Finite Group Databasebeta

← C3×#10595131 #13174696

Subgroups — C3×#10595131 #13174696

Order 1728.

1590 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3804C212yesmaximal, complemented
2C3×#64149C211yesmaximal, characteristic, complemented
3C32×#938C211yesmaximal, characteristic, complemented
4C32×D4×Dic3C211yesmaximal, characteristic, complemented
5C3×#63971C212yesmaximal, complemented
6C3×#63953C212yesmaximal, complemented
7C3×#63952C212yesmaximal, complemented
8C3×#63919C211yesmaximal, characteristic, complemented
9C3×#63909C211yesmaximal, characteristic, complemented
10C3×#63894C211yesmaximal, characteristic, complemented
11C3×C4×D3×Dic3C211yesmaximal, characteristic, complemented
12C3×#5596—31nomaximal
13C3×#5548—31nomaximal
14#10595131C311yesmaximal, characteristic, direct product factor
15C2×C33×D4C2211yescharacteristic
16C2×C3×#638C2212yes—
17C2×C3×#638C2212yes—
18C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C32×#67C2212yes—
20C22×C32×Dic3C2212yes—
21C2×C32×C4×D3C2211yescharacteristic
22C2×C3×#627C2212yes—
23C2×C3×#626C2212yes—
24C2×C3×#624C2212yes—
25C3×#3804—28no—
26C2×C3×D3×Dic3C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28C3×C4×C3⋊Dic3C2211yescharacteristic
29C32×#217C2212yes—
30C32×#217C2212yes—
31C32×C4⋊Dic3C2211yescharacteristic
32C32×C4⋊Dic3C2211yescharacteristic
33C32×C4×Dic3C2211yescharacteristic
34C3×#3724C2212yes—
35C3×#3722C2212yes—
36C3×#3722C2212yes—
37C3×Dic32C2211yescharacteristic
38C3×Dic32C2211yescharacteristic
39C2×C3×#237—32no—
40C2×C3×#235—32no—
41C2×#3804C2×C312yescomplemented
42C32×#121—31no—
43C32×C4×D4—31no—
44#64149C2×C311yescharacteristic, complemented
45C3×#940—31no—
46C3×#940—31no—
47C3×#940—61no—
48C3×#939—32no—
49C3×#938—21no—
50C3×#938D311yescharacteristic, complemented
51C3×#938C2×C311yescharacteristic, complemented
52C3×D4×Dic3—21no—
53C3×D4×Dic3D311yescharacteristic, complemented
54C3×D4×Dic3C2×C311yescharacteristic, complemented
55C3×#930—31no—
56C3×C4×#67—32no—
57C2×C3×C4×Dic3—31no—
58C3×#895—31no—
59C3×#893—31no—
60C3×#888—31no—
61C3×#888—31no—
62C3×#885—32no—
63C3×#885—32no—
64C3×#884—32no—
65C3×#67⋊C4—32no—
66C3×C4×D12—31no—
67C3×C42×D3—31no—
68#63971C2×C312yescomplemented
69#63953C2×C312yescomplemented
70#63952C2×C312yescomplemented
71#63919C2×C311yescharacteristic, complemented
72#63909C2×C311yescharacteristic, complemented
73#63894C2×C311yescharacteristic, complemented
74C4×D3×Dic3C2×C311yescharacteristic, complemented
75C23×C33C2312yes—
76C22×C3×C3⋊D3C2312yes—
77C22×C32×D3C2311yescharacteristic
78C33×D4—22no—
79C2×C33×C4C2311yescharacteristic
80C3×#638—24no—
81C3×#638—24no—
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C3×C4⋊(C3⋊D3)—22no—
85C32×#67—24no—
86C2×C32×Dic3—24no—
87C2×C32×Dic3C2311yescharacteristic
88C2×C32×Dic3C2311yescharacteristic
