Finite Group Databasebeta

← #13168099

Subgroups — #13168099

Order 1728.

1630 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3802C211yesmaximal, characteristic, complemented
2C2×C3×#3795C211yesmaximal, characteristic, complemented
3#11723674C211yesmaximal, characteristic, complemented
4C4×#6290C211yesmaximal, characteristic, complemented
5#11723499C211yesmaximal, characteristic, complemented
6#11723434C211yesmaximal, characteristic, complemented
7C3×#63908C211yesmaximal, characteristic, complemented
8#11722985C212yesmaximal, complemented
9#11722953C212yesmaximal, complemented
10#11722946C212yesmaximal, complemented
11D3×(C2×D3)⋊Dic3C212yesmaximal, complemented
12#10595244—31nomaximal
13#10595228—31nomaximal
14#10595070—31nomaximal
15C22×C3×D32C2212yes—
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C3×#634C2211yescharacteristic, complemented
18C2×C32×D12C2211yescharacteristic
19C2×C32×D12C2211yescharacteristic
20C2×C32×C4×D3C2211yescharacteristic, complemented
21C2×#6290C2211yescharacteristic
22C2×D3×C3⋊Dic3C2212yescomplemented
23C2×C3×#625C2212yes—
24C2×C3×#625C2212yescomplemented
25C2×C3×#625C2212yescomplemented
26C2×C3×D3×Dic3C2212yescomplemented
27C3×#3802—24no—
28C3×#3795—24no—
29C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
30C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
31#88815C2212yescomplemented
32#88814C2212yes—
33#88806C2211yescharacteristic, complemented
34#88803C2211yescharacteristic
35(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
36(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
37(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
38(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
39C3×(C2×D3)⋊Dic3C2212yescomplemented
40C2×C3×#237—31no—
41C2×C3×D3×D4—31no—
42C2×C3×D3×D4—31no—
43C2×C3×#235—31no—
44C2×#3802D311yescharacteristic, complemented
45C2×#3795D311yescharacteristic, complemented
46#64145—31no—
47D4×C3⋊Dic3—31no—
48C4×#638—31no—
49C3×#938—31no—
50C3×#930—31no—
51#63983—32no—
52#63980—32no—
53#63976—32no—
54#63976—32no—
55#63970—32no—
56#63970—32no—
57#63969—32no—
58D3×#217—32no—
59#63961—32no—
60C2×(C2×D3)⋊Dic3—32no—
61D3×(C2×D3)⋊C4—32no—
62#63908D311yescharacteristic, complemented
63#63905—32no—
64C4×#625—31no—
65C4×#625—31no—
66C4×#625—61no—
67#63898—31no—
68#63898—31no—
69#63898—61no—
70#63871—31no—
71#63863—31no—
72#63863—31no—
73#63863—61no—
74#63857—31no—
75#63856—31no—
76C22×C3×C3⋊D3C2311yescharacteristic
77C22×C32×D3C2312yes—
78C22×C32×D3C2311yescharacteristic
79C22×C32×D3C2312yes—
