Finite Group Databasebeta

← C3×#24403 #10643010

Subgroups — C3×#24403 #10643010

Order 768.

1332 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#575C211yesmaximal, characteristic
2C2×C3×#473C211yesmaximal, characteristic, complemented
3C2×C3×#471C211yesmaximal, characteristic, complemented
4C3×#3007C211yesmaximal, characteristic, complemented
5C2×C3×#452C211yesmaximal, characteristic, complemented
6C3×#2880C211yesmaximal, characteristic, complemented
7C3×#2052C211yesmaximal, characteristic, complemented
8C3×#2051C211yesmaximal, characteristic, complemented
9C3×#2020C211yesmaximal, characteristic, complemented
10C3×#2019C211yesmaximal, characteristic, complemented
11C3×#1908C211yesmaximal, characteristic, complemented
12C3×#1907C211yesmaximal, characteristic, complemented
13C3×#1901C211yesmaximal, characteristic, complemented
14C3×#1855C211yesmaximal, characteristic, complemented
15C3×#1785C211yesmaximal, characteristic, complemented
16#24403C311yesmaximal, 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×#137C2211yescharacteristic
25C2×C3×#137C2211yescharacteristic
26C2×C3×AGL(1,ℤ/8)—21no—
27C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
28C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
29C2×C3×#135—21no—
30C2×C3×#135—21no—
31C22×C3×Q16C2211yescharacteristic, complemented
32C22×C3×SD16C2211yescharacteristic, complemented
33C2×C3×#131C2211yescharacteristic
34C2×C3×#131C2211yescharacteristic
35C22×C3×M16C2211yescharacteristic
36C2×C3×C22⋊Q8C2211yescharacteristic
37C3×#473—24no—
38C3×#471—24no—
39C3×#452—21no—
40C3×#452—21no—
41C3×#452—21no—
42C3×#452—21no—
43C3×#452—21no—
44C3×#452—21no—
45C3×#451—21no—
46C3×#450—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×#101C2211yescharacteristic, complemented
56C2×C3×#101C2211yescharacteristic, 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
73C2×#473C2×C311yescharacteristic, complemented
74C2×#471C2×C311yescharacteristic, complemented
75#3007C2×C311yescharacteristic, complemented
76C2×#452C2×C311yescharacteristic, complemented
77#2880C2×C311yescharacteristic, complemented
78#2052C2×C311yescharacteristic, complemented
79#2051C2×C311yescharacteristic, complemented
80#2020C2×C311yescharacteristic, complemented
81#2019C2×C311yescharacteristic, complemented
82#1908C2×C311yescharacteristic, complemented
83#1907C2×C311yescharacteristic, complemented
84#1901C2×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×Q8C2311yescharacteristic
108C22×C3×D4—21no—
109C22×C3×D4—21no—
110C22×C3×D4D411yescharacteristic
111C22×C3×D4C2311yescharacteristic
112C23×C3×C4—21no—
113C23×C3×C4—21no—
114C23×C3×C4C2311yescharacteristic
115C3×#137—28no—
116C3×#137—22no—
117C3×#137—22no—
118C3×#137—22no—
119C3×#137—22no—
120C3×#137—22no—
121C3×#137—41no—
122C3×#137—41no—
123C3×#137D414yes—
124C3×AGL(1,ℤ/8)—28no—
125C3×AGL(1,ℤ/8)—22no—
126C3×AGL(1,ℤ/8)—22no—
127C3×AGL(1,ℤ/8)—22no—
128C3×AGL(1,ℤ/8)D414yes—
