Finite Group Databasebeta

← C3×#10595231 #13174794

Subgroups — C3×#10595231 #13174794

Order 1728.

1814 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×D3×D4C211yesmaximal, characteristic, complemented
2C2×C3×#3798C211yesmaximal, characteristic, complemented
3C3×#64147C211yesmaximal, characteristic, complemented
4C32×#938C211yesmaximal, characteristic, complemented
5C3×#63979C212yesmaximal, complemented
6C3×#63977C212yesmaximal, complemented
7C3×#63976C212yesmaximal, complemented
8C3×#63959C212yesmaximal, complemented
9C3×#63916C211yesmaximal, characteristic, complemented
10C3×#63908C211yesmaximal, characteristic, complemented
11C3×#63841C211yesmaximal, characteristic, complemented
12C3×#5805—31nomaximal
13C3×#5607—31nomaximal
14#10595231C311yesmaximal, characteristic, direct product factor
15C23×C32×D3C2212yes—
16C2×C33×D4C2211yescharacteristic
17C2×C3×#638C2212yescomplemented
18C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
19C2×C32×#67C2212yes—
20C2×C32×#67C2212yescomplemented
21C32×D3×D4—24no—
22C2×C32×D12C2211yescharacteristic
23C2×C32×C4×D3C2211yescharacteristic
24C2×C32×C4×D3C2211yescharacteristic, complemented
25C2×C3×#627C2211yescharacteristic, complemented
26C2×C3×#626C2211yescharacteristic
27C2×C3×#626C2211yescharacteristic, complemented
28C2×C3×#626C2212yescomplemented
29C2×C3×#625C2211yescharacteristic
30C2×C3×#625C2212yescomplemented
31C3×#3798—24no—
32C3×#3757C2212yescomplemented
33C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
34C32×#217C2212yescomplemented
35C32×C4⋊Dic3C2211yescharacteristic, complemented
36C3×(C2×D3)⋊Dic3C2212yes—
37C3×(C2×D3)⋊Dic3C2212yescomplemented
38C3×(C2×D3)⋊Dic3C2212yescomplemented
39C3×Dic32C2212yescomplemented
40C22×C32×D4—31no—
41C2×C3×D3×D4—21no—
42C2×C3×D3×D4D311yescharacteristic, complemented
43C2×C3×D3×D4C2×C311yescharacteristic, complemented
44C2×C3×#235—31no—
45C2×C3×#235—31no—
46C2×#3798C2×C311yescharacteristic, complemented
47C32×#121—31no—
48#64147C2×C311yescharacteristic, complemented
49C3×#953—32no—
50C3×#953—32no—
51C3×#940—32no—
52C3×#940—32no—
53C3×#938—21no—
54C3×#938—31no—
55C3×#938—31no—
56C3×#938—31no—
57C3×#938—31no—
58C3×#938—61no—
59C3×#938D311yescharacteristic, complemented
60C3×#938C2×C311yescharacteristic, complemented
61C3×#937—32no—
62C3×#936—32no—
63C3×#930—31no—
64C3×#926—31no—
65C3×#895—31no—
66C3×#892—31no—
67C3×#885—32no—
68C3×#882—32no—
69#63979C2×C312yescomplemented
70#63977C2×C312yescomplemented
71#63976C2×C312yescomplemented
72#63959C2×C312yescomplemented
73#63916C2×C311yescharacteristic, complemented
74#63908C2×C311yescharacteristic, complemented
75#63841C2×C311yescharacteristic, complemented
76C23×C33C2312yes—
77C22×C3×C3⋊D3C2311yescharacteristic
78C22×C32×D3—24no—
79C22×C32×D3—42no—
80C22×C32×D3—42no—
81C22×C32×D3C2312yes—
82C22×C32×D3C2311yescharacteristic
83C22×C32×D3C2311yescharacteristic
84C33×D4—22no—
85C2×C33×C4C2311yescharacteristic
