Finite Group Databasebeta

← #13177648

Subgroups — #13177648

Order 1728.

2116 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6293C211yesmaximal, characteristic, complemented
2C2×#89029C211yesmaximal, characteristic, complemented
3D4×C3⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
4C3×#64148C211yesmaximal, characteristic, complemented
5C32×#939C211yesmaximal, characteristic, complemented
6#11723642C211yesmaximal, characteristic, complemented
7#11723637C211yesmaximal, characteristic, complemented
8#67×C3⋊Dic3C211yesmaximal, characteristic, complemented
9Dic3×#638C211yesmaximal, characteristic, complemented
10#11723600C211yesmaximal, characteristic, complemented
11#11723591C211yesmaximal, characteristic, complemented
12#11723530C211yesmaximal, characteristic, complemented
13#11723491C211yesmaximal, characteristic, complemented
14#11723483C211yesmaximal, characteristic, complemented
15#11723391C211yesmaximal, characteristic, complemented
16#10596069—31nomaximal
17#10595142—34nomaximal
18C2×C33×D4C2211yescharacteristic
19C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
20C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C22×C3×C3⋊Dic3C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic
26C22×C32×Dic3C2211yescharacteristic
27C2×#6293—24no—
28C2×#6293C2211yescharacteristic
29C2×#6293C2211yescharacteristic
30C2×#6293C2211yescharacteristic
31C2×#6293C2211yescharacteristic
32C2×#6290C2211yescharacteristic
33C2×Dic3×C3⋊D3C2211yescharacteristic
34#89029—24no—
35C2×D3×C3⋊Dic3C2211yescharacteristic
36#88864C2211yescharacteristic
37#88864C2211yescharacteristic
38C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
39C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
40C3×#3757C2211yescharacteristic
41C3×#3752C2211yescharacteristic
42C3×#3750C2211yescharacteristic
43C32×#217C2211yescharacteristic
44C32×(C2×D3)⋊C4C2211yescharacteristic
45C32×Dic3⋊C4C2211yescharacteristic
46#88807C2211yescharacteristic
47#88806C2211yescharacteristic
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic
49#88803C2211yescharacteristic
50#88803C2211yescharacteristic
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
53Dic3×C3⋊Dic3C2211yescharacteristic
54Dic3×C3⋊Dic3C2211yescharacteristic
55C2×#3830—31no—
56C22×#634—31no—
57C22×#627—34no—
58C2×#3805—34no—
59C32×#121—31no—
60#64148—31no—
61#64148D311yescharacteristic, complemented
62#64145—31no—
63D4×C3⋊Dic3—31no—
64D4×C3⋊Dic3—31no—
65D4×C3⋊Dic3—34no—
66D4×C3⋊Dic3—64no—
67C4×#638—31no—
68#64106—31no—
69#64096—31no—
70#64094—31no—
71#64094—31no—
72#64087—31no—
73#64087—31no—
74C3×#939—34no—
75C3×#939D314yescomplemented
76#63982—34no—
77#63980—34no—
78Dic3×#67—34no—
79Dic3×#67—34no—
80#63959—34no—
81#63959—34no—
82#63915—34no—
83#63893—34no—
84#63893—34no—
85#63838—34no—