129C3×#135—28no—
130C3×#135—28no—
131C2×C3×Q16—21no—
132C2×C3×Q16—21no—
133C2×C3×Q16—22no—
134C2×C3×Q16—21no—
135C2×C3×Q16—21no—
136C2×C3×Q16—21no—
137C2×C3×Q16—21no—
138C2×C3×Q16—41no—
139C2×C3×SD16—21no—
140C2×C3×SD16—21no—
141C2×C3×SD16—21no—
142C2×C3×SD16—21no—
143C2×C3×SD16—22no—
144C2×C3×SD16—21no—
145C2×C3×SD16—21no—
146C2×C3×SD16—21no—
147C2×C3×SD16—21no—
148C2×C3×SD16—41no—
149C2×C3×D8—21no—
150C2×C3×D8—21no—
151C3×#131—22no—
152C3×#131—22no—
153C3×#131—41no—
154C3×#131—41no—
155C2×C3×M16—21no—
156C2×C3×M16—22no—
157C2×C3×M16—22no—
158C2×C3×M16—21no—
159C2×C3×M16—21no—
160C2×C3×M16C2311yescharacteristic
161C2×C3×M16C2311yescharacteristic
162C2×C3×M16C2311yescharacteristic
163C2×C3×M16C2311yescharacteristic
164C2×C3×M16C2311yescharacteristic
165C2×C3×M16C2311yescharacteristic
166C22×C3×C8—21no—
167C22×C3×C8—21no—
168C22×C3×C8—21no—
169C22×C3×C8C2311yescharacteristic
170C22×C3×C8C2311yescharacteristic
171C3×C22⋊Q8—21no—
172C3×C22⋊Q8—21no—
173C3×C22⋊Q8—21no—
174C3×C22⋊Q8—21no—
175C2×C3×C4⋊C4—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—22no—
190C3×#101—22no—
191C3×#101—41no—
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×#137C22×C311yescharacteristic
214C2×#137C22×C311yescharacteristic
215C2×AGL(1,ℤ/8)—21no—
216C2×AGL(1,ℤ/8)C22×C311yescharacteristic
217C2×AGL(1,ℤ/8)C22×C311yescharacteristic
218C2×#135—21no—
219C2×#135—21no—
220C22×Q16C22×C311yescharacteristic, complemented
221C22×SD16C22×C311yescharacteristic, complemented
222C2×#131C22×C311yescharacteristic
223C2×#131C22×C311yescharacteristic
224C22×M16C22×C311yescharacteristic
225C2×C22⋊Q8C22×C311yescharacteristic
226#473—24no—
227#471—24no—
228#452—21no—
229#452—21no—
230#452—21no—
231#452—21no—
232#452—21no—
233#452—21no—
234#451—21no—
235#450—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×#101C22×C311yescharacteristic, complemented
245C2×#101C22×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#4111yescharacteristic
264C3×#41—21no—
265C3×#41—21no—
266C3×#41—24no—
267C3×#41—24no—
268C3×#41—22no—
269C3×#41—22no—
270C3×#41—21no—
271C3×#41—21no—
272C3×#41—21no—
273C3×#41—21no—
274C3×#41—42no—
275C3×#41—42no—
276C3×#41—41no—
277C3×#41—41no—
278C3×#41—42no—
279C3×#41—42no—
280C3×#41—42no—
281C3×#41—42no—
282C3×#41—42no—
283C3×#41—42no—
284C3×#41—42no—
285C3×#41—42no—
286C3×#41C2×D412yes—
287C3×#41C2×D412yes—
288C2×C3×Q8—21no—
289C2×C3×Q8—21no—
290C2×C3×Q8—22no—
291C2×C3×Q8—21no—
292C2×C3×Q8—21no—
293C2×C3×Q8—21no—
294C2×C3×Q8—21no—
295C2×C3×Q8—21no—
296C2×C3×Q8—21no—
297C2×C3×Q8—21no—
298C2×C3×Q8—21no—
299C2×C3×Q8—21no—
300C2×C3×Q8—21no—
301C2×C3×Q8—41no—
302C2×C3×Q8C2×D412yes—
303C2×C3×Q8C2×D411yescharacteristic
304C2×C3×Q8C2×D411yescharacteristic
305C2×C3×D4—21no—
306C2×C3×D4—22no—
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—41no—
317C2×C3×D4—42no—
318C2×C3×D4—42no—
319C2×C3×D4—42no—
320C2×C3×D4—42no—
321C2×C3×D4—41no—
322C2×C3×D4—41no—
