Finite Group Databasebeta

← #13177367

Subgroups — #13177367

Order 1728.

2356 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89029C211yesmaximal, characteristic, complemented
2C22×D3×C3⋊Dic3C211yesmaximal, characteristic, complemented
3D4×C3⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
4C3×#64148C211yesmaximal, characteristic, complemented
5C32×#937C211yesmaximal, characteristic, complemented
6#11723641C211yesmaximal, characteristic, complemented
7#11723629C211yesmaximal, characteristic, complemented
8#11723626C211yesmaximal, characteristic, complemented
9#67⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
10#11723615C211yesmaximal, characteristic, complemented
11#11723614C211yesmaximal, characteristic, complemented
12#11723508C211yesmaximal, characteristic, complemented
13#11723491C211yesmaximal, characteristic, complemented
14#11723480C211yesmaximal, characteristic, complemented
15#11723460C211yesmaximal, characteristic, complemented
16#10596057—31nomaximal
17#10595130—34nomaximal
18C23×C32×D3C2211yescharacteristic
19C2×C33×D4C2211yescharacteristic
20C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
21C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic, complemented
24C22×C3×C3⋊Dic3C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic
26C2×C32×#67C2211yescharacteristic
27C2×#6293C2211yescharacteristic, complemented
28C2×#6290C2211yescharacteristic
29C2×#6290C2211yescharacteristic
30C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
31#89029—24no—
32C2×D3×C3⋊Dic3—24no—
33C2×D3×C3⋊Dic3C2211yescharacteristic
34C2×D3×C3⋊Dic3C2211yescharacteristic
35C2×D3×C3⋊Dic3C2211yescharacteristic
36C2×D3×C3⋊Dic3C2211yescharacteristic
37#88864C2211yescharacteristic
38#88864C2211yescharacteristic, complemented
39C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
40C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41C3×#3757C2211yescharacteristic, complemented
42C3×#3752C2211yescharacteristic, complemented
43C3×#3750C2211yescharacteristic, complemented
44C32×#217C2211yescharacteristic
45C32×(C2×D3)⋊C4C2211yescharacteristic
46C32×(C2×D3)⋊C4C2211yescharacteristic
47#88807C2211yescharacteristic, complemented
48#88807C2211yescharacteristic, complemented
49#88806C2211yescharacteristic, complemented
50Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
51#88803C2211yescharacteristic, complemented
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55C23×C3⋊Dic3—31no—
56C2×#3830—31no—
57C2×#3805—34no—
58C22×D3×Dic3—34no—
59C32×#120—31no—
60#64162—31no—
61#64148—31no—
62#64148D311yescharacteristic, complemented
63#64144—31no—
64D4×C3⋊Dic3—31no—
65D4×C3⋊Dic3—31no—
66D4×C3⋊Dic3—34no—
67D4×C3⋊Dic3—64no—