86C3×#638—42no—
87C2×C3×C3⋊Dic3C2312yes—
88C2×C3×C3⋊Dic3C2311yescharacteristic
89C3×C4×C3⋊D3—22no—
90C32×#67—24no—
91C32×#67—42no—
92C2×C32×Dic3C2311yescharacteristic
93C2×C32×Dic3C2312yes—
94C2×C32×Dic3C2311yescharacteristic
95C32×D12—22no—
96C32×C4×D3—22no—
97C32×C4×D3D414yescomplemented
98C3×#627—22no—
99C3×#626—22no—
100C3×#626—22no—
101C3×#626—42no—
102C3×#625—22no—
103C3×#625—42no—
104C3×#535—91no—
105#5805—31no—
106#5607—31no—
107C24×C32—32no—
108C23×C3×D3—22no—
109C23×C3×D3C2×D312yes—
110C23×C3×D3C22×C312yes—
111C2×C32×D4—21no—
112C2×C32×D4—21no—
113C2×C32×D4—21no—
114C2×C32×D4—32no—
115C2×C32×D4—32no—
116C2×C32×D4—31no—
117C2×C32×D4—41no—
118C2×C32×D4—64no—
119C2×C32×D4C2×D311yescharacteristic
120C2×C32×D4C2×D311yescharacteristic
121C2×C32×D4C22×C311yescharacteristic
122C22×C32×C4—31no—
123C22×C32×C4—31no—
124C2×#638C22×C312yescomplemented
125C2×C4×C3⋊D3C22×C311yescharacteristic, complemented
126C2×C3×#67—22no—
127C2×C3×#67—22no—
128C2×C3×#67—31no—
129C2×C3×#67—31no—
130C2×C3×#67—32no—
131C2×C3×#67—32no—
132C2×C3×#67—32no—
133C2×C3×#67—32no—
134C2×C3×#67—31no—
135C2×C3×#67—31no—
136C2×C3×#67—32no—
137C2×C3×#67—62no—
138C2×C3×#67C2×D312yes—
139C2×C3×#67C2×D312yescomplemented
140C2×C3×#67C22×C312yes—
141C2×C3×#67C22×C312yescomplemented
142C3×D3×D4—28no—
143C3×D3×D4—24no—
144C3×D3×D4—24no—
145C3×#235—64no—
146C3×#235—64no—
147C2×C3×D12—21no—
148C2×C3×D12—31no—
149C2×C3×D12—31no—
150C2×C3×D12—32no—
151C2×C3×D12C2×D311yescharacteristic
152C2×C3×D12C22×C311yescharacteristic
153C2×C3×C4×D3—21no—
154C2×C3×C4×D3—21no—
155C2×C3×C4×D3—31no—
156C2×C3×C4×D3—31no—
157C2×C3×C4×D3—61no—
158C2×C3×C4×D3C2×D311yescharacteristic
159C2×C3×C4×D3C2×D311yescharacteristic, complemented
160C2×C3×C4×D3C22×C311yescharacteristic
161C2×C3×C4×D3C22×C311yescharacteristic, complemented
162C2×C3×Dic6—31no—
163C2×C3×Dic6—31no—
164C2×#627C22×C311yescharacteristic, complemented
165C2×#626C22×C311yescharacteristic
166C2×#626C22×C311yescharacteristic, complemented
167C2×#626C22×C312yescomplemented
168C2×#625C22×C311yescharacteristic
169C2×#625C22×C312yescomplemented
170#3798—24no—
171C32×C4⋊C4—31no—
172C32×C22⋊C4—32no—
173#3757C22×C312yescomplemented
174C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
175C3×#217—22no—
176C3×#217—32no—
177C3×#217—32no—
178C3×#217—32no—
179C3×#217—32no—
180C3×#217—32no—
181C3×#217—62no—
182C3×#217C2×D312yescomplemented
183C3×#217C22×C312yescomplemented
184C3×(C2×D3)⋊C4—32no—
185C3×(C2×D3)⋊C4—32no—
186C3×(C2×D3)⋊C4—32no—
187C3×C4⋊Dic3—21no—
188C3×C4⋊Dic3—31no—
189C3×C4⋊Dic3—31no—
190C3×C4⋊Dic3—61no—
191C3×C4⋊Dic3C2×D311yescharacteristic, complemented
192C3×C4⋊Dic3C22×C311yescharacteristic, complemented
193C3×C4×Dic3—32no—
194C3×C4×Dic3—32no—
195(C2×D3)⋊Dic3C22×C312yes—
196(C2×D3)⋊Dic3C22×C312yescomplemented
197(C2×D3)⋊Dic3C22×C312yescomplemented
198Dic32C22×C312yescomplemented
199C22×C33—22no—
200C22×C33—22no—
