Finite Group Databasebeta

← #13177639

Subgroups — #13177639

Order 1728.

1876 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C3⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
2C3×#64148C211yesmaximal, characteristic, complemented
3C32×#937C211yesmaximal, characteristic, complemented
4#11723641C211yesmaximal, characteristic, complemented
5#11723637C211yesmaximal, characteristic, complemented
6#11723631C211yesmaximal, characteristic, complemented
7#11723629C211yesmaximal, characteristic, complemented
8#11723626C211yesmaximal, characteristic, complemented
9#11723603C211yesmaximal, characteristic, complemented
10C2×(C2×D3)⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
11#11723600C211yesmaximal, characteristic, complemented
12#11723530C211yesmaximal, characteristic, complemented
13#11723523C211yesmaximal, characteristic, complemented
14#11723432C211yesmaximal, characteristic, complemented
15#11723430C211yesmaximal, characteristic, complemented
16#10596064—31nomaximal
17#10595267—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#88864C2211yescharacteristic
32#88864C2211yescharacteristic, complemented
33C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
34C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
35C3×#3757C2211yescharacteristic, complemented
36C3×#3752C2211yescharacteristic, complemented
37C3×#3750C2211yescharacteristic, complemented
38C32×#217C2211yescharacteristic
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×(C2×D3)⋊C4C2211yescharacteristic
41#88807C2211yescharacteristic, complemented
42#88807C2211yescharacteristic, complemented
43#88806C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45#88803C2211yescharacteristic, complemented
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
47(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
48(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×#120—31no—
54#64162—31no—
55C2×#3757—31no—
56#64148—31no—
57#64148D311yescharacteristic, complemented
58#64147—31no—
59#64145—31no—
60#64144—31no—
61D4×C3⋊Dic3—31no—
62D4×C3⋊Dic3—34no—
63D4×C3⋊Dic3—64no—
64#64094—31no—
65#64092—31no—
66#64090—31no—
67#64088—31no—
68#64088—31no—
69#64087—31no—
70C3×#939—34no—
71C3×#937D314yescomplemented
72#63980—34no—
73#63976—34no—
74#67⋊Dic3—34no—
75#63970—34no—
76#63964—34no—
77#63962—34no—
78C2×(C2×D3)⋊Dic3—34no—
79#63959—34no—
80#63915—34no—
81#63891—34no—
82#63862—34no—
83#63861—34no—
84C23×C33C2311yescharacteristic
85C23×C33C2311yescharacteristic
86C22×C3×C3⋊D3C2311yescharacteristic
87C22×C32×D3—22no—
88C22×C32×D3—41no—
89C22×C32×D3—41no—
90C22×C32×D3C2311yescharacteristic
91C22×C32×D3C2311yescharacteristic
92C33×D4—22no—
93C2×C33×C4C2311yescharacteristic
94C2×C3⋊(C3⋊Dic3)—41no—
95C2×C3⋊(C3⋊Dic3)—41no—
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
