Finite Group Databasebeta

← #13178715

Subgroups — #13178715

Order 1728.

1512 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×#3832C211yesmaximal, characteristic, complemented
2C2×#89041C211yesmaximal, characteristic, complemented
3C3×#64155C211yesmaximal, characteristic, complemented
4C3×#64153C211yesmaximal, characteristic, complemented
5#11723694C212yesmaximal, complemented
6C4×#6295C211yesmaximal, characteristic, complemented
7#11723691C211yesmaximal, characteristic, complemented
8#11723687C212yesmaximal, complemented
9#11723686C212yesmaximal, complemented
10#11723682C212yesmaximal, complemented
11#11723674C211yesmaximal, characteristic, complemented
12#10595358—31nomaximal
13#10595357—31nomaximal
14#10595341—31nomaximal
15C2×C33×Q8C2211yescharacteristic
16C3×#3832—24no—
17C2×C3×C4⋊(C3⋊D3)C2212yes—
18C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C3×C4×C3⋊D3C2211yescharacteristic
20C2×C3×C4×C3⋊D3C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2212yes—
22C2×C3×#634C2211yescharacteristic
23C2×#6295C2212yes—
24C2×#6295C2211yescharacteristic
25C2×#6294C2212yes—
26C2×#6294C2212yes—
27#89041—24no—
28C3×#3752C2212yes—
29C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C3×#3750C2212yes—
31C3×#3750C2212yes—
32C3×#3750C2212yes—
33C3×C4×C3⋊Dic3C2211yescharacteristic
34#88815C2212yes—
35#88815C2211yescharacteristic
36#88814C2212yes—
37#88814C2211yescharacteristic
38#88814C2212yes—
39#88814C2211yescharacteristic
40C2×#3832D311yescharacteristic, complemented
41C2×C3×#239—31no—
42C2×C3×#239—31no—
43C2×C3×#239—61no—
44C2×#3799—31no—
45C2×#3796—31no—
46C2×#3795—31no—
47#64155D311yescharacteristic, complemented
48#64153D311yescharacteristic, complemented
49C3×#946—31no—
50C3×#946—31no—
51C3×#946—61no—
52C3×#944—31no—
53C3×#944—31no—
54C3×#944—61no—
55#63910—32no—
56#63905—32no—
57C4×#626—31no—
58C4×#626—31no—
59C4×#625—31no—
60#63898—31no—
61#63897—32no—
62#63894—31no—
63Dic3×D12—31no—
64#63886—32no—
65#63885—32no—
66#63884—32no—
67#63884—32no—
68#63883—32no—
69D3×Dic3⋊C4—32no—
70D3×Dic3⋊C4—32no—
71#63871—31no—
72#63857—31no—
73#63856—31no—
74#63853—32no—
75#63850—32no—
76C22×C3×C3⋊D3C2311yescharacteristic
77C22×C3×C3⋊D3C2311yescharacteristic
78C22×C3×C3⋊D3C2312yes—
79C33×Q8—22no—
80C2×C33×C4C2312yes—
81C2×C33×C4C2311yescharacteristic
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C2×C3×C3⋊Dic3C2312yes—
85C2×C3×C3⋊Dic3C2312yes—
86C2×C3×C3⋊Dic3C2311yescharacteristic
87C2×C3×C3⋊Dic3C2311yescharacteristic
88C3×C4⋊(C3⋊D3)—24no—