323C2×C3×D4C2×D412yes—
324C2×C3×D4C2×D411yescharacteristic
325C2×C3×D4C2×D411yescharacteristic
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
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—42no—
339C22×C3×C4—42no—
340C22×C3×C4—42no—
341C22×C3×C4—42no—
342C22×C3×C4—41no—
343C22×C3×C4—41no—
344C22×C3×C4C2×D411yescharacteristic
345C22×C3×C4C2×D411yescharacteristic
346C22×C3×C4C2×D411yescharacteristic
347C22×C3×C4C2×D411yescharacteristic
348C22×C3×C4#4111yescharacteristic
349C22×C3×C4C2411yescharacteristic
350C3×Q16—24no—
351C3×Q16—24no—
352C3×Q16—42no—
353C3×Q16—42no—
354C3×Q16—42no—
355C3×Q16—42no—
356C3×SD16—24no—
357C3×SD16—24no—
358C3×SD16—24no—
359C3×SD16—24no—
360C3×SD16—42no—
361C3×SD16—42no—
362C3×SD16—42no—
363C3×SD16—42no—
364C3×D8—24no—
365C3×D8—24no—
366C3×M16—24no—
367C3×M16—21no—
368C3×M16—21no—
369C3×M16—21no—
370C3×M16—21no—
371C3×M16—21no—
372C3×M16—21no—
373C3×M16—21no—
374C3×M16—21no—
375C3×M16—21no—
376C3×M16—21no—
377C3×M16—42no—
378C3×M16—42no—
379C3×M16C2×D412yes—
380C3×M16C2×D412yes—
381C2×C3×C8—24no—
382C2×C3×C8—21no—
383C2×C3×C8—21no—
384C2×C3×C8—21no—
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—42no—
393C2×C3×C8—42no—
394C2×C3×C8C2×D411yescharacteristic
395C2×C3×C8C2×D411yescharacteristic
396C2×C3×C8C2×D411yescharacteristic
397C2×C3×C8C2×D411yescharacteristic
398C3×C4⋊C4—21no—
399C3×C4⋊C4—21no—
400C3×C4⋊C4—41no—
401C3×C4⋊C4—41no—
402C3×C22⋊C4—41no—
403C3×C22⋊C4—41no—
404C2×#41—21no—
405C2×#41—21no—
406C2×#41—22no—
407C2×#41—22no—
408C2×#41—22no—
409C2×#41—22no—
410C2×#41—21no—
411C2×#41—21no—
412C2×#41—21no—
413C2×#41—21no—
414C2×#41—41no—
415C2×#41—41no—
416C2×#41—41no—
417C2×#41—41no—
418C2×#41C3×D411yescharacteristic
419C2×#41C3×D411yescharacteristic
420C2×#41C23×C311yescharacteristic
421C2×#41C23×C311yescharacteristic
422C22×Q8C3×D411yescharacteristic
423C22×Q8C23×C311yescharacteristic
424C22×Q8C23×C311yescharacteristic
425C22×D4—21no—
426C22×D4—21no—
427C22×D4C3×D411yescharacteristic
428C22×D4C23×C311yescharacteristic
429C23×C4—21no—
430C23×C4—21no—
431C23×C4C23×C311yescharacteristic
432#137—28no—
433#137—22no—
434#137—22no—
435#137—22no—
436#137—22no—
437#137—22no—
438#137—41no—
439#137—41no—
440#137C3×D414yes—
441AGL(1,ℤ/8)—28no—
442AGL(1,ℤ/8)—22no—
443AGL(1,ℤ/8)—22no—
444AGL(1,ℤ/8)—22no—
445AGL(1,ℤ/8)C3×D414yes—
446#135—28no—
447#135—28no—
448C2×Q16—21no—
449C2×Q16—21no—
450C2×Q16—22no—
451C2×Q16—21no—
452C2×Q16—21no—
453C2×Q16—21no—
454C2×Q16—21no—
455C2×Q16—41no—
456C2×SD16—21no—
457C2×SD16—21no—
458C2×SD16—21no—
459C2×SD16—21no—
460C2×SD16—22no—
461C2×SD16—21no—
462C2×SD16—21no—
463C2×SD16—21no—
464C2×SD16—21no—
465C2×SD16—41no—
466C2×D8—21no—
467C2×D8—21no—
468#131—22no—
469#131—22no—
470#131—41no—
471#131—41no—
472C2×M16—21no—
473C2×M16—22no—
474C2×M16—22no—
475C2×M16—21no—
476C2×M16—21no—
477C2×M16C23×C311yescharacteristic
478C2×M16C23×C311yescharacteristic
479C2×M16C23×C311yescharacteristic
