Finite Group Databasebeta

← #13176610

Subgroups — #13176610

Order 1728.

1888 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723936C211yesmaximal, characteristic, complemented
2C3×#64107C211yesmaximal, characteristic, complemented
3C32×#894C211yesmaximal, characteristic, complemented
4#11723542C211yesmaximal, characteristic, complemented
5#11723542C211yesmaximal, characteristic, complemented
6#11723540C211yesmaximal, characteristic, complemented
7#11723527C211yesmaximal, characteristic, complemented
8#11723525C211yesmaximal, characteristic, complemented
9#11723524C211yesmaximal, characteristic, complemented
10#11723516C211yesmaximal, characteristic, complemented
11#11723514C211yesmaximal, characteristic, complemented
12#11723486C211yesmaximal, characteristic, complemented
13#11723446C211yesmaximal, characteristic, complemented
14#11723422C211yesmaximal, characteristic, complemented
15#11723420C211yesmaximal, characteristic, complemented
16#10596137—31nomaximal
17#10594663—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
20C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
21C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
22C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
23C2×C32×D12C2211yescharacteristic
24C2×C32×C4×D3C2211yescharacteristic, complemented
25C2×#6292C2211yescharacteristic
26C2×#6292C2211yescharacteristic
27C2×#6291C2211yescharacteristic
28C2×#6291C2211yescharacteristic
29C2×#6291C2211yescharacteristic
30C2×#6291C2211yescharacteristic, complemented
31C2×#6291C2211yescharacteristic, complemented
32C2×#6290C2211yescharacteristic
33C2×#6289C2211yescharacteristic, complemented
34C33×C4⋊C4C2211yescharacteristic, complemented
35#88859C2211yescharacteristic
36#88859C2211yescharacteristic, complemented
37C3×#3752C2211yescharacteristic
38C3×#3752C2211yescharacteristic
39C3×#3752C2211yescharacteristic
40C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41C3×#3750C2211yescharacteristic, complemented
42C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
43C32×(C2×D3)⋊C4C2211yescharacteristic
44C32×(C2×D3)⋊C4C2211yescharacteristic
45C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C32×Dic3⋊C4C2211yescharacteristic, complemented
47#88806C2211yescharacteristic, complemented
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49#88804C2211yescharacteristic
50#88804C2211yescharacteristic
51#88804C2211yescharacteristic, complemented
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
53C32×#123—31no—
54#64149—31no—
55#64146—31no—
56#64139—31no—
57#64139—31no—
58#64107—31no—
59#64107D311yescharacteristic, complemented
60#64104—31no—
61#64104—31no—
62#64104—34no—
63#64104—64no—
64#64093—31no—
65#64093—31no—