80C2×C3×D32—24no—
81C2×C3×D32—24no—
82C2×C3×D32—42no—
83C2×C33×C4C2311yescharacteristic
84C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
85C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
86C2×C3×C3⋊Dic3C2312yes—
87C2×C3×C3⋊Dic3C2312yes—
88C2×C3×C3⋊Dic3C2311yescharacteristic
89C3×C4×C3⋊D3—22no—
90C3×#634—22no—
91C2×C32×Dic3C2311yescharacteristic
92C32×D12—22no—
93C32×D12D414yescomplemented
94C32×C4×D3—22no—
95#6290—22no—
96D3×C3⋊Dic3—42no—
97C3×#625—24no—
98C3×#625—24no—
99C3×#625—42no—
100C3×D3×Dic3—24no—
101#5829—91no—
102#5806—91no—
103#5612—91no—
104C23×C3×D3—32no—
105C23×C3×D3—32no—
106C22×D32C2×D312yes—
107C2×C32×D4—31no—
108C2×C32×D4—31no—
109C22×C32×C4—31no—
110C2×#638—31no—
111C22×C3⋊Dic3—32no—
112C2×C4×C3⋊D3C2×D311yescharacteristic
113C2×#634C2×D311yescharacteristic, complemented
114C2×C3×#67—32no—
115C2×C3×#67—32no—
116C2×C3×#67—32no—
117C2×C3×#67—32no—
118C2×C3×#67—32no—
119C2×C3×#67—32no—
120C22×C3×Dic3—32no—
121C3×#237—64no—
122C3×D3×D4—64no—
123C3×D3×D4—64no—
124C3×#235—64no—
125C2×C3×D12—21no—
126C2×C3×D12—21no—
127C2×C3×D12C2×D311yescharacteristic
128C2×C3×D12C2×D311yescharacteristic
129C2×C3×D12C2×D311yescharacteristic
130C2×C3×D12C2×D311yescharacteristic
131C2×C3×C4×D3—21no—
132C2×C3×C4×D3—32no—
133C2×C3×C4×D3—31no—
134C2×C3×C4×D3—31no—
135C2×C3×C4×D3—61no—
136C2×C3×C4×D3C2×D311yescharacteristic, complemented
137C2×C3×C4×D3C2×D311yescharacteristic, complemented
138C2×C3×Dic6—31no—
139C2×C3×Dic6—31no—
140C2×C3×Dic6—61no—
141C2×#625—31no—
142C2×#625—31no—
143C2×#625—61no—
144C2×#625C2×D312yes—
145C2×#625C2×D312yescomplemented
146C2×#625C2×D312yescomplemented
147C2×D3×Dic3—32no—
148C2×D3×Dic3—32no—
149C2×D3×Dic3—62no—
150C2×D3×Dic3C2×D312yescomplemented
151#3802—24no—
152#3795—24no—
153#3757—31no—
154#3757—32no—
155#3757—32no—
156#3757—32no—
157#3752—31no—
158C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
159#3750—31no—
160C4×C3⋊Dic3—31no—
161C4×C3⋊Dic3—31no—
162C4×C3⋊Dic3—31no—
163C4×C3⋊Dic3—61no—
164C4×C3⋊Dic3—61no—
165C4×C3⋊Dic3—61no—
166C4×C3⋊Dic3—121no—
167C3×#217—32no—
168C3×(C2×D3)⋊C4—32no—
169C3×C4⋊Dic3—31no—
170C3×C4⋊Dic3—31no—
171C3×C4⋊Dic3—61no—
172#3724—32no—
173#3724—31no—
174#3724—31no—
175#3724—61no—
176Dic3⋊Dic3—32no—
177Dic3⋊Dic3—32no—
178#3722—32no—
179(C2×D3)⋊Dic3—32no—
180(C2×D3)⋊Dic3—32no—
181(C2×D3)⋊Dic3—32no—
182(C2×D3)⋊Dic3—32no—
183(C2×D3)⋊Dic3—32no—
184(C2×D3)⋊Dic3—32no—
185(C2×D3)⋊Dic3—31no—
186(C2×D3)⋊Dic3—31no—
187(C2×D3)⋊Dic3—32no—
188(C2×D3)⋊Dic3—32no—
189(C2×D3)⋊Dic3—31no—
190(C2×D3)⋊Dic3—31no—
191(C2×D3)⋊Dic3—61no—