89C2×C32×Dic3C2312yes—
90C2×C32×Dic3C2312yes—
91C2×C32×Dic3C2311yescharacteristic
92C32×C4×D3—22no—
93C3×#627—24no—
94C3×#626—24no—
95C3×#624—24no—
96C3×D3×Dic3—22no—
97C3×D3×Dic3D414yescomplemented
98C3×#532—91no—
99#5596—31no—
100#5548—31no—
101C2×C32×D4—21no—
102C2×C32×D4—21no—
103C2×C32×D4—21no—
104C2×C32×D4—32no—
105C2×C32×D4—41no—
106C2×C32×D4C2×D311yescharacteristic
107C2×C32×D4C2×D311yescharacteristic
108C2×C32×D4C22×C311yescharacteristic
109C22×C32×C4—32no—
110C22×C32×C4—31no—
111C2×#638C22×C312yes—
112C2×#638C22×C312yes—
113C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
114C2×C3×#67—22no—
115C2×C3×#67—32no—
116C2×C3×#67—32no—
117C2×C3×#67—32no—
118C2×C3×#67—32no—
119C2×C3×#67—32no—
120C2×C3×#67—62no—
121C2×C3×#67—62no—
122C2×C3×#67C2×D312yes—
123C2×C3×#67C22×C312yes—
124C22×C3×Dic3—22no—
125C22×C3×Dic3—31no—
126C22×C3×Dic3—31no—
127C22×C3×Dic3C2×D312yes—
128C22×C3×Dic3C22×C312yes—
129C3×#237—68no—
130C3×#235—68no—
131C2×C3×D12—32no—
132C2×C3×D12—31no—
133C2×C3×D12—31no—
134C2×C3×D12—61no—
135C2×C3×C4×D3—21no—
136C2×C3×C4×D3—31no—
137C2×C3×C4×D3—31no—
138C2×C3×C4×D3—32no—
139C2×C3×C4×D3—32no—
140C2×C3×C4×D3C2×D311yescharacteristic
141C2×C3×C4×D3C22×C311yescharacteristic
142C2×C3×Dic6—32no—
143C2×C3×Dic6—32no—
144C2×#627C22×C312yes—
145C2×#626C22×C312yes—
146C2×#624C22×C312yes—
147#3804—28no—
148C2×D3×Dic3C22×C311yescharacteristic
149C2×D3×Dic3C22×C311yescharacteristic
150C32×C4⋊C4—31no—
151C32×C4⋊C4—31no—
152C32×C22⋊C4—32no—
153C32×C22⋊C4—32no—
154C32×C42—31no—
155C4×C3⋊Dic3C22×C311yescharacteristic
156C3×#217—22no—
157C3×#217—22no—
158C3×#217C2×D312yes—
159C3×#217C2×D312yes—
160C3×#217C22×C312yes—
161C3×#217C22×C312yes—
162C3×(C2×D3)⋊C4—32no—
163C3×(C2×D3)⋊C4—32no—
164C3×(C2×D3)⋊C4—32no—
165C3×(C2×D3)⋊C4—32no—
166C3×C4⋊Dic3—21no—
167C3×C4⋊Dic3—21no—
168C3×C4⋊Dic3C2×D311yescharacteristic
169C3×C4⋊Dic3C2×D311yescharacteristic
170C3×C4⋊Dic3C22×C311yescharacteristic
171C3×C4⋊Dic3C22×C311yescharacteristic
172C3×Dic3⋊C4—32no—
173C3×Dic3⋊C4—32no—
174C3×C4×Dic3—21no—
175C3×C4×Dic3—31no—
176C3×C4×Dic3—31no—
177C3×C4×Dic3—31no—
178C3×C4×Dic3—31no—
179C3×C4×Dic3—31no—
180C3×C4×Dic3—31no—
181C3×C4×Dic3—61no—
182C3×C4×Dic3C2×D311yescharacteristic
183C3×C4×Dic3C22×C311yescharacteristic
184#3724C22×C312yes—
185#3722C22×C312yes—
186#3722C22×C312yes—
187Dic32C22×C311yescharacteristic
188Dic32C22×C311yescharacteristic
189C22×C33—22no—
190C22×C33—22no—
191C22×C33—22no—
192C22×C33C2411yescharacteristic
193C2×C3×C3⋊D3—22no—
194C2×C3×C3⋊D3—22no—
195C2×C3×C3⋊D3—22no—
196C2×C32×D3—21no—
197C2×C32×D3—21no—
198C2×C32×D3C2×D412yes—
199C33×C4#4112yescomplemented
200C3×C3⋊Dic3C2×D412yes—
201C3×C3⋊Dic3#4112yescomplemented
202C32×Dic3—22no—
203C32×Dic3—22no—
204C32×Dic3—21no—
205C32×Dic3—21no—
206C32×Dic3C2×D412yes—
207C2×C3×#41—92no—
208C2×#237—32no—
209C2×#235—32no—
