Finite Group Databasebeta

← #13169202

Subgroups — #13169202

Order 1728.

1504 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3⋊D3×Dic6C211yesmaximal, characteristic, complemented
2C2×C3×#3799C211yesmaximal, characteristic, complemented
3#11723696C211yesmaximal, characteristic, complemented
4#11723439C211yesmaximal, characteristic, complemented
5#11723426C211yesmaximal, characteristic, complemented
6C3×C4×#626C211yesmaximal, characteristic, complemented
7C3×Dic3×Dic6C211yesmaximal, characteristic, complemented
8#11723002C212yesmaximal, complemented
9#11722972C212yesmaximal, complemented
10#11722962C212yesmaximal, complemented
11#11722934C212yesmaximal, complemented
12#10595414—31nomaximal
13#10594899—31nomaximal
14#10593899—31nomaximal
15C2×#6308C2211yescharacteristic
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×C32×C4×D3C2211yescharacteristic
19C2×C32×Dic6C2211yescharacteristic
20C2×#6295C2212yes—
21C2×#6293C2212yes—
22C2×Dic3×C3⋊D3C2212yes—
23C3⋊D3×Dic6—24no—
24C2×C3×#626C2211yescharacteristic
25C2×C3×#626C2212yes—
26C2×C3×#624C2212yes—
27C3×#3799—24no—
28C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C32×C4×Dic3C2211yescharacteristic
30#88814C2212yes—
31#88807C2212yes—
32#88803C2212yes—
33#88803C2212yes—
34(C2×D3)⋊(C3⋊Dic3)C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×Dic3⋊Dic3C2211yescharacteristic
37C3×#3722C2211yescharacteristic
38C3×(C2×D3)⋊Dic3C2211yescharacteristic
39C3×Dic32C2212yes—
40C2×Q8×C3⋊D3—31no—
41C2×C3×#239—31no—
42C2×C3×#235—31no—
43C2×#3799D311yescharacteristic, complemented
44C2×D3×Dic6—31no—
45C2×D3×Dic6—31no—
46C2×D3×Dic6—61no—
47#64133—31no—
48#64084—31no—
49C3×Q8×Dic3—31no—
50C3×C4×#67—31no—
51C3×C4×D12—31no—
52C3×C4×Dic6—31no—
53#63970—32no—
54#63959—32no—
55#63916—31no—
56#63916—32no—
57#63909—31no—
58#63908—31no—
59C4×#626—32no—
60C4×#626D311yescharacteristic, complemented
61#63895—32no—
62#63886—32no—
63#63880—32no—
64#63879—32no—
65#63860—31no—
66#63860—31no—
67#63860—32no—
68#63860—61no—
69#63857—31no—
70#63857—31no—
71#63857—32no—
72#63857—61no—
73#63852—32no—
74#63851—32no—
75Dic3×Dic6D311yescharacteristic, complemented
76C22×C3×C3⋊D3C2312yes—
77C22×C3×C3⋊D3C2311yescharacteristic
78C22×C32×D3C2311yescharacteristic
79C2×C33×C4C2311yescharacteristic
80C2×C3⋊(C3⋊Dic3)C2312yes—
81#6308—22no—
82C2×C3×C3⋊Dic3C2312yes—
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C3×C4⋊(C3⋊D3)—22no—
85C3×C4×C3⋊D3—22no—
86C2×C32×Dic3C2311yescharacteristic
87C2×C32×Dic3C2311yescharacteristic
88C2×C32×Dic3C2311yescharacteristic
89C2×C32×Dic3C2312yes—