192(C2×D3)⋊Dic3—62no—
193(C2×D3)⋊Dic3—62no—
194(C2×D3)⋊Dic3—62no—
195(C2×D3)⋊Dic3—61no—
196(C2×D3)⋊Dic3C2×D312yescomplemented
197C22×C33C2411yescharacteristic
198C2×C3×C3⋊D3—21no—
199C2×C3×C3⋊D3—21no—
200C2×C3×C3⋊D3#4112yescomplemented
201C2×C32×D3—22no—
202C2×C32×D3—22no—
203C2×C32×D3—21no—
204C2×C32×D3—22no—
205C2×C32×D3—21no—
206C2×C32×D3—22no—
207C2×C32×D3—21no—
208C2×C32×D3—22no—
209C2×C32×D3C2×D414yes—
210C3×D32—48no—
211C33×C4C2×D412yes—
212C3⋊(C3⋊Dic3)—21no—
213C3⋊(C3⋊Dic3)—21no—
214C3×C3⋊Dic3—22no—
215C3×C3⋊Dic3—21no—
216C3×C3⋊Dic3—22no—
217C32×Dic3—21no—
218C2×C3×#41—91no—
219C22×C3×D4—91no—
220C2×#237—31no—
221C2×D3×D4—31no—
222C2×D3×D4—31no—
223C2×#235—31no—
224C3×#121—91no—
225#953—92no—
226C2×#217—92no—
227#947—91no—
228#946—91no—
229#939—92no—
230#939—92no—
231#938—31no—
232#938—92no—
233#937—92no—
234#937—92no—
235#936—91no—
236#936—91no—
237#936—181no—
238#935—92no—
239D4×Dic3—91no—
240D4×Dic3—91no—
241D4×Dic3—181no—
242#930—31no—
243#929—92no—
244C4×#67—91no—
245C4×#67—91no—
246C4×#67—91no—
247C4×#67—181no—
248C2×(C2×D3)⋊C4—92no—
249#924—91no—
250#897—91no—
251#893—91no—
252#883—92no—
253D3×C22⋊C4—92no—
254C23×C32—32no—
255C23×C32—32no—
256C23×C32—31no—
257C22×C3⋊D3C22×D311yescharacteristic
258C22×C3×D3—22no—
259C22×C3×D3—21no—
260C22×C3×D3—22no—
261C22×C3×D3—31no—
262C22×C3×D3—31no—
263C22×C3×D3—61no—
264C22×C3×D3—64no—
265C22×C3×D3—64no—
266C22×C3×D3—64no—
267C22×C3×D3—64no—
268C22×C3×D3—122no—
269C22×C3×D3—122no—
270C22×C3×D3C22×D312yes—
271C22×C3×D3C22×D312yes—
272C22×C3×D3C22×D311yescharacteristic
273C22×C3×D3C22×D311yescharacteristic
274C22×C3×D3C22×D312yes—
275C22×C3×D3C22×D312yes—
276C2×D32—24no—
277C2×D32—24no—
278C2×D32—42no—
279C32×D4—34no—
280C32×D4—62no—
281C2×C32×C4—21no—
282C2×C32×C4—21no—
283C2×C32×C4—21no—
284C2×C32×C4—31no—
285C2×C32×C4—41no—
286C2×C32×C4—62no—
287C2×C32×C4C22×D311yescharacteristic
288C2×C32×C4C22×D311yescharacteristic
289C2×C32×C4C22×D311yescharacteristic
290#638—62no—
291C2×C3⋊Dic3—31no—
292C2×C3⋊Dic3—31no—
293C2×C3⋊Dic3—31no—
294C2×C3⋊Dic3—31no—
295C2×C3⋊Dic3—31no—
296C2×C3⋊Dic3—31no—
297C2×C3⋊Dic3—61no—
298C2×C3⋊Dic3—61no—
299C2×C3⋊Dic3—61no—
300C2×C3⋊Dic3—61no—
301C2×C3⋊Dic3—61no—
302C2×C3⋊Dic3—61no—
303C2×C3⋊Dic3—121no—
304C2×C3⋊Dic3—121no—
305C2×C3⋊Dic3—122no—
306C2×C3⋊Dic3C22×D312yes—
307C2×C3⋊Dic3C22×D312yes—
308C2×C3⋊Dic3C22×D311yescharacteristic
309C4×C3⋊D3—22no—
310#634—22no—
311C3×#67—64no—
312C3×#67—64no—
313C3×#67—64no—
314C3×#67—64no—
315C3×#67—122no—
316C3×#67—122no—
317C2×C3×Dic3—21no—