210C3×C4⋊Q8—91no—
211C3×#127—91no—
212C3×#124—92no—
213C3×#121—31no—
214C3×#121—31no—
215C3×#121—61no—
216C3×#121—92no—
217C3×#121—91no—
218C3×C4×D4—31no—
219C3×C4×D4—31no—
220C3×C4×D4—61no—
221C3×C4×D4—91no—
222C3×C4×D4—92no—
223C2×C3×C42—91no—
224#940—31no—
225#940—31no—
226#940—61no—
227#939—32no—
228#938C3×D311yescharacteristic, complemented
229D4×Dic3C3×D311yescharacteristic, complemented
230#930—31no—
231C4×#67—32no—
232C2×C4×Dic3—31no—
233#895—31no—
234#893—31no—
235#888—31no—
236#888—31no—
237#885—32no—
238#885—32no—
239#884—32no—
240#67⋊C4—32no—
241C4×D12—31no—
242C42×D3—31no—
243C23×C32—22no—
244C23×C32—22no—
245C23×C32—22no—
246C23×C32—31no—
247C23×C32—42no—
248C23×C32C22×D312yes—
249C23×C32C22×D312yes—
250C23×C32C23×C312yes—
251C22×C3⋊D3C23×C312yes—
252C22×C3×D3—21no—
253C22×C3×D3—32no—
254C22×C3×D3—32no—
255C22×C3×D3—62no—
256C22×C3×D3C22×D311yescharacteristic
257C22×C3×D3C23×C311yescharacteristic
258C32×D4—22no—
259C32×D4—24no—
260C32×D4—22no—
261C32×D4—22no—
262C32×D4—42no—
263C32×D4—42no—
264C32×D4—44no—
265C32×D4—64no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—31no—
270C2×C32×C4—31no—
271C2×C32×C4—31no—
272C2×C32×C4—32no—
273C2×C32×C4—32no—
274C2×C32×C4—41no—
275C2×C32×C4—64no—
276C2×C32×C4—62no—
277C2×C32×C4C22×D311yescharacteristic
278C2×C32×C4C22×D311yescharacteristic
279C2×C32×C4C23×C311yescharacteristic
280#638—24no—
281#638—24no—
282C2×C3⋊Dic3C23×C311yescharacteristic
283C2×C3⋊Dic3C23×C311yescharacteristic
284C4⋊(C3⋊D3)—22no—
285C3×#67—24no—
286C3×#67—24no—
287C3×#67—44no—
288C3×#67—64no—
289C3×#67—64no—
290C3×#67—64no—
291C3×#67—64no—
292C3×#67—64no—
293C3×#67—124no—
294C3×#67—124no—
295C2×C3×Dic3—24no—
296C2×C3×Dic3—24no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—22no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—31no—
303C2×C3×Dic3—31no—
304C2×C3×Dic3—31no—
305C2×C3×Dic3—31no—
306C2×C3×Dic3—34no—
307C2×C3×Dic3—44no—
308C2×C3×Dic3—61no—
309C2×C3×Dic3—61no—
310C2×C3×Dic3—62no—
311C2×C3×Dic3C22×D311yescharacteristic
312C2×C3×Dic3C22×D311yescharacteristic
313C2×C3×Dic3C22×D312yes—
314C2×C3×Dic3C22×D312yes—
315C2×C3×Dic3C22×D311yescharacteristic
316C2×C3×Dic3C23×C311yescharacteristic
317C2×C3×Dic3C23×C311yescharacteristic
318C2×C3×Dic3C23×C312yes—
319C2×C3×Dic3C23×C312yes—
320C2×C3×Dic3C23×C311yescharacteristic
321C3×D12—64no—
322C3×D12—62no—
323C3×D12—62no—
324C3×D12—122no—
325C3×C4×D3—22no—
326C3×C4×D3—22no—
327C3×C4×D3—34no—
328C3×C4×D3—42no—
329C3×C4×D3—64no—
330C3×C4×D3—62no—
331C3×C4×D3—64no—
332C3×Dic6—64no—
333C3×Dic6—64no—
334#627—24no—
335#626—24no—
336#624—24no—
337D3×Dic3—22no—
338D3×Dic3C3×D414yescomplemented
339#532—91noSylow
340C2×C33—42no—
341C2×C33C22×D411yescharacteristic
342C2×C33C2×#4111yescharacteristic
343C2×C33C2×#4111yescharacteristic
344C3×C3⋊D3—42no—
345C32×D3—22no—