90C32×C4×D3—22no—
91C32×Dic6D414yescomplemented
92#6295—24no—
93#6293—24no—
94Dic3×C3⋊D3—24no—
95C3×#626—22no—
96C3×#626—24no—
97C3×#624—24no—
98#5831—91no—
99#5576—91no—
100#5552—91no—
101C2×C32×Q8—31no—
102C22×C32×C4—31no—
103Q8×C3⋊D3—64no—
104C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
105C2×C4×C3⋊D3—32no—
106C2×C4×C3⋊D3C2×D311yescharacteristic
107C2×#634—31no—
108C2×#634—31no—
109C2×#634—31no—
110C2×#634—32no—
111C2×#634—61no—
112C2×#634—61no—
113C2×#634—61no—
114C2×#634—121no—
115C2×C3×#67—31no—
116C2×C3×#67—32no—
117C3×#239—64no—
118C3×#235—64no—
119C2×C3×D12—32no—
120C2×C3×D12—31no—
121C2×C3×D12—31no—
122C2×C3×D12—31no—
123C2×C3×D12—61no—
124C2×C3×C4×D3—21no—
125C2×C3×C4×D3—31no—
126C2×C3×C4×D3—31no—
127C2×C3×C4×D3—32no—
128C2×C3×C4×D3—32no—
129C2×C3×C4×D3—61no—
130C2×C3×C4×D3C2×D311yescharacteristic
131C2×C3×C4×D3C2×D311yescharacteristic
132C2×C3×Dic6—21no—
133C2×C3×Dic6C2×D311yescharacteristic
134C2×C3×Dic6C2×D311yescharacteristic
135C2×#627—32no—
136C2×#627—32no—
137C2×#627—62no—
138C2×#626—32no—
139C2×#626—32no—
140C2×#626C2×D312yes—
141C2×#626C2×D311yescharacteristic
142C2×#625—32no—
143C2×#624C2×D312yes—
144C2×D3×Dic3—32no—
145C2×D3×Dic3—32no—
146C2×D3×Dic3—62no—
147#3799—24no—
148D3×Dic6—68no—
149D3×Dic6—64no—
150D3×Dic6—64no—
151C32×C42—31no—
152#3757—32no—
153#3752—32no—
154#3752—32no—
155C4⋊(C3⋊Dic3)C2×D311yescharacteristic
156#3750—32no—
157C3×#217—31no—
158C3×(C2×D3)⋊C4—31no—
159C3×(C2×D3)⋊C4—31no—
160C3×(C2×D3)⋊C4—31no—
161C3×C4⋊Dic3—31no—
162C3×C4⋊Dic3—31no—
163C3×C4⋊Dic3—32no—
164C3×C4⋊Dic3—31no—
165C3×C4⋊Dic3—61no—
166C3×Dic3⋊C4—31no—
167C3×Dic3⋊C4—32no—
168C3×C4×Dic3—21no—
169C3×C4×Dic3—32no—
170C3×C4×Dic3—32no—
171C3×C4×Dic3C2×D311yescharacteristic
172C3×C4×Dic3C2×D311yescharacteristic
173Dic3⋊Dic3—32no—
174Dic3⋊Dic3—32no—
175Dic3⋊Dic3—62no—
176Dic3⋊Dic3C2×D312yes—
177Dic3⋊Dic3C2×D311yescharacteristic
178#3722—32no—
179#3722C2×D311yescharacteristic
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—32no—
186(C2×D3)⋊Dic3—32no—
187(C2×D3)⋊Dic3—32no—
188(C2×D3)⋊Dic3—62no—
189(C2×D3)⋊Dic3—62no—
190(C2×D3)⋊Dic3—62no—
191(C2×D3)⋊Dic3C2×D311yescharacteristic
192Dic32C2×D312yes—
193C22×C33C2411yescharacteristic
194C2×C3×C3⋊D3—21no—
195C2×C3×C3⋊D3—21no—
196C2×C3×C3⋊D3—22no—
197C2×C3×C3⋊D3—22no—
198C2×C3×C3⋊D3—22no—
199C2×C3×C3⋊D3#4112yescomplemented
200C2×C32×D3—21no—
201C2×C32×D3—21no—
202C2×C32×D3—21no—
203C33×C4C2×D412yes—
204C3⋊(C3⋊Dic3)—22no—
205C3×C3⋊Dic3—21no—
206C3×C3⋊Dic3—22no—
207C32×Dic3—21no—
208C32×Dic3—21no—
209C32×Dic3—21no—
210C32×Dic3C2×D414yes—
211C2×C3×#41—91no—