318C2×C3×Dic3—32no—
319C2×C3×Dic3—32no—
320C2×C3×Dic3—32no—
321C2×C3×Dic3—32no—
322C2×C3×Dic3—31no—
323C2×C3×Dic3—31no—
324C2×C3×Dic3—62no—
325C2×C3×Dic3—61no—
326C2×C3×Dic3—62no—
327C2×C3×Dic3—64no—
328C2×C3×Dic3C22×D311yescharacteristic
329C2×C3×Dic3C22×D311yescharacteristic
330C3×D12—22no—
331C3×D12—22no—
332C3×D12—24no—
333C3×D12—42no—
334C3×D12#6714yescomplemented
335C3×D12#6714yescomplemented
336C3×C4×D3—22no—
337C3×C4×D3—22no—
338C3×C4×D3—42no—
339C3×C4×D3—64no—
340C3×C4×D3—62no—
341C3×C4×D3—62no—
342C3×C4×D3—122no—
343C3×Dic6—62no—
344C3×Dic6—62no—
345C3×Dic6—122no—
346#625—24no—
347#625—24no—
348#625—42no—
349#625—62no—
350#625—62no—
351#625—64no—
352D3×Dic3—24no—
353D3×Dic3—122no—
354D3×Dic3—122no—
355D3×Dic3—124no—
356#546—271noSylow
357C2×C33C22×D411yescharacteristic
358C2×C33C2×#4111yescharacteristic
359C2×C33H(5,𝔽2)11yescharacteristic
360C3×C3⋊D3—22no—
361C32×D3—24no—
362C32×D3—41no—
363C32×D3—42no—
364C24×C3—92no—
365C23×D3—32no—
366C23×D3—32no—
367C3×#41—184no—
368C2×C3×Q8—91no—
369C2×C3×D4—31no—
370C2×C3×D4—31no—
371C2×C3×D4—31no—
372C2×C3×D4—31no—
373C2×C3×D4—61no—
374C2×C3×D4—61no—
375C2×C3×D4—92no—
376C2×C3×D4—92no—
377C2×C3×D4—92no—
378C2×C3×D4—184no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—61no—
382C22×C3×C4—92no—
383C22×C3×C4—91no—
384C2×#67—32no—
385C2×#67—32no—
386C2×#67—32no—
387C2×#67—32no—
388C2×#67—32no—
389C2×#67—32no—
390C2×#67—91no—
391C2×#67—91no—
392C2×#67—91no—
393C2×#67—181no—
394C22×Dic3—32no—
395C22×Dic3—92no—
396C22×Dic3—92no—
397C22×Dic3—182no—
398#237—64no—
399D3×D4—64no—
400D3×D4—64no—
401#235—64no—
402C2×D12D3211yescharacteristic
403C2×D12D3211yescharacteristic
404C2×C4×D3—32no—
405C2×C4×D3—31no—
406C2×C4×D3—31no—
407C2×C4×D3—61no—
408C2×C4×D3—92no—
409C2×C4×D3D3211yescharacteristic, complemented
410C2×Dic6—31no—
411C2×Dic6—31no—
412C2×Dic6—61no—
413C3×C4⋊C4—91no—
414C3×C22⋊C4—92no—
415#217—32no—
416#217—92no—
417#217—92no—
418#217—92no—
419#217—91no—
420#217—91no—
421#217—92no—
422#217—92no—
423#217—92no—
424#217—92no—
425#217—91no—
426#217—181no—
427#217—182no—
428#217—182no—
429#217—182no—
430(C2×D3)⋊C4—32no—
431(C2×D3)⋊C4—92no—
432(C2×D3)⋊C4—92no—
433(C2×D3)⋊C4—91no—
434(C2×D3)⋊C4—91no—
435(C2×D3)⋊C4—92no—
436(C2×D3)⋊C4—92no—
437(C2×D3)⋊C4—91no—
438(C2×D3)⋊C4—92no—
439(C2×D3)⋊C4—181no—
440C4⋊Dic3—31no—
441C4⋊Dic3—31no—
442C4⋊Dic3—61no—
443C4⋊Dic3—92no—
444Dic3⋊C4—92no—
445Dic3⋊C4—92no—
446Dic3⋊C4—91no—
447Dic3⋊C4—91no—
448Dic3⋊C4—91no—
449Dic3⋊C4—181no—
450C4×Dic3—91no—
451C4×Dic3—91no—
452C4×Dic3—91no—
453C4×Dic3—181no—