89C3×C4⋊(C3⋊D3)D414yescomplemented
90C3×C4×C3⋊D3—24no—
91C3×C4×C3⋊D3—22no—
92C3×C4×C3⋊D3—22no—
93C3×#634—22no—
94#6295—24no—
95#6295—22no—
96#6294—24no—
97#6294—24no—
98#5824—91no—
99#5726—91no—
100#5631—91no—
101C2×C32×Q8—21no—
102C2×C32×Q8—21no—
103C2×C32×Q8—21no—
104C2×C32×Q8—41no—
105C2×C32×Q8C2×D311yescharacteristic
106C2×C32×Q8C2×D311yescharacteristic
107C2×C32×Q8C2×D311yescharacteristic
108#3832—24no—
109C2×C4⋊(C3⋊D3)C2×D312yes—
110C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
111C2×C4×C3⋊D3C2×D311yescharacteristic
112C2×C4×C3⋊D3C2×D312yes—
113C2×C4×C3⋊D3C2×D311yescharacteristic
114C2×#634C2×D311yescharacteristic
115C3×#239—64no—
116C3×#239—64no—
117C3×#239—68no—
118C2×C3×D12—31no—
119C2×C3×D12—31no—
120C2×C3×D12—32no—
121C2×C3×D12—32no—
122C2×C3×D12—61no—
123C2×C3×D12—62no—
124C2×C3×C4×D3—31no—
125C2×C3×C4×D3—31no—
126C2×C3×C4×D3—32no—
127C2×C3×C4×D3—31no—
128C2×C3×C4×D3—31no—
129C2×C3×C4×D3—32no—
130C2×C3×C4×D3—62no—
131C2×C3×C4×D3—61no—
132C2×C3×C4×D3—61no—
133C2×C3×Dic6—31no—
134C2×C3×Dic6—31no—
135C2×C3×Dic6—61no—
136C2×#626—32no—
137C2×#626—32no—
138C2×#626—31no—
139C2×#626—31no—
140C2×#625—32no—
141C2×#625—31no—
142C2×#624—32no—
143C2×#624—32no—
144C2×D3×Dic3—32no—
145C2×D3×Dic3—32no—
146C2×D3×Dic3—32no—
147C2×D3×Dic3—32no—
148#3799—64no—
149#3796—64no—
150#3795—64no—
151#3752C2×D312yes—
152C4⋊(C3⋊Dic3)C2×D311yescharacteristic
153#3750C2×D312yes—
154#3750C2×D312yes—
155#3750C2×D312yes—
156C4×C3⋊Dic3C2×D311yescharacteristic
157C3×(C2×D3)⋊C4—32no—
158C3×(C2×D3)⋊C4—32no—
159C3×(C2×D3)⋊C4—62no—
160C3×C4⋊Dic3—31no—
161C3×C4⋊Dic3—31no—
162C3×C4⋊Dic3—61no—
163C3×Dic3⋊C4—32no—
164C3×Dic3⋊C4—32no—
165C3×Dic3⋊C4—32no—
166C3×Dic3⋊C4—32no—
167C3×Dic3⋊C4—32no—
168C3×Dic3⋊C4—32no—
169C3×Dic3⋊C4—62no—
170C3×Dic3⋊C4—62no—
171C3×Dic3⋊C4—62no—
172C3×C4×Dic3—31no—
173C3×C4×Dic3—31no—
174C3×C4×Dic3—61no—
175#3724—32no—
176#3724—31no—
177Dic3⋊Dic3—32no—
178Dic3⋊Dic3—32no—
179Dic3⋊Dic3—31no—
180Dic3⋊Dic3—31no—
181#3722—31no—
182#3722—32no—
183#3722—32no—
184#3722—31no—
185(C2×D3)⋊Dic3—32no—
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—32no—
192(C2×D3)⋊Dic3—31no—
193C22×C33C2411yescharacteristic
194C2×C3×C3⋊D3—22no—
195C2×C3×C3⋊D3—22no—
196C2×C3×C3⋊D3—21no—
197C2×C3×C3⋊D3—21no—
198C2×C3×C3⋊D3—21no—
199C2×C3×C3⋊D3—21no—
200C2×C3×C3⋊D3—21no—
201C2×C3×C3⋊D3—21no—
202C2×C3×C3⋊D3C2×D414yes—
203C33×C4—22no—
204C33×C4C2×D412yes—
205C3×C3⋊Dic3—21no—
206C3×C3⋊Dic3—21no—
207C3×C3⋊Dic3—22no—
208C3×C3⋊Dic3—22no—
209C3×C3⋊Dic3—21no—
210C3×C3⋊Dic3#4112yescomplemented
211C2×C3×#41—91no—