68#64095—31no—
69#64090—31no—
70#64090—31no—
71#64087—31no—
72#64087—31no—
73#64086—31no—
74C3×#939—34no—
75C3×#937D314yescomplemented
76#63976—34no—
77#67⋊Dic3—34no—
78#67⋊Dic3—34no—
79#63970—34no—
80#63969—34no—
81#63964—34no—
82#63902—34no—
83#63893—34no—
84#63891—34no—
85#63878—34no—
86C23×C33C2311yescharacteristic
87C23×C33C2311yescharacteristic
88C22×C3×C3⋊D3C2311yescharacteristic
89C22×C32×D3—22no—
90C22×C32×D3—22no—
91C22×C32×D3—22no—
92C22×C32×D3C2311yescharacteristic
93C22×C32×D3C2311yescharacteristic
94C33×D4—22no—
95C2×C33×C4C2311yescharacteristic
96C2×C3⋊(C3⋊Dic3)—22no—
97C2×C3⋊(C3⋊Dic3)—22no—
98C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
99C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
100C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
101C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
102C3×#638—22no—
103C3×#638—22no—
104C2×C3×C3⋊Dic3—22no—
105C2×C3×C3⋊Dic3C2311yescharacteristic
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C32×#67—22no—
109C32×#67—22no—
110C2×C32×Dic3C2311yescharacteristic
111C2×C32×Dic3C2311yescharacteristic
112#6293—22no—
113#6290—22no—
114#6290—22no—
115Dic3×C3⋊D3—22no—
116D3×C3⋊Dic3—22no—
117D3×C3⋊Dic3—22no—
118D3×C3⋊Dic3—22no—
119D3×C3⋊Dic3D414yescomplemented
120#5606—91no—
121#5586—94no—
122C24×C32—31no—
123C23×C3×D3C2×D314yes—
124C2×C32×D4—24no—
125C2×C32×D4—31no—
126C2×C32×D4—31no—
127C2×C32×D4C2×D314yes—
128C2×C32×D4C2×D311yescharacteristic
129C2×#638—31no—
130C2×#638—31no—
131C2×#638C2×D311yescharacteristic
132C2×#638C2×D311yescharacteristic, complemented
133C22×C3⋊Dic3—31no—
134C22×C3⋊Dic3—31no—
135C22×C3⋊Dic3—31no—
136C22×C3⋊Dic3—34no—
137C22×C3⋊Dic3—34no—
138C22×C3⋊Dic3—31no—
139C22×C3⋊Dic3—31no—
140C22×C3⋊Dic3—31no—
141C22×C3⋊Dic3—64no—
142C22×C3⋊Dic3—64no—
143C22×C3⋊Dic3—64no—
144C22×C3⋊Dic3C2×D311yescharacteristic
145#3830—64no—
146C2×C4×C3⋊D3—31no—
147C2×#634—31no—
148C2×C3×#67—34no—
149C2×C3×#67—34no—
150C2×C3×#67C2×D314yes—
151C2×C3×#67C2×D314yes—
152C22×C3×Dic3—34no—
153C2×#627—34no—
154C2×#625—34no—
155C2×#625—34no—
156#3805—616no—
157C2×D3×Dic3—34no—
158C2×D3×Dic3—34no—
159C2×D3×Dic3—34no—
160C2×D3×Dic3—34no—
161C2×D3×Dic3—34no—
162C2×D3×Dic3—616no—
163C32×C22⋊C4—31no—
164C32×C22⋊C4—31no—
165C32×C22⋊C4—31no—
166#3757—31no—
167#3757—31no—
168#3757—34no—
169#3757—34no—
170#3757—31no—
171#3757—31no—
172#3757—64no—
173#3757—64no—
174#3757C2×D311yescharacteristic, complemented
175#3752—31no—
176#3752C2×D311yescharacteristic, complemented
177C4⋊(C3⋊Dic3)—31no—
178C4⋊(C3⋊Dic3)—34no—
179C4⋊(C3⋊Dic3)—31no—
180C4⋊(C3⋊Dic3)—64no—
181#3750—31no—
182#3750—31no—
183#3750—31no—
184#3750C2×D311yescharacteristic, complemented
185C4×C3⋊Dic3—31no—