212C2×#239—31no—
213C2×D3×Q8—91no—
214C2×D3×Q8—91no—
215C2×D3×Q8—181no—
216C2×#235—31no—
217C22×Dic6—91no—
218C3×C4×Q8—91no—
219C3×C4×D4—91no—
220Q8×Dic3—31no—
221#939—92no—
222#938—91no—
223#938—92no—
224#936—92no—
225#936—91no—
226#930—91no—
227C4×#67—31no—
228C4×#67—92no—
229#924—92no—
230#924—91no—
231#924—91no—
232#924—181no—
233#897—92no—
234#897—91no—
235#896—92no—
236#895—91no—
237#895—92no—
238#885—92no—
239#67⋊C4—92no—
240#875—92no—
241#875—91no—
242#875—91no—
243#875—181no—
244C4×D12—31no—
245C4×D12—92no—
246C4×Dic6—31no—
247C23×C32—31no—
248C22×C3⋊D3C22×D312yes—
249C22×C3⋊D3C22×D311yescharacteristic
250C22×C3×D3—21no—
251C22×C3×D3—31no—
252C22×C3×D3—31no—
253C22×C3×D3—32no—
254C22×C3×D3—32no—
255C22×C3×D3—61no—
256C22×C3×D3—62no—
257C22×C3×D3C22×D311yescharacteristic
258C22×C3×D3C22×D311yescharacteristic
259C32×Q8—34no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—32no—
264C2×C32×C4—31no—
265C2×C32×C4—31no—
266C2×C32×C4—31no—
267C2×C32×C4—41no—
268C2×C32×C4—62no—
269C2×C32×C4C22×D311yescharacteristic
270C2×C32×C4C22×D311yescharacteristic
271C2×C32×C4C22×D311yescharacteristic
272C2×C3⋊Dic3—32no—
273C2×C3⋊Dic3—32no—
274C2×C3⋊Dic3—32no—
275C2×C3⋊Dic3—62no—
276C2×C3⋊Dic3—62no—
277C2×C3⋊Dic3—62no—
278C2×C3⋊Dic3—122no—
279C2×C3⋊Dic3C22×D312yes—
280C2×C3⋊Dic3C22×D311yescharacteristic
281C4⋊(C3⋊D3)—22no—
282C4×C3⋊D3—22no—
283C4×C3⋊D3—64no—
284#634—64no—
285#634—62no—
286#634—64no—
287#634—62no—
288#634—62no—
289#634—122no—
290#634—122no—
291#634—124no—
292C3×#67—62no—
293C3×#67—64no—
294C2×C3×Dic3—22no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—32no—
299C2×C3×Dic3—31no—
300C2×C3×Dic3—32no—
301C2×C3×Dic3—31no—
302C2×C3×Dic3—61no—
303C2×C3×Dic3—62no—
304C2×C3×Dic3C22×D311yescharacteristic
305C2×C3×Dic3C22×D311yescharacteristic
306C2×C3×Dic3C22×D311yescharacteristic
307C2×C3×Dic3C22×D311yescharacteristic
308C2×C3×Dic3C22×D311yescharacteristic
309C2×C3×Dic3C22×D311yescharacteristic
310C2×C3×Dic3C22×D312yes—
311C2×C3×Dic3C22×D312yes—
312C3×D12—64no—
313C3×D12—62no—
314C3×D12—62no—
315C3×D12—62no—
316C3×D12—122no—
317C3×C4×D3—22no—
318C3×C4×D3—22no—
319C3×C4×D3—42no—
320C3×C4×D3—64no—
321C3×C4×D3—64no—
322C3×C4×D3—62no—
323C3×C4×D3—62no—
324C3×C4×D3—64no—
325C3×Dic6—24no—
326C3×Dic6D1214yescomplemented
327C3×Dic6#6714yescomplemented
328#627—68no—
329#627—64no—
330#627—64no—
331#626—22no—
332#626—24no—
333#626—64no—
334#626—64no—
335#625—64no—
336#624—24no—
337D3×Dic3—68no—
338D3×Dic3—64no—
339D3×Dic3—64no—
340#548—271noSylow
341C2×C33C22×D411yescharacteristic
342C2×C33C2×#4111yescharacteristic