86C23×C33C2311yescharacteristic
87C23×C33C2311yescharacteristic
88C22×C3×C3⋊D3C2311yescharacteristic
89C22×C32×D3C2311yescharacteristic
90C33×D4—22no—
91C2×C33×C4C2311yescharacteristic
92C2×C3⋊(C3⋊Dic3)—22no—
93C2×C3⋊(C3⋊Dic3)—22no—
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C3×#638—22no—
99C3×#638—22no—
100C2×C3×C3⋊Dic3—22no—
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C2×C3×C3⋊Dic3C2311yescharacteristic
104C32×#67—22no—
105C32×#67—22no—
106C2×C32×Dic3—22no—
107C2×C32×Dic3C2311yescharacteristic
108C2×C32×Dic3C2311yescharacteristic
109C2×C32×Dic3C2311yescharacteristic
110#6293—22no—
111#6293—22no—
112#6293—22no—
113#6293D414yescomplemented
114#6290—22no—
115Dic3×C3⋊D3—22no—
116D3×C3⋊Dic3—22no—
117#5598—94no—
118#5598—91no—
119C2×C32×D4—24no—
120C2×C32×D4—31no—
121C2×C32×D4—31no—
122C2×C32×D4C2×D314yes—
123C2×C32×D4C2×D311yescharacteristic
124C22×C32×C4—31no—
125C2×#638—31no—
126C2×#638C2×D311yescharacteristic
127C2×#638C2×D311yescharacteristic
128C22×C3⋊Dic3—31no—
129C22×C3⋊Dic3—31no—
130C22×C3⋊Dic3—34no—
131C22×C3⋊Dic3—34no—
132C22×C3⋊Dic3—31no—
133C22×C3⋊Dic3—64no—
134C22×C3⋊Dic3—64no—
135C22×C3⋊Dic3C2×D311yescharacteristic
136#3830—64no—
137C2×C4×C3⋊D3—31no—
138C2×#634—31no—
139C2×#634—31no—
140C2×#634—31no—
141C2×#634—31no—
142C2×#634—64no—
143C2×C3×#67—34no—
144C2×C3×#67—34no—
145C2×C3×#67C2×D314yes—
146C2×C3×#67C2×D314yes—
147C22×C3×Dic3—34no—
148C22×C3×Dic3C2×D314yes—
149C2×#627—34no—
150C2×#627—34no—
151C2×#627—34no—
152C2×#627—34no—
153C2×#627—616no—
154C2×#625—34no—
155#3805—616no—
156C2×D3×Dic3—34no—
157C2×D3×Dic3—34no—
158C32×C4⋊C4—31no—
159C32×C22⋊C4—31no—
160C32×C22⋊C4—31no—
161#3757—31no—
162#3757—31no—
163#3757—34no—
164#3757—34no—
165#3757—31no—
166#3757—31no—
167#3757—64no—
168#3757—64no—
169#3757C2×D311yescharacteristic
170#3752—31no—
171#3752—31no—
172#3752C2×D311yescharacteristic
173C4⋊(C3⋊Dic3)—31no—
174C4⋊(C3⋊Dic3)—34no—
175C4⋊(C3⋊Dic3)—31no—
176C4⋊(C3⋊Dic3)—64no—
177#3750—31no—
178#3750—31no—
179#3750C2×D311yescharacteristic
180C4×C3⋊Dic3—31no—
181C4×C3⋊Dic3—34no—
182C4×C3⋊Dic3—31no—
183C4×C3⋊Dic3—31no—
184C4×C3⋊Dic3—64no—
185C3×#217—34no—
186C3×#217C2×D314yes—
187C3×(C2×D3)⋊C4—34no—
188C3×(C2×D3)⋊C4C2×D314yes—
189C3×Dic3⋊C4—34no—
190C3×Dic3⋊C4C2×D314yes—
191#3724—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×C33—21no—
204C22×C33—21no—
205C22×C33#4112yescomplemented
206C22×C33C2411yescharacteristic
207C2×C3×C3⋊D3—21no—
208C2×C3×C3⋊D3—21no—
209C2×C3×C3⋊D3—21no—
210C2×C32×D3—21no—
211C2×C32×D3—21no—
212C2×C32×D3—21no—
213C33×C4—21no—
214C3⋊(C3⋊Dic3)—21no—
215C3⋊(C3⋊Dic3)—21no—
216C3⋊(C3⋊Dic3)—21no—
217C3⋊(C3⋊Dic3)C2×D412yes—
218C3×C3⋊Dic3—21no—
219C3×C3⋊Dic3—21no—
220C3×C3⋊Dic3C2×D412yes—
221C32×Dic3—21no—
222C32×Dic3—21no—
223C32×Dic3C2×D412yes—
224C2×#237—94no—
225C2×#237—91no—
226C22×Dic6—94no—
