Finite Group Databasebeta

← C3×#10948665 #72222859

Subgroups — C3×#10948665 #72222859

Order 2304.

1464 conjugacy classes of subgroups.

The subgroup lattice has 807 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#5147C211yesmaximal, characteristic
2C3×#79249C211yesmaximal, characteristic, complemented
3C3×#83823C211yesmaximal, characteristic, complemented
4C3×#69254C218yesmaximal, complemented
5C3×#70685C211yesmaximal, characteristic, complemented
6C3×#71450C211yesmaximal, characteristic, complemented
7C3×#71425C211yesmaximal, characteristic, complemented
8C2×C32×#361C211yesmaximal, characteristic, complemented
9#10948665C311yesmaximal, characteristic, direct product factor
10C3×#33471—31nomaximal
11C22×C32×D8C2211yescharacteristic
12C3×#5798—21no—
13C3×#5745—21no—
14C2×C3×#904C2211yescharacteristic
15C2×C32×M32C2211yescharacteristic
16C2×C32×#108C2211yescharacteristic
17C3×#5215—21no—
18C3×#5152C2214yescomplemented
19C3×Dic3×D8—22no—
20C2×C3×#827C412yescomplemented
21C3×#5147C414yescomplemented
22C3×#5147C2214yes—
23C2×C3×#826C412yescomplemented
24C3×#5139—21no—
25C3×#5106C2211yescharacteristic
26C3×#5101C2211yescharacteristic
27C2×C3×#812C2211yescharacteristic
28C3×#4895—22no—
29C3×#4894C2214yescomplemented
30C32×#361C2214yescomplemented
31C3×#4518C2214yescomplemented
32C3×#4512C2214yescomplemented
33C3×#4494C2214yescomplemented
34C2×C3×#509—31no—
35C3×#2957—31no—
36C3×#2948—31no—
37#83823C2×C311yescharacteristic, complemented
38C2×#5147C2×C311yescharacteristic
39#79249C2×C311yescharacteristic, complemented
40C3×AGL(1,ℤ/16)—38no—
41C3×#2155—31no—
42C2×C3×#361—21no—
43C2×C3×#361D311yescharacteristic, complemented
44C2×C3×#361C2×C311yescharacteristic, complemented
45C3×#2145—31no—
46C3×#2110—31no—
47#71450C2×C311yescharacteristic, complemented
48#71425C2×C311yescharacteristic, complemented
49#70685C2×C311yescharacteristic, complemented
50#69254C2×C318yescomplemented
51C22×C32×D4—21no—
52C2×C3×#235—21no—
53C2×C32×D8—21no—
54C2×C32×D8—21no—
55C2×C32×D8—21no—
56C2×C32×D8C2×C412yes—
57C2×C32×D8C2×C412yes—
58C2×C32×D8C2312yes—
59C2×C32×M16—21no—
60C22×C32×C8C2311yescharacteristic
61C2×C3×#217—42no—
62C3×D4×Dic3—24no—
63C3×D4×Dic3—42no—
64C3×#926—21no—
65C3×#926D411yescharacteristic
66C2×C3×#208D411yescharacteristic
67C3×#907—24no—
68C3×D3×M16—42no—
69C2×C3×Dic12C2×C411yescharacteristic, complemented
70C3×#904—21no—
71C3×#904—21no—
72C3×#904C2×C412yescomplemented
73C3×#904C2312yes—
74C2×C3×D24C2×C411yescharacteristic, complemented
75C2×C3×#204—21no—
76C3×#901—42no—
77C32×M32—21no—
78C32×M32C2312yes—
79C2×C32×C16—21no—
80C32×#108—21no—
81C32×#108C2312yes—
82C3×#832—24no—
83C3×#827C2×C418yescomplemented
84C3×#826C2×C418yescomplemented
85C3×#825—24no—
86C3×#818—21no—
87C3×#817C2312yes—
88C3×#815C2312yes—
89C3×C8×Dic3D412yes—