186C4×C3⋊Dic3—34no—
187C4×C3⋊Dic3—31no—
188C4×C3⋊Dic3—64no—
189C3×#217—34no—
190C3×#217C2×D314yes—
191C3×(C2×D3)⋊C4—34no—
192C3×(C2×D3)⋊C4C2×D314yes—
193C3×(C2×D3)⋊C4C2×D314yes—
194C3×Dic3⋊C4—34no—
195#3724—34no—
196Dic3⋊Dic3—34no—
197Dic3⋊Dic3—34no—
198Dic3⋊Dic3—34no—
199(C2×D3)⋊Dic3—34no—
200(C2×D3)⋊Dic3—34no—
201(C2×D3)⋊Dic3—34no—
202Dic32—34no—
203C22×C33—21no—
204C22×C33—21no—
205C22×C33—21no—
206C22×C33—21no—
207C22×C33—21no—
208C22×C33#4112yescomplemented
209C22×C33C2411yescharacteristic
210C2×C3×C3⋊D3—21no—
211C2×C3×C3⋊D3—21no—
212C2×C3×C3⋊D3—21no—
213C2×C32×D3—28no—
214C2×C32×D3—21no—
215C2×C32×D3—21no—
216C2×C32×D3—21no—
217C2×C32×D3—21no—
218C2×C32×D3C2×D412yes—
219C2×C32×D3#4112yescomplemented
220C33×C4—21no—
221C3⋊(C3⋊Dic3)—21no—
222C3⋊(C3⋊Dic3)—21no—
223C3⋊(C3⋊Dic3)—21no—
224C3⋊(C3⋊Dic3)C2×D412yes—
225C3×C3⋊Dic3—21no—
226C3×C3⋊Dic3—21no—
227C3×C3⋊Dic3C2×D412yes—
228C32×Dic3—21no—
229C32×Dic3—21no—
230C23×Dic3—94no—
231C2×#237—94no—
232C2×#237—91no—
233C22×C4×D3—91no—
234C3×#121—91no—
235C3×#120—34no—
236#953—94no—
237#939—34no—
238#939—94no—
239#938—91no—
240#937—91no—
241#937C3⋊D311yescharacteristic, complemented
242#935—94no—
243D4×Dic3—94no—
244D4×Dic3—94no—
245D4×Dic3—91no—
246D4×Dic3—91no—
247D4×Dic3—184no—
248#924—91no—
249#897—91no—
250#892—91no—
251#886—94no—
252#883—91no—
253#883—91no—
254#67⋊C4—94no—
255#67⋊C4—94no—
256#67⋊C4—91no—
257#67⋊C4—91no—
258#878—94no—
259#878—94no—
260#877—94no—
261C23×C32—24no—
262C23×C32—24no—
263C23×C32—31no—
264C23×C32—31no—
265C23×C32—62no—
266C23×C32—62no—
267C23×C32—62no—
268C23×C32C22×D314yes—
269C23×C32C22×D314yes—
270C23×C32C22×D311yescharacteristic
271C23×C32C22×D311yescharacteristic
272C22×C3⋊D3C22×D311yescharacteristic
273C22×C3×D3—28no—
274C22×C3×D3—28no—
275C22×C3×D3—28no—
276C22×C3×D3—34no—
277C22×C3×D3C22×D314yes—
278C22×C3×D3C22×D314yes—
279C32×D4—216no—
280C32×D4—28no—
281C32×D4—22no—
282C32×D4—62no—
283C32×D4—62no—
284C2×C32×C4—24no—
285C2×C32×C4—31no—
286C2×C32×C4—31no—
287C2×C32×C4C22×D314yes—
288C2×C32×C4C22×D311yescharacteristic
289#638—22no—
290#638—22no—
291#638—62no—
292#638—62no—
293C2×C3⋊Dic3—22no—
294C2×C3⋊Dic3—31no—
295C2×C3⋊Dic3—34no—
296C2×C3⋊Dic3—31no—
297C2×C3⋊Dic3—31no—
298C2×C3⋊Dic3—31no—
299C2×C3⋊Dic3—34no—
300C2×C3⋊Dic3—34no—
301C2×C3⋊Dic3—34no—
302C2×C3⋊Dic3—34no—
303C2×C3⋊Dic3—64no—
304C2×C3⋊Dic3—64no—
305C2×C3⋊Dic3—64no—
306C2×C3⋊Dic3—64no—
307C2×C3⋊Dic3—62no—
308C2×C3⋊Dic3—62no—
309C2×C3⋊Dic3—62no—
310C2×C3⋊Dic3—62no—
311C2×C3⋊Dic3—62no—
312C2×C3⋊Dic3—68no—
313C2×C3⋊Dic3—68no—
314C2×C3⋊Dic3—128no—
315C2×C3⋊Dic3—128no—
316C2×C3⋊Dic3C22×D311yescharacteristic
317C2×C3⋊Dic3C22×D311yescharacteristic
318C2×C3⋊Dic3C22×D311yescharacteristic