343C2×C332−1+411yescharacteristic
344C3×C3⋊D3—22no—
345C3×C3⋊D3—42no—
346C32×D3—41no—
347C3×#41—184no—
348C2×C3×Q8—31no—
349C2×C3×Q8—31no—
350C2×C3×Q8—61no—
351C2×C3×D4—92no—
352C2×C3×D4—91no—
353C2×C3×D4—91no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—61no—
357C22×C3×C4—92no—
358C22×C3×C4—91no—
359C2×#67—32no—
360C2×#67—31no—
361C2×#67—92no—
362C2×#67—92no—
363C22×Dic3—92no—
364#239—64no—
365D3×Q8—184no—
366D3×Q8—184no—
367D3×Q8—188no—
368#235—64no—
369C2×D12—31no—
370C2×D12—32no—
371C2×D12—31no—
372C2×D12—31no—
373C2×D12—61no—
374C2×D12—92no—
375C2×C4×D3—31no—
376C2×C4×D3—31no—
377C2×C4×D3—32no—
378C2×C4×D3—32no—
379C2×C4×D3—61no—
380C2×C4×D3—92no—
381C2×C4×D3—92no—
382C2×C4×D3—182no—
383C2×C4×D3D3211yescharacteristic
384C2×Dic6—92no—
385C2×Dic6—92no—
386C2×Dic6—91no—
387C2×Dic6—91no—
388C2×Dic6—91no—
389C2×Dic6—92no—
390C2×Dic6—182no—
391C2×Dic6—181no—
392C2×Dic6—181no—
393C2×Dic6—181no—
394C2×Dic6—184no—
395C2×Dic6—361no—
396C2×Dic6D3211yescharacteristic
397C3×C4⋊C4—92no—
398C3×C4⋊C4—91no—
399C3×C4⋊C4—91no—
400C3×C22⋊C4—91no—
401C3×C22⋊C4—91no—
402C3×C42—31no—
403C3×C42—31no—
404C3×C42—61no—
405C3×C42—92no—
406#217—31no—
407#217—92no—
408#217—92no—
409#217—92no—
410#217—92no—
411#217—92no—
412#217—182no—
413(C2×D3)⋊C4—31no—
414(C2×D3)⋊C4—31no—
415(C2×D3)⋊C4—31no—
416(C2×D3)⋊C4—92no—
417(C2×D3)⋊C4—92no—
418(C2×D3)⋊C4—92no—
419(C2×D3)⋊C4—92no—
420(C2×D3)⋊C4—92no—
421(C2×D3)⋊C4—92no—
422(C2×D3)⋊C4—92no—
423(C2×D3)⋊C4—182no—
424(C2×D3)⋊C4—182no—
425C4⋊Dic3—31no—
426C4⋊Dic3—31no—
427C4⋊Dic3—31no—
428C4⋊Dic3—32no—
429C4⋊Dic3—61no—
430C4⋊Dic3—92no—
431Dic3⋊C4—32no—
432Dic3⋊C4—31no—
433Dic3⋊C4—92no—
434Dic3⋊C4—92no—
435Dic3⋊C4—182no—
436C4×Dic3—32no—
437C4×Dic3—32no—
438C4×Dic3D3211yescharacteristic
439C22×C32—21no—
440C22×C32—21no—
441C22×C32—21no—
442C22×C32—41no—
443C22×C32—61no—
444C22×C32—61no—
445C22×C32—61no—
446C22×C32C23×D311yescharacteristic
447C22×C32C23×D311yescharacteristic
448C22×C32C23×D311yescharacteristic
449C2×C3⋊D3—21no—
450C2×C3⋊D3—21no—
451C2×C3⋊D3—22no—
452C2×C3⋊D3—22no—
453C2×C3⋊D3—22no—
454C2×C3⋊D3#23512yescomplemented
455C2×C3×D3—22no—
456C2×C3×D3—21no—
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—32no—
463C2×C3×D3—32no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—62no—
467C2×C3×D3—62no—
468C2×C3×D3—62no—
469C2×C3×D3—61no—
470C2×C3×D3—61no—
471C2×C3×D3—61no—
472C2×C3×D3—61no—
473C2×C3×D3—62no—
474C2×C3×D3—62no—
475C2×C3×D3—62no—
476C2×C3×D3—62no—
477C2×C3×D3—62no—
478C2×C3×D3—62no—
479C2×C3×D3—122no—
480C2×C3×D3—122no—
481C2×C3×D3—122no—