201C22×C33—22no—
202C22×C33C2411yescharacteristic
203C2×C3×C3⋊D3—21no—
204C2×C3×C3⋊D3—21no—
205C2×C3×C3⋊D3—21no—
206C2×C32×D3—21no—
207C2×C32×D3—21no—
208C2×C32×D3—22no—
209C2×C32×D3—21no—
210C2×C32×D3—21no—
211C2×C32×D3—21no—
212C2×C32×D3—22no—
213C2×C32×D3—22no—
214C2×C32×D3—48no—
215C2×C32×D3C2×D412yes—
216C33×C4C2×D412yes—
217C3×C3⋊Dic3—21no—
218C3×C3⋊Dic3—22no—
219C32×Dic3—21no—
220C32×Dic3—22no—
221C32×Dic3C2×D412yes—
222C2×C3×#41—91no—
223C22×C3×D4—31no—
224C22×C3×D4—31no—
225C22×C3×D4—61no—
226C2×D3×D4C3×D311yescharacteristic, complemented
227C2×#235—31no—
228C2×#235—31no—
229C3×#127—92no—
230C3×#124—92no—
231C3×#121—31no—
232C3×#121—31no—
233C3×#121—61no—
234C3×#121—91no—
235C3×#121—91no—
236C3×#121—91no—
237C3×#120—92no—
238C3×#120—92no—
239C3×#117—91no—
240#953—32no—
241#953—32no—
242#940—32no—
243#940—32no—
244#938—31no—
245#938—31no—
246#938—31no—
247#938—31no—
248#938—61no—
249#938C3×D311yescharacteristic, complemented
250#937—32no—
251#936—32no—
252#930—31no—
253#926—31no—
254#895—31no—
255#892—31no—
256#885—32no—
257#882—32no—
258C23×C32—22no—
259C23×C32—22no—
260C23×C32—22no—
261C23×C32—31no—
262C23×C32—32no—
263C23×C32—31no—
264C23×C32—42no—
265C23×C32—64no—
266C23×C32—122no—
267C23×C32—122no—
268C23×C32C22×D312yes—
269C23×C32C22×D312yes—
270C23×C32C23×C312yes—
271C22×C3⋊D3C23×C311yescharacteristic
272C22×C3×D3—28no—
273C22×C3×D3—24no—
274C22×C3×D3—24no—
275C22×C3×D3—21no—
276C22×C3×D3—22no—
277C22×C3×D3—21no—
278C22×C3×D3—31no—
279C22×C3×D3—31no—
280C22×C3×D3—42no—
281C22×C3×D3—42no—
282C22×C3×D3—42no—
283C22×C3×D3—42no—
284C22×C3×D3—44no—
285C22×C3×D3—44no—
286C22×C3×D3—61no—
287C22×C3×D3C22×D312yes—
288C22×C3×D3C22×D311yescharacteristic
289C22×C3×D3C22×D311yescharacteristic
290C22×C3×D3C23×C312yes—
291C22×C3×D3C23×C311yescharacteristic
292C22×C3×D3C23×C311yescharacteristic
293C32×D4—22no—
294C32×D4—24no—
295C32×D4—22no—
296C32×D4—22no—
297C32×D4—42no—
298C32×D4—42no—
299C32×D4—44no—
300C32×D4—64no—
301C32×D4—62no—
302C32×D4—122no—
303C2×C32×C4—21no—
304C2×C32×C4—21no—
305C2×C32×C4—21no—
306C2×C32×C4—31no—
307C2×C32×C4—34no—
308C2×C32×C4—32no—
309C2×C32×C4—31no—
310C2×C32×C4—41no—
311C2×C32×C4—62no—
312C2×C32×C4C22×D311yescharacteristic
313C2×C32×C4C22×D311yescharacteristic
314C2×C32×C4C23×C311yescharacteristic
315#638—42no—
316C2×C3⋊Dic3C23×C312yes—
317C2×C3⋊Dic3C23×C311yescharacteristic
318C4×C3⋊D3—22no—
319C3×#67—28no—
320C3×#67—24no—
321C3×#67—24no—
322C3×#67—42no—
323C3×#67—42no—
324C3×#67—44no—
325C3×#67—62no—
326C3×#67—62no—
327C3×#67—62no—
328C3×#67—62no—
329C3×#67—122no—
330C3×#67—122no—
331C3×#67—122no—
332C3×#67—122no—
333C3×#67—122no—
334C3×#67—124no—
335C2×C3×Dic3—21no—
336C2×C3×Dic3—22no—
337C2×C3×Dic3—21no—
338C2×C3×Dic3—32no—
339C2×C3×Dic3—32no—
340C2×C3×Dic3—31no—
341C2×C3×Dic3—31no—
342C2×C3×Dic3—62no—
343C2×C3×Dic3—61no—
344C2×C3×Dic3C22×D312yes—
345C2×C3×Dic3C22×D311yescharacteristic