90C3×#812C2×C412yescomplemented
91C3×#812C2312yes—
92C2×C3×C3⋊C16C2×C412yescomplemented
93#33471—31noSylow
94C2×C3×#135—31no—
95C22×C3×D8—21no—
96C22×C3×D8C2×D311yescharacteristic
97C22×C3×D8C22×C311yescharacteristic
98C3×#568—61no—
99C3×#518—61no—
100#5798—21no—
101#5745—21no—
102C2×#904C22×C311yescharacteristic
103C3×#509—34no—
104C3×#509—34no—
105C2×C3×SD32—32no—
106C2×C3×D16—32no—
107C2×C3×M32—21no—
108C2×C3×M32—31no—
109C2×C3×M32C2×D311yescharacteristic
110C2×C3×M32C22×C311yescharacteristic
111C3×#444—34no—
112C3×#443—62no—
113C3×#442—34no—
114C3×C4×D8—62no—
115C2×C3×#108—21no—
116C2×C3×#108C2×D311yescharacteristic
117C2×C3×#108C22×C311yescharacteristic
118C3×#427—31no—
119C3×#421—61no—
120C3×#418—61no—
121C3×#405—31no—
122#5215—21no—
123#5152C22×C314yescomplemented
124Dic3×D8—22no—
125C2×#827C3×C412yescomplemented
126#5147C3×C414yescomplemented
127#5147C22×C314yes—
128C2×#826C3×C412yescomplemented
129#5139—21no—
130#5106C22×C311yescharacteristic
131#5101C22×C311yescharacteristic
132C2×#812C22×C311yescharacteristic
133#4895—22no—
134#4894C22×C314yescomplemented
135C3×#365—34no—
136C3×#361—24no—
137C3×#361C2×D314yescomplemented
138C3×#361C22×C314yescomplemented
139C3×#360—34no—
140C3×#347—34no—
141#4518C22×C314yescomplemented
142#4512C22×C314yescomplemented
143#4494C22×C314yescomplemented
144C24×C32—41no—
145C2×C32×D4—22no—
146C2×C32×D4—22no—
147C2×C32×D4—22no—
148C2×C32×D4—41no—
149C2×C32×D4—41no—
150C2×C32×D4—41no—
151C22×C32×C4C2×D411yescharacteristic
152C2×C3×#67—41no—
153C22×C3×Dic3—44no—
154C3×#235—22no—
155C3×#235—22no—
156C3×#235—41no—
157C3×#235—41no—
158C2×C3×D12—21no—
159C2×C3×C4×D3—41no—
160C2×C3×Dic6—21no—
161C32×D8—22no—
162C32×D8—22no—
163C32×D8—22no—
164C32×D8C22×C414yes—
165C32×M16—22no—
166C32×M16—41no—
167C2×C32×C8—41no—
168C2×C32×C8C22×C411yescharacteristic
169C2×C32×C8C22×C411yescharacteristic
170C2×C32×C8C2×D411yescharacteristic
171C2×C32×C8#4111yescharacteristic
172C2×C32×C8#4111yescharacteristic
173C2×C32×C8C2411yescharacteristic
174C3×#217—21no—
175C3×#217—44no—
176C3×#217—41no—
177C3×C4⋊Dic3—21no—
178C3×C4⋊Dic3—22no—
179C3×C4×Dic3—41no—
180C3×C4×Dic3C2×D412yes—
181C3×#208—21no—
182C3×#208—21no—
183C2×C3×C3⋊C8C2×D412yes—
184C3×Dic12—21no—
185C3×Dic12C22×C412yes—
186C3×D24—21no—
187C3×D24C22×C412yes—
188C3×#204—22no—
189C3×#204—22no—
190C3×ΓL(1,𝔽25)—44no—
191C3×D3×C8—44no—
192C32×C16—22no—
193C3×C3⋊C16C22×C414yes—
194C2×#509—31no—
195#2957—31no—
196#2948—31no—
197AGL(1,ℤ/16)—38no—
198#2155—31no—
199C2×#361C3×D311yescharacteristic, complemented
200#2145—31no—
201#2110—31no—
202C2×C3×#41—61no—
203C22×C3×D4—21no—
204C22×C3×D4—21no—
205C22×C3×D4—41no—
206C2×#235—21no—
207C3×#135—32no—
208C3×#135—32no—
209C3×#135—61no—
210C3×#135—61no—
211C2×C3×Q16—31no—
212C2×C3×SD16—61no—
213C2×C3×D8—21no—
214C2×C3×D8—21no—
215C2×C3×D8—21no—