212C2×#239—31no—
213C2×#239—31no—
214C2×#239—61no—
215C2×#239—91no—
216C2×#237—91no—
217C2×#235—91no—
218C3×C4⋊Q8—91no—
219C3×C22⋊Q8—91no—
220#946—31no—
221#946—31no—
222#946—61no—
223#946—91no—
224#944—31no—
225#944—31no—
226#944—61no—
227#939—92no—
228#935—92no—
229D4×Dic3—91no—
230#929—92no—
231C4×#67—91no—
232C4×#67—91no—
233#924—91no—
234C2×Dic3⋊C4—92no—
235#897—91no—
236#895—92no—
237#894—92no—
238#894—92no—
239#894—92no—
240#893—91no—
241D3×C4⋊C4—92no—
242D3×C4⋊C4—92no—
243#884—92no—
244#883—92no—
245C4×D12—91no—
246C4×D12—91no—
247C22×C3⋊D3C22×D311yescharacteristic
248C22×C3⋊D3C22×D311yescharacteristic
249C22×C3⋊D3C22×D312yes—
250C22×C3×D3—32no—
251C22×C3×D3—32no—
252C22×C3×D3—31no—
253C22×C3×D3—31no—
254C22×C3×D3—31no—
255C22×C3×D3—31no—
256C22×C3×D3—61no—
257C22×C3×D3—62no—
258C22×C3×D3—61no—
259C32×Q8—22no—
260C32×Q8—24no—
261C32×Q8—22no—
262C32×Q8—22no—
263C32×Q8—42no—
264C32×Q8—42no—
265C32×Q8—44no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—22no—
269C2×C32×C4—21no—
270C2×C32×C4—22no—
271C2×C32×C4—22no—
272C2×C32×C4—41no—
273C2×C32×C4—42no—
274C2×C32×C4C22×D312yes—
275C2×C32×C4C22×D312yes—
276C2×C32×C4C22×D312yes—
277C2×C32×C4C22×D311yescharacteristic
278C2×C32×C4C22×D311yescharacteristic
279C2×C32×C4C22×D311yescharacteristic
280C2×C3⋊Dic3C22×D311yescharacteristic
281C2×C3⋊Dic3C22×D312yes—
282C2×C3⋊Dic3C22×D311yescharacteristic
283C2×C3⋊Dic3C22×D311yescharacteristic
284C2×C3⋊Dic3C22×D312yes—
285C2×C3⋊Dic3C22×D311yescharacteristic
286C4⋊(C3⋊D3)—24no—
287C4⋊(C3⋊D3)#6714yescomplemented
288C4×C3⋊D3—24no—
289C4×C3⋊D3—22no—
290C4×C3⋊D3—22no—
291#634—22no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—31no—
294C2×C3×Dic3—31no—
295C2×C3×Dic3—32no—
296C2×C3×Dic3—31no—
297C2×C3×Dic3—31no—
298C2×C3×Dic3—31no—
299C2×C3×Dic3—32no—
300C2×C3×Dic3—32no—
301C2×C3×Dic3—31no—
302C2×C3×Dic3—31no—
303C2×C3×Dic3—32no—
304C2×C3×Dic3—61no—
305C2×C3×Dic3—61no—
306C2×C3×Dic3—61no—
307C2×C3×Dic3—62no—
308C2×C3×Dic3—61no—
309C2×C3×Dic3—62no—
310C3×D12—34no—
311C3×D12—34no—
312C3×D12—64no—
313C3×D12—64no—
314C3×D12—64no—
315C3×D12—68no—
316C3×C4×D3—64no—
317C3×C4×D3—64no—
318C3×C4×D3—68no—
319C3×C4×D3—64no—
320C3×C4×D3—62no—
321C3×C4×D3—62no—
322C3×C4×D3—62no—
323C3×C4×D3—62no—
324C3×C4×D3—122no—
325C3×Dic6—62no—
326C3×Dic6—62no—
327C3×Dic6—122no—
328#626—62no—
329#626—62no—
330#626—64no—
331#626—64no—
332#625—64no—
333#625—62no—
334#624—64no—
335#624—64no—
336D3×Dic3—64no—
337D3×Dic3—64no—
338D3×Dic3—64no—
339D3×Dic3—64no—
340#547—271noSylow