346C2×C3×Dic3C22×D311yescharacteristic
347C2×C3×Dic3C23×C312yes—
348C2×C3×Dic3C23×C311yescharacteristic
349C2×C3×Dic3C23×C311yescharacteristic
350C3×D12—24no—
351C3×D12—22no—
352C3×D12—22no—
353C3×D12—62no—
354C3×D12—62no—
355C3×D12—122no—
356C3×C4×D3—22no—
357C3×C4×D3—22no—
358C3×C4×D3—24no—
359C3×C4×D3—42no—
360C3×C4×D3—62no—
361C3×C4×D3—62no—
362C3×C4×D3—122no—
363C3×C4×D3#6714yescomplemented
364C3×C4×D3C3×D414yescomplemented
365C3×Dic6—62no—
366C3×Dic6—62no—
367#627—22no—
368#626—22no—
369#626—22no—
370#626—42no—
371#625—22no—
372#625—42no—
373#535—91noSylow
374C2×C33—42no—
375C2×C33C22×D411yescharacteristic
376C2×C33H(5,𝔽2)11yescharacteristic
377C2×C33H(5,𝔽2)11yescharacteristic
378C3×C3⋊D3—41no—
379C32×D3—22no—
380C32×D3—41no—
381C32×D3—42no—
382C24×C3—32no—
383C24×C3—32no—
384C24×C3—62no—
385C23×D3C2×C3×D312yes—
386C3×#41—184no—
387C2×C3×Q8—91no—
388C2×C3×D4—21no—
389C2×C3×D4—21no—
390C2×C3×D4—21no—
391C2×C3×D4—32no—
392C2×C3×D4—32no—
393C2×C3×D4—32no—
394C2×C3×D4—32no—
395C2×C3×D4—31no—
396C2×C3×D4—31no—
397C2×C3×D4—41no—
398C2×C3×D4—61no—
399C2×C3×D4—62no—
400C2×C3×D4—62no—
401C2×C3×D4—64no—
402C2×C3×D4—64no—
403C2×C3×D4—68no—
404C2×C3×D4—91no—
405C2×C3×D4—91no—
406C2×C3×D4—92no—
407C2×C3×D4—91no—
408C2×C3×D4—92no—
409C2×C3×D4—92no—
410C2×C3×D4D3211yescharacteristic
411C2×C3×D4C2×C3×D311yescharacteristic
412C2×C3×D4C2×C3×D311yescharacteristic
413C22×C3×C4—31no—
414C22×C3×C4—31no—
415C22×C3×C4—31no—
416C22×C3×C4—31no—
417C22×C3×C4—61no—
418C22×C3×C4—61no—
419C22×C3×C4—91no—
420C2×#67—31no—
421C2×#67—31no—
422C2×#67—32no—
423C2×#67—32no—
424C2×#67—32no—
425C2×#67—32no—
426C2×#67—31no—
427C2×#67—31no—
428C2×#67—32no—
429C2×#67—62no—
430C2×#67C2×C3×D312yes—
431C2×#67C2×C3×D312yescomplemented
432D3×D4—24no—
433#235—64no—
434#235—64no—
435C2×D12—31no—
436C2×D12—31no—
437C2×D12—32no—
438C2×D12C2×C3×D311yescharacteristic
439C2×C4×D3—31no—
440C2×C4×D3—31no—
441C2×C4×D3—61no—
442C2×C4×D3C2×C3×D311yescharacteristic
443C2×C4×D3C2×C3×D311yescharacteristic, complemented
444C2×Dic6—31no—
445C2×Dic6—31no—
446C3×C4⋊C4—31no—
447C3×C4⋊C4—31no—
448C3×C4⋊C4—61no—
449C3×C4⋊C4—91no—
450C3×C22⋊C4—32no—
451C3×C22⋊C4—32no—
452C3×C22⋊C4—62no—
453C3×C22⋊C4—92no—
454C3×C22⋊C4—92no—
455C3×C22⋊C4—92no—
456C3×C22⋊C4—92no—
457C3×C42—92no—
458#217—32no—
459#217—32no—
460#217—32no—
461#217—32no—
462#217—32no—
463#217—62no—
464#217C2×C3×D312yescomplemented
465(C2×D3)⋊C4—32no—
466(C2×D3)⋊C4—32no—
467(C2×D3)⋊C4—32no—
468C4⋊Dic3—31no—
469C4⋊Dic3—31no—
470C4⋊Dic3—61no—
471C4⋊Dic3C2×C3×D311yescharacteristic, complemented
472C4×Dic3—32no—
473C4×Dic3—32no—
474C22×C32—22no—
475C22×C32—24no—
476C22×C32—22no—
477C22×C32—22no—
478C22×C32—22no—
479C22×C32—22no—
480C22×C32—22no—
481C22×C32—22no—
482C22×C32—22no—
483C22×C32—22no—
484C22×C32—21no—
485C22×C32—21no—
486C22×C32—21no—
487C22×C32—32no—
488C22×C32—41no—
489C22×C32—42no—
490C22×C32—42no—
491C22×C32—44no—
492C22×C32—42no—