66#64092—31no—
67#64092—31no—
68#64091—31no—
69#64091—31no—
70C3×#898—34no—
71C3×#894D314yescomplemented
72#63923—34no—
73#63923—34no—
74#63922—34no—
75#63912—34no—
76#63911—34no—
77#63910—34no—
78#63910—34no—
79#63909—34no—
80#63906—34no—
81#63868—34no—
82#63854—34no—
83#63853—34no—
84C22×C3⋊(C3⋊D3)C2311yescharacteristic
85C22×C3⋊(C3⋊D3)C2311yescharacteristic
86C22×C3⋊(C3⋊D3)C2311yescharacteristic
87C22×C3×C3⋊D3C2311yescharacteristic
88C22×C32×D3C2311yescharacteristic
89C22×C32×D3C2311yescharacteristic
90C2×D3×C3⋊D3—41no—
91C2×D3×C3⋊D3—41no—
92C2×D3×C3⋊D3—41no—
93C2×C33×C4C2311yescharacteristic
94C2×C33×C4C2311yescharacteristic
95C2×C33×C4C2311yescharacteristic
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C4⋊(C3⋊(C3⋊D3))—41no—
98C4⋊(C3⋊(C3⋊D3))—41no—
99C4⋊(C3⋊(C3⋊D3))—41no—
100C4×C3⋊(C3⋊D3)—41no—
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C2×C3×C3⋊Dic3C2311yescharacteristic
104C2×C32×Dic3C2311yescharacteristic
105C2×C32×Dic3C2311yescharacteristic
106C32×D12—41no—
107C32×C4×D3—41no—
108#6292—41no—
109#6292—41no—
110#6291—41no—
111#6291—41no—
112#6291—41no—
113#6291—41no—
114#6291—41no—
115#6290—41no—
116#6289—41no—
117#5711—91no—
118#5666—94no—
119C23×C3⋊D3—31no—
120C22×D32—34no—
121C2×C32×D4—31no—
122C22×C32×C4—31no—
123C2×#638—31no—
124C2×#638—31no—
125C2×#638—31no—
126C2×#638—31no—
127C2×#638—31no—
128C2×#638—31no—
129C2×C4⋊(C3⋊D3)—31no—
130C2×C4⋊(C3⋊D3)—31no—
131C2×C4⋊(C3⋊D3)—31no—
132C2×C4⋊(C3⋊D3)—31no—
133C2×C4⋊(C3⋊D3)—31no—
134C2×C4⋊(C3⋊D3)—34no—
135C2×C4⋊(C3⋊D3)—34no—
136C2×C4⋊(C3⋊D3)—34no—
137C2×C4⋊(C3⋊D3)—64no—
138C2×C4⋊(C3⋊D3)—64no—
139C2×C4⋊(C3⋊D3)—64no—
140C2×C4×C3⋊D3—31no—
141C2×C4×C3⋊D3—34no—
142C2×C4×C3⋊D3—31no—
143C2×C4×C3⋊D3—64no—
144C2×C3×D12C2×D314yes—
145C2×C3×C4×D3C2×D314yescomplemented
146C2×#626—34no—
147C2×#626—34no—
148C2×#626—34no—
149C2×#626—34no—
150C2×#626—34no—
151C2×#626—34no—
152C2×#626—34no—
153C2×#625—34no—
154C2×#624—34no—
155C32×C4⋊C4—24no—
156C32×C4⋊C4—31no—
157C32×C4⋊C4C2×D314yescomplemented
158C32×C4⋊C4C2×D311yescharacteristic, complemented
159C32×C22⋊C4—31no—
160C32×C22⋊C4—31no—
161C32×C22⋊C4—31no—
162#3757—31no—
163#3752—31no—
164#3752—31no—
165#3752—34no—
166#3752—34no—
167#3752—31no—
168#3752—31no—
169#3752—31no—
170#3752—64no—
171#3752—64no—
172#3752C2×D311yescharacteristic
173#3752C2×D311yescharacteristic
174#3752C2×D311yescharacteristic
175C4⋊(C3⋊Dic3)—31no—
176C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
177#3750—31no—
178#3750C2×D311yescharacteristic, complemented
179C4×C3⋊Dic3C2×D311yescharacteristic, complemented
180C3×(C2×D3)⋊C4—34no—
181C3×(C2×D3)⋊C4—34no—
182C3×(C2×D3)⋊C4—34no—
183C3×(C2×D3)⋊C4C2×D314yes—
184C3×(C2×D3)⋊C4C2×D314yes—
185C3×(C2×D3)⋊C4C2×D314yescomplemented