482C32×C4—22no—
483C32×C4—22no—
484C32×C4—22no—
485C32×C4—34no—
486C32×C4—42no—
487C32×C4—61no—
488C32×C4—61no—
489C32×C4—61no—
490C32×C4C2×D1212yes—
491C32×C4D3×D412yes—
492C32×C4C2×#6712yes—
493C3⋊Dic3—21no—
494C3⋊Dic3—22no—
495C3⋊Dic3—62no—
496C3⋊Dic3—64no—
497C3⋊Dic3—62no—
498C3⋊Dic3—62no—
499C3⋊Dic3—122no—
500C3⋊Dic3—122no—
501C3⋊Dic3—124no—
502C3×Dic3—21no—
503C3×Dic3—21no—
504C3×Dic3—21no—
505C3×Dic3—21no—
506C3×Dic3—21no—
507C3×Dic3—21no—
508C3×Dic3—24no—
509C3×Dic3—41no—
510C3×Dic3—41no—
511C3×Dic3—41no—
512C3×Dic3—62no—
513C3×Dic3—61no—
514C3×Dic3—62no—
515C3×Dic3—62no—
516C3×Dic3—61no—
517C3×Dic3—122no—
518C3×Dic3C2×D1214yes—
519C3×Dic3C2×#6714yes—
520C2×#41—91no—
521C22×Q8—271no—
522#124—271no—
523#124—272no—
524C22⋊Q8—272no—
525C22⋊Q8—271no—
526#121—271no—
527#121—272no—
528C4×Q8—91no—
529C4×D4—91no—
530C4×D4—272no—
531C33#54811yescharacteristic, complemented, Sylow
532C23×C3—31no—
533C23×C3—31no—
534C23×C3—61no—
535C23×C3—91no—
536C23×C3—92no—
537C22×D3—31no—
538C22×D3—31no—
539C22×D3—32no—
540C22×D3—32no—
541C22×D3—61no—
542C22×D3—62no—
543C22×D3C2×D3211yescharacteristic
544C3×Q8—34no—
545C3×Q8—34no—
546C3×Q8—64no—
547C3×D4—184no—
548C3×D4—182no—
549C3×D4—182no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—32no—
554C2×C3×C4—32no—
555C2×C3×C4—31no—
556C2×C3×C4—31no—
557C2×C3×C4—31no—
558C2×C3×C4—31no—
559C2×C3×C4—31no—
560C2×C3×C4—31no—
561C2×C3×C4—41no—
562C2×C3×C4—62no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—62no—
567C2×C3×C4—62no—
568C2×C3×C4—92no—
569C2×C3×C4—91no—
570C2×C3×C4—122no—
571C2×C3×C4—184no—
572C2×C3×C4—182no—
573C2×C3×C4C2×D3211yescharacteristic
574C2×C3×C4C2×D3211yescharacteristic
575C2×C3×C4C2×D3211yescharacteristic
576#67—62no—
577#67—64no—
578#67—184no—
579#67—184no—
580C2×Dic3—32no—
581C2×Dic3—32no—
582C2×Dic3—31no—
583C2×Dic3—31no—
584C2×Dic3—61no—
585C2×Dic3—62no—
586C2×Dic3—92no—
587C2×Dic3—92no—
588C2×Dic3—92no—
589C2×Dic3—182no—
590C2×Dic3—182no—
591C2×Dic3—182no—
592C2×Dic3—184no—
593C2×Dic3—362no—
594C2×Dic3C2×D3211yescharacteristic
595C2×Dic3C2×D3211yescharacteristic
596C2×Dic3C2×D3211yescharacteristic
597C2×Dic3C2×D3212yes—
598D12—64no—
599D12—62no—
600D12—62no—
601D12—62no—
602D12—122no—
603D12—184no—
604C4×D3—22no—
605C4×D3—64no—
606C4×D3—64no—
607C4×D3—62no—
608C4×D3—62no—
609C4×D3—64no—
610C4×D3—184no—
611C4×D3—184no—
612C4×D3—188no—
613Dic6—184no—
614Dic6—184no—
615Dic6—188no—
616Dic6—184no—
617Dic6—182no—
618Dic6—182no—
619Dic6—182no—
620Dic6—184no—
621Dic6—362no—
622Dic6—362no—
623Dic6—364no—
624Dic6#62614yescomplemented
625C2×C32—21no—