341C2×C33C22×D411yescharacteristic
342C2×C33C2×#4111yescharacteristic
343C2×C332−1+411yescharacteristic
344C3×C3⋊D3—24no—
345C3×C3⋊D3—41no—
346C3×C3⋊D3—41no—
347C3×#41—184no—
348C2×C3×Q8—21no—
349C2×C3×Q8—21no—
350C2×C3×Q8—21no—
351C2×C3×Q8—41no—
352C2×C3×Q8—91no—
353C2×C3×Q8D3211yescharacteristic
354C2×C3×Q8D3211yescharacteristic
355C2×C3×Q8D3211yescharacteristic
356C2×C3×D4—91no—
357C2×C3×D4—92no—
358C22×C3×C4—92no—
359C22×C3×C4—91no—
360C22×C3×C4—91no—
361C2×#67—92no—
362C2×#67—91no—
363C2×#67—91no—
364C2×#67—92no—
365C22×Dic3—92no—
366C22×Dic3—92no—
367#239—64no—
368#239—64no—
369#239—68no—
370#239—184no—
371#237—184no—
372#235—184no—
373C2×D12—31no—
374C2×D12—31no—
375C2×D12—32no—
376C2×D12—32no—
377C2×D12—61no—
378C2×D12—62no—
379C2×D12—91no—
380C2×D12—92no—
381C2×C4×D3—31no—
382C2×C4×D3—31no—
383C2×C4×D3—32no—
384C2×C4×D3—32no—
385C2×C4×D3—31no—
386C2×C4×D3—31no—
387C2×C4×D3—62no—
388C2×C4×D3—61no—
389C2×C4×D3—61no—
390C2×C4×D3—92no—
391C2×C4×D3—92no—
392C2×C4×D3—92no—
393C2×C4×D3—92no—
394C2×Dic6—31no—
395C2×Dic6—31no—
396C2×Dic6—61no—
397C3×C4⋊C4—92no—
398C3×C4⋊C4—92no—
399C3×C4⋊C4—91no—
400C3×C4⋊C4—92no—
401C3×C22⋊C4—92no—
402C3×C42—91no—
403#217—91no—
404#217—92no—
405#217—91no—
406#217—92no—
407(C2×D3)⋊C4—32no—
408(C2×D3)⋊C4—32no—
409(C2×D3)⋊C4—62no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—92no—
412(C2×D3)⋊C4—91no—
413(C2×D3)⋊C4—92no—
414(C2×D3)⋊C4—92no—
415(C2×D3)⋊C4—91no—
416(C2×D3)⋊C4—92no—
417(C2×D3)⋊C4—91no—
418C4⋊Dic3—31no—
419C4⋊Dic3—31no—
420C4⋊Dic3—61no—
421C4⋊Dic3—91no—
422C4⋊Dic3—92no—
423Dic3⋊C4—32no—
424Dic3⋊C4—32no—
425Dic3⋊C4—32no—
426Dic3⋊C4—32no—
427Dic3⋊C4—32no—
428Dic3⋊C4—32no—
429Dic3⋊C4—62no—
430Dic3⋊C4—62no—
431Dic3⋊C4—62no—
432Dic3⋊C4—91no—
433Dic3⋊C4—92no—
434Dic3⋊C4—91no—
435Dic3⋊C4—92no—
436C4×Dic3—31no—
437C4×Dic3—31no—
438C4×Dic3—61no—
439C22×C32—21no—
440C22×C32—21no—
441C22×C32—21no—
442C22×C32—41no—
443C22×C32C23×D311yescharacteristic
444C22×C32C23×D311yescharacteristic
445C22×C32C23×D311yescharacteristic
446C2×C3⋊D3—21no—
447C2×C3⋊D3—21no—
448C2×C3⋊D3—22no—
449C2×C3⋊D3—22no—
450C2×C3⋊D3—21no—
451C2×C3⋊D3—21no—
452C2×C3⋊D3—21no—
453C2×C3⋊D3—21no—
454C2×C3⋊D3C2×#6714yes—
455C2×C3×D3—34no—
456C2×C3×D3—34no—
457C2×C3×D3—64no—
458C2×C3×D3—62no—
459C2×C3×D3—62no—
460C2×C3×D3—62no—
461C2×C3×D3—62no—
462C2×C3×D3—62no—
463C2×C3×D3—62no—
464C2×C3×D3—61no—
465C2×C3×D3—61no—
466C2×C3×D3—61no—
467C2×C3×D3—61no—
468C2×C3×D3—61no—
469C2×C3×D3—61no—
470C2×C3×D3—61no—
471C2×C3×D3—61no—
472C2×C3×D3—61no—
473C2×C3×D3—61no—
474C2×C3×D3—61no—