186C3×C4⋊Dic3—34no—
187C3×Dic3⋊C4—34no—
188C3×Dic3⋊C4C2×D314yescomplemented
189C3×C4×Dic3—34no—
190#3724—34no—
191Dic3⋊Dic3—34no—
192#3722—34no—
193#3722—34no—
194#3722—34no—
195(C2×D3)⋊Dic3—34no—
196C22×C33C2411yescharacteristic
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⋊D3)—21no—
203C2×C3⋊(C3⋊D3)—21no—
204C2×C3⋊(C3⋊D3)—21no—
205C2×C3⋊(C3⋊D3)—21no—
206C2×C3×C3⋊D3—21no—
207C2×C3×C3⋊D3—21no—
208C2×C3×C3⋊D3—21no—
209C2×C32×D3—21no—
210C2×C32×D3—21no—
211C2×C32×D3—21no—
212C2×C32×D3—21no—
213C2×C32×D3—21no—
214C2×C32×D3—21no—
215D3×C3⋊D3—44no—
216C33×C4—21no—
217C33×C4—21no—
218C33×C4—21no—
219C3⋊(C3⋊Dic3)—21no—
220C3×C3⋊Dic3—21no—
221C3×C3⋊Dic3—21no—
222C3×C3⋊Dic3—21no—
223C32×Dic3—21no—
224C32×Dic3—21no—
225C3×#126—91no—
226C3×#123—34no—
227#940—94no—
228#937—94no—
229#930—94no—
230#930—94no—
231#898—34no—
232#898—94no—
233#895—94no—
234#895—91no—
235#895—94no—
236#895—91no—
237#895—91no—
238#895—184no—
239#894—91no—
240#894—91no—
241#894C3⋊D311yescharacteristic, complemented
242#884—94no—
243#884—94no—
244#884—91no—
245#884—91no—
246#884—91no—
247#883—94no—
248#883—94no—
249#882—94no—
250#882—94no—
251#882—91no—
252#882—91no—
253#882—91no—
254#876—91no—
255#874—91no—
256C23×C32—31no—
257C23×C32—31no—
258C22×C3⋊D3—31no—
259C22×C3⋊D3—31no—
260C22×C3⋊D3—31no—
261C22×C3⋊D3—34no—
262C22×C3⋊D3—34no—
263C22×C3⋊D3—34no—
264C22×C3⋊D3—64no—
265C22×C3⋊D3—64no—
266C22×C3⋊D3—64no—
267C22×C3⋊D3—121no—
268C22×C3⋊D3—121no—
269C22×C3⋊D3—121no—
270C22×C3⋊D3C22×D311yescharacteristic
271C22×C3×D3—34no—
272C22×C3×D3C22×D314yes—
273C22×C3×D3C22×D314yes—
274C2×D32—124no—
275C2×D32—124no—
276C2×D32—124no—
277C32×D4—121no—
278C2×C32×C4—24no—
279C2×C32×C4—24no—
280C2×C32×C4—24no—
281C2×C32×C4—31no—
282C2×C32×C4—31no—
283C2×C32×C4—121no—
284C2×C32×C4C22×D314yes—
285C2×C32×C4C22×D314yes—
286C2×C32×C4C22×D314yes—
287C2×C32×C4C22×D311yescharacteristic
288C2×C32×C4C22×D311yescharacteristic
289C2×C32×C4C22×D311yescharacteristic
290#638—121no—
291#638—121no—
292#638—121no—
293#638—121no—
294#638—121no—
295#638—121no—
296C2×C3⋊Dic3—31no—
297C2×C3⋊Dic3—34no—
298C2×C3⋊Dic3—64no—
299C2×C3⋊Dic3C22×D311yescharacteristic
300C2×C3⋊Dic3C22×D311yescharacteristic
301C2×C3⋊Dic3C22×D311yescharacteristic
302C4⋊(C3⋊D3)—121no—
303C4⋊(C3⋊D3)—121no—
304C4⋊(C3⋊D3)—121no—
305C4⋊(C3⋊D3)—124no—
306C4⋊(C3⋊D3)—124no—
307C4⋊(C3⋊D3)—124no—
308C4⋊(C3⋊D3)—128no—
309C4⋊(C3⋊D3)—128no—
310C4⋊(C3⋊D3)—128no—
311C4⋊(C3⋊D3)—121no—
312C4⋊(C3⋊D3)—121no—
313C4×C3⋊D3—121no—
314C4×C3⋊D3—121no—
315C4×C3⋊D3—124no—
316C4×C3⋊D3—128no—
317C2×C3×Dic3—34no—
318C2×C3×Dic3—34no—
319C2×C3×Dic3—34no—
320C2×C3×Dic3C22×D314yes—
321C2×C3×Dic3C22×D314yes—
322C3×D12—44no—
323C3×C4×D3—44no—
324#626—124no—
325#626—124no—