626C2×C32—21no—
627C2×C32—21no—
628C2×C32—21no—
629C2×C32—21no—
630C2×C32—21no—
631C2×C32—21no—
632C2×C32—21no—
633C2×C32—21no—
634C2×C32—41no—
635C2×C32—41no—
636C2×C32—41no—
637C2×C32—121no—
638C2×C32C22×D1211yescharacteristic
639C2×C32C2×#23511yescharacteristic
640C2×C32C2×D3×D411yescharacteristic
641C2×C32#100711yescharacteristic
642C2×C32D3×#4111yescharacteristic
643C2×C32D3×#4111yescharacteristic
644C2×C32#101011yescharacteristic
645C2×C32#101011yescharacteristic
646C2×C32C22×#6711yescharacteristic
647C3⋊D3—22no—
648C3⋊D3—42no—
649C3×D3—42no—
650C3×D3—41no—
651C3×D3—41no—
652C3×D3—64no—
653C3×D3—62no—
654C3×D3—62no—
655C3×D3—122no—
656C3×D3—122no—
657C3×D3—242no—
658#41—184no—
659C2×Q8—31no—
660C2×Q8—272no—
661C2×Q8—271no—
662C2×Q8—544no—
663C2×D4—91no—
664C2×D4—92no—
665C2×D4—91no—
666C2×D4—272no—
667C22×C4—31no—
668C22×C4—92no—
669C22×C4—91no—
670C22×C4—272no—
671C4⋊C4—91no—
672C4⋊C4—92no—
673C4⋊C4—91no—
674C4⋊C4—272no—
675C22⋊C4—91no—
676C22⋊C4—91no—
677C22⋊C4—272no—
678C22⋊C4—272no—
679C22⋊C4—272no—
680C22⋊C4—272no—
681C42—31no—
682C42—92no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—41no—
687C22×C3—62no—
688C22×C3—61no—
689C22×C3—61no—
690C22×C3—61no—
691C22×C3—61no—
692C22×C3—61no—
693C22×C3—61no—
694C22×C3—92no—
695C22×C3—121no—
696C22×C3—121no—
697C22×C3—181no—
698C22×C3—181no—
699C22×C3—182no—
700C22×C3—182no—
701C22×C3—182no—
702C22×C3C22×D3211yescharacteristic
703C22×C3C22×D3211yescharacteristic
704C22×C3C22×D3211yescharacteristic
705C2×D3—21no—
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—32no—
709C2×D3—32no—
710C2×D3—62no—
711C2×D3—62no—
712C2×D3—62no—
713C2×D3—61no—
714C2×D3—61no—
715C2×D3—61no—
716C2×D3—61no—
717C2×D3—62no—
718C2×D3—62no—
719C2×D3—62no—
720C2×D3—62no—
721C2×D3—62no—
722C2×D3—62no—
723C2×D3—122no—
724C2×D3—122no—
725C2×D3—122no—
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—22no—
729C3×C4—34no—
730C3×C4—34no—
731C3×C4—42no—
732C3×C4—64no—
733C3×C4—61no—
734C3×C4—61no—
735C3×C4—61no—
736C3×C4—61no—
737C3×C4—61no—
738C3×C4—61no—
739C3×C4—121no—
740C3×C4—121no—
741C3×C4—121no—
742C3×C4—182no—
743C3×C4—181no—
744C3×C4D3×D1212yes—
745C3×C4C2×#62612yes—
746C3×C4D3×#6712yes—
747Dic3—21no—
748Dic3—21no—
749Dic3—21no—
750Dic3—62no—
751Dic3—61no—
752Dic3—62no—
753Dic3—62no—
754Dic3—61no—
755Dic3—122no—
756Dic3—184no—
757Dic3—182no—
758Dic3—182no—
759Dic3—182no—
760Dic3—362no—
761Dic3—362no—
762Dic3—364no—
763Dic3C2×#62614yes—
764C32—21no—
765C32—21no—
766C32—21no—
767C32—41no—
768C32#555211yescharacteristic, complemented
769C32#557611yescharacteristic, complemented
