Finite Group Databasebeta

← #13175863

Subgroups — #13175863

Order 1728.

2036 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89029C211yesmaximal, characteristic, complemented
2C2×D3×#634C211yesmaximal, characteristic, complemented
3#11723919C211yesmaximal, characteristic, complemented
4C3×#64094C211yesmaximal, characteristic, complemented
5C32×#884C211yesmaximal, characteristic, complemented
6#67⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
7#11723615C211yesmaximal, characteristic, complemented
8#11723600C211yesmaximal, characteristic, complemented
9#11723528C211yesmaximal, characteristic, complemented
10#11723506C211yesmaximal, characteristic, complemented
11D12×C3⋊Dic3C211yesmaximal, characteristic, complemented
12#11723487C211yesmaximal, characteristic, complemented
13#11723483C211yesmaximal, characteristic, complemented
14#11723474C211yesmaximal, characteristic, complemented
15#11723390C211yesmaximal, characteristic, complemented
16#10596069—31nomaximal
17#10594076—34nomaximal
18C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
19C2×#6308C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#634C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×C32×D12C2211yescharacteristic
25C2×C32×C4×D3C2211yescharacteristic
26C2×#6293C2211yescharacteristic
27C2×#6293C2211yescharacteristic
28C2×#6290C2211yescharacteristic
29C2×#6290C2211yescharacteristic
30C2×Dic3×C3⋊D3C2211yescharacteristic
31#89029—24no—
32C2×D3×C3⋊Dic3C2211yescharacteristic
33C2×D3×C3⋊Dic3C2211yescharacteristic
34C2×D3×C3⋊Dic3C2211yescharacteristic
35D3×#634—24no—
36C33×C22⋊C4C2211yescharacteristic
37#88864C2211yescharacteristic
38C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
39#88857C2211yescharacteristic
40#88857C2211yescharacteristic
41C3×#3757C2211yescharacteristic
42C3×#3752C2211yescharacteristic
43C3×#3752C2211yescharacteristic
44C3×C4×C3⋊Dic3C2211yescharacteristic
45C32×(C2×D3)⋊C4C2211yescharacteristic
46C32×Dic3⋊C4C2211yescharacteristic
47#88807C2211yescharacteristic
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic
49#88803C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
53Dic3×C3⋊Dic3C2211yescharacteristic
54Dic3×C3⋊Dic3C2211yescharacteristic
55C2×#3830—31no—
56C22×#634—31no—
57C2×#3805—34no—
58C2×D3×Dic6—34no—
59C32×#121—31no—
60#64148—31no—
61#64148—31no—
62#64145—31no—
63D4×C3⋊Dic3—31no—
64D4×C3⋊Dic3—31no—
65C4×#638—31no—
66#64106—31no—
67#64096—31no—
68#64094—31no—
69#64094D311yescharacteristic, complemented
70#64087—31no—
71#64087—31no—
72#64087—34no—
73#64087—64no—
74C3×#885—34no—
75C3×#884D314yescomplemented
76#67⋊Dic3—34no—
77#63970—34no—
78#63959—34no—
79#63913—34no—
80#63893—34no—
81Dic3×D12—34no—
82#63887—34no—
83#63885—34no—
84#63879—34no—
85#63837—34no—
86C23×C33C2311yescharacteristic