326#626—124no—
327#626—124no—
328#626—124no—
329#626—124no—
330#626—124no—
331#625—124no—
332#624—124no—
333#560—271noSylow
334C2×C33H(5,𝔽2)11yescharacteristic
335C2×C33H(5,𝔽2)11yescharacteristic
336C2×C33H(5,𝔽2)11yescharacteristic
337C3⋊(C3⋊D3)—41no—
338C3⋊(C3⋊D3)—41no—
339C3⋊(C3⋊D3)—41no—
340C3×C3⋊D3—41no—
341C32×D3—41no—
342C32×D3—41no—
343C23×D3—94no—
344C23×D3—91no—
345C2×C3×D4—34no—
346C22×C3×C4—34no—
347C2×#67—94no—
348C2×#67—94no—
349C2×#67—94no—
350C2×#67—94no—
351C2×#67—94no—
352C2×#67—94no—
353C2×#67—91no—
354C2×#67—91no—
355C2×#67—91no—
356C2×D12—94no—
357C2×D12—94no—
358C2×D12—91no—
359C2×D12—91no—
360C2×D12—91no—
361C2×D12—91no—
362C2×D12—91no—
363C2×D12—94no—
364C2×D12—94no—
365C2×D12—94no—
366C2×D12—91no—
367C2×D12—91no—
368C2×D12—91no—
369C2×D12—184no—
370C2×D12—184no—
371C2×D12—184no—
372C2×D12C2×C3⋊D311yescharacteristic
373C2×C4×D3—94no—
374C2×C4×D3—94no—
375C2×C4×D3—91no—
376C2×C4×D3—91no—
377C2×C4×D3—184no—
378C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
379C3×C4⋊C4—24no—
380C3×C4⋊C4—34no—
381C3×C4⋊C4—91no—
382C3×C4⋊C4—91no—
383C3×C4⋊C4D3214yescomplemented
384C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
385C3×C22⋊C4—34no—
386C3×C22⋊C4—34no—
387C3×C22⋊C4—34no—
388C3×C22⋊C4—91no—
389C3×C22⋊C4—91no—
390C3×C22⋊C4—91no—
391C3×C42—91no—
392#217—94no—
393(C2×D3)⋊C4—34no—
394(C2×D3)⋊C4—34no—
395(C2×D3)⋊C4—34no—
396(C2×D3)⋊C4—94no—
397(C2×D3)⋊C4—94no—
398(C2×D3)⋊C4—94no—
399(C2×D3)⋊C4—91no—
400(C2×D3)⋊C4—94no—
401(C2×D3)⋊C4—94no—
402(C2×D3)⋊C4—91no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—91no—
405(C2×D3)⋊C4—91no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—184no—
408(C2×D3)⋊C4—184no—
409(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
410(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
411(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
412C4⋊Dic3—34no—
413C4⋊Dic3—94no—
414Dic3⋊C4—34no—
415Dic3⋊C4—94no—
416Dic3⋊C4—91no—
417Dic3⋊C4—91no—
418Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
419C4×Dic3—34no—
420C22×C32—24no—
421C22×C32—61no—
422C22×C32—61no—
423C22×C32—61no—
424C22×C32—61no—
425C22×C32—61no—
426C22×C32—61no—
427C22×C32C23×D314yes—
428C22×C32C23×D311yescharacteristic
429C2×C3⋊D3—21no—
430C2×C3⋊D3—21no—
431C2×C3⋊D3—21no—
432C2×C3⋊D3—68no—
433C2×C3⋊D3—64no—
434C2×C3⋊D3—61no—
435C2×C3⋊D3—61no—
436C2×C3⋊D3—61no—
437C2×C3⋊D3—61no—
438C2×C3⋊D3—61no—
439C2×C3⋊D3—61no—
440C2×C3⋊D3—61no—
441C2×C3⋊D3—61no—
442C2×C3⋊D3—61no—
443C2×C3⋊D3—64no—
444C2×C3⋊D3—64no—
445C2×C3⋊D3—64no—
446C2×C3⋊D3—64no—
447C2×C3⋊D3—64no—
448C2×C3⋊D3—64no—
449C2×C3⋊D3—64no—
450C2×C3⋊D3—64no—
451C2×C3⋊D3—124no—
452C2×C3⋊D3—124no—
453C2×C3⋊D3—124no—
454C2×C3⋊D3—124no—
455C2×C3⋊D3—124no—