227C22×Dic6—91no—
228C3×#121—34no—
229C3×#121—91no—
230#939—34no—
231#939—94no—
232#939—91no—
233#939C3⋊D311yescharacteristic, complemented
234#936—94no—
235#936—91no—
236D4×Dic3—94no—
237D4×Dic3—94no—
238D4×Dic3—91no—
239D4×Dic3—91no—
240D4×Dic3—184no—
241C4×#67—94no—
242C4×#67—91no—
243#897—94no—
244#897—91no—
245#887—94no—
246#887—91no—
247#885—94no—
248#885—94no—
249#885—91no—
250#885—91no—
251#878—94no—
252#878—94no—
253#878—91no—
254#878—91no—
255C23×C32—24no—
256C23×C32—24no—
257C23×C32—31no—
258C23×C32C22×D314yes—
259C23×C32C22×D314yes—
260C23×C32C22×D311yescharacteristic
261C23×C32C22×D311yescharacteristic
262C22×C3⋊D3C22×D311yescharacteristic
263C22×C3×D3—34no—
264C22×C3×D3C22×D314yes—
265C32×D4—216no—
266C32×D4—28no—
267C32×D4—22no—
268C32×D4—62no—
269C32×D4—62no—
270C2×C32×C4—24no—
271C2×C32×C4—31no—
272C2×C32×C4—31no—
273C2×C32×C4—31no—
274C2×C32×C4—62no—
275C2×C32×C4C22×D314yes—
276C2×C32×C4C22×D311yescharacteristic
277#638—22no—
278#638—22no—
279#638—62no—
280C2×C3⋊Dic3—22no—
281C2×C3⋊Dic3—31no—
282C2×C3⋊Dic3—31no—
283C2×C3⋊Dic3—31no—
284C2×C3⋊Dic3—31no—
285C2×C3⋊Dic3—34no—
286C2×C3⋊Dic3—34no—
287C2×C3⋊Dic3—34no—
288C2×C3⋊Dic3—34no—
289C2×C3⋊Dic3—64no—
290C2×C3⋊Dic3—64no—
291C2×C3⋊Dic3—64no—
292C2×C3⋊Dic3—64no—
293C2×C3⋊Dic3—62no—
294C2×C3⋊Dic3—62no—
295C2×C3⋊Dic3—62no—
296C2×C3⋊Dic3—68no—
297C2×C3⋊Dic3—68no—
298C2×C3⋊Dic3—128no—
299C2×C3⋊Dic3—128no—
300C2×C3⋊Dic3C22×D311yescharacteristic
301C2×C3⋊Dic3C22×D311yescharacteristic
302C2×C3⋊Dic3C22×D311yescharacteristic
303C4×C3⋊D3—62no—
304#634—34no—
305#634—62no—
306#634—62no—
307#634—62no—
308C3×#67—28no—
309C3×#67—28no—
310C3×#67—68no—
311C3×#67—68no—
312C2×C3×Dic3—28no—
313C2×C3×Dic3—34no—
314C2×C3×Dic3—34no—
315C2×C3×Dic3—34no—
316C2×C3×Dic3—68no—
317C2×C3×Dic3C22×D314yes—
318C2×C3×Dic3C22×D314yes—
319C2×C3×Dic3C22×D314yes—
320#627—316no—
321#627—68no—
322#627—68no—
323#627—68no—
324#625—68no—
325D3×Dic3—68no—
326D3×Dic3—68no—
327#548—271noSylow
328C2×C33—22no—
329C2×C33—41no—
330C2×C33C22×D411yescharacteristic
331C2×C33C2×#4111yescharacteristic
332C2×C332−1+411yescharacteristic
333C3×C3⋊D3—41no—
334C32×D3—41no—
335C2×C3×D4—24no—
336C2×C3×D4—34no—
337C2×C3×D4—34no—
338C2×C3×D4—91no—
339C2×C3×D4—91no—
340C2×C3×D4D3214yes—
341C2×C3×D4C2×C3⋊D311yescharacteristic
342C22×C3×C4—34no—
343C22×C3×C4—91no—
344C2×#67—34no—
345C2×#67—34no—
346C2×#67—94no—
347C2×#67—91no—
348C2×#67C2×C3⋊D311yescharacteristic
349C2×#67C2×C3⋊D311yescharacteristic
350C22×Dic3—34no—
351C22×Dic3—94no—
352C22×Dic3—94no—
353C22×Dic3—94no—
354C22×Dic3—91no—
355C22×Dic3—91no—
356C22×Dic3—91no—
357C22×Dic3—184no—
358C22×Dic3—184no—
359C22×Dic3C2×C3⋊D311yescharacteristic
360#237—184no—
361#237—1816no—
362C2×C4×D3—94no—
363C2×C4×D3—91no—
364C2×Dic6—94no—
365C2×Dic6—91no—
366C2×Dic6—94no—
367C2×Dic6—94no—