346C3×#41—188no—
347C2×C3×Q8—92no—
348C2×C3×D4—21no—
349C2×C3×D4—21no—
350C2×C3×D4—21no—
351C2×C3×D4—32no—
352C2×C3×D4—32no—
353C2×C3×D4—41no—
354C2×C3×D4—62no—
355C2×C3×D4—92no—
356C2×C3×D4—92no—
357C2×C3×D4—92no—
358C2×C3×D4—91no—
359C2×C3×D4D3211yescharacteristic
360C2×C3×D4C2×C3×D311yescharacteristic
361C2×C3×D4C2×C3×D311yescharacteristic
362C22×C3×C4—32no—
363C22×C3×C4—32no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—61no—
367C22×C3×C4—62no—
368C22×C3×C4—92no—
369C22×C3×C4—91no—
370C22×C3×C4—91no—
371C2×#67—32no—
372C2×#67—32no—
373C2×#67—32no—
374C2×#67—32no—
375C2×#67—32no—
376C2×#67—62no—
377C2×#67—62no—
378C2×#67C2×C3×D312yes—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3C2×C3×D312yes—
382#237—68no—
383#235—68no—
384C2×D12—32no—
385C2×D12—31no—
386C2×D12—31no—
387C2×D12—61no—
388C2×C4×D3—31no—
389C2×C4×D3—31no—
390C2×C4×D3—32no—
391C2×C4×D3—32no—
392C2×C4×D3C2×C3×D311yescharacteristic
393C2×Dic6—32no—
394C2×Dic6—32no—
395C3×C4⋊C4—31no—
396C3×C4⋊C4—31no—
397C3×C4⋊C4—31no—
398C3×C4⋊C4—31no—
399C3×C4⋊C4—61no—
400C3×C4⋊C4—61no—
401C3×C4⋊C4—92no—
402C3×C22⋊C4—32no—
403C3×C22⋊C4—32no—
404C3×C22⋊C4—32no—
405C3×C22⋊C4—32no—
406C3×C22⋊C4—62no—
407C3×C22⋊C4—62no—
408C3×C22⋊C4—92no—
409C3×C22⋊C4—92no—
410C3×C42—31no—
411C3×C42—31no—
412C3×C42—61no—
413C3×C42—91no—
414C3×C42—91no—
415C3×C42—91no—
416#217C2×C3×D312yes—
417#217C2×C3×D312yes—
418(C2×D3)⋊C4—32no—
419(C2×D3)⋊C4—32no—
420(C2×D3)⋊C4—32no—
421(C2×D3)⋊C4—32no—
422C4⋊Dic3C2×C3×D311yescharacteristic
423C4⋊Dic3C2×C3×D311yescharacteristic
424Dic3⋊C4—32no—
425Dic3⋊C4—32no—
426C4×Dic3—31no—
427C4×Dic3—31no—
428C4×Dic3—31no—
429C4×Dic3—31no—
430C4×Dic3—31no—
431C4×Dic3—31no—
432C4×Dic3—61no—
433C4×Dic3C2×C3×D311yescharacteristic
434C22×C32—22no—
435C22×C32—24no—
436C22×C32—22no—
437C22×C32—22no—
438C22×C32—22no—
439C22×C32—22no—
440C22×C32—22no—
441C22×C32—22no—
442C22×C32—22no—
443C22×C32—22no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—32no—
448C22×C32—41no—
449C22×C32—42no—
450C22×C32—42no—
451C22×C32—44no—
452C22×C32—42no—
453C22×C32—42no—
454C22×C32—42no—
455C22×C32—42no—
456C22×C32—42no—
457C22×C32—42no—
458C22×C32—61no—
459C22×C32—61no—
460C22×C32—82no—
461C22×C32—82no—
462C22×C32C23×D311yescharacteristic
463C22×C32C23×D311yescharacteristic
464C22×C32C24×C311yescharacteristic
465C2×C3⋊D3—22no—
466C2×C3⋊D3—22no—
467C2×C3⋊D3—22no—
468C2×C3×D3—21no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—22no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—62no—
476C2×C3×D3—62no—
477C2×C3×D3—62no—
478C2×C3×D3—62no—
479C2×C3×D3—62no—
480C2×C3×D3—62no—
481C2×C3×D3—122no—
482C2×C3×D3—122no—
483C2×C3×D3—122no—
484C2×C3×D3D3×D412yes—
485C2×C3×D3C2×C3×D412yes—
486C32×C4—22no—
487C32×C4—22no—
488C32×C4—22no—
489C32×C4—32no—
490C32×C4—42no—
491C32×C4—61no—
492C32×C4—62no—