456C2×C3⋊D3—124no—
457C2×C3⋊D3—124no—
458C2×C3⋊D3—124no—
459C2×C3⋊D3—124no—
460C2×C3×D3—24no—
461C2×C3×D3—24no—
462C2×C3×D3—24no—
463C2×C3×D3—24no—
464C2×C3×D3—24no—
465C2×C3×D3—24no—
466C2×C3×D3—64no—
467C2×C3×D3—64no—
468C2×C3×D3—64no—
469D32—1216no—
470C32×C4—28no—
471C32×C4—24no—
472C32×C4—21no—
473C32×C4—21no—
474C32×C4—21no—
475C32×C4—24no—
476C32×C4—24no—
477C32×C4—44no—
478C32×C4—44no—
479C32×C4—61no—
480C32×C4—61no—
481C3⋊Dic3—21no—
482C3⋊Dic3—21no—
483C3⋊Dic3—21no—
484C3⋊Dic3—61no—
485C3⋊Dic3—64no—
486C3⋊Dic3—124no—
487C3×Dic3—24no—
488C3×Dic3—24no—
489C3×Dic3—64no—
490C3×Dic3—64no—
491C3×Dic3—64no—
492#127—271no—
493#126—91no—
494#126—271no—
495#123—31no—
496#123—271no—
497#123—271no—
498#121—271no—
499#121—271no—
500#121—271no—
501#121—271no—
502#121—271no—
503#121—271no—
504#120—271no—
505#120—271no—
506#120—271no—
507C33#56011yescharacteristic, complemented, Sylow
508C23×C3—34no—
509C23×C3—34no—
510C23×C3—91no—
511C22×D3—34no—
512C22×D3—94no—
513C22×D3—94no—
514C22×D3—94no—
515C22×D3—91no—
516C22×D3—91no—
517C22×D3—91no—
518C22×D3—184no—
519C22×D3—184no—
520C22×D3—184no—
521C22×D3—361no—
522C22×D3—361no—
523C22×D3—361no—
524C22×D3—364no—
525C22×D3—364no—
526C22×D3—364no—
527C22×D3C22×C3⋊D311yescharacteristic
528C22×D3C22×C3⋊D311yescharacteristic
529C3×D4—124no—
530C2×C3×C4—24no—
531C2×C3×C4—24no—
532C2×C3×C4—24no—
533C2×C3×C4—34no—
534C2×C3×C4—34no—
535C2×C3×C4—91no—
536C2×C3×C4—91no—
537C2×C3×C4—91no—
538C2×C3×C4—124no—
539C2×C3×C4C2×D3214yes—
540C2×C3×C4C2×D3214yes—
541C2×C3×C4C2×D3214yes—
542C2×C3×C4C22×C3⋊D311yescharacteristic
543C2×C3×C4C22×C3⋊D311yescharacteristic
544C2×C3×C4C22×C3⋊D311yescharacteristic
545#67—361no—
546#67—361no—
547#67—364no—
548#67—364no—
549#67—364no—
550#67—364no—
551#67—364no—
552#67—361no—
553#67—364no—
554C2×Dic3—34no—
555C2×Dic3—34no—
556C2×Dic3—34no—
557C2×Dic3—94no—
558C2×Dic3—91no—
559C2×Dic3—184no—
560C2×Dic3C22×C3⋊D311yescharacteristic
561C2×Dic3C22×C3⋊D311yescharacteristic
562D12—41no—
563D12—364no—
564D12—364no—
565D12—364no—
566D12—361no—
567D12—361no—
568D12—361no—
569D12—368no—
570D12—368no—
571D12—368no—
572D12—364no—
573D12—364no—
574D12—361no—
575D12—361no—
576D12—361no—
577D12—361no—
578D12—361no—
579C4×D3—41no—
580C4×D3—361no—
581C4×D3—364no—
582C4×D3—364no—
583C4×D3—361no—
584C4×D3—368no—
585C2×C32—24no—
586C2×C32—24no—
587C2×C32—24no—
588C2×C32—121no—
589C2×C32—121no—
590C2×C32#100414yes—
591C2×C32#100914yes—
592C2×C32#100914yes—
593C2×C32#100911yescharacteristic
594C2×C32#100911yescharacteristic
595C2×C32#100911yescharacteristic
596C3⋊D3—41no—
597C3⋊D3—128no—
598C3⋊D3—124no—
599C3⋊D3—121no—
600C3⋊D3—121no—
601C3⋊D3—121no—
602C3⋊D3—124no—
603C3⋊D3—124no—
604C3⋊D3—244no—
605C3⋊D3—244no—