368C2×Dic6—94no—
369C2×Dic6—91no—
370C2×Dic6—91no—
371C2×Dic6—91no—
372C2×Dic6—184no—
373C2×Dic6—1816no—
374C3×C4⋊C4—34no—
375C3×C4⋊C4—91no—
376C3×C22⋊C4—34no—
377C3×C22⋊C4—34no—
378C3×C22⋊C4—91no—
379C3×C22⋊C4—91no—
380#217—34no—
381#217—94no—
382#217—94no—
383#217—94no—
384#217—94no—
385#217—91no—
386#217—91no—
387#217—91no—
388#217—91no—
389#217—184no—
390#217—184no—
391#217C2×C3⋊D311yescharacteristic
392(C2×D3)⋊C4—34no—
393(C2×D3)⋊C4—94no—
394(C2×D3)⋊C4—94no—
395(C2×D3)⋊C4—91no—
396(C2×D3)⋊C4—91no—
397(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
398C4⋊Dic3—94no—
399C4⋊Dic3—94no—
400C4⋊Dic3—91no—
401C4⋊Dic3—91no—
402C4⋊Dic3—184no—
403Dic3⋊C4—34no—
404Dic3⋊C4—94no—
405Dic3⋊C4—94no—
406Dic3⋊C4—91no—
407Dic3⋊C4—91no—
408Dic3⋊C4C2×C3⋊D311yescharacteristic
409C4×Dic3—94no—
410C4×Dic3—94no—
411C4×Dic3—94no—
412C4×Dic3—91no—
413C4×Dic3—91no—
414C4×Dic3—91no—
415C4×Dic3—184no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—28no—
419C22×C32—21no—
420C22×C32—24no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32—24no—
424C22×C32—28no—
425C22×C32—24no—
426C22×C32—24no—
427C22×C32—24no—
428C22×C32—24no—
429C22×C32—44no—
430C22×C32—44no—
431C22×C32—44no—
432C22×C32—44no—
433C22×C32—61no—
434C22×C32—61no—
435C22×C32—61no—
436C22×C32#23718yescomplemented
437C22×C32#23712yescomplemented
438C22×C32C23×D314yes—
439C22×C32C23×D311yescharacteristic
440C2×C3⋊D3—21no—
441C2×C3⋊D3—21no—
442C2×C3⋊D3—21no—
443C2×C3×D3—24no—
444C2×C3×D3—24no—
445C2×C3×D3—24no—
446C2×C3×D3—64no—
447C2×C3×D3—64no—
448C2×C3×D3—64no—
449C32×C4—28no—
450C32×C4—24no—
451C32×C4—21no—
452C32×C4—32no—
453C32×C4—61no—
454C32×C4—61no—
455C3⋊Dic3—21no—
456C3⋊Dic3—21no—
457C3⋊Dic3—32no—
458C3⋊Dic3—38no—
459C3⋊Dic3—68no—
460C3⋊Dic3—61no—
461C3⋊Dic3—61no—
462C3⋊Dic3—61no—
463C3⋊Dic3—64no—
464C3⋊Dic3—64no—
465C3⋊Dic3—64no—
466C3⋊Dic3—124no—
467C3⋊Dic3—124no—
468C3⋊Dic3—124no—
469C3⋊Dic3D3×D412yes—
470C3×Dic3—24no—
471C3×Dic3—24no—
472C3×Dic3—38no—
473C3×Dic3—64no—
474C3×Dic3—64no—
475C3×Dic3D3×D418yes—
476C2×#41—271no—
477C22×Q8—271no—
478#124—271no—
479#124—271no—
480#124—271no—
481C22⋊Q8—271no—
482C22⋊Q8—271no—
483C22⋊Q8—271no—
484#121—31no—
485#121—91no—
486#121—271no—
487C4×Q8—271no—
488C4×D4—271no—
489C4×D4—271no—
490C4×D4—271no—
491C33#54811yescharacteristic, complemented, Sylow
492C23×C3—24no—
493C23×C3—24no—
494C23×C3—34no—
495C23×C3—91no—
496C23×C3C2×D3214yes—
497C23×C3C2×D3214yes—
498C23×C3C22×C3⋊D311yescharacteristic
499C23×C3C22×C3⋊D311yescharacteristic
500C22×D3—34no—
501C22×D3C22×C3⋊D311yescharacteristic
502C3×D4—216no—
503C3×D4—28no—
504C3×D4—22no—
505C3×D4—68no—
506C3×D4—68no—
507C3×D4—182no—
508C3×D4—182no—
509C2×C3×C4—24no—
510C2×C3×C4—34no—
511C2×C3×C4—34no—
512C2×C3×C4—34no—
513C2×C3×C4—68no—
514C2×C3×C4—91no—
515C2×C3×C4—91no—
516C2×C3×C4—91no—