319C4×C3⋊D3—62no—
320#634—62no—
321C3×#67—28no—
322C3×#67—28no—
323C3×#67—68no—
324C3×#67—68no—
325C2×C3×Dic3—34no—
326C2×C3×Dic3—34no—
327C2×C3×Dic3—34no—
328C2×C3×Dic3—68no—
329C2×C3×Dic3C22×D314yes—
330C2×C3×Dic3C22×D314yes—
331#627—68no—
332#625—68no—
333#625—68no—
334D3×Dic3—316no—
335D3×Dic3—68no—
336D3×Dic3—68no—
337D3×Dic3—68no—
338D3×Dic3—68no—
339#525—271noSylow
340C2×C33—22no—
341C2×C33—41no—
342C2×C33C22×D411yescharacteristic
343C2×C33C2×#4111yescharacteristic
344C2×C33C2×#4111yescharacteristic
345C3×C3⋊D3—41no—
346C32×D3—22no—
347C32×D3—22no—
348C24×C3—34no—
349C23×D3C2×C3⋊D311yescharacteristic
350C2×C3×D4—24no—
351C2×C3×D4—34no—
352C2×C3×D4—34no—
353C2×C3×D4—91no—
354C2×C3×D4—91no—
355C2×C3×D4D3214yes—
356C2×C3×D4C2×C3⋊D311yescharacteristic
357C22×C3×C4—91no—
358C2×#67—34no—
359C2×#67—34no—
360C2×#67—94no—
361C2×#67—94no—
362C2×#67—91no—
363C2×#67—91no—
364C2×#67C2×C3⋊D311yescharacteristic
365C2×#67C2×C3⋊D311yescharacteristic
366C22×Dic3—34no—
367C22×Dic3—94no—
368C22×Dic3—94no—
369C22×Dic3—94no—
370C22×Dic3—94no—
371C22×Dic3—94no—
372C22×Dic3—94no—
373C22×Dic3—91no—
374C22×Dic3—91no—
375C22×Dic3—91no—
376C22×Dic3—184no—
377C22×Dic3—184no—
378C22×Dic3—1816no—
379#237—184no—
380#237—1816no—
381C2×C4×D3—91no—
382C2×C4×D3—94no—
383C2×C4×D3—91no—
384C2×C4×D3—91no—
385C2×C4×D3—91no—
386C2×C4×D3—184no—
387C2×Dic6—94no—
388C2×Dic6—91no—
389C3×C4⋊C4—91no—
390C3×C22⋊C4—34no—
391C3×C22⋊C4—34no—
392C3×C22⋊C4—34no—
393C3×C22⋊C4—91no—
394C3×C22⋊C4—91no—
395#217—34no—
396#217—94no—
397#217—94no—
398#217—94no—
399#217—94no—
400#217—91no—
401#217—91no—
402#217—91no—
403#217—184no—
404#217—184no—
405#217C2×C3⋊D311yescharacteristic
406(C2×D3)⋊C4—34no—
407(C2×D3)⋊C4—94no—
408(C2×D3)⋊C4—91no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
411(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
412C4⋊Dic3—94no—
413C4⋊Dic3—94no—
414C4⋊Dic3—91no—
415C4⋊Dic3—91no—
416C4⋊Dic3—91no—
417C4⋊Dic3—184no—
418Dic3⋊C4—34no—
419Dic3⋊C4—94no—
420Dic3⋊C4—94no—
421Dic3⋊C4—94no—
422Dic3⋊C4—91no—
423Dic3⋊C4—91no—
424C4×Dic3—94no—
425C4×Dic3—94no—
426C4×Dic3—91no—
427C4×Dic3—91no—
428C4×Dic3—184no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—28no—
432C22×C32—21no—
433C22×C32—24no—
434C22×C32—21no—
435C22×C32—21no—
436C22×C32—24no—
437C22×C32—28no—
438C22×C32—24no—
439C22×C32—24no—
440C22×C32—24no—
441C22×C32—24no—
442C22×C32—32no—
443C22×C32—32no—
444C22×C32—44no—
445C22×C32—44no—
446C22×C32—44no—
447C22×C32—44no—
448C22×C32—68no—
449C22×C32—61no—
450C22×C32—61no—
451C22×C32—61no—
452C22×C32—61no—
453C22×C32#23718yescomplemented
454C22×C32#23712yescomplemented
455C22×C32C23×D314yes—
456C22×C32C23×D311yescharacteristic
457C2×C3⋊D3—21no—
458C2×C3⋊D3—21no—
