#20512
C3×#20192
C3×#20182
C3×#19082
C3×#19072
C3×#19002
C3×#18552
C3×#17852
#244023