606C3×D3—44no—
607C3×D3—44no—
608C3×D3—124no—
609C24—271no—
610C2×D4—31no—
611C2×D4—271no—
612C2×D4—271no—
613C2×D4—271no—
614C2×D4—271no—
615C2×D4—271no—
616C2×D4—271no—
617C2×D4—271no—
618C2×D4—271no—
619C2×D4—271no—
620C2×D4—271no—
621C2×D4—271no—
622C22×C4—31no—
623C22×C4—271no—
624C22×C4—271no—
625C4⋊C4—31no—
626C4⋊C4—91no—
627C4⋊C4—91no—
628C4⋊C4—271no—
629C4⋊C4—271no—
630C4⋊C4D3×C3⋊D311yescharacteristic, complemented
631C22⋊C4—31no—
632C22⋊C4—31no—
633C22⋊C4—31no—
634C22⋊C4—91no—
635C22⋊C4—91no—
636C22⋊C4—91no—
637C22⋊C4—271no—
638C22⋊C4—271no—
639C22⋊C4—271no—
640C22⋊C4—271no—
641C22⋊C4—271no—
642C22⋊C4—271no—
643C42—91no—
644C22×C3—24no—
645C22×C3—64no—
646C22×C3—64no—
647C22×C3—64no—
648C22×C3—64no—
649C22×C3—64no—
650C22×C3—64no—
651C22×C3—181no—
652C22×C3—181no—
653C22×C3—181no—
654C22×C3C22×D3214yes—
655C22×C3C23×C3⋊D311yescharacteristic
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—64no—
663C2×D3—64no—
664C2×D3—64no—
665C2×D3—188no—
666C2×D3—184no—
667C2×D3—184no—
668C2×D3—184no—
669C2×D3—184no—
670C2×D3—184no—
671C2×D3—184no—
672C2×D3—184no—
673C2×D3—184no—
674C2×D3—184no—
675C2×D3—181no—
676C2×D3—181no—
677C2×D3—181no—
678C2×D3—181no—
679C2×D3—181no—
680C2×D3—181no—
681C2×D3—181no—
682C2×D3—181no—
683C2×D3—181no—
684C2×D3—364no—
685C2×D3—364no—
686C2×D3—364no—
687C2×D3—364no—
688C2×D3—364no—
689C2×D3—364no—
690C2×D3—364no—
691C2×D3—364no—
692C2×D3—364no—
693C2×D3—3616no—
694C3×C4—28no—
695C3×C4—24no—
696C3×C4—24no—
697C3×C4—24no—
698C3×C4—21no—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—44no—
702C3×C4—44no—
703C3×C4—64no—
704C3×C4—64no—
705C3×C4—181no—
706C3×C4—181no—
707C3×C4—181no—
708Dic3—21no—
709Dic3—21no—
710Dic3—64no—
711Dic3—64no—
712Dic3—64no—
713Dic3—184no—
714Dic3—181no—
715Dic3—364no—
716C32—24no—
717C32#566614yescomplemented
718C32#571111yescharacteristic, complemented
719C23—31no—
720C23—31no—
721C23—91no—
722C23—271no—
723C23—271no—
724C23—271no—
725C23—1081no—
726C23—1081no—
727C23—1081no—
728D4—121no—
729D4—1081no—
730D4—1081no—
731D4—1081no—
732D4—1081no—
733D4—1081no—
734D4—1081no—
735D4—1081no—
736D4—1081no—
737D4—1081no—
738D4—1081no—
739D4—1081no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—91no—
743C2×C4—91no—
744C2×C4—91no—
745C2×C4—121no—
746C2×C4—271no—
747C2×C4—1081no—
748C2×C4—1081no—
749C2×C4C2×D3×C3⋊D311yescharacteristic
750C2×C4C2×D3×C3⋊D311yescharacteristic
751C2×C4C2×D3×C3⋊D311yescharacteristic
752C2×C3—24no—
753C2×C3—24no—
754C2×C3—24no—
755C2×C3—124no—
756C2×C3—124no—
757C2×C3—361no—
758C2×C3#6430814yes—
759C2×C3#6431414yes—
760C2×C3#6432014yes—
761C2×C3#6436111yescharacteristic
762C2×C3#6436611yescharacteristic
763C2×C3#6436611yescharacteristic
764D3—41no—
765D3—41no—