493C32×C4—62no—
494C32×C4—61no—
495C32×C4#23512yescomplemented
496C32×C4#23712yescomplemented
497C32×C4C3×#4112yescomplemented
498C3⋊Dic3C2×C3×D412yes—
499C3⋊Dic3C3×#4112yescomplemented
500C3×Dic3—22no—
501C3×Dic3—22no—
502C3×Dic3—21no—
503C3×Dic3—21no—
504C3×Dic3—22no—
505C3×Dic3—22no—
506C3×Dic3—21no—
507C3×Dic3—21no—
508C3×Dic3—22no—
509C3×Dic3—32no—
510C3×Dic3—32no—
511C3×Dic3—32no—
512C3×Dic3—32no—
513C3×Dic3—41no—
514C3×Dic3—41no—
515C3×Dic3—42no—
516C3×Dic3—42no—
517C3×Dic3—62no—
518C3×Dic3—62no—
519C3×Dic3D3×D412yes—
520C3×Dic3C2×C3×D412yes—
521C2×#41—92no—
522C4⋊Q8—91no—
523#127—91no—
524#124—92no—
525#121—31no—
526#121—92no—
527#121—91no—
528C4×D4—31no—
529C4×D4—91no—
530C4×D4—92no—
531C2×C42—91no—
532C33#53211yescharacteristic, complemented, Sylow
533C23×C3—22no—
534C23×C3—22no—
535C23×C3—22no—
536C23×C3—31no—
537C23×C3—31no—
538C23×C3—42no—
539C23×C3—61no—
540C23×C3—92no—
541C23×C3C2×D3212yes—
542C23×C3C22×C3×D312yes—
543C23×C3C22×C3×D312yes—
544C22×D3—32no—
545C22×D3—32no—
546C22×D3—62no—
547C22×D3C22×C3×D311yescharacteristic
548C3×Q8—184no—
549C3×D4—24no—
550C3×D4—22no—
551C3×D4—22no—
552C3×D4—22no—
553C3×D4—42no—
554C3×D4—42no—
555C3×D4—44no—
556C3×D4—64no—
557C3×D4—64no—
558C3×D4—124no—
559C3×D4—184no—
560C3×D4—184no—
561C3×D4—184no—
562C3×D4—182no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—31no—
567C2×C3×C4—31no—
568C2×C3×C4—31no—
569C2×C3×C4—31no—
570C2×C3×C4—32no—
571C2×C3×C4—32no—
572C2×C3×C4—31no—
573C2×C3×C4—31no—
574C2×C3×C4—32no—
575C2×C3×C4—32no—
576C2×C3×C4—41no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—62no—
581C2×C3×C4—62no—
582C2×C3×C4—64no—
583C2×C3×C4—64no—
584C2×C3×C4—62no—
585C2×C3×C4—62no—
586C2×C3×C4—94no—
587C2×C3×C4—91no—
588C2×C3×C4—91no—
589C2×C3×C4—122no—
590C2×C3×C4—124no—
591C2×C3×C4—184no—
592C2×C3×C4—182no—
593C2×C3×C4C2×D3211yescharacteristic
594C2×C3×C4C22×C3×D311yescharacteristic
595C2×C3×C4C22×C3×D311yescharacteristic
596#67—24no—
597#67—64no—
598#67—64no—
599#67—64no—
600#67—64no—
601#67—64no—
602#67—124no—
603#67—124no—
604C2×Dic3—24no—
605C2×Dic3—31no—
606C2×Dic3—31no—
607C2×Dic3—31no—
608C2×Dic3—31no—
609C2×Dic3—34no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—62no—
613C2×Dic3C22×C3×D311yescharacteristic
614C2×Dic3C22×C3×D311yescharacteristic
615C2×Dic3C22×C3×D312yes—
616C2×Dic3C22×C3×D312yes—
617C2×Dic3C22×C3×D311yescharacteristic
618D12—64no—
619D12—62no—
620D12—62no—
621D12—122no—
622C4×D3—22no—
623C4×D3—34no—
624C4×D3—64no—
625C4×D3—62no—
626C4×D3—64no—
627Dic6—64no—
628Dic6—64no—
629C2×C32—21no—
630C2×C32—21no—
631C2×C32—21no—
632C2×C32—21no—
633C2×C32—21no—
634C2×C32—21no—
635C2×C32—21no—
636C2×C32—21no—
637C2×C32—21no—
638C2×C32—41no—
639C2×C32—41no—
640C2×C32—41no—
641C2×C32—42no—
642C2×C32—44no—
643C2×C32—42no—
644C2×C32—42no—
645C2×C32—62no—