216C2×C3×D8—21no—
217C2×C3×D8—21no—
218C2×C3×D8—21no—
219C2×C3×D8—22no—
220C2×C3×D8—22no—
221C2×C3×D8—22no—
222C2×C3×D8—31no—
223C2×C3×D8—41no—
224C2×C3×D8—41no—
225C2×C3×D8—41no—
226C2×C3×D8C4×D312yes—
227C2×C3×D8C4×D312yes—
228C2×C3×D8C2×C3×C412yes—
229C2×C3×D8C2×C3×C412yes—
230C2×C3×D8C22×D312yes—
231C2×C3×D8C23×C312yes—
232C3×#131—64no—
233C3×#131—122no—
234C2×C3×M16—21no—
235C2×C3×M16—21no—
236C2×C3×M16—31no—
237C2×C3×M16—41no—
238C2×C3×M16—122no—
239C22×C3×C8—21no—
240C22×C3×C8C22×D311yescharacteristic
241C22×C3×C8C23×C311yescharacteristic
242C3×C4×D4—64no—
243C3×C4×D4—122no—
244C3×#117—31no—
245C3×#117—61no—
246C2×C3×C22⋊C4—122no—
247C2×#217—42no—
248D4×Dic3—24no—
249D4×Dic3—42no—
250#926—21no—
251#926C3×D411yescharacteristic
252C2×#208C3×D411yescharacteristic
253#907—24no—
254D3×M16—42no—
255C2×Dic12C2×C3×C411yescharacteristic, complemented
256#904—21no—
257#904—21no—
258#904C2×C3×C412yescomplemented
259#904C23×C312yes—
260C2×D24C2×C3×C411yescharacteristic, complemented
261C2×#204—21no—
262#901—42no—
263C3×SD32—38no—
264C3×D16—38no—
265C3×M32—21no—
266C3×M32—21no—
267C3×M32—22no—
268C3×M32—32no—
269C3×M32—32no—
270C3×M32—41no—
271C3×M32C22×D312yes—
272C3×M32C23×C312yes—
273C2×C3×C16—21no—
274C2×C3×C16—21no—
275C2×C3×C16—32no—
276C2×C3×C16—41no—
277C3×#108—21no—
278C3×#108—21no—
279C3×#108—22no—
280C3×#108—41no—
281C3×#108C22×D312yes—
282C3×#108C23×C312yes—
283C3×#107—61no—
284C3×#106—32no—
285C3×#104—64no—
286C3×#102—64no—
287C3×#97—32no—
288C3×C4×C8—32no—
289#832—24no—
290#827C2×C3×C418yescomplemented
291#826C2×C3×C418yescomplemented
292#825—24no—
293#818—21no—
294#817C23×C312yes—
295#815C23×C312yes—
296C8×Dic3C3×D412yes—
297#812C2×C3×C412yescomplemented
298#812C23×C312yes—
299C2×C3⋊C16C2×C3×C412yescomplemented
300C23×C32—42no—
301C23×C32—42no—
302C23×C32—42no—
303C23×C32—162no—
304C23×C32AGL(1,ℤ/8)11yescharacteristic
305C22×C3×D3—41no—
306C32×D4—24no—
307C32×D4—42no—
308C32×D4—42no—
309C32×D4—42no—
310C2×C32×C4C4×D411yescharacteristic
311C2×C32×C4C4×D411yescharacteristic
312C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
313C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
314C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
315C2×C32×C4C22×D411yescharacteristic
316C3×#67—42no—
317C3×#67—42no—
318C2×C3×Dic3—22no—
319C2×C3×Dic3—41no—
320C2×C3×Dic3—42no—
321C2×C3×Dic3—164no—
322C3×D12—22no—
323C3×D12—41no—
324C3×C4×D3—42no—
325C3×C4×D3—42no—
326C3×Dic6—22no—
327C3×Dic6—41no—
328C32×C8—42no—
329C32×C8C4×D411yescharacteristic
330C32×C8C4×D411yescharacteristic
331C32×C8C23×C411yescharacteristic
332C32×C8C2×#4111yescharacteristic
333C3×C3⋊C8—22no—
334C2×#135—31no—
335C22×D8C2×C3×D311yescharacteristic
336#568—61no—
337#518—61no—
338#509—34no—
339#509—34no—
340C2×SD32—32no—
341C2×D16—32no—
342C2×M32—31no—
343C2×M32C2×C3×D311yescharacteristic