766D3—124no—
767D3—368no—
768D3—361no—
769D3—361no—
770D3—361no—
771D3—364no—
772D3—364no—
773D3—364no—
774D3—724no—
775D3—724no—
776C22—61no—
777C22—61no—
778C22—61no—
779C22—61no—
780C22—61no—
781C22—61no—
782C22—181no—
783C22—181no—
784C22—181no—
785C22—541no—
786C22—541no—
787C22—541no—
788C22—541no—
789C22—541no—
790C22—541no—
791C22—541no—
792C22—541no—
793C22—541no—
794C22—1084no—
795C22C22×D3×C3⋊D311yescharacteristic
796C4—21no—
797C4—21no—
798C4—21no—
799C4—61no—
800C4—61no—
801C4—181no—
802C4—181no—
803C4—181no—
804C4—541no—
805C3—24no—
806C3#1059466314yescomplemented
807C3#1059613711yescharacteristic, complemented
808C2—121no—
809C2—121no—
810C2—361no—
811C2—1081no—
812C2—1081no—
813C2—1081no—
814C2#1172458111yescharacteristic
815C2#1172458811yescharacteristic
816C2#1172459711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
hypercenterC4⋊C4D3×C3⋊D3
hypocenterC33#560
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #11723936C2semidirect
2. C3×#64107C2semidirect
3. C32×#894C2semidirect
4. #11723542C2semidirect
5. #11723542C2semidirect
6. #11723540C2semidirect
7. #11723527C2semidirect
8. #11723525C2semidirect
9. #11723524C2semidirect
10. #11723516C2semidirect
11. #11723514C2semidirect
12. #11723486C2semidirect
13. #11723446C2semidirect
14. #11723422C2semidirect
15. #11723420C2semidirect
21. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
22. C2×C4×C3⋊(C3⋊D3)C22semidirect
24. C2×C32×C4×D3C22semidirect
30. C2×#6291C22semidirect
31. C2×#6291C22semidirect
33. C2×#6289C22semidirect
34. C33×C4⋊C4C22semidirect
36. #88859C22semidirect
40. C3×C4⋊(C3⋊Dic3)C22semidirect
41. C3×#3750C22semidirect
42. C3×C4×C3⋊Dic3C22semidirect
45. C32×(C2×D3)⋊C4C22semidirect
46. C32×Dic3⋊C4C22semidirect
47. #88806C22semidirect
48. Dic3⋊(C3⋊Dic3)C22semidirect
51. #88804C22semidirect
59. #64107D3semidirect
71. C3×#894D3semidirect
145. C2×C3×C4×D3C2×D3semidirect
157. C32×C4⋊C4C2×D3semidirect
158. C32×C4⋊C4C2×D3semidirect
176. C4⋊(C3⋊Dic3)C2×D3semidirect
178. #3750C2×D3semidirect
179. C4×C3⋊Dic3C2×D3semidirect
185. C3×(C2×D3)⋊C4C2×D3semidirect
188. C3×Dic3⋊C4C2×D3semidirect
241. #894C3⋊D3semidirect
378. C2×C4×D3C2×C3⋊D3semidirect
383. C3×C4⋊C4D32semidirect
384. C3×C4⋊C4C2×C3⋊D3semidirect
411. (C2×D3)⋊C4C2×C3⋊D3semidirect
418. Dic3⋊C4C2×C3⋊D3semidirect
507. C33#560semidirect
630. C4⋊C4D3×C3⋊D3semidirect
717. C32#5666semidirect
718. C32#5711semidirect
806. C3#10594663semidirect
807. C3#10596137semidirect

Maximal subgroups

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

subgroupindex
#117239362
C3×#641072
C32×#8942
#117235422
#117235402
#117235272
#117235252
#117235242
#117235162
#117235142
#117234862
#117234462
#117234222
#117234202
#105961373
#105946633