99C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
100C3×#638—22no—
101C3×#638—41no—
102C2×C3×C3⋊Dic3—41no—
103C2×C3×C3⋊Dic3C2311yescharacteristic
104C2×C3×C3⋊Dic3C2311yescharacteristic
105C2×C3×C3⋊Dic3C2311yescharacteristic
106C32×#67—41no—
107C32×#67—41no—
108C2×C32×Dic3C2311yescharacteristic
109C2×C32×Dic3C2311yescharacteristic
110#6293—41no—
111#6290—41no—
112#6290—41no—
113Dic3×C3⋊D3—41no—
114#5617—91no—
115#5593—94no—
116C24×C32—31no—
117C23×C3×D3C2×D314yes—
118C2×C32×D4—24no—
119C2×C32×D4—31no—
120C2×C32×D4—31no—
121C2×C32×D4C2×D314yes—
122C2×C32×D4C2×D311yescharacteristic
123C2×#638—31no—
124C2×#638—31no—
125C2×#638C2×D311yescharacteristic
126C2×#638C2×D311yescharacteristic, complemented
127C22×C3⋊Dic3—31no—
128C22×C3⋊Dic3—31no—
129C22×C3⋊Dic3—34no—
130C22×C3⋊Dic3—34no—
131C22×C3⋊Dic3—64no—
132C22×C3⋊Dic3—64no—
133C22×C3⋊Dic3C2×D311yescharacteristic
134C2×C4×C3⋊D3—31no—
135C2×#634—31no—
136C2×C3×#67—34no—
137C2×C3×#67—34no—
138C2×C3×#67C2×D314yes—
139C2×C3×#67C2×D314yes—
140C22×C3×Dic3—34no—
141C2×#627—34no—
142C2×#625—34no—
143C2×#625—34no—
144C2×D3×Dic3—34no—
145C32×C22⋊C4—31no—
146C32×C22⋊C4—31no—
147C32×C22⋊C4—31no—
148#3757—31no—
149#3757—31no—
150#3757—34no—
151#3757—34no—
152#3757—31no—
153#3757—31no—
154#3757—31no—
155#3757—31no—
156#3757—31no—
157#3757—31no—
158#3757—64no—
159#3757—64no—
160#3757C2×D311yescharacteristic, complemented
161#3752—31no—
162#3752C2×D311yescharacteristic, complemented
163C4⋊(C3⋊Dic3)—31no—
164C4⋊(C3⋊Dic3)—34no—
165C4⋊(C3⋊Dic3)—31no—
166C4⋊(C3⋊Dic3)—64no—
167#3750—31no—
168#3750—31no—
169#3750—31no—
170#3750C2×D311yescharacteristic, complemented
171C4×C3⋊Dic3—31no—
172C4×C3⋊Dic3—34no—
173C4×C3⋊Dic3—31no—
174C4×C3⋊Dic3—64no—
175C3×#217—34no—
176C3×#217C2×D314yes—
177C3×(C2×D3)⋊C4—34no—
178C3×(C2×D3)⋊C4C2×D314yes—
179C3×(C2×D3)⋊C4C2×D314yes—
180C3×Dic3⋊C4—34no—
181#3724—34no—
182Dic3⋊Dic3—34no—
183Dic3⋊Dic3—34no—
184Dic3⋊Dic3—34no—
185(C2×D3)⋊Dic3—34no—
186(C2×D3)⋊Dic3—34no—
187(C2×D3)⋊Dic3—34no—
188(C2×D3)⋊Dic3—34no—
189(C2×D3)⋊Dic3—34no—
190(C2×D3)⋊Dic3—34no—
191(C2×D3)⋊Dic3—34no—
192Dic32—34no—
193C22×C33—21no—
194C22×C33—21no—
195C22×C33—21no—
196C22×C33—21no—
197C22×C33—21no—
198C22×C33#4112yes—
199C22×C33C2411yescharacteristic
200C2×C3×C3⋊D3—21no—
201C2×C3×C3⋊D3—21no—
202C2×C3×C3⋊D3—21no—
203C2×C32×D3—21no—
204C2×C32×D3—21no—
205C2×C32×D3—21no—
206C2×C32×D3—21no—
207C2×C32×D3—21no—
208C2×C32×D3—21no—
209C2×C32×D3—44no—
210C33×C4—21no—
211C3⋊(C3⋊Dic3)—21no—
212C3⋊(C3⋊Dic3)—21no—
213C3⋊(C3⋊Dic3)—21no—
214C3⋊(C3⋊Dic3)—21no—
215C3×C3⋊Dic3—21no—
216C3×C3⋊Dic3—21no—
217C3×C3⋊Dic3—21no—
218C32×Dic3—21no—
219C32×Dic3—21no—
220C3×#121—91no—
221C3×#120—34no—
222#953—94no—
223C2×#217—94no—
224#939—34no—
225#939—94no—
226#939—91no—
227#939—91no—
228#938—94no—
229#937—91no—
230#937C3⋊D311yescharacteristic, complemented
231#936—94no—
232#935—94no—