454C4×Dic3—181no—
455C4×Dic3—181no—
456C4×Dic3—361no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—34no—
461C22×C32—41no—
462C22×C32—61no—
463C22×C32—62no—
464C22×C32—62no—
465C22×C32—61no—
466C22×C32—62no—
467C22×C32—62no—
468C22×C32—61no—
469C22×C32—62no—
470C22×C32C23×D311yescharacteristic
471C22×C32C23×D311yescharacteristic
472C22×C32C23×D311yescharacteristic
473C2×C3⋊D3—21no—
474C2×C3⋊D3—21no—
475C2×C3⋊D3#23712yescomplemented
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—21no—
482C2×C3×D3—22no—
483C2×C3×D3—22no—
484C2×C3×D3—21no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
487C2×C3×D3—21no—
488C2×C3×D3—21no—
489C2×C3×D3—22no—
490C2×C3×D3—21no—
491C2×C3×D3—21no—
492C2×C3×D3—22no—
493C2×C3×D3—24no—
494C2×C3×D3—32no—
495C2×C3×D3—32no—
496C2×C3×D3—42no—
497C2×C3×D3—41no—
498C2×C3×D3—42no—
499C2×C3×D3—41no—
500C2×C3×D3—42no—
501C2×C3×D3—42no—
502C2×C3×D3—42no—
503C2×C3×D3—62no—
504C2×C3×D3—61no—
505C2×C3×D3—61no—
506C2×C3×D3—61no—
507C2×C3×D3—61no—
508C2×C3×D3—121no—
509C2×C3×D3—121no—
510C2×C3×D3—128no—
511C2×C3×D3—128no—
512C2×C3×D3C2×#6714yes—
513C2×C3×D3C2×#6714yes—
514D32—48no—
515C32×C4—22no—
516C32×C4—22no—
517C32×C4—22no—
518C32×C4—42no—
519C32×C4—61no—
520C32×C4D3×D412yes—
521C32×C4C2×#6712yes—
522C32×C4C2×#6712yes—
523C3⋊Dic3—22no—
524C3⋊Dic3—22no—
525C3⋊Dic3—21no—
526C3⋊Dic3—61no—
527C3⋊Dic3—61no—
528C3⋊Dic3—62no—
529C3⋊Dic3—62no—
530C3⋊Dic3—61no—
531C3⋊Dic3—61no—
532C3⋊Dic3—61no—
533C3⋊Dic3—61no—
534C3⋊Dic3—121no—
535C3⋊Dic3—121no—
536C3⋊Dic3—121no—
537C3⋊Dic3—121no—
538C3⋊Dic3—122no—
539C3⋊Dic3—122no—
540C3×Dic3—21no—
541C3×Dic3—21no—
542C3×Dic3—41no—
543C3×Dic3—62no—
544C3×Dic3—61no—
545C3×Dic3—62no—
546C3×Dic3—62no—
547C3×Dic3—62no—
548C3×Dic3—61no—
549C3×Dic3—122no—
550C3×Dic3—122no—
551C3×Dic3—121no—
552C2×#41—91no—
553C22×D4—91no—
554#124—271no—
555#123—272no—
556C22⋊Q8—271no—
557#121—91no—
558#121—272no—
559#120—272no—
560C4×D4—271no—
561C4×D4—271no—
562C2×C22⋊C4—272no—
563C33#54611yescharacteristic, complemented, Sylow
564C23×C3—32no—
565C23×C3—32no—
566C23×C3—32no—
567C23×C3—32no—
568C23×C3—31no—
569C23×C3—31no—
570C23×C3—62no—
571C23×C3—61no—
572C23×C3—62no—
573C23×C3—91no—
574C23×C3—184no—
575C23×C3—184no—
576C23×C3—362no—
577C22×D3—31no—
578C22×D3—31no—
579C22×D3—61no—
580C22×D3—64no—
581C22×D3—64no—
582C22×D3—64no—
583C22×D3—64no—
584C22×D3—122no—
585C22×D3—122no—
586C22×D3C2×D3212yes—
587C22×D3C2×D3211yescharacteristic
588C22×D3C2×D3212yes—
589C3×Q8—182no—
590C3×D4—34no—
591C3×D4—34no—
592C3×D4—64no—
593C3×D4—62no—
594C3×D4—62no—