459C2×C3⋊D3—21no—
460C2×C3×D3—232no—
461C2×C3×D3—24no—
462C2×C3×D3—24no—
463C2×C3×D3—24no—
464C2×C3×D3—24no—
465C2×C3×D3—64no—
466C2×C3×D3—64no—
467C2×C3×D3—64no—
468C2×C3×D3D3×D418yes—
469C2×C3×D3#23718yescomplemented
470C32×C4—28no—
471C32×C4—24no—
472C32×C4—21no—
473C32×C4—61no—
474C32×C4—61no—
475C3⋊Dic3—21no—
476C3⋊Dic3—21no—
477C3⋊Dic3—32no—
478C3⋊Dic3—38no—
479C3⋊Dic3—68no—
480C3⋊Dic3—61no—
481C3⋊Dic3—61no—
482C3⋊Dic3—61no—
483C3⋊Dic3—64no—
484C3⋊Dic3—64no—
485C3⋊Dic3—64no—
486C3⋊Dic3—124no—
487C3⋊Dic3—124no—
488C3⋊Dic3—124no—
489C3⋊Dic3D3×D412yes—
490C3×Dic3—24no—
491C3×Dic3—24no—
492C3×Dic3—38no—
493C3×Dic3—64no—
494C3×Dic3—64no—
495C2×#41—271no—
496C23×C4—271no—
497#123—271no—
498#123—271no—
499C22⋊Q8—271no—
500C22⋊Q8—271no—
501#121—91no—
502#121—271no—
503#120—31no—
504#120—271no—
505C4×D4—271no—
506C4×D4—271no—
507C4×D4—271no—
508C4×D4—271no—
509#117—271no—
510C33#52511yescharacteristic, complemented, Sylow
511C23×C3—24no—
512C23×C3—24no—
513C23×C3—34no—
514C23×C3—34no—
515C23×C3—68no—
516C23×C3—68no—
517C23×C3—68no—
518C23×C3—91no—
519C23×C3C2×D3214yes—
520C23×C3C2×D3214yes—
521C23×C3C22×C3⋊D311yescharacteristic
522C23×C3C22×C3⋊D311yescharacteristic
523C22×D3—22no—
524C22×D3—22no—
525C22×D3—22no—
526C22×D3—34no—
527C22×D3C22×C3⋊D311yescharacteristic
528C22×D3C22×C3⋊D311yescharacteristic
529C3×D4—216no—
530C3×D4—28no—
531C3×D4—22no—
532C3×D4—68no—
533C3×D4—68no—
534C3×D4—182no—
535C3×D4—182no—
536C2×C3×C4—24no—
537C2×C3×C4—34no—
538C2×C3×C4—34no—
539C2×C3×C4—91no—
540C2×C3×C4—91no—
541C2×C3×C4—91no—
542C2×C3×C4—182no—
543C2×C3×C4C2×D3214yes—
544C2×C3×C4C22×C3⋊D311yescharacteristic
545#67—22no—
546#67—22no—
547#67—68no—
548#67—68no—
549#67—188no—
550#67—188no—
551#67—182no—
552#67—182no—
553C2×Dic3—34no—
554C2×Dic3—34no—
555C2×Dic3—34no—
556C2×Dic3—68no—
557C2×Dic3—916no—
558C2×Dic3—94no—
559C2×Dic3—91no—
560C2×Dic3—94no—
561C2×Dic3—94no—
562C2×Dic3—94no—
563C2×Dic3—91no—
564C2×Dic3—91no—
565C2×Dic3—91no—
566C2×Dic3—184no—
567C2×Dic3—184no—
568C2×Dic3—184no—
569C2×Dic3—184no—
570C2×Dic3—182no—
571C2×Dic3—188no—
572C2×Dic3—188no—
573C2×Dic3—188no—
574C2×Dic3—182no—
575C2×Dic3—182no—
576C2×Dic3—188no—
577C2×Dic3—188no—
578C2×Dic3—368no—
579C2×Dic3—368no—
580C2×Dic3C22×C3⋊D311yescharacteristic
581C2×Dic3C22×C3⋊D311yescharacteristic
582C4×D3—94no—
583C4×D3—188no—
584C4×D3—182no—
585C4×D3—182no—
586C4×D3—182no—
587Dic6—182no—
588Dic6—188no—
589C2×C32—22no—
590C2×C32—24no—
591C2×C32—24no—
592C2×C32—24no—
593C2×C32—28no—
594C2×C32—48no—
595C2×C32—48no—
596C2×C32—44no—
597C2×C32—41no—
598C2×C32—62no—
599C2×C32—62no—
600C2×C32C2×D3×D414yes—
601C2×C32C2×D3×D411yescharacteristic
602C2×C32C2×#23714yes—
603C2×C32C2×#23714yes—