233D4×Dic3—94no—
234D4×Dic3—91no—
235D4×Dic3—91no—
236D4×Dic3—184no—
237C2×(C2×D3)⋊C4—91no—
238#924—91no—
239#898—91no—
240#898—91no—
241#886—91no—
242#886—91no—
243#885—94no—
244#885—91no—
245#885—91no—
246#883—94no—
247#67⋊C4—94no—
248#879—94no—
249#879—94no—
250#878—94no—
251C23×C32—24no—
252C23×C32—24no—
253C23×C32—31no—
254C23×C32—31no—
255C23×C32—62no—
256C23×C32—121no—
257C23×C32—121no—
258C23×C32C22×D314yes—
259C23×C32C22×D314yes—
260C23×C32C22×D311yescharacteristic
261C23×C32C22×D311yescharacteristic
262C22×C3⋊D3C22×D311yescharacteristic
263C22×C3×D3—28no—
264C22×C3×D3—34no—
265C22×C3×D3—44no—
266C22×C3×D3—44no—
267C22×C3×D3C22×D314yes—
268C22×C3×D3C22×D314yes—
269C32×D4—216no—
270C32×D4—28no—
271C32×D4—22no—
272C32×D4—121no—
273C32×D4—121no—
274C2×C32×C4—24no—
275C2×C32×C4—31no—
276C2×C32×C4—31no—
277C2×C32×C4C22×D314yes—
278C2×C32×C4C22×D311yescharacteristic
279#638—22no—
280#638—41no—
281#638—121no—
282#638—121no—
283C2×C3⋊Dic3—31no—
284C2×C3⋊Dic3—31no—
285C2×C3⋊Dic3—31no—
286C2×C3⋊Dic3—31no—
287C2×C3⋊Dic3—34no—
288C2×C3⋊Dic3—34no—
289C2×C3⋊Dic3—34no—
290C2×C3⋊Dic3—34no—
291C2×C3⋊Dic3—41no—
292C2×C3⋊Dic3—64no—
293C2×C3⋊Dic3—64no—
294C2×C3⋊Dic3—64no—
295C2×C3⋊Dic3—64no—
296C2×C3⋊Dic3—121no—
297C2×C3⋊Dic3—121no—
298C2×C3⋊Dic3—124no—
299C2×C3⋊Dic3—124no—
300C2×C3⋊Dic3—128no—
301C2×C3⋊Dic3—128no—
302C2×C3⋊Dic3C22×D311yescharacteristic
303C2×C3⋊Dic3C22×D311yescharacteristic
304C2×C3⋊Dic3C22×D311yescharacteristic
305C4×C3⋊D3—121no—
306#634—121no—
307C3×#67—44no—
308C3×#67—44no—
309C3×#67—68no—
310C3×#67—124no—
311C2×C3×Dic3—34no—
312C2×C3×Dic3—34no—
313C2×C3×Dic3—34no—
314C2×C3×Dic3—124no—
315C2×C3×Dic3C22×D314yes—
316C2×C3×Dic3C22×D314yes—
317#627—124no—
318#625—124no—
319#625—124no—
320D3×Dic3—124no—
321#538—271noSylow
322C2×C33—22no—
323C2×C33—41no—
324C2×C33C2×#4111yescharacteristic
325C2×C33H(5,𝔽2)11yescharacteristic
326C2×C33H(5,𝔽2)11yescharacteristic
327C3×C3⋊D3—41no—
328C32×D3—41no—
329C32×D3—41no—
330C24×C3—34no—
331C23×D3C2×C3⋊D311yescharacteristic
332C2×C3×D4—24no—
333C2×C3×D4—34no—
334C2×C3×D4—34no—
335C2×C3×D4—91no—
336C2×C3×D4—91no—
337C2×C3×D4D3214yes—
338C2×C3×D4C2×C3⋊D311yescharacteristic
339C22×C3×C4—91no—
340C2×#67—34no—
341C2×#67—34no—
342C2×#67—94no—
343C2×#67—94no—
344C2×#67—91no—
345C2×#67—91no—
346C2×#67C2×C3⋊D311yescharacteristic
347C2×#67C2×C3⋊D311yescharacteristic
348C22×Dic3—34no—
349C22×Dic3—94no—
350C22×Dic3—94no—
351C22×Dic3—91no—
352C22×Dic3—91no—
353C22×Dic3—91no—
354C22×Dic3—184no—
355C22×Dic3—184no—
356C2×C4×D3—94no—
357C2×Dic6—94no—
358C2×Dic6—91no—
359C3×C4⋊C4—91no—
360C3×C22⋊C4—34no—
361C3×C22⋊C4—34no—
362C3×C22⋊C4—34no—
363C3×C22⋊C4—91no—
364C3×C22⋊C4—91no—
365#217—34no—
366#217—94no—
367#217—94no—
368#217—94no—
369#217—94no—
370#217—94no—
371#217—94no—
372#217—94no—
373#217—94no—
374#217—91no—
375#217—91no—