493C22×C32—42no—
494C22×C32—42no—
495C22×C32—42no—
496C22×C32—42no—
497C22×C32—42no—
498C22×C32—61no—
499C22×C32—61no—
500C22×C32—62no—
501C22×C32—61no—
502C22×C32—61no—
503C22×C32—62no—
504C22×C32—62no—
505C22×C32—61no—
506C22×C32—82no—
507C22×C32—82no—
508C22×C32—128no—
509C22×C32C23×D311yescharacteristic
510C22×C32C23×D311yescharacteristic
511C22×C32C24×C311yescharacteristic
512C2×C3⋊D3—21no—
513C2×C3⋊D3—21no—
514C2×C3⋊D3—21no—
515C2×C3×D3—22no—
516C2×C3×D3—22no—
517C2×C3×D3—21no—
518C2×C3×D3—21no—
519C2×C3×D3—21no—
520C2×C3×D3—21no—
521C2×C3×D3—24no—
522C2×C3×D3—22no—
523C2×C3×D3—21no—
524C2×C3×D3—22no—
525C2×C3×D3—21no—
526C2×C3×D3—22no—
527C2×C3×D3—21no—
528C2×C3×D3—22no—
529C2×C3×D3—21no—
530C2×C3×D3—22no—
531C2×C3×D3—21no—
532C2×C3×D3—22no—
533C2×C3×D3—22no—
534C2×C3×D3—21no—
535C2×C3×D3—22no—
536C2×C3×D3—41no—
537C2×C3×D3—41no—
538C2×C3×D3—42no—
539C2×C3×D3—42no—
540C2×C3×D3—416no—
541C2×C3×D3—48no—
542C2×C3×D3—48no—
543C2×C3×D3—62no—
544C2×C3×D3—61no—
545C2×C3×D3—61no—
546C2×C3×D3—61no—
547C2×C3×D3—61no—
548C2×C3×D3—61no—
549C2×C3×D3—61no—
550C2×C3×D3—121no—
551C2×C3×D3—121no—
552C2×C3×D3C2×#6712yes—
553C2×C3×D3C2×C3×D412yes—
554C32×C4—22no—
555C32×C4—22no—
556C32×C4—22no—
557C32×C4—32no—
558C32×C4—42no—
559C32×C4—62no—
560C32×C4—61no—
561C32×C4D3×D412yes—
562C32×C4C2×#6712yes—
563C32×C4C2×C3×D412yes—
564C3⋊Dic3—21no—
565C3⋊Dic3—22no—
566C3×Dic3—21no—
567C3×Dic3—22no—
568C3×Dic3—21no—
569C3×Dic3—22no—
570C3×Dic3—22no—
571C3×Dic3—41no—
572C3×Dic3—42no—
573C3×Dic3—61no—
574C3×Dic3—62no—
575C3×Dic3—62no—
576C3×Dic3—61no—
577C3×Dic3—121no—
578C3×Dic3—122no—
579C3×Dic3C2×#6712yes—
580C3×Dic3C2×C3×D412yes—
581C2×#41—91no—
582C22×D4—31no—
583#127—92no—
584#124—92no—
585#121—31no—
586#121—91no—
587#121—91no—
588#121—91no—
589#120—92no—
590#120—92no—
591#117—91no—
592C33#53511yescharacteristic, complemented, Sylow
593C23×C3—22no—
594C23×C3—22no—
595C23×C3—22no—
596C23×C3—31no—
597C23×C3—31no—
598C23×C3—32no—
599C23×C3—31no—
600C23×C3—32no—
601C23×C3—31no—
602C23×C3—42no—
603C23×C3—61no—
604C23×C3—61no—
605C23×C3—62no—
606C23×C3—64no—
607C23×C3—64no—
608C23×C3—68no—
609C23×C3—91no—
610C23×C3—122no—
611C23×C3—122no—
612C23×C3—122no—
613C23×C3—122no—
614C23×C3—124no—
615C23×C3—124no—
616C23×C3C2×D3212yes—
617C23×C3C22×C3×D312yes—
618C23×C3C22×C3×D312yes—
619C22×D3—24no—
620C22×D3—31no—
621C22×D3—31no—
622C22×D3—42no—
623C22×D3—42no—
624C22×D3—61no—
625C22×D3C22×C3×D312yes—
626C22×D3C22×C3×D311yescharacteristic
627C22×D3C22×C3×D311yescharacteristic
628C3×Q8—182no—
629C3×D4—24no—
630C3×D4—22no—
631C3×D4—22no—
632C3×D4—22no—
633C3×D4—42no—
634C3×D4—42no—
635C3×D4—44no—
636C3×D4—64no—
637C3×D4—64no—
638C3×D4—64no—
639C3×D4—68no—
640C3×D4—62no—
641C3×D4—62no—
642C3×D4—122no—
643C3×D4—122no—
644C3×D4—124no—
645C3×D4—182no—
646C3×D4—182no—
647C3×D4—182no—
648C3×D4—362no—
649C3×D4—362no—
650C3×D4—362no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—31no—