344#444—34no—
345#443—62no—
346#442—34no—
347C4×D8—62no—
348C2×#108C2×C3×D311yescharacteristic
349#427—31no—
350#421—61no—
351#418—61no—
352#405—31no—
353#365—34no—
354#361C2×C3×D314yescomplemented
355#360—34no—
356#347—34no—
357C24×C3—41no—
358C24×C3—41no—
359C24×C3—81no—
360C3×#41—62no—
361C3×#41—62no—
362C3×#41—121no—
363C3×#41—121no—
364C2×C3×Q8—61no—
365C2×C3×D4—22no—
366C2×C3×D4—22no—
367C2×C3×D4—22no—
368C2×C3×D4—22no—
369C2×C3×D4—22no—
370C2×C3×D4—22no—
371C2×C3×D4—42no—
372C2×C3×D4—42no—
373C2×C3×D4—42no—
374C2×C3×D4—41no—
375C2×C3×D4—41no—
376C2×C3×D4—41no—
377C2×C3×D4—41no—
378C2×C3×D4—41no—
379C2×C3×D4—41no—
380C2×C3×D4—61no—
381C2×C3×D4—81no—
382C2×C3×D4—81no—
383C2×C3×D4—81no—
384C2×C3×D4—121no—
385C22×C3×C4—21no—
386C22×C3×C4—124no—
387C22×C3×C4—121no—
388C22×C3×C4D3×D411yescharacteristic
389C22×C3×C4C2×C3×D411yescharacteristic
390C2×#67—41no—
391C22×Dic3—44no—
392#235—22no—
393#235—22no—
394#235—41no—
395#235—41no—
396C2×D12—21no—
397C2×C4×D3—41no—
398C2×Dic6—21no—
399C3×Q16—32no—
400C3×Q16—61no—
401C3×SD16—62no—
402C3×SD16—62no—
403C3×D8—22no—
404C3×D8—22no—
405C3×D8—22no—
406C3×D8—22no—
407C3×D8—22no—
408C3×D8—22no—
409C3×D8—24no—
410C3×D8—32no—
411C3×D8—42no—
412C3×D8—42no—
413C3×D8—42no—
414C3×D8—61no—
415C3×D8C2×C4×D314yes—
416C3×D8C22×C3×C414yes—
417C3×M16—22no—
418C3×M16—22no—
419C3×M16—42no—
420C3×M16—41no—
421C3×M16—41no—
422C3×M16—61no—
423C3×M16—61no—
424C3×M16—81no—
425C3×M16—124no—
426C2×C3×C8—21no—
427C2×C3×C8—21no—
428C2×C3×C8—21no—
429C2×C3×C8—21no—
430C2×C3×C8—21no—
431C2×C3×C8—21no—
432C2×C3×C8—32no—
433C2×C3×C8—41no—
434C2×C3×C8—41no—
435C2×C3×C8—81no—
436C2×C3×C8—124no—
437C2×C3×C8C2×C4×D311yescharacteristic
438C2×C3×C8C2×C4×D311yescharacteristic
439C2×C3×C8D3×D411yescharacteristic
440C2×C3×C8#23711yescharacteristic
441C2×C3×C8#23711yescharacteristic
442C2×C3×C8C22×C3×C411yescharacteristic
443C2×C3×C8C22×C3×C411yescharacteristic
444C2×C3×C8C2×C3×D411yescharacteristic
445C2×C3×C8C3×#4111yescharacteristic
446C2×C3×C8C3×#4111yescharacteristic
447C2×C3×C8C23×D311yescharacteristic
448C2×C3×C8C24×C311yescharacteristic
449C3×C4⋊C4—61no—
450C3×C4⋊C4—62no—
451C3×C22⋊C4—61no—
452C3×C22⋊C4—124no—
453C3×C22⋊C4—121no—
454C3×C42—32no—
455C3×C42—121no—
456#217—21no—
457#217—44no—
458#217—41no—
459C4⋊Dic3—21no—
460C4⋊Dic3—22no—
461C4×Dic3—41no—
462C4×Dic3C2×C3×D412yes—
463#208—21no—
464#208—21no—
465C2×C3⋊C8C2×C3×D412yes—
466Dic12—21no—
467Dic12C22×C3×C412yes—
468D24—21no—
469D24C22×C3×C412yes—
470#204—22no—
471#204—22no—
472ΓL(1,𝔽25)—44no—
473D3×C8—44no—
474C3×C16—22no—
475C3×C16—22no—
476C3×C16—34no—
477C3×C16—42no—
478C3⋊C16C22×C3×C414yes—
479C22×C32—41no—
480C22×C32—44no—
481C22×C32—84no—
482C22×C32—162no—
483C22×C32—162no—
484C22×C32#44211yescharacteristic
485C22×C32#44211yescharacteristic