376#217—91no—
377#217—184no—
378#217—184no—
379#217C2×C3⋊D311yescharacteristic
380(C2×D3)⋊C4—34no—
381(C2×D3)⋊C4—94no—
382(C2×D3)⋊C4—91no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—91no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—91no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
389(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
390C4⋊Dic3—94no—
391C4⋊Dic3—94no—
392C4⋊Dic3—91no—
393C4⋊Dic3—91no—
394C4⋊Dic3—91no—
395C4⋊Dic3—184no—
396Dic3⋊C4—34no—
397Dic3⋊C4—94no—
398Dic3⋊C4—94no—
399Dic3⋊C4—94no—
400Dic3⋊C4—91no—
401Dic3⋊C4—91no—
402C4×Dic3—94no—
403C4×Dic3—94no—
404C4×Dic3—91no—
405C4×Dic3—91no—
406C4×Dic3—184no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—28no—
410C22×C32—24no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—24no—
415C22×C32—28no—
416C22×C32—24no—
417C22×C32—24no—
418C22×C32—24no—
419C22×C32—24no—
420C22×C32—44no—
421C22×C32—44no—
422C22×C32—44no—
423C22×C32—44no—
424C22×C32—61no—
425C22×C32—61no—
426C22×C32—61no—
427C22×C32—61no—
428C22×C32—61no—
429C22×C32—61no—
430C22×C32—124no—
431C22×C32#23718yes—
432C22×C32#23712yes—
433C22×C32C23×D314yes—
434C22×C32C23×D311yescharacteristic
435C2×C3⋊D3—21no—
436C2×C3⋊D3—21no—
437C2×C3⋊D3—21no—
438C2×C3×D3—24no—
439C2×C3×D3—24no—
440C2×C3×D3—24no—
441C2×C3×D3—24no—
442C2×C3×D3—24no—
443C2×C3×D3—24no—
444C2×C3×D3—416no—
445C2×C3×D3—64no—
446C2×C3×D3—64no—
447C2×C3×D3—64no—
448C32×C4—28no—
449C32×C4—24no—
450C32×C4—21no—
451C32×C4—61no—
452C32×C4—61no—
453C3⋊Dic3—21no—
454C3⋊Dic3—21no—
455C3⋊Dic3—21no—
456C3⋊Dic3—68no—
457C3⋊Dic3—61no—
458C3⋊Dic3—64no—
459C3⋊Dic3—61no—
460C3⋊Dic3—61no—
461C3⋊Dic3—61no—
462C3⋊Dic3—64no—
463C3⋊Dic3—64no—
464C3⋊Dic3—64no—
465C3⋊Dic3—124no—
466C3⋊Dic3—124no—
467C3⋊Dic3—124no—
468C3×Dic3—24no—
469C3×Dic3—24no—
470C3×Dic3—64no—
471C3×Dic3—64no—
472C3×Dic3—64no—
473#126—271no—
474#126—271no—
475#124—271no—
476#124—271no—
477#123—271no—
478#123—271no—
479C22⋊Q8—271no—
480#121—91no—
481#121—271no—
482#121—271no—
483#120—31no—
484#120—271no—
485C4×D4—271no—
486C4×D4—271no—
487C2×C22⋊C4—271no—
488C33#53811yescharacteristic, complemented, Sylow
489C23×C3—24no—
490C23×C3—24no—
491C23×C3—34no—
492C23×C3—34no—
493C23×C3—68no—
494C23×C3—91no—
495C23×C3—124no—
496C23×C3—124no—
497C23×C3C2×D3214yes—
498C23×C3C2×D3214yes—
499C23×C3C22×C3⋊D311yescharacteristic
500C23×C3C22×C3⋊D311yescharacteristic
501C22×D3—22no—
502C22×D3—34no—
503C22×D3—41no—
504C22×D3—41no—
505C22×D3C22×C3⋊D311yescharacteristic
506C22×D3C22×C3⋊D311yescharacteristic
507C3×D4—216no—
508C3×D4—28no—
509C3×D4—22no—
510C3×D4—124no—
511C3×D4—124no—
512C3×D4—182no—
513C3×D4—361no—
514C2×C3×C4—24no—
515C2×C3×C4—34no—
516C2×C3×C4—34no—
517C2×C3×C4—91no—
518C2×C3×C4—91no—
519C2×C3×C4—91no—
520C2×C3×C4—361no—
521C2×C3×C4C2×D3214yes—
522C2×C3×C4C22×C3⋊D311yescharacteristic
523#67—41no—
524#67—41no—