475C2×C3×D3—61no—
476C2×C3×D3—121no—
477C2×C3×D3—122no—
478C2×C3×D3—122no—
479C2×C3×D3—121no—
480C2×C3×D3—121no—
481C2×C3×D3—121no—
482C32×C4—22no—
483C32×C4—24no—
484C32×C4—22no—
485C32×C4—22no—
486C32×C4—22no—
487C32×C4—22no—
488C32×C4—22no—
489C32×C4—42no—
490C32×C4—42no—
491C32×C4—42no—
492C32×C4—44no—
493C32×C4D3×D412yes—
494C32×C4D3×D412yes—
495C32×C4C2×#6712yes—
496C3⋊Dic3—21no—
497C3⋊Dic3—21no—
498C3⋊Dic3—21no—
499C3⋊Dic3—22no—
500C3⋊Dic3—22no—
501C3⋊Dic3#23912yescomplemented
502C3×Dic3—32no—
503C3×Dic3—32no—
504C3×Dic3—62no—
505C3×Dic3—62no—
506C3×Dic3—62no—
507C3×Dic3—61no—
508C3×Dic3—62no—
509C3×Dic3—61no—
510C3×Dic3—61no—
511C3×Dic3—62no—
512C3×Dic3—61no—
513C3×Dic3—62no—
514C3×Dic3—61no—
515C3×Dic3—61no—
516C3×Dic3—62no—
517C3×Dic3—122no—
518C3×Dic3—121no—
519C3×Dic3—122no—
520C2×#41—91no—
521C2×#41—271no—
522C4⋊Q8—91no—
523#123—272no—
524#123—272no—
525C22⋊Q8—91no—
526C22⋊Q8—271no—
527#121—272no—
528C4×D4—271no—
529C4×D4—271no—
530C2×C4⋊C4—272no—
531C33#54711yescharacteristic, complemented, Sylow
532C23×C3—92no—
533C23×C3—91no—
534C23×C3—91no—
535C22×D3—32no—
536C22×D3—32no—
537C22×D3—31no—
538C22×D3—31no—
539C22×D3—31no—
540C22×D3—31no—
541C22×D3—61no—
542C22×D3—62no—
543C22×D3—61no—
544C3×Q8—24no—
545C3×Q8—22no—
546C3×Q8—22no—
547C3×Q8—22no—
548C3×Q8—42no—
549C3×Q8—42no—
550C3×Q8—44no—
551C3×Q8—182no—
552C3×D4—94no—
553C3×D4—184no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—22no—
557C2×C3×C4—21no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—42no—
561C2×C3×C4—41no—
562C2×C3×C4—91no—
563C2×C3×C4—91no—
564C2×C3×C4—91no—
565C2×C3×C4—92no—
566C2×C3×C4—92no—
567C2×C3×C4—91no—
568C2×C3×C4—184no—
569C2×C3×C4—182no—
570C2×C3×C4—182no—
571C2×C3×C4C2×D3212yes—
572C2×C3×C4C2×D3212yes—
573C2×C3×C4C2×D3212yes—
574C2×C3×C4C2×D3211yescharacteristic
575C2×C3×C4C2×D3211yescharacteristic
576C2×C3×C4C2×D3211yescharacteristic
577#67—182no—
578#67—182no—
579#67—184no—
580#67—184no—
581C2×Dic3—31no—
582C2×Dic3—31no—
583C2×Dic3—31no—
584C2×Dic3—31no—
585C2×Dic3—32no—
586C2×Dic3—31no—
587C2×Dic3—32no—
588C2×Dic3—31no—
589C2×Dic3—32no—
590C2×Dic3—32no—
591C2×Dic3—31no—
592C2×Dic3—31no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—62no—
597C2×Dic3—61no—
598C2×Dic3—62no—
599C2×Dic3—184no—
600C2×Dic3—184no—
601D12—34no—
602D12—34no—
603D12—64no—
604D12—64no—
605D12—64no—
606D12—68no—
607D12—182no—
608D12—184no—
609C4×D3—64no—
610C4×D3—64no—
611C4×D3—68no—
612C4×D3—64no—
613C4×D3—62no—
614C4×D3—62no—
615C4×D3—62no—
616C4×D3—62no—
617C4×D3—122no—