87C22×C3×C3⋊D3C2311yescharacteristic
88C22×C32×D3C2311yescharacteristic
89C22×C32×D3C2311yescharacteristic
90C2×C33×C4C2311yescharacteristic
91C2×C33×C4C2311yescharacteristic
92C2×C3⋊(C3⋊Dic3)—22no—
93C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97#6308—22no—
98C3×#638—22no—
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C3×#634—22no—
103C32×#67—22no—
104C32×#67—22no—
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C32×D12—22no—
108C32×C4×D3—22no—
109#6293—22no—
110#6293D414yescomplemented
111#6290—22no—
112#6290—22no—
113Dic3×C3⋊D3—22no—
114D3×C3⋊Dic3—22no—
115D3×C3⋊Dic3—22no—
116D3×C3⋊Dic3—22no—
117#5677—91no—
118#5598—94no—
119C2×C32×D4—31no—
120C2×C32×D4—31no—
121C2×C32×D4—31no—
122C22×C32×C4—31no—
123C2×#638—31no—
124C2×#638—31no—
125C2×#638C2×D311yescharacteristic
126C22×C3⋊Dic3—31no—
127C22×C3⋊Dic3—34no—
128C22×C3⋊Dic3—31no—
129C22×C3⋊Dic3—31no—
130C22×C3⋊Dic3—31no—
131C22×C3⋊Dic3—64no—
132#3830—64no—
133C2×C4×C3⋊D3—31no—
134C2×#634—31no—
135C2×#634—31no—
136C2×#634—34no—
137C2×#634—31no—
138C2×#634—64no—
139C2×#634—64no—
140C2×#634C2×D311yescharacteristic
141C2×C3×#67—34no—
142C2×C3×#67C2×D314yes—
143C2×C3×#67C2×D314yes—
144C2×C3×D12C2×D314yes—
145C2×C3×C4×D3C2×D314yes—
146C2×C3×Dic6—34no—
147C2×#627—34no—
148C2×#627—34no—
149C2×#625—34no—
150C2×#625—34no—
151#3805—616no—
152C2×D3×Dic3—34no—
153C2×D3×Dic3—34no—
154C2×D3×Dic3—34no—
155C2×D3×Dic3—34no—
156D3×Dic6—616no—
157C32×C4⋊C4—31no—
158C32×C22⋊C4—24no—
159C32×C22⋊C4—31no—
160C32×C22⋊C4C2×D314yes—
161C32×C22⋊C4C2×D311yescharacteristic
162#3757—31no—
163#3757—34no—
164#3757—31no—
165#3757—31no—
166#3757—31no—
167#3757—64no—
168#3757C2×D311yescharacteristic
169#3752—31no—
170#3752C2×D311yescharacteristic
171#3752C2×D311yescharacteristic
172C4⋊(C3⋊Dic3)—31no—
173C4⋊(C3⋊Dic3)—34no—
174C4⋊(C3⋊Dic3)—31no—
175C4⋊(C3⋊Dic3)—64no—
176#3750—31no—
177#3750—31no—
178#3750—34no—
179#3750—34no—
180#3750—31no—
181#3750—64no—
182#3750—64no—
183C4×C3⋊Dic3—31no—
184C4×C3⋊Dic3—31no—
185C4×C3⋊Dic3C2×D311yescharacteristic
186C3×#217—34no—
187C3×(C2×D3)⋊C4—34no—
188C3×(C2×D3)⋊C4—34no—
189C3×(C2×D3)⋊C4C2×D314yes—
190C3×Dic3⋊C4C2×D314yes—
191C3×C4×Dic3—34no—
192Dic3⋊Dic3—34no—
193Dic3⋊Dic3—34no—
194(C2×D3)⋊Dic3—34no—
195(C2×D3)⋊Dic3—34no—
196(C2×D3)⋊Dic3—34no—
197(C2×D3)⋊Dic3—34no—
198Dic32—34no—
199Dic32—34no—
200C22×C33—21no—
201C22×C33—21no—
202C22×C33—21no—
203C22×C33C2411yescharacteristic
204C2×C3×C3⋊D3—21no—
205C2×C3×C3⋊D3—21no—
206C2×C3×C3⋊D3—21no—
207C2×C32×D3—21no—
208C2×C32×D3—21no—
209C2×C32×D3—21no—
210C2×C32×D3—21no—
211C2×C32×D3—21no—
212C2×C32×D3#4112yescomplemented
213C33×C4—21no—
214C33×C4—21no—
215C3⋊(C3⋊Dic3)—21no—
216C3⋊(C3⋊Dic3)—21no—
217C3⋊(C3⋊Dic3)—21no—
218C3⋊(C3⋊Dic3)C2×D412yes—
219C3×C3⋊Dic3—21no—