525#67—68no—
526#67—124no—
527#67—361no—
528#67—361no—
529#67—364no—
530#67—364no—
531C2×Dic3—34no—
532C2×Dic3—34no—
533C2×Dic3—34no—
534C2×Dic3—94no—
535C2×Dic3—94no—
536C2×Dic3—94no—
537C2×Dic3—94no—
538C2×Dic3—91no—
539C2×Dic3—91no—
540C2×Dic3—91no—
541C2×Dic3—91no—
542C2×Dic3—124no—
543C2×Dic3—184no—
544C2×Dic3—184no—
545C2×Dic3—184no—
546C2×Dic3—184no—
547C2×Dic3—361no—
548C2×Dic3—364no—
549C2×Dic3—364no—
550C2×Dic3—361no—
551C2×Dic3—361no—
552C2×Dic3—368no—
553C2×Dic3—368no—
554C2×Dic3C22×C3⋊D311yescharacteristic
555C2×Dic3C22×C3⋊D311yescharacteristic
556C4×D3—364no—
557Dic6—361no—
558Dic6—364no—
559C2×C32—22no—
560C2×C32—24no—
561C2×C32—24no—
562C2×C32—24no—
563C2×C32—28no—
564C2×C32—48no—
565C2×C32—48no—
566C2×C32—44no—
567C2×C32—41no—
568C2×C32—121no—
569C2×C32—121no—
570C2×C32C2×#23714yes—
571C2×C32C2×#23711yescharacteristic
572C2×C32#100414yes—
573C2×C32#100414yes—
574C2×C32#100411yescharacteristic
575C2×C32#100911yescharacteristic
576C3⋊D3—41no—
577C3×D3—44no—
578C3×D3—44no—
579C3×D3—124no—
580C24—31no—
581C2×Q8—271no—
582C2×D4—31no—
583C2×D4—31no—
584C2×D4—91no—
585C2×D4—91no—
586C2×D4—271no—
587C2×D4—271no—
588C2×D4D3×C3⋊D311yescharacteristic
589C22×C4—91no—
590C22×C4—271no—
591C22×C4—271no—
592C22×C4—271no—
593C4⋊C4—91no—
594C4⋊C4—271no—
595C4⋊C4—271no—
596C4⋊C4—271no—
597C4⋊C4—271no—
598C4⋊C4—271no—
599C22⋊C4—31no—
600C22⋊C4—31no—
601C22⋊C4—31no—
602C22⋊C4—91no—
603C22⋊C4—91no—
604C22⋊C4—271no—
605C22⋊C4—271no—
606C22⋊C4—271no—
607C22⋊C4—271no—
608C22⋊C4—271no—
609C22⋊C4—271no—
610C22⋊C4—271no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C42—271no—
614C42—271no—
615C22×C3—24no—
616C22×C3—24no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—28no—
620C22×C3—24no—
621C22×C3—24no—
622C22×C3—24no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—24no—
627C22×C3—28no—
628C22×C3—44no—
629C22×C3—44no—
630C22×C3—44no—
631C22×C3—44no—
632C22×C3—64no—
633C22×C3—64no—
634C22×C3—64no—
635C22×C3—64no—
636C22×C3—64no—
637C22×C3—64no—
638C22×C3—1216no—
639C22×C3—181no—
640C22×C3—181no—
641C22×C3—181no—
642C22×C3#380518yes—
643C22×C3#383012yes—
644C22×C3C22×D3214yes—
645C22×C3C23×C3⋊D311yescharacteristic
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—44no—
653C2×D3—64no—
654C2×D3—64no—
655C2×D3—64no—
656C3×C4—28no—
657C3×C4—24no—
658C3×C4—21no—
659C3×C4—64no—
660C3×C4—64no—
661C3×C4—181no—
662C3×C4—181no—
663C3×C4—181no—
664Dic3—21no—
665Dic3—21no—
666Dic3—64no—
667Dic3—64no—
668Dic3—64no—
669Dic3—188no—
670Dic3—184no—
671Dic3—184no—
672Dic3—184no—
673Dic3—184no—
674Dic3—181no—
675Dic3—181no—
676Dic3—181no—
677Dic3—181no—
678Dic3—364no—
679Dic3—364no—
680Dic3—364no—
681C32—24no—
682C32#559314yescomplemented
683C32#561711yescharacteristic, complemented
684C23—31no—
685C23—31no—
686C23—62no—
687C23—91no—
688C23—121no—
689C23—121no—