655C2×C3×C4—31no—
656C2×C3×C4—34no—
657C2×C3×C4—34no—
658C2×C3×C4—32no—
659C2×C3×C4—31no—
660C2×C3×C4—32no—
661C2×C3×C4—31no—
662C2×C3×C4—41no—
663C2×C3×C4—64no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—62no—
667C2×C3×C4—62no—
668C2×C3×C4—62no—
669C2×C3×C4—92no—
670C2×C3×C4—91no—
671C2×C3×C4—122no—
672C2×C3×C4—182no—
673C2×C3×C4C2×D3211yescharacteristic
674C2×C3×C4C22×C3×D311yescharacteristic
675C2×C3×C4C22×C3×D311yescharacteristic
676#67—24no—
677#67—42no—
678#67—62no—
679#67—62no—
680#67—62no—
681#67—62no—
682#67—122no—
683#67—122no—
684#67—122no—
685#67—122no—
686#67—122no—
687#67—124no—
688C2×Dic3—32no—
689C2×Dic3—32no—
690C2×Dic3—31no—
691C2×Dic3—31no—
692C2×Dic3—62no—
693C2×Dic3—61no—
694C2×Dic3C22×C3×D312yes—
695C2×Dic3C22×C3×D311yescharacteristic
696C2×Dic3C22×C3×D311yescharacteristic
697D12—22no—
698D12—62no—
699D12—62no—
700D12—122no—
701C4×D3—22no—
702C4×D3—62no—
703C4×D3—62no—
704C4×D3—122no—
705C4×D3C3×#6714yescomplemented
706Dic6—62no—
707Dic6—62no—
708C2×C32—21no—
709C2×C32—21no—
710C2×C32—21no—
711C2×C32—21no—
712C2×C32—21no—
713C2×C32—21no—
714C2×C32—21no—
715C2×C32—21no—
716C2×C32—21no—
717C2×C32—41no—
718C2×C32—41no—
719C2×C32—41no—
720C2×C32—42no—
721C2×C32—44no—
722C2×C32—42no—
723C2×C32—42no—
724C2×C32—62no—
725C2×C32—82no—
726C2×C32—82no—
727C2×C32—84no—
728C2×C32—121no—
729C2×C32—122no—
730C2×C32C2×D3×D411yescharacteristic
731C2×C32#100411yescharacteristic
732C2×C32#100411yescharacteristic
733C2×C32#100411yescharacteristic
734C2×C32#100911yescharacteristic
735C2×C32C22×#6711yescharacteristic
736C2×C32C22×C3×D411yescharacteristic
737C2×C32C3×H(5,𝔽2)11yescharacteristic
738C2×C32C3×H(5,𝔽2)11yescharacteristic
739C3⋊D3—41no—
740C3×D3—24no—
741C3×D3—22no—
742C3×D3—22no—
743C3×D3—42no—
744C3×D3—44no—
745C3×D3—42no—
746C3×D3—41no—
747C3×D3—41no—
748C3×D3—42no—
749C3×D3—122no—
750C3×D3—121no—
751C3×D3—121no—
752C24—32no—
753#41—184no—
754C2×Q8—91no—
755C2×D4—32no—
756C2×D4—32no—
757C2×D4—31no—
758C2×D4—64no—
759C2×D4—91no—
760C2×D4—91no—
761C2×D4—92no—
762C2×D4—91no—
763C2×D4—92no—
764C2×D4—92no—
765C2×D4C3×D3211yescharacteristic
766C22×C4—31no—
767C22×C4—31no—
768C22×C4—91no—
769C4⋊C4—31no—
770C4⋊C4—91no—
771C22⋊C4—32no—
772C22⋊C4—92no—
773C22⋊C4—92no—
774C22⋊C4—92no—
775C22⋊C4—92no—
776C42—92no—
777C22×C3—24no—
778C22×C3—22no—
779C22×C3—22no—
780C22×C3—22no—
781C22×C3—22no—
782C22×C3—22no—
783C22×C3—22no—
784C22×C3—22no—
785C22×C3—22no—
786C22×C3—22no—
787C22×C3—21no—
788C22×C3—21no—
789C22×C3—21no—
790C22×C3—32no—
791C22×C3—32no—
792C22×C3—42no—
793C22×C3—42no—
794C22×C3—42no—
795C22×C3—42no—
796C22×C3—42no—
797C22×C3—42no—
798C22×C3—42no—
799C22×C3—42no—
800C22×C3—44no—
801C22×C3—41no—
802C22×C3—62no—
803C22×C3—62no—
804C22×C3—62no—
805C22×C3—64no—
806C22×C3—62no—
807C22×C3—61no—
808C22×C3—61no—
809C22×C3—61no—
810C22×C3—61no—
811C22×C3—61no—
812C22×C3—62no—
813C22×C3—61no—
814C22×C3—62no—