646C2×C32—82no—
647C2×C32—82no—
648C2×C32—84no—
649C2×C32C2×#23511yescharacteristic
650C2×C32C2×D3×D411yescharacteristic
651C2×C32C2×D3×D411yescharacteristic
652C2×C32C2×#23711yescharacteristic
653C2×C32D3×#4111yescharacteristic
654C2×C32D3×#4111yescharacteristic
655C2×C32C22×C3×D411yescharacteristic
656C2×C32C2×C3×#4111yescharacteristic
657C2×C32C2×C3×#4111yescharacteristic
658C3⋊D3—42no—
659C3×D3—22no—
660C3×D3—22no—
661C3×D3—42no—
662C3×D3—122no—
663C3×D3—122no—
664C3×D3—242no—
665#41—188no—
666C2×Q8—92no—
667C2×D4—32no—
668C2×D4—92no—
669C2×D4—92no—
670C2×D4—92no—
671C2×D4—91no—
672C2×D4C3×D3211yescharacteristic
673C22×C4—32no—
674C22×C4—31no—
675C22×C4—92no—
676C22×C4—91no—
677C22×C4—91no—
678C4⋊C4—31no—
679C4⋊C4—31no—
680C4⋊C4—92no—
681C22⋊C4—32no—
682C22⋊C4—32no—
683C22⋊C4—92no—
684C22⋊C4—92no—
685C42—31no—
686C42—91no—
687C42—91no—
688C42—91no—
689C22×C3—24no—
690C22×C3—22no—
691C22×C3—22no—
692C22×C3—22no—
693C22×C3—22no—
694C22×C3—22no—
695C22×C3—22no—
696C22×C3—22no—
697C22×C3—22no—
698C22×C3—22no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—32no—
703C22×C3—32no—
704C22×C3—42no—
705C22×C3—42no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—44no—
713C22×C3—41no—
714C22×C3—62no—
715C22×C3—61no—
716C22×C3—61no—
717C22×C3—61no—
718C22×C3—61no—
719C22×C3—82no—
720C22×C3—82no—
721C22×C3—121no—
722C22×C3—121no—
723C22×C3—182no—
724C22×C3—182no—
725C22×C3—182no—
726C22×C3C22×D3211yescharacteristic
727C22×C3C23×C3×D311yescharacteristic
728C22×C3C23×C3×D311yescharacteristic
729C2×D3—21no—
730C2×D3—21no—
731C2×D3—62no—
732C2×D3—62no—
733C2×D3—62no—
734C2×D3—62no—
735C2×D3—62no—
736C2×D3—62no—
737C2×D3—122no—
738C2×D3—122no—
739C2×D3—122no—
740C2×D3C3×D3×D412yes—
741C3×C4—22no—
742C3×C4—22no—
743C3×C4—22no—
744C3×C4—32no—
745C3×C4—32no—
746C3×C4—42no—
747C3×C4—62no—
748C3×C4—62no—
749C3×C4—62no—
750C3×C4—61no—
751C3×C4—61no—
752C3×C4—61no—
753C3×C4—62no—
754C3×C4—62no—
755C3×C4—61no—
756C3×C4—92no—
757C3×C4—92no—
758C3×C4—121no—
759C3×C4—122no—
760C3×C4—122no—
761C3×C4—121no—
762C3×C4#380412yescomplemented
763C3×C4C3×#23512yescomplemented
764C3×C4C3×#23712yescomplemented
765Dic3—22no—
766Dic3—22no—
767Dic3—21no—
768Dic3—21no—
769Dic3—32no—
770Dic3—32no—
771Dic3—32no—
772Dic3—32no—
773Dic3—62no—
774Dic3—62no—
775Dic3C3×D3×D412yes—
776C32—21no—
777C32—21no—
778C32—21no—
779C32—41no—
780C32#554811yescharacteristic, complemented
781C32#559611yescharacteristic, complemented
782C32C3×#53211yescharacteristic, complemented
783C23—31no—
784C23—92no—
785C23C2×C3×D3212yes—
786Q8—184no—
787D4—22no—
788D4—64no—
789D4—184no—
790D4—184no—
791D4—184no—
792D4—182no—
793C2×C4—31no—
794C2×C4—31no—
795C2×C4—31no—
796C2×C4—32no—
797C2×C4—32no—
798C2×C4—64no—
799C2×C4—62no—
800C2×C4—94no—
801C2×C4—91no—
802C2×C4—91no—
803C2×C4—184no—
804C2×C4—182no—