486C22×C32C2×AGL(1,ℤ/8)11yescharacteristic
487C2×C3×D3—42no—
488C2×C3×D3—161no—
489C32×C4#44211yescharacteristic
490C32×C4#44211yescharacteristic
491C32×C4C2×C4×D411yescharacteristic
492C32×C4C2×AGL(1,ℤ/8)11yescharacteristic
493C3×Dic3—42no—
494C3×Dic3—42no—
495C3×Dic3—82no—
496C2×#41—61no—
497C22×D4—21no—
498#135—32no—
499#135—32no—
500#135—61no—
501#135—61no—
502C2×Q16—31no—
503C2×SD16—61no—
504C2×D8—21no—
505C2×D8—21no—
506C2×D8—21no—
507C2×D8—31no—
508C2×D8C3×C4×D312yes—
509C2×D8C3×C4×D312yes—
510C2×D8C22×C3×D312yes—
511#131—64no—
512#131—122no—
513C2×M16—21no—
514C2×M16—31no—
515C2×M16—122no—
516C22×C8C22×C3×D311yescharacteristic
517C4×D4—64no—
518C4×D4—122no—
519#117—31no—
520#117—61no—
521C2×C22⋊C4—122no—
522SD32—38no—
523D16—38no—
524M32—21no—
525M32—32no—
526M32—32no—
527M32C22×C3×D312yes—
528C2×C16—21no—
529C2×C16—32no—
530#108—21no—
531#108C22×C3×D312yes—
532#107—61no—
533#106—32no—
534#104—64no—
535#102—64no—
536#97—32no—
537C4×C8—32no—
538C23×C3—21no—
539C23×C3—42no—
540C23×C3—42no—
541C23×C3—42no—
542C23×C3—42no—
543C23×C3—42no—
544C23×C3—42no—
545C23×C3—82no—
546C23×C3—82no—
547C23×C3—82no—
548C23×C3—121no—
549C23×C3—162no—
550C23×C3—162no—
551C23×C3—164no—
552C23×C3#91411yescharacteristic
553C23×C3C3×AGL(1,ℤ/8)11yescharacteristic
554C22×D3—41no—
555C3×Q8—62no—
556C3×Q8—121no—
557C3×D4—24no—
558C3×D4—24no—
559C3×D4—44no—
560C3×D4—42no—
561C3×D4—42no—
562C3×D4—42no—
563C3×D4—42no—
564C3×D4—42no—
565C3×D4—42no—
566C3×D4—62no—
567C3×D4—82no—
568C3×D4—82no—
569C3×D4—82no—
570C3×D4—122no—
571C3×D4—122no—
572C3×D4—121no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—62no—
580C2×C3×C4—121no—
581C2×C3×C4—122no—
582C2×C3×C4—122no—
583C2×C3×C4—122no—
584C2×C3×C4—484no—
585C2×C3×C4#67⋊C411yescharacteristic
586C2×C3×C4#67⋊C411yescharacteristic
587C2×C3×C4#91111yescharacteristic
588C2×C3×C4#91111yescharacteristic
589C2×C3×C4#91411yescharacteristic
590C2×C3×C4C3×C4×D411yescharacteristic
591C2×C3×C4C3×C4×D411yescharacteristic
592C2×C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
593C2×C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
594C2×C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
595C2×C3×C4C2×D3×D411yescharacteristic
596C2×C3×C4C22×C3×D411yescharacteristic
597#67—42no—
598#67—42no—
599C2×Dic3—22no—
600C2×Dic3—41no—
601C2×Dic3—42no—
602C2×Dic3—164no—
603D12—22no—
604D12—41no—
605C4×D3—42no—
606C4×D3—42no—
607Dic6—22no—
608Dic6—41no—
609C3×C8—21no—
610C3×C8—21no—
611C3×C8—21no—
612C3×C8—21no—
613C3×C8—42no—
614C3×C8—42no—
615C3×C8—62no—
616C3×C8—82no—
617C3×C8#67⋊C411yescharacteristic
618C3×C8#67⋊C411yescharacteristic
619C3×C8C3×C4×D411yescharacteristic
620C3×C8C3×C4×D411yescharacteristic
621C3×C8C22×C4×D311yescharacteristic
622C3×C8C2×#23711yescharacteristic
623C3×C8C23×C3×C411yescharacteristic
624C3×C8C2×C3×#4111yescharacteristic