815C22×C3—61no—
816C22×C3—62no—
817C22×C3—62no—
818C22×C3—61no—
819C22×C3—62no—
820C22×C3—61no—
821C22×C3—62no—
822C22×C3—61no—
823C22×C3—82no—
824C22×C3—82no—
825C22×C3—121no—
826C22×C3—122no—
827C22×C3—122no—
828C22×C3—121no—
829C22×C3—1216no—
830C22×C3—128no—
831C22×C3—128no—
832C22×C3—181no—
833C22×C3—181no—
834C22×C3—181no—
835C22×C3C22×D3211yescharacteristic
836C22×C3C23×C3×D311yescharacteristic
837C22×C3C23×C3×D311yescharacteristic
838C2×D3—21no—
839C2×D3—21no—
840C2×D3—21no—
841C2×D3—22no—
842C2×D3—21no—
843C2×D3—22no—
844C2×D3—21no—
845C2×D3—22no—
846C2×D3—48no—
847C2×D3—62no—
848C2×D3—61no—
849C2×D3—61no—
850C2×D3—61no—
851C2×D3—61no—
852C2×D3—61no—
853C2×D3—61no—
854C2×D3—121no—
855C2×D3—121no—
856C2×D3C2×C3×#6712yes—
857C3×C4—22no—
858C3×C4—22no—
859C3×C4—22no—
860C3×C4—32no—
861C3×C4—32no—
862C3×C4—42no—
863C3×C4—62no—
864C3×C4—62no—
865C3×C4—61no—
866C3×C4—62no—
867C3×C4—61no—
868C3×C4—121no—
869C3×C4—122no—
870C3×C4—182no—
871C3×C4—181no—
872C3×C4D3×#6712yes—
873C3×C4C3×D3×D412yes—
874C3×C4C2×C3×#6712yes—
875Dic3—21no—
876Dic3—22no—
877Dic3—61no—
878Dic3—62no—
879Dic3—62no—
880Dic3—61no—
881Dic3—121no—
882Dic3—122no—
883Dic3C2×C3×#6712yes—
884C32—21no—
885C32—21no—
886C32—21no—
887C32—41no—
888C32#560711yescharacteristic, complemented
889C32#580511yescharacteristic, complemented
890C32C3×#53511yescharacteristic, complemented
891C23—31no—
892C23—32no—
893C23—31no—
894C23—64no—
895C23—91no—
896C23—122no—
897C23—122no—
898C23C2×C3×D3212yes—
899Q8—182no—
900D4—22no—
901D4—64no—
902D4—62no—
903D4—122no—
904D4—182no—
905D4—182no—
906D4—182no—
907D4—362no—
908D4—362no—
909D4—362no—
910C2×C4—31no—
911C2×C4—34no—
912C2×C4—32no—
913C2×C4—31no—
914C2×C4—62no—
915C2×C4—92no—
916C2×C4—91no—
917C2×C4—182no—
918C2×C4C2×C3×D3211yescharacteristic
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—21no—
923C2×C3—21no—
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—44no—
929C2×C3—42no—
930C2×C3—42no—
931C2×C3—42no—
932C2×C3—41no—
933C2×C3—41no—
934C2×C3—41no—
935C2×C3—64no—
936C2×C3—62no—
937C2×C3—62no—
938C2×C3—82no—
939C2×C3—82no—
940C2×C3—84no—
941C2×C3—124no—
942C2×C3—122no—
943C2×C3—121no—
944C2×C3—122no—
945C2×C3—122no—
946C2×C3—121no—
947C2×C3—361no—
948C2×C3#6431311yescharacteristic
949C2×C3#6431411yescharacteristic
950C2×C3C2×D3×#6711yescharacteristic
951C2×C3C2×C3×D3×D411yescharacteristic
952C2×C3C3×#100411yescharacteristic
953C2×C3C3×#100411yescharacteristic
954C2×C3C3×#100411yescharacteristic
955C2×C3C3×#100911yescharacteristic
956C2×C3C22×C3×#6711yescharacteristic
957D3—22no—
958D3—42no—
959D3—41no—
960D3—122no—
961D3—121no—
962D3—121no—
963C22—22no—
964C22—22no—
965C22—22no—
966C22—32no—
967C22—61no—
968C22—61no—
969C22—61no—
970C22—62no—
971C22—61no—
972C22—62no—
973C22—61no—
974C22—62no—
975C22—128no—
976C22—181no—
977C22—181no—
978C22—181no—
979C22C22×C3×D3211yescharacteristic
980C4—32no—
981C4—61no—