595C3×D4—122no—
596C3×D4—184no—
597C3×D4—184no—
598C3×D4—362no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—31no—
603C2×C3×C4—31no—
604C2×C3×C4—41no—
605C2×C3×C4—61no—
606C2×C3×C4—62no—
607C2×C3×C4—62no—
608C2×C3×C4—91no—
609C2×C3×C4—92no—
610C2×C3×C4—92no—
611C2×C3×C4—122no—
612C2×C3×C4—184no—
613C2×C3×C4—182no—
614C2×C3×C4C2×D3211yescharacteristic
615C2×C3×C4C2×D3211yescharacteristic
616C2×C3×C4C2×D3211yescharacteristic
617#67—64no—
618#67—64no—
619#67—64no—
620#67—64no—
621#67—122no—
622#67—122no—
623#67—182no—
624#67—182no—
625#67—182no—
626#67—184no—
627C2×Dic3—31no—
628C2×Dic3—32no—
629C2×Dic3—32no—
630C2×Dic3—31no—
631C2×Dic3—32no—
632C2×Dic3—32no—
633C2×Dic3—61no—
634C2×Dic3—62no—
635C2×Dic3—62no—
636C2×Dic3—64no—
637C2×Dic3—91no—
638C2×Dic3—91no—
639C2×Dic3—91no—
640C2×Dic3—91no—
641C2×Dic3—91no—
642C2×Dic3—91no—
643C2×Dic3—181no—
644C2×Dic3—181no—
645C2×Dic3—181no—
646C2×Dic3—181no—
647C2×Dic3—181no—
648C2×Dic3—181no—
649C2×Dic3—361no—
650C2×Dic3—361no—
651C2×Dic3—362no—
652C2×Dic3—362no—
653C2×Dic3—364no—
654C2×Dic3C2×D3211yescharacteristic
655D12—22no—
656D12#62514yescomplemented
657C4×D3—22no—
658C4×D3—64no—
659C4×D3—62no—
660C4×D3—62no—
661C4×D3—122no—
662C4×D3—362no—
663Dic6—62no—
664Dic6—62no—
665Dic6—122no—
666C2×C32—21no—
667C2×C32—21no—
668C2×C32—21no—
669C2×C32—21no—
670C2×C32—21no—
671C2×C32—21no—
672C2×C32—21no—
673C2×C32—21no—
674C2×C32—21no—
675C2×C32—41no—
676C2×C32—41no—
677C2×C32—41no—
678C2×C32—64no—
679C2×C32—121no—
680C2×C32—122no—
681C2×C32C2×D3×D411yescharacteristic
682C2×C32C2×#23711yescharacteristic
683C2×C32#100411yescharacteristic
684C2×C32#100411yescharacteristic
685C2×C32D3×#4111yescharacteristic
686C2×C32D3×#4111yescharacteristic
687C2×C32#100911yescharacteristic
688C2×C32C22×#6711yescharacteristic
689C2×C32C22×#6711yescharacteristic
690C3⋊D3—22no—
691C3×D3—24no—
692C3×D3—24no—
693C3×D3—44no—
694C3×D3—42no—
695C3×D3—42no—
696C3×D3—41no—
697C3×D3—41no—
698C3×D3—42no—
699C3×D3—62no—
700C3×D3—62no—
701C3×D3—82no—
702C3×D3—122no—
703C24—92no—
704#41—184no—
705C2×Q8—91no—
706C2×D4—31no—
707C2×D4—31no—
708C2×D4—92no—
709C2×D4—92no—
710C2×D4—92no—
711C2×D4—184no—
712C2×D4—271no—
713C22×C4—31no—
714C22×C4—92no—
715C22×C4—91no—
716C22×C4—272no—
717C4⋊C4—91no—
718C4⋊C4—271no—
719C4⋊C4—272no—
720C22⋊C4—92no—
721C22⋊C4—271no—
722C22⋊C4—272no—
723C22⋊C4—272no—
724C22⋊C4—272no—
725C22⋊C4—271no—
726C22⋊C4—272no—
727C42—271no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—34no—
732C22×C3—34no—
733C22×C3—41no—
734C22×C3—64no—