604C2×C32C2×#23711yescharacteristic
605C2×C32D3×#4111yescharacteristic
606C3⋊D3—41no—
607C3×D3—28no—
608C3×D3—28no—
609C3×D3—124no—
610C24—31no—
611#41—544no—
612C2×Q8—271no—
613C2×D4—31no—
614C2×D4—31no—
615C2×D4—91no—
616C2×D4—91no—
617C2×D4—271no—
618C2×D4—271no—
619C2×D4D3×C3⋊D311yescharacteristic
620C22×C4—91no—
621C22×C4—271no—
622C22×C4—271no—
623C22×C4—271no—
624C22×C4—271no—
625C22×C4—271no—
626C22×C4—271no—
627C22×C4—271no—
628C22×C4—544no—
629C4⋊C4—91no—
630C4⋊C4—271no—
631C4⋊C4—271no—
632C4⋊C4—271no—
633C4⋊C4—271no—
634C4⋊C4—271no—
635C22⋊C4—31no—
636C22⋊C4—31no—
637C22⋊C4—31no—
638C22⋊C4—91no—
639C22⋊C4—91no—
640C22⋊C4—271no—
641C22⋊C4—271no—
642C22⋊C4—271no—
643C22⋊C4—271no—
644C22⋊C4—271no—
645C42—271no—
646C42—271no—
647C22×C3—24no—
648C22×C3—24no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—28no—
652C22×C3—24no—
653C22×C3—24no—
654C22×C3—24no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—24no—
659C22×C3—28no—
660C22×C3—38no—
661C22×C3—38no—
662C22×C3—44no—
663C22×C3—44no—
664C22×C3—44no—
665C22×C3—44no—
666C22×C3—632no—
667C22×C3—64no—
668C22×C3—64no—
669C22×C3—64no—
670C22×C3—64no—
671C22×C3—181no—
672C22×C3—181no—
673C22×C3—181no—
674C22×C3#380518yescomplemented
675C22×C3#383012yescomplemented
676C22×C3C22×D3214yes—
677C22×C3C23×C3⋊D311yescharacteristic
678C2×D3—28no—
679C2×D3—21no—
680C2×D3—21no—
681C2×D3—21no—
682C2×D3—21no—
683C2×D3—64no—
684C2×D3—64no—
685C2×D3—64no—
686C2×D3D4×C3⋊D312yes—
687C2×D3#383012yescomplemented
688C3×C4—28no—
689C3×C4—24no—
690C3×C4—21no—
691C3×C4—64no—
692C3×C4—64no—
693C3×C4—92no—
694C3×C4—181no—
695C3×C4—181no—
696Dic3—21no—
697Dic3—21no—
698Dic3—38no—
699Dic3—64no—
700Dic3—64no—
701Dic3—98no—
702Dic3—92no—
703Dic3—188no—
704Dic3—184no—
705Dic3—184no—
706Dic3—184no—
707Dic3—181no—
708Dic3—181no—
709Dic3—181no—
710Dic3—364no—
711Dic3—364no—
712Dic3—364no—
713C32—24no—
714C32#558614yescomplemented
715C32#560611yescharacteristic, complemented
716C23—31no—
717C23—31no—
718C23—62no—
719C23—62no—
720C23—62no—
721C23—91no—
722C23C2×D3×C3⋊D311yescharacteristic
723C23C2×D3×C3⋊D311yescharacteristic
724Q8—542no—
725D4—22no—
726D4—62no—
727D4—62no—
728D4—182no—
729D4—182no—
730D4—542no—
731D4—542no—
732C2×C4—31no—
733C2×C4—31no—
734C2×C4—91no—
735C2×C4—91no—
736C2×C4—91no—
737C2×C4—182no—
738C2×C4—274no—
739C2×C4—271no—
740C2×C4—271no—
741C2×C4—271no—
742C2×C4—271no—
743C2×C4—542no—
744C2×C4—542no—
745C2×C4—542no—
746C2×C4—542no—
747C2×C4—542no—
748C2×C4—542no—
749C2×C4C2×D3×C3⋊D311yescharacteristic
750C2×C3—28no—
751C2×C3—22no—
752C2×C3—24no—
753C2×C3—24no—
754C2×C3—24no—
755C2×C3—48no—
756C2×C3—48no—
757C2×C3—44no—
758C2×C3—41no—
759C2×C3—68no—
760C2×C3—68no—