982C4—62no—
983C4—181no—
984C4—182no—
985C4C3×D3×#6712yes—
986C3—21no—
987C3—21no—
988C3—21no—
989C3—41no—
990C3#1059523111yescharacteristic, direct product factor
991C3C3×#560711yescharacteristic, complemented
992C3C3×#580511yescharacteristic, complemented
993C2—42no—
994C2—62no—
995C2—122no—
996C2—121no—
997C2—361no—
998C2C3×#6431311yescharacteristic
999C2C3×#6431411yescharacteristic
1000C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C3×#535
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×C32×D3×D4C2semidirect
2. C2×C3×#3798C2semidirect
3. C3×#64147C2semidirect
4. C32×#938C2semidirect
5. C3×#63979C2semidirect
6. C3×#63977C2semidirect
7. C3×#63976C2semidirect
8. C3×#63959C2semidirect
9. C3×#63916C2semidirect
10. C3×#63908C2semidirect
11. C3×#63841C2semidirect
14. #10595231C3direct (N × H)
17. C2×C3×#638C22semidirect
18. C2×C3×C4×C3⋊D3C22semidirect
20. C2×C32×#67C22semidirect
24. C2×C32×C4×D3C22semidirect
25. C2×C3×#627C22semidirect
27. C2×C3×#626C22semidirect
28. C2×C3×#626C22semidirect
30. C2×C3×#625C22semidirect
32. C3×#3757C22semidirect
33. C3×C4⋊(C3⋊Dic3)C22semidirect
34. C32×#217C22semidirect
35. C32×C4⋊Dic3C22semidirect
37. C3×(C2×D3)⋊Dic3C22semidirect
38. C3×(C2×D3)⋊Dic3C22semidirect
39. C3×Dic32C22semidirect
42. C2×C3×D3×D4D3semidirect
43. C2×C3×D3×D4C2×C3semidirect
46. C2×#3798C2×C3semidirect
48. #64147C2×C3semidirect
59. C3×#938D3semidirect
60. C3×#938C2×C3semidirect
69. #63979C2×C3semidirect
70. #63977C2×C3semidirect
71. #63976C2×C3semidirect
72. #63959C2×C3semidirect
73. #63916C2×C3semidirect
74. #63908C2×C3semidirect
75. #63841C2×C3semidirect
97. C32×C4×D3D4semidirect
124. C2×#638C22×C3semidirect
125. C2×C4×C3⋊D3C22×C3semidirect
139. C2×C3×#67C2×D3semidirect
141. C2×C3×#67C22×C3semidirect
159. C2×C3×C4×D3C2×D3semidirect
161. C2×C3×C4×D3C22×C3semidirect
164. C2×#627C22×C3semidirect
166. C2×#626C22×C3semidirect
167. C2×#626C22×C3semidirect
169. C2×#625C22×C3semidirect
173. #3757C22×C3semidirect
174. C4⋊(C3⋊Dic3)C22×C3semidirect
182. C3×#217C2×D3semidirect
183. C3×#217C22×C3semidirect
191. C3×C4⋊Dic3C2×D3semidirect
192. C3×C4⋊Dic3C22×C3semidirect
196. (C2×D3)⋊Dic3C22×C3semidirect
197. (C2×D3)⋊Dic3C22×C3semidirect
198. Dic32C22×C3semidirect
226. C2×D3×D4C3×D3semidirect
249. #938C3×D3semidirect
363. C3×C4×D3#67semidirect
364. C3×C4×D3C3×D4semidirect
431. C2×#67C2×C3×D3semidirect
443. C2×C4×D3C2×C3×D3semidirect
464. #217C2×C3×D3semidirect
471. C4⋊Dic3C2×C3×D3semidirect
592. C33#535semidirect
705. C4×D3C3×#67semidirect
888. C32#5607semidirect
889. C32#5805semidirect
890. C32C3×#535semidirect
990. C3#10595231direct (N × H)
991. C3C3×#5607semidirect
992. C3C3×#5805semidirect

Maximal subgroups

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

subgroupindex
C2×C32×D3×D42
C2×C3×#37982
C3×#641472
C32×#9382
C3×#639792
C3×#639772
C3×#639762
C3×#639592
C3×#639162
C3×#639082
C3×#638412
C3×#58053
C3×#56073
#105952313