735C22×C3—62no—
736C22×C3—62no—
737C22×C3—62no—
738C22×C3—62no—
739C22×C3—62no—
740C22×C3—62no—
741C22×C3—62no—
742C22×C3—61no—
743C22×C3—61no—
744C22×C3—62no—
745C22×C3—61no—
746C22×C3—61no—
747C22×C3—62no—
748C22×C3—61no—
749C22×C3—62no—
750C22×C3—61no—
751C22×C3—62no—
752C22×C3—92no—
753C22×C3—122no—
754C22×C3—121no—
755C22×C3—122no—
756C22×C3—121no—
757C22×C3—122no—
758C22×C3—122no—
759C22×C3—122no—
760C22×C3—181no—
761C22×C3—181no—
762C22×C3—368no—
763C22×C3C22×D3211yescharacteristic
764C22×C3C22×D3211yescharacteristic
765C22×C3C22×D3211yescharacteristic
766C2×D3—22no—
767C2×D3—22no—
768C2×D3—21no—
769C2×D3—21no—
770C2×D3—22no—
771C2×D3—22no—
772C2×D3—21no—
773C2×D3—22no—
774C2×D3—32no—
775C2×D3—32no—
776C2×D3—62no—
777C2×D3—61no—
778C2×D3—61no—
779C2×D3—61no—
780C2×D3—61no—
781C2×D3—121no—
782C2×D3—121no—
783C2×D3—128no—
784C2×D3—128no—
785C2×D3C2×#62514yes—
786C3×C4—22no—
787C3×C4—22no—
788C3×C4—22no—
789C3×C4—42no—
790C3×C4—61no—
791C3×C4—61no—
792C3×C4—121no—
793C3×C4—182no—
794C3×C4—181no—
795C3×C4—182no—
796C3×C4C2×#62512yes—
797C3×C4D3×#6712yes—
798C3×C4D3×#6712yes—
799Dic3—21no—
800Dic3—62no—
801Dic3—62no—
802Dic3—62no—
803Dic3—61no—
804Dic3—62no—
805Dic3—61no—
806Dic3—122no—
807Dic3—121no—
808Dic3—122no—
809Dic3—182no—
810Dic3—182no—
811Dic3—181no—
812Dic3—181no—
813Dic3—181no—
814Dic3—181no—
815Dic3—181no—
816Dic3—181no—
817Dic3—361no—
818Dic3—361no—
819Dic3—361no—
820Dic3—361no—
821Dic3—362no—
822Dic3—362no—
823C32—21no—
824C32—21no—
825C32—21no—
826C32—41no—
827C32#561211yescharacteristic, complemented
828C32#580611yescharacteristic, complemented
829C32#582911yescharacteristic, complemented
830C23—32no—
831C23—32no—
832C23—31no—
833C23—91no—
834C23—184no—
835C23—184no—
836C23—362no—
837Q8—182no—
838D4—34no—
839D4—62no—
840D4—184no—
841D4—184no—
842D4—362no—
843D4—542no—
844C2×C4—31no—
845C2×C4—62no—
846C2×C4—92no—
847C2×C4—92no—
848C2×C4—91no—
849C2×C4—184no—
850C2×C4—182no—
851C2×C4—271no—
852C2×C4—271no—
853C2×C4—1082no—
854C2×C4D3311yescharacteristic
855C2×C3—21no—
856C2×C3—21no—
857C2×C3—21no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—21no—
861C2×C3—21no—
862C2×C3—21no—
863C2×C3—21no—
864C2×C3—41no—
865C2×C3—41no—
866C2×C3—41no—
867C2×C3—64no—
868C2×C3—64no—
869C2×C3—124no—
870C2×C3—122no—
871C2×C3—121no—
872C2×C3—122no—
873C2×C3—121no—
874C2×C3—122no—
875C2×C3—182no—
876C2×C3—242no—
877C2×C3#6430611yescharacteristic
878C2×C3#6430711yescharacteristic
879C2×C3D3×#23711yescharacteristic
880C2×C3D3×#23711yescharacteristic
881C2×C3#6431311yescharacteristic