517C2×C3×C4—182no—
518C2×C3×C4C2×D3214yes—
519C2×C3×C4C22×C3⋊D311yescharacteristic
520#67—22no—
521#67—22no—
522#67—68no—
523#67—68no—
524#67—182no—
525#67—188no—
526C2×Dic3—22no—
527C2×Dic3—34no—
528C2×Dic3—34no—
529C2×Dic3—34no—
530C2×Dic3—68no—
531C2×Dic3—94no—
532C2×Dic3—91no—
533C2×Dic3—94no—
534C2×Dic3—94no—
535C2×Dic3—94no—
536C2×Dic3—91no—
537C2×Dic3—91no—
538C2×Dic3—91no—
539C2×Dic3—184no—
540C2×Dic3—184no—
541C2×Dic3—184no—
542C2×Dic3—184no—
543C2×Dic3—188no—
544C2×Dic3—182no—
545C2×Dic3—182no—
546C2×Dic3—188no—
547C2×Dic3—188no—
548C2×Dic3—182no—
549C2×Dic3—368no—
550C2×Dic3—368no—
551C2×Dic3C22×C3⋊D311yescharacteristic
552C2×Dic3C22×C3⋊D311yescharacteristic
553C2×Dic3C22×C3⋊D311yescharacteristic
554C4×D3—188no—
555C4×D3—182no—
556Dic6—916no—
557Dic6—94no—
558Dic6—182no—
559Dic6—182no—
560Dic6—188no—
561Dic6—188no—
562Dic6—188no—
563Dic6—182no—
564C2×C32—22no—
565C2×C32—24no—
566C2×C32—24no—
567C2×C32—24no—
568C2×C32—28no—
569C2×C32—48no—
570C2×C32—48no—
571C2×C32—44no—
572C2×C32—41no—
573C2×C32—121no—
574C2×C32C2×D3×D414yes—
575C2×C32C2×D3×D411yescharacteristic
576C2×C32C2×#23714yes—
577C2×C32C2×#23711yescharacteristic
578C2×C32#101014yes—
579C2×C32#101011yescharacteristic
580C3⋊D3—41no—
581C3×D3—44no—
582C3×D3—124no—
583#41—544no—
584C2×Q8—271no—
585C2×Q8—271no—
586C2×Q8—271no—
587C2×Q8—271no—
588C2×Q8—544no—
589C2×D4—31no—
590C2×D4—31no—
591C2×D4—91no—
592C2×D4—91no—
593C2×D4—271no—
594C2×D4D3×C3⋊D311yescharacteristic
595C22×C4—31no—
596C22×C4—91no—
597C22×C4—271no—
598C22×C4—271no—
599C22×C4—271no—
600C22×C4—271no—
601C4⋊C4—31no—
602C4⋊C4—91no—
603C4⋊C4—271no—
604C4⋊C4—271no—
605C4⋊C4—271no—
606C4⋊C4—271no—
607C22⋊C4—31no—
608C22⋊C4—31no—
609C22⋊C4—91no—
610C22⋊C4—91no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C22⋊C4—271no—
614C22⋊C4—271no—
615C22⋊C4—271no—
616C22⋊C4—271no—
617C42—271no—
618C42—271no—
619C42—271no—
620C22×C3—24no—
621C22×C3—24no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—28no—
625C22×C3—24no—
626C22×C3—24no—
627C22×C3—24no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—24no—
632C22×C3—28no—
633C22×C3—44no—
634C22×C3—44no—
635C22×C3—44no—
636C22×C3—44no—
637C22×C3—64no—
638C22×C3—64no—
639C22×C3—64no—
640C22×C3—181no—
641C22×C3—181no—
642C22×C3—181no—
643C22×C3#380518yescomplemented
644C22×C3#383012yescomplemented
645C22×C3C22×D3214yes—
646C22×C3C23×C3⋊D311yescharacteristic
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—64no—
651C2×D3—64no—
652C2×D3—64no—
653C3×C4—28no—
654C3×C4—24no—
655C3×C4—21no—
656C3×C4—38no—
657C3×C4—64no—
658C3×C4—64no—
659C3×C4—92no—
660C3×C4—181no—
661C3×C4—181no—
662Dic3—21no—
663Dic3—21no—
664Dic3—38no—
665Dic3—64no—
666Dic3—64no—
667Dic3—98no—
668Dic3—92no—
669Dic3—188no—
670Dic3—184no—
671Dic3—184no—
672Dic3—184no—
673Dic3—181no—
674Dic3—181no—