480C2×M16C23×C311yescharacteristic
481C2×M16C23×C311yescharacteristic
482C2×M16C23×C311yescharacteristic
483C22×C8—21no—
484C22×C8—21no—
485C22×C8—21no—
486C22×C8C23×C311yescharacteristic
487C22×C8C23×C311yescharacteristic
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4C23×C311yescharacteristic
494C2×C22⋊C4—21no—
495#108—22no—
496#108—22no—
497#103—21no—
498#103—21no—
499#103—21no—
500#103—21no—
501#102—21no—
502#102—21no—
503#102—21no—
504#102—21no—
505#101—22no—
506#101—22no—
507#101—22no—
508#101—41no—
509#100—22no—
510#100—41no—
511C22⋊C8—21no—
512C22⋊C8—21no—
513C22⋊C8—21no—
514C22⋊C8—21no—
515C22⋊C8—21no—
516C22⋊C8—21no—
517C22⋊C8—21no—
518C22⋊C8—21no—
519C22⋊C8C3×D411yescharacteristic
520C22⋊C8C3×D411yescharacteristic
521C22⋊C8C3×D411yescharacteristic
522C22⋊C8C3×D411yescharacteristic
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—22no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—42no—
531C23×C3—42no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—81no—
535C23×C3—81no—
536C23×C3—81no—
537C23×C3#12111yescharacteristic
538C23×C3#12111yescharacteristic
539C23×C3C2×#4111yescharacteristic
540C3×Q8—21no—
541C3×Q8—21no—
542C3×Q8—22no—
543C3×Q8—21no—
544C3×Q8—22no—
545C3×Q8—42no—
546C3×Q8—41no—
547C3×Q8—41no—
548C3×Q8—41no—
549C3×Q8—41no—
550C3×Q8—41no—
551C3×Q8—41no—
552C3×Q8#12012yes—
553C3×D4—22no—
554C3×D4—22no—
555C3×D4—21no—
556C3×D4—22no—
557C3×D4—21no—
558C3×D4—21no—
559C3×D4—22no—
560C3×D4—42no—
561C3×D4—42no—
562C3×D4—42no—
563C3×D4—44no—
564C3×D4—44no—
565C3×D4—41no—
566C3×D4—41no—
567C3×D4—41no—
568C3×D4—41no—
569C3×D4#12012yes—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—22no—
585C2×C3×C4—42no—
586C2×C3×C4—42no—
587C2×C3×C4—42no—
588C2×C3×C4—44no—
589C2×C3×C4—44no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—81no—
599C2×C3×C4#12111yescharacteristic
600C2×C3×C4#12111yescharacteristic
601C2×C3×C4C22×D411yescharacteristic
602C2×C3×C4C22×D411yescharacteristic
603C2×C3×C4C22×D411yescharacteristic
604C2×C3×C4C22×D411yescharacteristic
605C2×C3×C4H(5,𝔽2)11yescharacteristic
606C2×C3×C4H(5,𝔽2)11yescharacteristic
607C3×C8—22no—
608C3×C8—22no—
609C3×C8—21no—
610C3×C8—21no—
611C3×C8—21no—
612C3×C8—21no—
613C3×C8—41no—
614C3×C8—41no—
615C3×C8—41no—
616C3×C8—41no—
617C24—21no—
618C24—21no—
619C24C3×#4111yescharacteristic
620#41—21no—
621#41—21no—
622#41—24no—
623#41—24no—
624#41—22no—
625#41—22no—
626#41—21no—
627#41—21no—
628#41—21no—
629#41—21no—
630#41—42no—
631#41—42no—
632#41—41no—
633#41—41no—
634#41—42no—
635#41—42no—
636#41—42no—
637#41—42no—
638#41—42no—
639#41—42no—
640#41—42no—
641#41—42no—
642#41C2×C3×D412yes—
643#41C2×C3×D412yes—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—22no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
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—41no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—41no—
678C2×D4—41no—
679C2×D4C2×C3×D412yes—