220C3×C3⋊Dic3—21no—
221C3×C3⋊Dic3C2×D412yes—
222C32×Dic3—21no—
223C32×Dic3C2×D412yes—
224C2×D3×Q8—91no—
225C2×#237—94no—
226C2×#237—91no—
227C22×Dic6—94no—
228C3×#124—91no—
229C3×#121—34no—
230#946—91no—
231#939—94no—
232#939—94no—
233#938—91no—
234#936—94no—
235D4×Dic3—94no—
236D4×Dic3—94no—
237C4×#67—94no—
238#897—94no—
239#887—94no—
240#885—34no—
241#885—94no—
242#885—91no—
243#885—91no—
244#884—91no—
245#884C3⋊D311yescharacteristic, complemented
246#67⋊C4—91no—
247#67⋊C4—91no—
248#878—94no—
249#878—94no—
250#878—91no—
251#878—91no—
252#878—184no—
253C4×D12—91no—
254C4×Dic6—91no—
255C23×C32—24no—
256C23×C32—31no—
257C23×C32—31no—
258C23×C32C22×D314yes—
259C23×C32C22×D311yescharacteristic
260C22×C3⋊D3C22×D311yescharacteristic
261C22×C3×D3—34no—
262C22×C3×D3C22×D314yes—
263C22×C3×D3C22×D314yes—
264C32×D4—62no—
265C32×D4—62no—
266C32×D4—62no—
267C2×C32×C4—24no—
268C2×C32×C4—24no—
269C2×C32×C4—31no—
270C2×C32×C4—31no—
271C2×C32×C4—62no—
272C2×C32×C4C22×D314yes—
273C2×C32×C4C22×D314yes—
274C2×C32×C4C22×D311yescharacteristic
275C2×C32×C4C22×D311yescharacteristic
276#638—22no—
277#638—62no—
278#638—62no—
279C2×C3⋊Dic3—31no—
280C2×C3⋊Dic3—31no—
281C2×C3⋊Dic3—31no—
282C2×C3⋊Dic3—31no—
283C2×C3⋊Dic3—34no—
284C2×C3⋊Dic3—34no—
285C2×C3⋊Dic3—34no—
286C2×C3⋊Dic3—34no—
287C2×C3⋊Dic3—64no—
288C2×C3⋊Dic3—64no—
289C2×C3⋊Dic3—64no—
290C2×C3⋊Dic3—64no—
291C2×C3⋊Dic3—62no—
292C2×C3⋊Dic3—62no—
293C2×C3⋊Dic3—62no—
294C2×C3⋊Dic3—62no—
295C2×C3⋊Dic3—68no—
296C2×C3⋊Dic3—128no—
297C2×C3⋊Dic3C22×D311yescharacteristic
298C2×C3⋊Dic3C22×D311yescharacteristic
299C2×C3⋊Dic3C22×D311yescharacteristic
300C4×C3⋊D3—62no—
301#634—22no—
302#634—34no—
303#634—62no—
304#634—62no—
305#634—68no—
306#634—128no—
307C3×#67—28no—
308C3×#67—28no—
309C3×#67—68no—
310C2×C3×Dic3—34no—
311C2×C3×Dic3—34no—
312C2×C3×Dic3—34no—
313C2×C3×Dic3C22×D314yes—
314C2×C3×Dic3C22×D314yes—
315C3×D12—28no—
316C3×C4×D3—28no—
317C3×Dic6—68no—
318#627—316no—
319#627—68no—
320#625—68no—
321#625—68no—
322D3×Dic3—68no—
323D3×Dic3—68no—
324D3×Dic3—68no—
325D3×Dic3—68no—
326#548—271noSylow
327C2×C33—41no—
328C2×C33C22×D411yescharacteristic
329C2×C33C2×#4111yescharacteristic
330C2×C332−1+411yescharacteristic
331C3×C3⋊D3—41no—
332C32×D3—22no—
333C32×D3—41no—
334C2×C3×Q8—91no—
335C2×C3×D4—34no—
336C2×C3×D4—34no—
337C2×C3×D4—34no—
338C2×C3×D4—91no—
339C22×C3×C4—34no—
340C2×#67—34no—
341C2×#67—94no—
342C2×#67—94no—
343C2×#67—91no—
344C2×#67—91no—
345C2×#67C2×C3⋊D311yescharacteristic
346C2×#67C2×C3⋊D311yescharacteristic
347C22×Dic3—94no—
348C22×Dic3—94no—
349C22×Dic3—94no—
350C22×Dic3—94no—
351C22×Dic3—91no—
352C22×Dic3—91no—
353C22×Dic3—184no—
354D3×Q8—184no—
355#237—184no—
356#237—1816no—
357C2×D12C2×C3⋊D311yescharacteristic
358C2×C4×D3—94no—
359C2×C4×D3—91no—
360C2×C4×D3—91no—