761C2×C3—361no—
762C2×C3D32×D414yes—
763C2×C3D3×#23714yes—
764C2×C3C2×#380514yes—
765C2×C3C2×D4×C3⋊D311yescharacteristic
766C2×C3C2×#383011yescharacteristic
767C2×C3C2×#383011yescharacteristic
768D3—22no—
769D3—22no—
770D3—124no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—32no—
777C22—32no—
778C22—68no—
779C22—61no—
780C22—61no—
781C22—61no—
782C22—61no—
783C22—181no—
784C22—181no—
785C22—181no—
786C22#8902912yescomplemented
787C22C22×D3×C3⋊D311yescharacteristic
788C4—21no—
789C4—61no—
790C4—61no—
791C4—92no—
792C4—181no—
793C4—181no—
794C4—272no—
795C4—541no—
796C4—541no—
797C4—541no—
798C3—24no—
799C3#1059513014yescomplemented
800C3#1059605711yescharacteristic, complemented
801C2—22no—
802C2—41no—
803C2—62no—
804C2—62no—
805C2—361no—
806C2D3×D4×C3⋊D311yescharacteristic
807C2D3×#383011yescharacteristic
808C2C2×#8902911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33#525
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#89029C2semidirect
2. C22×D3×C3⋊Dic3C2semidirect
3. D4×C3⋊(C3⋊Dic3)C2semidirect
4. C3×#64148C2semidirect
5. C32×#937C2semidirect
6. #11723641C2semidirect
7. #11723629C2semidirect
8. #11723626C2semidirect
9. #67⋊(C3⋊Dic3)C2semidirect
10. #11723615C2semidirect
11. #11723614C2semidirect
12. #11723508C2semidirect
13. #11723491C2semidirect
14. #11723480C2semidirect
15. #11723460C2semidirect
21. C22×C3⋊(C3⋊Dic3)C22semidirect
23. C2×C3×#638C22semidirect
27. C2×#6293C22semidirect
30. C2×Dic3×C3⋊D3C22semidirect
38. #88864C22semidirect
39. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
40. C4×C3⋊(C3⋊Dic3)C22semidirect
41. C3×#3757C22semidirect
42. C3×#3752C22semidirect
43. C3×#3750C22semidirect
47. #88807C22semidirect
48. #88807C22semidirect
49. #88806C22semidirect
50. Dic3⋊(C3⋊Dic3)C22semidirect
51. #88803C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
62. #64148D3semidirect
75. C3×#937D3semidirect
119. D3×C3⋊Dic3D4semidirect
132. C2×#638C2×D3semidirect
174. #3757C2×D3semidirect
176. #3752C2×D3semidirect
184. #3750C2×D3semidirect
208. C22×C33#41semidirect
219. C2×C32×D3#41semidirect
241. #937C3⋊D3semidirect
453. C22×C32#237semidirect
454. C22×C32#237semidirect
469. C2×C3×D3#237semidirect
510. C33#525semidirect
674. C22×C3#3805semidirect
675. C22×C3#3830semidirect
687. C2×D3#3830semidirect
714. C32#5586semidirect
715. C32#5606semidirect
786. C22#89029semidirect
799. C3#10595130semidirect
800. C3#10596057semidirect

Maximal subgroups

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

subgroupindex
C2×#890292
C22×D3×C3⋊Dic32
D4×C3⋊(C3⋊Dic3)2
C3×#641482
C32×#9372
#117236412
#117236292
#117236262
#67⋊(C3⋊Dic3)2
#117236152
#117236142
#117235082
#117234912
#117234802
#117234602
#105960573
#105951303