675Dic3—181no—
676Dic3—364no—
677Dic3—364no—
678Dic3—364no—
679Dic3D4×C3⋊D312yes—
680C32—24no—
681C32#559814yescomplemented
682C32#559811yescharacteristic, complemented
683C23—31no—
684C23—91no—
685C23C2×D3×C3⋊D311yescharacteristic
686C23C2×D3×C3⋊D311yescharacteristic
687Q8—274no—
688Q8—542no—
689Q8—542no—
690Q8—542no—
691D4—22no—
692D4—62no—
693D4—62no—
694D4—182no—
695D4—182no—
696D4—542no—
697C2×C4—31no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—62no—
701C2×C4—91no—
702C2×C4—91no—
703C2×C4—91no—
704C2×C4—182no—
705C2×C4—271no—
706C2×C4—271no—
707C2×C4—271no—
708C2×C4—271no—
709C2×C4—542no—
710C2×C4—542no—
711C2×C4—542no—
712C2×C4—542no—
713C2×C4C2×D3×C3⋊D311yescharacteristic
714C2×C3—28no—
715C2×C3—22no—
716C2×C3—24no—
717C2×C3—24no—
718C2×C3—24no—
719C2×C3—48no—
720C2×C3—48no—
721C2×C3—44no—
722C2×C3—41no—
723C2×C3—124no—
724C2×C3—361no—
725C2×C3#6430914yes—
726C2×C3D32×D414yes—
727C2×C3C2×#380514yes—
728C2×C3C2×D4×C3⋊D311yescharacteristic
729C2×C3C2×#383011yescharacteristic
730C2×C3#6436711yescharacteristic
731D3—41no—
732D3—124no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—61no—
739C22—61no—
740C22—61no—
741C22—181no—
742C22—181no—
743C22—181no—
744C22#8902912yescomplemented
745C22C22×D3×C3⋊D311yescharacteristic
746C4—21no—
747C4—32no—
748C4—61no—
749C4—61no—
750C4—92no—
751C4—181no—
752C4—181no—
753C4—272no—
754C4—541no—
755C4—541no—
756C4—541no—
757C3—24no—
758C3#1059514214yescomplemented
759C3#1059606911yescharacteristic, complemented
760C2—22no—
761C2—41no—
762C2—121no—
763C2—361no—
764C2#1172458211yescharacteristic
765C2D3×D4×C3⋊D311yescharacteristic
766C2C2×#8902911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33#548
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C22×#6293C2semidirect
2. C2×#89029C2semidirect
3. D4×C3⋊(C3⋊Dic3)C2semidirect
4. C3×#64148C2semidirect
5. C32×#939C2semidirect
6. #11723642C2semidirect
7. #11723637C2semidirect
8. #67×C3⋊Dic3C2semidirect
9. Dic3×#638C2semidirect
10. #11723600C2semidirect
11. #11723591C2semidirect
12. #11723530C2semidirect
13. #11723491C2semidirect
14. #11723483C2semidirect
15. #11723391C2semidirect
61. #64148D3semidirect
75. C3×#939D3semidirect
113. #6293D4semidirect
205. C22×C33#41semidirect
233. #939C3⋊D3semidirect
436. C22×C32#237semidirect
437. C22×C32#237semidirect
491. C33#548semidirect
643. C22×C3#3805semidirect
644. C22×C3#3830semidirect
681. C32#5598semidirect
682. C32#5598semidirect
744. C22#89029semidirect
758. C3#10595142semidirect
759. C3#10596069semidirect

Maximal subgroups

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

subgroupindex
C22×#62932
C2×#890292
D4×C3⋊(C3⋊Dic3)2
C3×#641482
C32×#9392
#117236422
#117236372
#67×C3⋊Dic32
Dic3×#6382
#117236002
#117235912
#117235302
#117234912
#117234832
#117233912
#105960693
#105951423