618C4×D3—184no—
619C4×D3—184no—
620C4×D3—184no—
621C4×D3—184no—
622Dic6—62no—
623Dic6—62no—
624Dic6—122no—
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×C32C2×D3×D411yescharacteristic
638C2×C32C2×D3×D411yescharacteristic
639C2×C32C2×#23911yescharacteristic
640C2×C32#100711yescharacteristic
641C2×C32#100711yescharacteristic
642C2×C32D3×#4111yescharacteristic
643C2×C32D3×#4111yescharacteristic
644C2×C32#101011yescharacteristic
645C2×C32C22×#6711yescharacteristic
646C3⋊D3—24no—
647C3⋊D3—41no—
648C3⋊D3—41no—
649C3×D3—64no—
650C3×D3—64no—
651C3×D3—124no—
652C3×D3—122no—
653C3×D3—122no—
654C3×D3—121no—
655C3×D3—121no—
656C3×D3—121no—
657C3×D3—121no—
658#41—184no—
659#41—544no—
660C2×Q8—91no—
661C2×Q8#111311yescharacteristic
662C2×D4—91no—
663C2×D4—92no—
664C2×D4—271no—
665C2×D4—272no—
666C22×C4—92no—
667C22×C4—91no—
668C22×C4—91no—
669C22×C4—272no—
670C22×C4—272no—
671C4⋊C4—92no—
672C4⋊C4—92no—
673C4⋊C4—91no—
674C4⋊C4—92no—
675C4⋊C4—271no—
676C4⋊C4—272no—
677C22⋊C4—92no—
678C22⋊C4—272no—
679C22⋊C4—271no—
680C22⋊C4—271no—
681C22⋊C4—272no—
682C42—91no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—41no—
687C22×C3—94no—
688C22×C3—182no—
689C22×C3—182no—
690C22×C3—181no—
691C22×C3—181no—
692C22×C3—181no—
693C22×C3—181no—
694C22×C3—181no—
695C22×C3—181no—
696C22×C3C22×D3211yescharacteristic
697C22×C3C22×D3211yescharacteristic
698C22×C3C22×D3211yescharacteristic
699C2×D3—34no—
700C2×D3—34no—
701C2×D3—64no—
702C2×D3—62no—
703C2×D3—62no—
704C2×D3—62no—
705C2×D3—62no—
706C2×D3—62no—
707C2×D3—62no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—61no—
711C2×D3—61no—
712C2×D3—61no—
713C2×D3—61no—
714C2×D3—61no—
715C2×D3—61no—
716C2×D3—61no—
717C2×D3—61no—
718C2×D3—61no—
719C2×D3—61no—
720C2×D3—121no—
721C2×D3—122no—
722C2×D3—122no—
723C2×D3—121no—
724C2×D3—121no—
725C2×D3—121no—
726C3×C4—24no—
727C3×C4—22no—
728C3×C4—22no—
729C3×C4—22no—
730C3×C4—22no—
731C3×C4—22no—
732C3×C4—22no—
733C3×C4—42no—
734C3×C4—42no—
735C3×C4—44no—
736C3×C4—42no—
737C3×C4—92no—
738C3×C4—181no—
739C3×C4—182no—
740C3×C4—181no—
741C3×C4—182no—
742C3×C4—181no—
743C3×C4D3×#6712yes—
744C3×C4D3×#6712yes—
745C3×C4#381112yes—
746Dic3—32no—
747Dic3—32no—
748Dic3—62no—
749Dic3—62no—
750Dic3—62no—
751Dic3—61no—
752Dic3—61no—
753Dic3—62no—
754Dic3—62no—
755Dic3—62no—
756Dic3—61no—
757Dic3—61no—
758Dic3—61no—
759Dic3—62no—
760Dic3—61no—
761Dic3—122no—
762Dic3—121no—
763Dic3—122no—
764C32—21no—
765C32—21no—
766C32—21no—
767C32—41no—
768C32#563111yescharacteristic, complemented