625C3⋊C8—22no—
626C2×C32—21no—
627C2×C32—21no—
628C2×C32—21no—
629C2×C32—84no—
630C2×C32C2×#44211yescharacteristic
631C3×D3—82no—
632C24—41no—
633#41—62no—
634#41—62no—
635#41—121no—
636#41—121no—
637C2×Q8—61no—
638C2×D4—22no—
639C2×D4—22no—
640C2×D4—22no—
641C2×D4—41no—
642C2×D4—41no—
643C2×D4—41no—
644C2×D4—61no—
645C2×D4—121no—
646C22×C4—124no—
647C22×C4—121no—
648C22×C4C3×D3×D411yescharacteristic
649Q16—32no—
650Q16—61no—
651SD16—62no—
652SD16—62no—
653D8—22no—
654D8—22no—
655D8—22no—
656D8—32no—
657D8—61no—
658D8C2×C3×C4×D314yes—
659M16—22no—
660M16—41no—
661M16—61no—
662M16—61no—
663M16—124no—
664C2×C8—32no—
665C2×C8—41no—
666C2×C8—124no—
667C2×C8C2×C3×C4×D311yescharacteristic
668C2×C8C2×C3×C4×D311yescharacteristic
669C2×C8C3×D3×D411yescharacteristic
670C2×C8C3×#23711yescharacteristic
671C2×C8C3×#23711yescharacteristic
672C2×C8C23×C3×D311yescharacteristic
673C4⋊C4—61no—
674C4⋊C4—62no—
675C22⋊C4—61no—
676C22⋊C4—124no—
677C22⋊C4—121no—
678C42—32no—
679C42—121no—
680C16—22no—
681C16—34no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—42no—
688C22×C3—44no—
689C22×C3—44no—
690C22×C3—84no—
691C22×C3—84no—
692C22×C3—84no—
693C22×C3—122no—
694C22×C3—164no—
695C22×C3—162no—
696C22×C3—162no—
697C22×C3—162no—
698C22×C3—162no—
699C22×C3—164no—
700C22×C3—164no—
701C22×C3—481no—
702C22×C3#478511yescharacteristic
703C22×C3#478511yescharacteristic
704C22×C3C3×#44211yescharacteristic
705C22×C3C3×#44211yescharacteristic
706C22×C3C2×#91411yescharacteristic
707C22×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
708C2×D3—42no—
709C2×D3—161no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—122no—
715C3×C4—122no—
716C3×C4—242no—
717C3×C4#478511yescharacteristic
718C3×C4#478511yescharacteristic
719C3×C4C3×#44211yescharacteristic
720C3×C4C3×#44211yescharacteristic
721C3×C4C2×#67⋊C411yescharacteristic
722C3×C4C2×#91111yescharacteristic
723C3×C4C2×C3×C4×D411yescharacteristic
724C3×C4C2×C3×AGL(1,ℤ/8)11yescharacteristic
725Dic3—42no—
726Dic3—42no—
727Dic3—82no—
728C32#3347111yescharacteristic, complemented, Sylow
729C23—42no—
730C23—42no—
731C23—42no—
732C23—121no—
733C23—162no—
734C23C3×#91411yescharacteristic
735Q8—62no—
736Q8—121no—
737D4—24no—
738D4—42no—
739D4—42no—
740D4—42no—
741D4—62no—
742D4—122no—
743D4—122no—
744D4—121no—
745C2×C4—62no—
746C2×C4—121no—
747C2×C4—122no—
748C2×C4—122no—
749C2×C4—122no—
750C2×C4—484no—
751C2×C4C3×#67⋊C411yescharacteristic
752C2×C4C3×#67⋊C411yescharacteristic
753C2×C4C3×#91111yescharacteristic
754C2×C4C3×#91111yescharacteristic
755C2×C4C3×#91411yescharacteristic
756C2×C4C2×C3×D3×D411yescharacteristic
757C8—42no—
758C8—62no—
759C8C3×#67⋊C411yescharacteristic
760C8C3×#67⋊C411yescharacteristic
761C8C22×C3×C4×D311yescharacteristic
762C8C2×C3×#23711yescharacteristic