770C32#583111yescharacteristic, complemented
771C23—31no—
772C23—91no—
773C23—92no—
774Q8—34no—
775Q8—544no—
776Q8—542no—
777D4—184no—
778D4—182no—
779D4—182no—
780D4—544no—
781C2×C4—32no—
782C2×C4—31no—
783C2×C4—31no—
784C2×C4—31no—
785C2×C4—62no—
786C2×C4—92no—
787C2×C4—91no—
788C2×C4—184no—
789C2×C4—182no—
790C2×C4—272no—
791C2×C4—544no—
792C2×C4D3311yescharacteristic
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—41no—
803C2×C3—41no—
804C2×C3—41no—
805C2×C3—122no—
806C2×C3—121no—
807C2×C3—121no—
808C2×C3—182no—
809C2×C3—362no—
810C2×C3#6429711yescharacteristic
811C2×C3#6429811yescharacteristic
812C2×C3C2×D3×D1211yescharacteristic
813C2×C3D3×#23511yescharacteristic
814C2×C3D3×#23511yescharacteristic
815C2×C3#6431511yescharacteristic
816C2×C3#6431911yescharacteristic
817C2×C3C22×#62611yescharacteristic
818C2×C3C2×D3×#6711yescharacteristic
819D3—41no—
820D3—64no—
821D3—62no—
822D3—62no—
823D3—122no—
824D3—122no—
825D3—242no—
826C22—61no—
827C22—61no—
828C22—61no—
829C22—92no—
830C22—181no—
831C22—181no—
832C22—182no—
833C22—182no—
834C22—182no—
835C22C2×D3311yescharacteristic
836C4—34no—
837C4—61no—
838C4—61no—
839C4—61no—
840C4—182no—
841C4—181no—
842C4—542no—
843C4D3×#62612yes—
844C3—21no—
845C3—21no—
846C3—21no—
847C3—41no—
848C3#1059389911yescharacteristic, complemented
849C3#1059489911yescharacteristic, complemented
850C3#1059541411yescharacteristic, complemented
851C2—121no—
852C2—182no—
853C2—362no—
854C2#1172438911yescharacteristic
855C2#1172439611yescharacteristic
856C2C2×D3×#62611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#548
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⋊D3×Dic6C2semidirect
2. C2×C3×#3799C2semidirect
3. #11723696C2semidirect
4. #11723439C2semidirect
5. #11723426C2semidirect
6. C3×C4×#626C2semidirect
7. C3×Dic3×Dic6C2semidirect
8. #11723002C2semidirect
9. #11722972C2semidirect
10. #11722962C2semidirect
11. #11722934C2semidirect
43. C2×#3799D3semidirect
60. C4×#626D3semidirect
75. Dic3×Dic6D3semidirect
91. C32×Dic6D4semidirect
199. C2×C3×C3⋊D3#41semidirect
326. C3×Dic6D12semidirect
327. C3×Dic6#67semidirect
454. C2×C3⋊D3#235semidirect
531. C33#548semidirect
624. Dic6#626semidirect
768. C32#5552semidirect
769. C32#5576semidirect
770. C32#5831semidirect
848. C3#10593899semidirect
849. C3#10594899semidirect
850. C3#10595414semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊D3×Dic62
C2×C3×#37992
#117236962
#117234392
#117234262
C3×C4×#6262
C3×Dic3×Dic62
#117230022
#117229722
#117229622
#117229342
#105954143
#105948993
#105938993