805C2×C4C2×C3×D3211yescharacteristic
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—44no—
816C2×C3—42no—
817C2×C3—42no—
818C2×C3—42no—
819C2×C3—41no—
820C2×C3—41no—
821C2×C3—41no—
822C2×C3—62no—
823C2×C3—62no—
824C2×C3—82no—
825C2×C3—82no—
826C2×C3—84no—
827C2×C3—122no—
828C2×C3—362no—
829C2×C3D32×D411yescharacteristic
830C2×C3#6431211yescharacteristic
831C2×C3C2×#380411yescharacteristic
832C2×C3C2×C3×#23511yescharacteristic
833C2×C3C2×C3×D3×D411yescharacteristic
834C2×C3C2×C3×D3×D411yescharacteristic
835C2×C3C2×C3×#23711yescharacteristic
836C2×C3C3×D3×#4111yescharacteristic
837C2×C3C3×D3×#4111yescharacteristic
838D3—22no—
839D3—122no—
840D3—122no—
841D3—242no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—32no—
846C22—61no—
847C22—61no—
848C22—182no—
849C22—182no—
850C22—182no—
851C22C22×C3×D3211yescharacteristic
852C4—32no—
853C4—61no—
854C4—62no—
855C4—62no—
856C4—61no—
857C4—92no—
858C4—92no—
859C4C3×#380412yescomplemented
860C3—21no—
861C3—21no—
862C3—21no—
863C3—41no—
864C3#1059513111yescharacteristic, direct product factor
865C3C3×#554811yescharacteristic, complemented
866C3C3×#559611yescharacteristic, complemented
867C2—42no—
868C2—62no—
869C2—362no—
870C2C3×D32×D411yescharacteristic
871C2C3×#6431211yescharacteristic
872C2C2×C3×#380411yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C3×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3804C2semidirect
2. C3×#64149C2semidirect
3. C32×#938C2semidirect
4. C32×D4×Dic3C2semidirect
5. C3×#63971C2semidirect
6. C3×#63953C2semidirect
7. C3×#63952C2semidirect
8. C3×#63919C2semidirect
9. C3×#63909C2semidirect
10. C3×#63894C2semidirect
11. C3×C4×D3×Dic3C2semidirect
14. #10595131C3direct (N × H)
41. C2×#3804C2×C3semidirect
44. #64149C2×C3semidirect
50. C3×#938D3semidirect
51. C3×#938C2×C3semidirect
53. C3×D4×Dic3D3semidirect
54. C3×D4×Dic3C2×C3semidirect
68. #63971C2×C3semidirect
69. #63953C2×C3semidirect
70. #63952C2×C3semidirect
71. #63919C2×C3semidirect
72. #63909C2×C3semidirect
73. #63894C2×C3semidirect
74. C4×D3×Dic3C2×C3semidirect
97. C3×D3×Dic3D4semidirect
199. C33×C4#41semidirect
201. C3×C3⋊Dic3#41semidirect
228. #938C3×D3semidirect
229. D4×Dic3C3×D3semidirect
338. D3×Dic3C3×D4semidirect
495. C32×C4#235semidirect
496. C32×C4#237semidirect
497. C32×C4C3×#41semidirect
499. C3⋊Dic3C3×#41semidirect
532. C33#532semidirect
762. C3×C4#3804semidirect
763. C3×C4C3×#235semidirect
764. C3×C4C3×#237semidirect
780. C32#5548semidirect
781. C32#5596semidirect
782. C32C3×#532semidirect
859. C4C3×#3804semidirect
864. C3#10595131direct (N × H)
865. C3C3×#5548semidirect
866. C3C3×#5596semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38042
C3×#641492
C32×#9382
C32×D4×Dic32
C3×#639712
C3×#639532
C3×#639522
C3×#639192
C3×#639092
C3×#638942
C3×C4×D3×Dic32
C3×#55963
C3×#55483
#105951313