769C32#572611yescharacteristic, complemented
770C32#582411yescharacteristic, complemented
771C23—92no—
772C23—91no—
773C23—91no—
774Q8—22no—
775Q8—182no—
776D4—94no—
777D4—184no—
778D4—542no—
779D4—544no—
780C2×C4—91no—
781C2×C4—91no—
782C2×C4—92no—
783C2×C4—91no—
784C2×C4—92no—
785C2×C4—91no—
786C2×C4—184no—
787C2×C4—182no—
788C2×C4—182no—
789C2×C4—544no—
790C2×C4—544no—
791C2×C4C2×#111312yes—
792C2×C4C2×#111311yescharacteristic
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—184no—
806C2×C3—361no—
807C2×C3—361no—
808C2×C3#6431511yescharacteristic
809C2×C3#6431511yescharacteristic
810C2×C3#6431611yescharacteristic
811C2×C3D3×#23911yescharacteristic
812C2×C3D3×#23911yescharacteristic
813C2×C3#6431911yescharacteristic
814C2×C3C2×D3×#6711yescharacteristic
815C2×C3C2×D3×#6711yescharacteristic
816C2×C3C2×#381111yescharacteristic
817D3—64no—
818D3—64no—
819D3—124no—
820D3—122no—
821D3—122no—
822D3—121no—
823D3—121no—
824D3—121no—
825D3—121no—
826C22—94no—
827C22—182no—
828C22—182no—
829C22—181no—
830C22—181no—
831C22—181no—
832C22—181no—
833C22—181no—
834C22—181no—
835C22C22×#111311yescharacteristic
836C4—22no—
837C4—92no—
838C4—181no—
839C4—182no—
840C4—181no—
841C4—181no—
842C4—182no—
843C4#8904912yes—
844C3—21no—
845C3—21no—
846C3—21no—
847C3—41no—
848C3#1059534111yescharacteristic, complemented
849C3#1059535711yescharacteristic, complemented
850C3#1059535811yescharacteristic, complemented
851C2—184no—
852C2—361no—
853C2—361no—
854C2#1172462411yescharacteristic
855C2#1172462611yescharacteristic
856C2C2×#8904911yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×Q8C22
hypercenterC2×Q8#1113
hypocenterC33#547
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3832C2semidirect
2. C2×#89041C2semidirect
3. C3×#64155C2semidirect
4. C3×#64153C2semidirect
5. #11723694C2semidirect
6. C4×#6295C2semidirect
7. #11723691C2semidirect
8. #11723687C2semidirect
9. #11723686C2semidirect
10. #11723682C2semidirect
11. #11723674C2semidirect
40. C2×#3832D3semidirect
47. #64155D3semidirect
48. #64153D3semidirect
89. C3×C4⋊(C3⋊D3)D4semidirect
210. C3×C3⋊Dic3#41semidirect
287. C4⋊(C3⋊D3)#67semidirect
501. C3⋊Dic3#239semidirect
531. C33#547semidirect
768. C32#5631semidirect
769. C32#5726semidirect
770. C32#5824semidirect
848. C3#10595341semidirect
849. C3#10595357semidirect
850. C3#10595358semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38322
C2×#890412
C3×#641552
C3×#641532
#117236942
C4×#62952
#117236912
#117236872
#117236862
#117236822
#117236742
#105953583
#105953573
#105953413