361C2×C4×D3—91no—
362C2×C4×D3C2×C3⋊D311yescharacteristic
363C2×Dic6—34no—
364C2×Dic6—94no—
365C2×Dic6—91no—
366C2×Dic6—94no—
367C2×Dic6—94no—
368C2×Dic6—91no—
369C2×Dic6—91no—
370C2×Dic6—184no—
371C2×Dic6—1816no—
372C3×C4⋊C4—34no—
373C3×C22⋊C4—24no—
374C3×C22⋊C4—34no—
375C3×C22⋊C4—91no—
376C3×C22⋊C4—91no—
377C3×C22⋊C4—91no—
378C3×C22⋊C4D3214yes—
379C3×C22⋊C4C2×C3⋊D311yescharacteristic
380C3×C42—91no—
381#217—34no—
382#217—94no—
383#217—94no—
384#217—94no—
385#217—94no—
386#217—91no—
387#217—91no—
388#217—184no—
389(C2×D3)⋊C4—34no—
390(C2×D3)⋊C4—34no—
391(C2×D3)⋊C4—94no—
392(C2×D3)⋊C4—91no—
393(C2×D3)⋊C4—91no—
394(C2×D3)⋊C4—91no—
395(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
396C4⋊Dic3—94no—
397C4⋊Dic3—94no—
398C4⋊Dic3—91no—
399C4⋊Dic3—91no—
400C4⋊Dic3—184no—
401Dic3⋊C4—94no—
402Dic3⋊C4—94no—
403Dic3⋊C4—94no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406Dic3⋊C4—91no—
407Dic3⋊C4—184no—
408Dic3⋊C4—184no—
409Dic3⋊C4C2×C3⋊D311yescharacteristic
410C4×Dic3—34no—
411C4×Dic3—94no—
412C4×Dic3—94no—
413C4×Dic3—91no—
414C4×Dic3—91no—
415C22×C32—28no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—24no—
419C22×C32—21no—
420C22×C32—24no—
421C22×C32—24no—
422C22×C32—24no—
423C22×C32—32no—
424C22×C32—44no—
425C22×C32—44no—
426C22×C32—61no—
427C22×C32—61no—
428C22×C32—61no—
429C22×C32—61no—
430C22×C32—61no—
431C22×C32C23×D314yes—
432C22×C32C23×D311yescharacteristic
433C2×C3⋊D3—21no—
434C2×C3⋊D3—21no—
435C2×C3⋊D3—21no—
436C2×C3×D3—24no—
437C2×C3×D3—24no—
438C2×C3×D3—24no—
439C2×C3×D3—24no—
440C2×C3×D3—24no—
441C2×C3×D3—64no—
442C2×C3×D3—64no—
443C2×C3×D3—64no—
444C2×C3×D3#23718yescomplemented
445C32×C4—21no—
446C32×C4—21no—
447C32×C4—24no—
448C32×C4—24no—
449C32×C4—32no—
450C32×C4—44no—
451C32×C4—44no—
452C32×C4—61no—
453C3⋊Dic3—21no—
454C3⋊Dic3—21no—
455C3⋊Dic3—32no—
456C3⋊Dic3—38no—
457C3⋊Dic3—68no—
458C3⋊Dic3—61no—
459C3⋊Dic3—61no—
460C3⋊Dic3—61no—
461C3⋊Dic3—64no—
462C3⋊Dic3—64no—
463C3⋊Dic3—64no—
464C3⋊Dic3—124no—
465C3⋊Dic3—124no—
466C3⋊Dic3—124no—
467C3⋊Dic3D3×D412yes—
468C3×Dic3—24no—
469C3×Dic3—38no—
470C3×Dic3—64no—
471C3×Dic3—64no—
472C3×Dic3D3×D418yes—
473C2×#41—271no—
474C22×Q8—271no—
475#124—91no—
476#124—271no—
477#124—271no—
478C22⋊Q8—271no—
479C22⋊Q8—271no—
480C22⋊Q8—271no—
481#121—31no—
482#121—271no—
483#121—271no—
484C4×Q8—271no—
485C4×D4—271no—
486C4×D4—271no—
487C4×D4—271no—
488C33#54811yescharacteristic, complemented, Sylow
489C23×C3—24no—
490C23×C3—34no—
491C23×C3—34no—
492C23×C3—91no—
493C23×C3C2×D3214yes—
494C23×C3C22×C3⋊D311yescharacteristic
495C22×D3—34no—
496C22×D3C22×C3⋊D311yescharacteristic
497C22×D3C22×C3⋊D311yescharacteristic
498C3×Q8—182no—
499C3×D4—68no—
500C3×D4—68no—
501C3×D4—68no—
502C3×D4—182no—
503C2×C3×C4—24no—
504C2×C3×C4—24no—
505C2×C3×C4—34no—