680C2×D4C2×C3×D411yescharacteristic
681C2×D4C2×C3×D411yescharacteristic
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—41no—
699C22×C4—41no—
700C22×C4C2×C3×D411yescharacteristic
701C22×C4C2×C3×D411yescharacteristic
702C22×C4C2×C3×D411yescharacteristic
703C22×C4C2×C3×D411yescharacteristic
704C22×C4C3×#4111yescharacteristic
705C22×C4C24×C311yescharacteristic
706Q16—24no—
707Q16—24no—
708Q16—42no—
709Q16—42no—
710Q16—42no—
711Q16—42no—
712SD16—24no—
713SD16—24no—
714SD16—24no—
715SD16—24no—
716SD16—42no—
717SD16—42no—
718SD16—42no—
719SD16—42no—
720D8—24no—
721D8—24no—
722M16—24no—
723M16—21no—
724M16—21no—
725M16—21no—
726M16—21no—
727M16—21no—
728M16—21no—
729M16—21no—
730M16—21no—
731M16—21no—
732M16—21no—
733M16—42no—
734M16—42no—
735M16C2×C3×D412yes—
736M16C2×C3×D412yes—
737C2×C8—24no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—42no—
749C2×C8—42no—
750C2×C8C2×C3×D411yescharacteristic
751C2×C8C2×C3×D411yescharacteristic
752C2×C8C2×C3×D411yescharacteristic
753C2×C8C2×C3×D411yescharacteristic
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—41no—
757C4⋊C4—41no—
758C22⋊C4—41no—
759C22⋊C4—41no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—22no—
765C22×C3—21no—
766C22×C3—21no—
767C22×C3—21no—
768C22×C3—21no—
769C22×C3—41no—
770C22×C3—41no—
771C22×C3—41no—
772C22×C3—42no—
773C22×C3—41no—
774C22×C3—41no—
775C22×C3—81no—
776C22×C3—81no—
777C22×C3—82no—
778C22×C3—82no—
779C22×C3—84no—
780C22×C3—81no—
781C22×C3—81no—
782C22×C3C2×#12111yescharacteristic
783C22×C3#54611yescharacteristic
784C22×C3#54611yescharacteristic
785C3×C4—21no—
786C3×C4—21no—
787C3×C4—22no—
788C3×C4—41no—
789C3×C4—42no—
790C3×C4—81no—
791C3×C4—81no—
792C3×C4C2×#12011yescharacteristic
793C3×C4#53411yescharacteristic
794C3×C4D4211yescharacteristic
795C3×C4D4211yescharacteristic
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—22no—
801C23—41no—
802C23—41no—
803C23—42no—
804C23—42no—
805C23—41no—
806C23—41no—
807C23—81no—
808C23—81no—
809C23—81no—
810C23C3×#12111yescharacteristic
811C23C3×#12111yescharacteristic
812C23C2×C3×#4111yescharacteristic
813Q8—21no—
814Q8—21no—
815Q8—22no—
816Q8—21no—
817Q8—22no—
818Q8—42no—
819Q8—41no—
820Q8—41no—
821Q8—41no—
822Q8—41no—
823Q8—41no—
824Q8—41no—
825Q8C3×#12012yes—
826D4—22no—
827D4—22no—
828D4—21no—
829D4—22no—
830D4—21no—
831D4—21no—
832D4—22no—
833D4—42no—
834D4—42no—
835D4—42no—
836D4—44no—
837D4—44no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4C3×#12012yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—22no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—44no—
862C2×C4—44no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—81no—
872C2×C4C3×#12111yescharacteristic
873C2×C4C3×#12111yescharacteristic
874C2×C4C22×C3×D411yescharacteristic
875C2×C4C22×C3×D411yescharacteristic
876C2×C4C22×C3×D411yescharacteristic
877C2×C4C22×C3×D411yescharacteristic
878C2×C4C3×H(5,𝔽2)11yescharacteristic