690C23C2×D3×C3⋊D311yescharacteristic
691C23C2×D3×C3⋊D311yescharacteristic
692Q8—1081no—
693D4—22no—
694D4—121no—
695D4—121no—
696D4—182no—
697D4—361no—
698D4—1081no—
699D4—1081no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—91no—
703C2×C4—91no—
704C2×C4—91no—
705C2×C4—271no—
706C2×C4—271no—
707C2×C4—271no—
708C2×C4—271no—
709C2×C4—361no—
710C2×C4—1081no—
711C2×C4—1081no—
712C2×C4—1081no—
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—124no—
725C2×C3—361no—
726C2×C3#6431314yes—
727C2×C3#6431414yes—
728C2×C3C2×#380514yes—
729C2×C3C2×#383011yescharacteristic
730C2×C3#6436111yescharacteristic
731C2×C3#6436111yescharacteristic
732D3—41no—
733D3—41no—
734D3—124no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—61no—
741C22—61no—
742C22—61no—
743C22—61no—
744C22—61no—
745C22—61no—
746C22—124no—
747C22—181no—
748C22—181no—
749C22—181no—
750C22#8902912yes—
751C22C22×D3×C3⋊D311yescharacteristic
752C4—21no—
753C4—61no—
754C4—61no—
755C4—181no—
756C4—181no—
757C4—181no—
758C4—541no—
759C4—541no—
760C4—541no—
761C4—541no—
762C3—24no—
763C3#1059526714yescomplemented
764C3#1059606411yescharacteristic, complemented
765C2—22no—
766C2—41no—
767C2—121no—
768C2—121no—
769C2—361no—
770C2#1172458711yescharacteristic
771C2#1172458811yescharacteristic
772C2C2×#8902911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. D4×C3⋊(C3⋊Dic3)C2semidirect
2. C3×#64148C2semidirect
3. C32×#937C2semidirect
4. #11723641C2semidirect
5. #11723637C2semidirect
6. #11723631C2semidirect
7. #11723629C2semidirect
8. #11723626C2semidirect
9. #11723603C2semidirect
10. C2×(C2×D3)⋊(C3⋊Dic3)C2semidirect
11. #11723600C2semidirect
12. #11723530C2semidirect
13. #11723523C2semidirect
14. #11723432C2semidirect
15. #11723430C2semidirect
21. C22×C3⋊(C3⋊Dic3)C22semidirect
23. C2×C3×#638C22semidirect
27. C2×#6293C22semidirect
30. C2×Dic3×C3⋊D3C22semidirect
32. #88864C22semidirect
33. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
34. C4×C3⋊(C3⋊Dic3)C22semidirect
35. C3×#3757C22semidirect
36. C3×#3752C22semidirect
37. C3×#3750C22semidirect
41. #88807C22semidirect
42. #88807C22semidirect
43. #88806C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
45. #88803C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
57. #64148D3semidirect
71. C3×#937D3semidirect
126. C2×#638C2×D3semidirect
160. #3757C2×D3semidirect
162. #3752C2×D3semidirect
170. #3750C2×D3semidirect
230. #937C3⋊D3semidirect
488. C33#538semidirect
682. C32#5593semidirect
683. C32#5617semidirect
763. C3#10595267semidirect
764. C3#10596064semidirect

Maximal subgroups

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

subgroupindex
D4×C3⋊(C3⋊Dic3)2
C3×#641482
C32×#9372
#117236412
#117236372
#117236312
#117236292
#117236262
#117236032
C2×(C2×D3)⋊(C3⋊Dic3)2
#117236002
#117235302
#117235232
#117234322
#117234302
#105960643
#105952673