506C2×C3×C4—34no—
507C2×C3×C4—68no—
508C2×C3×C4—91no—
509C2×C3×C4—91no—
510C2×C3×C4—91no—
511C2×C3×C4C2×D3214yes—
512C2×C3×C4C2×D3214yes—
513C2×C3×C4C22×C3⋊D311yescharacteristic
514C2×C3×C4C22×C3⋊D311yescharacteristic
515#67—22no—
516#67—22no—
517#67—68no—
518#67—182no—
519#67—188no—
520#67—188no—
521#67—182no—
522C2×Dic3—34no—
523C2×Dic3—34no—
524C2×Dic3—34no—
525C2×Dic3—94no—
526C2×Dic3—91no—
527C2×Dic3—94no—
528C2×Dic3—94no—
529C2×Dic3—94no—
530C2×Dic3—91no—
531C2×Dic3—91no—
532C2×Dic3—91no—
533C2×Dic3—184no—
534C2×Dic3—184no—
535C2×Dic3—184no—
536C2×Dic3—184no—
537C2×Dic3—188no—
538C2×Dic3—188no—
539C2×Dic3—188no—
540C2×Dic3—182no—
541C2×Dic3—188no—
542C2×Dic3—182no—
543C2×Dic3—368no—
544C2×Dic3C22×C3⋊D311yescharacteristic
545C2×Dic3C22×C3⋊D311yescharacteristic
546D12—22no—
547C4×D3—22no—
548C4×D3—182no—
549C4×D3—188no—
550C4×D3—182no—
551C4×D3—182no—
552Dic6—68no—
553Dic6—916no—
554Dic6—94no—
555Dic6—188no—
556Dic6—182no—
557Dic6—188no—
558Dic6—182no—
559Dic6—368no—
560C2×C32—24no—
561C2×C32—24no—
562C2×C32—24no—
563C2×C32—48no—
564C2×C32—41no—
565C2×C32—44no—
566C2×C32—62no—
567C2×C32—121no—
568C2×C32C2×D3×D414yes—
569C2×C32C2×D3×D411yescharacteristic
570C2×C32C2×#23714yes—
571C2×C32D3×#4111yescharacteristic
572C2×C32#101014yes—
573C2×C32#101011yescharacteristic
574C3⋊D3—41no—
575C3×D3—28no—
576C3×D3—44no—
577C3×D3—124no—
578#41—544no—
579C2×Q8—91no—
580C2×Q8—271no—
581C2×Q8—271no—
582C2×Q8—271no—
583C2×Q8—544no—
584C2×D4—31no—
585C2×D4—31no—
586C2×D4—31no—
587C2×D4—91no—
588C2×D4—271no—
589C2×D4—271no—
590C22×C4—31no—
591C22×C4—271no—
592C22×C4—271no—
593C22×C4—271no—
594C22×C4—271no—
595C22×C4—271no—
596C4⋊C4—31no—
597C4⋊C4—271no—
598C4⋊C4—271no—
599C4⋊C4—271no—
600C4⋊C4—271no—
601C4⋊C4—271no—
602C22⋊C4—31no—
603C22⋊C4—91no—
604C22⋊C4—91no—
605C22⋊C4—91no—
606C22⋊C4—271no—
607C22⋊C4—271no—
608C22⋊C4—271no—
609C22⋊C4—271no—
610C22⋊C4—271no—
611C22⋊C4D3×C3⋊D311yescharacteristic
612C42—91no—
613C42—271no—
614C42—271no—
615C22×C3—28no—
616C22×C3—24no—
617C22×C3—24no—
618C22×C3—24no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—24no—
623C22×C3—38no—
624C22×C3—44no—
625C22×C3—44no—
626C22×C3—64no—
627C22×C3—64no—
628C22×C3—64no—
629C22×C3—64no—
630C22×C3—64no—
631C22×C3—181no—
632C22×C3—181no—
633C22×C3—181no—
634C22×C3C22×D3214yes—
635C22×C3C23×C3⋊D311yescharacteristic
636C2×D3—21no—
637C2×D3—21no—
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—64no—
642C2×D3—64no—
643C2×D3—64no—
644C2×D3#383012yescomplemented
645C3×C4—24no—
646C3×C4—24no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—38no—
650C3×C4—44no—
651C3×C4—44no—
652C3×C4—64no—
653C3×C4—92no—
654C3×C4—181no—
655C3×C4—181no—
656Dic3—21no—
657Dic3—38no—
658Dic3—64no—
659Dic3—64no—
660Dic3—98no—
661Dic3—92no—
662Dic3—188no—