763C2×C3—22no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—41no—
772C2×C3—41no—
773C2×C3—84no—
774C2×C3—84no—
775C2×C3—164no—
776C2×C3—242no—
777C2×C3C2×#478511yescharacteristic
778C2×C3C2×C3×#44211yescharacteristic
779D3—82no—
780C22—41no—
781C22—44no—
782C22—84no—
783C22—122no—
784C22—162no—
785C22—162no—
786C22—481no—
787C22C3×#478511yescharacteristic
788C22C3×#478511yescharacteristic
789C22C2×C3×#91411yescharacteristic
790C4—122no—
791C4—122no—
792C4—242no—
793C4C3×#478511yescharacteristic
794C4C3×#478511yescharacteristic
795C4C2×C3×#67⋊C411yescharacteristic
796C4C2×C3×#91111yescharacteristic
797C3—21no—
798C3C3×#3347111yescharacteristic, complemented
799C3#1094866511yescharacteristic, direct product factor
800C2—21no—
801C2—21no—
802C2—21no—
803C2—84no—
804C2—242no—
805C2C2×C3×#478511yescharacteristic
subgroupG/H
centerC2×C3C2×#4785
commutatorC3×C8C23×C3×C4
FrattiniC2×C8C23×C3×D3
FittingC2×C32×#361C2
socleC2×C32C2×#442
prime radicalC2×C3×#5147C2
cosocleC2×C3×C8C24×C3
hypercenterC2×C3×#361D3
hypocenterC3C3×#33471
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C22×C3×C8 ◁ C2×C3×#361

Complements

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

NH ≅ G/Ntype
2. C3×#79249C2semidirect
3. C3×#83823C2semidirect
4. C3×#69254C2semidirect
5. C3×#70685C2semidirect
6. C3×#71450C2semidirect
7. C3×#71425C2semidirect
8. C2×C32×#361C2semidirect
9. #10948665C3direct (N × H)
18. C3×#5152C22semidirect
20. C2×C3×#827C4semidirect
21. C3×#5147C4semidirect
23. C2×C3×#826C4semidirect
29. C3×#4894C22semidirect
30. C32×#361C22semidirect
31. C3×#4518C22semidirect
32. C3×#4512C22semidirect
33. C3×#4494C22semidirect
37. #83823C2×C3semidirect
39. #79249C2×C3semidirect
43. C2×C3×#361D3semidirect
44. C2×C3×#361C2×C3semidirect
47. #71450C2×C3semidirect
48. #71425C2×C3semidirect
49. #70685C2×C3semidirect
50. #69254C2×C3semidirect
69. C2×C3×Dic12C2×C4semidirect
72. C3×#904C2×C4semidirect
74. C2×C3×D24C2×C4semidirect
83. C3×#827C2×C4semidirect
84. C3×#826C2×C4semidirect
90. C3×#812C2×C4semidirect
92. C2×C3×C3⋊C16C2×C4semidirect
123. #5152C22×C3semidirect
125. C2×#827C3×C4semidirect
126. #5147C3×C4semidirect
128. C2×#826C3×C4semidirect
134. #4894C22×C3semidirect
137. C3×#361C2×D3semidirect
138. C3×#361C22×C3semidirect
141. #4518C22×C3semidirect
142. #4512C22×C3semidirect
143. #4494C22×C3semidirect
199. C2×#361C3×D3semidirect
255. C2×Dic12C2×C3×C4semidirect
258. #904C2×C3×C4semidirect
260. C2×D24C2×C3×C4semidirect
290. #827C2×C3×C4semidirect
291. #826C2×C3×C4semidirect
297. #812C2×C3×C4semidirect
299. C2×C3⋊C16C2×C3×C4semidirect
354. #361C2×C3×D3semidirect
728. C32#33471semidirect
798. C3C3×#33471semidirect
799. C3#10948665direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#51472
C3×#792492
C3×#838232
C3×#692542
C3×#706852
C3×#714502
C3×#714252
C2×C32×#3612
#109486653
C3×#334713