882C2×C3#6431411yescharacteristic
883C2×C3C22×#62511yescharacteristic
884C2×C3C2×D3×#6711yescharacteristic
885C2×C3C2×D3×#6711yescharacteristic
886D3—24no—
887D3—42no—
888D3—41no—
889D3—62no—
890D3—62no—
891D3—122no—
892C22—34no—
893C22—62no—
894C22—62no—
895C22—61no—
896C22—62no—
897C22—61no—
898C22—62no—
899C22—61no—
900C22—62no—
901C22—92no—
902C22—181no—
903C22—181no—
904C22—368no—
905C22C2×D3311yescharacteristic
906C4—61no—
907C4—182no—
908C4—181no—
909C4—182no—
910C4—541no—
911C4—541no—
912C4D3×#62512yes—
913C3—21no—
914C3—21no—
915C3—21no—
916C3—41no—
917C3#1059507011yescharacteristic, complemented
918C3#1059522811yescharacteristic, complemented
919C3#1059524411yescharacteristic, complemented
920C2—64no—
921C2—122no—
922C2—121no—
923C2—182no—
924C2#1172437311yescharacteristic
925C2#1172438111yescharacteristic
926C2C2×D3×#62511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3802C2semidirect
2. C2×C3×#3795C2semidirect
3. #11723674C2semidirect
4. C4×#6290C2semidirect
5. #11723499C2semidirect
6. #11723434C2semidirect
7. C3×#63908C2semidirect
8. #11722985C2semidirect
9. #11722953C2semidirect
10. #11722946C2semidirect
11. D3×(C2×D3)⋊Dic3C2semidirect
17. C2×C3×#634C22semidirect
20. C2×C32×C4×D3C22semidirect
22. C2×D3×C3⋊Dic3C22semidirect
24. C2×C3×#625C22semidirect
25. C2×C3×#625C22semidirect
26. C2×C3×D3×Dic3C22semidirect
29. C4×C3⋊(C3⋊Dic3)C22semidirect
30. C3×C4⋊(C3⋊Dic3)C22semidirect
31. #88815C22semidirect
33. #88806C22semidirect
35. (C2×D3)⋊(C3⋊Dic3)C22semidirect
36. (C2×D3)⋊(C3⋊Dic3)C22semidirect
37. (C2×D3)⋊(C3⋊Dic3)C22semidirect
38. (C2×D3)⋊(C3⋊Dic3)C22semidirect
39. C3×(C2×D3)⋊Dic3C22semidirect
44. C2×#3802D3semidirect
45. C2×#3795D3semidirect
62. #63908D3semidirect
93. C32×D12D4semidirect
113. C2×#634C2×D3semidirect
136. C2×C3×C4×D3C2×D3semidirect
137. C2×C3×C4×D3C2×D3semidirect
145. C2×#625C2×D3semidirect
146. C2×#625C2×D3semidirect
150. C2×D3×Dic3C2×D3semidirect
158. C4⋊(C3⋊Dic3)C2×D3semidirect
196. (C2×D3)⋊Dic3C2×D3semidirect
200. C2×C3×C3⋊D3#41semidirect
334. C3×D12#67semidirect
335. C3×D12#67semidirect
409. C2×C4×D3D32semidirect
475. C2×C3⋊D3#237semidirect
563. C33#546semidirect
656. D12#625semidirect
827. C32#5612semidirect
828. C32#5806semidirect
829. C32#5829semidirect
917. C3#10595070semidirect
918. C3#10595228semidirect
919. C3#10595244semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38022
C2×C3×#37952
#117236742
C4×#62902
#117234992
#117234342
C3×#639082
#117229852
#117229532
#117229462
D3×(C2×D3)⋊Dic32
#105952443
#105952283
#105950703