663Dic3—184no—
664Dic3—184no—
665Dic3—184no—
666Dic3—181no—
667Dic3—181no—
668Dic3—181no—
669Dic3—364no—
670Dic3—364no—
671Dic3—364no—
672Dic3D4×C3⋊D312yes—
673C32—24no—
674C32#559814yescomplemented
675C32#567711yescharacteristic, complemented
676C23—31no—
677C23—31no—
678C23—91no—
679C23C2×D3×C3⋊D311yescharacteristic
680Q8—182no—
681Q8—274no—
682Q8—542no—
683Q8—542no—
684D4—62no—
685D4—62no—
686D4—62no—
687D4—182no—
688D4—542no—
689D4—542no—
690C2×C4—31no—
691C2×C4—31no—
692C2×C4—62no—
693C2×C4—91no—
694C2×C4—91no—
695C2×C4—91no—
696C2×C4—271no—
697C2×C4—271no—
698C2×C4—271no—
699C2×C4—271no—
700C2×C4—542no—
701C2×C4—542no—
702C2×C4—542no—
703C2×C4—542no—
704C2×C4—542no—
705C2×C4C2×D3×C3⋊D311yescharacteristic
706C2×C4C2×D3×C3⋊D311yescharacteristic
707C2×C3—24no—
708C2×C3—24no—
709C2×C3—24no—
710C2×C3—48no—
711C2×C3—44no—
712C2×C3—41no—
713C2×C3—68no—
714C2×C3—124no—
715C2×C3—361no—
716C2×C3#6429814yes—
717C2×C3D32×D414yes—
718C2×C3D3×#23714yes—
719C2×C3C2×D4×C3⋊D311yescharacteristic
720C2×C3C2×#383011yescharacteristic
721C2×C3#6436711yescharacteristic
722D3—22no—
723D3—41no—
724D3—124no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—32no—
729C22—61no—
730C22—61no—
731C22—61no—
732C22—61no—
733C22—61no—
734C22—181no—
735C22—181no—
736C22—181no—
737C22C22×D3×C3⋊D311yescharacteristic
738C4—21no—
739C4—21no—
740C4—32no—
741C4—61no—
742C4—92no—
743C4—181no—
744C4—181no—
745C4—272no—
746C4—541no—
747C4—541no—
748C4—541no—
749C3—24no—
750C3#1059407614yescomplemented
751C3#1059606911yescharacteristic, complemented
752C2—41no—
753C2—62no—
754C2—121no—
755C2—361no—
756C2#1172456311yescharacteristic
757C2D3×D4×C3⋊D311yescharacteristic
758C2D3×#383011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33#548
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#89029C2semidirect
2. C2×D3×#634C2semidirect
3. #11723919C2semidirect
4. C3×#64094C2semidirect
5. C32×#884C2semidirect
6. #67⋊(C3⋊Dic3)C2semidirect
7. #11723615C2semidirect
8. #11723600C2semidirect
9. #11723528C2semidirect
10. #11723506C2semidirect
11. D12×C3⋊Dic3C2semidirect
12. #11723487C2semidirect
13. #11723483C2semidirect
14. #11723474C2semidirect
15. #11723390C2semidirect
69. #64094D3semidirect
75. C3×#884D3semidirect
110. #6293D4semidirect
212. C2×C32×D3#41semidirect
245. #884C3⋊D3semidirect
444. C2×C3×D3#237semidirect
488. C33#548semidirect
644. C2×D3#3830semidirect
674. C32#5598semidirect
675. C32#5677semidirect
750. C3#10594076semidirect
751. C3#10596069semidirect

Maximal subgroups

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

subgroupindex
C2×#890292
C2×D3×#6342
#117239192
C3×#640942
C32×#8842
#67⋊(C3⋊Dic3)2
#117236152
#117236002
#117235282
#117235062
D12×C3⋊Dic32
#117234872
#117234832
#117234742
#117233902
#105960693
#105940763