879C2×C4C3×H(5,𝔽2)11yescharacteristic
880C8—22no—
881C8—22no—
882C8—21no—
883C8—21no—
884C8—21no—
885C8—21no—
886C8—41no—
887C8—41no—
888C8—41no—
889C8—41no—
890C2×C3—21no—
891C2×C3—21no—
892C2×C3—41no—
893C2×C3—41no—
894C2×C3—42no—
895C2×C3—81no—
896C2×C3—82no—
897C2×C3#241011yescharacteristic
898C2×C3#306711yescharacteristic
899C2×C3#306911yescharacteristic
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—22no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—42no—
913C22—41no—
914C22—41no—
915C22—81no—
916C22—81no—
917C22—82no—
918C22—82no—
919C22—84no—
920C22—81no—
921C22—81no—
922C22C2×C3×#12111yescharacteristic
923C22C3×#54611yescharacteristic
924C22C3×#54611yescharacteristic
925C4—21no—
926C4—21no—
927C4—22no—
928C4—41no—
929C4—42no—
930C4—81no—
931C4—81no—
932C4C2×C3×#12011yescharacteristic
933C4C3×#53411yescharacteristic
934C4C3×D4211yescharacteristic
935C4C3×D4211yescharacteristic
936C3#2440311yescharacteristic, direct product factor, Sylow
937C2—21no—
938C2—21no—
939C2—41no—
940C2—41no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2C3×#241011yescharacteristic
945C2C3×#306711yescharacteristic
946C2C3×#306911yescharacteristic
subgroupG/H
center, socleC22×C3C2×#121
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#575C2
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
2. C2×C3×#473C2semidirect
3. C2×C3×#471C2semidirect
4. C3×#3007C2semidirect
5. C2×C3×#452C2semidirect
6. C3×#2880C2semidirect
7. C3×#2052C2semidirect
8. C3×#2051C2semidirect
9. C3×#2020C2semidirect
10. C3×#2019C2semidirect
11. C3×#1908C2semidirect
12. C3×#1907C2semidirect
13. C3×#1901C2semidirect
14. C3×#1855C2semidirect
15. C3×#1785C2semidirect
16. #24403C3direct (N × H)
31. C22×C3×Q16C22semidirect
32. C22×C3×SD16C22semidirect
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×#101C22semidirect
56. C2×C3×#101C22semidirect
57. C2×C3×#100C22semidirect
58. C2×C3×#100C22semidirect
68. C3×#343C22semidirect
69. C3×#343C22semidirect
70. C3×#341C22semidirect
71. C3×#341C22semidirect
73. C2×#473C2×C3semidirect
74. C2×#471C2×C3semidirect
75. #3007C2×C3semidirect
76. C2×#452C2×C3semidirect
77. #2880C2×C3semidirect
78. #2052C2×C3semidirect
79. #2051C2×C3semidirect
80. #2020C2×C3semidirect
81. #2019C2×C3semidirect
82. #1908C2×C3semidirect
83. #1907C2×C3semidirect
84. #1901C2×C3semidirect
85. #1855C2×C3semidirect
86. #1785C2×C3semidirect
220. C22×Q16C22×C3semidirect
221. C22×SD16C22×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×#101C22×C3semidirect
245. C2×#101C22×C3semidirect
246. C2×#100C22×C3semidirect
247. C2×#100C22×C3semidirect
257. #343C22×C3semidirect
258. #343C22×C3semidirect
259. #341C22×C3semidirect
260. #341C22×C3semidirect
936. C3#24403direct (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×#4732
C2×C3×#4712
C3×#30072
C2×C3×#4522
C3×#28802
C3×#20522
C3×#20512
C3×#20202
C3×#20192
C3×#19082
C3×#19072
C3×#19012
C3×#18552
C3×#17852
#244033